Mengying Li, Noam Lior, Energy analysis for guiding the design of well systems of deep Engineered Geothermal Systems (EGS), Energy 93 Part 1 (2015), Pages 1173 1188.

Mengying Li, Noam Lior, Energy analysis for guiding the design of well systems of deep Engineered Geothermal Systems (EGS), Energy 93 Part 1 (2015), Pages 1173 1188.
Energy 93 (2015) 1173e1188
Contents lists available at ScienceDirect
Energy
journal homepage: www.elsevier.com/locate/energy
Energy analysis for guiding the design of well systems of deep
Enhanced Geothermal Systems
Mengying Li, Noam Lior*
University of Pennsylvania, Department of Mechanical Engineering and Applied Mechanics, Philadelphia, PA 19104-6315, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 7 August 2015
Received in revised form
23 September 2015
Accepted 24 September 2015
Available online xxx
The focal objective of this work is to calculate the energy consumption for constructing the EGS
(Enhanced Geothermal Systems) wells, to examine the energy (heat and power) performance of such
well systems, and to propose and evaluate several ways for improving that performance. A model was
developed to compute the pressure and temperature fields of the geofluid flowing in the production and
injection wells to be able to calculate the flow pumping energy consumption, and the heat gain/loss
during its flow in/out of the enhanced reservoir, for wells up to 10 km deep. The total well construction
energy consumption was calculated to be 19.40 TJ/(km of well) for the considered well configurations,
and increases approximately linearly with the flow cross section area of the well. Several ways to
improve the energy performance of the wells, by increasing the heat output of the production wells and
decreasing the required power for pumping the geofluid were evaluated: (1) increasing the number of
injection/production wells to reduce the pressure drop in each, (2) increasing the flow cross section of
the injection/projection well, and (3) adding thermal insulation to the circumference of the production
wells (to reduce the geofluid heat loss to the rock). Most of these methods were found to indeed increase
the power output of the geothermal system but have increased the construction energy requirement
somewhat more. More energy efficient drilling methods and materials of lower embodied energy can
lead to a higher EROI (energy return on investment). The EROI of the recommended EGS well system
designs ranged from 33.8 to 286.2.
© 2015 Elsevier Ltd. All rights reserved.
Keywords:
EGS (Enhanced Geothermal System)
Geothermal well drilling
Flow and heat transfer in geothermal wells
Energy reduction for constructing EGS well
systems
Well-construction embodied energy
EROI (energy return on investment)
1. Introduction
Geothermal energy is abundant, practically renewable, and has
a long-term potential estimated to be more than 200,000-fold of
current world energy demand [1]. In the continental United States,
over 99% of the geothermal heat within depths of about 10 km is
available in HDR (hot dry rock) where little natural fluid exists and
the rock has low permeability [1,2]. One characteristic of an HDR
resource is the geothermal gradient (G C/km), which quantifies the
temperature increase with resource depth. To extract the
geothermal heat, a large volume of the hot rock (reservoir) must be
fractured in the high geothermal gradient region (Fig. 1). The
fractures are created by means of hydro-fracturing and etc. [1] to
allow liquid flow through the hot rock. Injection and production
wells are drilled to connect the fractures to allow liquid circulation
between the reservoir and the surface structures. Cold fluid
* Corresponding author. 220 S. 33rd Street, 212 Towne Building, Philadelphia, PA
19104, USA. Tel.: þ1 215 898 4803.
E-mail address: lior@seas.upenn.edu (N. Lior).
http://dx.doi.org/10.1016/j.energy.2015.09.113
0360-5442/© 2015 Elsevier Ltd. All rights reserved.
(“geofluid”, usually water) is injected into this reservoir to be
heated and brought back to the surface for direct use or for
generating electricity in a power plant. The injection wells (IW-s),
production wells (PW-s), fractured reservoir and surface power
plant constitute a typical EGS (Enhanced Geothermal System)
where IW-s and PW-s are essential components of an EGS system,
which connect the engineered reservoir with the surface power
plant.
To bring as much thermal energy to the surface while incurring
least energy consumption, the design goals for IW-s and PW-s
should be to minimize:
(1) The energy consumption for constructing the wells.
(2) The heat losses from the geofluid to surrounding rock during
its flow through the PW-s.
(3) The pumping energy consumption for driving the geofluid
flow through these wells.
The focal objective of this work is therefore to calculate the
energy consumption of constructing the EGS wells (Section 2), and
1174
M. Li, N. Lior / Energy 93 (2015) 1173e1188
The contribution of this work is to examine quantitatively the
energy input and output for typical EGS wells in an EGS system (the
analysis of the power generation plant and engineered reservoirs
can be found in Refs. [3] and [8]), and examine their sensitivity to
the number of IW/PW, flow cross section of IW/PW and adding
insulation to PW-s, for ultimately proposing highest net energy
output well system design. Here the energy input is the energy
consumption for constructing the wells. The energy output is the
electricity generated by the EGS power plant minus the geofluid
circulating pumping energy. The temperature and pressure changes
of the geofluid flowing through the wells are calculated by a finite
difference method.
The detailed contributions of this work are:
Fig. 1. Schematic diagram of an EGS system [1,3].
to model the pressure and temperature fields of the geofluid
flowing in the wells to be able to calculate the flow pumping energy
consumption, and the heat gain/loss during its flow in/out of the
engineered reservoir (Section 3). Since deeper reservoirs typically
contain more heat and that at higher temperature, they require
longer and deeper wells that negate some of the benefit because
they require more energy for their construction and also incur
higher heat and pressure losses. It thus clearly poses a design
optimization problem focused on maximizing overall energy performance, addressed here by varying the reservoir depth, number
of wells, well flow cross sections and the best energy performance
design are proposed (Section 4).
While costs are of paramount importance, this study was
focused on the energy analysis because (1) energy perspective
analyses are lacking in the published literature while cost analyses
are widely available [1,4,5]. (2) Knowledge of energy quantities can
be translated relatively easily to costs if the price of energy, which
fluctuates wildly, is known.
Nine cases were calculated: 3 depths each at 3 geothermal
gradients, as shown in Table 1, assuming in all that the ground
surface temperature is Ts ¼ 15 C [6]. The average PW bottom
temperature Tb,pw (assumed to be equal to the reservoir temperature) is:
Tb;pw ¼ 15 þ Z$G;
(1)
where Z is the well depth (km) and G is the geothermal gradient
( C/km).
When the geofluid is injected into the EGS subsurface system
(wells and reservoirs), it is preferred to keep it in the liquid phase
throughout the subsequent heating and recovery process, rather
than allow it to flash or otherwise evaporate, as explained in Refs.
[2] and [7]. To accomplish this, the pressure in the subsurface
system must be maintained high enough to keep the hot liquid
below its boiling point.
(1) Our calculations extend to well depths of 10 km.
(2) A simplified mathematical model was developed and used to
compute the EGS well construction energy consumption.
(3) A model for flow and heat transfer in EGS wells was developed to include both subcritical and supercritical geofluid
and density changes in wells.
(4) Methods that improve the performance of IW/PW were
examined. They include the possibility to add more IW/PW,
to enlarge the flow cross section areas of IW/PW and to
add thermal insulation to the PW-s.
2. Energy consumption for constructing EGS wells
The drilling process of EGS wells is in many ways similar to that
used for the gas and oil. After exploration to determine the location,
the drilling rig is set in place. The drilling rig creates a hold to the
ground and provides the torque to rotate the drill bits and power to
circulate drilling mud (fluid to lubricate and cool the bits and
remove the cuttings while drilling). The rig also provides monitoring equipment along the well to do measurements and diagnosis
needed for the well drilling process.
In the traditional drilling method, rock in the drill's path is
broken into small pieces under the high pressure applied by the
drill bits. A hole of desired depth is created typically in a few
months. There are also proposals for novel drilling methods like jet
drilling and thermal drilling as introduced in Refs. [9] and [10].
After creating the hole, it needs to be cased and cemented to
complete the well (Fig. 2). Casing is to install permanent hardware
(usually metal tubes) inside the borehole to maintain its integrity
and isolate it from its surrounding environment. After casing, the
gaps between casings and the borehole are filled with cement [11].
The geofluid in EGS applications flows inside the inner diameter of
the casing.
The well system of deep EGS consists of at least one IW and one
PW. More than one PW per IW is common. For example, there are
doublets, one IW for one PW; triplets, two PW-s for each IW;
quartet, three PW-s with a single IW and five-spots, and so on [1].
After reaching the desired depth, the wells must typically be
deviated to a horizontal section into the reservoir region (Fig. 1) to
eventually stimulate (fracture) it. The deviated well arrangement
offers a larger drilling window along the created horizontal part,
and could create nearly parallel vertical fracture [1,11]. The casing in
Table 1
Average PW bottom temperatures Tb,pw for the depths and geothermal gradients considered in this work.
Geothermal gradient G, C/km
40
Well depth Z, km
Average PW bottom temperature Tb,pw, C
5
215
60
7.5
315
10
415
5
315
80
7.5
465
10
615
5
415
7.5
615
10
815
M. Li, N. Lior / Energy 93 (2015) 1173e1188
1175
Fig. 2. Configurations of (a) 5 km wells and (b) 7.5 and 10 km wells [1,11]. In (b), the numbers in parenthesis represents 10 km wells.
the deviated part of the IW in the reservoir region is perforated to
allow hydro-fracturing [1]. As discussed in Ref. [3], the length of the
deviated part is a product of the chosen number of fractures in the
reservoir and the distance between them. That inter-fracture distance was found in Ref. [3] to be 120 m to maintain the heat
extraction decay from the rock within 10% during 40 years of
operation and to make the thermal interference between adjacent
fractures negligible.
The length of the deviated part, shown in Table 2 is calculated
based on the recommended number of fractures from Ref. [3]
(under certain assumptions). Since the number of fractures is
highly dependent on how fast the heat extraction from the reservoir decay one can tolerate that beyond the scope of this work, in
the following analysis, we only consider the vertical part of the
wells.
In this study, the borehole is considered to be drilled using PDC
(polycrystalline diamond compact) and roller cone hybrid bits [12]
in a traditional drilling method. The energy for drilling EGS wells
consists of three parts: the energy consumed to create the borehole
and operating casing and cementing (drilling operation), the
embodied energy of well casings and cement and other miscellaneous such as the embodied energy of the drilling mud.
2.1. Well configurations
Studies in Ref. [4] identified that the need for an increasing
number of casing strings or liners with depth is a reason for the
significant increase of drilling costs with depth. A liner is a special
casing string that does not extend to the top of the wellbore, but
instead is anchored or suspended from inside the bottom of the
previous casing string [13]. Ref. [1] provides the recommended
number of casing strings or liners of EGS wells for different depths,
and the information is reproduced in Table 3. For wells over 6 km
deep, liners instead of casing strings can be used to reduce the
casing cost [11].
We therefore chose 4 casing strings/liners for the 5 km well, and
6 casing strings/liners for the 7.5 km and 10 km wells, and assumed
that wells with the same number of casing strings/liners have the
same well configurations [1], as shown in Fig. 2 (b), and that the
7.5 km and 10 km wells have the same configurations.
PW-s are of same configuration design as corresponding IW-s of
the same depth. The number of PW-s per IW depends on the
temperature and pressure changes of the geofluid transporting in
them (Section 4).
2.2. Energy consumption of the drilling operation
According to Ref. [11], making a 6 km well (including borehole
creation and casings/cement operation) requires 8475 kg/day of
diesel fuel. The specific chemical energy of the diesel fuel is 45.3 MJ/
kg [14], thus the daily chemical energy consumption is
E_ dr ¼ 0.384 TJ/day. The energy is for rotating the drill bits and
operating the drilling mud pump, as well as for installing the casings and cementing. For different types of soil and underground
rock stresses, the rate of penetration (ROP, m/day) would differ, and
so would the time required to drill wells of the same depth. For
typical drilling conditions considered in Ref. [11], the ROP for
different borehole diameters is listed in Table 4, which, incidentally,
also shows that it is not directly proportional to the borehole
diameter. The total drilling time is around 1.554 times of borehole
creation time, which takes into consideration the additional time
needed for installing the casings and for cementing [11].
The total energy consumption of the drilling operation can thus
be calculated as:
Table 2
Length of the horizontal part of wells for the depths and geothermal gradient considered in this work.
Well depth Z, km
5
Geothermal gradient G, C/km
Recommended number of fractures [3]
Length of horizontal part of well, km
40
30
3.60
7.5
60
23
2.76
80
19
2.28
40
10
1.20
10
60
8
0.96
80
7
0.84
40
5
0.60
60
4
0.48
80
4
0.48
1176
M. Li, N. Lior / Energy 93 (2015) 1173e1188
where Mcm is the mass of cement (kg), rcm is the density of cement
(1522 kg/m3 [18]), Dwb is the diameter of wellbore (m), D is the
diameter of casing (m) and Lc is the length of casings/cement well
segment (m).
Table 5 presents the embodied energy of casing and cement for
5 km, 7.5 km and 10 km wells. Column 3 presents the unit casing
weight obtained from Refs. [11] and [17], columns 4e6 present the
casings/cement length of well segments, columns 7e9 present the
calculated casing mass, which equals to the length of the casing
multiplied by the corresponding unit weight, columns 10e12 present the calculated cement mass, using Eq. (4). The embodied energy of casing and cements are also presented in Table 5.
The total energy consumption of well construction is:
Table 3
Number of recommended casing strings or liners for EGS wells (from Ref. [1]).
Depth, km
1.5
2.5
3
4
5
5
6
6
7.5
10
No. of Casing Strings
4
4
4
4
4
5
5
6
6
6
Table 4
Energy consumption of borehole creation for 5 km, 7.5 km and 10 km wells.
Hole diameters Dwb,
inch (Fig. 2)
Well depth, km
3600
2600
17-1/200
12-1/400
8-1/200
Sum
Energy consumed,
TJ (Eq. (2))
Edr
ROP, m/day [11]
33.5
83.8
83.8
62.5
45.7
Drilling length Ldr, m (Fig. 2)
5
0
112.5
2375
2500
0
4987.5
42.9
7.5
168.75
1687.5
1875
2625
1125
7481.25
70.3
10
225
2250
2500
3500
1500
9975
93.7
Ewell ¼ Edr þ Bcs þ Bcm þ Eother :
(5)
where Eother (TJ) represents the embodied energy of drilling mud,
the energy consumption of measurements and diagnosis during
drilling and are obtained from Ref. [19].
2.4. Well construction analysis results and discussion
E_ L
¼ dr dr :
ROP
(2)
The construction energy consumptions for wells of depths 5, 7.5
and 10 km, calculated by using Eqs. (2)e(5) are shown in Fig. 3. The
drilling energy consumption and casings' embodied energy
compose over 93.1% of the total energy consumption while the
cement embodied energy and the miscellaneous energy consists
less than 6.9%. The associated embodied energy requirement was
found to be about 43.0%e49.8% of the total energy requirement.
The well construction energy increases nearly linearly with depth
(Fig. 3). The specific energy consumption is ewell ¼ 19.4 TJ/(km of
well).
To validate our calculations, we compared our results with those
in Ref. [19] and the comparisons are listed in Table 6, which show
that they are within ±7%. It is noteworthy that our calculations are
simpler, more detailed and easier to duplicate.
A dimensionless parameter A* is defined to indicate the relative
flow cross section area of a well compared to the wells in Fig. 2,
where A* ¼ 2 indicates that the flow cross section area of the well is
doubled (i.e. the diameter is enlarged √2 times) and A* ¼ 3 indicates that the flow cross section area of the well is tripled (the
diameter is enlarged √3 times). For A* ¼ 1, the energy requirement
to construct a well is presented in Fig. 3. For A* ¼ 2, the volume of
rock that must be removed is doubled and the casing and cement
material weight is doubled. So the energy consumed to construct a
well is approximately doubled. In a similar way, for A* ¼ 3, the
energy consumed to construct a well is approximately tripled.
To reduce the heat exchange between geofluid in the wells and
surrounding rock, the cement can be replaced by a more thermal
insulating material, such as ceramic insulation. For the magnesia
where Ldr is the drilling distance (m).
The energy consumptions for borehole creation we calculated
using Eq. (2) are listed in Table 4. Columns 1 and 3e5 of the table
present the diameter and length of the considered well segments
(Fig. 2) and column 2 presents the ROP values obtained from Ref.
[11].
2.3. The embodied energy of well casings and cement
Typically, the well casings are made of stainless steels to resist
corrosion from the geofluid, and the cementing material is Portland
cement [15]. The specific embodied energy of stainless steel is
bcs ¼ 56.7 MJ/kg and of Portland cement is bcm ¼ 5.5 MJ/kg [16]. The
unit casing weights are found from the American Petroleum Institute casing dimensions chart [17] and reference [11], where the
casing thickness is dependent on its diameter.
The casing stainless steels embodied energy is thus:
Bcs ¼ bcs Mcs
(3)
where Mcs is the mass of casing (kg).
The embodied energy of the cement is,
Bcm ¼ bcm Mcm ¼ bcm rcm
p 2
Dwb D2 Lc ;
4
(4)
Table 5
Embodied energy of casing and cement for 5 km, 7.5 km and 10 km deep wells.
Column 1
2
3
4
Hole diameters Dwb,
inch (Fig. 2)
Casing diameter D,
inch (Fig. 2)
Unit casing weight,
kg/m [11,17]
Casing length/Cementing
length Lc, m (Fig. 2)
Casing mass Mcs, ton (Casing
length unit casing weight)
Cement mass Mcm, ton (Eq. (4))
5
7.5
10
5
7.5
10
5
7.5
10
0
125
2500
2500
0
187.5
1875
3750
2625
1125
250
2500
5000
3500
1500
0.0
24.7
267.9
281.3
0.0
573.9
32.5
55.7
371.1
401.8
295.3
95.6
1219.5
69.1
74.2
494.8
535.8
393.8
127.5
1626.0
92.2
0.0
26.6
232.4
110.7
0.0
369.7
2.03
57.2
398.9
348.6
116.2
20.2
941.1
5.18
76.3
531.9
464.8
154.9
26.9
1254.8
6.90
Well depth, km
3000
3600
2600
2600
17-1/200
13-5/800
12-1/400
9-5/800
8-1/200
700
Sum
Embodied energy, TJ (Eqs. (3)e(4))
460.73
251.17
131.08
79.62
47.62
5
6
7
8
9
10
11
12
M. Li, N. Lior / Energy 93 (2015) 1173e1188
1177
3.1. The mathematical model for flow and heat transfer of geofluid
The assumptions are:
Fig. 3. Itemized and total (numbers on top of each bar) well construction energy
consumption as a function of well depth.
considered here the thermal conductivity (km ¼ 0.07 W/(m K) [20])
is 4.12-fold lower than that of Portland cement (kcm ¼ 0.29 W/(m K)
[20]). The magnesia is much more expensive than cement, and its
specific embodied energy is bm ¼ 45 MJ/kg [16], which is much
higher than that of Portland cement (bcm ¼ 5.5 MJ/kg [16]). The
embodied energy of insulation material is calculated similarly to Eq.
(4) by,
Bm ¼ bm Mm ¼ bm rm
p
4
D2wb D2 Lm
(6)
where rm is the density of the insulation material, 3400 kg/m [21].
3
3. Modeling and analysis of flow and heat transfer in the
wells
The underground system of deep EGS consists of at least one IW
and one PW, and the stimulated reservoir. Section 2 provides the
model for calculating the energy consumption for well construction. In pursuit of our objective (described in Section 1), the energy
gains/losses of the geofluid and geofluid pumping energy demand
are calculated. Energy gains/losses of geofluid are due to heat gain/
loss from the IW/PW, and the geofluid pumping energy demand is
proportional to the pressure changes. A model is therefore developed here to calculate the pressure and temperature changes of the
geofluid flowing in the IW-s and PW-s. Knowledge of the pressure
and temperature profile of the geofluid in the wells allows the
determination of these energy components, and the effects of
adding IW/PW, of enlarging their flow cross section areas and of
adding thermal insulation to them. This produces the information
needed for recommending a highest net energy output design of
geothermal well systems.
Table 6
Well construction energy consumption results validation.
(1) For the purpose of this study it is not necessary to consider
interactions between IW-s and PW-s, which are also typically
far apart.
(2) The pressure is kept high enough to prevent the geofluid
from evaporating.
(3) The time dependences of geofluid properties such as temperature, pressure, density, velocity and etc. are not included
in the governing equations but are introduced in the
dimensionless temperature parameter TD (see Eqs. (21) and
(22)). The heat transfer between the geofluid and the surrounding rock is therefore varying with time, and so are thus
the geofluid temperature, pressure, velocity, and density and
other fluid properties.
(4) The EGS geofluid is pure water devoid of gases and minerals.
Water injected into an EGS reservoir often picks up various
minerals and gases, but the associated complexity that is
associated with their consideration in heat transfer analysis,
accompanied by insufficient experimental information on
their amount in various EGS systems, and since typically
their content in the geofluid is low in EGS system, led most of
the past studies to assume that the geofluid is pure
[1,22e27].
Setting the mass flow rate of the injection geofluid to m_ iw , the
mass flow rate of geofluid in each PW is:
m_ pw ¼
This work, TJ
Ref. [19], TJ
Difference, %
5
7.5
10
80.2
149.1
199.5
84.0
139.5
208.3
4.57
6.85
4.24
(7)
where m_ iw=pw is mass flow rate of the geofluid in a well, kg/s, rwl is
the geofluid loss rate in the reservoir (assumed to be 10% [1]) and
Npw is the number of PW-s per IW. So Npw ¼ 1 for doublet wellconfiguration, Npw ¼ 3 for quartet, etc.
Considering that the resistance pressure loss SKV2/2 is minor
compared to pipe friction loss S2fLV2/D [28] for deep EGS wells
where L >> DK/4f, the total pressure gradient during fluid flow is the
sum of gravity, friction and the flow acceleration gradients [25,29]:
2
dP
V r
dV
þ grHfD
þ rV
¼ 0;
dz
2D
dz
(8)
where the minus sign before fD applies for IW-s and the plus sign
applies for PW-s, and,
P e the geofluid pressure in wells, Pa;
z e the vertical position (along g) of the geofluid, m;
g e the gravitational acceleration, here 9.8 m/s2;
r e the geofluid density in the wells, r ¼ r (P,T), kg/m3 and T is
the geofluid temperature, C;
fD e the Darcy friction factor;
V e the average flow velocity of the geofluid in the wells, m/s:
V¼
Well depth, km
ð1 rwl Þm_ iw
;
Npw
4m_ iw=pw
prD2
(9)
Using Chen's explicit equation for Darcy friction factor fD in
pipes to simplify the calculation (this equation was reported to
satisfy nearly the whole related range of Reynolds numbers (4 103
to 4 108) [30]):
1178
M. Li, N. Lior / Energy 93 (2015) 1173e1188
2
ε=D
5:0452
log10 L
fD ¼ 2 log10
3:7065
Re
ðε=DÞ1:1098
7:149 0:8981
þ
L¼
Re
2:8257
1 1 ln DDwb
Dwb
D
U
¼
þ
:
h
2 1
kcm
2 f
(12)
(10)
where:
hf e convection heat transfer coefficient between the geofluid
and the casing inside surface, W/(m2∙K) [32]:
where:
ε e casing inner roughness factor, m;
Re e Reynolds number, Re ¼ VD/n ¼ Re (P,T), where n is the kinematic viscosity of the geofluid, n ¼ n (P,T), m2/s;
hf D
¼ 0:23Re0:8 Pr0:4
k
(13)
The specific enthalpy of the geofluid in the wells can be calculated from the energy balance equation [26]:
dh
dV Q_
þgþV
H ¼ 0;
dz
dz m_
k e thermal conductivity of the geofluid, k ¼ k (P,T), W/(m∙K);
Pr e Prandtl number of the geofluid, Pr ¼ Pr (P, T);
kcm e thermal conductivity of cement, here 0.29 W/(m∙K) [20].
(11)
The minus sign in front of Q_ applies to IW-s and the plus sign
applies to PW-s, and
h e specific enthalpy of geofluid, h ¼ h (P,T), J/kg;
Q_ e the heat transfer rate from surrounding rock to the geofluid
per unit depth of wells, W/m. It is positive when the geofluid
gains heat from the surrounding rock (in IW-s) while it is
negative when it loses heat to the surroundings (in PW-s).
Using the heat transfer e electric resistance analogy (as shown
in Fig. 4(b)), the heat transfer between the geofluid and surrounding rock has two thermal resistances in series: (1) Combined heat transfer from the geofluid to the wellbore/rock
interface 1/U1, and (2) conduction heat transfer from the wellbore/rock interface to the undisturbed rock 1/U2 (the rock at some
distance from wells where the temperature is undisturbed by the
operation of wells).
The overall heat transfer coefficient from geofluid to wellbore/
rock interface U1 is calculated as:
The thickness of casings is neglected here because it is less than
1% of the casing diameter [17], and since they are made of stainless
steel, which has high heat conductivity relative to cement or rock
(the ratio of conductivities of steel and cement is over 55 [20]).
Therefore, the thermal resistance of the casings is neglected.
Assuming the temperature of the surrounding rock is a function
of time t and radial location r, an energy balance of the surrounding
rock can be expressed in cylindrical coordinates as [32],
1 vTr v2 Tr 1 vTr
¼ 2 þ
;
ar vt
r vr
vr
(14)
where:
ar e Thermal diffusivity of the surrounding rock, here
7.69 107 m2/s [33];
Tr e temperature of surrounding rock at time t and location r,
W/(m∙K);
t e well operation time, s;
r e distance from center of the well, m.
Fig. 4. (a) Sketch of well segment in the finite difference simulation scheme, and (b) the heat transfer process in the ith interval of an IW [31].
M. Li, N. Lior / Energy 93 (2015) 1173e1188
1179
The initial condition is,
Tr ðr; 0Þ ¼ Tr;∞
(15)
Based on the geothermal gradient, G, at the well site, the temperature of the undisturbed rock is,
Tr;∞ ¼ Ts zðG=1000Þ:
(16)
The boundary conditions are,
vTr Q_ ¼ pkr Dwb vr r¼Dwb =2
vTr ¼0
vr r¼þ∞
(17)
where kr is the thermal conductivity of surrounding rock, here
1.61 W/(m∙K) [33];
Defining a dimensionless temperature of the surrounding rock
as,
TD ¼ 2pkr Twb Tr;∞
_
Q
(18)
The continuity of heat flow yields [25],
2pkr Q_ ¼ pDwb U1 ðTwb TÞ ¼ Twb Tr;∞
TD
(19)
Eliminating Twb in (19), we have,
Q_ ¼
2pDwb U1 kr Tr;∞ T ;
TD Dwb U1 þ 2kr
(20)
As derived in Refs. [34] and [27], an algebraic equation for TD
represents the solutions of Eqs. (14)e(17) quite accurately,
pffiffiffiffiffii
h
TD ¼ ln e0:2tD þ 1:5 0:3719etD
tD
(21)
where tD is the dimensionless well operation time [27]:
tD ¼
4ar t
;
D2wb
(22)
As plotted in Fig. 5, TD increases with tD, indicating that a
decreasing amount of heat Q_ is transferred to the geofluid in the
wells from the rock because the geofluid temperature gradually
rises due to the heat transfer from the surrounding rock, the rock
temperature drops as it transfers its heat to the geofluid, and
consequently the temperatures of the geofluid and rock approach
each other over time until a steady state is reached.
3.2. The solution method, range and validation
A finite difference method is used to solve Eqs. (8) and (11),
modeling a well composed of N longitudinal intervals, as shown in
Fig. 4 (a). Fig. 4 (b) (modified from Ref. [31]) depicts the heat exchange with the surroundings in the ith interval of an IW. The
geofluid flow and heat flow directions are reversed in PW-s.
Within each interval i, the geofluid is considered to be incompressible, with a constant density ri ¼ r(Pi,Ti). All other geofluid
thermal properties in each depth (z) interval i are evaluated at Ti
and Pi. Eqs. (8) and (11) are thus expressed as [35]:
2
2
2
Piþ1 Pi V iþ1 V i
ðz zi ÞV i
þ gðziþ1 zi ÞHfDi iþ1
þ
¼0
ri
2
2Di
2
2
V
V i Q_ i ðziþ1 zi Þ
H
hiþ1 hi þ gðziþ1 zi Þ þ iþ1
¼0
2
m_
(23)
Fig. 5. The dimensionless temperature TD as a function of the dimensionless well
operating time tD
The coupled finite difference Eq. (23) was solved by using the
Engineering Equation Solver program (EES [36]). Simultaneous
solution of Eq. (23) successively for each interval i leads to the
determination of Piþ1 and Tiþ1 from known Pi and Ti.
The surrounding rock is assumed to be granite. The geofluid
properties are calculated in EES using its fluid property database
‘Steam_IAPWs’ [30]. All other used values are tabulated in the
Nomenclature section at the end.
For validation of our analytical method, we first note that the
conservation Eqs. (8) and (11) are consistent with the widely used
ones in geothermal wellbore models GWELL, GWNACL, and HOLA
[37,38]. Further validation, of the numerical results, was done by
examining the effect of grid size on the resulting mass, pressure,
and enthalpy balance, and choosing then a grid at which further
size decreases have a negligible effect. For the validation, we chose
the case of one 7.5 km deep PW with a geothermal gradient of
60 C/km. The geofluid mass flow rate was assumed to be 100 kg/s.
The geofluid at the wellhead is either saturated liquid or supercritical fluid at 23 MPa. The calculation procedure for the PW is
shown in Fig. 6, where Tc is the critical temperature of pure water.
The geofluid temperature at the PW well-bottom is assumed to be
equal to the average reservoir temperature of 465 C (Table 1). The
calculation is to find the PW head geofluid temperature Th,pw and
pressure Ph,pw, as well as the well-bottom pressure Pb,pw.
The resulting sensitivity of the numerical solution after 1 year of
operation to grid size, where the size here is the well segment
length, is shown in Fig. 7 (a). It can be seen that well segments
length of 50 m is small enough to make the numerical solution
essentially grid-size independent, and we therefore chose a well
segments length of 25 m for all the computations in this study.
The numerical solutions were also tested by examining the
magnitudes of the absolute mass, pressure, and enthalpy residuals
of the governing Eq. (23).
V pr D2 Rm;i ¼ m_ pm i i i 4
2
2
2
P
ðziþ1 zi ÞV i iþ1 Pi V iþ1 V i
Rp;i ¼ þ gðziþ1 zi Þ þ fDi
þ
;
ri
2
2Di
2
2
V
V 1 Q_ i ðziþ1 zi Þ
Rh;i ¼ hiþ1 hi þ gðziþ1 zi Þ þ iþ1
þ
2
m_ pw
(24)
1180
M. Li, N. Lior / Energy 93 (2015) 1173e1188
Fig. 6. The calculation procedure diagram for the sample PW.
Fig. 7. (a) Grid size dependence of the PW wellhead temperature Th,pw and well bottom pressure Pb,pw; (b) numerical calculation residuals of flow in wells at the operation time of
t ¼ 1 yr.
Substituting all the values in Eq. (24) with the numerical
calculation results, gives the residuals at each well segment i,
presented in Fig. 7(b), which shows that the absolute residuals are
all smaller than 104, indicating a satisfactory and converged
solution.
3.3. The time dependence of the results
Considering for example a 7.5 km deep PW with a geothermal
gradient of 60 C/km and geofluid flow rate of 100 kg/s the time
variation of the wellhead temperature Th,pw and well bottom
pressure Pb,pw are shown in Fig. 8. The changes are rapid within the
first year and then markedly slow down. The 40-year timeaveraged wellhead temperature and well bottom pressure were
calculated to be 381.5 C and 46.5 MPa, respectively, which is
approximately equal to the values after the operating time of 5
years. The results presented in the following sections are for the 40year time-averaged values.
3.4. Results for injection wells
As described in Section 3.2, a 25 m long well segment was
chosen for the finite difference analysis. The geofluid in the IW-s is
kept as a supercooled liquid. The dynamic pressure change of
geofluid in IW is defined as,
DPd;iw ¼ Pb;iw Ph;iw rh;iw gZ
(25)
where rh,iw is the density (in kg/m3) of the geofluid at IW head and
it is a function of the IW head temperature Th,iw. For the considered
Th,iw ¼ 35 C, 70 C and 105 C, the rh,iw is 994.0 kg/m3, 977.8 kg/m3
and 955.0 kg/m3 [8], respectively.
The temperature change of geofluid in IW is defined as,
M. Li, N. Lior / Energy 93 (2015) 1173e1188
1181
enthalpy (caused by reduced geofluid and rock heat transfer
area), resulting in a slightly increased geofluid temperature.
Regression of the resulting data produces the following
approximate equations to express the well bottom pressure Pb,iw
and temperature Tb,iw as a function of the studied parameters:
Pb;iw yPh;iw þ rh;iw gZ C1
m_
A*
C2
C3
(27)
Tb;iw yTh;iw þ C4 Z$G þ C5 m_ þ C6
where C1 ¼ 4.87 107 sC2/kgC2, C2 ¼ 3.13, C3 ¼ 0.9 MPa,
C4 ¼ 2.26 102, C5 ¼ 4.87 107 s/kg and C6 ¼ 16.84 C.
3.5. Results for production wells
Fig. 8. Time variation of wellhead temperature Th,pw and well bottom pressure Pb,pw in
a 7.5 km deep PW with a geothermal gradient of 60 C/km.
DTiw ¼ Tb;iw Th;iw
(26)
Fig. 9 presents the results of a sensitivity analysis of DPd,iw and
DTiw to six parameters, the well depth Z, geothermal gradients G,
geofluid flow rate m_ iw , well relative flow cross section area A*,
geofluid injection temperature Th,iw and geofluid injection pressure
Ph,iw. Their chosen values are presented in Table 7.
The following conclusions can be drawn from the results presented in Fig. 9:
(1) The dynamic pressure change DPd,iw rises with decreased
flow rate m_ iw and increased well relative flow cross section
area A* because of decreased friction pressure loss in both
cases. The well depth Z, geothermal gradient G, injection
temperature and Th,iw and pressure Ph,iw have negligible effect on the dynamic pressure change (the symbols in the
plots of Fig. 9 overlap).
(2) The temperature change DTiw rises with increased well depth
Z and geothermal gradient G because hotter rock transfers
heat to the geofluid. The temperature change rises with
decreased flow rate m_ iw because the heat gained from rock
per unit geofluid mass increases. It also slightly rises with the
decreased well relative flow cross section area A* because the
decrease of well bottom geofluid pressure (caused by friction) over-compensates the decrease of well bottom geofluid
The PW bottom temperature is assumed to be equal to the
average temperature of the reservoir (Table 1). The pressure of the
geofluid is continuous in the EGS system, as shown in the explanatory schematic Fig. 10. The PW head pressure Ph,pw is the lowest in
the subsurface system, which needs to be kept high enough to
maintain the geofluid in saturated liquid (Ph,pw ¼ Psat (Th,pw)) or
supercritical state (Ph,pw ¼ 23 MPa, ~1 MPa above the critical
pressure of water). The arrows in Fig. 10 indicate the flow direction
of the geofluid. The pressure change to be provided by the injection
pump is:
DPip ¼ DPpw DPiw þ DPr þ DPpp ;
(28)
where:
DPpw e the geofluid pressure drop in PW-s, DPpw ¼ Pb,pw Ph,pw,
MPa, calculated using Eq. (23).
DPiw e the geofluid pressure change in the IWs, MPa.
DPiw ¼ Pb,iw Ph,iw , calculated using Eq. (27).
DPr e the geofluid pressure drop in the fractured reservoir, MPa.
It is a function of reservoir depth, geothermal gradient and the
characteristics of reservoir fractures including the number of
fractures, fracture radius, fracture width and permeability [3].
DPpp e the geofluid pressure drop in the power plant, MPa. For
flash and supercritical power plants analyzed by us in Ref. [8],
the pump within the power plant is to bring the geofluid to the
pressure at which it enters the plants. For a binary power plant,
the geofluid exchanges heat with a secondary working fluid in a
Fig. 9. (a) Geofluid dynamic pressure change and (b) temperature change in IW with respect to the well depth Z, geothermal gradients G, geofluid flow rate m_ iw , well relative flow
cross section A*, geofluid injection temperature Th,iw and geofluid injection pressure Ph,iw.
1182
M. Li, N. Lior / Energy 93 (2015) 1173e1188
Table 7
Chosen values for the IW DPd,iw and DTiw sensitivity analysis.
Upper values
Base values
lower values
Well depth
Z, km
Geothermal gradients
G, C/km
Flow rate m_ iw , kg/s
Well relative flow cross
section area A*
Injection temperature
Th,iw, C
Injection pressure
Ph,iw, MPa
11.3
7.5
3.8
90.0
60.0
30.0
166.7
111.1
55.6
1.5
1.0
0.5
105.0
70.0
35.0
15.0
10.0
5.0
heat exchanger. The pressure drop in the heat exchanger is
relatively small and assumed to be negligible [2]. Therefore,
DPpp ¼ 0.
(29)
The energy output (in TJ) from the EGS well system is the net
electricity output of the geothermal power plant minus the
required pumping energy due to the frictions in the wells, over its
lifetime,
!
DPpw DPiw m_ iw
Epp FLf ;
rip hp
Eout ¼
(30)
where:
Epp e the net power output from the surface power plant, MJ. It
is an increasing function of PW head temperature Ph,pw (equivalent to power plant inflow geofluid temperature) and is fitted
using the results presented in our paper [8], as follows:
2:6466
Epp ¼ 5:0 105 Th;pw
Epp
Npw
X
m_ pw ; Th;pw 2 200 C; Tc
1
Npw
X
¼ 937:78 ln Th;pw 4815:5
m_ pw ; Th;pw 2 Tc ; 800 C
1
(31)
Fig. 10. Explanatory schematic of the pressure profile in the EGS system.
rip e the density of the geofluid flowing through the injection
pump. Assumed to be 977.8 kg/m3 [36] because the geofluid
injection temperature is approximately 70 C [8];
hp e the energy efficiency of the injection pump, assumed here
to be 80%;
F e the capacity factor of the surface geothermal power plant,
assumed to be 70% [39];
Lf e the life of EGS well system, assumed to be 40 years [3].
The 40-yrs-averaged PW head temperature Th,pw and pressure
drop DPpw as well as IW pressure drop DPiw are used in Eqs. (30) and
(31) to calculate Eout.
To increase the energy output Eout, the design of PW-s should
either increase the PW head geofluid temperature Th,pw or decrease
the pressure drop in PW-s DPpw (Eq. (30)). The geofluid pressure
drop in PW-s, DPpw, for a given flow cross section area can be
reduced by reducing the mass flow rate in a well to reduce the
friction pressure loss. To attain a chosen overall hot geofluid
extraction rate, the number of such wells needs to be increased.
Another way to reduce the friction pressure loss is to increase the
flow cross section area of the wells for the same flow rate. The PW
head geofluid temperature Th,pw can be increased by reducing the
heat loss from the hot geofluid to the surrounding rock, e.g., by
replacing the cement between the casing outer surface and the rock
by thermal insulation materials, such as ceramic insulation (that
has high temperature resistance).
3.5.1. Effects of increasing the number of PW-s
The geofluid pressure drop in PW-s, DPpw, and temperature at
the PW head, Th,pw, for different numbers of PW-s and whether
insulation is incorporated are plotted in Fig. 11, for different well
depths and geothermal gradients. As mentioned, the total mass
flow rate of the geofluid in the PW-s was assumed to be 100 kg/s.
The pressure drop DPpw decreases with increased geothermal
gradients because of the increased buoyancy effect when the geofluid becomes hotter. Fig. 11 also shows that insulation has little
effect on the pressure drop, while the number of PW-s has large
effect on the pressure drop. For deeper wells (7.5 km) with larger
geothermal gradients (60 C/km), adding more PW-s can reduce
the pressure drop by over 60%.
The insulation could increase Th,pw but the degree of improvement is less than 10 C. Adding more PW-s will increase Th,pw
because reduced geofluid velocity reduces the convective heat loss
(Eq. (13)) to the surrounding rock.
3.5.2. Effects of increasing the flow cross section area of PW-s
As mentioned, another way to reduce the pressure drop in a PW
is to increase its flow cross section area. While this may be difficult
due to the cost and even technology limitations, we analyze this
option here to examine the potential resulting improvements. The
following results are calculated by solving Eq. (23) with enlarged
flow cross section areas.
The computed geofluid pressure drop in PW-s, DPpw, and PW
head geofluid temperature Th,pw for PW-s with different cross
section areas and whether insulation is incorporated are plotted in
Fig. 12 for different well depths and geothermal gradients. As
M. Li, N. Lior / Energy 93 (2015) 1173e1188
1183
Fig. 11. The geofluid pressure drop DPpw in PW-s (top row) and the geofluid temperature Th,pw at PW head (bottom row) of different numbers of PW-s and whether insulation is
incorporated. The black symbols: Npw ¼ 1, blue symbols: Npw ¼ 2, red symbols: Npw ¼ 3. The crosses ‘x’: no insulation is incorporated, circles ‘o’: the insulation is incorporated. (For
interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
shown in Fig. 12, the effect of insulation on the pressure drop was
found to be very small, but the flow cross section areas of PW-s
have large effect on the pressure drop. For deeper wells
(7.5 km) with larger geothermal gradients (60 C/km), enlarging
the flow cross sections areas of PW-s was found here to reduce the
pressure drop by over 60%.
The insulation could increase Th,pw but by less than 8 C.
Enlarging the flow cross section areas of PW-s increases Th,pw
because reduced geofluid velocity reduces the convective heat loss
(Eq. (13)) to the surrounding rock.
Comparison of Fig. 11 to Fig. 12 shows that the effects of
enlarging the well flow cross section area and those of drilling more
wells, on PW pressure drop and PW head temperature, are similar.
account the increase of the energy output Eout (TJ) as a result of such
changes as well as the corresponding energy input Ein (TJ) needed
to construct them, and this are calculated below, noting that the
energy input of preparing the drilling site as well as setting the
drilling rigs have however not been included. The total energy
input (Section 2.4) to construct the EGS well system is,
Ein ¼ Npw þ 1 Ewell þ Npw Im ðBm Bcm Þ;
where:
Ewell e energy consumed to construct one well, TJ, which is given
in Section 2.4.
Im e indicator of whether the cement of PW-s is replaced with
insulation material to reduce heat loss to surrounding rock;
Im ¼ 1 when cement is replaced with insulation material while
Im ¼ 0 when cement is not replaced with insulation material.
4. Design guidance for well system
The design guidance for well systems is based on net-energy
and EROI (energy return on investment) performance criteria, as
presented in this section.
(32)
The net energy output of EGS well system is listed in Table 8 and
defined as,
4.1. Net-energy-based design guidance for PW systems
Improving system energy performance by increasing the number of PW-s or increasing their flow cross section areas, or by
insulating them from the surrounding rock, consumes more energy
to construct. Suitable thermal insulation materials (such as
magnesia) are much more expensive than cement, and their specific embodied energy is much higher than that of Portland cement
(Section 2.4). An optimal energy-based design would thus take into
Enet ¼ Eout Ein
(33)
The chosen performance criterion for comparison is the relative
j
net energy increment for case j, ðDEnet ÞR , defined as,
j
DEnet
j
R
≡
base
Enet Enet
base
Enet
(34)
1184
M. Li, N. Lior / Energy 93 (2015) 1173e1188
Fig. 12. The geofluid pressure drop in PW-s DPpw (top row) and the geofluid temperature Th,pw at PW head (bottom row) of different PW flow cross section areas and whether
insulation is incorporated. The black symbols: A* ¼ 1, the blue symbols: A* ¼ 2 and the red symbols: A* ¼ 3. The crosses ‘x’: no insulation is incorporated and the circles ‘o’: the
insulation is incorporated. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
where the chosen base design is D0, which is a single PW with
A* ¼ 1 using Portland cement casing. Cases D1 to D9 correspond to
designs with different numbers of PW-s, different flow cross sections of PW-s and replacement of the Portland cement by magnesia
insulation. Comparison in Table 8 of the results for D1 vs. D6, D2 vs.
D7, D4 vs. D8, and D5 vs. D9, shows that enlarging the well cross
sections raises the net energy output only by 0.05%e2.43% more
than adding more wells for the same total geofluid output flow rate
(assumed to be 100 kg/s).
In this comparative study of 10 different PW system designs, the
highest net energy output designs characterized by largest positive
(DEnet)R are shown in bold underlined font in Table 8 and are listed
in Table 9. Use of the magnesia insulation increases the energy
output from the 40 C/km resource with 5 km deep wells, the 60 C/
km resource with 5 km and 10 km deep wells, and the 80 C/km
resource with 7.5 km and 10 km deep wells, because the heat loss
from the geofluid to surrounding rock in PW-s is significant. For the
resource with 40 C/km geothermal gradient, the highest net energy output design of PW-s system is single 10 km PW with cross
section doubled as compared to Fig. 2, and without magnesia
insulation. For a resource with 60 C/km gradient, the recommended design is single 10 km PW with tripled cross section, and
with magnesia insulation. For a resource with 80 C/km gradient,
the recommended design is single 7.5 km PW with cross section
tripled, and with magnesia insulation.
Table 9 presents the corresponding geofluid pressure drop in the
PW-s DPpw, the geofluid temperature at PW head Th,pw, and the
geofluid temperature drop in the PW-s, DTpw (DTpw ¼ Tb,pw Th,pw)
of the highest net energy output designs. The asterisked numbers
in Table 9 indicate when the produced geofluid is supercritical.
Table 9 shows that when the geothermal gradient is 40 C/km for
5 kme10 km deep wells, and 60 C/km for the 5 km deep well, the
produced geofluid is at saturated liquid phase, and under the other
conditions the produced geofluid is in the supercritical phase.
The pressure drop in PW-s DPpw, decreases with higher
geothermal gradient because of the increased assistance from
buoyancy of the geofluid. The values of DPpw are much smaller for
supercritical geofluid than for saturated geofluid because of its
larger density variation.
The temperature drop in PW-s DTpw increases with increased
well depths and geothermal gradients because of the corresponding
increased area and consequent heat loss to the surrounding rock,
and larger acceleration energy. The acceleration energy component
in Eq. (11) (the 3rd term) is larger because the velocity increases due
to decreased density of the geofluid for hotter resources.
The temperature at PW head, Th,pw, is the geofluid inflow temperature to the power plant, from which the net electricity generation from power plant can be calculated using Eq. (31).
4.2. EROI-based design guidance for PW systems
The EROI (energy return on investment), defined as the life-time
ratio of the energy output of an energy conversion system relative
to the energy required to construct it, is an important and widely
used performance criterion, so we have calculated it for the EGS
well systems considered in this study. Specifically for the well
system j, the EROI is defined as:
M. Li, N. Lior / Energy 93 (2015) 1173e1188
1185
Table 8
Net energy output (Enet) and relative ((DEnet)R) differences for 10 designs over the lifetime of wells (40 years). Bolded underlined numbers show the maximal positive Enet and
(DEnet)R. Asterisked numbers show the maximal positive Enet and (DEnet)R for a given geothermal gradient.
Geothermal gradient G, C/km
40
Well depth Z, km
5
Design#
D0
D1
D2
D3
D4
D5
D6
D7
D8
D9
Npw
1
2
3
1
2
3
1
1
1
1
Im
0
0
0
1
1
1
0
0
1
1
A*
1
1
1
1
1
1
2
3
2
3
D0
D1
D2
D3
D4
D5
D6
D7
D8
D9
1
2
3
1
2
3
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
3
2
3
60
7.5
10
Net energy output Enet, PJ
6.39
16.50
29.99
17.10
6.29
16.32
29.90
16.92
6.14
16.07
29.49
16.70
6.41
16.48
29.96
17.11
6.26
16.27
29.83
16.96
6.11
15.89
29.37
16.74
6.34
16.51
30.18**
17.05
6.26
16.31
29.97
17.08
6.31
16.44
30.08
17.05
6.23
16.19
29.80
16.92
Relative net energy output increments (DEnet)R, %
0.00
0.00
0.00
0.00
1.54
1.14
0.27
1.02
3.85
2.64
1.65
2.33
0.24
0.16
0.10
0.09
2.00
1.41
0.52
0.80
4.36
3.71
2.05
2.12
0.79
0.02
0.63*
0.30
2.10
1.19
0.06
0.13
1.25
0.42
0.32
0.26
2.57
1.90
0.64
1.02
j
EROIj ¼
Eout
j
where Eout
is the power output from the EGS system j, as calculated
j
from Eq. (30), and Ein is the energy input needed to construct the
well system j, as calculated by Eq. (32).
The relationship between EROI and (DEnet)R for each Design j can
be derived from Eqs. (33)e(35) as:
EROIj ¼
base @
Enet
j
DEnet
R
þ1
j
Ein
1
Aþ1
7.5
10
5
7.5
10
72.61
76.24
77.11
72.54
76.22
77.11
77.33
78.19
77.26
78.16
97.51
103.30
103.69
97.67
103.69
104.34
105.14
106.06
105.44
106.48**
68.53
68.57
68.45
68.53
68.52
68.40
68.61
68.54
68.59
68.50
99.10
104.06
104.42
99.26
104.41
104.95
105.58
106.30
105.80
106.57
126.49
130.28
130.04
126.83
130.86
130.84
132.03
132.56
132.45
133.08**
0.00
5.00
6.21
0.09
4.97
6.20
6.51
7.69
6.41
7.65
0.00
5.94
6.34
0.17
6.34
7.01
7.82
8.77
8.13
9.20*
0.00
0.07
0.12
0.00
0.00
0.19
0.12
0.02
0.10
0.03
0.00
5.01
5.37
0.16
5.36
5.91
6.54
7.27
6.77
7.54*
0.00
3.00
2.81
0.27
3.46
3.44
4.38
4.80
4.71
5.22
The EROI was found to decrease with the increase of the number
of PW-s and with the increase of their flow cross section areas,
because the required energy input Ein of design D0 is substantially
lower than for the other designs, while its energy output Eout is
relatively just a little lower. For example, doubling the number of
PWs or doubling the cross section of a PW will approximately
double the required energy input Ein, but the corresponding increase of energy output Eout is less than 8%. Replacement of regular
cement by Magnesia insulation decreases the EROI for the same
reason.
Table 10 shows that the simplest design, D0, with a single
production well of the smallest considered flow cross section and
no thermal insulation has the highest EROI in comparison with all
the proposed and analyzed alternatives D1 e D9. While many of
these alternative designs raise the well systems energy output Eout,
the energy input Ein required to construct them was found to increase relatively more. It is noteworthy, however, that employment of more energy efficient drilling methods and materials of
lower embodied energy can lead to designs employing the proposed improvement approaches that would also have a larger
EROI.
(35)
j
Ein
0
80
5
(36)
base is a selected positive constant, Eq. (36) shows that the
SinceEnet
EROIj of EGS well system j increases with the ratio of the relative net
j
energy increment for case j as ðDEnet
ÞR , which represents an energy
efficiency for that system relative to the base-case in the energy
comparison sample (Table 8), to the total energy input to construct
j
j
j
this EGS well system j, Ein , thus from Eq. (36) as½ðDEnet ÞR þ 1=Ein .
This explains why the values of EROIj (Table 10) were found to
j
decrease even when the values of ðDEnet
ÞR (Table 8) were positive,
j
simply the value of the energy input Ein
in all these cases rose by
j
more than the rise in ½ðDEnet
ÞR þ 1.
To avoid misunderstanding, it is noteworthy that the EROI and
the ‘relative net energy increment’ (DEnet)R, used in Section 4.1, have
different definitions and purposes: the former is absolute for a
given well system, while the latter is comparative among a selected
sample of different well systems.
5. Conclusions
The objective of this study is to examine quantitatively the energy input and output for typical EGS well systems up to 10 km
deep and by developing models and using them to analyze various
Table 9
The highest net energy output designs of PW system for different well depths and geothermal gradients. Asterisked numbers indicates that the geofluid is supercritical.
Geothermal gradient G, C/km
40
Well depth Z, km
5
7.5
10
5
7.5
10
5
7.5
10
# of PWs
Im
A*
DPpw, MPa
DTpw, C
Th,pw, C
1
1
1
42.9
7.7
207.3
1
0
2
55.3
21.7
293.3
1
0
2
57.3
53.6
361.4
1
1
1
36.5
15.0
300.0
1
0
3
11.6
83.7
381.3*
1
1
3
9.2
68.1
546.9*
1
0
2
23.4
39.1
375.9*
1
1
3
6.6
51.3
563.7*
1
1
3
7.5
62.8
752.2*
60
80
1186
M. Li, N. Lior / Energy 93 (2015) 1173e1188
Table 10
Energy return on investment EROI for 10 designs over the lifetime of wells (40 years).
Geothermal gradient G, C/km
40
Well depth Z, km
5
60
7.5
10
Design#
Npw
Im
A*
Energy return on investment, EROI
D0
D1
D2
D3
D4
D5
D6
D7
D8
D9
1
2
3
1
2
3
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
3
2
3
40.8
27.1
20.2
33.8
21.2
15.3
27.3
20.5
21.3
15.6
56.3
37.5
27.9
43.5
27.0
19.4
37.9
28.3
27.2
19.7
76.2
51.0
38.0
58.8
36.6
26.4
51.4
38.6
36.9
26.8
ways to improve the well-system energy performance. The main
results include:
The well construction energy consumption was found to be
19.40 TJ/(km of well) for wells with flow cross sections recommended in Ref. [11], and it increases approximately linearly with
the increase of the well flow cross section area.
The associated embodied energy requirement was found to be
about 43.0%e49.8% of the total energy requirement.
A correlation equation was developed to express the injection
wells' bottom pressure Pb,iw as a function of the injection pressure Ph,iw, well depth Z, mass flow rate m_ iw and well relative flow
cross section area A*.
A correlation equation was developed to express the IW bottom
temperature Tb,iw as a function of the injection temperature Th,iw,
well depth Z, geothermal gradient G and mass flow rate m_ iw .
The pressure drop in a PW decreases with increased geothermal
gradients because of the increased flow-supporting buoyancy
effect when the geofluid becomes hotter.
Adding insulation to PW-s has little effect on the pressure drop
in PW but can increase the wellhead temperature by 8e10 C.
The number of PW-s and their flow cross section areas have a
strong effect on the geofluid pressure drop in a PW: e.g., for
deeper wells (7.5 km) with larger geothermal gradients
(60 C/km), adding more PW-s or enlarging their flow cross
section areas can reduce the pressure drop by over 60%.
Adding more PW-s or enlarging their flow cross section areas
will increase Th,pw because the reduced geofluid velocity reduces
the convective heat loss to the surrounding rock.
Constructing wells with larger flow cross section areas has only
0.05%e2.43% more net energy output than constructing more
wells.
It is advantageous to add insulation to PW-s when (1) G ¼ 40 C/
km, Z ¼ 5 km, (2) G ¼ 60 C/km, Z ¼ 5 km or 10 km and (3)
G ¼ 80 C/km, and Z ¼ 7.5 km or 10 km.
Single 10 km deep production wells with doubled flow cross
section are recommended for a 40 C/km resource. Single 10 km
deep production wells with tripled flow cross section and
insulation are recommended for a 60 C/km resource, and single
7.5 km deep production wells with tripled flow cross section and
insulation are recommended for an 80 C/km resource.
Supercritical geofluid will be produced for (1) G ¼ 60 C/km,
Z ¼ 7.5 km or 10 km and (2) G ¼ 80 C/km, and Z 5 km.
The EROI was found to decrease with the increase of the
number of PW-s, with the increase of their flow cross sections
and the addition of insulation, because the energy input in all
these cases rose relatively more than did the resulting energy
output. Employment of more energy efficient drilling methods
and materials of lower embodied energy can, however, lead to
80
5
7.5
10
5
7.5
10
107.6
71.3
53.1
88.6
55.6
40.3
71.9
54.2
55.9
40.7
244.5
171.4
130.3
188.1
122.7
90.2
173.9
132.1
124.4
91.4
245.4
173.6
130.9
189.5
124.9
91.3
176.7
133.9
127.0
93.1
428.2
286.0
214.4
351.6
221.5
161.6
286.2
214.7
221.7
161.8
333.3
233.6
176.1
257.0
167.7
122.3
237.0
179.2
169.9
124.2
318.0
218.7
164.0
245.7
157.4
114.2
221.6
167.1
159.3
116.2
designs employing the proposed improvement approaches
that would also have a larger EROI. The design with a single
PW, smallest cross section with no insulation had the largest
EROI
The considered EGS well systems have EROI of 33.8e286.2.
Nomenclature and abbreviations
All the values of thermal properties listed below are evaluated at
the average temperature in the considered temperature range.
Parameters related to the construction energy consumption of wells
(Section 2)
Symbol,
A*
Bcm
Bcs
Bm
bcm
bcs
bm
D
Dwb
E_
dr
Edr
Eother
Ewell
ewell
Im
Lc
Ldr
Mm
Mcm
Mcs
Z
rcm
rm
name, value and unit
relative flow cross section area
embodied energy of the cement, TJ
embodied energy of the casings, TJ
embodied energy of the magnesia insulation, TJ
specific embodied energy of cement, 5.5 MJ/kg [16]
specific embodied energy of casing, 56.7 MJ/kg [16]
specific embodied energy of magnesia insulation,
45.0 MJ/kg [16]
the diameter of casing, m
the diameter of wellbore, m
daily chemical energy consumption, 0.384 TJ/day[11,14]
energy consumption of creating boreholes, TJ
the other energy consumption of drilling, TJ
energy consumption of constructing wells, TJ
specific energy consumption of wells, TJ/km
indicator of whether cement is replaced with magnesia
insulation
casing length/cementing length, m
drilling distance, m
mass of magnesia insulation, kg
mass of cement, kg
mass of casing, kg
well depth, km
density of cement, 1522 kg/m3 [18]
density of magnesia insulation, 3400 kg/m3 [21]
Parameters related to the flow and heat transfer of geofluid in wells
(Section 3)
Symbol, name, value and unit
F
capacity factor of surface power plant, 70% [39]
fD
the Darcy friction factor
M. Li, N. Lior / Energy 93 (2015) 1173e1188
G
g
h
hf
k
kcm
km
kr
Lf
m_ iw=pw
N
P
Pr
Q_
Re
Rh
Rm
Rp
r
rwl
T
Tc
TD
tD
Ts
Tr
Tr,∞
Twb
U1
V
z
ar
DPpp
ε
hp
n
r
rip
t
the average geothermal gradient, C/km
the gravitational acceleration, 9.8 m/s2
the specific enthalpy of geofluid, J/kg
convection heat transfer coefficient between geofluid and
casing inside surface, W/(m2∙K)
thermal conductivity of geofluid, W/(m∙K)
thermal conductivity of cement, 0.29 W/(m∙K) [20]
thermal conductivity of magnesia insulation, 0.07 W/
(m∙K) [20]
thermal conductivity of surrounding rock, 1.61 W/(m∙K)
[33]
lifetime of wells, 40 yrs [3]
mass flow rate of geofluid in each IW/PW, kg/s
the number of longitudinal intervals of a wellbore
the geofluid pressure in wells, Pa
Prandtl number of geofluid
heat transfer rate from surrounding rock to the geofluid
per unit length of wells, W/m
the Reynolds number
absolute residual of energy conservation equation, J/kg
absolute residual of mass flow rate conservation equation,
kg/s
absolute residual of pressure conservation equation, Pa
distance from center of the well, m
the geofluid mass loss rate in reservoir, 10% [1]
the geofluid temperature in wells, C
the critical temperature of pure water, 374.1 C [40]
dimensionless temperature
dimensionless well operation time
the ground surface temperature, 15 C [6]
the temperature of rock, C
the temperature of undisturbed rock, C
the temperature of wellbore/rock interface, C
overall heat transfer coefficient, W/(m2∙K)
the average flow velocity of geofluid in wells, m/s
the vertical position of geofluid, m
thermal diffusivity of surrounding rock, 7.69 107 m2/s
[33]
geofluid pressure drop in surface power plant, 0 Pa [8]
the inner casing roughness factor, 0.2 103 m [33]
energy efficiency of injection pump, 80% (our
assumption)
the kinematic viscosity of geofluid, m2/s
the geofluid density in wells, kg/m3
geofluid density through injection pump, 977.8 kg/m3[8]
wells operation time, yrs
Parameters related to the design guidance for well system (Section 4)
Ein
Enet
Epp
Eout
Npw
Pb,iw
Pb,pw
Ph,iw
Ph,pw
Tb,iw
Tb,pw
Th,iw
Th,pw
(DEnet)R
energy input to construct the well system, TJ
energy output of the EGS well system, TJ
net power output from the surface power plant, MJ
net electricity output from the EGS system over its
lifetime, TJ
number of PW-s per IW
the geofluid pressure at IW bottom, Pa
the geofluid pressure at PW bottom, Pa
the geofluid pressure at IW head, Pa
the geofluid pressure at PW head, Pa
the geofluid temperature at IW bottom, C
the geofluid temperature at PW bottom, C
the geofluid temperature at IW head, C
the geofluid temperature at PW head, C
relative increased net energy output, %
DPd,iw
DPip
DPiw
DPpw
DPr
DTiw
rh,iw
1187
dynamic pressure change in IW, MPa
geofluid pressure increase in injection pump, MPa
geofluid pressure drop in IW, MPa
geofluid pressure drop in PW, MPa
geofluid pressure drop in reservoir, MPa
geofluid temperature increase in IW, MPa
density of geofluid in at IW head, kg/m3
Abbreviations
EES
Engineering Equation Solver
EGS
Enhanced Geothermal System
EROI
energy return on investment
HDR
hot dry rock
IW
injection well
PDC
polycrystalline diamond compact
PW
production well
ROP
rate of penetration
References
[1] Tester JW, Anderson B, Batchelor A, Blackwell D, DiPippo R, Drake E, et al. The
future of geothermal energy: impact of enhanced geothermal systems (EGS)
on the United States in the 21st century, vol. 209. Massachusetts Institute of
Technology; 2006.
[2] DiPippo R. Geothermal power plants: principles, applications and case studies.
Oxford; New York: Elsevier; 2005.
[3] Li M, Lior N. Analysis of hydraulic fracturing and reservoir performance in
enhanced geothermal systems. J Energy Resour Technol 2015;137:042904.
[4] Augustine C, Tester JW, Anderson B, Petty S, Livesay B. A comparison of
geothermal with oil and gas well drilling costs. In: Thirty-first workshop on
geothermal reservoir engineering. New York, New York: Curran Associates
Inc; 2006. p. 5e19.
[5] Mansure AJ, Bauer SJ, Livesay BJ. Geothermal well cost analyses, vol. 29; 2005.
p. 515e9.
[6] Augustine CR. Hydrothermal spallation drilling and advanced energy conversion technologies for engineered geothermal systems. PhD Thesis. Cambridge, MA: MIT; 2009.
[7] Kruger P, Otte C, American Nuclear Society. Geothermal energy; resources,
production, stimulation. Stanford, Calif: Stanford University Press; 1973.
[8] Li M, Lior N. Comparative analysis of power plant options for enhanced
geothermal systems (EGS). Energies 2014;7:8427e45.
[9] Teodoriu C, Cheuffa C. A comprehensive review of past and present drilling
methods with application to deep geothermal environment. In: Thirty-Sixth
Workshop on Geothermal Reservoir Engineering, SGP-TR-191. Stanford, California: Stanford University; 2011.
[10] Graves RM, O'Brien DG. StarWars laser technology applied to drilling and
completing gas wells. In: SPE Annual Technical Conference and Exhibition.
Society of Petroleum Engineers; 1998.
[11] Polsky Y, Capuano Jr L, Finger J, Huh M, Knudsen S, Chip A, et al. Enhanced
geothermal systems (EGS) well construction technology evaluation report.
SAND2008e7866. Sandia National Laboratories; 2008.
[12] Pessier R, Damschen M. Hybrid bits offer distinct advantages in selected
roller-cone and PDC-bit applications. SPE Drill Complet 2011;26:96e103.
[13] Schlumberger. Oil field glossary, http://www.glossary.oilfield.slb.com/en/
Terms/l/liner.aspx.
[14] The Physics Hypertextbook. Chemical potential energy. http://physics.info/
energy-chemical/.
[15] Edwards LM, Chilingar G, Rieke III H, Fertl W. Handbook of geothermal energy.
Houston, TX: Gulf Publishing Company; 1982.
[16] Hammond G, Jones C, Lowrie F, Tse P. Embodied carbon: the inventory of
carbon and energy (ICE). BSRIA 2011;201.
[17] American Petroleum Institute. API 5CT specification for casing and tubing. 9th
ed. 2011.
[18] Engineering toolbox. Densities of some common materials. http://www.
engineeringtoolbox.com/density-materials-d_1652.html.
[19] Mansure A. Engineered geothermal systems energy return on energy investment. No. DOE/EE/0002740-F. 2012.
[20] Engineering Toolbox. Thermal conductivity of some common materials and
gases.
http://www.engineeringtoolbox.com/thermal-conductivity-d_429.
html.
[21] Engineering Toolbox. Densities of miscellaneous solid. http://www.
engineeringtoolbox.com/density-solids-d_1265.html.
[22] Dong T. Thermodynamic analysis of thermal responses in horizontal wellbores. J Energy Resour Technol 2015;137:032903.
[23] Zeng Y, Wu N, Su Z, Hu J. Numerical simulation of electricity generation potential from fractured granite reservoir through a single horizontal well at
Yangbajing geothermal field. Energy 2014;65:472e87.
1188
M. Li, N. Lior / Energy 93 (2015) 1173e1188
[24] Zeng Y, Su Z, Wu N. Numerical simulation of heat production potential from
hot dry rock by water circulating through two horizontal wells at Desert Peak
geothermal field. Energy 2013;56:92e107.
[25] Hasan AR, Kabir CS. Modeling two-phase fluid and heat flows in geothermal
wells. J Pet Sci Eng 2010;71:77e86.
[26] Hasan AR, Kabir CS, Wang X. A robust steady-state model for flowing-fluid
temperature in complex wells. SPE Prod Operat 2009;24:269e76.
[27] Hasan AR, Kabir CS, Sarica C. Fluid flow and heat transfer in wellbores. Society
of Petroleum Engineers; 2002.
[28] Bejan A, Tsatsaronis G, Moran MJ. Thermal design and optimization. New
York: John Wiley; 1996.
[29] Brill J. Multiphase flow in wells. J Pet Technol 1987;39:15e21.
[30] Chen NH. An explicit equation for friction factor in pipe. Ind Eng Chem Fundam 1979;18:296e7.
[31] Mozaffari S, Ehsani M, Nikookar M, Sahranavard L. Heat and mass transfer
modeling in wellbore during steam injection process. Can J Chem Eng Technol
2011;2:74e104.
[32] Bergman TL, Incropera FP, Lavine AS. Fundamentals of heat and mass transfer.
John Wiley & Sons; 2011.
[33] Çengel YA, Ghajar AJ. Heat and mass transfer: fundamentals & applications.
4th ed. New York: McGraw-Hill; 2011.
[34] Hassan A, Kabir C. Aspect of heat transfer during twophase flow in wellbores.
SPE Paper. 1994. p. 211e6.
[35] Pruess K. Enhanced geothermal systems (EGS) using CO2 as working fluidea
novel approach for generating renewable energy with simultaneous sequestration of carbon. Geothermics 2006;35:351e67.
[36] Klein S, Alvarado F. Engineering equation solver. Madison, WI: F-Chart Software; 2002.
[37] Huang X, Zhu J, Niu C, Li J, Hu X, Jin X. Heat extraction and power production
forecast of a prospective Enhanced Geothermal System site in Songliao Basin,
China. Energy 2014;75:360e70.
[38] Aunzo ZP. Wellbore models GWELL, GWNACL, and HOLA user's guide. Lawrence Berkeley National Laboratory; 2008.
[39] U.S. Energy Information Administration. Electric power monthly with data for
March 2015. 2015.
[40] Engineering Toolbox. Critical points some common substances. http://www.
engineeringtoolbox.com/critical-point-d_997.html.
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Related manuals

Download PDF

advertising