Report_MScThesis_LvZ.

Report_MScThesis_LvZ.
AES/PE/10-34
Evaluation of post-fracture production in tight gas
reservoirs:
The impact of unconventional reservoir behaviour on
production and well test interpretation.
November 3rd, 2010
L.F. van Zelm
MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
2
MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Title
:
Evaluation of post-fracture production analysis in tight gas
reservoirs:
The impact of unconventional reservoir behaviour on
production and well test interpretation.
Author
:
L.F. van Zelm
Date
:
November 3rd, 2010
Professor
:
Prof. dr. W.R. Rossen
Supervisors
:
Prof. dr. W.R. Rossen
Dr. C.J. de Pater
Committee Members
:
Prof. dr. W.R. Rossen
Dr. C.J. de Pater
Prof. dr. P.L.J. Zitha
Dr. ir. C.W.J. Berentsen
TA Report number
:
AES/PE/10-34
Postal Address
:
Section for Petroleum Engineering
Department of Applied Earth Sciences
Delft University of Technology
P.O. Box 5028
The Netherlands
Telephone
:
(31) 15 2781328 (secretary)
Telefax
:
(31) 15 2781189
Copyright ©2010
Section for Petroleum Engineering
All rights reserved.
No parts of this publication may be reproduced,
stored in a retrieval system, or transmitted,
In any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise,
without the prior written permission of the
Section for Petroleum Engineering.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Abstract
Worldwide rising gas demand is creating new opportunities for low-permeability gas
reservoirs to be exploited with large hydraulic fracturing campaigns. These so-called tight
gas reservoirs have been subject of much research over the past three decades, primarily
because it is difficult to optimize recovery. In this thesis, post-fracture production of tight gas
reservoirs is simulated and interpreted through well test analyses. The focus lies on the
impact of unconventional reservoir behaviour, specifically the impact of leakoff water on gas
production and assessing the accuracy of post-fracture evaluation using production data and
well tests.
Specific characteristics of tight gas reservoirs, such as high capillary pressure, a ‘permeability
jail’, and reservoir heterogeneity, may invoke phase trapping mechanisms that could
potentially harm gas production. The ‘permeability jail’ is a hypothesis that gas-water
relative permeability functions include a large saturation range with little or no fluid
mobility, caused by the complex pore-structure of tight gas sandstone reservoirs.
This thesis presents reservoir simulations of both the short and the long-term gas and water
production, performed with a commercial numerical simulator. Simulations show that high
capillary pressures alone do not harm gas production significantly. Assuming a permeability
jail in lower-permeability reservoir zones in a heterogeneous reservoir results in an extended
cleanup period and a reduction in total recoverable gas. This result is comparable to the
simulation of mechanical or chemical damage to the reservoir surrounding the fracture, or
so-called fracture face damage. With mechanical or chemical damage, the water production
is impaired initially and slowly recovers with time. This distinguishes this type of damage
from a permeability jail, which shows rapid water flow-back of approximately 50% of the
leakoff water. Finally, the impact of leakoff water on a permeability jail is severe. Therefore,
it is advisable to control leakoff during the treatment.
The simulation output data is analyzed with a commercial pressure transient analysis
software package. The well test analyses show that a heterogeneous reservoir with
permeability jail damage can also be interpreted as a homogeneous reservoir with either a
very short or low-conductivity fracture: all three hypotheses fit the well-test data. This
confirms that well tests may be inconclusive for distinguishing among these cases.
Subsequent performed simulations show that reduction in fracture length does not extend
the initial cleanup period, but strongly correlates with a shift of the production decline curve
to lower gas rates. A reduced fracture length and damage from leakoff and a permeability
jail are therefore distinguishable. On the other hand, it’s difficult to separate production
results for a model with a low-conductivity fracture from a model with permeability jail
damage: both show strongly reduced initial gas rates and followed by long cleanup periods.
Water production can be used to discriminate between a fracture with reduced permeability
and reservoir damage, however. This allows for a correct diagnosis and appropriate actions
to be taken to optimize subsequent fracture treatments.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Preface / Acknowledgements
This report presents my final thesis work of the MSc. Petroleum Engineering, as part of the
section Petroleum Engineering at the department of Geotechnology of the Delft University
of Technology.
This thesis work is performed in close cooperation StrataGen Delft, an engineering
consulting company. StrataGen offers a broad range of services, including fracture and
reservoir studies, fracture treatment design and onsite treatment supervision.
I would like to thank Prof. dr. W.R. Rossen deeply for his guidance during this project, his
expertise on reservoir engineering and his out-of-the-box thinking on hydraulic fracturing
operations and simulations. Furthermore, I would like to thank him greatly for helping me to
structure my thesis report by providing many edits and comments until the last moment.
I owe my gratitude to my supervisor dr. Hans de Pater, manager of StrataGen Delft, for the
possibility to do my research on this very interesting topic in cooperation with StrataGen.
Furthermore, I am very grateful for all his advise and that he has been willing to share his
knowledge and expertise with me.
Special thanks goes out to Josef Shaoul, for all his support on the various software
programmes I needed for this thesis and for sharing his ideas and expertise on hydraulic
fracturing with me. I would like to thank him for always being open to questions and his
enthusiasm in helping me to tackle various problems.
Also, I would like to thank Bart, Winston and Marcello for the many tips and tricks on
fracturing, the oil industry and other important things in life over the last year. I very much
enjoyed working with you!
I would like to thank my committee members, Prof. dr. Pacelli Zitha and dr. ir. Cas
Berentsen, for their interest in my work and their willingness to be part of my graduation
committee.
Last, but certainly not least: I would like to deeply thank my family and friends for their
support, understanding, believe, love, enjoyable reliefs and laughter!
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Table of Contents
Abstract ..................................................................................................................5
Preface / Acknowledgements .................................................................................7
Table of Contents....................................................................................................9
1
Introduction.................................................................................................. 11
1.1
Problem statement and objectives......................................................... 11
1.2
State-of-the-art of tight gas stimulation and evaluation........................... 12
1.2.1
Water blocking principle ................................................................ 12
1.2.2
Fracture damage and cleanup ........................................................ 13
1.2.3
Well test analysis .......................................................................... 13
1.3
Thesis structure................................................................................... 14
2
Theory........................................................................................................... 15
2.1
Single phase gas flow .......................................................................... 15
2.2
Multiphase (gas-water) flow ................................................................. 17
2.2.1
Relative permeability ..................................................................... 17
2.2.2
Fluid saturations and capillary pressure........................................... 17
2.3
Characterization of tight gas reservoirs.................................................. 19
2.3.1
Rock properties............................................................................. 19
2.3.2
Phase trapping and the ‘permeability jail’ ........................................ 20
2.3.3
Capillary pressure ......................................................................... 22
2.3.4
Heterogeneity............................................................................... 22
2.4
Well test analysis................................................................................. 23
2.4.1
Dimensionless variables ................................................................. 23
2.4.2
Theory of buildup analysis ............................................................. 24
2.4.3
Analysis plots................................................................................ 24
2.4.4
Hydraulic fracture evaluation: procedure and accuracy ..................... 27
3
Modelling of Tight Gas Reservoirs................................................................. 28
3.1
Simulation Model Setup........................................................................ 28
3.1.1
Tight gas properties ...................................................................... 28
3.1.2
Well, hydraulic fracture and grid properties ..................................... 31
3.1.3
Base case initiation........................................................................ 34
3.2
Tight-gas capillary pressure .................................................................. 36
3.2.1
The impact of capillary pressure on gas production .......................... 36
3.2.2
Capillary end effect and its water block potential ............................. 40
3.3
Permeability jail................................................................................... 49
3.4
Heterogeneity model............................................................................ 54
3.4.1
Heterogeneity model: preparation .................................................. 54
3.4.2
Heterogeneity model: production simulation.................................... 61
3.4.3
Heterogeneity modelling results: cleanup period .............................. 65
3.4.4
Heterogeneity modelling results: long-term production..................... 68
3.4.5
Heterogeneity modelling results: impact of injected water ................ 72
3.4.6
Controlling damage from leakoff water ........................................... 74
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
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Well Test Interpretation of Simulation Results............................................. 76
4.1
Well test preparation ........................................................................... 76
4.2
Well test results................................................................................... 77
4.2.1
Pre-fracture well test ..................................................................... 77
4.2.2
Post-fracture well test ................................................................... 78
4.3
Well test interpretation and implications ................................................ 82
4.4
Closing the circle: using well test results................................................ 85
5
Conclusion and Recommendations ............................................................... 91
5.1
Conclusions......................................................................................... 91
5.2
Recommendations ............................................................................... 94
6
Bibliography.................................................................................................. 95
6.1
Books and articles ............................................................................... 95
6.2
Software and internet ........................................................................ 100
7
Nomenclature ............................................................................................. 102
8
Appendix - Flow calculations in simulator .................................................. 103
9
Appendix - Modelling hysteresis effect ....................................................... 105
10
Appendix – Equilibrium Sw profile: a spreadsheet calculation.................. 107
11
Appendix - Hydraulic Fracture Design and Simulation ............................. 110
12
Appendix - Grid refinement options ......................................................... 112
13
Appendix - Reservoir model test runs ...................................................... 115
14
Appendix - Simulation of fluid leakoff process ......................................... 117
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
1 Introduction
1.1 Problem statement and objectives
Worldwide rising gas demand is creating new opportunities for low-permeability gas
reservoirs to be exploited. These so-called tight gas reservoirs have been subject of much
research over the past three decades, primarily because it is difficult to optimize recovery.
Economic development of tight gas reservoirs is only possible through the use of well
stimulation techniques, mainly hydraulic fracturing, in vertical or horizontal wells. Hydraulic
fracturing is the technique of pumping fluid with sand or ceramic proppant into the
reservoir, where the downhole pumping pressure exceeds the formation stress. This will
cause the formation to break and split in the direction perpendicular to the minimum stress.
The fracture will improve the well productivity by creating a conductive channel that
provides much better contact between well and reservoir (Economides and Nolte 2000).
The production enhancement for any well, whether oil or gas, can be simulated with use of
combined reservoir and fracture simulators. In general, the well productivity increase can be
calculated to a certain degree. For tight gas wells, the improved well productivity is
nevertheless generally overestimated by simulation programs using fracture characteristics
estimated from fracture simulation software (Cramer 2005). Several factors may result in the
unrealistic forecasting of the production. One issue is that in tight reservoirs, it is very
difficult to measure kh and reservoir pressure (Britt et al. 2004), which are needed for basic
flow calculations and are crucial for evaluating stimulation success. The problem arises
because it takes a long time to measure these parameters in well tests. Furthermore, in tight
gas reservoirs an additional problem is to evaluate the performance to optimize the
stimulation. Estimating productivity after stimulation requires pre-determined or estimated
values for fracture geometry (length-width-height) and conductivity, all which are hard to
quantify without an accurate estimate of the kh.
A second cause for the underperformance is the strong and long-lasting cleanup that is often
observed in tight gas reservoir with a hydraulic fracture. The cleanup of a well is the initial
period (a few days) in which gas rates are slowly increasing over time, instead of starting
with peak production. An extended cleanup, up to weeks or months, can be caused by
fracture face damage, water blockage in the reservoir, fluid leakoff behaviour, fracture gel
cleanup in the fracture or a combination of these effects. Generally, the influence of each of
the individual factors remains an ‘unanswered question’ (Wang et al. 2009). Over the past
decades, many researchers have focused on the influence of these mechanisms for the
well’s potential is significantly affected. A brief review of the most important findings is
included in section 1.2.
The thesis objectives are to research proposed ideas on phase trapping mechanisms, such as
relative permeability reduction and the effect of heterogeneity in fracture face cleanup.
Secondly, to build a reservoir simulation model to test proposed ideas and to perform postfracture analysis on modelled production data. In this analysis, the objective is to test
whether the input data for the reservoir simulation (reservoir and hydraulic fracture
properties) can be obtained from the well test results. It will also be tested how unique and
accurate the solution is. The aim is to improve the understanding and interpretation of the
impact of unconventional fluid behaviour on production and well test analysis.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
1.2 State-of-the-art of tight gas stimulation and evaluation
1.2.1 Water blocking principle
During the fracturing process, water invades the formation and remains there until
production starts and the cleanup commences. Then, if pressure drawdown overcomes
capillary pressure within the reservoir, some or all of the water returns to the fracture. This
water can also remain trapped in the pores of the reservoir by capillary forces and it can
negatively affect well productivity (Mahadevan et al. 2009). This process is called water
blocking.
Holditch (1979) explored various factors affecting water blocking and gas flow from
hydraulically fractured wells. He shows that if formation damage is present due to fluid
invasion and capillary pressures exceed pressure drawdown, the damaged zone acts as a
pressure sink to attract and trap water. This causes the relative permeability of gas to be
reduced and hence influences the production dramatically. A limitation is that this work
addresses uniform reservoir only. Cramer (2005) shows that the production reduction from
water blocking can be expressed as an additional skin which is added to the existing skin
factors in a producing well, and is defined as a function of hydraulic fracture length, damagezone width and the ratio of undamaged permeability and the permeability in the damaged
zone. He calculates dramatically reduced well productivity.
The impact of the combined effects of damaged zones surrounding the hydraulic fracture
and water blockage is recognized and tested widely by many authors. Apart from previously
referenced work, Settari et al. (2002) shows that water blockage alone is not a major cause
of concern in gas wells, but in combination with absolute permeability damage can cause
serious productivity reduction. Recently, Friedel (2004) also concludes that the so-called
hydraulic damage, caused by increased water saturation and relative permeability effects in
the vicinity of the fracture, has less impact on production than reduction of porosity and
permeability surrounding the fracture (mechanical damage) caused by the fracturing
process.
As shown in the referenced papers, many different causes can be found for the reduction in
production by the water invasion in the formation. In this thesis, the focus will be on damage
caused by the invasion of leakoff water into the reservoir surrounding the hydraulic fracture.
Some factors seem to be important in this process, such as capillary pressures, initial water
saturations and pressure drawdown. But also wettability of the reservoir rock (Bang et al.
2008) may play an important role in this process. The increased focus on reservoir properties
and their importance to describe gas recovery and post-fracture production results is also
noted by Rickman and Jaripatke (2010).
Water block mechanisms, such as high capillary pressures, are taken into consideration for
the simulation models. More details are provided in the specific sections of this thesis
(chapter 3).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
1.2.2 Fracture damage and cleanup
The fluid used in hydraulic fracturing operations contains apart from water certain polymer
additives, which are mainly responsible for viscosifying the fluid, proppant transport, and
fluid-loss control. The main design criterion for fracturing fluids is viscosity (Economides and
Nolte 2000). After the proppant placement, ideally the polymer should degrade chemically
and be produced back through the well. If this does not happen, severe damage within the
fracture can occur. This is referred to in the industry as a slow or incomplete fracture
cleanup. A proper cleanup of the fracture after the pumping stage is important for
determining the fracture properties and estimating the long-term well performance
(Montgomery et al. 1990).
Tight gas wells with an infinite-conductivity fracture should show a high initial production
peak, followed by a steep decline in rate. This so-called hyperbolic decline curve is typical for
tight gas reservoirs, compared to more common exponential decline (Holditch 2006). In
some producing wells, a slowly increasing production plateau has been observed, which may
be the result of the viscous gels remaining in the proppant pack. When gel remains in the
fracture, a reduction up to 80% in initial gas rate can be seen (Voneiff et al. 1996). In order to
simulate this kind of behaviour, one must represent the flow of three phases: gas,
formation/fracturing water and unbroken gel (Wang et al. 2009). Multiphase flow and the
gel remaining in the fracture are important factors affecting fracture cleanup and it should
be taken into account when simulating the well productivity of tight gas wells with special
focus on the role of the fracture itself.
The simulations in this thesis will only be performed with two phases present: gas and water.
The water represents both the initial reservoir water and the leakoff fluid. When referred to
´the cleanup period´, this then refers to the initial gas rate reduction caused by the water
phase only (see section 1.2.1 for examples). This thesis does not include research on fracture
damage. However, low-conductivity (e.g. unbroken gels) and short (e.g. poorly placed
proppant) fractures are taken into consideration during the post-fracture evaluation
(chapter 4).
1.2.3 Well test analysis
For many years, the most common way to obtain important reservoir properties is to
perform a well test analysis. Early interpretation methods, such as semi-log or log-log
pressure plots, were limited to the estimation of well performance, near-wellbore effects or
assumptions of reservoirs with homogeneous properties (Gringarten 2006). With the
introduction of the pressure-derivatives plot by Bourdet et al (1989), the analysis of well
tests changed dramatically, allowing for heterogeneous reservoirs, limited wellbore entry
and boundary effects. Where early pressure-analysis methods recorded the movement of a
pressure wave through the reservoir, the pressure derivative can reveal much more detail.
By definition, the pressure derivative is more sensitive to changes that occur in the
movement of this wave and therefore it is capable of detecting changing patterns in the
reservoir. This results in different patterns for different scenarios, which can be recognized
on specific log-log plots. Examples are boundary dominated flow, wellbore storage
dominated flow, early flow times (transient), infinite reservoir (radial flow), (in)finite
hydraulic fracture, and many more.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
For conventional reservoirs, this practice has been proved to be simple, effective and
inexpensive. Nevertheless, in low-permeability formations, the use of tests such as Pressure
Buildup (PBU) analysis are mostly inadequate, mainly due to operational aspects (Cipolla and
Mayerhofer 1998). PBU tests require a long shut-in period to obtain pseudo-radial flow from
which permeability can be calculated using a log-log plot. In low-permeability formations
with long hydraulic fractures this flow transition might take months or years, as proved by
Gringarten et al. (1974) and Cinco-Ley et al. (1978). This will make the operation expensive
and therefore mostly unwanted by operators.
Furthermore, research shows (Montgomery et al. 1990) that conventional PBU analysis
methods will, at best, provide only fair to poor results in low permeability reservoirs.
Additional variables, such as low conductivity in the fracture, formation damage in the
fracture, water invasion of the reservoir and natural fractures networks, tend to complicate
the results of these analyses further. This makes it hard to obtain a unique solution to the
problem, which is necessary for the appropriate actions to be taken.
Chapter 4 focuses on well test analyses (PBU) performed on the simulated production data.
Several scenarios are analyzed and the accuracy of the outcome is tested. Focus lies on the
interpretation of multiphase fluid flow, complicated reservoir behaviour and fracture
damage. For a good post-fracture production analysis, it’s crucial to obtain the basic
reservoir and fracture properties.
1.3 Thesis structure
This thesis consists of 4 main chapters, starting with the introduction to the general problem
statement and objectives of thesis in chapter 1. Next, chapter 2 provides the theoretical
background on fluid flow in a reservoir towards a hydraulically fractured well, the
characteristics of tight gas reservoirs and the basics of well test analysis. The next two
sections (chapter 3 and 4) both discuss specific parts of the thesis problem.
Chapter 3 provides the reservoir model used in the numerical production simulations of this
thesis. The first section (3.1) describes the model setup, followed by a presentation of the
simulation results of high capillary pressures and the effect of phase relative permeability
reduction on gas and water production (section 3.2 and 3.3). Finally, section 3.4 introduces a
heterogeneous reservoir model to more realistically simulate specific tight gas reservoir
properties and the impact of water invasion around the hydraulic fracture.
Chapter 4 focuses on well test analyses performed in the models of chapter 3 and shows the
obtained results. It’s shown that these may lead to various interpretations, regarding the
state of the reservoir and the hydraulic fracture. The implications are discussed
subsequently.
Chapter 5 concludes with the main findings of the thesis and provides recommendations for
fracture treatments in tight gas reservoirs and ideas for further research.
Finally, after the thesis bibliography (chapter 6), a total of 7 appendices are included in the
back of this thesis report (chapters 7 to 14). These chapters provide background information
on the simulations and elaborate on decisions made in the process.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
2 Theory
This chapter describes the theoretical background of gas flow in the reservoir and gas
production. The formulas are from Hagoort (1988). The first section (2.1) discusses singlephase flow and the introduction of the hydraulic fracture into the model. Multiphase (gaswater) flow (section 2.2) requires an update of the inflow equation and the introduction of
additional parameters. The water phase is introduced and the corresponding multiphase
equations are presented.
The second part of this chapter (section 2.3) discusses the specific properties of tight gas
reservoirs and introduces complications related to the standard fluid flow equations. This
introduction will be the base of the tight gas modelling in chapter 3. Finally, this chapter
concludes with the theory of well test analyses (section 2.4), which will be used in the postfracture analyses in chapter 4.
2.1 Single phase gas flow
Production from gas bearing formations in the subsurface occurs through the flow of gas
towards the well. A pressure difference between the bottom of the well and the reservoir
causes flow of the gas into the wellbore. The pressure near the wellbore rapidly decreases
towards the wellbore pressure. The initial decrease in pressure is referred to as the
‘transient period’. The pressure wave continues outward through the reservoir, until a
pressure boundary is ‘felt’. After this period pressure declines with time at a uniform rate
throughout the reservoir and flow is stabilized. This is named either ‘steady state’ or
‘pseudo-steady state’, depending on whether the boundary is perfectly transparent (steady
state) or sealing (pseudo-steady state) (Lake 2003).
Single-phase flow in a porous medium is described by two equations: Darcy’s Law (Eq. 2-1)
and mass conservation (Eq. 2-2). Darcy’s Law is valid in the absence of inertial effects and
neglecting gravity and the mass conservation is for an infinitesimal Cartesian volume
element at steady-state.
k
q
u = = − grad ( P )
A
µ
Eq. 2-1
δ
δ
δ
( ρ ux ) +
( ρu y ) +
( ρ u y ) = div( ρ u ) = 0
δx
δy
δy
Eq. 2-2
These equations can be combined into a working gas radial inflow well equation (Eq. 2-3)
under assumptions of pseudo-steady state and isotropic and uniform reservoir properties.
The individual steps and elaborate discussions are found in Hagoort (1988) and will not be
thoroughly discussed here. Subscript r is used here for reference state of the gas.
q=
2π kH ( mR − mbh )
3


( µ B ) r  ln( Re / Rw ) − + stot 
4


Eq. 2-3
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Under certain circumstances, the assumption of steady state is not applicable to describe
the flow of gas in reservoirs. Especially in low-permeability gas formations, transient flow
can dominate much of the life of a well (Wattenbarger et al. 1969). A good mathematical
approximation is achieved with the pseudo-steady state equation for the inflow of gas into
the wellbore and a skin factor combining any flow resistance in the near-wellbore area (stot).
The basic properties of gas depend on pressure and can therefore not be assumed constant
throughout production. This requires introducing a quantity called pseudo pressure (AlHussainy et al. 1966). Pseudo pressure (Eq. 2-4) can be calculated from (reference) pressure
and the property state at this reference pressure.
m( p ) =
1
(ρ / µ ) r
p
∫ ( ρ / µ )dP
Eq. 2-4
pr
So far, the radial inflow equation (Eq. 2-3) has not considered flow into a hydraulic fracture.
To do so, the radius of the well is replaced by the so-called ‘effective wellbore radius r’w to
account for the increased fracture inflow area. Prats (1961) was the first to introduce this
term and showed that for an infinite-conductivity fracture the following relation applies,
where xf is the fracture half-length:
Eq. 2-5
R ' = 0.5 x
w
f
Combining this with Eq. 2-3, the equation for gas flow into a hydraulically fractured well is as
follows:
q=
2π kh(mR − mbh )
3


( µ B )r ln( Re / Rw' ) − + s frac 
4


Eq. 2-6
where R’w is effective wellbore radius after stimulation and sfrac is the skin resulting from
damage to the fracture face and damage to the fracture, e.g. reduction of permeability.
Eq. 2-6 assumes (pseudo-) radial single-phase gas flow in the reservoir towards the well.
Initially a fractured well shows strong transient flow behaviour, which includes a period of
linear flow, which gradually changes to radial flow. In low-permeability reservoirs, this
transition can take a very long time. The rate given by Eq. 2-6 is therefore a theoretical
value, which can only be used for comparing rates at longer simulation times and not in the
early transient period of the well. Chapter 13 (Appendix for reservoir model test runs)
discusses the validation of the numerical simulator by comparing the simulated rate with the
calculated rate using Eq. 2-6.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
2.2 Multiphase (gas-water) flow
Section 2.1 provides an introduction to the flow of gas in the reservoir towards the hydraulic
fracture and then into the wellbore. Throughout the whole derivation single-phase flow is
assumed. Both initial formation water and invading fracturing fluid can lead to a
systematically different and more complex behaviour of gas flow in the reservoir. This
section focuses on the theory behind these important multiphase phenomena that need to
be taken into consideration for the modelling of gas production in tight gas reservoirs.
2.2.1 Relative permeability
The introduction of the water phase into the system has an impact on both the material
balance and the flow through the reservoir. Therefore, the mass balance equation and
Darcy’s Law need to be updated. Darcy’s Law for a single phase α in a multiphase system, is
uα = −
kkrα
µα
grad ( Pα )
Eq. 2-7
Laboratory experiments are used to determine the relative permeabilities of gas and water
as functions of water saturations. When experimental data is lacking, some empirical
relations are available. The most widely used relations for relative permeabilities are the
Brook-Corey relations (Brooks and Corey 1964). Many studies refer to the use of these
correlations in calculating the relative permeabilities for a given system. For this study, the
relations used are presented in section 3.1.1.
2.2.2 Fluid saturations and capillary pressure
Throughout section 2.1 steady state is assumed. In order to describe the multiphase flow
processes that occur during fracturing-fluid invasion of the formation and later gas
production, this assumption has to be relaxed. Multiphase flow in reservoirs is described in
detail by Dake (1978).
In multiphase flow, the two phases require a separate approach with respect to flow and
mass conservation. It’s therefore necessary to introduce the phase saturations; water
saturation Sw and gas phase Sg. The sum of Sw and Sg is 1. This now allows one to calculate a
mass balance per phase. The simulator works with discretized forms of the mass balance and
fluid flow equations to allow the solution to be solved numerically. More detail on the use of
the flow equations in Eclipse 100 (Schlumberger 2009) is provided in chapter 7 (Appendix for
flow calculations).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
A second parameter needed to correctly model the flow of gas and water, is the capillary
pressure Pc. The capillary pressure is defined by
Eq. 2-8
Pc = Pnw − Pw
The most common form of the capillary-pressure function is from Leverett (1941),
introducing a dimensionless J-function. The capillary pressure is a function of the interfacial
tension (σ), the contact angle between rock and fluid (θ), the porosity (φ) and the function
J(Sw).
φ 
Pc = σ cos(θ )   J ( S w )
k
Eq. 2-9
This relation reveals that for tight gas reservoirs with generally smaller pores, the capillary
pressure is high. This will be discussed in more detail in 2.3.3.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
2.3 Characterization of tight gas reservoirs
This section presents an overview of rock properties of low-permeability rocks, which
dominates the flow behaviour of tight gas reservoirs. In particular, this section discusses
capillary pressure, the ‘permeability jail,’ and reservoir heterogeneity, which are the focus of
much of this thesis.
2.3.1 Rock properties
Many authors have focused on classifying and determining the various types of tight gas
sands in the US, after the immense potential became more evident in the last decades.
Spencer (1985) describes the geological aspects of tight gas reservoirs in the Rocky Mountain
Region. He states that there are generally 4 types of reservoir: marginal marine blankets,
shallow marine blankets, lenticular fluvial reservoirs and finally chalk reservoirs, each with
specific lateral reservoir continuity (Holditch 2006). As an example, Table 2-1 below presents
an overview of general properties of some reservoirs located in the Rocky Mountains
(Shanley et al. 2004), one of the most thoroughly studied regions of low-permeability
reservoirs worldwide.
Property
Porosity
Permeability (Klinkenberg corrected)
Stressed permeability (Klinkenberg corrected)
Water saturation (producible range)
Irreducible water
Pore type
Pore-throat description
Description
5-10%
0.1 – 10 mD
0.001 – 10 mD
<50%
20 – 40%
Slot pores dominated permeability
Micro- to nanopore throats
Table 2-1 rock property values, tight sands in Rocky Mountains region (Shanley et al.
2004).
Overall, tight sandstones have low porosity, which is a result of heavy compaction; pores
present are of micrometer to nanometer-size. Rushing et al. (2008) states that ‘the low
permeabilities and porosities associated with tight gas sands can be attributed directly to a
large distribution of small and very small pores and/or a very tortuous system of pore
throats connecting these pores’.
Byrnes (1996) describes the reservoir characteristics of the typical low-permeability
sandstones found in the Rocky Mountains, and comments that ‘the influence of confining
stress on permeability can be attributed primarily to the decrease in size of the pore throats
that connect the larger pores, which result in permeability decreases of 10 to 40 times’. An
example is shown in Fig. 2-1.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 2-1 Thin section of slot and fracture porosity in Deep Basin of Canada (Aguilera 2008).
2.3.2 Phase trapping and the ‘permeability jail’
A number of authors argue that the complex pore structure of tight-gas reservoirs,
dominated by slot pores and sheet-like pore throats and high effective overburden stress,
gives rise to specific issues concerning multiphase flow. This complex structure may form a
potential damage to gas production, for example by phase trapping.
Bennion (2009) describes favourable and unfavourable pore structures for phase trapping.
He concludes that a pore structure in which most of the effective permeability is contained
in a relatively small fraction of the pore space, which consists of interconnected meso- or
macropores or small fractures, is not sensitive to water-based phase trapping. They have a
rather large ‘capacity’ to store the water without it blocking the main pores. A structure of a
more uniform distribution of micro-pores (1-10 µD) will, by a slight increase in water
saturation, result in the clogging of most of the pores with water and thus a reduction in
effective permeability to gas throughout the whole pore structure. A pore structure that
consists of narrow pore throats, he argues, is susceptible to this kind of behaviour.
Apart from phase trapping, the high effect stresses in the rock may impact the permeability
to fluids so severely that classical theories for multiphase flow are no longer applicable. The
relative permeabilities to both water and gas can be so low that neither phase has significant
relative permeability over some range of saturations. This idea is named the ‘permeability
jail’ (Shanley et al. 2004).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 2-2 The relative permeability and capillary pressure in low-permeability gas reservoirs
(Shanley et al. 2004).
Fig. 2-2 illustrates this concept for relative permeability and capillary pressure functions. In
some tight gas formations water ceases to flow at a ‘critical’ water saturation that is
substantially greater than connate water saturation. Normally, field observations of low
water production would imply that the reservoir is at irreducible saturation, and one would
expect gas to flow freely, but it does not. Second, the lowered permeability causes the two
phases to increasingly interfere in the restricted flow paths of the rock pore space. Sgc
increases toward initial water saturation. This region of saturations where neither phase has
significant relative permeability is named ‘permeability jail’.
Cluff and Byrnes (2010) also discuss the existence of a permeability jail in low-permeability
reservoir rocks, where the water is trapped by the high capillary pressure and thereby
reduces the permeability to gas significantly. Although hard laboratory evidence in the form
of published studies is missing, the authors believe that multiple gas-brine drainageimbibition hystereses can cause this typical fluid behaviour. This form of hysteresis is
believed to occur in lithologies with complex pore geometries, as presented for example by
Bennion (2009).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Gdanski and Walters (2010) demonstrate the impact of relative permeability functions on
gas and fracture treatment water production in low-permeability gas reservoirs. The ‘poorquality matrix rel-perms’ are referred to as ‘rel-perm jail’ and not considered to be typical
drainage relative permeability functions. Nevertheless, the authors also believe that indeed
multiple hystereses may cause strong relative permeability reduction.
Britt and Schoeffler (2009) describe the permeability jail as ‘extremely important for
reservoir and petrophysical assessment of resource quality’. Contrary, Blasingame (2008)
refers to it as ‘a provocative study with regard to their concept of capillarity controlled
production’, but he also states that ‘the reality of poor well performance is explained […] by
the concept of permeability jail, but there are other specific factors influencing flow at the
reservoir scale’.
The area of repeated hysteresis and the impact on low-permeability gas reservoirs is a topic
that requires much more study. For example, at the time of this writing, the Ecole Centrale
de Lille (2010) has a research position open for petrophysical analysis at micro-pore scale,
for normal analysis method often fail to result in consequent output. The geology
department of the University of Utah (2010) works on a project which aims at the interplay
between multiphase flow and hydraulic fracture models in tight gas reservoirs, also
specifically naming ‘permeability jail’ as an important research topic.
Although the idea for the existence of a ‘permeability jail’ has so far not been proven in any
laboratory tests, this thesis will investigate this phenomenon as part of the post-fracture
production analysis of tight gas reservoirs.
2.3.3 Capillary pressure
Low-permeability reservoirs have small pores, and under stress ‘pore throats decrease in
diameter by up to 50% to 70%’ (Byrnes 1996). Eq. 2-9 illustrates the relation between low
permeability and capillary pressure. For a quick order-of-magnitude calculation, assume
cos(θ) = 1 = J(Sw). For a tight-gas sandstone, common values for interfacial tension, porosity
and permeability are respectively 50 mN/m, 0.05 and 0.001 mD (= 1 x 10-18 m2), which gives a
reference capillary pressure of 111 bars. Because, according to Eq. 2-9 capillary pressure is
proportional with the inverse of the square root of the permeability, a higher permeability
implies significantly lower capillary pressure. This thesis investigates the impact of capillary
pressure on post-fracture production.
2.3.4 Heterogeneity
Reservoirs are heterogeneous both vertically and laterally. Barree (2009) states that in some
reservoirs a large part of the fracture face contacts low-permeability regions with high
capillary pressures. Other higher-permeability regions have lower capillary pressure and
allow gas to flow freely, at higher velocity. Section 3.4 discusses the influence of
heterogeneity in more detail.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
2.4 Well test analysis
The success of a hydraulic fracture in a tight gas reservoir is determined by the increase in
gas production as a result of an increased effective wellbore radius. The extent of the
improvement can be predicted with reservoir simulations, which require a few important
input parameters. Amongst other methods, well test analyses can provide these parameters
(pressure and permeability) prior to the fracture treatment. An example is a Pressure
Buildup (PBU) test. A post-fracture well test analysis can also determine fracture half-length
for further production forecasting.
This thesis focuses on the use and accuracy of the PBU test in tight gas reservoirs, by
analyzing the production results of a numerical reservoir simulation model. This section
introduces the theory of these tests and discusses the procedure and accuracy of a PBU test.
2.4.1 Dimensionless variables
In well test analysis, often the use of dimensionless variables aids the search for the
unknown reservoir parameters (Horne 1995). Using dimensionless variables reduces the
amount of unknowns and provides a solution for any system of units. The variables used are
pressure, time and radius. The dimensionless pressure is defined as (SI units):
pD =
2π kh
( m( pi ) − m( pwf ) )
QBµ
Eq. 2-10
The dimensionless time is as follows:
tD =
kt
Φµ ct rw2
Eq. 2-11
Finally, the dimensionless radius is:
rD =
r
rw
Eq. 2-12
For the analysis of hydraulically fractured wells, the dimensionless time is mostly re-written
to obtain the fracture half-length xf instead of the wellbore radius. By applying Eq. 2-13, the
resulting dimensionless time is derived as shown in Eq. 2-14.
rw2
x 2f
Eq. 2-13
kt
Φµ ct x 2f
Eq. 2-14
tD,x f = tD
tD,x f =
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
2.4.2 Theory of buildup analysis
Buildup tests and analyses are based on the theory of superposition, which uses the
principle that a linear combination of particular solutions is also a solution. This is a wellknown and widely applicable theory in science and engineering (Horne 1995). For a buildup
test it means that the well is controlled at two different rates over two pre-defined period of
time, whereby the second rate is set to zero. Superposing the two pressure solutions results
in a pressure response that can be analyzed by various methods, including a Horner plot. The
simulations in this thesis can accurately control bottomhole rate or pressure and will allow a
proper analysis to be made.
A few important assumptions are made and should be taken into account when examining
the results. First, the analysis of the PBU is based on single-phase flow (gas only) and
therefore a combined inflow of liquid and gas may cause divergence from the solution.
Other assumptions behind the PBU theory include infinite drainage area, homogeneous and
isotropic reservoir, slightly compressible fluids and constant fluid and rock properties. These
assumptions do not necessarily match the conditions in the simulator. Finally, the theoretical
model assumes radial flow, while in hydraulically fractured wells in low permeability
formations this may take much longer than an average well test last. The calculated
properties from a PBU are therefore possibly inaccurate. Nevertheless, the absence of other
quick, cheap and practical methods make a PBU test still widely used in the field and
therefore useful to include in this thesis as the method of post-fracture analysis.
2.4.3 Analysis plots
A standard method to analyze the pressure behaviour in a well during a pressure buildup
(PBU) test is to perform a type curve match on a log-log plot. By matching the data to a type
curve, reservoir parameters are estimated from plotted curves with known properties.
Dimensionless time and pressure are linear functions of ‘real’ time and pressure and can
hence be derived from a match. This method assumes pseudo-radial or radial flow and is
incorrect for other flow regimes. When plotted on a log-log basis, the difference between
the log functions and the actual data is a constant amount, as shown by Eq. 2-15 and Eq.
2-16 (Horne 1995). For example, from the pressure match a good estimate for kH can be
obtained, when the rate q, formation volume factor B and the viscosity μ are known.
 2π kH 
log ∆m( p ) = log m( pD ) − log 

 qB µ 
 k 
log t = log t D − log 
2 
 Φµ ct rw 
Eq. 2-15
Eq. 2-16
In a medium permeability reservoir without a hydraulic fracture, the first part of the
pressure response is dominated by wellbore storage. Later in time, the pressure wave is
stabilized in the reservoir and the response defines radial inflow into the well. The radial
flow is seen in a horizontal line in the derivative plot. Fig. 2-3 shows a typical pressure
response for such reservoir.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
A fractured well produces a different pressure response due to the high permeability in the
fracture, thereby usually diminishing any apparent wellbore effect. Therefore, a log-log plot
will display significantly different features, where two main cases are most apparent (Horne
1995). For this, first, the principle of fracture conductivity is introduced (Eq. 2-17). The
fracture conductivity (CfD or FCD) provides a measurement for the fluid handling capacity of
the hydraulic fracture and is an important design criterion in fracture treatments
(Economides and Nolte 2000).
C fD =
kf w
kx f
Eq. 2-17
A finite-conductivity fracture will exhibit linear flow through the fracture, with a resulting
pressure drop over the total fracture half-length (Cinco-Ley et al. 1978), and linear flow in
the reservoir towards the fracture. The observed flow regime is referred to as bilinear flow
and may also represent the cleanup period of the fracture.
An infinite-conductivity fracture shows no gradient of pressure in the fracture and only
linear flow towards the fracture from the reservoir, and thus the flow regime is named linear
flow. This can be seen as a ‘cleaned up’ fracture. Mostly, the linear flow regime is preceded
by bilinear flow, after which finally radial flow may occur.
Fig. 2-3 Typical log-log plot (pseudo pressure (psi2/cp) versus dt (hr)) for mediumpermeability reservoir without a hydraulic fracture (Cipolla and Mayerhofer 1998).
In the most ideal cases, these flow regimes show typical responses in a pressure derivative
plot. Of course, field examples may display more complicated pressure behaviour, which
need computer-aided matching processes to obtain a good match (Cipolla and Mayerhofer
1998). In Fig. 2-4 the pressure response of a high-conductivity fracture is presented, showing
a characteristic ½ slope of the pressure derivative on the log-log plot. The half slope
originates from the pressure drop which is related to the square of the fracture
dimensionless time.
The finite-conductivity fracture with bilinear flow is noticeable as a line with a ¼ slope, as
shown in Fig. 2-5. Again the slope on the log-log plot is determined by the relation between
the pressure and the time, with time now raised to the power of ¼.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 2-4 Typical log-log plot (pseudo pressure (psi2/cp) versus dt (hr)) for high-conductivity
fracture in a low-permeability reservoir (Cipolla and Mayerhofer 1998).
Fig. 2-5 Typical log-log plot (pseudo pressure (psi2/cp) versus dt (hr)) finite-conductivity
fracture in low-permeability reservoir (Cipolla and Mayerhofer 1998).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
2.4.4 Hydraulic fracture evaluation: procedure and accuracy
In the following section, an overview is given of the general workflow for determining some
important parameters for the evaluation of the hydraulic fracture. To get an idea of the time
involved in these tests, a brief overview of a standard well test schedule in tight gas
reservoirs in Alberta (Canada) is given.
Before the hydraulic fracture is created in the reservoir, often a PBU is performed right after
drilling and completing the well. This test can provide the reservoir permeability and the
reservoir pressure uniquely. This is common practice in oil and gas fields around the world,
although in tight gas formations it causes severe operational issues. The well needs to be
shut-in for a long time to reach (pseudo-) radial flow to determine the reservoir properties.
For example, for a typical tight gas well with a hydraulic fracture with half-length of 100 ft, in
a reservoir with permeability of 0.01 mD, porosity of 0.15, gas viscosity of 0.03 cp and total
compressibility of 1.0 x 10-4 psi-1, it may take 213 days to reach pseudo-radial flow (Cheng et
al. 2007). It is clear that this is rather expensive for the operator. Nevertheless, the
importance of the test is well recognized, for the determination of the virgin reservoir
permeability and pressure is not again so easily determined as in this phase of the
characterization and evaluation process.
After a hydraulic fracture is placed in the reservoir, some basic parameters are needed for a
proper evaluation of the treatment. A well test (PBU) can provide information on fracture
length (effective/productive) and fracture conductivity and can confirm the reservoir
pressure and permeability obtained from a pre-frac PBU test. Nevertheless, without either
input for pressure or permeability, the analysis is non-unique for fracture length. This is
related to the use of 2 equations (Eq. 2-10 and Eq. 2-14) to calculate 3 unknowns (pressure,
permeability and effective half-length). This is a parametric equation, and cannot be solved
uniquely. Without a fracture, the wellbore radius is known, and the remaining 2 unknowns
can be solved for with the 2 equations
Independent input to the post-fracture analysis is therefore essential at this stage. Reservoir
pressure and permeability can be obtained from field analogues, which can provide some
guidance to the results. Permeability can also be obtained from logging or core samples.
Although, high pressure compaction at reservoir conditions, or an unexpected permeability
jail will also limit the use of core analyses as a trustful source of information for
permeability. Finally, the fracture half-length can also be determined from the fracture
design process before the actual treatment takes place. In essence, it’s one of the main
design criteria. Nevertheless, there’s a rather important difference between the two
estimated fracture half-lengths. The fracture model mainly predicts the pumped or created
half-length; the production analysis shows the effective or productive half-length. It has
been reported that the effective half-length can decrease up to only 5% of the modelled
fracture half-length due to width loss, complicated fracture cleanup, and multiphase effects
(Barree et al. 2003b). Assuming a value of fracture half-length based on fracture design or
treatment, therefore, is not completely accurate to production analysis.
For a proper analysis of post-fracture gas production, the understanding of the theory and
possible resulting inaccuracies of well test analysis in tight gas is crucial. This thesis will
discuss the possible impact of these complicated processes on field development plans or
subsequent fracture campaigns.
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3 Modelling of Tight Gas Reservoirs
This chapter discusses the results of the post-fracture production simulations of tight gas
reservoirs, whereby special attention is given to different phase trapping mechanisms. The
first section (3.1) introduces the base case simulation model, including reservoir, hydraulic
fracture and grid properties. The specific tight gas reservoir properties are highlighted in
detail (3.1.1), for it’s an important part of the simulations.
Next, variations in capillary pressure (section 3.2) and a ‘permeability jail’ (section 3.3) are
presented. Each section introduces the specific adjustments made in the setup of the model
regarding fluid, rock, grid or fracture properties. This is followed by presenting the modelling
result.
The final section of this chapter (section 3.4) introduces a new reservoir model with a
different grid and fracture properties. The aim of this model is to allow for heterogeneity
modelling with separate relative-permeability and capillary-pressure functions assigned to
different rock type classes. An extensive discussion on the results is presented (3.4.2 to
3.4.6).
All simulations in this thesis are performed with the commercial numerical reservoir
simulator Eclipse 100 (Schlumberger 2009).
3.1 Simulation Model Setup
3.1.1 Tight gas properties
The base case model is designed to capture the typical characteristics of a producing tight
gas field. The following parameters are chosen (Table 3-1).
Reservoir properties
Model size (L - W - H)
250 – 20 – 100
m
Depth top reservoir
2800
m
Reservoir pressure
250
bar
Reservoir permeability
0.001
mD
Water saturation
0.40
Porosity
5.0
%
Table 3-1 Reservoir properties of base scenario model.
Chapter 1 explains that a reservoir is classified as a tight gas field if it’s not economically
producible without the use of a hydraulic fracture. The model has a permeability of 1 x 10-3
mD or 1 µD. The base case model is uniform in all its properties, and the horizontal and
vertical permeabilities are both 1 µD. For 1-µD reservoirs the porosity is generally between
the 4 and 10%, as is shown in studies on the MesaVerde Basin (Byrnes et al. 2009). The base
case model has therefore porosity of 5% and this is uniform throughout the reservoir. In the
simulations in Section 3.4 the assumption of homogeneous reservoir properties is relaxed.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Hydrostatic pressure is taken as a rough predictor of pressure at the depth of the reservoir,
which gives an initial pressure of 250 bars. It’s not possible to talk about a ‘typical pressure’
for tight gas reservoirs, for many variations exist worldwide (Holditch 2006). Tight gas
reservoirs can be deep or shallow, high-pressure or low-pressure, high-temperature or lowtemperature, and heterogeneous, relatively homogeneous or naturally fractured.
A uniform water saturation of 0.4 is assumed throughout the reservoir, and gravity/capillary
effects in the vertical direction are not factored into the initial water distribution.
The reservoir gas PVT properties are taken from a study of a tight gas reservoir at similar
pressure and temperature (Shaoul et al. 2009). The viscosity (Fig. 3-2) and the gas formation
volume factor (Fig. 3-1) are presented below as functions of pressure.
Fig. 3-1 Gas formation volume factor used
in this study.
Fig. 3-2 Gas viscosity used in this study.
The relative permeabilities for water and gas used in this study are shown in Fig. 3-3. The
gas relative permeability is based on a study on the tight gas reservoirs of the MesaVerde
Basin in United States (Byrnes 2009). From this elaborate study, I selected the function
corresponding to the base case permeability of 1 x 10-3 mD.
For validation purposes, a fit of krg is made with an extended Corey relation (Eq. 3-1) for
which the input parameters are taken from another tight gas study (Cluff and Byrnes 2010).
The connate water saturation for krg (Swc,kr) and the critical gas saturation gas (Sgc) are
determined from the permeability of the reservoir model, following equations provided by
the authors. For calculation of the gas relative permeability, I used Swc,kr to establish the
point at which the gas relative permeability curve reaches it maximum. Fig. 3-3 shows the
match between the curve from the Corey relation and the base case functions.
p
q

( S w − S wc ,kr )    ( S w − S wc , kr )  
krg = 1 −
 
 * 1 − 
−
−
−
(1
S
S
)
(1
S
)

  
gc
wc , kr 
wc , kr
 

Eq. 3-1
Fitting property
Value
Unit
Swc,kr
0.0
(-)
Sgc
0.3
(-)
p
1.7
(-)
q
2.0
(-)
Table 3-2 Fitting parameters to Corey extended relative permeability function.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
I have chosen the water relative permeability curve for the base case scenario to match the
data used in a recent study of tight gas reservoir modelling (Wills 2009), which includes a
study on the influence of water. In low-permeability sandstones, the general trend is that
the lower the absolute permeability, the more reduction in gas relative permeability is
caused by the presence of a given saturation of water (Jones and Owens 1980). The authors
contend that this caused by the sheet-like tabular structure of the pore-throats in
combination with the strong water-wet behaviour, trapping water and blocking the flow to
gas (Cluff and Byrnes 2010). Therefore krw takes a low value at Sgc and generally low values
over the complete saturation range. The connate water saturation Swc is different than the
endpoint of the krg curve, but represents the water trapping in the small pores, and results in
a higher residual (or connate) water.
The choice for the water relative permeability curve, including Swc,kr has a great influence of
the overall mobility of the two phases present. The result of these equations and parameter
values is that any water in the pore space interferes with gas flow and greater gas saturation
is needed to establish a connective path to allow a given amount of gas production. When
initial water saturation approaches (1-Sgc), there is hardly any permeability to gas.
Fig. 3-3 Relative permeability functions of the base case scenario including a match for the
krw obtained by Corey’s formula.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The base case model uses a lower capillary pressure function than expected in a reservoir
with permeability of 1 µD (see Fig. 3-4). The capillary pressure function corresponds to a
permeability of 0.05 mD calculated by Eq. 2-9, a higher permeability than the base case
permeability. I choose this capillary pressure function in order to neglect any possible
blockage of the gas flow or capillary suction of the water into the reservoir from the
fracture. As a result, in the base case drawdown easily overcomes the capillary pressure, and
gas can be produced without hindrance.
Fig. 3-4 Capillary pressure curve used in the base case model.
3.1.2 Well, hydraulic fracture and grid properties
The static features of the reservoir model (production well, hydraulic fracture and grid) are
specifically chosen for this study. This section briefly introduces the chosen options; a more
detailed description is provided in the appropriate appendices at the end of the thesis report
(chapters 11, 12, 13 and 14).
The length of the well from surface to the top of the reservoir is 2800 m, after which the
reservoir continues for 100 m. The well has a production tubing of inner diameter 7.67 cm (3
inch). Initially, we assume that the well is perforated over an interval of 80 m for the
fracturing treatment, but during modelling of the production period, this is adjusted (see
chapter 12 for additional discussion).
The hydraulic fracture is designed and analyzed using FracproPT (Carbo Ceramics 2007), a
hydraulic fracture software tool. The model requires the input of a simplified 2D reservoir
model. The model consists of a layer cake model of a homogenous, uniform sandstone with
a 100 meters net pay height confined by shale layers, which are not considered as part of
the reservoir and thus is not included in the model.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
After the design, the fracture treatment can be simulated (Crocket et al. 1986) and the
resulting fracture dimensions are imported into a 3D numerical simulator (Behr et al. 2003).
Here we use Eclipse 100 (Schlumberger 2009). Table 3-3 shows a brief overview of the
fracture treatment and the resulting fracture dimensions. The fracture covers the complete
height of the reservoir and extends with a propped fracture half-length of 117 meters into
the reservoir. The resulting dimensionless fracture conductivity is calculated by FracproPT
(Carbo Ceramics 2007) from the fracture properties (Table 3-3) with the use of Eq. 2-17. The
created fracture has a CfD of 2444, and thus can be considered infinitely conductive
(Economides and Nolte 2000). More detail on the input data, the fracture treatment and
output files are presented in chapter 11 (Appendix on hydraulic fracture design and
simulation).
Property
Value
Unit
Property
Value
Unit
Fracture half-length Xf
131
m
Propped half-length
117
m
Total fracture height
118
m
Total propped height
105
m
Max. fracture height
0.33
cm
Avg. fracture width
0.25
cm
Total clean fluid pumped 244.3
m³
Total proppant
98006.1
kg
pumped
Table 3-3 Overview of fracture treatment data and the resulting fracture dimensions as
computed by FracproPT (Carbo Ceramics 2007).
In any reservoir model, the grid-block size and simulation time step are the most important
parameters controlling the stability and accuracy of the numerical solution method (see
chapter 8 for more information). The introduction of a hydraulic fracture requires a special
grid to model the complex fluid behaviour in and around the fracture. The grid blocks of the
fracture are upscaled and, on the other hand, the reservoir grid blocks in the fracture face
are refined. Finally, for simulation purposes, only ¼ of the model modelled. Due to this
symmetry, the simulated well rates are 25% of the actual values and the well is located in
the corner grid block.
In this study, the fracture is modelled with a row of grid blocks with a width of 50 cm (ydirection), which represents ½ of one fracture wing and thus ¼ of the hydraulic fracture. The
actual width of the fracture created is 0.25 cm. Too-small grid blocks within the fracture
slows down the model (Friedel 2004). In order to model the same fracture storage space and
transmissibility as in the real fracture, the porosity and permeability of the fracture is scaled
down proportionately, by a factor of 300. This procedure is standard in hydraulic fracture
modelling and results in sufficiently accurate simulations (Shaoul et al. 2006).
This grid contains a refinement in the y-direction, the direction perpendicular to the fracture
length. Here, the fluids flow from the lower permeability matrix, where pressure and
saturation changes are small, into the high-permeability fracture. This discontinuity requires
sufficient grid resolution, and therefore smaller grid blocks and small time steps, especially
early in production. A fine grid is also needed to capture the fracture-face cleanup period
accurately. If too-large grid blocks are present in the fracture face, the water imbibition does
not increase Sw significantly and results in only minor impact on the gas relative
permeability. It’s assumed that capturing this effect with a grid refinement is important in
the analysis of the cleanup period (Gdanski et al. 2006). On the other hand, smaller grid
blocks increase simulation times. The initiation of the leakoff water around the fracture prior
to the production simulation is discussed in section 3.1.3.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
This refinement can be modelled by two approaches; a refinement of a part of the reservoir
host grid and a so-called Local Grid Refinement (LGR), whereby a second and more refined
grid is placed inside the host grid. In this thesis, the host grid refinement is chosen for the
reservoir model (Fig. 3-5). This refinement option allows us to more closely examine the
process of water invasion and potential blockage around the fracture. More detail is
provided in chapter 12 (Appendix on grid refinement options), presenting some simulations
(single- and multiphase) to test the accuracy and speed of the refinement options.
Concluding on these results, chapter 12 discusses the decision for the host grid refinement in
favour of the LGR.
Fig. 3-5 Host grid refinement in the reservoir model. The fracture is located in the first row
of grid blocks starting at the well location (0,0) and the fracture face refinement extents
perpendicular to the fracture. The same level of grid refinement extends beyond the end
of the fracture to the edge of the reservoir model (see chapter 12 for more detail on the
grid).
Fig. 3-6 Host grid refinement in the reservoir model, zoomed in close to the fracture.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
3.1.3 Base case initiation
To this point, the base case model has been set up with dynamic properties (section 3.1.1)
and static features (section 3.1.2). Before the model is used for the modelling of postfracture gas production, it’s compared to an analytical solution. This should confirm the
initial flow period of the well and test the simulation outcome for accuracy. A detailed
description and a discussion on the results are provided in chapter 13 (Appendix for
reservoir model test runs). For the base case model, it’s important that the analysis confirms
a long transient period in the reservoir. The understanding of this is important in this thesis,
especially in the well test analysis (chapter 4).
One final aspect of the base case model remains to be specified: the initial zone of increased
water saturation around the fracture as a result of the fracture treatment. It’s expected that
when the simulation is started, the initial gas rate is influenced by this leakoff water. This is
the so-called cleanup phase; a delay in the maximum gas rate. The water rate is in decline
from the beginning of the production phase. After some time, the gas rate enters the
transient period and dominates the flow into the hydraulic fracture and the wellbore.
To examine fracture and fracture face cleanup, it’s important to properly model how, when
and where the fluid moves into the reservoir during the hydraulic fracture treatment. There
are two methods to simulate leakoff behaviour. First method is to determine the fluid
distribution during the fracturing simulation in the separate software programme FracproPT
(Carbo Ceramics 2007) and to export this model into a reservoir simulator for further
simulations (named “leakoff model” in this thesis). Or, the second method is to simulate an
injection period prior to production in the reservoir simulator itself.
For this thesis, I chose the second approach, i.e. injection of the treatment volume to
simulate the water invasion into the fracture face. Appendix G (chapter 14) provides more
insight into the assumptions of the two models and shows the result of a test simulation.
Although the leakoff model is suitable and very accurate for long-term production forecasts,
the injection method is more applicable for the use in this thesis. The model in FracproPT
(Carbo Ceramics 2007) does not allow for specific heterogeneity in the reservoir, which
could influence the water distribution. Second, fluid and rock properties such as capillary
pressure or relative permeabilities cannot be changed in FracproPT (Carbo Ceramics 2007) to
test whether it will influence the fluid distribution in the fracture face and hence the cleanup
phase.
The injection of water gives rise to an imbibition process near the fracture face, which
results in possible hysteresis effects. Hysteresis is named as a possible cause for the
existence of a permeability jail (section 2.3.2), but it introduces more complexity and
uncertainty in the model. First, the model is not initialized with experimental data, so there’s
no imbibition curve available. Modelling this thus introduces another unknown variable.
Second, the modelling of hysteresis in the numerical simulator (Schlumberger 2009) is rather
complex and is not considered to be part of this thesis and therefore not studied in detail.
For the base case scenario and subsequent simulations, hysteresis is therefore not taken into
consideration; more detail and an extensive discussion on the effects is provided in chapter
9 (Appendix for hysteresis effect modelling).
The gas and water production profiles and a 3D-image of the pressure response of the base
case model are presented in Fig. 3-7 and Fig. 3-8.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 3-7 Base case model production overview: gas (red) and water (blue) rate and
cumulative gas (green). Note: the model is ¼ symmetry.
Fig. 3-8 Base case pressure response after 2 years of production. The well is produced at a
pressure of 150 bars; the reservoir is initially at 250 bars.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
3.2 Tight-gas capillary pressure
Holditch (1979) describes the possible impact of capillary pressure in the reservoir on the
flow of fluids and gas towards the hydraulic fracture. His conclusion is that ‘generally no gas
block occurs by capillary pressure only, if the rock permeability is not damaged’, but ‘gas
production can be impaired if the applied pressure drawdown is lower than the capillary
pressures’. Capillary pressure can prevent water flowback to the fracture, but also drive
water imbibition further into the reservoir, away from the fracture, and thus reduce the
water blockage of gas flow. Mahadevan et al. (2009) state that evaporation and capillary
suction are the two major cleanup mechanisms in tight gas reservoirs. They conclude that
when comparing the two, capillary suction results in faster recovery of the gas relative
permeability surrounding the fracture. This ultimately reduces the water blockage impact
near the hydraulic fracture. This section evaluates the effect of the higher capillary pressures
expected at low absolute permeability.
3.2.1 The impact of capillary pressure on gas production
Holditch (1979) shows a variety of capillary pressure curves in his classic investigation,
including a ‘representative low-permeability reservoir’ with capillary pressure ranging from
200 to 600 psi (14 – 40 bars) over the saturation range. With scaling function Eq. 2-9, this
can be calculated back to a 20 µD reservoir rock. He also performs calculation on the effect
of a damaged zone around the fracture in a more porous (porosity 0.12) and permeable (k =
0.28 mD) reservoir. The capillary pressure functions for this damaged zone vary from 40 to
200 psi (or 2 – 14 bars), representing a small permeability reduction as can be calculated
from Eq. 2-9. In this thesis, the scaling parameter is also used to link the capillary pressure to
the reservoir water saturation. As a result of the lower permeability (1 µD) and porosity
(0.05), the capillary pressures are much higher than used in the Holditch’ study (1979),
approximately 100 bars over the saturation range.
Second, the data from the MesaVerde tight gas basin (Byrnes et al. 2009) suggests that
capillary pressure is larger in tight-gas sandstones than suggested simply by the lower
permeability. Fig. 3-9 shows data for a permeability of 1 µD, or 1 x 10-3 mD. It should be
noted that these capillary pressures are for a mercury-air system fluid pair, and need to be
scaled down by a factor of 0.15 for hydrocarbon-brine capillary pressure using appropriate
data (Jennings et al. 1971). Specifically, the Purcell equation (1949) is used to relate the
values for the two systems:
Pcres = Pclab (
σ cos θ res
)
σ cos θlab
Eq. 3-2
The resulting capillary pressure curve for the high capillary pressure scenario is presented in
Fig. 3-10, with the base case capillary pressure for comparison.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 3-9 Reference data set from
MesaVerde study.
Fig. 3-10 Capillary pressures used in the
base case and high capillary pressure
scenario.
Fig. 3-11 shows the results of the simulated water invasion and production of gas for the
two capillary pressure regimes (Fig. 3-10) and one scenario with zero capillary pressure.
Some obvious differences are present during the cleanup period.
First, the higher the capillary pressure, the higher is the initial gas peak (Fig. 3-12). Second,
after approximately 10-12 days of production the gas rates of the three scenarios converge,
with the high-Pc case outperforming the other two cases by a small margin. Finally, there’s a
large contrast in the water production of the various models (Fig. 3-13); no water is backproduced in the case with the largest Pc.
Because all reservoir, fracture and fluid properties are the same among the cases, the
capillary pressure is the cause of differences between the gas and water rates. When
examining the water-saturation profile in the reservoir near the hydraulic fracture for the
two extreme cases of large capillary pressure and no capillary pressure (Fig. 3-14 and Fig.
3-15), it’s possible to relate this to the observed gas rates. In the high capillary pressure
case, a large capillary pressure gradient pulls water phase into the reservoir, as reported by
Mahadevan et al (2009).
Furthermore, the high pressure gradient draws out the water that is initially present in the
fracture and leaves the fracture grid blocks at Swc, where the case without capillary pressure
produces back significant amounts of water. This explains the observation that the high
capillary pressure scenario has more water in the invaded zone surrounding the hydraulic
fracture. During the first days, as presented in Fig. 3-14, the high water saturation around
the fracture, reduces the gas relative permeability and thus hinders gas production. After 6
months of simulated production both scenarios have strongly reduced water saturations
around the fracture (Fig. 3-15 – note change of scale), either by production or by further
imbibition into the reservoir and thus the impact on the gas rate is limited.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 3-11 Cleanup gas rate comparison
(¼ symmetry model) of three scenarios: base
case scenario, and high and no capillary
pressure regimes.
Fig. 3-12 Detailed gas rate of the first hours;
the high peak of the high capillary pressure
scenario is clearly visible. Note change of
scale with Fig. 3-11.
Fig. 3-13 Total water production in the first 100 days
of the three scenarios presented. The pink curve
is along the horizontal axis (no water produced).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 3-14 Comparison of water saturation near Fig. 3-15 Comparison of water saturation near
the fracture face for two capillary pressure the fracture face for two capillary pressure
scenarios after a few days.
scenarios after 6 months of production. Note
change of scale with Fig. 3-14.
Simulation
Scenario
(Base Case = 1.00)
Cumulative
Water
Production
(-) 2 months
Cumulative
Water
Production
(-) 2 yrs
Cumulative
Gas
Production
(-) 2 months
Cumulative
Gas
Production
(-) 2 yrs
Base Case
1.00
1.00
1.00
1.00
No capillary pressure
1.07
1.52
1.01
0.99
High capillary pressure
0.03
0.01
0.95
1.01
Table 3-4 Gas and water production overview of the different scenarios related to the
reservoir capillary pressure regime as discussed in this section.
The cumulative production over time is presented in Table 3-4, which reveals that long-term
production is not much impacted by the change in assumptions about capillary pressure in
the reservoir. For the short-term cleanup effect, modest differences are observed. It’s
important to realize that the capillary pressure function in the low-Pc and zero-Pc cases is not
consistent with the low reservoir permeability and the Leverett J-function (Eq. 2-9). The high
capillary pressure case is most representative of tight gas reservoirs. The production table
also shows water production for the two scenarios; the high-capillary-pressure scenario
back-produces virtually no water from the reservoir. This lack of water production is
demonstrated by other authors, e.g. Soliman and Hunt (1985). In a later section (3.2.2), a
more thorough investigation is presented on the water production in hydraulically fractured
reservoirs.
The tests performed in this section show the effect of the capillary pressure on post-fracture
gas production. The main conclusion is that capillary pressures alone not impact the gas
productivity severely and that the amount back-produced water is strongly reduced with
high capillary pressures. The results could be used as analogue for the use of chemical
additives to reduce surface tensions between gas and water, as described by Gdanski (2007).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
3.2.2 Capillary end effect and its water block potential
A component of the capillary effects discussed in the previous section is the capillary end
effect. The capillary end effect is described in the literature (Huang and Honarpour 1996) as
a result of the discontinuity of capillarity at the outlet end of a core sample. The capillary
pressure differential is related to the gas and water phase pressure differentials, as
displayed in the formula below.
Eq. 3-3
∆P = ∆P − ∆P
cap
gas
water
At an interface of two different porous media, a change in capillary-pressure functions
occurs. This step in the capillary pressure causes large capillary pressure gradient over that
interface. A result of this gradient is a reduced flow of water across the interface and hence
the water saturation rises towards the discontinuity. In the limit of an extremely abrupt
transition, no flow of wetting phase (water) across the interface is possible unless the
capillary pressures on both sides of the interface are equal. If the capillary pressure on the
downstream side is zero (as at the outlet of a core in a core flood, or a wellbore in the field),
the capillary pressure in the formation at the interface must be zero also for water to flow
across the interface. This phenomenon causes problems in small-scale core flood
experiments at the outlet of the sample and is called the capillary end effect. For reservoir
engineering purposes, the capillary end effect is relevant at large permeability
discontinuities in the reservoir, where water is present on both sides. For the type of
simulations in this thesis, the change in permeability and capillary pressure functions
between the reservoir and the fracture may give rise to this effect. Here the fracture face
between the reservoir rock and the proppant-filled fracture is the location of the
discontinuity. Section 3.2.1 examines the capillary pressure effect in the full reservoir model;
in this section the focus is more specifically on the discontinuity at the fracture face.
The simulations of the base case model show an increased water saturation in the formation
around the fracture as a result of water invasion (chapter 14). This high Sw reduces the gas
flow slightly, but forms no permanent ‘water block’ in the base case. The high water
saturations in the base case decrease over time due to water production into the wellbore
or imbibe into the reservoir, depending on the capillary pressures. This is not specifically a
capillary end effect.
If water is produced, that should imply that capillary pressures at the fracture face is almost
zero, or that the pressure gradient caused by the bottomhole pressure is large enough to
overcome the capillary pressure gradient. This latter condition is complicated by the fact
that the simulator calculates pressure gradient numerically, and therefore will the
magnitude of the capillary pressure gradient at the fracture face depend on grid block size.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
This section reports on simulations that investigate the following issues:
- Is there a steep increase in Sw visible in simulations and does the size of the grid have
an influence?
- Is the Sw profile dependent on the magnitude of capillary pressures in the reservoir?
- What is the possible effect of the increased saturation near the fracture face; i.e. is
the gas transmissibility reduced in the fracture face because of the capillary effect?
- Does the simulator validate the principle that water is produced only when the
applied pressure gradient is larger than the gradient of the capillary pressure?
Many papers discuss the effect of capillary pressures and the end effect on gas production in
low-permeability reservoirs with hydraulic fractures. I present a brief overview of the most
important findings below.
First, Mahadevan et al. (2009) use their simulator to focus on the effect of capillary suction
on the gas production. Their results show an increase in Sw near the fracture face. Moreover,
they conclude that higher capillary pressure in the reservoir, thereby creating more capillary
suction pulling water into the formation away from the fracture, is beneficial for the
prevention of a water block near the fracture face.
Friedel (2004) too shows the presence of the steep saturation gradient near the fracture
face (Fig. 3-16). He comments that the affected zone is no more than 1 cm wide and
depends on capillary forces in the reservoir and the ratio of gas and water rates. He
concludes that by itself the zone does not impact the gas production and that the numerical
simulator is capable of solving for this discontinuity.
Gaupp et al. (2005) studied the Rotliegendes Tight Gas Formation in North-Germany. There,
a capillary end effect is observed in the post-fracture production and it impacts the
permeability to gas locally. They conclude that proper numerical simulation of these
phenomena requires the use of ‘ultra-fine’ discretization of the near-fracture region.
Finally, Gdanski et al. (2005) comments that his simulations show increased water
saturations near the fracture, where it ‘pooled’ against the fracture face discontinuity. He
concludes that the water saturation would remain increased near the face, until the gas
relative permeability is reduced to a level where the pressure drop is large enough to
overcome the capillary pressure discontinuity. If this does not occur, the high value of Sw can
cause a permanent reduction in gas production.
Fig. 3-16 Saturation distribution around fracture (Friedel, 2004).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
With these observations regarding the water saturation profile and capillary pressure
distribution along the hydraulic fracture face, we consider the process of water invasion,
imbibition further from the fracture, and back-production into the fracture in more detail.
We assume that during leakoff a certain volume of water enters the formation. The water
saturation around the fracture increases, and the distance of the invaded zone is determined
by the initial water saturation, formation porosity, relative permeabilities (i.e., the final
water saturation) and the total leakoff volume. The water saturation profile is at maximum
saturation at the fracture, and decreases with distance from the fracture because of capillary
suction. During the process capillary pressure equality applies at the fracture face, and
presumably capillary pressure increases with distance into the formation.
Depending on the capillary pressure and relative permeabilities in the reservoir, the water
will then either be back-produced, imbibe further away into the reservoir, or remain
trapped. High capillary pressures imply water flow in the opposite direction of the gas during
production, i.e. into the reservoir. A small capillary pressure will allow water to be backproduced into the fracture. The change in saturation profile with permeability and time can
be seen in Fig. 3-16 from Friedel (2004).
To investigate these issues, I performed a sensitivity study with different grid properties to
see more detail in water saturation close to the fracture face. First, I adjusted the 1st row of
grid blocks adjacent to the fracture, which are at maximum water saturation (1-Sg,r) shortly
after the injection period. I split this row into 100 grid blocks of 0.004 ft (or 0.12 cm). To
create a smooth transition at the fracture face discontinuity, I also adjusted the original
fracture grid block of 1.640 ft (or 50 cm) into 100 grid blocks. This allows for more gradual
saturation and pressure variation in the fracture.
Apart from adjusted grid block sizes, the simulations in this chapter also include a variety of
capillary-pressure functions (Table 3-5). The use of the base case capillary pressures
represents a medium to low-permeability rock type; the high capillary pressure scenario
represents a poor (tight) reservoir rock (Fig. 3-10). I examine the amount of water close to
the fracture, water production and the effect of the water block surrounding the fracture.
Reservoir rock type
Capillary pressure
range (bar)
Scenarios tested
- fine grid
- base case grid
- fine grid
Medium
0 – 25 (low)
- base case grid
Table 3-5 Capillary pressure regimes tested for capillary end effect.
Poor
0 – 2000 (high)
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 3-17 Water saturation profile over time
in the grid block adjacent to the fracture
face; dark blue is the fine grid, light blue the
base case grid; shown are two months of
simulation for the medium reservoir rock.
Fig. 3-18 Water saturation profile over
time in the grid block adjacent to the
fracture face; dark blue is the fine grid,
light blue the base case grid; shown are
two months of simulation for the poor
reservoir rock.
The first comparison is the water saturation over time in the first reservoir grid block
adjacent to the fracture face, for the both rock types, either with or without the fine grid.
Fig. 3-17 shows the medium-quality reservoir, Fig. 3-18 represents the poor-quality rock with
much higher capillary pressures. The figures show that the more refined grids have higher
water saturations adjacent to the fracture over the period of 2 months. This partly reflects
averaging over the grid blocks. With the finer grid, the saturation is that of a zone 0.12 cm
thick; for the coarser grid, the saturation is of a zone 100 times thicker. The high capillary
pressure scenario shows a strong decline in water saturation in the first grid block with time,
for both grids. This can be explained by capillary suction of water into the reservoir. This
effect is not sensitive to grid refinement near the fracture face.
Fig. 3-19, Fig. 3-20, Fig. 3-21 and Fig. 3-22 show water saturation profiles in the formation
near the fracture (which is off to the left in these plots) for the four different scenarios. The
various curves represent various times through the simulation, starting right after the water
invasion (dark blue), and respectively after 5 (light blue) and 15 days (pink) of production.
Fig. 3-20 and Fig. 3-22 show the result of the models with the normal grid, clearly showing a
profile with abrupt changes in saturation moving into the reservoir. This grid is used in the
base case model of this thesis.
In contrast, Fig. 3-19 and Fig. 3-21 show a more gentle slope in the Sw profile. The differences
between the two reservoir rock types, and thus the capillary pressure, are important. Fig.
3-21 is the scenario with low capillary pressures and water production, and shows a rapid
decline of Sw in the fracture face. But there’s also a clear distinct steep increase in Sw
towards the fracture face in the final reservoir grid blocks adjacent the fracture. This is not
visible in the coarser grid, neither in the poorer rock type. This shows good agreement with
the example of Friedel’s simulation (2004) in Fig. 3-16, where the higher-permeability rock
(thus low capillary pressure) also reveals this steep slope in Sw. This is the 1-cm capillary end
effect he refers to in his paper. Nevertheless, in the poor rock, the capillary end effect can be
masked by the high Sw in much larger part of the reservoir.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 3-19 Sw profile perpendicular to the
fracture (which is off plot to left) for poor
rock and fine grid; shown are 3 moments
during the simulation.
Fig. 3-20 Sw profile perpendicular to the
fracture (which is off plot to left) for poor
rock and base case grid; shown are 3
moments during the simulation.
Fig. 3-21 Sw profile perpendicular to the Fig. 3-22 Sw perpendicular to the fracture
fracture (which is off plot to left) for (which is off plot to left) profile for medium
medium rock and fine grid; shown are 3 rock and base case grid; shown are 3
moments during the simulation.
moments during the simulation.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Now that the presence of a capillary end effect is shown to appear in a simulation model
with low capillary pressure and very fine grid, two important questions remain.
- Is this steep water saturation profile realistic or a simulation artefact?
- Does this small zone of high capillary pressure affect the flow of gas and water
around the fracture?
If the saturation profile is realistic and a result of the multiphase flow equations and capillary
pressures, it can be approached in spreadsheet calculation with a 1D – model. Mahadevan
and Sharma (2003) state that the nature of the saturation profile is related to the shape of
the capillary pressure. Chapter 10 describes the spreadsheet calculation in detail, including
the equations and assumptions used. In particular, the calculation assumes that gas flows at
a fixed volumetric rate in the vicinity of the fracture, and the water saturation is at
equilibrium: that is, the capillary-pressure gradient in the water just balances the pressure
gradient in the gas, leaving zero pressure gradient for the water.
Although the calculated profile does not match the conditions in the reservoir, it provides
some guidance in examining the simulations. The static saturation profile in the mediumquality reservoir rock (Fig. 3-23) shows a similar steep increase in Sw close to the fracture
face, as in the simulation. The water distribution visible in the simulation models is therefore
reasonable, based on the theoretical saturation distribution, and not a result of a
miscalculation in the simulator. For a detailed discussion, including a comparison of the scale
of the profile compared with the simulation, see chapter 10.
Fig. 3-23 Water saturation profile from 1D flow calculation – medium reservoir rock with
low capillary pressure.
The final issues regarding the capillary end effect in the models are related to the flow of gas
and water in the model. It needs to be testes if the gas production is affected by the
increased water saturation in the very fine grid. For water it’s important to understand if it
flows into the fracture over the capillary discontinuity. Before this can be properly examined,
it’s important to refer again to chapter 7, where a description of the flow calculations by
upstream weighing is presented. Upstream weighing calculates the flow of a phase from grid
block i to grid block n by the pressure difference and the fluid properties of grid block i.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 3-24 shows gas production rate for the low-capillary pressure (medium rock) case.
There’s some difference in gas production rates based on level of grid refinement, but only
in the first 4 days of production. This can be the result of higher water saturations in the grid
blocks adjacent to the fracture in the fine grid model compared (Fig. 3-17).
Fig. 3-24 Gas rate overview of the two models in the first days of production: base case
grid (red) and fine grid (green).
Second, the reduction of relative permeability close to the fracture is different per grid. To
determine whether this reduction impacts the gas flow towards the fracture, it’s important
to calculate the transmissibility. The transmissibility coefficient is described as follows:
∆T =
 kkrg 1  ∆krg
∆λ
= ∆
∼
∆x
 B µ x  ∆x
Eq. 3-4
Many of these input parameters are considered constant such as absolute permeability, or
assumed to be relatively constant (Bµ). The transmissibility is therefore strongly related to
the relative permeability of the gas phase. Table 3-6 shows the transmissibility over a zone
of 0.5 m for both grids, related to the reduction in relative permeability and hence a
negative value. The calculation is performed for the low-capillary pressure (medium rock)
case, which shows a clear capillary end effect (Fig. 3-21).
Start production
After 10 days
After 1 month
(10-3 mD/m)
(10-3 mD/m)
(10-3 mD/m)
Fine grid
-0.34
-0.34
- .34
Base case grid
-0.37
-0.26
-0.25
Table 3-6 Transmissibility over time for a 0.5 m invaded zone in the fracture face area for
the two grid sizes.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Figures Fig. 3-19 up to Fig. 3-22 present the variation in water saturation for the first grid
blocks and indicate a large Sw contrast per grid size. Table 3-6 shows a reduction in
transmissibility with time for the base case grid to 0.25 x 10-3 mD/m, where the fine grid
remains to see a transmissibility reduction of 0.34 x 10-3 mD/m over the investigated zone.
This seems to be rather significant, but most of the difference in transmissibility occurs in a
thinner zone (< 1 cm). Although the process of gas flow in a reservoir can be considered like
electrical series circuits, where the total resistance is the sum of all separate resistances, the
large transmissibility reduction in the final 1 cm does not harm the gas rate significantly.
Over time, the fine grid model has a gas flow rate in the grid block adjacent the fracture of
just a few percentages lower than in the base case grid. When the cumulative gas totals are
compared, only a small difference (0.5%) is showing after 1 month whereby the base case
grid is more favourable.
In conclusion, the fine grid is more precise in the representation of the capillary end effect,
whereby a thin zone of high water saturation and decreased capillary pressure and gas
relative permeability is seen. But the impact on the flow of gas into the fracture is not
significant, accounting for only a few percent deviation on the long-term production
forecast.
The final comments on the behaviour of capillary pressures are related to how much water is
produced in a 1 month period in all scenarios, after the injection of 50 m3 at the start of the
simulation. It’s examined if the simulator is capable of properly modelling the movement of
the water and gas phase.
Water production
High Pc - Fine Grid
High Pc - Normal Grid
4 days cleanup
(m3)
0
0.03
1 month production
(m3)
0
0.03
Low Pc - Fine Grid
21.86
32.98
Low Pc - Normal Grid
18.23
36.4
Table 3-7 Water production after 4 days of cleanup and 1 month of total production.
Table 3-7 presents an overview of water production, with the water volumes in cubic
meters. Only with the medium reservoir rock model, i.e. with low capillary pressure, is there
a substantial water production. Fig. 3-25 shows that the capillary pressure is almost zero
after the injection, due to the high Sw, and increasing to a maximum of 2 bars. The poor rock
with high capillary pressures shows high capillary pressures in the first reservoir grid block
(Fig. 3-25). This is not overcome by the pressure gradient created by the well and breaches
the idea that no capillary pressure difference may exist at the boundary during the
simultaneous flow of water and gas. Hence no water is flowing over the fracture face
discontinuity into the hydraulic fracture.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 3-25 Capillary pressure in the first grid block adjacent the fracture. Low Pc means
medium reservoir model, and High Pc poor reservoir model, i.e. steep Pc(Sw) function.
In the first 50 cm of the reservoir, the wellbore pressure creates a pressure drawdown in
both models of approximately 75-90 bars, where the capillary pressure gradient in the low
and high capillary pressure model is respectively 4 and 170 bars.
This observation is important, for it proves that in the poor rock indeed no water flows over
the fracture discontinuity when capillary pressure gradient is too large. The low capillary
pressures in the medium reservoir rock of just a few bars can easily be overcome by the
pressure drawdown, which hence explains the water production.
Concluded is that a very fine grid model is needed to model the specific capillary end effect,
on top of a more gentle increase in Sw after water injection. This is shown in both a 1D
spreadsheet calculation and in the production simulations. However, the capillary end effect
is only present in a very thin zone along the hydraulic fracture interface and does not affect
the gas rate over a longer production period. Hence, this effect alone does not cause a water
block to gas flow. Furthermore, low-permeability reservoirs with high capillary pressure in
the rock matrix can prevent any water, both from the reservoir and from the fracture
treatment, from being produced.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
3.3 Permeability jail
The ‘permeability jail’ is introduced in section (2.3.2). The relative-permeability and capillarypressure curves are presented there in accordance with the theory provided by Shanley et
al. (2004) and Cluff and Byrnes (2010). This section discusses two permeability-jail scenarios
where the mobilities of gas and water are modelled differently. The reservoir is assumed to
be homogeneous with respect to permeability, porosity and initial water saturation, using
the properties provided in Section 3.1.1.
The first scenario is the total permeability jail, where the relative permeability curves of the
fluids do not intersect and where within a region of width 0.2 in water saturation no fluids
are mobile at all. This represents the state of very poor reservoir rocks with extremely low
permeability, which Shanley et al. (2004) describe to be present in some reservoirs
worldwide. To be able to represent this scenario, both the water and gas relative
permeability curves have been shifted across the water saturation range as in Fig. 3-26. At
the initial reservoir water saturation (Sw = 0.4) gas is mobile, while water is totally immobile.
Fig. 3-26 Water and gas relative
permeability curves of the total
permeability jail, after Shanley et al. (2004).
Fig. 3-27 Water and gas relative
permeability curves of the small
permeability jail, after Shanley et al. (2004).
Fig. 3-28 Capillary pressure functions for the two permeability jail models.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The second scenario is named the small permeability jail and is based on low, but finite fluid
mobility in the jail saturation range, or jail zone. The relative permeability curves are
constructed to have a permeability reduction of at least 98% across the jail zone. This is in
line with data presented by Cluff and Byrnes (2010), who refer to a jail of width 0.3 in water
saturation for a rock with absolute permeability of 1 µD. Fig. 3-27 shows a reduction over a
width 0.25 in Sw.
Finally, the capillary pressures are very high; around 250 bars across the jail zone for the
total permeability jail and lower for the small permeability jail; around 20 bars across the jail
zone (Fig. 3-28).
The two permeability scenarios are tested in two separate simulations with a homogeneous
reservoir model including a hydraulic fracture as presented in section 3.1.2. In the
simulations, the complete reservoir is modelled either as total permeability jail or as small
permeability jail respectively. After the injection period, the well is opened to flow at a
bottom hole pressure (BHP) of 150 bars and allowed to flow with this pressure constraint for
2 years. The results of the simulations are shown in Table 3-8 and Fig. 3-29. The base case
model (section 3.1) is included for comparison and discussion of the results. In this and
similar tables below, gas and water production rates are normalized by their values in the
base case.
Fig. 3-29 Gas rate comparison of the base case model and the two relative permeability jail
scenarios: Small permeability jail (green) with an extended cleanup and total permeability
jail (pink) (pink lies on the horizontal axis (no production)).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Simulation
Scenario
(Base Case = 1)
Base Case
Small permeability jail
Cumulative
Water
Production
(-) 1 month
Cumulative
Water
Production
(-) 2 yrs
Cumulative
Gas
Production
(-) 1 month
Cumulative
Gas
Production
(-) 2 yrs
1
1
1
1
0.40
0.51
0.10
0.38
Total permeability jail
<0.001
<0.001
<0.001
<0.001
Table 3-8 Production overview of the two permeability jail scenarios compared with the
base case model.
Table 3-8 shows that the total permeability jail lives up to its expectations; hardly any
reservoir fluids are produced in two years of production. The water injection and the
resulting increased water saturations around the fracture apparently reduce the gas mobility
completely. During this time, the simulator has great trouble with converging towards a
condition that satisfies the reservoir flow and well equations.
This problem can be explained by examining the numerical solution method used by the
Eclipse 100 software (Schlumberger 2009) to solve the flow of the two phases in the
reservoir grid blocks. At initial reservoir water saturation, gas is mobile, but the relative
permeability to water is zero in the reservoir and thus no water can move. When the water
injection commences, a water pressure gradient is created from the fracture grid block to
the adjacent first reservoir grid block. Due to the upstream weighing method used in the
Eclipse simulator (Schlumberger 2009), the fluid properties needed to calculate the flow
from the fracture grid block into the first reservoir grid block, are derived from the fracture
grid block. This is explained in more detail in chapter 7. Because the water phase is mobile in
the fracture (at Sw = 1.0), the water will move into the first grid block adjacent the fracture.
The numerical problems will now emerge, because in the reservoir grid block neither the gas
nor water can initially move out of this grid block, as governed by their relative permeability
functions, to create space for this additional water. This contradiction causes abnormal
saturations to be reported in the grid block where the water wants to enter. This continues
until Sw exceeds Swc,kr in that grid block and the water will be mobile and can move freely to
the next grid block. With the water, also the ‘problem’ moves towards this grid block.
The result is that grid blocks in the fracture face area are at high water saturation and krg is
completely reduced to zero. The latter is a result of the gas relative permeability functions
illustrated in Fig. 3-26; it prevents any gas flow in this zone upon reversal of the flow when
production is started unless Sw decreases.
The water around the fracture remains present throughout the whole simulation. The
simulator has much trouble with the combination of the fluid immobility over a large
saturation range and the high capillary pressures. Only minor movement of the water phases
is reported in the simulation and the result is that no water is back-produced through the
fracture into the well (Table 3-8).
The gas phase in the grid blocks in the rest of the reservoir, still at the initial value of Sw and
thus mobile, can move towards the fracture by the pressure gradient. But no fluid
movement occurs in the grid blocks of the invaded zone and therefore the zone is
permanently blocked to gas flow. The result is that no gas is produced, as presented in Table
3-8.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
In conclusion, the relative permeability functions of the total permeability jail describe that
at the initial reservoir water saturation, gas is mobile and can be produced water-free. It’s
with the injection of water, that numerical problems occur. Solutions to phase saturations
and pressures are not always physically correct in the fracture face grid blocks at all times
due water invasion and the resulting extreme simulation conditions. The numerical
simulator allows water to move slowly after the initial period of invasion of the reservoir, but
no gas is allowed to move during flowback.
Despite the numerical instability of this scenario, the observation of the water bank appears
to be similar to, though more extreme than, the well-known ‘water blockage’ by reservoir
permeability impairment as presented by Holditch (1979). He describes a water block as a
situation where ‘the water mobility is low due to reduced absolute permeability and
increased capillary pressure, so that fracture fluids remain immobile around the fracture’.
This occurs with the total permeability jail, except that water is not trapped by reduced
absolute permeability, but by a strong reduction of relative permeabilities in combination of
high capillary pressures. Second, at these high water saturations, the gas is immobile.
Nevertheless, the approach of modelling the total permeability jail uniformly throughout a
reservoir, is not realistic. The concept of a total permeability jail is extended to the lowpermeability zones of heterogeneous reservoirs in section 3.4. It’s expected to be more
realistically modelled if only occurring in a small part of the reservoir, similar to very poor
reservoir rock, shaly or non-pay sections.
The second variation on the permeability jail concept, the small permeability jail, represents
a tight gas reservoir with a relative permeability reduction of at least 99% across the jail zone
(Fig. 3-27). This means that compared to the total permeability jail both fluids are mobile
across the jail and is a more realistic variation on the permeability jail concept. The capillary
pressure in the matrix is around the 20 bars. The result of this modification is that after
invasion, water moves more deeply into the matrix surrounding the fracture, at lower Sw
than with the total permeability jail. Second, and more important, due to lower capillary
pressures and the improved krw, the water is mobile in the invaded zone. When backproduction is started by opening the well, the water moves back into the fracture and is
produced through the wellbore. This results in a Sw reduction near the fracture face, and the
gas phase is mobile as described by the gas relative permeability in Fig. 3-27. Fig. 3-29
reveals an initial dip in gas production and a slow rise to a maximum over some 200 days.
Thereafter gas production is still substantially reduced compared to the base case, which
shows a minor water impact in the first 2 days (Fig. 3-7).
Table 3-8 shows that over the first month of production there’s a reduction in gas
production of 90%. This effect is caused by both the reduction in the gas relativepermeability function in comparison to the base case scenario, and the decreased water
mobility around the fracture (which prevents more-rapid cleanup and gas flow). As shown in
Table 3-8, approximately 60% less water is produced after 1 month of cleanup. With the
total permeability jail, no water is produced due to the combination of high capillary
pressure in the reservoir (this represents a very poor reservoir rock) and the large saturation
range with no fluid mobility to either phase.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
When the mobility of the two fluids is increased over the jail saturation, the water is more
mobile as mentioned above. The water production in Table 3-8 also shows this. In the
invaded zone, the water retains a larger fraction of its base-case mobility than the gas: the
water production after 1 month is relatively closer to its base-case value than is the gas
production (0.4 versus 0.1).
To recapitulate: for the total permeability jail, water invasion is modelled by the numerical
solution method used in Eclipse (Schlumberger 2009). Whether this numerical method is
accurate for this case is beyond the scope of this thesis, but it’s a stable numerical solution
method used in many routine simulations (Schlumberger 2009). Nevertheless, the solution
method has trouble handling the immobility of the fluids over such a large saturation range.
The model predicts water to invade the reservoir grid blocks near the fracture and remain
present around the fracture due to a strongly impaired water flow caused by reduced
relative permeability. Moreover, the gas mobility also remains also zero and no gas is
produced. Finally, the total permeability jail is not considered realistic to be modelled
uniformly in a homogeneous model.
In the small permeability jail, the water phase is more mobile. It’s produced through the
fracture back into the wellbore. This reduces the Sw near the fracture over time, and allows
gas to reach the fracture through the invaded zone, albeit with a lower rate and with a
longer cleanup period compared to the base case scenario. This long cleanup can possibly
explain observations made in the field (Wang et al. 2009). Furthermore, the water
production is impaired in both scenarios due to the reduction in relative permeability and
the increased capillary pressures in the reservoir. Nevertheless, in the small permeability jail
the water is relatively mobile and thus an increased water-gas production ratio is observed
in the initial cleanup period.
Therefore, for the homogeneous reservoir model, it can be concluded that the small
permeability jail is a possible explanation to the gas production impairment often seen in
tight gas reservoirs. In another section (3.4), a heterogeneous model including the
permeability jail of both types will be tested to extend these findings.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
3.4 Heterogeneity model
In many reservoir engineering studies the aim is to best replicate the lateral and small scale
variations in layers and subsurface formations of a particular area of interest. The models
used are therefore equipped to capture the heterogeneous nature of the reservoir, for
which the input for the permeability and porosity distributions is taken from logs, core or
geological models. For the production analysis of hydraulically fractured tight gas reservoir,
the reservoir model used is often homogeneous or consisting of a layer-cake reservoir with
uniform layer properties, because detailed geological data and broadly applicable property
relations are often not available (Rushing et al. 2008).
This section examines if the simplification of the reservoir model with respect to the geology
is an acceptable assumption for modelling hydraulically fractured tight gas reservoirs. The
hypothesis is that the combination of low porosity areas along the hydraulic fracture,
abnormal fluid behaviour and high capillary pressure result in fully water saturated areas
which hinder the gas flow from the reservoir towards the fracture. This blockage can result
in a reduction in effective fracture half-length, which is an important parameter to
understand in post-fracture production analysis. It can dramatically impact both the fracture
and reservoir cleanup period and the long-term gas production. Second, it may result in
better insight in the behaviour of tight gas reservoirs to water invasion following a fracture
treatment. A detailed description and initiation of the model is given, the results are
presented and concluded with some finals remarks. All the data and results presented in this
chapter are valid for the parameters chosen and under acknowledgement of the
assumptions made during the process.
3.4.1 Heterogeneity model: preparation
To generate a heterogeneous permeability field, a new full field model is created in a
geological modelling software programme (Schlumberger 2009). The model is divided into
20 layers with height of 5 meters of each: in total, 40 by 40 by 10 grid blocks (representing a
region of 250 by 250 by 100 m). Furthermore, at this point the model is still unrefined near
the wellbore. Multiple cases are examined to probe the effect of heterogeneity.
The permeability field of the heterogeneous model is constrained to be comparable to the
permeability of the homogeneous scenario using a logarithmic Gaussian distribution
function. The criteria for this match are both an approximation of the average permeability
throughout the whole field and in the first row of grid blocks in the reservoir (fracture face).
During the tests, the maximum and minimum values of permeability are constrained to
respectively 0.1 mD and 1.0 x 10-6 mD and the property is modelled to behave
logarithmically.
I used two statistical methods to assign the permeability spatial distribution; a logarithmic
Gaussian and a Spherical distribution (Schlumberger 2009). These two distributions have
specific variograms that determine the amount of permeability variation allowed over a
specific distance (spatial dependence or variability) in the model. The two distributions
functions are chosen to test the difference between the two, although it’s expected that the
differences in range is more influential.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 3-30 Example of variogram, displaying the range, sill and the nugget effect
(WaveMetrics 2010).
A variogram is created by plotting the semivariance versus the separation distance of a data
set. An example is shown below in Fig. 3-30, where three important features are shown on
the graph. The range is the point where the curve flattens, indicating the distance over
which no more correlation between two data points exist. Decreasing the range reduces the
maximum correlation length and shortens the distance over which permeability varies. The
maximum variance is the sill, which is enforced at 1.0, because Petrel (Schlumberger 2009)
uses a unit sill thereby making the variogram independent on scale. Smaller or large values
for the sill may indicate a spatial trend, which is not intended in this model (Schlumberger
2009). Finally, the ‘jump’ in the semivariance at the origin of the graph is referred to as the
nugget effect. The nugget effect is commonly present in measured data, where it either
represents an error in the measurement due to sparse sampling, or in reservoir modelling it
can relate to variation smaller than the grid size used. If larger grid blocks are chosen, one
can increase the nugget and thereby acknowledge this artefact in the model. For this model,
the nugget is set to zero; adjacent grid blocks can have similar permeability. For the
theoretical background on the statistical methods behind the heterogeneity model, see
Deutsch and Journel (1998).
The two models prepared for the heterogeneity study have the following specifications
(Table 3-9) in order to represent generic tight sand gas reservoirs, albeit, as mentioned, no
standard tight reservoirs exist. The following models are created to examine the effect of
heterogeneity on the production period following a hydraulic fracturing treatment. Some
generic features are included, but it’s not a detailed reservoir model or an analogue of a
specific producing tight gas reservoir.
The first model (H-Fluvial) contains sediment bodies modelled with the maximum and
minimum range of respectively 75 and 25 m. The thickness of these bodies is controlled by
the vertical range, which in this scenario is 10 m. This results in a model with strong
correlation over small lengths, but less correlation at points further spread out. Geologically
this can be interpreted as more and larger concentrated flow bodies and barriers and can
therefore be classified as fluvial systems with lenticular shapes (Spencer 1985). The model is
therefore named H-Fluvial throughout the rest of the thesis.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The second model, with longer major and minor range has long sediment packages with
improved horizontal continuity in high-permeability flow bodies. Of course, low permeability
layers also may form continuous flow barriers throughout the model. By the description of
Spencer (1985) this could be classified as marine blanket reservoirs, as for example as the
Frontier formation in the Greater Green River Basin in the United States Rocky Mountains. In
this thesis, this model is referred to as H-Marine.
Name
H-Fluvial
H-Marine
Variogram type
Gaussian
Spherical
Major range (m)
75
250
Minor range (m)
25
50
Vertical range (m)
10
25
Azimuth
0⁰ / -90⁰
0⁰ / -90⁰
Sill
1.0
1.0
Nugget
0
0
Table 3-9: Specific details of the geostatistical variogram used to create multiple
heterogeneity realizations.
For each of the models, also two variations in the azimuth are generated: a model with the
major direction of the flow bodies towards (0⁰) and parallel (-90⁰) to the hydraulic fracture.
In the simulations, it’s examined if this has any impact on flow behaviour at short and longer
times, where it’s expected that if the flow bodies are directed towards the fracture result in
higher cumulative production due to the increased drainage area (Gatens et al. 1991). These
models are referred to in this thesis as respectively H-Fluvial and H-Marine, with major range
perpendicular to the fracture. The rotated models, with major range parallel to the fracture,
are named respectively H-Fluvial-90 and H-Marine-90. Fig. 3-31 shows the H-Marine-90
model with long sediment bodies along the fracture face. The figure is shown to give an
indication of the variation in permeability in the models, rather than to provide a detailed
overview of the permeability per grid block.
Fig. 3-31 Permeability distribution of H-Marine model; a side view of the fracture face
shows the long sediment bodies along the fracture.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The spatial permeability distributions are generated in Petrel (Schlumberger 2009). The
resulting overall log-normal permeability distribution is shown in Fig. 3-32 below. Here the
permeability is plotted as function of the inverse log, which allows for easy grouping of the
rock type classes.
Fig. 3-32 Permeability distribution of the H- Fig. 3-33 Porosity distribution of the HFluvial model; the x-axis is the inverse Fluvial model; the porosity is derived from
logarithmic of k in mD.
the permeability distribution.
The porosity Φ is not modelled in Petrel (Schlumberger 2009), but is related to the
permeability (k in mD) by the following equation (Eq. 3-5), whereby k0 is taken as a
reference permeability of 1 mD. The scaling is done to match the porosity for the base case
scenario permeability. The resulting porosity distribution is shown above in Fig. 3-33, after
all negative or zero values have been automatically edited to 1 x 10-5. The other initial
reservoir parameters are similar to the base case scenario of section 3.1.1: water saturation
of 0.4 and a reservoir pressure of 250 bars for all reservoir grid blocks of the model.
k 
log   + 4.5
k
φ = 0.1  0 
2.5
Eq. 3-5
The resulting models used in this thesis are presented in Table 3-10 and are used to examine
the effects of the heterogeneity on cleanup and production phase. The average kH is based
on the arithmetic averaged permeability of the complete model as results from the
geostatistical method. The two permeability distribution directions (0° and -90°) generated
by the geostatistical analysis are used to specifically test the impact of the fracture
placement in the reservoir with respect to the local geology.
Model
Arithmetic
Spherical
Gaussian
Flow bodies Flow bodies
averaged heterogeneity heterogeneity
towards
along
distribution
distribution
reservoir
fracture
fracture
kH
(md.m)
Homogeneous
0.1
H-Fluvial
0.079
X
X
H-Fluvial-90
0.079
X
X
H-Marine
0.075
X
X
Table 3-10 Details of the simulation models: one homogeneous and three heterogeneous
models in total.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
After the specification of the reservoir properties, the hydraulic fracture is introduced into
the model in a different manner than in the previous models of section 3.1.2. The hydraulic
fracture is now modelled completely into two directions from the wellbore through the
reservoir and located in the centre of the model instead of in a corner grid block. This results
in a newly created full field model which is needed for a detailed production analysis with a
well test later on in this thesis (chapter 4). This analysis requires a full 360° pressure and rate
response around the hydraulic fracture and therefore does not work with ¼ symmetry
models.
The fracture is modelled as a row of grid blocks of width 33 cm with an upscaled porosity of
5.9 x 10-3 to preserve storage capacity of the fracture. Furthermore, the fracture has an
upscaled permeability of 500 mD to maintain transmissibility in the grid, and a half-length of
100 meters. This results in a high-conductivity fracture. The relative-permeability and
capillary pressure functions of the hydraulic fracture are as described in chapter 11.
Once all properties are assigned to the grid blocks, a double refinement is put into the model
to capture the fluid flow behaviour near the wellbore and the hydraulic fracture (Fig. 3-34).
Again, note that the hydraulic fracture now extends in two and the refinement into four
directions, contrary to as what is shown in Fig. 3-5 and Fig. 3-6. First, the row of grid blocks
of the fracture is adjusted to match the fracture model as described above. Next to the
fracture there are four rows of very fine (10 cm) grid blocks to capture small changes in Sw
and Pc. Moving away from the fracture, the size of the grid blocks is slowly increased with a
maximal enlargement of 1.3 per next grid block to maintain a stable solution.
Fig. 3-34 Top view of the grid around the well in the heterogeneity scenario models; the
hydraulic fracture is now completely modelled and located in the centre of the model.
The two fracture wings in this top view extend from top to bottom in this figure with the
upscaled fracture and the more refined fracture face grid blocks.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The final properties needed are the relative-permeability and capillary-pressure functions in
the model. In the simulations of this chapter, I will use two scenarios of each model
presented in Table 3-10; one including normal relative-permeability and capillary-pressure
functions (see section 3.1.1) and one using permeability jail functions. The homogeneous
model has either the normal relative-permeability and capillary-pressure functions or the
small permeability jail functions (section 3.3) assigned to all reservoir grid blocks.
For the heterogeneous model, it’s necessary to divide the model grid blocks into various rock
type classes according to the permeability variation. Each of these classes is assigned a
specific set of saturation, rock deformation and PVT functions in order to best capture the
effects of heterogeneity on all these properties. I have chosen to divide the full range of
permeabilities in the reservoir into 5 different classes, each with different relativepermeability and capillary-pressure functions. Rock type class 6 is used for the properties of
the hydraulic fracture. Fig. 3-35 shows the distribution of the various classes in the reservoir
along the hydraulic fracture.
Fig. 3-35 Side view of the rock type classes distribution in the first row of grid blocks in
reservoir along the hydraulic fracture in the model H-Fluvial; in Fig. 3-34 this would be the
first row on the right side of the fracture. The refinement in the y-direction is also clearly
visible.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Rock Permeability range Presence Permeability jail functions
(mD)
in model
Type
Class
(%)
1
< 1.0x10-4
4
Poor rock ; total permeability jail
2
1.0x10-4 <> 3.5x10-4
24
Tight sand ; small permeability jail
-4
-3
3
3.5x10 <> 1.0x10
43
Tight sand ; small permeability jail
4
1.0x10-3 <> 3.5x10-3
25
Tight sand ; small permeability jail
5
> 3.5x10-3
4
Low permeability sand ; normal functions
Table 3-11: Rock type classes in the heterogeneous model with their normal relativepermeability and capillary-pressure and permeability jail functions.
Table 3-11 presents the 5 classes for the heterogeneous model with permeability jail
functions with increasing permeability and fluid mobility, but with similar PVT and rock
deformation properties. The lowest class with permeability smaller than 0.1 µD is
characterized as very tight sand (poor rock or non-pay section), and is therefore assigned
with the total permeability jail (section 3.3) in all its grid blocks. Furthermore, these grid
blocks have high capillary pressures (100-300 bars). The permeability in the next three
classes are in range of the homogeneous model (0.1-3 µD) and the fluid behaviour is
therefore described by the small permeability jail, keeping water and gas still slightly mobile
in the jail. The capillary pressures in these classes are moderately high, with values ranging
between 10 and 150 bars. This setup makes comparison to the homogeneous model
possible and can show the impact of the heterogeneity in the model. Finally, rock type class
number 5 includes the highest permeabilities, which is up to the maximum value of 0.1 mD.
Here relative permeability curves and capillary pressures are as described in section 3.1.1.
Finally, for the heterogeneous models with normal relative-permeability and capillarypressure functions, all the above presented rock type classes are assigned with the normal
functions as in rock type class 5. The only difference between the homogeneous model is
thus the permeability variation. For the permeability jail models, the homogeneous model is
assigned with small permeability functions in all reservoir grid blocks, and the
heterogeneous model as described in Table 3-11.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
3.4.2 Heterogeneity model: production simulation
This section introduces the first simulation results of the homogeneous and heterogeneous
models. First, the models with normal relative-permeability and capillary-pressure functions
are tested and compared, both before and after a correction for the reservoir arithmetic
averaged kH (Table 3-10). Finally, the impact of the permeability jail relative-permeability
and capillary-pressure functions on gas and water production is shown, which results in the
research questions for the following sections of this chapter.
All simulations start with an injection period of 24 hours in which 100 m3 is injected to
simulate the leakoff process during the fracture treatment. The well is then shut-in for 1 day
to simulate the complete process of fracturing, retrieval of downhole tools and preparing
site of production. The production phase has a short initial rate constraint to control the
flow towards the well and continues with a BHP constraint 150 bars throughout the rest of
the simulation.
The following two figures show the results of the first simulation, which is used to compare
the two models and to comment on possible differences. Fig. 3-36 presents the early
production period, including a distinct short period of fracture face cleanup, and Fig. 3-37
shows the long-term cumulative gas production of the two scenarios. Note the change of xaxis scale in both figures (days and years).
Fig. 3-36 Cleanup rates of the homogeneous Fig. 3-37 Comparison between the longand heterogeneous H-Fluvial model, with term total cumulative gas of the
matching generic saturation functions.
homogeneous and heterogeneous H-Fluvial
model.
At first sight, the cleanup phase gas rate shows a very good match, with the same maximum
gas rate and subsequent decline. Over two years, the production of the homogeneous model
starts to exceed the heterogeneous model. To examine if this is related to the permeability
and porosity distribution of the heterogeneous model, I use the results after a correction for
the average permeability in the model as presented by the kH values (see Table 3-10).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The results are presented in Table 3-12, and show a different outcome than outlined in Fig.
3-36 and Fig. 3-37. The cleanup gas production in the H-Fluvial model is significantly higher
than in the homogeneous model when corrected for the kH. After one month and two years,
this difference is still present; only after 10 years is the production of the models is similar.
This effect is caused by variations in permeability around the hydraulic fracture in the
heterogeneous models. Local high-permeability zones are controlling the short term
production in favour of the low-permeability zones.
To calculate the ultimate production recovery of the gas in the models, I used an
approximation by taking the production after 50 years to compare with the Gas Initially In
Place (GIIP). After this period, one can assume that the well has had its most economical
period and would probably already have been abandoned due to increasing operational
costs. The simulation of the homogeneous model results in an ‘ultimate’ recovery (UR) of
30.8%. The two heterogeneous models (H-Fluvial and H-Marine) have a simulated UR of
resp. 26.2 and 25.5% (see Table 3-12). So although the corrected production totals are very
similar, the recovery of the models is different after 50 years of production. Nevertheless,
for field economics the production after a specific period is a more interesting figure, for it
governs the cash flow; ultimate recovery is only a snapshot of the gas produced versus the
remaining gas in the reservoir.
In conclusion, the gas production of the homogeneous model and the two heterogeneous
models, both with normal relative-permeability and capillary-pressure functions and no
permeability jail, can be explained by the variation in permeability (kH) in the models.
Second, heterogeneity can cause an increase in the short term gas (and water) production if
local higher-permeability zones are present.
Cleanup
1 month
2 years
10 years
gas
gas
gas
gas
production production production production
(-)
(-)
(-)
(-)
Homogeneous
0.1
1.00
1.00
1.00
1.00
H-Fluvial
0.079
1.27
1.25
1.13
1.02
H-Marine
0.075
1.05
1.11
1.10
1.00
Table 3-12 Production overview of the homogeneous and heterogeneous models;
the data is corrected for average kH in the model.
Simulation
Scenario
kH
(mD.m)
Fig. 3-38 and Fig. 3-39 show the injected and subsequently produced water per rock type
class for the homogeneous and heterogeneous H-Fluvial model with normal relativepermeability and capillary-pressure functions. Here, the water volume is scaled with the
pore volume (PV) of the 5 rock type classes. The sum of the injected volume is therefore not
100 m3, but results in a dimensionless factor. The volumetric scaling is calculated as follows
(Eq. 3-6):
Vscaled =
PVrock type
PVtotal
=
Vrock type
Vtotal
Φ rock type
Eq. 3-6
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The result for the homogeneous model requires some more explanation, since the nature of
the model states that there’s no difference in permeability and therefore no differences in
rock types. Grid blocks here are assigned to the rock types according to the distribution of
rock types at the same positions as in the heterogeneous model. This assignment and the
adjustment using Eq. 3-6 normalizes for position along the fracture and frequency of
occurrence of the various rock types in the heterogeneous model. The homogenous model
shows a rather uniform water injection per rock type. The small difference is related to the
position of the grid blocks; rock type 1 and 5 are located respectively more at the far end or
the top of the fracture wings and therefore less water invades these classes during the
injection process. During a real-life hydraulic fracture pumping treatment the leakoff is also
not uniform, with most water leaking off close to the wellbore due to highest pressure
difference there. The variation in leakoff volume along the fracture is therefore realistic. In
the heterogeneous H-Fluvial model most water accumulates in the higher-permeability rocks
(type 4 and 5) and no water is injected into rock type 1. Zone 4 has accumulated relatively
most of the injected water, which is caused by the favourable location of that rock type
along the fracture face.
A more detailed inspection of the water production in both models shows, upon reversal of
the flow, relatively uniform movement of the water in the homogeneous model. Only rock
type 1 shows an unexpected large production, but this could be related to the relatively
small sample size. In the H-fluvial model, the high-permeability zones (rock type 4 and 5)
produce more water than the other, lower-permeability zones. Finally, after 4 days of
cleanup, the total water production of both models is the same after correction for average
kH.
Fig. 3-38 Distribution of the injected water
volume over the 5 rock type classes in the
model in the homogeneous and H-Fluvial
model.
Fig. 3-39 Classification of the origin of the
water flow during the first 4 days of
production per rock type class in the
homogeneous and H-Fluvial model.
In conclusion, the comparison between the homogeneous and heterogeneous models with
normal relative-permeability functions (i.e., those without a relative permeability jail) shows
a match for both the cleanup and long-term water and gas production when corrected for a
arithmetically averaged reservoir kH. The early production is dominated by the fracture face
area and local variations in permeability can have a significant impact on the gas production.
This is can be economically interesting for field development. Finally, the two model types
show the same response to the injected leakoff fluid, which causes only a small reduction in
gas production in the first days of production.
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Next, the impact of relative permeability jail on the homogenous and the heterogeneous HFluvial is examined. Fig. 3-40 presents the gas production impairment in the cleanup period
for the homogeneous and heterogeneous (H-Fluvial) model. The damage appears to be
significant and can be economically very important.
The focus in the remainder of this chapter is on the following issues regarding the presence
of a relative permeability jail:
- what causes the gas rate to be reduced?
- is the effect of the fluid leakoff on gas production more severe?
- what is the effect of introducing heterogeneity in the model?
- are there zones surrounding the fracture or elsewhere in the reservoir of high water
saturation, and/or where no flow occurs?
- is the effective fracture length or area reduced by any fluid retention?
During the following discussions in sections 3.4.3 to 3.4.6, thee heterogeneous models (HFluvial and H-Fluvial-90 and H-Marine) are used in the analysis of the issues raised above.
These models are more realistic representations of the subsurface, and allow for assigning
specific properties to specific parts of the reservoir as explained in section 3.4.1.
Fig. 3-40 Cleanup gas rate comparison between the homogeneous and H-Fluvial model;
shown are the scenarios without and with the permeability jail.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
3.4.3 Heterogeneity modelling results: cleanup period
The first period of production is the period where most impairment is seen in the gas rate
and is often referred to as the cleanup period of a well. During the cleanup, it’s therefore
important to focus on the effect of the additional water that is introduced by the hydraulic
fracture treatment. The hypothesis is that the severe damage observed in the field is caused
by the leakoff fluid in combination with the relative permeability jail. A heterogeneous
model (H-Fluvial) can simulate this in parts along the fracture face. An often-heard
explanation is that the leakoff fluid can only cause problems around the hydraulic fracture if
mechanical damage is simultaneously occurring during the fracture treatment process
(Holditch (1971); Friedel (2004)). We examine whether relative-permeability effects of liquid
near the fracture face could cause damage similar to that ascribed to mechanical damage.
This section starts with a close look at the water in the fracture face after the injection
period ends of the heterogeneous H-Fluvial model. As described in section 3.4.1, the initial
water saturation is 0.4 throughout the reservoir and with the normal relative-permeability
functions (section 3.1.1) and permeability jail functions (section 3.23.3), this means it’s
immobile. On the other hand, the injected leakoff water is mobile and can be produced back
through the hydraulic fracture. As shown in Fig. 3-41, the H-Fluvial model with normal
relative-permeability and capillary-pressure functions shows a gradual increase of water
production in the scenario with zones of increasing permeability. The gas flow in this
scenario is also distributed according to the absolute permeability of the regions.
Introducing the permeability jail in the low-permeability rock type classes (type 1 to 4)
causes a large difference in the water production. First, in the H-Fluvial the total amount of
water produced after 4 days falls to 64% with the permeability jail, leaving more potentially
harmful water surrounding the fracture. Fig. 3-41 shows that hardly any water is produced
from the rock type classes affected by the permeability jail; almost all the water flows from
rock type 5 (81%). The other heterogeneity models show the same pattern in the water
production; a reduction of 55% of total water produced is seen in the H-Fluvial-90 model,
where rock type class 5 contributes 56% of the total water. The high-permeability rock class
of H-Marine model is responsible for the majority of the water production during the
cleanup, more than 80%. Also here the total amount of water produced is reduced to half.
Fig. 3-41 Detailed overview of the origin of the water produced over a period of 4 days
during the cleanup of the fracture and fracture face in model H-Fluvial.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
To fully understand the cleanup in the heterogeneous models, the impact of changed water
distribution on the gas production is examined. Fig. 3-40 shows a significant reduction in the
gas rates when a permeability jail is introduced, but it does not discriminate between the
various permeability zones.
Fig. 3-42 Detailed overview of the origin of
the total gas produced over a period of 4 days
during the cleanup of the fracture and
fracture face.
Fig. 3-43 Detailed overview of the origin of
the gas produced over a period of 4 days
during the cleanup of the fracture and
fracture face, but now scaled according to Eq.
3-6.
In Fig. 3-42, total gas production in the first 4 days of production is allocated by rock type.
The figure presents the total gas and the rock type from which it’s produced, where clearly
the difference in total amount between the two scenarios is visible. The large contribution of
rock classes 3 and 4 in the normal relative-permeability and capillary-pressure functions is
striking. This pattern is not visible in the permeability jail and requires more explanation.
Fig. 3-43 presents more detail into the gas production: the large contribution of rock classes
3 and 4 is completely related to scaled pore volume distribution as governed by Eq. 3-6.
Generally, the higher permeability of the rock matrix, the higher the contribution of total gas
flow into the hydraulic fracture.
For the permeability jail scenario, rock class 5 is the dominant gas supplier. This doesn’t
come to a surprise considering the relative-permeability and capillary-pressure functions of
that class, but nevertheless the complete dependency is interesting. What’s more important,
is the strong decline in gas production from the other zones, especially zone 4. The zones are
almost completely blocked and do not contribute to the total gas production in the short
term. For the other heterogeneity models, the same dependency on rock type 5 modelled
with the permeability jail is seen. Model H-Fluvial-90 and H-Marine show respectively a net
reduction of gas production of 85% and 83%, and with a contribution of 74% and 81% of
rock type 5.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Rock type class 1, modelled as total permeability jail, does not contribute to the total gas
production. The numerical method used in the simulations is discussed in the description of
the permeability jail model (section 3.23.3), where it’s stated that the upstream weighing
allows the injected water to enter a grid block with a total permeability jail due to the
properties of the fracture grid block. In the heterogeneous model, rock type 1 is in total jail
and the grid blocks adjacent the fracture indeed take up some leakoff water. Nevertheless,
because of the small storage capacity and transmissibility compared to the other rock type
classes, Sw never reaches the critical flowing saturation in these grid blocks. Therefore
there’s neither water (Fig. 3-41) nor gas production (Fig. 3-43).
It should now be noted that there seems to be a strong connection between the poor leakoff
fluid retrieval and the gas production of a zone, with rock type class 4 as a clear example. In
other words, the leakoff water seems to result in more impairment to gas flow in regions of
the reservoir where a permeability jail is present. Fig. 3-44 below shows the reduction of the
gas relative permeability in a grid block of model H-Fluvial adjacent to the fracture where
the permeability falls in the rock type class 3. The reduction seems to be a combined effect
of the leakoff water increasing the Sw and the permeability jail reducing the krg directly.
This leads to two questions; is damage by leakoff water permanent or will it resolve with
time, and second can we prevent this type of gas flow impairment by controlling our leakoff
fluid during the hydraulic fracture treatment? The second issue will be discussed in later
phase of this chapter (3.4.6); first a closer look is taken at the gas production after
approximately 2 years of production.
Fig. 3-44 Gas relative permeability in the first week compared with normal relative
permeability (green) and permeability jail functions (red).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
3.4.4 Heterogeneity modelling results: long-term production
Section 3.4.3 demonstrates that the effect of the relative permeability jail on the short term
cleanup of the fracture and the fracture face is significant. The overall gas permeability is
reduced in most rock type classes of the reservoir, and the gas well rates are significantly
lower. Second, most of the leakoff fluid is not produced back shortly after opening of the
flow through the hydraulic fracture and into the wellbore. When liquid remains trapped near
the fracture, the gas flow is additionally impaired. This section focuses on whether the gas
flow remains impaired also for the long term and what the effect of the heterogeneity is.
Results are presented for two years production, all scaled according to Eq. 3-6, including a
detailed analysis of where (through which rock type class) the gas enters the fracture. A
comparative overview of 10 years of production is also given to provide better insight to gas
reserves present and possible economic consequences of typical tight-gas flow behaviour.
Fig. 3-45 shows the production of each of the rock type classes after approximately two
years. The figure shows gas-rate impairment per rock type similar to that in the short-term
gas production. With normal saturation functions (no permeability jail) most gas flows into
the fracture through high-permeability rock type 5, accounting for approximately 50% of the
gas flow into the fracture. With the permeability jail, one observes the same apparent
reduction in gas flow in permeability regions 1 to 4 as seen in the analysis of the short term
production. The difference in gas production after two years is now 42%. And again, while
rock type 5 represents only some 4% of the total reservoir, is responsible for 72% of the flow
towards the fracture.
Fig. 3-46 shows similar results for the H-Marine model; an overall reduction in gas
production of 44%, with a larger percentage of the gas (80%) entering the fracture from
region 5.
Fig. 3-45 Scaled production of the H-Fluvial
model, with specified origin of each of the
rock types classes.
Fig. 3-46 Scaled production of the H-Marine
model, with specified origin of each of the
rock types classes.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
After two years of production gas flow is still hindered by the gas relative permeability
reduction in combination with the water trapped in the lower-permeability zones of the
reservoir. The permeability jail saturation functions decrease the overall gas cumulative
production over 2 years by 42%, which is significant for this most important economic period
of a well.
Table 3-13 presents an overview of the gas production at different times and the ‘ultimate’
gas recovery after 50 years. The impact of the relative permeability jail is clearly visible on
the short term production, as discussed in section 3.4.3. After 10 years of production this
effect is smaller. But with a reduction for the homogeneous and heterogeneous model of
respectively 35% and 33% compared to normal relative-permeability and capillary-pressure
functions, it is still economically significant.
4 days
1 month
2 years
10 years
Simulation
gas
gas
gas
gas
production production production production
Scenario
kH
(Hom = 1.0)
(-)
(-)
(-)
(-)
(mD.m)
Homogeneous
0.100
1.00
1.00
1.00
1.00
H-Fluvial
0.079
1.27
1.25
1.13
1.02
H-Marine
0.075
1.05
1.11
1.10
1.00
Perm Jail
Simulations
Homogeneous
0.100
0.10
0.12
0.50
0.65
H-Fluvial
0.079
0.18
0.33
0.65
0.67
H-Marine
0.075
0.17
0.29
0.63
0.63
Table 3-13 Production comparison between the various models simulated in this thesis;
the results have been corrected for kH and normalized to the homogeneous model with
normal relative permeability functions for comparison.
Simulation
Scenario
Homogeneous
H-Fluvial
H-Marine
Perm Jail
Simulations
Homogeneous
H-Fluvial
H-Marine
Normalized 50
years gas
production
(-)
1.00
Numeric
50 years gas
production
(m3)
1.13 x 107
Model
GIIP
(m3)
50 years
“recovery” (%)
3.67 x 107
31
3.48 x 10
7
26
3.31 x 10
7
26
9.14 x 10
6
1.00
8.45 x 10
6
0.75
8.52 x 106
3.67 x 107
23
0.68
6.11 x 10
6
3.48 x 10
7
18
5.36 x 10
6
3.31 x 10
7
16
1.02
0.63
Table 3-14 Normalized (and kH corrected) and numeric gas production after 50 years, GIIP
and 50 years “recovery” presented for the various models simulated in this thesis.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Table 3-14 shows the gas production after 50 years, both as a normalized (and kH corrected)
and the numeric gas volume. The heterogeneous models remain at the same normalized
production level as after 10 years (Table 3-13) for the scenario with normal relativepermeability and capillary-pressure functions. The simulations with the modelled
permeability jail only show improvement in the homogeneous model over the additional
production period of 40 years; the heterogeneous models remain at the same normalized
productivity. This proofs again that, when corrected for kH, the production of the
homogeneous and heterogeneous models are similar throughout the production life, even
at the long term.
Table 3-14 also presents the Gas Initially in Place (GIIP) of the various models. The GIIP is a
function of the average porosity (pore space) and gas saturation of the models, and is
therefore slightly different for the homogeneous and heterogeneous models. The porosity of
the heterogeneous models is determined from the permeability by Eq. 3-5, and is therefore
distributed differently in the model. The GIIP can be combined with the numeric gas
production volumes to calculate a “recovery” after 50 years, or ‘ultimate recovery’ (UR).
Table 3-13 shows that the recovery is much affected by the permeability jail in both the
homogeneous and the heterogeneous reservoirs. For the homogeneous reservoir there is a
reduction of 8% in total producible gas after 50 years, which accounts for a significant
economic depreciation of the gas field. The heterogeneous models show a lower UR of resp.
18 and 16% for the H-Fluvial and H-Marine models. This caused by the lowered normalized
and kH corrected gas production after 50 years; resp. 0.68 and 0.63 compared to 0.75 for
the homogeneous model. Thus, the permeability jail reduces the recoverable gas in the
whole model and it specifically impacts the lower-permeability rock classes of
heterogeneous models.
During the first month of production, the heterogeneous H-Fluvial model with permeability
jail produces more than twice as much gas than the homogeneous model, as shown in Fig.
3-47. This can be explained by earlier observations of the significant contribution of rock
type class 5 in this model, and the limited hindrance the leakoff water imposes on this rock
type. After 2 years of production there is still more production in the two heterogeneous
models with permeability jail compared to the homogeneous model; only after 10 years
does the homogeneous model produce as much as the other models.
Fig. 3-47 Normalized gas production of the homogeneous and the two heterogeneous
models, all modelled with the permeability jail functions.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The reason for this change is related to heterogeneous nature of the models. The higherpermeability rock (rock class 5) is not affected by the permeability jail and produce gas at
high rates for short periods, after which a strong decline is seen. Because the other (lower)
permeability regions only contribute with small discharges, the cumulative gas profile will
show strong curvature at early times and will flatten with time. The same pattern is seen in
the cumulative gas curve of H-Marine.
The homogeneous model is uniformly affected by the gas permeability reduction and the
water blockage, thus shows a lower gas rate during cleanup and a slow decline throughout
the field life. A potential blockage to gas flow at the rock face is therefore either present or
not present, and the degree of damage throughout the reservoir is therefore also uniform.
The heterogeneous model has zones of very low gas and water mobility, and higherpermeability rock classes that supply ample gas production in the early field life and thus
resulting in a better cleanup. But the blocked zones of lower permeability still impact longterm production.
Because some variation in grain size and pore distribution is to be expected (Fig. 3-48) and
moreover some parts of the reservoir might have responded differently to diagenesis
throughout their burial history (Claverie and Hansen 2009), the proposed heterogeneous
model attempts to represent this. Moreover, the application of the heterogeneous model
best captures the true impact of the relative permeability jail saturation functions. It shows
that regions of lower permeability and porosity can cause natural traps for leakoff water
introduced by the fracturing process. Both the short term and long-term gas production is
impacted and the impact can be quite severe.
Fig. 3-48 Permeability distribution in four common productive tight sandstone gas
formations in Texas (Holditch 2006). The Cleveland and Wilcox Lobo data lie on nearly on
the same trend.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
3.4.5 Heterogeneity modelling results: impact of injected water
In the discussions in this chapter so far it is shown that the introduction of the relative
permeability jail in different permeability regions of a heterogeneous reservoir causes severe
impairment to the gas production of a hydraulically fractured well. In the simulations the
fracture treatment is simulated by an injection of a total amount of 100 m3 over a period of
24 hours, followed by a 24 hours shut in. The injected water and its damage potential have
up to now not been considered separately, but more as a starting condition for our
simulations. As shown in the section 3.4.4, the long-term gas production is still impacted by
the mobility of the water in the reservoir. In this section, I test the effect of the leakoff fluid
is on the gas production over time and whether the leakoff fluid has an impact on the UR, if
it only impacts the cleanup period.
Table 3-15 presents an overview of the cumulative gas production volumes at four times
during production. In contradiction to the previous table with production data, the gas
cumulative totals are now normalized with respect to the heterogeneous model with normal
relative-permeability and capillary-pressure functions (no permeability jail) and the injection
of 100 m3 water to represent the leakoff volume.
Simulation
Scenario
(H-Fluvial Normal = 1.00)
Cleanup
1 month
2 years
10 years
gas
gas
gas
gas
production production production production
(-)
(-)
(-)
(-)
H-Fluvial Normal kri-Pc
1.00
1.00
1.00
1.00
H-Fluvial Perm Jail
0.14
0.27
0.58
0.66
H-Fluvial - No Leakoff
1.76
1.07
1.01
1.00
H-Fluvial Perm Jail - No Leakoff
1.33
0.80
0.72
0.69
H-Fluvial - 99% Face Damage
0.07
0.06
0.30
0.56
Table 3-15 Normalized gas production overview of the heterogeneous H-Fluvial model: with
or without the permeability jail and the injection of 100 m3 water. Final entry is the H-Fluvial
model with 99% permeability reduction in the fracture face.
The second row of Table 3-15 shows the effect of the permeability jail. The next two rows
present the scenarios in which in the water injection period is skipped. The effect of leakoff
water on gas production modelled in the conventional way (H-Fluvial – No Leakoff) is rather
severe in the cleanup phase, but quickly diminishes.
More interesting for this study is the fourth row which shows the effect of the leakoff fluids
to a reservoir with a permeability jail present. Where the leakoff fluid reduces gas
production during cleanup by 43% with normal relative-permeability functions (comparing
H-Fluvial Normal kri-Pc to H-fluvial - No Leakoff: 1.00 v. 1.76), its impact on the permeability
jail is 89% (comparing H-Fluvial Perm Jail to H-Fluvial Perm Jail - No Leakoff: 0.14 v. 1.33).
This is caused by the strong reduced krg at high Sw in the permeability jail.
After one month, the reduction caused by the leakoff fluid in combination with the
permeability jail is still very significant (comparing 0.27 to 0.80), while H-Fluvial with normal
relative-permeability and capillary-pressure functions shows just minor hindrance by the
additional water phase (comparing 1.00 to 1.07). At longer production times, the impact of
the leakoff fluid on the permeability jail slowly diminishes and but still impacts the gas
production nevertheless after 10 years (comparing 0.69 to 0.66).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
It can therefore be concluded that the total leakoff volume still impacts production after
many years of production when a permeability jail is present. The observation of long-term
production impairment caused by water invasion combined with the permeability jail is very
similar to what other authors have presented regarding mechanical damage (clay swelling,
fines migration) in combination with high capillary pressures near the hydraulic fracture
(Friedel (2004); Holditch (1979); Gdanski et al. (2005)).
As a comparison, therefore, the final entry in Table 3-15 which shows the impact of a 99%
reservoir permeability reduction in a heterogeneous model (to 0.01 µD) in a zone of 30 cm
surrounding the fracture, following an idea of Holditch (1979). The capillary pressure in this
zone is equal to the reservoir capillary pressure, so the blockage effect is only related to a
reduction in absolute permeability. Also in this scenario, the most severe impact is at early
production times (comparing 1.00 to 0.07), where the combined effect of both absolute and
relative permeability of gas reduction occurs.
Nevertheless, some differences are seen in these two types of damage models, especially in
the water production. In the heterogeneity models with the permeability jail most water is
produced rapidly during the cleanup from the high-permeability zones, after which the
water production almost falls to zero (Fig. 3-49). This is due to the permeability jail, which
traps water in the pores of the poorer (lower permeability) rock type classes. Also, the
leakoff water is very mobile at high Sw in the permeability jail and can thus be produced back
during the cleanup period. In the simulation with a mechanically damaged zone, the water
production is more evenly distributed over time and continues for a much longer period.
Also more water is produced back after the injection period, as seen in Fig. 3-49. Gdanski et
al. (2005) provides a far more detailed discussion on the effect of a zone of reduced
permeability around the fracture and the impact on water and gas production. He reports a
decrease in gas production and a significant increase in water production over time when a
damaged zone with increased capillary pressures is present around the fracture. This
confirms the reported high water production in Fig. 3-49.
Fig. 3-49 Water production comparison between three heterogeneous models: H-Fluvial
Normal kri-Pc, H-Fluvial Perm Jail and H-Fluvial - 99% Face Damage.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
In conclusion, fracture face permeability reduction has long been considered (Friedel (2004);
Holditch (1979); Gdanski et al. (2005)) as a potential damage mechanism in tight gas
reservoirs. Sections 3.4.3 and 3.4.4 show that permeability jail also has the potential to
cause large reductions in gas rate for both short and long term and hence could explain field
observations of unexpected impaired gas production. This section discusses the water
production as a potential discriminating factor between the two types of damage. It´s
observed that the permeability jail mostly impacts the gas permeability, and mobile water is
quickly produced during the cleanup period. Fracture face damage causes slow water
cleanup, but can eventually lead to more water production at longer production times.
Finally, it´s shown that the impact of the leakoff water on the gas production is rather severe
and provides additional reduction, especially when a permeability jail is present. The
potential gas rate improvement is interesting and therefore discussed in the next section.
3.4.6 Controlling damage from leakoff water
Section 3.4.5 above describes the potential damage caused by water leaked off during the
fracture treatment in reservoirs with a permeability jail or with mechanical damage. It’s
shown that some resemblance exists when the gas production is examined after the
injection of a large amount of water. In chapter 4 the well test results are discussed for
several damage scenarios, which include a discussion of possible observed behaviour. Here, I
briefly discuss proposed methods to reduce the amount of leakoff water lost to the
formation in a fracturing treatment.
Gas production impairment can be caused by both a reduction in absolute and relative
permeability, as governed by Darcy’s Law. Water can reduce the absolute permeability by
swelling of clays in the reservoir. This can even lead to a ‘total permeability block’ around
the fracture (Bennion et al. 1996). In addition, simulation results in this thesis shows that a
permeability jail is capable of strong reduction of krg when the fracture face consists of
regions of increased Sw.
An obvious potential remedy for this type of damage is to reduce the amount of water
leakoff during a fracture treatment. This issue has been discussed over the years, but using
water as main component of fracturing fluids is by far the most economical solution. Some
large horizontal well multiple stage hydraulic fracturing campaigns in the shale basins of the
USA require up to millions of litres of fracturing fluid. Replacing the water with oil-based
fracturing fluids is a proposed method (Bennion et al. 2006) to reduce the impact on watersensitive reservoirs. Nevertheless, it’s generally more expensive and has strong
environmental impact. Recently, various service companies have introduced new
technologies that use either high-pressured nitrogen or carbon dioxide gas as carrier for the
proppant, e.g. VaporFrac (BJ Services), ThermaFOAM CO2 (Schlumberger) or MISCO2 Frac
(Halliburton). These new type of fracturing fluids cause no water imbibition into the
reservoir and therefore reduce the impact of phase trapping by either a permeability jail or
reservoir damage.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
This thesis focuses on gas production impairment as a result of specific properties of tight
gas reservoirs, and not as a result of permeability damage by fracturing treatments. I
demonstrate the impact of capillary pressures and the capillary end effect (section 3.2 and
3.2.2) and introduce the relative permeability jail in a heterogeneous model (section 3.4) to
aid the understanding of long cleanup periods and gas rate reduction in tight gas reservoirs.
Considering that both effects are properties of reservoirs with a permeability jail, it raises
the question whether this can be altered or if these reservoirs are not to be considered as
potential reserves.
Both these properties are a result of the physical interaction between rock and fluid, and are
based on physical and chemical principles. Penny et al. (2006) discuss the use of surfactants
as additives in fracture treatment fluids for low-permeability shale reservoirs. These microemulsions alter the rock-fluid interfacial tension, decreasing capillary pressures and the end
effect by 50% and increasing krg substantially. Their results show a 50% increase in water
production and 30 to 40% increased gas production. This is confirmed by other research,
such as Rickman and Jaripatke (2010). Parekh and Sharma (2004) state that the alteration of
strongly water-wet reservoir rock to intermediate-wet enhances the cleanup of the fracture
face after a hydraulic fracture treatment. As a result better gas production is seen.
It seems that the use of these chemicals would allow a reduction of the impact of the
permeability jail to a certain extent, of course depending on the initial saturation state of the
reservoir and the relative permeability curves. If the mobility of the water-phase can be
improved, then gas can flow more easily through the pores and hence result in higher gas
production. This resembles a change from a total permeability jail to the small permeability
jail as shown in section 3.3. Moreover, this remedy is especially valuable to improve the
relative permeability of a fluid, and not the absolute permeability of the reservoir. Damage
caused by clay swelling or fines migration as shown in section 3.4.5 does not benefit. The
effect of this treatment can hence be tested accordingly.
In the next chapter, an overview is presented of the post-fracture analysis with well testing
methods. It is examined if a distinction between damage to the fracture and the reservoir
can be made, in order to find a solution for the correct problem.
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4 Well Test Interpretation of Simulation Results
The previous chapter (chapter 3) focuses on modelling hydraulic fractured reservoirs
including the introduction of a permeability jail into the reservoir. The production results
show an extended cleanup period. So far, the analysis only focuses on the forward modelling
of these reservoirs generating pressure and gas-water rate profiles. The outcome of these
simulations can be used for two types of analysis.
First, history matching is based on matching the simulator output with the observed data
over a period of production by adjusting various input parameters. Examining the impact of
each of the parameters may then lead to a better understanding of the well, hydraulic
fracture and reservoir. A problem is that this process is not unique, for some parameters are
correlated, resulting in a possible solution rather than necessarily the true solution. A second
method, as introduced in section 2.4, is to perform a well test analysis in the simulation
models. A common test is a Pressure Buildup (PBU) test; this simulates a shut-in and
following pressure increase. As the theory predicts, it should be possible to obtain the basic
reservoir parameters from this type of tests. Nevertheless, the introduction of the hydraulic
fracture makes the solution often non-unique. Assumption is that we use a simple, uniform
model and investigate the validity of the matched parameters for heterogeneous reservoirs.
This section describes the set up of the PBU analysis performed in the various models from
section 3.4. The analysis results in values of the basic reservoir properties, which are
compared to the original model input. The accuracy of these results is important to a
discussion of the value of the post-fracture production evaluation, specifically if leakoff and
permeability jail are detected.
4.1 Well test preparation
To simulate a PBU test, the simulation is set up for a production period of 2 weeks followed
by a shut-in of 1 month. Long test periods (flow and shut-in) are necessary to improve the
quality of the PBU results (Garcia et al. 2006). The data is recorded every time step (minute)
to provide high quality data for calculating the pressure derivative. The data is then loaded
into a commercial pressure transient analysis software programme, Saphir (Kappa
Engineering 2009), which analyses the data with pre-determined plots.
I found that controlling the well by a constant pressure constraint during production results
in difficulty with acquiring an acceptable solution for both fracture length and reservoir
pressure. The theoretical background of the PBU analysis is based on the principle of
superposition, which is based on two constant-rate periods of which the latter is the shut-in
(gas rate = zero). Nevertheless, for many gas wells, pressure constraints are the method of
production control, and this is rather unfavourable for a PBU test. A constant pressure
implies a varying rate, which requires the superposition of the rate to be calculated at each
time step. The accumulation of errors may lead to the unsatisfactory results as observed.
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Therefore, I simulated a second round of tests with constant rate during the initial two-week
production period, and followed by 4-week shut in. In total 4 unfractured models and 6
models with a hydraulic fracture were tested. The pre-fractured models are included to
complete the full circle of production analysis usually performed in tight gas reservoirs. Prefracture test are used to obtain the basic reservoir properties, which can then be used for
treatment design. During the discussion of the results, it’s important to understand the
expected and desired accuracy of the results for fracture length and reservoir permeability.
In the field, due to various reasons as discussed by Lolon et al. (2003), the effective fracture
length is often reduced by 50% or more compared to the created length. Therefore a match
for fracture length can be considered accurate, if it results within a 10% margin of the actual
(model) input value. More accuracy is in the field practically impossible and therefore not
necessary in these analyses. Second, the equations Eq. 2-10 and Eq. 2-14 provide solutions
to permeability and fracture length, but these are both dependent on the initial (and
possibly unknown) reservoir pressure. During the analysis, the reservoir pressure is
therefore taken as input in order to reduce the uncertainty.
4.2 Well test results
4.2.1 Pre-fracture well test
Before discussing any of the simulation models of section 3.4, the results of the unfractured
models are presented in Table 4-1. The models are the same as used in the simulations of
chapter 3 and are highlighted in Table 3-10 with properties as discussed in section 3.1.1 for
the normal relative-permeability and capillary-pressure functions and section 3.4.1 for the
permeability jail functions; the only difference is the removal of the hydraulic fracture in the
model. For clarity, the data of the initial homogeneous model with hydraulic fracture is
included to examine the accuracy. The reported kH consists of the height of the total paylayer (100 m) and the permeability to gas (krg multiplied with reservoir permeability of 1 µD).
At the initial water saturation, for the normal relative-permeability results in krg = 0.2 and
the relative permeability jail in krg = 0.1.
Details of model
Homogenous Normal kri and Pc
Homogenous Perm Jail
Pre-frac Homogeneous Normal kri and Pc
Pre-frac H-Fluvial Normal kri and Pc
kH
(µD.m)
20
10
0.846
1.92
Error
(%)
-96%
-90%
Pre-frac Homogeneous Perm Jail
0.464
-95%
Pre-frac H-Fluvial Perm Jail
0.99
-90%
Table 4-1 Results of pressure buildup analyses of the pre-fracture models.
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The resulting kH for the pre-fracture scenarios show a general poor match with the model
input values, for which two possible causes can be found. First, no radial flow is achieved
despite the rather long shut-in period, as shown in the pressure derivative plots of the
homogeneous (Fig. 4-1) and H-Fluvial (Fig. 4-2) with normal relative-permeability and
capillary-pressure functions. The two plots never reach the time where the pressure
derivative line (in red) stabilises horizontally. The outcome of the analysis is therefore nonunique, as explained in section 1.2.3 and can be incorrect for kH (Garcia et al. 2006).
Second, the reported kH for the fractured models assumes correctly a height of the total
pay-layer, but this total height is not sensed in the pre-frac scenario. The permeability
estimate from the reported kH is therefore wrong and misleading. It’s therefore better to
refer to the reported kH from the software itself instead. The practical implications of these
results are discussed in a later part of this chapter (section 4.3).
Gas potential [psi2/cp]
Gas potential [psi2/cp]
The kH of both H-Fluvial scenarios is significantly higher than the homogeneous model. This
is an interesting result, because the models match overall fracture permeability in the
wellbore area. Apparently, a long shut-in of 4 weeks in low-permeability reservoirs only
senses the local permeability close to the well, which can vary to a certain extent. I highlight
the influence of local permeability variations in the analysis of the initial production period
(section 3.4.3).
1E+8
1E+7
1E+6
1E-3
0.01
0.1
1
10
100
1E+8
1E+7
1E+6
1E-3
0.01
0.1
Time [hr]
Log-Log plot: m(p)-m([email protected]=0) and derivative [psi2/cp] vs dt [hr]
Fig. 4-1 Pressure derivative plot of the prefracture homogeneous model with normal
relative-permeability and capillary-pressure
functions.
1
10
100
Time [hr]
Log-Log plot: m(p)-m([email protected]=0) and derivative [psi2/cp] vs dt [hr]
Fig. 4-2 Pressure derivative plot of the prefracture H-Fluvial model with normal
relative-permeability
functions.
and
capillary-pressure
4.2.2 Post-fracture well test
Next, the results of the well test analyses on the hydraulically fractured wells are presented.
In total 6 different models are evaluated: the homogeneous and H-Fluvial models as
described in Table 3-13, and two scenarios without water injection (“No Leakoff”) as
described in Table 3-15 of section 3.4.5.
Fig. 4-3 and Fig. 4-4 present obtained results for permeability and fracture length matches
for all models. The results are normalized to the model input values, thus a result of 1.0 is a
good match. The initial pressure and reservoir height are fixed input parameters during
these analyses.
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Both the homogeneous and heterogeneous models show fairly accurate results for the
important parameters for the post-fracture analysis of tight gas wells, except when the
permeability jail is modelled. The models without water injection produce almost no water,
and the good match is as expected. For with leakoff water and modelled with normal
relative-permeability and capillary-pressure functions, the resulting match for fracture
length and reservoir permeability are very well within the error margin of the analysis
method. The injected leakoff fluid apparently does not cause major errors in the final
solution. This is a very encouraging result and confirms that despite simplifying assumptions
(section 2.4) a match can be obtained for low permeability hydraulic fractured gas wells. Of
course, this is achieved with a known initial reservoir pressure.
The results of two scenarios are included below for illustration, and show good matches for
the log-log (Fig 4-5 and Fig. 4-6) and history plots (Fig. 4-7 and Fig. 4-8) obtained by the well
test analysis software (Kappa Engineering 2009). I have used these two plot types for the
iterative matching process during the analyses.
Fig. 4-3 Results of post-fracture PBU analyses for permeability to gas for the models with
normal relative-permeability and capillary-pressure functions.
Fig. 4-4 Results of post-fracture PBU analyses for fracture length of all models. Again,
note the poor match for the permeability jail models.
79
Gas po tential [psi2/cp]
Gas potential [psi2/cp]
MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
1E+8
1E+7
1E+6
1E-3
0.01
0.1
1
10
1E+8
1E+7
1E+6
1E-3
100
Time [hr]
0.01
0.1
1
10
100
Time [hr]
3000
2000
1000
Pre ssure [p sia]
Pressure [psia]
Fig 4-5 Pressure derivative plot of the H- Fig. 4-6 Pressure derivative plot of the
Fluvial model with normal saturation homogeneous
model
with
normal
functions, but excluding the injection of saturation functions.
fluids.
3300
2800
Fig. 4-7 PBU history match plot of the H- Fig. 4-8 PBU history match plot of the
model
with
normal
Fluvial model with normal saturation homogeneous
saturation
functions.
functions, but excluding the injection of
fluids.
Fig. 4-9 shows the pressure-derivative plot of the homogeneous model with normal
saturation functions including the representative specialized lines for the ¼ and ½ slope for
the two fluid-flow periods in the model. The fracture is initially filled with water and
therefore does not provide enough conductivity to the gas, which results in a ¼ slope at
early test times. The ¼ slope is always present in a hydraulic fracture analysis, though
sometimes not visible due to a short duration. In Fig. 4-9, the ¼ slope is present for the first
hour approximately.
At later times, a ½ slope would have been expected to represent the highly conductive
fracture present in the model, but no good match is obtained. This simulation shows that
after a few months gas production, still a small pressure drop is visible in the fracture. The
missing of the linear flow is therefore expected in the PBU analysis. Furthermore, the
pressure derivative curve does not show the characteristic flat line representing radial flow.
For these types of wells it’s not expected to see radial flow at such a time scale, as
highlighted in section 2.4.4. Nevertheless, this means that the analysis is non-unique.
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Gas potential [psi2/cp]
MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
1E+8
1E+7
1E+6
1E-3
0.01
0.1
1
10
100
Time [hr]
Fig. 4-9 Homogeneous model pressure derivative plot including specialized lines for
detecting the ¼ and ½ slope, representing respectively the two flow periods within the
fracture: bilinear flow (dark line) for the early times and linear flow (green line) expected
for the flow in a highly conductive fracture.
G a s p o te n tia l [p s i2 /c p ]
G a s p o te n tia l [p si2 /cp ]
The relative permeability jail scenarios for the homogeneous and H-Fluvial reservoirs show
extended and complicated cleanup behaviour during the production simulation (see chapter
3) and it´s expected that causes problems for the PBU analyses as well. The matches for the
reservoir permeability (Fig. 4-3) and fracture length (Fig. 4-4) show that both parameters
clearly deviate from the input values. The fitted reservoir permeability is far higher than the
expected input value; but a much-shorter fracture half-length is inferred, as short as just a
few meters. With the observed strong reduction in productivity of the well, we did not
expect a long fracture anyhow.
1E+8
1E+7
1E+6
0.01
0.1
1
10
Time [hr]
100
1E+8
1E+7
1E+6
1E-3
0.01
0.1
1
10
100
Time [hr]
Fig. 4-10 Pressure derivative plot of the Fig. 4-11 Pressure derivative plot of the Hhomogeneous model modelled with a Fluvial model modelled with a relative
relative permeability jail.
permeability jail.
Fig. 4-10 and Fig. 4-11 show the pressure derivative plots for the two scenarios including a
relative permeability jail, whereby especially the homogeneous model shows a distorted
pressure curve. This distortion is caused by the inability of the pressure wave to move
through the reservoir due to the impaired gas relative permeability around the fracture. It’s
therefore difficult to match this curve with a standard model provided by the well test
software. The heterogeneous model shows a slightly less distorted and possibly more
realistic results. Nevertheless, both clearly deviate from the scenarios with normal
saturation functions.
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4.3 Well test interpretation and implications
The next step in the well test analyses is to interpret the results and comment on the
accuracy and uniqueness. Because the PBU is performed with known input parameters, it’s
one can identify incorrect interpretations and the implications for a possible next fracture
treatment.
The pre-frac PBU tests show that radial flow is not reached and that makes the results nonunique. As a result, the output kH deviates significantly from the model input value for kH.
Also the unknown H causes a large uncertainty in the results. In my models, I could examine
the investigation radius of the pressure wave during the test period, which is of course
impossible in a real well. If from logging while drilling or core tests, a net-pay of 100 m is
detected, one obtains a too low kH and ends up with a far too low permeability. This can
affect subsequent decisions in the field development process or can even lead to
abandonment of the well due to insufficient proven reservoir quality. The pre-frac
permeability to gas in a low-permeability or tight reservoir should therefore always be
backed-up with a second independent source of information, as explained in section 2.4.4.
The PBU results for the fractured wells show a clear distinction between the scenarios with
normal (Fig 4-5 and Fig. 4-6) and permeability jail relative-permeability and capillarypressure functions (Fig. 4-10 and Fig. 4-11). The two results are discussed separately in this
section, starting with the results for the normal saturation functions.
The interpretation of the simulation with normal fluid behaviour (with or without) leakoff
water causes no interpretation problems. The plots of Fig 4-5 and Fig. 4-6 show a good
match, and the slope clearly indicates the presence of a hydraulic fracture. When these
results are compared with an example of a fractured well in a tight gas field in Texas (Fig.
4-12), much resemblance is seen. From this PBU analysis, the fracture was believed to be
long and highly conductive. The input values of the thesis scenarios indeed also represent a
long and conductive fracture. It’s therefore concluded that a PBU analysis in a hydraulic
fractured tight reservoir can result in a good estimate when either no water leaks off into
the reservoir, or the fluid behaviour allows for rapid cleanup and minor damage to the
fracture face. Moreover, the results in Fig. 4-3 and Fig. 4-4 show that the estimates for
permeability and fracture length are very accurate, when the pressure is known.
Fig. 4-12 Example of PBU test performed in tight gas field in Texas, interpreted as a long
and conductive fracture (Cipolla and Mayerhofer 1998).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 4-13 Example of PBU test performed in tight gas field in Texas, interpreted as a long
fracture with very low-conductivity (Cipolla and Mayerhofer 1998).
For the analysis of the permeability jail PBU results, this accuracy is not to seen at all. The
matches on the log-log and history plots are all poor and the resulting fracture lengths and
reservoir permeabilities are inaccurate compared to the input values. In practice, this
interpretation could results in false conclusions. This section discusses some possible next
(wrong) steps in the interpretation of the PBU test results.
Fig. 4-13 shows an example of a fractured well in a tight gas field in Texas (Cipolla and
Mayerhofer 1998) for which the PBU output resulted in a long fracture with very low
conductivity. The shape of the pressure derivative shows much resemblance with Fig. 4-11
and can possibly reveal similar problems. The authors considered excessive fracture fluid
damage, poor proppant placement or slower fracture cleanup. Only after testing the
example well again after 3 years of production, where a high-conductivity fracture was seen,
it was concluded that the problem was a slow fracture cleanup.
Analyzing the H-Fluvial permeability jail scenario as a low-conductivity fracture in the well
test software results in a fair match on the log-log plot and on the history plot for the
buildup period only. The resulting output parameters are a fracture half-length of 139 m, a
permeability of 2.4 x 10-4 mD and a conductivity of 0.035 mD per meter. Thus the PBU
analysis results in a longer fracture with too low a conductivity in a reservoir with a fairly
accurate permeability compared to the actual model. In Fig. 4-11, a ¼ slope seems to appear
at later times, indicating a low-conductivity fracture. The extended cleanup period due to
the permeability jail can apparently easily be identified as fracture cleanup when the well
test is performed before production has commenced. This suggests that modifications are
made to the treatment in subsequent fracturing stages, or future wells, which will enhance
the gel breaking or cleanup in the fracture, while the actual problem lies in the reservoir
response to excessive leakoff of water. Without a re-test after some time, it’s apparently
difficult to distinguish fracture damage or reservoir cleanup. This is an important conclusion,
indicating that an interpretation of a well test can be inconclusive with respect to the type of
damage.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
A second way to interpret the outcome of the PBU analysis is to set the permeability during
the matching process at the expected value, as if accurately determined by pre-fracture well
tests, core measurements or previous experience in the area of interest. This is the absolute
reservoir permeability multiplied by the relative permeability at initial water saturation,
resulting in a value of 0.2 µD. The software programme can then iterate only on fracture
half-length until a match is obtained. This analysis assumes that no damage occurs to the
fracture itself and the high design fracture conductivity is achieved. The homogeneous
permeability jail model shows a match with a fracture half-length of 6 m; the H-Fluvial
permeability jail model reports fracture half-lengths of 26 m for 0.2 µD.
As Fig. 4-10 shows, the homogeneous perm jail model shows deviant pressure response as a
result of the zone of increased water saturation around the fracture. This is because the
entire formation is affected by the permeability jail so that the fluid movement is totally
impaired. Even a poor match in the well test analysis can therefore only be obtained by
using a very short fracture length, i.e. only 6 m. For the H-Fluvial model the solution of a
fracture of length 26 m length is more realistic. This solution can therefore invoke a false test
interpretation of a strongly reduced fracture length, while the permeability jail is the actual
cause of the poor test response. The fracture only appears to be reduced.
The reverse process, i.e. setting the fracture length and iterating for reservoir permeability,
is not a very common practice, but is useful to bound the ranges of the solution space of the
results. Nevertheless, the analysis yields in no match for either model after numerous
iterations in the software programme on both history and pressure derivative plots. This
result implies that it´s impossible to match the behaviour with long effective hydraulic
fractures. If this would be the result of a well test in a real tight gas reservoir, the effective
fracture appears to be short. Whether this is caused by ineffective fracture cleanup cannot
be determined. This is an important and difficult issue.
A shorter created fracture can be the result of poor proppant placement as suggested by
Cipolla and Mayerhofer (1998) or the creation of multiple fractures, which requires the
engineer to focus on the treatment schedule, or fluids and proppant used. These scenarios
require a different solution. An independent measurement could possibly verify if the
created fracture length is indeed reduced, for example micro-seismic monitoring during the
fracture treatment.
Nevertheless, if the fracture treatment schedule design is based on experience, and the
treatment execution shows no problems, another interpretation is that the fracture appears
to be shorter. A reduction in effective fracture length can result if along a fracture the inflow
for gas is reduced, as is the hypothesis for the permeability jail models. Section 3.4 indeed
shows that certain areas along the fracture have a strongly impaired contribution to the
total gas inflow, especially as a result of the leakoff water. It also describes possible
remedies to prevent the impact of a reduction in fluid mobility by the use of surfactants.
Penny et al. (2005) describe the use of surfactants can increase the flow area after damage
has occurred due to phase trapping. They reach this conclusion from a production analysis in
a Barnett shale well, which showed signs of increased effective fracture length after the use
of surfactants. Although not concluded from a well test, this result nevertheless provides
insight into the possibility of a permeability jail to reduce the effective fracture length in
heterogeneous models.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
This leads to an interesting conclusion on the use of well tests in post-fracture production
analysis of low permeability gas wells. I have demonstrated that a PBU match results in good
matches for hydraulic fractures in reservoirs governed by normal fluid saturations. The
simplified approach to reservoir response used by well test analysis software is capable of
handling a cleanup from leakoff water injection. Second, the use of the heterogeneous
model with no permeability jail does not cause any serious trouble; despite that local
permeability variations may influence the pressure response.
The presence of a relative permeability jail severely impairs the fluid mobility surrounding
the fracture and the PBU analysis is much more complicated. A good match is impossible,
and the result for reservoir permeability and fracture half-length are incorrect. The
homogeneous perm jail model shows more reduction in gas rate (section 3.4) and also
results in a poorer match on reservoir permeability and fracture half-length. The
permeability jail modelled in a heterogeneous reservoir also results in incorrect estimates,
though the error in fracture half-length is less severe.
Moreover, if iteration is performed on fracture half-length only, a much shorter fracture is
estimated. Considering that frequently the effective fracture is found to be much shorter
than the created length, this is a dangerous conclusion. The fluid response to a relative
permeability jail may lead to a false interpretation of a PBU, and mistakenly report a shorter
fracture length. This can have great consequences for possible further well stimulation
treatments to the well and further field development.
4.4 Closing the circle: using well test results
Section 4.3 concludes that it’s hard to determine the origin of the damage to gas flow in
specific cases through well tests. A simulation of production provides a possible solution.
Specifically, this section compares gas production of fractures with low conductivity or
reduced fracture length with the observed production from the scenarios with and without a
permeability jail.
Fig. 4-3 and Fig. 4-4 show that a conductive and long fracture does not give unexpected
results for fracture length and reservoir permeability in a PBU in a reservoir with normal
saturation functions. On the other hand, when a permeability jail is modelled, the results
become very inaccurate and the best matches are for short fracture lengths. This result is
now used in the production simulations and compared to the other scenarios. Fig. 4-14
shows the early production of 5 different scenarios of the homogeneous model: specifically
the permeability jail and the scenarios with normal relative-permeability and capillarypressure functions, both used in the analysis of section 3.4. Finally, three scenario of
reduced fracture length, resp. 45, 30 and 6 meters with normal relative-permeability and
capillary-pressure functions.
The homogeneous model is used for modelling convenience in this section, although the
response of the heterogeneous model is more realistic. Nevertheless, the impact of the
permeability jail is rather similar (Fig. 3-36) and the normalized production matches. Hence
the homogeneous model is applicable for this comparison and a discussion on the different
scenarios.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 4-14 Gas rate profile of early production period of various scenarios, including reduced
fracture half-lengths.
Fig. 4-15 Gas rate profile of early production period of various scenarios, including reduced
fracture permeability.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The permeability jail scenario (green line) with the half-length of 100 m is interpreted in the
well test as a fracture with a fracture half-length of 6 m, and indeed shows some
resemblance in the first 10 days. Both scenarios result in low rates for gas after an initial
small peak. Nevertheless, the short fracture retains a low gas rate due to the decreased
drainage area, while the permeability jail shows signs of cleanup and improving rates. If
somewhat longer fractures (30 and 45 m half-length) are modelled, a very short cleanup
period is seen. After approximately 2 months of production, the gas rate of the two
scenarios matches the permeability jail scenario.
Section 4.3 also shows that the H-Fluvial reservoir with a permeability jail can be interpreted
as a long fracture, but with a lower conductivity. The gas production is therefore simulated
for 4 scenarios with lower-conductivity fractures and compared to the production of the
model with and without a permeability jail. Again, the homogeneous permeability jail model
(Fig. 4-10) is used for modelling convenience instead of the heterogeneous model; this
model has a base case fracture permeability of 500mD. The other scenarios consist of
fractures with reduced fracture permeability to respectively 150, 50, 10 and 5 mD. The
production simulation results of long fractures with reduced permeability are presented in
Fig. 4-15.
All scenarios have apparent cleanup periods, increasing in time and magnitude as the
fracture permeability is reduced. This confirms earlier findings on the importance of fracture
conductivity on the cleanup of fracture fluids (Wang et al. 2009). Second, the scenario with a
fracture of permeability of 5 mD in the fracture (yellow line), resulting in an interpretation of
a low-conductivity fracture, shows much resemblance with the permeability jail scenario
(light green line) during the cleanup period including a gas rate increase over time. The well
tests also present a match for a long but low-conductivity fracture with the permeability jail
in the heterogeneous H-Fluvial model. Production analysis (Fig. 4-15) apparently does not
provide better discrimination between these cases.
Homogeneous simulation scenarios
(Normalized)
1 year
gas production
(-)
Normal saturation functions (kri and Pc)
1.00
Permeability jail
0.40
Fracture with 6 m half-length
0.10
Fracture with 30 m half-length
0.34
Fracture with 45 m half-length
0.46
Fracture permeability 150 mD – infinite conductive
0.99
Fracture permeability 50 mD – infinite conductive
0.95
Fracture permeability 10 mD – high conductivity
0.74
Fracture permeability 5 mD – low conductivity
0.57
Table 4-2 Gas production overview after 1 year simulation of various scenarios.
Table 4-2 presents simulation results of 1 year production of all fracture damage scenarios
and a few interesting characteristics of the scenarios appear. The production impairment for
the first scenarios in the table (shorter fractures) seems to be rather proportional to the
reduction in the fracture length. The permeability jail showed a more severe cleanup
initially, but results in more gas production after one year. The fracture with 6 m fracture
half-length produces the least gas, as a result of the small drainage area.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
It can be concluded that there are some features which help to discriminate between a
permeability jail and a reduction in apparent fracture length. Most significant is strong
correlation of a shift in production decline curve to lower gas rates with reduced fracture
length, rather than an extended and more severe cleanup period with gas rates improving
over time. A reduction of fracture length results in a smaller drainage area rather than a
reduction in fluid flow capacity. So, though the two types of damage give similar results in
well test analysis, they do not match in production simulation performed with a numerical
reservoir simulator. In real field examples, this different behaviour can help to diagnose the
cause for the gas production impairment.
On the other hand, it’s very hard to distinguish damage from a permeability jail from
reduction in fracture permeability. First, a good match is obtained in a well test analysis for
the permeability jail with model including a low-conductivity fracture due to the reduced
capacity of fluid flow handling in the fracture. Second, it’s observed that the lower the
conductivity, the more apparent the fracture cleanup period. At some point, it even
resembles the strong cleanup seen in the permeability jail scenario and the 1-year
production results also are similar. Because a reduction in fracture conductivity is common,
it’s a problem that is shows close resemblance with the permeability jail. Moreover, it
requires a totally different approach for optimizing treatments. To properly evaluate the
post-fracture production of a hydraulically fractured well and distinguish between a lowconductivity fracture and a relative permeability reduction, it’s necessary to find some
discriminating factor. We consider next water production.
Simulation
Cleanup
1 month water
1 year water
Scenario
water production
production
production
(Homogeneous = 1.00)
(-)
(-)
(-)
Homogeneous Normal
1.00
1.00
1.00
Homogeneous Perm Jail
0.45
0.51
0.52
H-Fluvial Normal
1.28
1.25
1.25
H-Fluvial Perm Jail
0.58
0.77
0.78
Fracture Perm – 150 mD
0.80
0.98
1.02
Fracture Perm – 50 mD
0.51
0.85
0.98
Fracture Perm – 10 mD
0.14
0.44
0.72
Fracture Perm – 5 mD
0.08
0.30
0.61
Table 4-3 Water production of various simulation models, including homogeneous models
with strong reduced fracture permeability.
Table 4-3 provides an overview of the water production of the homogeneous and H-Fluvial
model and the homogeneous models of Table 4-2 with reduced fracture permeability.
Because the homogeneous models have a slightly higher average kH throughout the
reservoir, the results for H-Fluvial have been normalized accordingly (section 3.4.2) to allow
for proper comparison. The hydraulic fractures with permeabilities of 150 and 50 mD can
still be considered infinitely conductive and show a no resemblance with the permeability
jail when comparing gas production. (Fig. 4-15 and Table 4-2). It is Interesting that the water
production during cleanup of the 50 mD fracture is nevertheless similar to the permeability
jail models. Section 3.3 also shows that the water mobility is less impaired by the
permeability jail than the gas mobility.
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This difference in water production becomes even more prominent when examining the
low-conductive fractures, with strongly reduced water production. The water production of
the permeability jail models stabilizes after approximately a few weeks. The same holds for
the more conductive fractures, that produce the mobile water around the fracture within a
few months. On the contrary, the low-conductivity fractures still produce significant
amounts of water after 1 year and approach (H-Fluvial) or exceed (homogeneous reservoir)
the reported water production in a permeability jail.
Another way of presenting this data is by a cross-plot of water and gas production for three
times during the production period (Fig. 4-16). Here, the H-Fluvial Normal is the model with
normal relative-permeability and capillary-pressure functions (as described in section 3.1.1)
to which all other models are normalized for comparison for both water and gas production.
In the figure, the orange dot represents this model at position (1,1) in the top right corner.
The permeability jail model (blue dot) is the obvious outlier in all three plots, representing a
relatively more water than gas production. This makes the water production a discriminating
factor and aids the post-fracture production analysis significantly. Secondly, the permeability
jail model matches the gas production of the 50 mD scenario during the cleanup period, but
over time resembles more the gas production of the very low-conductivity fracture.
Fig. 4-16 Three cross-plots plotting gas and
water production. Both the water and gas
production is normalized to the H-Fluvial
Normal model.
This leads to the conclusion that the reduction in fracture conductivity impairs the ability of
the fracture to conduct the reservoir fluids to the wellbore, whether gas or water. For the
gas phase, this results in an apparently extended cleanup period for low-conductivity
fractures and an increase in gas rate with time. The water production is equally hindered by
an extended cleanup period. This is a large contrast with the permeability jail models in this
thesis, which shows a more strongly impaired gas than water production. A cross-plot such
as Fig. 4-16 can assist in this procedure and the shown trends can result in an improved
interpretation of post-fracture production analysis in tight gas reservoirs.
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If low-conductivity fractures are the result of poorly broken fracturing fluid and remaining
gel residues, the fracture conductivity sometimes improves over time as shown by the
example in Fig. 4-13. The comparisons in Fig. 4-16 are therefore even more interesting. A
fracture with very low conductivity initially produces less gas and water than expected, but
the gas rate gradually improves over time. Or as Fig. 4-16 displays it, the point of the graph
will move towards the top of the graph with time. On the contrary, if the lower than
expected gas production is combined with relatively high water production, it’s possibly
caused by a permeability jail. But now the gas production impairment will remain present
throughout the well’s lifetime. No remedy for a permeability jail at full reservoir scale is
available, only surfactants can provide possible local improvement. It can therefore be
concluded that the production of relatively more water than gas is less desirable from a
tight-gas production standpoint.
Finally, to conclude the evaluation of the post-fracture gas production, Table 4-4 shows the
effect of the injection of leakoff water on the reduced fracture conductivity fracture models
and the response when action are taken to control such leakoff. The results for the
heterogeneous models with or without a permeability jail are shown as well in Table 3-15
and are repeated for convenience. The scenarios without leakoff represent a fracture
treatment without the use of water, as discussed in section 3.4.6. Important is that the
normalized gas production of the permeability jail model shows a far more significant
increase in the early gas production than the low-conductivity fracture models; even the
reference model is surpassed (comparing 1.33 to 1.00). The low-conductivity fracture
models also show an increased gas production due to the removal of the water (respectively
0.43 v. 0.03 and 0.26 v. 0.02), but it’s apparent that another damage factor is present in the
model. Nevertheless, as in the H-Fluvial models, the additional gas production caused by the
removal of leakoff water is more apparent in the early production times than after 1 year of
production (comparing 0.43 v. 0.03 to 0.74 v. 0.64 for the 10 mD fracture).
Simulation
Cleanup
1 month gas
1 year gas
Scenario
gas production
production
production
(H-Fluvial= 1.00)
(-)
(-)
(-)
H-Fluvial Normal
1.00
1.00
1.00
H-Fluvial Normal - no leakoff
1.76
1.07
1.02
H-Fluvial Perm Jail
0.15
0.27
0.52
H-Fluvial Perm Jail - no leakoff
1.33
0.79
0.73
Fracture Perm – 10 mD
0.03
0.17
0.64
Fracture Perm – 10 mD - no leakoff
0.43
0.53
0.74
Fracture Perm – 5 mD
0.02
0.08
0.49
Fracture Perm – 5 mD - no leakoff
0.26
0.38
0.63
Table 4-4 Gas production of various simulation models, including homogenous models
with strong reduced fracture permeability.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
5 Conclusion and Recommendations
5.1 Conclusions
Chapter 3 introduces the reservoir base-case simulation model to research the impact of
unconventional reservoir behaviour and water leakoff on gas production. The main findings
are as follows.
Capillary pressures in tight gas reservoirs are very high, due to correlation with low porosity
and permeability. Simulations show that these high capillary pressures alone do not have a
large effect on the gas production. On the other hand, water production is strongly reduced.
The specific impact of the capillary end effect is considered by using different grid
refinements around the fracture. With a very fine grid, the capillary end effect is visible at
the fracture face discontinuity. Nevertheless, the resulting high water saturations have little
impact on long-term gas production.
Simulations of a total permeability jail (relative permeability functions with a large range of
saturations with zero mobility of both gas and water) in a homogeneous reservoir show
complete blockage to water and gas flow and high water saturations around the fracture
following the injection period. This case showed many convergence errors in the numerical
solution of the simulator. Therefore this case is dropped from further consideration in this
thesis, in favour of more-realistic models of a total permeability jail modelled in parts of a
heterogeneous reservoirs, representing poor-reservoir rock, shaly or non-pay sections.
We define a small permeability jail as a case with a range of saturations with near-zero
mobility of gas and water. The simulation results for a homogenous reservoir with a small
permeability jail show a significant initial reduction in gas rate and a slow recovery over time
(a "cleanup" effect). The leakoff water in the fracture face is mobile and an increased watergas production ratio is observed.
A heterogeneous model is created to model specific fluid transport properties in regions of
low and high permeability. Specifically, for the case of ‘permeability jail’ in the
heterogeneous reservoir, we assign a total permeability jail to rock type classes with the
lowest permeability, a small permeability jail to intermediate-permeability rock classes, and
normal relative-permeability and capillary-pressure functions to rock with the highest
permeabilities. A comparison between the homogeneous and heterogeneous models with
normal relative-permeability functions (i.e., those without a relative permeability jail) shows
a match for both the cleanup and long-term water and gas production when corrected for
reservoir-average kH. The early production is dominated by the fracture face area and local
variations in permeability can have a significant impact on the gas production. Including the
permeability jail in the heterogeneous model as described above, results in strongly reduced
gas production compared to the normal relative-permeability functions. The higherpermeability rock classes, with no jail, supplies ample gas in early field life and reduces the
overall cleanup effect. The long-term gas production is impacted by the permeability jail,
however; a 60-70% reduction over 10 years and 70-75% reduction over 50 years of gas
production.
The remainder of chapter 3 focuses on a heterogeneous reservoir, and ‘permeability jail’
means a jail assigned for rock type classes according to permeability, as defined in the
previous paragraph.
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The effect of the leakoff water on gas production is examined separately by removing the
water-injection period prior to production. The improvement in gas production with leakoff
water eliminated is significant during the cleanup period, for both the normal relativepermeability and capillary-pressure functions (+76%) and the permeability-jail functions
(+850%). Nevertheless, the impact of the leakoff water on gas production diminishes over
time and is negligible after 1 year of production. For the fracture treatment, it is advised to
control leakoff or use surfactants to improve local relative permeability for it can improve
the well’s potential significantly during the early production period.
The heterogeneous model with a permeability jail is compared to a simulation of a
heterogeneous model with additional mechanical or chemical damage, modelled as a 30 cm
thick zone with permeability reduced by 99% (to 0.01 µD) along the entire face of the
hydraulic fracture. Gas production is strongly impaired and shows close resemblance with
the permeability jail. Water production is different between the two cases, however. With
the permeability jail, the water phase is relatively mobile at high Sw, resulting in high water
flow-back rates. The damaged zone impairs the fluid flow of both phases towards the
fracture and therefore low water rates are observed. Thus one can distinguish between a
permeability jail and chemical or mechanical damage (as modelled here) by examining water
production during the cleanup period.
Chapter 4 focuses on the interpretation of Pressure Buildup (PBU) tests performed on the
models of chapter 3. Second, this chapter discusses the accuracy of post-fracture production
analysis using a PBU test. The tests are simulated with an initial production period of 2
weeks, followed by a 1-month shut-in. The main conclusions are as follows.
The PBU tests performed on unfractured homogeneous and heterogeneous reservoir
models show that no radial flow is detected and no match with conventional type curves
(pressure derivative, or log-log plots) is obtained. The results are therefore non-unique and
inaccurate. Second, the full net-pay height is not sensed in the well test duration, and thus
the reservoir height estimate is unreliable. This results in large errors for the final kH
measurement. An independent second source of information is needed to confirm reservoir
permeability or pressure.
With a hydraulic fracture, the analysis of the models with normal relative-permeability and
capillary-pressure functions, both with and without simulated leakoff water, result in good
matches on the log-log plots. Although radial flow is not detected, the fit for fracture and
reservoir properties is accurate. Second, heterogeneity does not result in inaccuracies,
although the well-test theory assumes homogeneous reservoirs.
The models with permeability jail damage show a disturbed pressure response, for both the
homogeneous and heterogeneous models. The results cannot be fitted with type-curves and
the obtained reservoir and fracture properties are not matching the model values; the best
match incorrectly implies a very short hydraulic fracture. A fair match is obtained assuming a
low-conductivity fracture instead. Without some way to distinguish between a short
fracture, a fracture with internal damage, and a permeability jail, appropriate actions cannot
be taken to optimize subsequent fracture treatments.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Production simulations with the numerical simulator over longer periods than a well test
show that short fractures, modelled in a homogeneous model for simulation convenience,
impact the drainage area and a shift in decline curve to lower gas rates. Short fractures do
not extend the cleanup period as does a permeability jail, and this difference allows for
discrimination between a short fracture and a permeability jail.
On the other hand, reduced gas production in the simulations of homogenous models with
low-conductivity fractures resemble the extended cleanup observed with a permeability jail.
Differences in water production, however, allow for discrimination between a fracture with
damaged internal permeability and a fracture with a permeability jail. Low-conductivity
fractures have impaired flow capacity for both phases, and the water production is therefore
reduced along with gas. On the other hand, the permeability jail reduces gas flow much
more than water. With the aid of a normalized water-gas production cross-plot, it’s possible
to distinguish between the two cases.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
5.2 Recommendations
Some recommendations for future fracture treatment procedures and further research are
presented in this section.
-
The permeability jail concept should be further explored. Laboratory experiments are
needed to verify the presence of a permeability jail in low-permeability sandstones, e.g.
by simulations of multiple drainage and imbibition cycles under ambient conditions.
Hysteresis is mentioned as a possible cause for the existence of a permeability jail.
-
The leakoff of large volume of water should be controlled during fracture treatments in
tight-gas reservoirs. The use of non-aqueous fracture fluids is a possibility.
-
The use of surfactants is recommended to improve the relative phase permeability in
the fracture vicinity. This will increase the cleanup of the leakoff water and improve gas
flow in the fracture face.
-
During the cleanup period of a well, following the fracture treatment, water monitoring
allows for proper evaluation of back-produced water. If chemical analysis is performed
on this water, it can be tested whether it’s formation or fracture treatment water. This
could provide insight in the cleanup phase and the mobility of the water phase in the
reservoir. Second, it can help to discriminate between types of damage, if present, as
explained in this thesis.
-
After a treatment, fracture fluid components (e.g. gels) can break down slower than
designed. When the production period is started, the fracture is then assumed to be
low-conductive. Over time, nevertheless, the remaining residues can dissolve and the
fracture regains it infinite conductivity. Fracture conductivity is thus not a constant
factor throughout production. Simulations with fracture conductivity improvement over
time can therefore be more realistic. This can be modelled, for example, by changing
the transmissibility of fracture grid blocks throughout the simulation. Or a third phase
can be introduced with specific properties, such as very low viscosity. It can
subsequently be examined if with this model the cleanup period is different: more or
less initial gas rate reduction, shorter or longer affected and water production.
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Parekh, B. and Sharma, M.M. 2004. Cleanup of Water Blocks in Depleted LowPermeability Reservoirs. Paper SPE 89837 presented at SPE Annual Technical
Conference and Exhibition, Houston, Texas,26-29 September. DOI: 10.2118/89837MS.
Penny, G., Pursley, J.T. and Holcomb, D. 2005. The Application of Micro-emulsion
Additives in Drilling and Stimulation Results in Enhanced Gas Production. Paper SPE
94274 presented at SPE Production Operations Symposium, Oklahoma City,
Oklahoma, 16-19 April. DOI: 10.2118/94274-MS.
Penny, G.S., Pursley, J.T. and Clawson, T.D. 2006. Field Study of Completion Fluids
To Enhance Gas Production in the Barnett Shale. Paper SPE 100434 presented at SPE
Gas Technology Symposium, Calgary, Alberta, Canada, 15-17 May. DOI:
10.2118/100434-MS.
Prats, M. 1961. Effect of Vertical Fractures on Reservoir Behaviour - Incompressible
Fluid Case. SPE J 1 (2): 105-118. SPE-1575-G. DOI: 10.2118/1575-G.
Purcell, W.R. 1949. Capillary Pressures - Their Measurement Using Mercury and the
Calculation of Permeability Therefrom. Petr Trans AIME 186: 39-48. SPE 949039-G.
Rickman, R.D. and Jaripatke, O. 2010. Optimizing Micro-emulsion/Surfactant
Packages for Shale and Tight-Gas Reservoirs. Paper SPE 1131107 presented at SPE
Deep Gas Conference and Exhibition, Manama, Bahrain, 24-26 January. DOI:
10.2118/131107-MS.
Rushing, J.A., Newsham, K.E. and Blasingame, T.A. 2008. Rock Typing-Keys to
Understanding Productivity in Tight Gas Sands. Paper SPE 114164 presented at SPE
Unconventional Reservoirs Conference, Keystone, Colorado, 10-12 February. DOI:
10.2118/114164-MS.
Settari, A., Sullivan, R.B. and Bachman, R.C. 2002. The Modelling of the Effect of
Water Blockage and Geomechanics in Waterfracs. Paper SPE 77600 presented at SPE
Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September-2
October. DOI: 10.2118/77600-MS.
Shanley, K.W., Cluff, R.M. and Robinson, J.W. 2004. Factors controlling prolific gas
production from low-permeability sandstone reservoirs: Implications for resource
assessment, prospect development, and risk analysis. AAPG Bulletin 88 (8): 10831121. DOI: 10.1306/03250403051.
Shaoul, J.R., Behr, A. and Mtchedlishvili, G. 2006. Automatic generation of 3D
reservoir simulation input files directly from a fracture simulation model. OIL and
GAS European Magazine 4: 176-182. SPE
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•
•
•
•
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•
•
•
•
Shaoul, J.R., De Koning, J., Chapuis, C. and Rochon, J. 2009. Successful Modelling of
Post-Fracture Cleanup in a Layered Tight Gas Reservoir. Paper SPE 122021 presented
at 8th European Formation Damage Conference, Scheveningen, The Netherlands,
27-29 May. DOI: 10.2118/122021-MS.
Soliman, M.Y. and Hunt, J.L. 1985. Effect of Fracturing Fluid and Its Cleanup on Well
Performance. Paper SPE 14514 presented at SPE Eastern Regional Meeting,
Morgantown, West Virginia, 6-8 November. DOI: 10.2118/14514-MS.
Spencer, C.H. 1985. Geologic Aspects of Tight Gas Reservoirs in the Rocky Mountain
Region. J Pet Technol 37 (7): 1308-1314. SPE-11647-PA. DOI: 10.2118/11647-PA.
Spencer, C.W. 1985. Geologic Aspects of Tight Gas Reservoirs in the Rocky Mountain
Region. J Pet Technol 37 (7): 1308-1314. SPE-11647-PA. DOI: 10.2118/11647-PA.
Von Schroeter, T., Hollaender F. and Gringarten, A.C. 2001. Deconvolution of Well
Test Data as a Nonlinear Total Least Squares Problem. Paper SPE 71574 presented at
SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30
September-3 October. DOI: 10.2118/71574-MS.
Voneiff, G.W., Robinson, B.M. and Holditch, S.A. 1996. The Effects of Unbroken
Fracture Fluid on Gaswell Performance. SPE Proj & Fac 11(4): 223-229. SPE-26664PA. DOI: 10.2118/26664-PA.
Wang, J., Holditch, S.A., McVay, D. 2009. Modelling Fracture Fluid Cleanup in Tight
Gas Wells. Paper SPE 119624 presented at SPE Hydraulic Fracturing Technology
Conference, The Woodlands, Texas, 19-21 January. DOI: 119624-MS.
Wattenbarger, R.A. and Ramey Jr., H.J. 1969. Well Test Interpretation of Vertically
Fractured Gas Wells. J Pet Technol 21 (5): 625-632. SPE-2155-PA. DOI: 10.2118/2155PA.
Wills, H.A. 2009. 3D Numerical Investigation of hydraulic fracture cleanup processes.
PhD dissertation, Colorado School of Mines, Golden, Colorado, USA.
6.2 Software and internet
•
•
•
•
•
•
BJ Services. VaporFrac,
http://www.bjservices.com/website/index.nsf/WebPages/Shale-Papers-ExpandableSection/$FILE/VaporFrac%20Stimulation%20Services.pdf (accessed 12 September
2010.)
CarboCeramics.
Carbo-Prop,
http://www.carboceramics.com/CARBO-PROP/
(assessed 9 September 2010).
Eclipse 100, 2009. Houston, Texas: Schlumberger Information Solutions.
Ecole Centrale de Lille. PhD Proposal 2010, http://csc-centrale.eclyon.fr/sujets/PhD_Proposal_CSC2010_ECLille_LML_Skoczylas.pdf (assessed 14 July
2010).
FracproPT, 2007. Houston: Carbo Ceramics - GTI.
Halliburton. MISCO2 Frac,
http://www.halliburton.com/ps/default.aspx?pageid=475&navid=104&prodid=PRN:
:IQTUARO62 (accessed 12 September 2010.)
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Petrel, 2009. Houston, Texas: Schlumberger Information Solutions.
Saphir, 2009. Paris, France: Kappa Engineering.
Schlumberger. ThermaFOAM CO2,
http://www.slb.com/services/stimulation/tight_gas_stimulation/thermafoam.aspx
(accessed 12 September 2010.)
University of Utah, Utah Geological Survey, Golder and Associates and Itasca. Inc.
Research proposal,
http://geology.utah.gov/emp/tightgas/pdf/tightgas_soa.pdf (assessed 14 July,
2010).
WaveMetrics. Image Interpolation software,
http://www.wavemetrics.com/products/igorpro/imageprocessing/imagetransforms
/imageinterpolation.htm, (assessed 18 October, 2010).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
7 Nomenclature
Symbol
A
B
C
H
J
k
L
m(p)
P
p/q
PV
Q
q
R
s
t
T
u
w
W
x
ϴ
σ
φ
ρ
µ
λ
Unit
Description
m2
m
m2
m
Pa
Pa
m3
m3/s
m
S
m2/m
m/s
m
m
m
°
N/m
kg/m3
Pa.s
m2/Pa.s
Cross section area
Formation volume factor
Conductivity
Height / thickness
Leverett J-function
Permeability
Length model (x-direction)
Pseudo-pressure
Pressure
Corey coefficients
Pore volume
Volumetric flow rate
Corey coefficient
Radius
Skin
Time
Transmissibility
Volumetric velocity
Fracture Width
Width model (y-direction)
Distance
Contact angle
Interfacial tension
Porosity
Density
Viscosity
Mobility
Subscript Description
bh
c
D
f
g
gc
irr
lab
nw
R
r
res
tot
w
wc
α
Bottomhole
Capillary
Dimensionless
Fracture
Gas
Critical gas
Irreducible
Laboratory
Non-wetting
Reservoir
Relative
Reservoir
Total
Water / wetting
Connate water
Phase α
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8 Appendix - Flow calculations in simulator
Eclipse (Schlumberger 2009) uses by default a fully implicit method to calculate the changes
in pressure and saturation over time. Implicit calculation of properties takes the state of the
property into consideration at both the current time and the next time step. The method is
therefore relatively stable, but can be time-consuming. The equations used by Eclipse
(Schlumberger 2009) are explained briefly in this appendix.
The starting equation is the mass balance equation solved for pressure and saturation
implicitly. In Eclipse (Schlumberger 2009), the solution vector is referred to as X, the residual
vector as R and the Jacobian J. Here X is defined as:
 Po 
 
X = Sw 
Sg 
 
Eq. 8-1
Next comes solution for oil pressure Po and the saturations for water and gas. For this
research, the primary parameter is not of use. The residual vector looks like:
 Ro 
 
R =  Rw 
 Rg 
 
Eq. 8-2
Each of these non-linear residuals is examined separately, by the following equation:
R fl =
dM t
+ F ( Pt , St ) + Q( Pt , St )
dt
Eq. 8-3
With
Rfl
dM
F
Q
= non-linear residual, for each cell and each fluid
= mass, per unit surface density, accumulated during time step dt
= net flow rate into neighbouring grid blocks
= net flow rate into wells during the time step
The Jacobian is calculated by taking the derivative of the R to X, thereby creating a matrix
where the residuals are evaluated for all saturations and pressures.
The goal of the numerical method is to approach R = 0, by taking ‘small enough time steps’
throughout the simulation. This can be accomplished by reducing the error in the mass
balance solution and the maximum saturation normalized residual, which is related to the
change in saturation per grid cell. In order to solve for the mass balance implicitly, the
following equations for a gas-water system are used (Eq. 8-4 and Eq. 8-5).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
dM = M t + dt − M t
Eq. 8-4
 Sw 
B 
w
M = PV *  
 Sg 
 
 Bg 
Eq. 8-5
With
M
t
dt
PV
Bw
Bg
= mass or volume of cell
= time
= time change (time step)
= cell pore volume
= water formation volume factor
= gas formation volume factor
For the calculation of the flow, not only the time step is important, but also the location of
the grid blocks and in which direction the equation is solved using down- or upstream
weighing. The flow rate F into cell i from neighbouring cell n is calculated by the following
equation:
 kro

 Bo µo

Fni = Tni  0


 Rs kro
 Bo µo

0
krw
Bw µ w
0
Rv krg 

Bg µ g 


  dPoni 
0  *  dPwni 
 
dPgni 
krg  
Bg µ g 
U
Eq. 8-6
For the system under review in this thesis, the equation will simply be reduced to:


0

Fni = Tni  0


0


0
krw
Bw µ w
0


0 


  dPoni 
0  *  dPwni 
 
dPgni 
krg  
Bg µ g 
U
Eq. 8-7
where
Fni
Tni
dPαni
= flow rate from cell n into cell i
= transmissibility between cell n and cell i
= phase α potential difference between the cells
The transmissibility term is a function of pressure and the fluid properties. Furthermore, the
subscript U in the formula stands for upstream weighing, which refers to the numerical
calculation method used in Eclipse (Schlumberger 2009). When dP is positive, the phase flow
occurs from cell n to into cell i the fluid properties in cell n are used for the flow calculations.
This is important in some of the simulations of this thesis. As mentioned, the pressure is
evaluated in both cells, and its differential determines the flow directions. Finally, the total
flow rate is calculated by the summation of the individual cells in each direction.
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9 Appendix - Modelling hysteresis effect
Injection of liquid into a gas reservoir introduces the possibility of relative permeability
hysteresis to occur after the fluid invasion has taken place. Hysteresis is the process that
determines the relative permeability of a certain path as a function of the saturation path
and history. Basically, as a porous medium experiences a change in saturation (e.g. by water
imbibition due to injection), the reverse process will not follow the same relative
permeability curves. There has been much discussion on the effect on hysteresis and its
impact on the post-fracture gas production. In section 2.3.2 it is explained as a possible
cause for the existence of a ‘permeability jail’. The exact origin of this effect is not part of the
problem statement of this thesis and is not discussed. Furthermore, in post-fracture
production analysis (Friedel 2004), the hysteresis of the relative permeabilities is not taken
into consideration. This section discusses the differences in the results for the cleanup
period and long-term production when hysteresis is considered.
The reservoir simulator Eclipse allows one to simulate the hysteresis effect using the model
of Killough (1976). This model allows the input of multiple relative permeability curves to
describe imbibition and drainage processes. The imbibition curves for the gas relative
permeability and the capillary pressure are presented in Fig. 9-1 and Fig. 9-2. The drainage
curves are the relative permeability and capillary pressure curves used in the base case in
the thesis, as shown in section 3.1.1 (Fig. 3-3 and Fig. 3-4).
Fig. 9-1 The drainage and imbibition curves Fig. 9-2 The drainage and imbibition curves
for the gas relative permeability used in the for the capillary pressure used in the
hysteresis model.
hysteresis model.
During water injection, Sw increases in grid blocks close to the fracture blocks, and the
capillary pressure and relative permeability are now determined by the imbibition curves.
This continues until the maximum Sw is reached in the grid block. When the flow direction is
reversed upon opening of the well, the water saturation will start to decrease in each of the
grid blocks and gas starts to flow. This is a drainage process and thus requires the drainage
curves as presented in Fig. 9-1 and Fig. 9-2. The Killough model creates an interpolated curve
between the imbibition and the drainage curve starting at the current value of Sw decreasing
to the residual gas saturation. This method, therefore, uses a slightly different gas relative
permeability during production than the input drainage curve. This provides an additional
complexity to the permeability that is assigned to the gas phase at a specific Sw. For this
thesis, it’s chosen not to thoroughly investigate this complexity and the possibilities of this
method.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
The gas production profile with and without hysteresis is shown in Fig. 9-3. The cleanup
phase reflected in the initial gas rate reduction is much more apparent with hysteresis. Only
after some 15 days of production does the gas rate catch up with the case excluding the
hysteresis effect. As can be interpreted from Fig. 9-1, the new interpolated permeability
curve is always below the initial drainage curve, and thus providing less permeability to the
gas phase.
In both models the water phase is in exponential decline from the beginning of the field life,
where initially rates up to 30 m3 per day are reached. With hysteresis, a total of 50 m3 is
recovered after approximately 1 year, at which point the water rate is almost zero. For
injection without hysteresis, slightly less water is produced, 44 m3 after 1 year. The injected
volume is 61 m3, so not all fluid is produced back. The difference in fluid recovery is related
to the capillary pressures in the two models, which shows an average lower capillary
pressure when hysteresis is modelled. Lower capillary allows more water to be produced
back into the fracture.
If more water is produced and water saturation near the fracture falls, the gas also becomes
more mobile. The slightly increased gas rate at longer times (20+ days) as seen in Fig. 9-3 can
be possibly explained by this.
In conclusion, there are some differences in the two models, but both predict a cleanup
effect and similar gas rates. Because of the complexity in the relative permeability and
capillary pressure functions used in the hysteresis model, we do not use the hysteresis
model in this thesis. Further and more thorough investigation is needed in the possibilities to
use hysteresis in the model.
Fig. 9-3 Production profile after water injection showing the gas and water rates. Two
models are presented: with and without hysteresis.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
10 Appendix – Equilibrium Sw profile: a spreadsheet
calculation
In order to compare the saturation profiles shown in the simulations of section 3.2 to
capillary equilibrium, a spreadsheet calculation has been performed. This calculation
provides insight in the relation between the capillary pressure and water distribution in the
reservoir near a hydraulic fracture. References to rock types and capillary pressure regimes
in the model in this appendix are similar to those outlined in section 3.2.
The spreadsheet is a 1D – model, from the fracture on the left side at x = 0.5 m, extending
into the reservoir. The gas flow is controlled by Darcy’s Law under the assumption that water
is immobile (i.e., at capillary equilibrium), and thus the pressure gradient in the gas phase is
equal to the capillary-pressure gradient. This allows the capillary pressure to be calculated as
follows:
∆Pc ( S w ) =
µ g ug
kkrg ( S w )
∆x
Eq. 10-1
with
ug
∆x
= gas superficial velocity
= calculation steps
Important considerations include the following:
- the calculation assumes static equilibrium solution, not dynamic behaviour as is seen
in the simulations.
- water flow occurs in the simulations: water can produced or imbibe further into the
reservoir.
- the total amount of water given by Eq. 10-1 may not correspond to the actual
volume of water invading the formation.
The input data for the flow calculations are taken from the simulations in section 3.2 in order
to represent as closely as possible the saturation profile from the simulation models. Darcy’s
Law requires specification of reservoir permeability, gas viscosity and the gas superficial
velocity. Furthermore, the calculation requires gas relative permeability and capillary
pressure as functions of water saturation relations. The capillary pressure regimes (low and
high) are the same as the two scenarios presented in Fig. 3-10 as the base case and high
scenarios. The relative permeability curves are the same as in the base case (Fig. 3-3).
Finally, water saturation at the fracture face (x = 0.5 m) is set at Sw = 0.699, representing
nearly zero capillary pressure, as required if water flows back into the fracture. The
additional parameters in Eq. 10-1 are the gas superficial velocity and the distance increment
∆x.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Fig. 10-1 Water saturation profile along the
fracture face into the reservoir – poor
reservoir rock with high capillary pressures
Fig. 10-2 Water saturation profile along the
fracture face into the reservoir – medium
reservoir rock with low capillary pressures
Fig. 10-1 and Fig. 10-2 show the saturation profiles near the fracture face for both models.
The results shown are calculated with an average gas velocity of 5 m3/day or 3.6 x 10-5 m/s
which is a good reference velocity for the early production period. A very small step size ∆x
is needed to calculate a smooth profile, especially for the low permeability rock model; I use
a step ∆x of 1.0 x 10-9, increasing to 1.0 x 10-4 in approximately 100 steps. The mediumpermeability rock model has an initial step ∆x of 1.0 x 10-7 at the rock face, increasing to 1.0
x 10-4 further from the fracture.
The low capillary pressure profile (Fig. 10-2) extends further into the reservoir, which is a
result of lower pressure gradient in this case, with higher absolute permeability. This is
contrary to what Friedel (2004) shows (Fig. 3-16), where the higher permeability (lower Pc)
scenario has a small zone of water invasion during production. This is also seen in the
simulation results in Fig. 3-19 to Fig. 3-22. The profiles do match the simulation results in the
early production, because the initial amount of water is not the same. Furthermore, the high
capillary pressure in the poor reservoir rock model drains water out of the fracture, whereby
a large inflow of water is created into the reservoir and thus more invasion into the
reservoir.
It can therefore be stated the 1D approach with a simple spreadsheet calculation predicts a
saturation profile based on assumptions of capillary equilibrium in the water phase, zero
capillary pressure at the fracture face, and a fixed gas superficial velocity toward the
fracture. These assumptions used do not allow simple comparison with the simulations in
Eclipse (Schlumberger 2009). At a point in the simulation when injected water is produced,
the condition of zero Pc applies, and the model may predict a correct saturation profile if the
water in the formation is close to capillary equilibrium.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Finally, Fig. 10-3 and Fig. 10-4 show the possible impact of the large predicted increase in
water saturation, taken from the 1D flow spreadsheet exercise. The gas relative permeability
(Fig. 10-3) and its inverse (Fig. 10-4) are plotted over the same distance as the saturation
profile for the medium-permeability formation. Close to the fracture the resistance to gas
flow is steeply increases, which is caused by the capillary end effect. The additional
resistance for gas flow can be approximated by taking the integral of the resistance to gas
flow with position close the fracture. The logarithmic scale of Fig. 10-4 may under-represent
this resistance, which increases the resistance over a zone of 10 cm wide by more than a
factor of 250. Nevertheless, results in section 3.2.2 shows that the gas flow in only slightly
impaired and not completely blocked by this additional resistance. Second, the
transmissibility is only affected over a short distance.
Fig. 10-3 Plot of gas relative permeability as
calculated from 1D Darcy’s Law in a
medium- permeability rock.
Fig. 10-4 Plot of resistance to flow (inverse
of krg) as calculated from 1D Darcy’s Law in
a medium-permeability rock.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
11 Appendix - Hydraulic Fracture Design and Simulation
The hydraulic fracture is designed and analyzed in FracproPT (Carbo Ceramics 2007), a
software tool for hydraulic fracture treatments. The software uses a simplified 2D reservoir
model and treatment details such as total proppant and fluid used, as input for calculation of
the fracture dimensions. The calculation of the fracture in FracproPT (Carbo Ceramics 2007)
is based on literature (Crocket et al. 1986) and is governed by volume of fluid, rate and
pressure of injection, the leakoff to the formation and the properties of the rock. The latter
two are defined as defaults in the fracturing software for the rock types used. FracproPT
(Carbo Ceramics 2007) has an option to convert the 2D fracture model into 3D simulator
input files (Behr et al. 2003). These files can then be loaded into the dynamic reservoir
model in Eclipse (Schlumberger 2009) and used for reservoir modelling and production
forecasting.
The following table (Table 11-1) provides more detail on the lithology and a selection of the
reservoir rock properties used in the calculations. The yellow highlighted zone is the net-pay
reservoir layer.
Top of
Stress
Young's
Stress
Poisson's Permeability
Layer # Lithology zone
Gradient modulus
(bar)
ratio
(mD)
(m
(bar/m)
(bar)
1
Shale
2700
458.1
0.1697
4.1x105
0.25
1x10-8
5
2
Shale
2750
469.9
0.1697
4.1x10
0.25
1x10-8
3
Shale
2790
474.2
0.1697
4.1x105
0.25
1x10-8
5
4
Sandstone 2800
399.7
0.1402
3.4x10
0.20
1x10-3
5
5
Shale
2900
492.8
0.1697
4.1x10
0.25
1x10-8
5
6
Shale
2910
495.8
0.1697
4.1x10
0.25
1x10-8
Table 11-1 Layer properties in the reservoir, used for the design of the hydraulic fracture.
Layer 4 in yellow is the main target layer of the reservoir, with a height of 100 meters.
The resulting dimensions and the total fluid and proppant are listed in section 3.1.2 (Table
3-3). A total of 244 m3 fluid is pumped, including the pad, slurry and final flush. The pad is
the initial volume of fluid (here 50 m3) without proppant injected to create width and length
in the fracture (Economides and Nolte 2000).
Next in the treatment is the slurry, which carriers the proppant into the fracture and is the
part of the treatment that last the longest and uses most fluid (182 m3). The slurry can
contain a gel and is used for transport of the proppant through the wellbore into the
hydraulic fracture, where its high viscosity should help place all the proppant evenly
throughout the fracture. The decision on the density of the slurry is crucial for the execution
of the hydraulic fracture treatment (Economides and Nolte 2000). Finally, the flush is used to
clean the wellbore of any remaining proppant.
Fig. 11-1 shows a side view of the fracture in FracproPT (Carbo Ceramics 2007), including the
width and proppant concentration after complete closure. Note that the vertical and
horizontal scales are not matching; the fracture is actually almost round.
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
Width Profile (cm)
TVD(m) 1
0
Fracture Conductivity (mD·m)
1
25
50
75
2800
Layer Properties
100
125
150
Fracture Length (m)
131.4
Propped Length (m)
116.6
Total Fracture Height (m)
118.5
Total Propped Height (m)
105.2
Fracture Top Depth (m)
2787.5
Fracture Bottom Depth (m)
2906.0
Average Fracture Width (cm)
0.247
Dimensionless Conductivity
2444.521
Rocktype
Stress (b...
450
700
Permeabi...
TVD(m)
Shale
Sandstone
2850
2800
2850
2900
Shale
2900
Fracture Conductivity (mD·m)
0
54
108
162
216
270
324
378
432
486
540
Fig. 11-1 Side view of propped hydraulic fracture, as presented after the treatment design
in FracproPT (Carbo Ceramics 2007).
Finally, to model the flow
permeability function. The
laboratory tests by Barree
provides high performance
Ceramics.
in the fracture properly, the simulator requires a relativefollowing figure (Fig. 11-2) shows the curves taken from
et al. (2003a) for CarboProp 20/40 mesh proppant, which
in low- to moderate-permeability wells, according to Carbo
Finally, in the hydraulic fracture, near-zero capillary pressure is assumed for to the high
permeability of the proppant pack.
Fig. 11-2 Relative permeabilities for the hydraulic fracture in the model (Barree et al.
2004).
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MSc. Petroleum Engineering – Thesis report - L.F. van Zelm
12 Appendix - Grid refinement options
This appendix describes the tests that were conducted to select the grid option, and includes
a general discussion of the two grid options.
Two approaches for refining a grid are common in reservoir simulations; a refinement of a
part of the reservoir host grid and a so-called Local Grid Refinement (LGR), whereby a
second and more refined grid is placed inside the host grid around the hydraulic fracture.
The first option requires a grid refinement in the near-fracture area to be created separately
in the reservoir simulator and the properties for the hydraulic fracture need to be updated
accordingly (Ehrl and Schueler 2000). This is nevertheless a time-consuming task and often
results in the assumption of constant properties to speed up the model preparation (Shaoul
et al. 2006).
The second option is to create a built-in additional grid, a LGR, which contains the hydraulic
fracture including detailed property description and a fluid distribution in the reservoir (Behr
et al. 2003). The output of the hydraulic fracture simulator used in this thesis (Carbo
Ceramics 2007), produces its output in the LGR format which can be used by many
commercial simulators. This method has one major advantage, especially in large reservoir
simulations, where it can refine a smaller part of the model instead of refinements in the
complete model over a specific direction. This is best illustrated in Fig. 12-1 and Fig. 12-2,
where the host grid refinement stretches out through the complete reservoir.
Fig. 12-1 LGR model refinement model.
Fig. 12-2 Host grid refinement.
Two simulations were run to test the speed and accuracy of the two grids, introducing more
complexity in each simulation. First, a single-phase run was simulated; the model contains
only gas. Second, the water phase was introduced by an initial water saturation (Sw = 0.4)
and a water relative permeability function (Fig. 3-3). This option does not take into account
the leakoff as a result of the fracturing process. This issue is dealt with separately in section
3.1.3.
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For proper modelling of multiphase flow, the well connections opened for flow need to be
reduced in order to control the water flow into the wellbore. The modelling software is not
capable of simulating the independent inflow of water into the wellbore at multiple
locations. Probably the cause is to be found in the low flow velocities in the well. The water
probably flows downward within the wellbore and reappears in grid blocks lower in the well.
The symptom is that the wellbore equations are not solved within an acceptable amount of
iterations.
The simulation performance is tested by looking at the total amount of grid blocks in the
model, the total simulation time and cumulative production for 1 year. For clarity, the
refinement of the two models near the fracture is the same, only the host grid refinement
extends the refinement further out into the model (Fig. 12-2). Table 12-1 provides an
overview of the results, where the gas production is normalized at 100 for the single-phase
LGR run. Together with Fig. 12-3 and Fig. 12-4, it reveals that for the prediction of total
volumes and rates, there’s no significant difference between the two refinement options.
The difference in cumulative production between the local grid refinement is small and the
host grid refinement is both the single phase and multiphase scenario.
Simulation method
Local Grid
Host grid
(full field results)
Refinement (LGR)
refinement
Total amount of grid blocks
18,064
21,120
Single phase
Simulation time (s)
101
61
Normalized cum. gas production
100
100.08
Multi phase
Simulation time (s)
164 (+62%)
86 (+40%)
Normalized cum. gas production
33.20
33.23
Normalized cum. water production
100
100
Table 12-1 Overview of grid sensitivity study performed on two grid model options
frequently used in the post-fracture production analysis of low-permeable reservoirs. The
gas production is normalized at 100 for the single-phase LGR run.
There is, however, a difference in the simulation time required to obtain the results. The LGR
option has fewer grid blocks, but it takes more time to run the simulation. The reduction in
calculation speed might be related to matching the boundary conditions of both grids
throughout the simulation. Additional time required to perform the simulation also applies
with two phases present, where the LGR has to update the boundary conditions of the two
grids with the more complicated two-phase pressure and flow equations.
For modelling production in hydraulically fractured wells, both models are accurate and
show no difference in both water and gas production. There is however, a difference in total
simulation time, whereby the LGR is slower.
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Fig. 12-3 Production profile single phase,
comparison per grid option (¼ symmetry
model rates). Here the Red line lies
underneath green line.
Fig. 12-4 Cumulative production multi
phase, comparison per grid option (¼
symmetry model volumes). Here the green
line lies underneath the red line.
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13 Appendix - Reservoir model test runs
A single-phase run is used to test the model. The reservoir contains only gas and no reservoir
water is present. Furthermore, no permeability damage or fluid invasion is present. The rest
of the model, e.g. grid dimension, well, fracture and gas properties, are the same as in the
base case model described in section 3.1.
To analyze the outcome of the simulations I compare it to the analytical solution calculated
from Eq. 13-1. This equation uses reservoir and fluid properties as input (Table 13-1). The
effective wellbore radius is calculated with the relation of Prats (1961) because the hydraulic
fracture is assumed infinitely conductive (Eq. 2-5). This results in rw’ = 60 meters, which is
half of the fracture half-length.
q=
2π kh(mR − mbh )
3


( µ B )r ln( Re / Rw' ) − + s frac 
4


Eq. 13-1
Average Properties
k
1.0 x 10-18
m2
H
117
m
Re
25
m
Rw’
60
m
Sfrac
0
Xf
120
m
Table 13-1 Properties used for the analytical calculation of the gas rate.
Finally, there are two parameters in the equation that require some more explanation,
namely the gas pseudo pressure and the reference PVT properties. As explained in the
theory presented in section 2.1, the changing pressures in the reservoir, the fracture and
near the wellbore require constant updating of the gas properties, which are highly variable
with pressure. A general approach is used, where the PVT properties are evaluated at
reservoir and bottomhole pressure and averaged accordingly. This is line with the theory
presented by Hagoort (1988), where a straight-line relation between m(p) and p is assumed.
Fig. 13-1 shows that this assumption can be made for two pressure ranges in the reservoir.
The condition at the bottomhole is approached with the match of the lower pressure range;
the gas properties at the outer edge of the reservoir are approached with the second trend
line. These two lines are used separately in the calculation, because for the calculation of 1
year production, the two pressures remain almost constant. The intersection of the two lines
does therefore not influence the measurements.
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Fig. 13-1 The straight-line relationship between pressure and the product of two gas
properties (viscosity and formation volume factor) used in the analytical solution.
Fig. 13-2 shows the simulated gas rate versus the analytical solution calculated from Eq.
13-1. Apparent is the transient flow period in the simulated gas rate, which predicts very
high initial rates. This period is dominated by linear flow towards the fracture and therefore
does not allow for comparison with the analytical radial flow gas rate. After one year of
production, the analytical production forecast matches the simulated rate. This implies that
radial flow is established in the simulation and the outcome can be approached with the
pseudo-steady state radial inflow equations. This approach seems therefore be valid for gas
rate production at late times. Second, this result validates the outcome of the simulation
prior to modelling more complex scenarios.
Fig. 13-2 Single phase gas rate comparison with theoretical value for a full field
simulation.
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14 Appendix - Simulation of fluid leakoff process
The base case model is initialised with the leakoff water modelled by injection of the total
fluid pumped in the fracture treatment. As explained in section 3.1.3, another option for
leakoff water modelling is available. This appendix demonstrates possible differences
between the two and comment on the final choice made for this thesis.
The first method (leakoff model) is based on the use of a separate fracturing modelling
software programme which predicts the saturation profile around the fracture. This is done
by including fracture propagation and coefficients for leakoff and wall-building for each
reservoir layer (Behr et al. 2003). The underlying assumption is one-dimensional plug-flow
(or Buckley-Leverett flow) of the treatment water into the reservoir normal to the hydraulic
fracture face. This method is the default method in FracproPT (Carbo Ceramics 2007) and
will be referred to as the ‘leakoff model’ method throughout this section.
After the hydraulic fracture is generated in FracProPT and the leakoff saturation distribution
is determined, a grid is exported into the reservoir simulator (LGR) including the appropriate
permeabilities, porosities and increased water saturation defined per grid block. The part of
the fracture filled with proppant is at water saturation Sw = 1. The remaining leaked off
water is distributed in the reservoir along the fracture, with the first row of grid blocks
initialized at maximum water saturation (Sw = 0.7). Depending on the total amount of water
that leaks off, the next grid blocks either have increased water saturations or are at initial Sw
(= 0.4). This process continues until there is only enough water to saturate one column of
grid blocks at Sw between 0.4 and 0.7. This fluid distribution is solely based on a material
balance, and not controlled by relative permeabilities or capillary pressures.
The leakoff model method, used by FracproPT (Carbo Ceramics 2007), allows the user to
simulate a fracture treatment and generate a leakoff water distribution in the grid blocks
near the fracture face. The grid blocks with increased Sw have reduced gas permeability upon
opening of the well and this results in a short, but still apparent, cleanup period.
The injection method, chosen in this thesis, is based on simulating the leakoff of fracturing
fluid separate of the fracturing process by water injection prior to the production simulation
using the reservoir simulator Eclipse (see similar work in Gdanski et al. 2005; Wang et al.
2009). In this case, the fracture dimensions are set at the start of the simulation as simulated
by a separate fracture treatment programme (e.g. FracproPT by Carbo Ceramics). The
correct permeabilities and porosities are again included in the grid, and Sw is initially 0.4
throughout the formation. The total leakoff volume is then derived from the total fluids
pumped during the treatment minus the fluids that remain in the fracture. This volume is
injected through the well and static fracture into the reservoir. For this simulation, the total
clean volume of the fracture treatment is 244 m3, of which 61 m3 is injected, due to the ¼
symmetry of the model.
This injection method is a simplification of the true process, but results in a method capable
of examining the effect of leakoff on the cleanup process (Soliman and Hunt 1985). For this
thesis, it’s important to be able to influence the fluid leakoff process.
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Although the injection method has a few advantages over importing a grid with a predetermined fluid distribution, it’s important to compare the results for both water and gas
production. The model is setup with the properties of the base case scenario, including the
relative-permeability (Fig. 3-3) and capillary-pressure functions (Fig. 3-4), the initial Sw of 0.4
and the hydraulic fracture properties (section 3.1.2).
Fig. 14-1 Gas production shortly after the well has started producing gas. The water
invasion causes a reduction in the expected gas rate in the first few days.
Fig. 14-1 shows the cleanup period of both leakoff modelling methods. The leakoff model
used by FracproPT (Carbo Ceramics 2007) has an increasing gas rate up to 3 days, after
which the expected hyperbolic decline is seen. The injection method starts with a high peak
followed by a strong reduction. This difference is related to the water saturation in the first
grid blocks adjacent the fracture after the shut-in period. Fig. 14-2 shows the injection
method and Fig. 14-3 the leakoff model. The injection method spreads out the water more
evenly, also governed by the presence of capillary pressures in the reservoir, whereby the
water saturation is generally lower close to the fracture in comparison to the leakoff model.
Second, the leakoff model initiates a higher Sw at the tip of the fracture, which is not
simulated with an injection. A part of the leakoff water volume is therefore located at a
different location in the reservoir at the start of the production.
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Fig. 14-2 Water distribution around fracture after the injection and shut-in period in the
injection model. Note the scale: the y-direction perpendicular to the fracture is enlarged far
clarity.
Fig. 14-3 Water distribution around fracture after shut-in period in the leakoff model by
FracproPT (Carbo Ceramics 2007). Note the scale: the y-direction perpendicular to the fracture is
enlarged far clarity.
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Simulation scenario
production comparison
(fluid injection = 1)
Fluid injection (Eclipse)
Water
Production
2 months
(m3)
1.0
Water
Production
2 yrs
(m3)
1.0
Gas
Production
2 months
(m3)
1.0
Gas
Production
2 yrs
(m3)
1.0
Leakoff model (FracproPT)
0.80
0.73
0.97
0.98
Table 14-1 Production comparison of total water and gas produced after 2 months and 2
years.
Table 14-1 compares gas production for the two models over a longer period than the
cleanup period. Some deviation in the cumulative gas production can be seen, although just
a few percent after two months. More apparent is the change in water production, although
the total water in place in the model is matching. This is probably related to the distribution
of the leakoff water at the tip of the fracture as shown in Fig. 14-3. This part of the LGR is
initialized with an elevated Sw, but the fracture does not extend that far, thereby not
creating a drawdown to produce the water. It’s not investigated if this is realistic or not, but
it can explain the observed differences.
In conclusion, for the modelling of the cleanup period there are some difference apparent in
the gas and water production. This is directly related to the distribution of the water around
the fracture. It is difficult to predict which method is more realistic, for the leakoff process
cannot be monitored in the subsurface. It is apparent that the leakoff in these scenarios only
influences the short-term production, because the long-term gas production is matching.
With this observation and the arguments stated above, the injection method is chosen for
the rest of the simulations in chapter 3.
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