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MODELING THE LONGEVITY OF
INFILTRATION SYSTEMS FOR PHOSPHORUS
REMOVAL
Lin Yu
January 2012
TRITA-LWR Degree Project 12:01
ISSN 1651-064X
LWR-EX-12-01
Modeling the Longevity of Infiltration System for Phosphorus Removal
© Lin Yu 2012
Degree Project for master program in Water System Technology
Environmental Geochemistry and Ecotechnology
Department of Land and Water Resources Engineering
Royal Institute of Technology (KTH)
SE-100 44 STOCKHOLM, Sweden
Reference should be written as: Lin, Y (2012) “A Modeling Method for Longevity Study of
Infiltration System for Phosphorus Removal” TRITA LWR Degree Project 12:01, 39 p
ii
Lin Yu
TRITA LWR Degree Project 12:01
S UMMARY IN S WEDISH
En ny modell metod för uppskattning av livslängden för infiltration
system som föreslås i denna studie. Modellen var en-dimensionell,
baserat på resultat från långfristiga infiltration platser i Sverige, med vissa
fysiska och kemiska parametrar som styrande faktorer. Den definierar
livslängden för infiltration system som den tid under vilken P lösningen i
effulent är under nationella kriterier (1 mg / L i denna studie), och det
syftar till att ge livslängden för en viss punkt i infiltration systemet.
Marken i modellen antas vara helt homogen och ISO-tropism och
vattenflöde antogs vara omättat flöde och konstant ständiga inflödet.
Flödet beräknades från den svenska kriterierna för infiltration system.
Den dominerande processen i modellen skulle vara lösta transporten
processen, men skulle utvecklingsstörning styrs av sorption spela en
viktigare roll än advektion och dispersion för att bestämma livslängden i
modellen.
Genom att använda den definition av ett långt liv i denna studie var
livslängd tre jordkolonner vid 1 m djup (Knivingaryd, Ringamåla och
Luvehult) 1703 dagar, 1674 dagar och 2575 dagar. Konsumtion tiden för
tre jordkolonner i inflödet av 5 mg / l 2531 dagar, 2709 dagar och 3673
dagar. Den beräknade sorberas fosfor kvantitet för jord från platser Kn,
Lu och Ri när de når uppskattade livslängd var 0,177, 0,288 och 0,168
mg / g, medan den maximala sorption av Kn, Lu och Ri var 0,182, 0,293
och 0,176 mg / g separat.
Från resultatet av känslighetsanalyser av modellen var sorption kapacitet
och flödeshastighet som är viktigast för livslängd infiltration systemet.
Lägre strömningshastighet och högre P sorption kapacitet förlänga
livslängden för en infiltration säng. På grund av sorption isoterm valts i
denna studie och antagandet om omedelbar jämvikt, var sorption graden
av jorden kolumnen ganska linjär, även om den beräknade livslängden
var betydligt kortare än den verkliga utmattning tid på jorden kolumnen.
Faktum är att jorden har nästan nått sitt sorption maximalt när systemet
når sin livslängd.
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Modeling the Longevity of Infiltration System for Phosphorus Removal
iv
Lin Yu
TRITA LWR Degree Project 12:01
A CKNOWLEDGEMENTS
First of all, I would like to thank my supervisor Jon Petter Gustafsson,
who helped me a lot with all the lab work designing and preliminary data
processing. His suggestions on literature reading really helped me learn
about the processes and construct the idea of my model.
I also want to thank Professor Per-Erik Jansson for his precious advices
during my modeling work. His rich experiences and constructive suggestions really saved me lots of time and lead me to the right way of building the model.
Moreover, I also would like to express my special thanks to David Eveborn and Elin Elmefors. Because of their hard work, I got the possibility
to work on the soil samples for my thesis. And it is really happy to work
with them in the labs of SLU in Uppsala, although it was really hard
work back then, I am so greatful to work with them.
Last but not least, I would like to thank David Gustafsson who helped
me know more on the hydrogeology process in the subsurface, and Professor Gunno Renman, from whose articles I got really inspired about
the phosphorus sorption process, and I really appreciate his appreciation
on my thesis work.
Finally, thank all the persons who helped and cared about me during my
study in KTH.
爸爸媽媽，我愛你們！
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Modeling the Longevity of Infiltration System for Phosphorus Removal
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Lin Yu
TRITA LWR Degree Project 12:01
T ABLE OF C ONTENT
Summary in Swedish ........................................................................................................ iii Acknowledgements ............................................................................................................v Table of Content .............................................................................................................. vii Nomenclature ................................................................................................................... ix Abstract .............................................................................................................................. 1 1. Introduction ............................................................................................................. 1 Phosphorus chemistry ....................................................................................... 2 Sorption and desorption of inorganic phosphorus .......................................... 2 Literature review and study objective............................................................... 3 Contaminant Solute Transport Equation......................................................... 5 1.4.1. Parameters in the Advection Dispersion Equation .................................................. 6 2. Material and methods ............................................................................................. 9 2.1. Site description and field sampling .................................................................. 9 2.2. Analytical work................................................................................................. 10 2.2.1. Oxalate-soluble iron and aluminum ....................................................................... 10 2.2.2. Batch experiment .................................................................................................. 10 2.3. Parameters for Modeling ................................................................................. 12 2.3.1. Flow velocity ......................................................................................................... 12 2.3.2. Retardation factor ................................................................................................. 12 2.3.3. Hydrogeological Parameters .................................................................................. 13 2.4. Numerical solution scheme ............................................................................ 14 2.5. Model description ............................................................................................ 15 2.5.1. Modeling tools ...................................................................................................... 16 2.5.2. Modeling scenarios................................................................................................ 16 3. Results .................................................................................................................... 17 3.1. Oxalate extraction ............................................................................................ 17 3.2. Batch Experiments .......................................................................................... 19 3.2.1. Phosphorus sorption experiments ......................................................................... 19 3.2.2. pHdependence experiments .................................................................................. 22 3.2.3. Chemical Speciation Results .................................................................................. 25 3.3. Modeling results .............................................................................................. 26 3.3.1. Calculated Model Inputs ....................................................................................... 26 3.3.2. Longevity prediction of Kn, Lu and Ri .................................................................. 26 3.3.3. Effect of the Modeling time .................................................................................. 27 3.3.4. Effect of the Soil Sorption Capacity ...................................................................... 27 3.3.5. Effect of inflow concentration and background concentration .............................. 29 3.3.6. Sensitivity analysis of soil properties ...................................................................... 30 3.3.7. Sorption capacity study and sorption velocity ........................................................ 31 3.4. D I S C U S S I O N O N M O D E L I N G R E S U L T S .................................................. 33 3.4.1. Factors influencing the longevity of soil column .................................................... 33 3.4.2. Longevity of infiltration bed and evaluations with current method ........................ 34 4. Further study ......................................................................................................... 35 4.1. Boundary Condition ........................................................................................ 35 4.2. Flow velocity & hydrogeology ........................................................................ 35 4.3. Desorption & Operation Mode ....................................................................... 35 4.4. Influence of pH ................................................................................................ 36 References ........................................................................................................................ 37 Other references............................................................................................................... 39 Apendix I – Measured dry weight of soil samples .......................................................... 1 1.1. 1.2. 1.3. 1.4. vii
Modeling the Longevity of Infiltration System for Phosphorus Removal
Apendix II – Measured oxalate-soluble phosphorus of soil samples ............................ 2 Appendix III: Batch Experiment lab design ................................................................... 3 Series A - 5d equilibration of soils. .............................................................................. 3 Series B - 5d equilibration of soils. .............................................................................. 4 Series C - 5d equilibration of soils. .............................................................................. 5 Appendix IV: Empirical data for porosity calculation .................................................... 6 Appendix V: Comparison of desorbedP........................................................................... 7 Appendix VI: Matlab Codes for Modeling ...................................................................... 8 pdeadeT.m: main m-file for the solution of the ADE equation in the model .......... 8 Isotherm.m: the m-file for isorthem plotting ............................................................. 9 Soilp.m: the m-file for calculation of soil property parameters .............................. 12 MultiLineReg.m: the m-file for the multi-linear regression of the data ................. 13 viii
Lin Yu
TRITA LWR Degree Project 12:01
N OMENCLATURE
A
cross-section area of control volume
longitudinal and transverse dispersivity
αL, αT
β
kinetic rate constant for sorption
C
solute concentration in water phase
Cini
the original phosphorus in soil matrix
solute concentration in solid phase
CS
DL, DT longitudinal and transverse dispersion coefficient
D*
molecular bulk diffusion coefficient
h
time step in discretization of PDE
I
coefficient for C in Freundlich equation
ψ
water tension
k
distance step in discretization of PDE
K
hydraulic conductivity
*
diffusion coefficient
K
dispersion coefficient (partitioning coefficient)
Kd
KF
coefficient in Freundlich equation
L
longevity of infiltration beds
dry weight of soil
Ms
Mt
total mass of soil
n
porosity
ne
effective porosity
θ
volumetric water content
ρ
density
bulk density of soil
ρb
ρs
particle density of soil
q
Darcy’s flux
R
retardation factor
S
phosphate sorption in equilibrium state
phosphorus sorption capacity
Spsc
phosphorus sorption in modeling soil column
Stotal
average pore velocity
ux
v
Darcy’s velocity
V
volume of the substrate per person
specific discharge in longitudinal, lateral and vertical directions
Vx,y,z
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Modeling the Longevity of Infiltration System for Phosphorus Removal
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Lin Yu
TRITA LWR Degree Project 12:01
A BSTRACT
A new modeling method for estimation of the longevity of infiltration
system was suggested in this study. The model was one-dimensional,
based on results from long-term infiltration sites in Sweden, taking some
physical and chemical parameters as controlling factors. It defines the
longevity of infiltration systems as the time during which the P solution
in effulent is under national criteria (1 mg/L in this study), and it aims at
providing the longevity for any given point of the infiltration system.
The soil in the model was assumed to be totally homogenous and isotropic and water flow was assumed to be unsaturated flow and constant
continuous inflow. The flow rate was calculated from the Swedish criteria for infiltration systems. The dominant process in the model would be
the solute transport process; however, retardation controlled by sorption
would play a more important role than advection and dispersion in determining the longevity in the model.
By using the definition of longevity in this study, the longevity of the
three soil columns at 1 m depth (Knivingaryd, Ringamåla and Luvehult)
were 1703 days, 1674 days and 2575 days. The exhaustion time of the
three soil columns under inflow of 5 mg/L were 2531 days, 2709 days
and 3673 days. The calculated sorbed phosphorus quantity for soil from
sites Kn, Lu and Ri when they reach estimated longevity were 0.177,
0.288 and 0.168 mg/g, while the maximum sorption of Kn, Lu and Ri
were 0.182, 0.293 and 0.176 mg/g separately.
From the result of sensitivity study of the model, the sorption capacity
and flow velocity were most important to the longevity of the infiltration
system. Lower flow velocity and higher P sorption capacity extend the
longevity of an infiltration bed. Due to the sorption isotherm selected in
this study and the assumption of instant equilibrium, the sorption rate of
the soil column was quite linear, although the estimated longevity was
much shorter than the real exhaustion time of the soil column. In fact
the soil has almost reached its sorption maximum when the system
reaches its longevity.
Key words: phosphorus sorption isotherm; infiltration system; transport model;
longevity.
1. I NTRODUCTION
Phosphorus in high concentrations is considered to be one controlling
factor of eutrophication of natural water bodies. Since 1960s, the concentrations of phosphorus (P) and nitrogen (N) have increased worldwide as a result of agricultural application of manure and synthetic fertilizers and input of wastewater (Appelo and Postma, 1996). Society starts
to pay more attentions on the removal of nutrients by applying different
technics to wastewater treatment systems. Septic tank systems with soil
infiltration are widely used for on-site domestic wastewater disposal in
rural and isolated communities as well as in many unsewered urban localities (Cheung and Venkitachalam, 2006). Artificial infiltration beds can
be used when natural soil exhibits inadequate drainage or pollutant attenuation. In recent research, an increasing number of filter materials
have proved to be suitable media for P removal in on-site wastewater
treatment systems. Batch experiments and column experiments are run
to test the phosphorus sorption capacity (PSC) of filter materials, which
can be regarded one important criterion for the selection of filter materials (Cucarella and Renman, 2009). However, conventional on-site sys1
Modeling the Longevity of Infiltration System for Phosphorus Removal
tems are still using soil or gravel as filter materials, in this situation, poor
phosphorous retention is often noted and P entering groundwater can
subsequently cause eutrophication problems in streams, lakes and estuaries.
There are approximately 850 000 onsite systems in Sweden. 1/3 has no
treatment or only septic tanks. An additional 250 000-300 000 systems
(about 1/3) have poor treatment and needs improvement. Only the remaining 1/3 are using traditional P removal techniques as soil filters or
soil infiltration (Johansson, 2008). The Swedish framework for regulation
of on-site treatment systems was updated in 2006 and 2008. One specification is that on-site systems need to reduce BOD7 and phosphorus by
90% and nitrogen by 50% in sensitive areas, whereas systems in other
areas must reduce BOD7 and phosphorus by 90% and 70% respectively
(Weiss et al., 2008). The performance of the on-site infiltration systems
remains unknown. David Eveborn and Deguo Kong’s research about
the performances of several long-term infiltration beds in south Sweden
indicates that the removal of phosphorus in long-term septic systems is
really disappointing; a removal rate of only about 8% was reported for an
open infiltration system operating over a period of 16 years (Kong, 2009;
Eveborn et al., 2009). The estimation of the longevity of these infiltration beds therefore is crucial for a correct assessment of the operation of
septic systems.
1.1. Phosphorus chemistry
In the lithosphere, phosphorus occurs predominantly as phosphates,
PO4-3, although a rare iron-nickel phosphide, schreibersite ((Fe, Ni)3P8) is
also known in nature (Hocking, 2006). Orthophosphate is the simplest
phosphate, and consists of phosphoric acid (H3PO4) and its dissociate
forms. In water, orthophosphate mostly exists as H2PO4- in acidic conditions or as HPO42- in alkaline conditions. Many phosphate compounds
are not very soluble in water; therefore, most of the phosphate in natural
systems exists in solid form. However, soil water and surface water (rivers and lakes) usually contain relatively low concentrations of dissolved
(or soluble) phosphorus (online literature from Minnesota University).
In soils, P may exist in many different forms, which in practical terms
can be divided into organic P and inorganic P. Water in soil typically
contains about 0.05 mg L-1 of inorganic phosphate in solution. Two
types of reactions control the concentration of inorganic phosphate in
soil solution: precipitation-dissolution and sorption-desorption
processes. It is now generally accepted that precipitation-dissolution
reactions do not play an important role in controlling the concentration
of phosphate in the solution of majority of soils. Thus, the second type
of reaction, sorption-desorption, is considered more important (Cornforth, 2009). However, the precipitation of calcium phosphates is considered to be an exception, and recent research (Weiss et al., 2008) has
shown that aluminium phosphate precipitation can also influence the
concentration of phosphorus in some situations.
1.2. Sorption and desorption of inorganic phosphorus
A large number of papers have studied the process of phosphorus sorption in the soil. Sorption refers to simply to the observable uptake of a
compound by a material, and can include several different processes
such as absorption and adsorption. In adsorption the chemical is bound
to the surface of the solid. In absorption, the chemical enters into the
matrix of the solid, i.e. diffusing into the solid volume. Concerning the
sorption of phosphorus, there is a number of complicating and also un-
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Lin Yu
TRITA LWR Degree Project 12:01
known factors that are as yet not fully understood. A two-step sorption
process is accepted by most researchers; it is generally agreed that the
first step is fast and reversible (McGechan and Lewis, 2002a; Spiteri et
al., 2007; Cheung and Venkitachalam, 2006). The nature of the second,
slow, step is much less understood. McGechan and Lewis (2002a) describe the second step as consisting of various slower time-dependent
processes, some of which lead to deposition of P at a depth below the
surface of particles, while in the study of Spiteri et al. (2007), the slow
step consists of slow diffusion into micropores or aggregates or precipitation of metal phosphate phases (Spiteri et al., 2007). Normally the fast
step would take very short time, but the slow step takes much longer
time and different studies show different times for P sorption to reach
equilibrium (Cheung and Venkitachalam, 2006). Opinions also differ
about the extent to which the slow step is reversible. Desorption is the
reverse of sorption, and it is usually induced by dilution of the soil solution. The desorption process may be very complicated because of the
multiple sorption processes, since the extent to which slow deposition
has progressed influences the quantity of sorbed material available for
fast desorption from the surface sorption sites (McGechan and Lewis,
2002a).
As for other reactive inorganic ions, the extent to which P is adsorbed
relative to that in solution is highly non-linear. As the chemical affinity
towards P varies between different binding sites on the solid surfaces;
high-affinity sites becoming occupied before low-affinity sites. This nonlinearity is commonly represented mathematically by a number of empirical equations (‘isotherms’), which can be calibrated after logarithmic or
other transformations. The most common sorption isotherms include linear KD model, basic Freundlich, extended Freundlich, Langmuir, Langmuir-Freundlich, Gaines-Thomas and so on (Gustafsson et al., 2007).
In this case, desorption is not taken into account in the modeling part
because no dilution happen in the system. The status of the sorption is
assumed to be in the equilibrium state, since the studied sites have been
running for a long time, at least more than 18 years.
1.3. Literature review and study objective
There is no standard definition for the longevity of infiltration beds.
However, of those studies related with longevity or lifetime of infiltration beds, two main methods are applied. One method used by lots of
researchers, is to estimate the longevity of infiltration beds or constructed wetlands by estimating the longevity of phosphorus absorbents.
Sakadevan and Bavor pointed out in 1998 that the expected longevity of
a constructed wetland can be estimated by using a P sorption maximum;
phosphorus sorption capacity (Xu et al., 2006), phosphorus saturation
potential (Drizo et al., 2002) or the phosphorus retention capacity (Seo et
al., 2005). Of course, this method could be used also to study longevity
of some infiltration systems. The equation used in this method is
straightforward,
L=
(1)
Psorp
Pcons
=
V × ρ × S psc
PPE
Where,
L = longevity of infiltration beds, T
Psorp = total phosphorus that can be removed by substrate, M
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Modeling the Longevity of Infiltration System for Phosphorus Removal
Pcons = total phosphorus been emitted to the substrate, MT-1
V = volume of the substrate per person, L3
ρ = density of substrate, ML-3
Spsc = phosphorus sorption capacity, MM-1
PPE = emission of phosphorus per person, MT-1
Most of studies applying this method (Xu and et al., 2006; Seo et al.,
2005; Drizo et al., 2002; Drizo et al., 1999) use the value of emission of
phosphorus per person from the study of Laak (1986), i.e. 3g of phosphate (PO4) excreted per person per day with additional 4g discharge
from cleaning compounds, giving a total of 7g of PO4 (or 2.3g of P). For
the volume of the substrate per person, different countries have different
guidance value, mostly used in the literature are 3m3 PE (0.6m in depth,
5m2 in area) and 9m3 PE (0.9m in depth, 10m2 in area). As for Sweden,
according to the EC/EWPCA method published in 1990, the volume of
substrate per person is 3m3 or 4.5 tons of substrate. The volumetric
phosphorus sorption capacity depends on the substrates used. Batch experiments or column experiments are run to measure the quantity of
phosphorus sorption. Based on the experiment results, sorption isotherms are applied to calculate the maximum phosphorus sorption of a
certain substrate, usually after extrapolation (e.g. Cucarella and Renman,
2009).
The other method used to estimate the longevity of infiltration systems
is based on the results of column studies. In this kind of studies, researchers set up column experiments to simulate the real infiltration system. Detailed data (effluent phosphorus concentration) are recorded
continuously for a long time. Thus, a prediction of longevity of the system is made in agreement with the data. The definition of longevity here
is the time during which the effluent concentration is under the national
criteria (Heistad et al., 2006; Renman and Renman, 2010). The estimated
longevity of infiltration beds is between 7 and 22 years (results are correlated into Swedish standard: 3 cubic meters substrate per person) of all
the studies, as showed in the table below.
However, there are many uncertainties in both methods. The first method actually estimates the theoretical exhaustion time for an infiltration
system, which cannot be equaled to the longevity of the system. As Heistad et al. (2006) pointed out: the effluent concentration should be a key
factor to predict the longevity of the infiltration bed. Whereas, the estimation in the second method is a “fine guess” based on specified column experiments; this, indicates the results are not of universal value.
For wetland system using Pulverized fuel ash, gravel-based system, light
expanded clay aggregates (LECA) and shell-based units are studied, results from the literature indicate a typical life span of constructed wetland system (CWS) for P removal only 2-5 years (Drizo et al., 1999). The
current way to estimate longevity ignores certain operational and experimental parameters, such as loading rate, age of system, hydraulic design, temperature and physical and chemical properties of substrates.
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Lin Yu
TRITA LWR Degree Project 12:01
Table 1 Longevity studies from the literature. a the column
volume is 6 cubic meters designed for a house. b a system
loaded with 1 cubic meter substrates can treat the wastewater
of a household with 5 people for at least one year.
3
Longevity
V(m )
Spsc(gP/kg)
Substrate
Source
22 yr
3
8.89
furnace slag
Xu et al., 2006
7 yr
3
0.73
shale
Drizo et al., 2002
13 yr
3
1.35
EAF steel slag
8 yr
3
0.83
oyster shell
Seo et al., 2005
5 yr
1.2
Null
Filtralite
Heistad et al., 2006
1+ yr
0.2
Null
Polonite
Renman and Renman,
b
2010
a
A new modeling method for estimation of the longevity of infiltration
system is suggested in this study. The model is one-dimensional, based
on results from long-term infiltration sites in Sweden, taking some physical and chemical parameters as controlling factors. It uses Heistad’s definition for longevity, and it aims at providing the longevity for any given
point of the infiltration system.
1.4. Contaminant Solute Transport Equation
Lots of textbooks about groundwater and pollution have the same equation for solute transport in groundwater, but sometimes with different
notations. In reality, lots of different processes can influence the solute
concentration in groundwater. When it comes to the solute transport equation, five terms are defined as influencing factors.
Advection: advection is the transport of solute by the groundwater flow.
The one-dimensional advective transport equation in a homogeneous
aquifer can be expressed as:
∂C
∂C
= −u x
∂x
(2) ∂t
, where
C = solute concentration, ML-3
t = time, T
ux = average pore velocity, ux = q/ne. here q is Darcy’s flux, ne is effective
porosity
Diffusion: Diffusion is the flux of solute from a zone of higher concentration to one of lower concentration due to the Brownian motion of ionic and molecular species. In steady state, the change of concentration
caused by diffusion can be deduced using Fick’s law:
(3)
∂C
∂ 2C
= K∗ 2
∂t
∂x
, where K* is the diffusion coefficient.
Dispersion: Dispersion is the spreading of the plume that occurs along
and across the main flow direction due to aquifer heterogeneities at both
the small scale (pore scale) and at the macroscale (regional scale). Factors
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Modeling the Longevity of Infiltration System for Phosphorus Removal
that contribute to dispersion include: faster flow at center of the pores
than at the edges; some pathways are longer than others; the flow velocity is larger in smaller pores than in larger ones. This is known as mechanical dispersion. The spreading due to both mechanical dispersion and
molecular diffusion is known as hydrodynamic dispersion (Delleur,
1999). There is the famous advection-dispersion equation for solute
transport problem, which in one-dimension is:
∂C
∂C
∂ 2C
= −u x
+ DL 2
∂t
∂x
(4) ∂t
, where DL is the longitudinal dispersion coefficient.
Sorption and Reactions: sorption can influence solute transport as well.
Normally a retardation factor R is introduced to the equation to express
the influence of sorption, which will be discussed in the coming chapter.
Reactions include chemical, physical and biological processes which
would change the solute concentration in the transport. Those first order
reactions such as radioactive decay and degradation would be simple to
integrate into the equation, but for complicated second or high order
reactions, integration would be very difficult. Then a simplified reaction
term can be used in the transport equation,
(5)
∂C
∂C
∂ 2C n
= −u x
+ DL 2 ± ∑ rm
∂t
∂x
∂x
m =1
The last term on the right side is for reactions.
1.4.1. Parameters in the Advection Dispersion Equation
1.4.1.1Sorption and Retardation factor
Soil P can be considered as being contained in a number of ‘pools’, including (amongst others) dissolved inorganic P, inorganic P sorbed onto
surface sites, inorganic P sorbed or deposited by various slow timedependent processes and various organic P pools (McGechan and Lewis,
2002a). In this study, organic P pools are ignored because of their low
concentration in infiltration systems for wastewater treatment, and inorganic P is divided into only two pools, the one in the water phase and
the one in the solid phase, which is highly immobile. So the sorption
process can be seen as the process of P in water phase turning into P in
solid phase.
A control volume with length dx and cross-section area A is defined
(Fig. 1). For simplicity, set ∂/∂y = ∂/∂z = 0 and sorption is everywhere
at equilibrium. As the system studied is unsaturated, the volumetric water
content is θ, and the mean pore velocity is ux. Here the partitioning coefficient (distribution coefficient) Kd is induced to describe the fraction that
will sorb onto the solid phase.
Kd =
concentration associated with solid [mass chemical / mass solid ] Cs
=
concentration in water[mass / volume water ]
C
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Lin Yu
TRITA LWR Degree Project 12:01
Fig. 1. One dimension control volume: blue points reprensent
P in solid phase, red points represent P in liquid phase
Where Cs is the solute concentration in solid phase (M/M), C is the solute concentration in water phase (M/L3).
The conservation of mass for this volume is:
∂M
= [uxCA]1 −
∂t
∂C ⎤
⎡
⎢⎣−DL ∂x Aθ ⎥⎦ −
1
advection in advection out dispersion at 1
[uxCA]2 +
∂C ⎤
⎡
⎢⎣−DL ∂x Aθ ⎥⎦
2
dispersion at 2
Because advection and dispersion happen only in water, the flux term in
the equation only includes the dissolved concentration C.
If C and ∂C/∂x are continuous function of x, then approximate C2 = C1
+ (∂C/∂x)dx and (∂C/∂x)2 = (∂C/∂x)1 + (∂2C/∂x2)dx. Then equation (5)
becomes:
∂M
∂C
∂ 2C
= −u x A
dx + DL Aθ 2 dx
∂x
∂x
(6) ∂t
The total mass M consists of both solid and water components, the bulk
density ρb is the mass of solid matrix per unit volume, since V = Adx, so
the total mass can be written, M = CsρbV + CθV. If Ct = M/V, then (6)
becomes,
(7)
∂ (Cs ρb + Cθ )
∂C
∂ 2C
= −u x
+ DLθ 2
∂t
∂x
∂x
Since ρb and θ are not changing with time, one can, after rearranging, get
the equation for one-dimensional unsaturated transport including sorption,
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Modeling the Longevity of Infiltration System for Phosphorus Removal
u ∂C
∂C
∂ 2C ρ ∂Cs
=− x
+ DL 2 − b
θ ∂x
∂x
θ ∂t
(8) ∂t
As Cs = Kd×C, for the equilibrium state Kd is a constant, so ∂Cs/∂t =
Kd(∂C/∂t), then equation (8) becomes,
(9)
(1 + K d
ρb ∂C
u ∂C
∂ 2C
=− x
+ DL 2
)
θ ∂t
θ ∂x
∂x
The retardation factor R is defined as R = 1 + K d
ρb
, and because ux/θ
θ
equals the Darcy’s velocity v, so equation (9) can be written,
∂C
v ∂C DL ∂ 2C
=−
+
∂t
R ∂x R ∂x 2
(10)
1.4.1.2 Fluid velocity
Before the solution of transport equation, the flow equation should be
solved first to get the flow velocity of the system. Equations of groundwater flow are derived from consideration Darcy’s law and of an equation of continuity that describes the conservation of fluid mass during
flow through a porous material. In this case, unsaturated conditions are
assumed for the infiltration system. For flow in an elemental control volume that is partially saturated, the equation of continuity must now express the rate of change of moisture content as well as the rate of change
of storage due to water expansion and aquifer compaction.
∂ ( ρ vx ) ∂ ( ρ v y ) ∂ ( ρ vz ) ∂ ( ρθ )
∂ρ
∂θ
+
+
=
=θ
+ρ
∂y
∂z
∂t
∂t
∂t
(11) ∂x
Where
ρ = water density, ML-3
vx,y,z = specific discharge in longitudinal, lateral, and vertical directions,
LT-1
θ = moisture content
t = time, T
The first term on the right hand side of equation (11) is negligible and by
inserting the unsaturated form of Darcy’s law, in which the hydraulic
conductivity is a function of the pressure head, K(ψ), then the equation
becomes, upon canceling the ρ term:
∂
∂h
∂
∂h
∂
∂h ∂θ
( K (ψ ) ) + ( K (ψ ) ) + ( K (ψ ) ) =
∂x ∂y
∂y ∂z
∂z
∂t
(12) ∂x
Hence, after noting that h = z + ψ, and one-dimension condition is applied; the equation turns into the Richards Equation (1931),
∂θ ∂ ⎛
⎛ ∂ψ
⎞⎞
= ⎜ K (ψ ) ⎜
+ 1⎟ ⎟
∂t ∂x ⎝
⎝ ∂x
⎠⎠
(13)
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The water retention curve and hydraulic conductivity function are necessary to solve equation (13).
1.4.1.3Dispersion Coefficient
Dispersion coefficients are difficult to determine for use in contaminant
transport models. They are usually empirical and they are a strong function of scale.
Following the treatment of Scheidegger, a scaling factor is used that correlates with a length scale in laboratory soil columns and field tracer
tests. The scaling factor is called dispersivity, α.
(14)
DL = α L u L + D*(a )
DT = αT uL + D* (b)
Where
DL = longitudinal dispersion coefficient, L2T-1
DT = transverse dispersion coefficient, L2T-1
αL, αT =longitudinal and transverse dispersivity, L
uL = longitudinal velocity, LT-1
D* = molecular bulk diffusion coefficient, L2T-1, is on the order of 105cm2s-1 (Schnoor, 1996)
A rough approximation based on averaging published data is αL ≈ 0.1 L,
where L is the length of flow path. Another estimate for flow lengths
less than 3500 m was given by Neuman (1990) as
αL ≈ 0.0175 L1.46(Delleur,1999).
2. M ATERIAL AND METHODS
2.1. Site description and field sampling
Six ground-based infiltration systems were selected for sampling. These
beds are: Glanshammar situated near Örebro, Tullingsås which is located
in the vicinity of Strömsund, Ringamåla and Halahult located near Karlshamn, and Knivingaryd and Luvehult located near Nybro. The sampled
sites are built between 1985 and 1992, which indicates at least 18 years of
operation for all of them. The positions of these beds are summarized in
Fig. 2.
Fig. 2. Positions of the sampling
sites:
1. Glanshammar,
2. Tullingsås,
3. Ringamåla and Halahult,
4. Knivingaryd and Luvehult
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Modeling the Longevity of Infiltration System for Phosphorus Removal
Sampling work was conducted by David Eveborn and Elin Elmefors between 2010-10-12 and 2010-11-05. Generally, sampling was performed
in all the beds by digging a test pit in an infiltrated part of the bed and by
taking one or two reference samples in a part of the bed that was so unaffected as possible. A large amount of soils (20 – 40 kg) from every
sampling depth was excavated and placed in separated black garbage
bags for later use. The sampling depths were: 0-5 cm, 5-15 cm, 15-30 cm,
30-60 cm and deeper than 60 cm. In order to homogenize the sample,
samples from different depth were mixed in a cement mixer for 30 minutes. After homogenization, about 30 g of soil were taken out from
0-5 cm, 5-15 cm depth and from the reference soil. They were labeled
and sealed into separated smaller bags and stored in a fridge (max 8℃)
before the batch experiments.
2.2. Analytical work
2.2.1. Oxalate-soluble iron and aluminum
From November 15 to November 24, 2010, oxalate extractions of samples were performed at the Department of Soil and Environment at
Swedish University of Agricultural Sciences. The oxalate extraction used
a buffer solution of ammonium oxalate and oxalic acid, which had a
concentration of 0.2 M and a pH of 3. 1.00 g of soil of each sample were
weighed in plastic bottles, 100 ml of water was added using a pipette to
each plastic bottle with soil sample and then be shaken on a end-overend-shaker in the dark for four hours. The solutions were transferred to
acid-washed centrifuge tubes and were centrifuged at 4000 rpm for 15-20
minutes. The supernatant from the centrifuge tubes were transferred to
plastic. The supernatant were filtered with Acrodisc® filters and then diluted five times. All samples were submitted along with 200 ml of reference solution for analysis by means of an ICP Optima 7300 DV instrument from Perkin-Elmer (ICP-OES). The reference solutions were
prepared by diluting the original oxalate solution five times in order to
get the same concentration of oxalate solution as the samples.
Since soil samples were more or less humid but laboratory instructions
were based on air-dry samples, the results were corrected for dry weight
measured for each sample. The dry weight was measured by weighing
about 5 g of soil from the current samples, recording the weight, and
drying them at 105 ℃ in an oven overnight. After being taken out from
the oven, the samples were cooled down for about half an hour in desiccators, whereafter the weights were recorded again.
2.2.2. Batch experiment
Soil samples from the 0-5 and 5-15 cm depths, and reference samples
were selected from all four sampling sites (Knivingaryd, Ringamåla, Luvehult and Tullingsås). From December 8, 2010 to January 21, 2011,
batch experiments were carried out in the Department of Land and Water Resources Engineering at Royal Institute of Technology. Two series
of batch experiments were designed to study the phosphorus sorption
isotherms (series A&B) and the effect of pH on sorption capacity (series C). The detailed design of batch experiments can be seen in Appendix III.
In series A&B, a group of eight centrifuge bottles were prepared for
every soil sample. 4 g of soil sample was added into each bottle, and then
10ml 0.03 M NaNO3 was added into each bottle(to get a background
electrolyte of 0.01 M), and then 20 ml solution with different phosphorus concentration was added into the bottles to test the phosphorus
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Lin Yu
TRITA LWR Degree Project 12:01
sorption capacity of the soils as a function of aqueous concentration.
The additions made corresponded to 0, 0.15, 0.375, 0.75, 1.125, 1.5, 2.25,
and 3.75 mmol P kg-1 soil. After preparation, the samples were shaken
for 5 days at room temperature. All the samples were centrifuged for 20
minutes at 3000 rpm before the next step. 5 ml of the supernatant was
removed from the centrifuge bottle to a pH bottle for pH measurement
immediately after centrifugation. The rest of the supernatant was added
into scintillation bottle for ο-PO4 measurement by spectrophotometry
(molybdate-blue method) using FIA-Aquatec®.
Series C was designed to study the pH-dependent desorption of P from
the samples. For this purpose, six centrifuge bottles were prepared for
every soil sample. 4g soil and 10 ml 0.03 M NaNO3were added to every
bottle as in series A&B. Afterwards, 20 ml solution with different concentrations of acid (as HNO3) and alkali (as NaOH) were added into the
bottles. The procedures after preparation were the same as those in series A&B, i.e. shaking for 5 days, centrifugation for 20 minutes in
3000 rpm. 5 ml of the supernatant was taken out for pH measurement
immediately after the centrifuge. The rest of the supernatant was filtered
through an Acrodisc® PF single-use filter connected to the syringe, but
the filtered solution was divided into two scintillation bottles for later
measurements. The first scintillation bottle had 8 ml solution to which
267 μl ultrapure HNO3 was added. The rest of the filtered solution was
put into another scintillation bottle. The pH measurements and the following process were repeated for all the supernatant. After pH measurement, all the acidified and non-acidified extracts were subjected to οPO4 measurement P by spectrophotometry using FIA-Aquatec®. Afterwards, analysis of Ca, Mg, Fe and Al was performed using ICP-OES
(this analysis was performed at the Department of Geological Sciences,
Stockholm University) on non-acidified bottles.
2.2.2.1 Data processing scheme of batch experiment
The aim of series A&B was to study the sorption isotherm of the sampled soil. From the design details of series A&B, the processes determining sorption can be expressed as follows:
(15)
(16)
Water
Pimo + SiniSolid + PiniLiquid ⎯⎯⎯⎯
→ Pimo + S1Solid + P1Liquid
desorption
P Solution
Pimo + SiniSolid + PiniLiquid ⎯⎯⎯⎯
→ Pimo + SnSolid + PnLiquid
sorption
The left side of both equations are the components of the sample soil,
Pimo is the phosphorus in the soil which would not participate in the sorption/desorption process during the experiment; the second and third
term in the left side represent the sorbed P and the initial dissolved P in
the pore water of the sample soil. The first equation is the process for
the No.1 sample in every group, where water is added and desorption is
the governing process. The second equation is what happened in sample
No.2 to sample No. 8 in every group, in which P solution was added and
sorption is the main process. For the terms on the right side, S stands for
sorbed phosphorus in solid phase, and P stands for dissolved phosphorus; the subscript n represents the sample number.
The sorbed phosphorus on the right-hand side needs to be known to
plot isotherm curves, and a mass balance is applied for this. The added
phosphorus and the dissolved phosphorus after the experiment are
known from experiment. The immobile phosphorus does not influence
the mass balance. So the only unknown parameters are the initially
sorbed phosphorus and the initially dissolved phosphate in the porewa11
Modeling the Longevity of Infiltration System for Phosphorus Removal
ter of the sample. Since only 4 g of soil was added in every sample, and
the dry weight of soil samples indicates a very low water content, the initially dissolved phosphorus term can be safely ignored in the following
data processing. So the initial sorbed phosphorus need to be estimate in
order to plot the sorption isotherms.
2.3. Parameters for Modeling
2.3.1. Flow velocity
The average pore velocity would be used as one important parameter in
the model, but there is not enough hydrogeological data to solve the
flow equation. So a simplified flow velocity is assumed on the basis of
the infiltration system design criterion, and the soil in the model is assumed to be both homogeneous and isotropic.
The sampled sites are designed for the sewage treatment of one household with 5 persons. The estimated inflow into the infiltration bed is
150 – 200 L/D for one person, so the total inflow per day is between
750 L and 1000 L (0.75 – 1 m3). In the design criteria EC/EWPCA
(1990), the area of the infiltration system is 5 m2 per person, so the area
of the whole infiltration bed is about 25 m2. The inflow and outflow of
the system is the same since the system is assumed to be in a water balance, so the estimated mean pore velocity should be between 0.03 and
0.04 m/D throughout the whole infiltration bed.
2.3.2. Retardation factor
The basic Freundlich sorption isotherm is chosen to study the relationship between the dissolved P concentration and phosphate sorption of
the solid phase. The basic Freundlich is written as below,
(17)
S = KF × C I
, where
S = sorbed phosphate in equilibrium state, MM-1
KF = coefficient, dimensionless
C = equilibrium phosphate concentration
I = coefficient, dimensionless
Incorporating the kinetic component into the Freundlich equation requires a solution to the following first order differential equation:
∂S
= β (KF C I − S )
(18) ∂t
, where
β = kinetic rate constant for the reaction, L-1
Cs in equation (8) can be considered of including two parts, the original
P in soil matrix and the sorbed P, which is S in the Freundlich equation.
So
(19)
Cs = Cini + S = Cini + K F × C I
As Cini does not change with time, ∂Cs/∂t actually equals with ∂S/∂t,
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Lin Yu
TRITA LWR Degree Project 12:01
∂Cs ∂S
∂C
=
= K F × I × C I −1 ×
∂t
∂t
(20) ∂t
Substitute equation (19) with equation (8). One gets,
ρb
∂C
∂C
∂ 2C
K F IC I −1 )
= −v
+ DL 2
θ
∂t
∂x
∂x
(21)
ρ
Set R = 1 + b K F IC I −1 , thus the final transport equation in this study
θ
(1 +
becomes:
∂C
v ∂C DL ∂ 2C
=−
+
R ∂x R ∂x 2
(22) ∂t
ρ
, where R = 1 + b K F IC I −1 .
θ
2.3.3. Hydrogeological Parameters
In equation (21), ρb (bulk density), θ (volumetric water content) and v
(Darcy’s flux) are required to solve the equation. The bulk (dry) density is
the ratio of the solid phase of the soil to its total volume and can be determined from the knowledge of dry weight (Ms), solid particle density
(ρs) and porosity (n). The equation is:
ρb =
(23)
, where V =
Mt
Ms 1
×
ρs n
Ms
ρs
×
1
and Mt is the total mass of the soil, then the volun
metric water content can also be obtained,
(24)
θ=
Mt − Ms
V
Darcy’s flux represents the real transport velocity of the solute in soil,
with the definition,
(25) v =
ux
θ
Where ux is the average pore velocity; it is already estimated in section
2.3.1.
The dry weight of the soil had already been measured (Appendix I), and
the particle density is well accepted to be about 2.4 kg/dm3. The porosity
would be estimated based on soil texture using empirical data (See Appendix IV). A simplified linear pedofunction was used in the calculation
process.
The dipersion coefficient was approximated as αL ≈ 0.1 L, where the
flow path length L was assumed to be the length of the soil column in
the model.
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Modeling the Longevity of Infiltration System for Phosphorus Removal
2.4. Numerical solution scheme
Forward difference methods were applied in this study to solve equation
(21) numerically. After assuming that the ADE had a rectangle domain R
= {(x, t): 0≤x≤a, 0≤t≤b}, R was subdivided into n-1 by m-1 rectangles
with sides ∆x=h, ∆t=k, as shown in Fig. 3. C(x,t) would be approximated
at grid points in successive rows {C(xi, tj): i = 1,2,…,m, j = 1,2,…,n}.
The length of the time step (∆t) is of importance to the stability of the
numerical solution scheme. The timestep must satisfy ∆t ≤ (∆x)2/2DL
(Mathews and Fink, 2003). The sorption process in this study was assumed to be finished instantly in every grid. Therefore the time step
must be smaller than both advective time and dispersive time during one
grid (Parkhurst and Appelo, 1999). The time step can slso be simplified
just as ∆t ≤ ∆x/v (Notodarmojo et al., 1992).
The grid point C(xi, tj) is written as Ci,j in the following deduction.
(26)
∂C Ci , j +1 − Ci , j
=
+ ο (k )
∂t
k
∂C Ci , j − Ci −1, j
=
+ ο ( h)
h
(27) ∂x
∂ 2C Ci +1, j − 2Ci , j + Ci −1, j
=
+ ο (h 2 )
2
2
∂
x
h
(28)
Equation (21) was substituted with equations (26) - (28), and the terms
ο(k), ο(h) and o(h2) were dropped:
Ci , j +1 − Ci , j
(29)
k
=−
v ⎡ Ci , j − Ci −1, j ⎤ DL ⎡ Ci +1, j − 2Ci , j + Ci −1, j ⎤
⎥+ R ⎢
⎥
R ⎢⎣
h
h2
⎦
⎣
⎦
Fig. 3. The grid for solving equation (21) over domain
rectangular
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Lin Yu
TRITA LWR Degree Project 12:01
ρb
K IC I −1 . In order to avoid confuθ F
ρ
sion in notations, set R = 1 + UCu-1, where U = b K F I , u = I in exθ
As assumed before, here R = 1 +
pression R. One will get:
(30)
(1 + UC
i, j
u −1
)
Ci , j +1 − Ci , j
k
= −v
Ci , j − Ci −1, j
h
+ DL
Ci +1, j − 2Ci , j + Ci −1, j
h2
Rearrange terms, the new function can be used for the computation:
kD L
kv 2 kD L ⎞
vk kD L
⎛
C i , j +1 (1 + UC i , j u −1 ) = UC i , j u + ⎜ 1 −
−
⎟ C i , j + ( + 2 ) C i −1, j + 2 C i +1, j
2
h
h ⎠
h
h
h
⎝
(31)
2.5. Model description
Conceptual model for the column study: A simplified model was built to study
the longevity from using a column study which aims at simulating the
real infiltration system. Many researchers used such column experiments
as tools to predict the sorption capacity and longevity expect of sorbent
materials (Heistad et al., 2006; Renman and Renman, 2010). Since the
boundary condition of the model is not certain, the depth of the model
is set to 2 m in order to weaken the impact of unknown boundary condition in the numerical solution. The soil in the model was assumed to be
totally homogenous and isotropic and the same as in other real column
studies. Water flow is assumed to be unsaturated flow and constant continuous inflow. The flow rate is calculated from the Swedish criteria for
infiltration systems. The dominant process in the model would be the
solute transport process; however, retardation would play a more important role than advection and dispersion in determining the longevity in
the model. The discretization of the domain is setting distance step to
0.01 m and the time step to 0.1 day.
The structure of the model for simulating column experiment is shown
in Fig. 4 (Matlab codes of the model see Appendix VI).
Fig. 4. Conceptual model
for the soil column
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Modeling the Longevity of Infiltration System for Phosphorus Removal
2.5.1. Modeling tools
2.5.1.1 Matlab
MATLAB® is a high-level technical computing language and interactive
environment for algorithm development, data visualization, data analysis,
and numerical computation. Developed by MathWorks, MATLAB
allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran.
MATLAB was developed by Cleve Moler, the chairman of the
computer-science department at the University of New Mexico in the
late 1970s. Jack Little, an engineer, was exposed to it during a visit Moler
made to Stanford University in 1983. Recognizing its commercial potential, he joined with Moler and Steve Bangert. They rewrote MATLAB in
C and founded MathWorks in 1984 to continue its development.
MATLAB was first adopted by researchers and practitioners in control
engineering, Little's specialty, but quickly spread to many other domains.
It is now also used in education, in particular the teaching of linear
algebra and numerical analysis, and is popular amongst scientists involved in image processing (Wikipedia).
2.5.1.2 Visual MINTEQ
Visual MINTEQ is a freeware chemical equilibrium model for the calculation of metal speciation, solubility equilibria, sorption etc. for natural
waters. It combines state-of-the-art descriptions of sorption and complexation reactions with easy-to-use menus and options for importing
and exporting data from/to Excel.
The latest version of Visual MINTEQ (ver. 3.0, Jon Petter Gustafsson,
2011) was used in this study to process the chemical speciation of the extracts from the pH-dependence experiments. The solution activities were
calculated from the output of Visual MINTEQ and compared to the
solubility constants from the literature.
2.5.2. Modeling scenarios
Basic Scenario: three basic scenarios were applied for the preliminary
prediction of longevity of soil column system with soil from three sampling sites. Parameters input are derived from the raw experiment data,
the modeling time period was set to 5000 days. A reference phosphorus
concentration of 0.015 mg/L all along the column is set to be the initial
condition at starting time. A constant inflow of 5mg/L at starting point
is accepted as one boundary condition; as for the boundary condition at
depth equals 2 meters, a slow linear increasing is assumed in the modeling period, and the concentration would increase from the reference
concentration till the critical concentration, 1 mg/L. Table 2 shows the
inputs for Basic Scenario.
In order to get shorter running time for the sensitivity analysis and better
comparison Fig.s, a new set of input was used as the basis for the scenarios. With U = 0.03 m/D, θ = 0.12 kg/m3, n = 0.40, Kf = 3.0213 and I
= 0.5968. The modeling time was set to 300 days, and it is refered as
Scenario 0 in the following text.
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Lin Yu
TRITA LWR Degree Project 12:01
Table 2 Model Setting for Basic Scenario, ux is the average
pore velocity, θ is the volumetric water content, n is the porosity, ρb is the bulk density, Kf and I are coefficients in equation
(12)
3
3
ux(m/D)
θ(kg/m )
n
ρb( kg/m )
Kf
Kn
0.03
0.12035
0.3984
1.5642
10
Lu
0.03
0.13375
0.3932
1.5901
Ri
0.03
0.12045
0.3965
1.5688
IC
C(x,0)=c1=0.015 mg/L
BC
C(0,t)=c2=5 mg/L; C(2,t)= c1+t*(1-c1)/2*5000
I
1.9201
0.4866
10
2.2282
0.3423
10
1.8278
0.5968
Scenario 1: this scenario was created to study the influence of modeling
time. The setting of this model was the same as Scenario 0, but with a
modeling time of 5000 days as comparison.
Scenario 2: this scenario was set up to study the influence of P sorption
capacity of the soil. Two sub-scenarios were set to study the impacts of
Kf and I from Freundlich isotherm separately. In sub-scenario 2.1, the
value of Kf was entered as 0.5, 1, 2, 3 and 5, and the rest of the inputs
were the same as Scenario 0. In sub-scenario 2.2, the value of I was input
as 0.25, 0.35, 0.45, 0.55 and 0.7, and the rest of inputs were the same as
Scenario 0.
Scenario 3: this scenario was built to study the influence of inflow P
concentration and background P concentration. It was also built on Scenario 0 with the modeling time of 1000 days, and contains two subscenarios. Sub-scenario 3.1 has a changing inflow P concentrations of 3
mg/L, 5 mg/L, 8 mg/L and 10 mg/L; sub-scenario 3.2 has various
background concentrations of 0.001 mg/L, 0.015 mg/L, 0.05 mg/L and
0.1 mg/L.
Scenario 4: this scenario was built to study the sensitivity of flow velocity
to the P concentration. It was built on Scenario 0 with 1000 days as
modleing time, with different flow velocities: 0.003 m/D, 0.01 m/D,
0.02 m/D, 0.03 m/D and 0.05 m/D.
Scenario 5: this scenario was built to study the model reactions to the
change of volumetric water content under two different flow velocities.
It was built on the basis of Scenario 0 under 1000 days’ modeling time,
with two different flow velocities: 0.01 m/D and 0.03 m/D, and three
volumetric water contents: 0.08, 0.12 and 0.2.
3. R ESULTS
3.1. Oxalate extraction
Appendix II shows the oxalate-soluble phosphorus concentrations of all
sampling sites. All the reference samples from the six sampling sites had
lower oxalate-soluble phosphorus than their correlated surface soil.
However, in Glanshammar, the oxalate-soluble phosphorus was only
slightly less than the phosphorus of surface soil in the infiltration bed; it
might indicate that the reference plot has been subject to P from the
infiltration bed. Oxalate-soluble phosphorus from the surface horizons
(0-5, 5-15 cm) of most sites had a value of around 0.25 mg/g. Meanwhile, in Luvehult, the oxalate soluble P in 0-5 cm and 5-15 cm soil were
1.14 mg/g and 1.04 mg/g, and in Tullingsås the oxalate-soluble P in 5-15
cm was 7.07 mg/g (Appendix II). No obvious difference between the 0.5
17
Modeling the Longevity of Infiltration System for Phosphorus Removal
and 5-15 cm horizons could be observed in the Luvehult soil. However,
the P concentration in the reference sample was also quite low, and one
can conclude that the high P in the surface horizons are probably
because of the high P level in sewage or exhausting P retention ability in
the soil. For all the sites, there were obvious positive correlations
between P and Al, as well as between P and Fe. But the relationship
between P and Al (r2=0.93) was much stronger than that of P and Fe
(r2=0.77)
The dry weights are presented in Appendix I. The horizon 0-5 cm in site
Tullingsås had a very low dry weight of 0.332 g/g, which indicates quite
high water content in that layer. The rest of the results were in the normal range of mineral soils.
Fig. 5. Relation between oxalate-soluble P and oxalate-soluble Al
Fig. 6. Relation between oxalate-soluble P and oxalate-soluble
Fe
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TRITA LWR Degree Project 12:01
3.2. Batch Experiments
3.2.1. Phosphorus sorption experiments
Four sampling sites were selected for the batch experiments; they are
Knivingaryd, Ringamåla, Luvehult and Tullingsås. Due to the high organic content and remnant vegetation in the soil from Tullingsås, the filtering step failed during the experiments, therefore the data from Tullingsås were not used anymore.
As shown in Appendix III, soil from every sample was added into 8 bottles for isotherm experiments, which can be used to determine the phosphorus sorption capacity at different concentrations of dissolved phosphate. As tested by Kafkafi et al. (1967) the plotting of isotherms from
sorption data is appropriate where the sorbing surfaces are on a prepared
pure mineral material or a virgin soil. Barrow (1978) discusses the need
to consider P already present in the soil when fitting the basic Freundlich
isotherm to experimental sorption data, suggesting an extra term in the
isotherm:
S =S +S
= K CI
ini
sorb
f
(32)
, where S is the total sorbed phosphorus in the soil, it is also S nSolid in
equation (15) and (16). Sini is the already sorbed phosphorus in the soil
sample and Ssorb is the newly sorbed phosphorus during the experiment.
In the data processing, Sini needs to be estimated to plot the Freundlich
isotherms. An estimation of the quantity of phosphorus in the solid
phase is needed to plot the Freundlich isotherm curve. For each group
of test, to get an initial value of the solid phase phosphorus concentration in the added soil sample, log-linear regression was run by the means
of trial and error using Microsoft Excel as first estimation. Then optimization was made by applying log-linear regression of all three groups of
data (reference soil, horizon 0-5 cm and horizon 5-15 cm) in a same
sampling site. All the three estimated Sini of reference soil, horizon 0-5
cm and horizon 5-15 cm would change at the same time, in the extent of
±20% of the first estimation value. A new determining number was used
to decide the best estimated Sini in the concern of the whole sampling
site; it was the sum of the three r2 (from the linear regressions of reference soil, horizon 0-5 cm and horizon 5-15 cm) and three times r2 from
the linear regression of the whole sampling site. Matlab was used to
execute the optimization. Data from samples with no P addition was
excluded in this step since the process in these was desorption not sorption.
The results are shown in Fig. 7. When the estimated phosphorus concentration in the solid phase and the oxalate soluble P were compared, a
quite good linear fit (r2 = 0.97) was obtained (Fig. 8). Generally, all the
soils sorbed more phosphorus while supplied with higher P concentration in water phase; for the highest added P concentration in this study
(0.5 mM), no obvious evidence of sorption ability exhaustion could be
found.
19
Modeling the Longevity of Infiltration System for Phosphorus Removal
(a)
(b)
Fig. 7. Phosphorus sorption isotherms
of sampling sites:
(a) Knivingaryd;
(b) Luvehult;
(c) Ringamåla.
(c)
As for the sorption isotherms, all the 9 groups of tests turned out to get
a quite good fit after first estimation, 4 groups had r2 of 0.99, 3 groups
had r2 of 0.98 and the other 2 groups had r2 of 0.96. While the fit for
every site were also quite good after adjusting, with r2 = 0.979 in Knivingaryd, r2 = 0.928 in Ringamåla and r2 = 0.969 in Luvehult. However,
from the shape of regression curve, it is observed that the curve for reference site has slightly deviation compared with curves for soils from
infiltration beds. And the result of log-linear regression of all the three
sites gave a really unsatisfying r2 of 0.699. It implies that in fact the sorption of phosphorus is also influenced not only by the solution concentration of phosphorus, but also by many other factors, such as concentration of Ca, Fe and Al and so on. For soils in the same infiltration beds,
the other factors have similar or same impact on the P sorption, but in
the correlated reference site, the influence of those other factors is not
the same as that in infiltration bed, and bigger difference can be
observed among different sites (Fig. 7).
(a)
(b)
Fig. 8. Relation between estimated initial solid P (Sini) and oxalate soluble P. In (a), x
axis stands for Pox and y axis stands for Sini, both in mg/g; in (b) y axis stands for the
sampling sites.
20
Lin Yu
TRITA LWR Degree Project 12:01
It is interesting to mention another researcher’s description about the
oxalate-extractable P content of the soil. Lookman et al. (1995) describes
the oxalate-extractable P as: Pox = Pfast + Pslow, where Pox is oxalateextractable P, Pfast is P pool for the fast desorption and Pslow is the P pool
for slow reaction. However, it is obvious in this study that the estimated
Sini is much smaller than the Pox, which might imply that 5 days’ shaking
in this study is not long enough for the soil sample to complete the slow
reaction, especially under the consideration that these soils were taken
from infiltration beds which have had a service time of longer than 18
years. Noticing that 5 days’ shaking time is not enough for the slow
action of sorption/desorption, it is necessary to use the sorption kinetics
in the modeling rather than the isotherm, given the possibility that the
sorption capacity might also increase during the process because the
accumulation of metal (hydr)oxides. If the fast step of
sorption/desorption is an instant reaction, so the estimated Sini here
might contain all the fast reaction P pool and a very small part of the
slow reaction P pool, which is small enough here to be neglected. So the
isotherm obtained in this study is just for the fast reaction of sorption.
Noticing the different sizes of the slow reaction P pool from Fig. 8(b),
relations between the metal concentration and slow reaction P pool were
plotted to see the correlation. Results (Fig. 9) give a stronger correlation
with Fe than Al, while in Fig. 5 and Fig. 6, Al has stronger correlation
with oxalate-soluble P. It can be concluded that Al would influence more
on the fast reaction and Fe would impact more on the slow reaction of
sorption/desorption of P.
Supportive information for the necessity of including sorption/desorption kinetics in the modeling is presented above. If the estimated Sini value is returned to the isotherm obtained in this study, to
calculate the initial P concentration in the dissolved phase, an unreasonably small value would be returned. However, if the measured oxalatesoluble P is used to calculate the initial P concentration in the dissolved
phase, the results turn to be much realistic except for the results for Lu
(Table 3). From the returned value of initially dissolved in the Luvehult
site, one can make a guess that the sewage P concentration there is really
high. At the same time, due to the relative high metal (hydr)oxide concentration in site Luvehult, it is reasonable to point out that the basic
Freundlich isotherm obtained in this study is not applicable to the Luvehult site due to high metal concentrations and possibly other factors. Use
of other approaches (such as the Extended Freundlich isotherm with kinetics), including concentrations of metal (hydr)oxides should be studied
for site Luvehult
P mg/g
Fig. 9. Relation between slow P pool and oxalate-soluble Al & Fe.
21
M
Modeling
the Longevity
L
of In
nfiltration Systtem for Phosp
phorus Removval
Table
le 3 Return
rned value of
o initial P concentratio
c
ion in liquid
d
phasee
returned by Sini
returned byy Pox
PiniLiquid
PiniLiquid mgg/L
mg/L
Kn ref
0.0836
0.351
Kn 0-5
5
0.122
4.341
Kn 5-15
0.120
4.082
Lu ref
0.000488
8
0.076
Lu 0-5
0.712
266.226
Lu 5-15
5
0.780
201.02
Ri ref
0.676
0.737
Ri 0-5
0.558
7.377
Ri 5-15
5
0.751
7.100
3.2.2. pHdep
pendence expe
periments
Phosph
horus desorption was fouund to be verry sensitive tto pH (Fig. 10).
1
In veryy acid envirronments (p
pH<4.0), muuch phospho
orus would be
desorbeed; while pH
H stays from 4.0 to its no
ormal pH vallue (5.2 to 6..1),
less butt similar amount of phosp
phorus wouldd be desorbedd. However, ded
sorption
n increases aggain at higher pH; a smalll rise in pH frrom the norm
mal
pH con
ndition causees P desorptiion to increaase dramaticaally. Soils fro
om
differen
nt sites tendeed to have different sensittivity to pH cchange. In RinR
gamåla and Knivinggaryd, desorp
ption at loweer pH was o
obviously muuch
higher than at otheer pH condiitions; but in
n Luvehult ddesorption was
w
much higher
h
when alkali
a
was add
ded.
(a)
(b)
Fig.
g. 10. pH an
nd dissolved
d phosphorrus
con
ncentration in pH depen
ndence test:
(a) Knivingaryd
K
d;
(b) Luvehult;
L
(c) Ringamåla.
R
(c)
22
Lin Yu
TRITA LWR Degree Project 12:01
Wang et al. (2005) has also got similar results on the relation between pH
and phosphorus concentration during desorption process. Meanwhile
the influence of pH on sorption process is also different from that of
desorption. Similar conclusion is also drawn by Mohsen Jalali et al. (2011)
that H+ contribute most to the release of phosphorus from soil. As for
now, no general understanding of sorption/desorption processes is accepted by the academic field. It is still considered to be a mix of many
processes, such as “deposition”, “fixation”, “pricipitation” and “solidphase diffusion”. It is believe that the adsorption and desorption capacity of P with different sediments is a rather complex consequence of
multiple factors and their interactions, e.g., pH value, electrical conductivity, mineral or metal oxide type, particle size in related to the total surface area, organic matter, etc (Wang and Li, 2010). Indicated by this
study and study of Wang et al. (2005), the influence of pH was more
probably on fast reaction of sorption/desorption, but due to the lack of
experiment data and well-fit kinetics, it is still unknown if pH would also
impact the slow reaction of sorption/desorption.
The effort of trying to plot desorption isotherm with Freundlich isotherm has also turned out to be unsatisfying in this study. The hypothesis
was adopted that sorption/desorption was totally reversible before the
plotting. Estimated values of initial solid phase P from isotherm tests (Sini) were used at first, but the data based on those values had really bad
fitting. The r2 for Kn was 0.865, for Lu was 0.938 and for Ri was 0.742,
which are all worse than the fits for the sorption isotherms. The r2 for all
the three sites taken together was only 0.01, which can be considered as
an indication of no correlation. This result indicates that desorption
process is not a totally reversible process of sorption, and possibly that
the Freundlich isotherm is not the best model for the isotherm of
desorption. New isotherms for desorption should be applied. Many
researchers (Hooda et al., 2000; Lookman et al., 1995; Jalali and Varasteh, 2011) have suggested several isotherms and kinetics for the desorption of phosphorus in soils.
(a)
(b)
Fig. 11. Relations between desorbed
phosphorus and Al, Ca, Mg concentration
in
pH
dependence
experiments:
(a) Knivingaryd;
(b) Luvehult;
(c) Ringamåla.
(c)
23
Modeling the Longevity of Infiltration System for Phosphorus Removal
(a)
(b)
Fig. 12. Relations between pH and
Ca, Mg concentration in pH dependencen experiments:
(a) Knivingaryd;
(b) Luvehult;
(c) Ringamåla.
(c)
Fig. 11 shows the relationships between desorbed phosphorus and Al,
Ca and Fe concentration. The solution concentration of Al follows a
good linear correlation with desorbed P in all the three sites (in site
Luvehult two bad points were excluded), the linear r2 for Knivingaryd,
Luvehult and Ringamåla are 0.93, 0.90 and 0.87, but no apparent relations between Ca and P, Fe and P could be found. Fig. 12 shows a good
exponential correlation between pH and Ca & Mg concentration, but the
mechanisms among pH, metal (hydro) oxides and P sorption are still
unknown from these simple results.
Fig. 13. Solubility constants and heat of reaction for Ca phosphates
in this study
24
Lin Yu
TRITA LWR Degree Project 12:01
3.2.3. Chemical Speciation Results
Chemical speciation modeling was made using Visual MINTEQ (ver. 3.0,
Jon Petter Gustafsson, 2010). Of all the input concentrations to Visual
MINTEQ, Na+ and NO3- were calculated from the experiment design
details, and the rest are measured results from lab work. Four calcium
phosphates are studied as potential precipitates, which are amorphous
calcium phosphate, ACP ((Ca)3(PO4)2(s)), hydroxyapatite, Hap
(Ca5(PO4)3OH(s)), octacalcium phosphate, OCP (Ca4H(PO4)3(s)), monetite, DCP (CaHPO4(s)) and brushite, DCPD (CaHPO4·2H2O). The solubility constants of them were taken from one previous study of Kong
(2009), which can be seen in Fig. 13.
The results of chemical speciation for the calcium phosphates in the pH
dependence extracts are shown in Fig. 14. As is seen in the Fig. 14, only
HAp becomes supersaturated as pH increases to 6 or higher. It is consistent with the results from Kong (2009), while they had got more samples
supersaturated with respect to HAp than in this study, as well as samples
that were close saturation with respect to ACP. However their extracts
did not appear to precipitate as the model results indicate. The present
study shows that calcium phosphate probably did not control the solubility of P, as the solubility lines were much higher than the data from the
samples.
-24
-45
-26
ACP1
-28
-50
HAP
ACP2
-30
-32
-55
-34
-36
-60
-38
-40
-65
-42
-44
3
3.5
4
4.5
5
pH
5.5
6
6.5
-70
7
-40
3.5
4
4.5
5
pH
5.5
6
6.5
7
6
6.5
7
-12
-45
-13
OCP
-50
-14
-55
-15
-60
-16
-65
-17
-70
-18
-75
-19
-80
-20
-85
3
3
3.5
4
4.5
5
pH
5.5
6
6.5
-21
7
DCPD
DCP
3
3.5
4
4.5
5
pH
5.5
Fig. 14. Solubility diagrams for soils from horizons 0-5 cm and 5-15 cm of Knivingaryd, Luvehult and Ringamåla. The red + stands for results from Knivingaryd, the
blue circles stand for results from Luvehult and the cyan stars stand for results
from Ringamåla. Points above the lines represent supersaturation.
25
Modeling the Longevity of Infiltration System for Phosphorus Removal
3.3. Modeling results
3.3.1. Calculated Model Inputs
Some of the unknown inputs of the model were derived from the experiment data; sorption data, soil dry weight and soil texture data were used
in this study to calculate the inputs needed for model.
After optimization of the initial solid phosphorus concentration, the
returned Kf and I values for Knivingaryd, Luvehult and Ringamåla were
calculated from sorption data, they were 101.9201, 102.2282, 101.8278 and
0.4866, 0.3423, 0.5968. The I values in Kn and Ri were higher compared
with related studies on Freundlich isotherms; many researchers have
obtained I values around 0.35 (Gustafsson, 2011). Since limited soil data
were measured in the study sites, bulk density and volumetric water content can be only obtained in the 0-5 cm and 5-15 cm soil horizons. So in
the prediction of longevity for the studied sites, the average value of the
two surface horizons is used as input for the whole modeling column.
The bulk densities of Kn, Lu and Ri were 1.5642, 1.5901 and 1.56885
g/cm3, and the volumetric water content of Kn, Lu and Ri were 0.12035,
0.13375 and 0.12045 g/cm3.
3.3.2. Longevity prediction of Kn, Lu and Ri
Based on the input from Basic Scenario, the concentration of soil
column at a depth of 1 m is plot as Fig. 15. An obvious retardation can
be noticed in all the three soil columns, while when advective/dispersive
transport reaches the studying depth, the concentration of phosphorus
would increase dramatically. In the soil column from Kn, the P concentration would reach 1 mg/L at 1703th day, and on 2531th day, the
concentration would reach the inflow concentration (5 mg/L) of the system. For the soil column from Ri and Lu, the time to reach the critical
concentration and max concentration were 1674th day & 2709th day and
2575th day & 3673th day. By using the definition of longevity in this study,
the longevity of the three soil columns were 1703 days, 1674 days and
2575 days. The exhaustion time of the three soil columns under inflow
of 5 mg/L were 2531 days, 2709 days and 3673 days.
6
concentration: mg/L
5
4
3
Lu
2
1
0
Ri
0
500
Kn
1000
1500
2000
2500 3000
time: Day
3500
4000
4500
5000
Fig. 15. Results of Basic Scenario – the estimation of longevity for
soil column in three sampling sites
26
Lin Yu
TRITA LWR Degree Project 12:01
6
6
5
5
concentration: mg/L
concentration: mg/L
3.3.3. Effect of the Modeling time
4
3
2
1
0
4
3
2
1
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0
0
50
100
150
time: Day
time:Day
(a)
(b)
200
250
300
Fig. 16. Modeling results of Scenario 1 – Different modeling time:
(a) modeling time = 5000 days; (b) modeling time = 300 days
The preliminary modeling time in Basic Scenario was set to 5000 days.
The prediction from basic scenarios shows that, during most of the
modeling period, the P concentration at depth of 1 m is as high as the
inflow P concentration. Variations of modeling time were made to study
the impacts on the concentration at 1 m depth. Two sub-scenarios were
run on the basis of Scenario 0, while the modeling times in the two scenarios were 5000 days and 300 days, separately. The results can be seen
in Fig. 16. By plotting the time required to reach the critical concentration, it is found that the concentration curves are almost the same compared to the Scenario 0. However, the surface curves for all the modeling
time and depth are quite different in these three scenarios. The reason
for this is the discretization scheme in the numerical solution. For the
finite different method, the computation of every grid point depends on
the neighboring grids; while in this study, in order to keep the stability of
the numerical solution, a smaller time step was required during the discretization. It caused the model to be less sensitive in the change of
modeling time. Another reason is that, the study depth is the middle
point of the whole modeling depth, small change in the boundary conditions would be weaken because of too much grid points between the
study spot and the boundary.
3.3.4. Effect of the Soil Sorption Capacity
In order to study the impact of sorption capacity, a new scenario was set
up with the same soil properties for all three sites but remains their own
phosphorus sorption capacity, and the modeling time was set to be 300
days for a better visual effect. As Fig. 17 shows, with the same soil properties, the soil column from Ri has the longest life expectancy and Lu has
the shortest, which is the same as the Basic Scenario suggests. By comparing the longevity of this scenario with Basic Scenario, it is noticed that
both give similar results. This demonstrates the similarity of soil conditions of the three sampling sites.
27
Modeling the Longevity of Infiltration System for Phosphorus Removal
6
5
concentration: mg/L
Kn
4
Lu
3
Ri
2
1
0
0
50
100
150
time: Day
200
250
300
Fig. 17. Modeling results for the P sorption capacity comparison
It can also be easily concluded from Fig. 18 that a higher I value gives a
longer longevity of the soil column, and another curious appearance is
that a higher I value also extends the sorption time of the soil column.
While from the Fig. its appearance is the slope of the curve decreases as
I value increases, but in Fig. 18(a), since the change of Kf value is really
small in this sub-scenario, no obvious change in sorption time can be
observed. One extra test was done by varying the Kf in the range of real
situation (101.5, 101.8, 102), the result showed that the increasing Kf value
would also cause a longer sorption time, but the rise of sorption time is
much less comparing to the rise of Kf.
6
5
concentration: mg/L
Kf=0.5
4
Kf=1
Kf=2
3
Kf=3
2
Kf=5
1
0
0
50
100
150
time: Day
200
250
200
250
300
(a)
6
5
concentration: mg/L
I=0.25
4
I=0.35
I=0.45
3
I=0.55
I=0.7
2
1
0
0
50
100
150
time: Day
300
(b)
Fig. 18. Modeling results of Scenario 2 – Different P sorption
capacity: (a) sub-scenario 2.1; (b) sub-scenario 2.2.
28
Lin Yu
TRITA LWR Degree Project 12:01
The sorption capacity is the most import factor to evaluate the filter
material and researchers normally are using batch experiments and column experiments to evaluate the PSC of filter materials with sorption
isotherms. However, it is pointed out by Cucarella, V. and Renman, G.
(2009) that forms and amounts of filter materials, material to solution ratio, intial P concentration and contact time, agitation & temperature
would all have influences on the PSC results from batch experiments.
Concerning this study, it could also be possible the PSC achieved in this
study is overestimated comparing to real filed data, or even to column
experiment data.
3.3.5. Effect of inflow concentration and background concentration
Two sub-scenarios were run to test the sensitivity to the change of
inflow concentrations and background concentrations. Results are
shown in Fig. 19. The background concentration of the model, which is
also the initial condition in the ADE equation, has a very low influence
on the concentration change and life expectancy. The model is much
more sensitive to the change of inflow P concentration. As the inflow P
concentration decreases; both the time for the soil column to reach the
critical concentration and the time for the soil column to reach exhaustion would increase. In reality, the sewage phosphorus concentration can
be a key factor for the sorption of the infiltration beds and the longevity,
also changing inflow concentration may be expected in real infiltration
systems. But unfortunately, for normal household on-site infiltration
systems, it is expected to have an intermittent sewage inflow. The situation could be that, during peak hours such as morning or dinner time,
most sewage with a high P concentration would go into the infiltration
system, and for most time of the day, little or no sewage would be
emitted, with relatively lower concentration of phosphorus also. Both
flow condtions and sorption mechanisms could change due to the complicated sewage inflow, and more detailed modeling should be done to
cope with the real situation.
12
6
10
5
8
concentration: mg/L
concentration: mg/L
C2=10 mg/L
C2=8 mg/L
6
C2=5 mg/L
4
2
0
50
100
150
time: Day
3
2
1
C2=3 mg/L
0
4
200
250
0
300
(a)
0
50
100
150
time: Day
200
250
300
(b)
Fig. 19. Modeling results of Scenario 3 – Different inflow P concentration and
background P concentration: (a) sub-scenario 3.1; (b) sub-scenario 3.2, where
yellow line for c2 = 0.001 mg/L, red line for c2 = 0.015 mg/L, blue line for c2
= 0.05 mg/L and cyan line for c2 = 0.1 mg/L.
29
Modeling the Longevity of Infiltration System for Phosphorus Removal
6
5
concentration: mg/L
U=0.05 m/D
4
U=0.03 m/D
U=0.02 m/D
3
U=0.01 m/D
2
U=0.003 m/D
1
0
0
100
200
300
400
500
600
time: Day
700
800
900
1000
Fig. 20. Modeling results of Scenario 4 – Different flow velocity
(average pore velocity)
3.3.6. Sensitivity analysis of soil properties
Flow velocity: the average flow velocity was estimated by the amount of
sewage emission and infiltration bed areas from design criteria. It
affected the dispersion and advection at the same time in this study and
can be of considerable interest in the sensitivity analysis. Scenario 4 was
set up on the basis of Scenario 0, with changing velocities 0.003 m/D,
0.01 m/D, 0.02 m/D 0.03 m/D and 0.05 m/D. The results are shown in
Fig. 20.
Higher velocity gives a shorter retardation period for the soil to start
sorption, and at the same time shorter time for the soil to reach sorption
capacity. When velocity decreases, the life expectancy of the soil column
increases, and the increase is larger with decreasing velocity. In other
words, the model is more sensitive when the flow velocity is lower.
It is noticed that the above scenario is built on very small volumetric water content; it would somehow amplify the effect of velocity change
since in the model the flux velocity is applied for advective transport,
rather than the average pore velocity. The sensitivity of volumetric water
content is also interesting in this study, since it is both related with retardation and advection in transport equation. Scenario 5 is developed with
various volumetric water content and velocity, with results shown in
Fig. 21.
The smaller volumetric water content can contribute to a decrease of the
slope of the concentration curve, which means that it can increase the
longevity of the soil column and at the same time decrease the sorption
time of the system. However, from the above Fig., the increase of
longevity seems to be affteced by other factors such as velocity in Fig. 21,
and other factors may also have influence on the amount of longevity
change.
The last input of soil property in the model is the bulk density. From
equation (21) it is easy to see that the bulk density has the same sensitivity as the volumetric water content, but with an opposite direction of
change.
30
Lin Yu
TRITA LWR Degree Project 12:01
6
concentration: mg/L
5
4
3
Blue: U=0.03, theta=0.08
Red: U=0.03, theta=0.12
Cyan: U=0.03, theta=0.2
Green: U=0.01,theta=0.08
Yellow: U=0.01, theta=0.12
Black: U=0.01, theta=0.2
2
1
0
0
100
200
300
400
500
600
time: Day
700
800
900
1000
Fig. 21. Modeling results of Scenario 5 – Different volumetric
water contents under two flow velocities
It needs to be pointed out that the flow velocity in this modeling study is
quite simplified due to the lack of data for soil properties and limited
time. Even for the estimation of bulk density and volumetric water
content, simplified equations and methods were applied. Theoretically
the better way for the required soil properties in the model should be direct measurement, and the input of flow velocity should be based on the
real situation as mentioned in last section, and also based on flow equations, where even more details of flow conditions could be used for the
estimation of dispersion coefficient in the Advection-Dispersion equation.
3.3.7. Sorption capacity study and sorption velocity
5
5
4.5
4.5
4
4
t=1703 D
3.5
3
concentration: mg/L
concentration: mg/L
3.5
t=2531 D
2.5
2
1.5
2.5
t=3673 D
2
1.5
1
1
0.5
0.5
0
t=2575 D
3
0
0.2
0.4
0.6
0.8
1
1.2
depth: m
1.4
1.6
1.8
0
2
(a)
0
0.2
0.4
0.6
0.8
1
1.2
depth: m
1.4
1.6
1.8
2
(b)
5
Fig. 22. Soil column P concentration
distribution, red lines represent the time
for depth = 1 m to reach 1 mg/L, the
blue lines represent the time for depth
= 1 m to reach inflow concentration:
(a) Knivingaryd;
(b) Luvehult;
(c) Ringamåla.
4.5
t=1674 D
4
concentration: mg/L
3.5
3
t=2709 D
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
0.8
1
1.2
depth: m
1.4
1.6
1.8
2
(c)
31
Modeling the Longevity of Infiltration System for Phosphorus Removal
It is well accepted that the sorption capacity can not be fully predicted
based on the Freundlich isotherm. As in this study, the sorption capacity
of the soil can be determined by the coefficient Kf and I in equation (17),
and the only available outcome based on those coefficients is the maximum P sorption under a certain inflow concentration. Compared to the
phosphorus sorption capacity (Spsc) used in equation (1), the maximum P
sorption under a certain inflow is a much reasonable value to predict the
longevity of sorbents/infiltration beds using that method. However, the
time to reach maximum P sorption and the time to reach critical P concentration are also different. As shown in Fig. 17, the time for Lu to
reach the critical concentraton at 1 m depth is 2575 days, and the time
for Lu to reach its exhaustion at 5 mg/L inflow P concentration is 3673
days.
In fact the sorbed phosphorus in the soil column can be calculated based
on the result of the model if the size and density of the soil column is
known.
100
(33)
Stotal = m × ∑ K f C ( x, t ) I
n =1
Where Stotal is the sorbed quantity of phosphorus, m is the unit mass for a
single model cell shown in Fig. 4, and t here is a fixed number. Since the
column soil with 1 m depth is divided into 100 cells in this study, the
accumulated number is set to be 100. The calculated sorbed phosphorus
quantity for soil from sites Kn, Lu and Ri when they reach the critical
concentration are 0.177, 0.288 and 0.168 mg/g, while the maximum
sorption of Kn, Lu and Ri are 0.182, 0.293 and 0.176 mg/g separately. It
is obvious that after the concentration reaches critical concentration,
actually not much P would be sorbed into the soil column in all the sites,
which can be easier to infer from Fig. 22.
300
Lu
250
sorption: ug/kg
200
150
Kn
100
Ri
50
0
0
500
1000
1500
2000
time: Day
2500
3000
3500
4000
Fig. 23. Relation between P sorption and time in soil column
from 0 to 1 m.
32
Lin Yu
TRITA LWR Degree Project 12:01
Based on equation (33), the time is varied from 1 to 4000 days to get the
relation between sorption quantity and time for a 1-m soil column,
which can be seen in Fig. 22. The sorption P in the soil column seems to
have a linear relation with time before the concentration start to increase
at depth 1 m, when the concentration at 1 m starts to increase; the sorption curve slows to increase and finally stops at a peak value when the
concentration reaches the inflow concentration. The reasons for this are
the assumption of instant sorption and the homogeneity and isotrope of
the soil. Once the sewage enters a modeled layer, instant sorption would
happen, and before this layer reaches inflow concentration, the next
modeled layer will not have sorption. Since the inflow concentration and
flow velocity are set to be the same in all the three sites, it is not strange
to have the sorption curves in Fig. 23 paralleled, because the rates of the
curves are the inflow P into the soil column per unit time.
The disficiency of the sorption velocity prediction in this study is quite
obvious. Since only the fast sorption is considered in this study, the sorption velocity attained by this model turns out to be very linear and starts
with an abrupt big velue. The need for the sorption isotherm is quite
essential in the analysis of sorption rate, at the same time, as discussed in
previous section, batch experiment could also be a big uncertainty in the
sorption rate predisction, because it would more or less accelerate the
sorption process. If the intermittent flow is also considered in the model,
the situation of sorption rate could be even more complex since desorption process might also happen in the system. Anyhow, it is possible to
analyse the sorption capacity and sorption rate of the system if the
concentration curve is well studied.
3.4. D ISCUSSION ON MODELING RESULTS
3.4.1. Factors influencing the longevity of soil column
From the results of modeling study, the most sensitive factors for P concentration in soil column to reach critical concentration are the flow
velocity and the P sorption capacity of the soil. Lower flow velocity and
higher P sorption capacity extend the longevity of an infiltration bed. A
literature study on different soil shows that soil with higher proportion
of small-size particles such as clay tends to have higher phosphorus sorption capacity (McGechen et al., 2002a; b). Normally clay soil has lower
bulk density and higher volumetric water content than the soil in this
study, which is coarse sand. The model results also show that a lower
bulk density and a higher volumetric water content will extend the
longevity of the soil column. So a conclusion can be drawn that soil with
a high proportion of small-sized particles also has longer longevity when
used as soil column for infiltration. It is easier to understand that a
higher P sorption capacity would lead to higher longevity of soil column.
A much longer longevity is estimated in Luvehult than in the other two
sites. It is obvious to notice that in a sample with soil from surface
horizons Luvehult, higher solution P concentrations are measured after
batch experiments, and much higher Sini are estimated also. It is also
concluded in this study that oxalate-extractable Al and Fe are correlated
to P sorption, of which Al is more related to the fast reaction and Fe is
more related to the slow reaction. Meanwhile, other researchers have
pointed out that soils containing high proportions of Al or Fe oxide
minerals have particularly high P sorption capacity (Bowden et al., 1977;
Robertson, 2003; Zanini et al., 2003). In a comparative study, Singh et al.
(2005) also found highest P sorption with high amounts of Fe, Al and
clay particles.
33
Modeling the Longevity of Infiltration System for Phosphorus Removal
Another very sensitive parameter in the model is the average pore
velocity, in this thesis mostly referred to as the flow velocity. A constant
insistent influent is assumed in the conceptual model, with a quite high
flow velocity 0.03 m/D. From the sensitivity analysis, it can be noticed
that in lower range of flow velocity, the longevity of a soil column is very
sensitive to the change of flow velocity. As a matter of fact, the assumption made in conceptual models about the flow velocity can be quite
unrealistic in experimental column studies, not to mention in the real
infiltration system. However, principally lower velocity or in other lower
sewage load would result in a longer longevity of soil column.
3.4.2. Longevity of infiltration bed and evaluations with current method
The results from the Basic Scenario show the longevity estimation based
on the current model. Compared to the service time of those infiltration
sites, the longevity estimation by this model is relatively short. From the
Fig. 8(b), it is clearly noticed that the estimated Sini is much smaller than
the measured Pox, which indicates the necessity to add time as a controlling factor for P sorption in soil. However, it is really difficult to make a
simple judgment as to whether the estimated longevity after applying
sorption kinetics would be bigger or smaller than the previous model,
since the ADE equation in the model would change.
In order to make a comparison with the first method mentioned in the
introduction part, the inflow P concentration was recalibrated according
to the literature (Xu and et al., 2006; Seo et al., 2005; Drizo et al., 2002;
Drizo et al., 1999). This gives a new inflow P concentration of
9.333 mg/L. Based on this inflow, the estimated longevity is shown in
Fig. 22. The calculated maximum sorption P under 9.333 mg/L P inflow
for Kn, Lu and Ri are 0.247, 0.255 and 0.363 g/kg separately. According
to Fig. 24, this will lead to longevities of 1243, 1746 and 1295 days for
sites Kn, Lu and Ri. Considering the difference of the substrates’ bulk
densities, the estimated longevity is of the same order as those in the literature study. From the results in section 3.3.7, it can be seen that for the
1-m soil column, all the P from inflow would be sorbed instantly before
the concentration at 1 m starts to increase. Since in this model, instant
equilibrium is assumed in every layer. So when the concentration at 1 m
depth starts to increase, in fact the previous soil layer has already reached
its sorption maximum according to equation (17).
X: 1865
Y: 9.333
10
9
X: 2128
Y: 9.333
8
Kn
Ri
7
concentration: mg/L
X: 2507
Y: 9.333
6
Lu
5
4
3
2
X: 1243 X: 1746
Y: 1.004 Y: 1.003
1
0
X: 1295
Y: 1.001
0
500
1000
1500
2000
2500 3000
time: Day
3500
4000
4500
5000
Fig. 24. Estimated longevity of soil columns under sewage P
concentration of 9.333 mg/L.
34
Lin Yu
TRITA LWR Degree Project 12:01
Therefore, although the theoretical definition of longevity in the first
method from literature review is wrong, it gives a result of system
longevity that is very close compared to the result from the model study.
However, another big problem is the phosphorus sorption capacity (Spsc)
used in this method. According to Drizo et al. (2002), they increase the P
concentration in inflow until the substrate no longer sorbs more phosphate, and the maximum sorption is then taken as Spsc. Firstly, this sorption capacity is only the maximum fast P pool of the substrate since the
incubation time of their study is very short. Secondly, for normal sewage
in infiltration systems, it is unknown if this Spsc would be reached by the
soil under low inflow concentration, and if this can be reached, it must
take a really long period of sorption, which can be concluded from
Fig. 8(b).
For the second method from literature study, since no P sorption
quantity is measured in their study, it is really difficult to compare with
the model estimation. However, during the estimated longevity in the
second method, the substrate is quite reliable for P removal since it is
based on experiment data. The problems in those studies are that the
estimated longevity might be underestimated, which may lead to substrates being changed too early compared to their real longevity.
4. F URTHER STUDY
4.1. Boundary Condition
One uncertainty of this model is the assumption for the boundary condition at C(2,t). The correct boundary condition should be that the concentration at infinite distance is always 0, but that is really unrealistic for
the numerical solution of the PDE equation. Normally the boundary of
the model should be set as the boundary of the study area, but due to the
lack of relative data, the model boundary is enlarged in order to ease up
the influence of the unsure boundary condition on the study area. This is
also the reason why the modeling time is set to be quite long, so that all
the modeling results of the study area are ideal results from advection,
dispersion and retardation. Further research needs to be done to make a
better boundary condition for the model, or as Van der Zee et al. (1992)
did, discuss about alternative boundary conditions.
4.2. Flow velocity & hydrogeology
The estimation of flow velocity in the study is really simplified and not
much hydrogeological details are considered in the model of soil column.
In reality, groundwater flow is quite complicated and influenced by many
factors. A possible way of acquiring flow velocity is solving flow
equation, which in the unsaturated condition is known as Richards’ equation. This also requires many hydrogeology properties as input, and
boundary conditions as well, because Richards’ equation itself is also a
partial differential equation. Nicholas J. Jarvis and colleagues have done
modeling work with a model named MACRO, which also includes
macropore flow. Further development of the model could also try to
coup the flow equation with the ADE equation in order to have more
accurate flow velocity input for the model. This effort can also help the
model to be applicable not only in soil column study in the lab, but also
in some real infiltration systems with well studied soil properties.
4.3. Desorption & Operation Mode
Some of the infiltration beds are divided into two or more parts. One of
them is run for sewage treatment, while the rest of them are kept free in
order to recover the treatment capacity of the soil. So it is an interesting
35
Modeling the Longevity of Infiltration System for Phosphorus Removal
topic to study the recovered capacity of soil column for P removal.
However, the recovery of P sorption capacity of soil is mainly controlled
by desorption process, which are not discussed in detail in this study.
Because the recovery process is more controlled by natural precipitation
rather than the sewage inflow, climate data are also necessary for the
recovery capacity modeling. Besides, for most of infiltration beds, the
sewage inflows are not always consistent, and intermittent sewage inflow
also might include the process of desorption. Further study can focus on
the desorption isotherms of phosphorus in the soil, the combine of both
sorption and desorption in the transport model would give more reasonable consequence for the longevity study of infiltration beds. It is
suggested to use sorption/desorption kinetics in further development of
the model, so that the model would be more applicable to the real infiltration system.
4.4. Influence of pH
Further study can also focus on ascertaining the pH influence on the P
sorption capacity, by designing of new experiment strategies. By integrating the isotherms which include the pH into the ADE equation, new improved models can be derived for simulation of the longevity of
infiltration beds.
36
Lin Yu
TRITA LWR Degree Project 12:01
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A. A. Balkema Publishers: New York; pp. 253 – 279.
Barrow, N.J. 1978. The description of phosphate adsorption curves. Soil
Science. 29: 447–462.
Bowden, J.W., Posner, A., Quirk, J. 1977. Ionic adsorption on variable
charge mineral surfaces. Theoretical-charge development and titration
curves. Australian Journal of Soil Research. 15: 121–136.
Cheung, K.C., Venkitachalam, T.H. 2006. Kinetic studies on phosphorus
sorption by selected soil amendments for septic tank effluent renovation. Environmental Geochemistry and Health. 28:121–131.
Cucarella, V., Renman, G. 2009. Phosphorus Sorption Capacity of Filter
Materials Used for On-site Wastewater Treatment Determined in
Batch Experiments–A Comparative Study. Journal of Environmental
Quality. 38(2), 381-392.
Delleur, J. 1999. The handbook of groundwater engineering. CRC Press LLC:
Boca Raton; pp. 96-102.
Drizo, A., Comeau, Y., Forget, C., Chapuis, R.P. 2002. Phosphorus Saturation Potential: A Parameter for Estimating the Longevity of Constructed Wetland Systems. Environmental Science and Technology. 36 (21),
4642-4648.
Drizo, A., Frost, C.A., Grace, J., Smith, K.A. 1999. Physical-chemical
screening of phosphate-removing substrates for use in constructed
wetland systems. Water Research 33(17): 3595 - 3602.
Eveborn, D., Gustafsson, J.P., Holm, C. 2009. Fosfor i infiltrationsbäddar –
fastläggning, rörlighet och bedömningsmetoder. Svenskt Vatten Utveckling,
Rapport nr 2009-07, Stockholm.
Gustafsson, J.P., Jacks, G., , Simonsson, M., Nilsson, I. 2007. Soil and water chemistry. KTH Department of Land and Water Resources Engineering, Stockholm; pp. 60 – 72.
Heistad, A., Paruch, A.M., Vråle, L., Adam, K., Jenssen, P.D. 2006. A
high–performance compact filter system treating domestic wastewater. Ecological Engineering. 28: 374–379.
Hocking, M.B. 2006. Handbook of Chemical Technology and Pollution Control
(third edition). Elsevier Science & Technology Books, Amsterdam; p.
297.
Hooda, P.S., Rendell, A.R., Edwards, A.C., Withers, P.J.A., Aitken, M.N.,
Truesdale, V.W. 2000. Relating soil phosphorus indices to potential
phosphorus release to water. Journal of Environmental Quality. 29: 1166–
1171.
Jalali, M., Khanlar, Z.V. 2011. The Impacts of Common Ions and Electrolyte Concentration on the Release of P from Some Calcareous
Soils. Arid Land Research and Management. 25: 217 – 233.
Jalali, M., Zinli, N.A.M. 2011. Kinetics of phosphorus release from calcareous soils under different land use in Iran. J. Plant Nutr. Soil Sci. 174:
38 – 46.
Johansson, M. 2008. The market for onsite sustainable sanitation technologies – an example from Sweden. In Report of the World Water Week
Seminar: Europe’s Sanitation Problem: Stockholm.
Kafkafi, U., Posner, A.M., Quirk, J.P. 1967. Desorption of phosphate
from kaolinite. Soil Science Society of America Proceedings. 31: 348–353.
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Modeling the Longevity of Infiltration System for Phosphorus Removal
Kong, D. 2009. Phosphate sorption in soil infiltration systems for
wastewater treatment. TRITA LWR Degree Project 09:19. KTH, Department of Land and Water Resources Engineering, Stockholm.
Laak, R. 1986. Wastewater engineering design for unsewered areas.
Technomic Publishers, The Hague, Netherlands.
Lookman, R., Freese, D., Merckx, R., Vlassek, K., van Riemsdijk, W.H.
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Mathews, J.H., Fink, K.D. 2004. Numerical Methods Using Matlab (4th Edition). Prentice Hall, Upper Saddle River; pp. 514 – 554.
McGechan, M.B., Lewis, D.R. 2002. Sorption of Phosphorus by Soil,
Part 1: Principles, Equations and Models. Biosystems Engineering. 82 (1):
1–24.
McGechan, M.B. 2002. Sorption of Phosphorus by Soil, Part 2: Measurement Methods, Results and Model Parameter Values. Biosystems
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McWorter, S. 1977. Ground-water hydrology and hydraulics. Water Resources
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Notodarmojo, S., Ho, G.E., Scott, W.D., Davis, G.B. 1991. Modeling
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Robertson, W.D. 2003. Enhanced Attenuation of Septic System Phosphate in Nocalcareous Sediments. Ground Water. 41: 48 – 56.
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38
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van der Zee, S.E.A.T.M., Gjaltema A, van Riemsdijk, W.H., de Haan,
F.A.M. 1992. Simulation of phosphate transport in soil columns. II.
Simulation results. Geoderma. 52 (1-2): 111–132.
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Wikipedia.
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39
Modeling the Longevity of Infiltration System for Phosphorus Removal
40
Lin Yu
TRITA LWR Degree Project 12:01
A PENDIX I – M EASURED DRY WEIGHT OF SOIL
SAMPLES
Measured dry weight of soil samples
Sample
Dry Weight (g/g)
Ri ref 1
0.978
Kn ref 1
0.965
Lu ref grov
0.972
Tu ref
0.963
Gl 0-5
0.836
Ri 0-5
0.902
Tu 5-15
0.878
Ha 5-15
0.923
Kn 5-15
0.926
Ri 5-15
0.946
Lu 5-15
0.925
Ha 0-5
0.942
Lu 0-5
0.907
Kn 0-5
0.920
Gl ref 0-5
0.825
Gl ref 5-15
0.879
Ha ref 2
0.976
Gl 5-15
0.822
Tu 0-5
0.332
Ha ref 1
0.970
1
Modeling the Longevity of Infiltration System for Phosphorus Removal
A PENDIX II – M EASURED OXALATE - SOLUBLE
PHOSPHORUS OF SOIL SAMPLES
Oxalate-soluble Phosphorus
Sample
Oxalate-soluble P mg/g
Gl ref 0-5
0.202
Gl ref 5-15
0.109
Gl 0-5
0.274
Gl 5-15
0.215
Ha 0-5
0.248
Ha 5-15
0.200
Ha ref 1
0.0134
Ha ref 2
0.0115
Kn 0-5
0.168
Kn 5-15
0.164
Kn ref
0.0480
Lu 0-5
1.143
Lu 5-15
1.043
Lu ref grov
0.0695
Ri 0-5
0.221
Ri 5-15
0.216
Ri ref 1
0.0554
Tu 0-5
2.226
Tu 5-15
0.323
Tu ref
0.152
2
Lin Yu
TRITA LWR Degree Project 12:01
A PPENDIX III: B ATCH E XPERIMENT LAB DESIGN
27: 10 ml A, 0.5 ml P, 19.5 ml H2O
28: 10 ml A, 1 ml P, 19 ml H2O
29: 10 ml A, 1.5 ml P, 18.5 ml H2O
30: 10 ml A, 2 ml P, 18 ml H2O
31: 10 ml A. 3 ml P, 17 ml H2O
32: 10 ml A, 5 ml P, 15 ml H2O
Series A - 5d equilibration of soils.
Solutions:
A = 0.03 M NaNO3
B = 0.03 M HNO3
E = 0.03 M NaOH
P = 3 mM NaH2PO4
PL = 0.3 mM NaH2PO4
4 g of Lu 0-5
33: 10 ml A, 20 ml H2O
34: 10 ml A, 2 ml PL, 18 ml H2O
35: 10 ml A, 0.5 ml P, 19.5 ml H2O
36: 10 ml A, 1 ml P, 19 ml H2O
37: 10 ml A, 1.5 ml P, 18.5 ml H2O
38: 10 ml A, 2 ml P, 18 ml H2O
39: 10 ml A. 3 ml P, 17 ml H2O
40: 10 ml A, 5 ml P, 15 ml H2O
4 g of Kn ref 1
1: 10 ml A, 20 ml H2O
2: 10 ml A, 2 ml PL, 18 ml H2O
3: 10 ml A, 0.5 ml P, 19.5 ml H2O
4: 10 ml A, 1 ml P, 19 ml H2O
5: 10 ml A, 1.5 ml P, 18.5 ml H2O
6: 10 ml A, 2 ml P, 18 ml H2O
7: 10 ml A. 3 ml P, 17 ml H2O
8: 10 ml A, 5 ml P, 15 ml H2O
4 g of Lu 5-15
41: 10 ml A, 20 ml H2O
42: 10 ml A, 2 ml PL, 18 ml H2O
43: 10 ml A, 0.5 ml P, 19.5 ml H2O
44: 10 ml A, 1 ml P, 19 ml H2O
45: 10 ml A, 1.5 ml P, 18.5 ml H2O
46: 10 ml A, 2 ml P, 18 ml H2O
47: 10 ml A. 3 ml P, 17 ml H2O
48: 10 ml A, 5 ml P, 15 ml H2O
4 g of Kn 0-5
9: 10 ml A, 20 ml H2O
10: 10 ml A, 2 ml PL, 18 ml H2O
11: 10 ml A, 0.5 ml P, 19.5 ml H2O
12: 10 ml A, 1 ml P, 19 ml H2O
13: 10 ml A, 1.5 ml P, 18.5 ml H2O
14: 10 ml A, 2 ml P, 18 ml H2O
15: 10 ml A. 3 ml P, 17 ml H2O
16: 10 ml A, 5 ml P, 15 ml H2O
4 g of Kn 5-15
17: 10 ml A, 20 ml H2O
18: 10 ml A, 2 ml PL, 18 ml H2O
19: 10 ml A, 0.5 ml P, 19.5 ml H2O
20: 10 ml A, 1 ml P, 19 ml H2O
21: 10 ml A, 1.5 ml P, 18.5 ml H2O
22: 10 ml A, 2 ml P, 18 ml H2O
23: 10 ml A. 3 ml P, 17 ml H2O
24: 10 ml A, 5 ml P, 15 ml H2O
4 g of Lu ref grov
25: 10 ml A, 20 ml H2O
26: 10 ml A, 2 ml PL, 18 ml H2O
3
Modeling the Longevity of Infiltration System for Phosphorus Removal
28: 10 ml A, 1 ml P, 19 ml H2O
29: 10 ml A, 1.5 ml P, 18.5 ml H2O
30: 10 ml A, 2 ml P, 18 ml H2O
31: 10 ml A. 3 ml P, 17 ml H2O
32: 10 ml A, 5 ml P, 15 ml H2O
Series B - 5d equilibration of soils.
Solutions:
A = 0.03 M NaNO3
B = 0.03 M HNO3
E = 0.03 M NaOH
P = 3 mM NaH2PO4
PL = 0.3 mM NaH2PO4
4 g of Tu 0-5
33: 10 ml A, 20 ml H2O
34: 10 ml A, 2 ml PL, 18 ml H2O
35: 10 ml A, 0.5 ml P, 19.5 ml H2O
36: 10 ml A, 1 ml P, 19 ml H2O
37: 10 ml A, 1.5 ml P, 18.5 ml H2O
38: 10 ml A, 2 ml P, 18 ml H2O
39: 10 ml A. 3 ml P, 17 ml H2O
40: 10 ml A, 5 ml P, 15 ml H2O
4 g of Ri ref 1
1: 10 ml A, 20 ml H2O
2: 10 ml A, 2 ml PL, 18 ml H2O
3: 10 ml A, 0.5 ml P, 19.5 ml H2O
4: 10 ml A, 1 ml P, 19 ml H2O
5: 10 ml A, 1.5 ml P, 18.5 ml H2O
6: 10 ml A, 2 ml P, 18 ml H2O
7: 10 ml A. 3 ml P, 17 ml H2O
8: 10 ml A, 5 ml P, 15 ml H2O
4 g of Tu 5-15
41: 10 ml A, 20 ml H2O
42: 10 ml A, 2 ml PL, 18 ml H2O
43: 10 ml A, 0.5 ml P, 19.5 ml H2O
44: 10 ml A, 1 ml P, 19 ml H2O
45: 10 ml A, 1.5 ml P, 18.5 ml H2O
46: 10 ml A, 2 ml P, 18 ml H2O
47: 10 ml A. 3 ml P, 17 ml H2O
48: 10 ml A, 5 ml P, 15 ml H2O
4 g of Ri 0-5
9: 10 ml A, 20 ml H2O
10: 10 ml A, 2 ml PL, 18 ml H2O
11: 10 ml A, 0.5 ml P, 19.5 ml H2O
12: 10 ml A, 1 ml P, 19 ml H2O
13: 10 ml A, 1.5 ml P, 18.5 ml H2O
14: 10 ml A, 2 ml P, 18 ml H2O
15: 10 ml A. 3 ml P, 17 ml H2O
16: 10 ml A, 5 ml P, 15 ml H2O
4 g of Ri 5-15
17: 10 ml A, 20 ml H2O
18: 10 ml A, 2 ml PL, 18 ml H2O
19: 10 ml A, 0.5 ml P, 19.5 ml H2O
20: 10 ml A, 1 ml P, 19 ml H2O
21: 10 ml A, 1.5 ml P, 18.5 ml H2O
22: 10 ml A, 2 ml P, 18 ml H2O
23: 10 ml A. 3 ml P, 17 ml H2O
24: 10 ml A, 5 ml P, 15 ml H2O
4 g of Tu ref
25: 10 ml A, 20 ml H2O
26: 10 ml A, 2 ml PL, 18 ml H2O
27: 10 ml A, 0.5 ml P, 19.5 ml H2O
4
Lin Yu
TRITA LWR Degree Project 12:01
26:
27:
28:
29:
30:
Series C - 5d equilibration of soils.
Solutions:
A = 0.03 M NaNO3
B = 0.03 M HNO3
E = 0.03 M NaOH
4 g of Ri 5-15
31:
32:
33:
34:
35:
36:
4 g of Kn 0-5
1:
2:
3:
4:
5:
6:
10 ml A, 3 ml B, 17 ml H2O
10 ml A, 2 ml B, 18 ml H2O
10 ml A, 1 ml B, 19 ml H2O
10 ml A, 0.5 ml B, 19.5 ml H2O
10 ml A, 20 ml H2O
10 ml A, 0.5 ml E, 19.5 ml H2O
37:
38:
39:
40:
41:
42:
10 ml A, 3 ml B, 17 ml H2O
10 ml A, 2 ml B, 18 ml H2O
10 ml A, 1 ml B, 19 ml H2O
10 ml A, 0.5 ml B, 19.5 ml H2O
10 ml A, 20 ml H2O
10 ml A, 0.5 ml E, 19.5 ml H2O
43:
44:
45:
46:
47:
48:
10 ml A, 3 ml B, 17 ml H2O
10 ml A, 2 ml B, 18 ml H2O
10 ml A, 1 ml B, 19 ml H2O
10 ml A, 0.5 ml B, 19.5 ml H2O
10 ml A, 20 ml H2O
10 ml A, 0.5 ml E, 19.5 ml H2O
4 g of Lu 5-15
19:
20:
21:
22:
23:
24:
10 ml A, 3 ml B, 17 ml H2O
10 ml A, 2 ml B, 18 ml H2O
10 ml A, 1 ml B, 19 ml H2O
10 ml A, 0.5 ml B, 19.5 ml H2O
10 ml A, 20 ml H2O
10 ml A, 0.5 ml E, 19.5 ml H2O
4 g of Ri 0-5
25:
10 ml A, 3 ml B, 17 ml H2O
10 ml A, 2 ml B, 18 ml H2O
10 ml A, 1 ml B, 19 ml H2O
10 ml A, 0.5 ml B, 19.5 ml H2O
10 ml A, 20 ml H2O
10 ml A, 0.5 ml E, 19.5 ml H2O
4 g of Tu 5-15
4 g of Lu 0-5
13:
14:
15:
16:
17:
18:
10 ml A, 3 ml B, 17 ml H2O
10 ml A, 2 ml B, 18 ml H2O
10 ml A, 1 ml B, 19 ml H2O
10 ml A, 0.5 ml B, 19.5 ml H2O
10 ml A, 20 ml H2O
10 ml A, 0.5 ml E, 19.5 ml H2O
4 g of Tu 0-5
4 g of Kn 5-15
7:
8:
9:
10:
11:
12:
10 ml A, 2 ml B, 18 ml H2O
10 ml A, 1 ml B, 19 ml H2O
10 ml A, 0.5 ml B, 19.5 ml H2O
10 ml A, 20 ml H2O
10 ml A, 0.5 ml E, 19.5 ml H2O
10 ml A, 3 ml B, 17 ml H2O
5
10 ml A, 3 ml B, 17 ml H2O
10 ml A, 2 ml B, 18 ml H2O
10 ml A, 1 ml B, 19 ml H2O
10 ml A, 0.5 ml B, 19.5 ml H2O
10 ml A, 20 ml H2O
10 ml A, 0.5 ml E, 19.5 ml H2O
Modeling the Longevity of Infiltration System for Phosphorus Removal
A PPENDIX IV: E MPIRICAL DATA FOR POROSITY
CALCULATION
Empirical data for porosity calculation
Material
Total Porosity, n
Range
Arithmetic Mean
Sandstone
(medium)
0.14 - 0.49
0.34
Siltstone
0.21 – 0.41
0.35
Sand (fine)
0.25 – 0.53
0.43
Sand (coarse)
0.31 – 0.46
0.39
Gravel (fine)
0.25 – 0.38
0.34
Gravel (coarse)
0.24 – 0.36
0.28
Silt
0.34 – 0.51
0.45
Clay
0.34 – 0.57
0.42
Limestone
0.07 -0.52
0.3
Weathered
granite
0.34 -0.57
0.45
Weathered
gabbro
0.42 – 0.45
0.43
Basalt
0.03 - 0.35
0.17
Schist
0.04 – 0.49
0.38
Source: McWorter and Sunada (1977).
h
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Lin Yu
TRITA LWR Degree Project 12:01
A PPENDIX V: C OMPARISON OF DESORBED P BETWEEN
ACID SAMPLE AND NON - ACID SAMPLE OF P H
DEPENDENCE TEST (X AXIS : SAMPLE NUMBER ; Y AXIS :
P CONCENTRATION MG /L)
2500
2000
2000
1500
Kn 0‐5
1500
Kn 5‐15
1000
1000
Kn 0‐5 acid
500
Kn 5‐15 acid
500
0
0
1
2
3
4
5
6
1
3000
2500
2500
2000
2000
Lu 0‐5
4
5
6
Lu 5‐15 acid
500
0
Lu 5‐15
1000
Lu 0‐5 acid
500
3
1500
1500
1000
2
0
1
2
3
4
5
6
1
2
3
4
5
6
5000
7000
6000
5000
4000
3000
2000
1000
0
4000
Ri 5‐15
3000
Ri 0‐5
2000
Ri 0‐5 acid
Ri 5‐15 acid
1000
0
1 2 3 4 5 6
1
7
2
3
4
5
6
Modeling the Longevity of Infiltration System for Phosphorus Removal
A PPENDIX VI: M ATLAB C ODES FOR M ODELING
pdeadeT.m: main m-file for the solution of the ADE equation in the
model
function pdeadeT
% input parameters
m = 0;
a=2;
b=1000;
x = linspace(0,a,a*100);
t = linspace(0,b,b*10);% n is the estimated time for x=1 to reach
0.1mg/L
sol = pdepe(m,@pdeadeTpde,@pdeadeTic,@pdeadeTbc,x,t);
u = sol(:,:,1);
Fig.
plot(t,u(:,100),'r');
% define the ADE equation
function [c,f,s] = pdeadeTpde(x,t,u,DuDx)
a=2;
U=0.03;
alpha=0.1*a;
[Kf,I]=isotherms(sorptions);
[theta,porosity,BD]=soilp(soilprofile,Dryweight);
DL=U*alpha;
v=U/mean(theta(3,:));
c=1+mean(BD(3,:))/mean(theta(3,:))*I(3)*Kf(3)*u^(I(3)-1);
f=DL*DuDx;
s=-v*DuDx;
% define initial condition
function u0=pdeadeTic(x)
c1=0.015;
u0=c1;
% define boundary condition
function [pl,ql,pr,qr] = pdeadeTbc(xl,ul,xr,ur,t)
b=1000;
c1=0.015;
c2=5;
pl=ul-c2;
ql=0;
pr=ur(1)-c1-(1-c1)/b*t;
qr=0;
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Lin Yu
TRITA LWR Degree Project 12:01
Isotherm.m: the m-file for isorthem plotting which returns parameter Kf
and I to the main program
function [Kf,I]=isotherms(sorptions)
load sorptions.txt;
j=length(sorptions);
K=zeros(j,1);
K1=zeros(j,1);
K=sorptions(:,3);
for num=1:j
K1(num,1)=log10((sorptions(num,1)+sorptions(num,2))/1000/0.004/so
rptions(num,4));
end
Kn=[K(1:21)
K1(1:21)];Kn0=[K(1:7)
K1(1:7)];Kn5=[K(8:14)
K1(8:14)];Kn15=[K(15:21) K1(15:21)];
Lu=[K(22:41) K1(22:41)];Lu0=[K(22:27) K1(22:27)];Lu5=[K(28:34)
K1(28:34)];Lu15=[K(35:41) K1(35:41)];
Ri=[K(42:62)
K1(42:62)];Ri0=[K(42:48)
K1(42:48)];Ri5=[K(49:55)
K1(49:55)];Ri15=[K(56:62) K1(56:62)];
m1=sorptions(:,1);m2=sorptions(:,2);m3=sorptions(:,4);
% select the best value for sampling site Kn
[ c1,c2 ] = MultiLineReg( Kn0(:,1),Kn0(:,2) );
[ c3,c4 ] = MultiLineReg( Kn5(:,1),Kn5(:,2) );
[ c5,c6 ] = MultiLineReg( Kn15(:,1),Kn15(:,2) );
[ c7,c8 ] = MultiLineReg( Kn(:,1),Kn(:,2) );
mx=c2+c4+c6+c8*3;
R1=linspace(0.8*m1(1),1.2*m1(1),50);R2=linspace(0.8*m1(8),1.2*m1(8),
50);R3=linspace(0.8*m1(15),1.2*m1(15),50);
mx=0;KnB=m1(1:21);
for i=1:50
for j=1:50
for k=1:50
m4(1:7)=R1(i);
m4(8:14)=R2(j);
m4(15:21)=R3(k);
for l=1:21
K1(l)=log10((m4(l)+m2(l))/1000/0.004/m3(l));
end
Kn=[K(1:21)
K1(1:21)];Kn0=[K(1:7)
K1(1:7)];Kn5=[K(8:14)
K1(8:14)];Kn15=[K(15:21) K1(15:21)];
[ c1,c2 ] = MultiLineReg( Kn0(:,1),Kn0(:,2) );
[ c3,c4 ] = MultiLineReg( Kn5(:,1),Kn5(:,2) );
[ c5,c6 ] = MultiLineReg( Kn15(:,1),Kn15(:,2) );
[ c7,c8 ] = MultiLineReg( Kn(:,1),Kn(:,2) );
K2=c2+c4+c6+c8*3;
if K2>mx
mx=K2;
KnB=m4(1:21);
9
Modeling the Longevity of Infiltration System for Phosphorus Removal
BKfKn=c7;
end
end
end
end
Kf(1)=BKfKn(1);
I(1)=BKfKn(2);
% select the best value for sampling site Lu
[ c1,c2 ] = MultiLineReg( Lu0(:,1),Lu0(:,2) );
[ c3,c4 ] = MultiLineReg( Lu5(:,1),Lu5(:,2) );
[ c5,c6 ] = MultiLineReg( Lu15(:,1),Lu15(:,2) );
[ c7,c8 ] = MultiLineReg( Lu(:,1),Lu(:,2) );
mx=c2+c4+c6+c8*3;
R4=linspace(0.8*m1(22),1.2*m1(22),50);R5=linspace(0.8*m1(28),1.2*m1
(28),50);R6=linspace(0.8*m1(35),1.2*m1(35),50);
mx=0;LuB=m1(22:41);
for i=1:50
for j=1:50
for k=1:50
m4(22:27)=R4(i);
m4(28:34)=R5(j);
m4(35:42)=R6(k);
for l=22:42
K1(l)=log10((m4(l)+m2(l))/1000/0.004/m3(l));
end
Lu=[K(22:41) K1(22:41)];Lu0=[K(22:27) K1(22:27)];Lu5=[K(28:34)
K1(28:34)];Lu15=[K(35:41) K1(35:41)];
[ c1,c2 ] = MultiLineReg( Lu0(:,1),Lu0(:,2) );
[ c3,c4 ] = MultiLineReg( Lu5(:,1),Lu5(:,2) );
[ c5,c6 ] = MultiLineReg( Lu15(:,1),Lu15(:,2) );
[ c7,c8 ] = MultiLineReg( Lu(:,1),Lu(:,2) );
K2=c2+c4+c6+c8*3;
if K2>mx
mx=K2;
LuB=m4(22:41);
BKfLu=c7;
end
end
end
end
Kf(2)=BKfLu(1);
I(2)=BKfLu(2);
%Calculation of the best value for sampling site Ri
[ c1,c2 ] = MultiLineReg( Ri0(:,1),Ri0(:,2) );
10
Lin Yu
TRITA LWR Degree Project 12:01
[ c3,c4 ] = MultiLineReg( Ri5(:,1),Ri5(:,2) );
[ c5,c6 ] = MultiLineReg( Ri15(:,1),Ri15(:,2) );
[ c7,c8 ] = MultiLineReg( Ri(:,1),Ri(:,2) );
mx=c2+c4+c6+c8*3;
R7=linspace(0.8*m1(42),1.2*m1(42),50);R8=linspace(0.8*m1(49),1.2*m1
(49),50);R9=linspace(0.8*m1(56),1.2*m1(56),50);
mx=0;RiB=m1(42:62);
for i=1:50
for j=1:50
for k=1:50
m4(42:48)=R7(i);
m4(49:55)=R8(j);
m4(56:62)=R9(k);
for l=42:62
K1(l)=log10((m4(l)+m2(l))/1000/0.004/m3(l));
end
Ri=[K(42:62) K1(42:62)];Ri0=[K(42:48) K1(42:48)];Ri5=[K(49:55)
K1(49:55)];Ri15=[K(56:62) K1(56:62)];
[ c1,c2 ] = MultiLineReg( Ri0(:,1),Ri0(:,2) );
[ c3,c4 ] = MultiLineReg( Ri5(:,1),Ri5(:,2) );
[ c5,c6 ] = MultiLineReg( Ri15(:,1),Ri15(:,2) );
[ c7,c8 ] = MultiLineReg( Ri(:,1),Ri(:,2) );
K2=c2+c4+c6+c8*3;
if K2>mx
mx=K2;
RiB=m4(42:62);
BKfRi=c7;
end
end
end
end
Kf(3)=BKfRi(1);
I(3)=BKfRi(2);
AllB=[KnB LuB RiB];
% the final initial sorption data
%calculation of Freundlich coefficients from related data, all the input
are from
%batch experiments
11
Modeling the Longevity of Infiltration System for Phosphorus Removal
Soilp.m: the m-file for calculation of soil property parameters for the
main m-file
function [theta,porosity,BD]=soilp(soilprofile,Dryweight)
load soilprofile.txt;
load Dryweight.txt;
ProR=soilprofile(9,:)';
ProM=soilprofile(1:8,:)*ProR;
porosity=[ProM(6) ProM(8) ProM(5)
ProM(6) ProM(8) ProM(5)]';
DryInput=[Dryweight(14) Dryweight(9)
Dryweight(13) Dryweight(11)
Dryweight(6) Dryweight(10)];
for i=1:3
Volume(i,:)=(DryInput(i,:)/2.4)*100/(100-porosity(i));
end
BD=1./Volume;
WaterInput=ones(3,2)-DryInput;
theta=WaterInput./Volume;
12
Lin Yu
TRITA LWR Degree Project 12:01
MultiLineReg.m: the m-file for the multi-linear regression of the data,
which returns r2 to the Isotherm.m
function [ RegCoef,R2,F,FX,TX ] = MultiLineReg( X,Y )
format long;
sz=size(X);
N=sz(1);
nn=sz(2);
RegCoef=zeros(nn+1,1);
Z=mean(X);
yp=mean(Y);
A=transpose(X)*X-N*transpose(Z)*Z;
C=transpose(X)*Y-N*transpose(Z)*yp;
RegCoef(2:nn+1)=A\C;
RegCoef(1)=yp-Z*RegCoef(2:nn+1);
S=norm(Y)^2-N*yp^2;
YR=X*RegCoef(2:nn+1)+RegCoef(1)*ones(N,1);
U=transpose(RegCoef(2:nn+1))*C;
Q=S-U;
R=sqrt(U/S);
R2=U/S;
UR=U/(length(RegCoef)-1);
QR=Q/(N-length(RegCoef));
s=sqrt(QR);
inA=inv(A);
F=UR/QR;
for i=1:length(RegCoef)-1
FX(i)=RegCoef(i+1)^2/inA(i,i)/QR;
TX(i)=RegCoef(i+1)/sqrt(inA(i,i)*s);
end
format short;
13

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