Elango L. et al. (2004) A Review of Recent Solute Transport Models and a Case
Study. Chapter 5 of Environmental Sciences and Environmental Computing. Vol.
II (P. Zannetti, Editor). Published by The EnviroComp Institute
(http://www.envirocomp.org)
Chapter 5
A Review of Recent Solute Transport
Models and a Case Study
L. Elango1, F. Stagnitti
2, D. Gnanasundar
1, N. Rajmohan
1, S. Salzman
2, M.
LeBlanc2, J. Hill
3
1 Department of Geology, College of Engineering, Anna University, India.
2 School of Ecology & Environment, Deakin University, Australia. [email protected]
3 Portland Smelter, PMB 1, Portland, Victoria, 3305, Australia.
Abstract
This chapter reviews the functional and operational characteristics of several classes of models that are
capable of simulating solute transport and equilibrium chemical processes in soils. The various physical
and chemical components in models are identified for a wide range of current models. Most solute transport
models are developed for one- or two- dimensional flow domains. However, increasingly, many
researchers in this field indicate that the three dimensional approach is necessary when dealing with
contaminant transport and site remediation. There are many models that are site specific and complex in
nature. In general, there are only a few models incorporating complex chemical equilibrium processes that
are broadly applicable to many sites. Field scale validation of existing geochemical models is therefore
essential. To illustrate these concepts, a case study is presented. The case study focuses on modelling
fluoride transport in groundwater at the Portland Smelter in Victoria, Australia. Future research should be
oriented towards geochemical models involving many geochemical equilibrium reactions, with more
emphasis on cation exchange and redox reactions.
Keywords
Solute transport models, pollution, groundwater contamination, nutrients, smelter, fluoride
© The EnviroComp Institute 2004 1
2 ESEC II
1 Introduction
Chemical substances transported with the groundwater are often predicted using
mathematical models. Mathematical models, being an important predictive tool, have
been developed to simulate the mechanisms responsible for the movement of chemical
species. The development of geochemical transport models or hydrogeochemical models
is a relatively new pursuit, although some models date back to the late 1960’s. The early
models consider only a limited number of species and a few chemical reactions.
However, in recent years, many researchers have developed models capable of describing
multidimensional and multiple species solute transport that can be applied to studies
based on a local scale (e.g. vadose zone experiments) ranging up to a regional scale (e.g.
movement in confined and unconfined aquifers). In this chapter we shall describe a
regional-scale model to describe solute transport on a small catchment using detailed
vadose-zone information. Thus the study represents a unique opportunity to critically
evaluate contaminant transport techniques.
Several previous reviews of solute transport model have emphasised different
capabilities based either on method application or computational requirements. Some of
the more important reviews are from [1-13]. Van Genuchten [1] reviewed models
applicable to saturated and unsaturated zones that include simple geochemistry. Anderson
[2] reviewed primarily advection-dispersion models for the saturated zone. This was one
of the first attempts to apply such models in field scale problems including basic
geochemistry. Travis and Etnier [3] studied how various adsorption isotherms can be
incorporated into transport models. Jury [4] reviewed different unsaturated zone models
with and without chemical incorporation. Albriola [5] reviewed geochemical aspects,
sorption, biological transformation, immiscible phase transport, fractured media and
dispersion models. Chemical solute transport models, in terms of their physical and
chemical components, their verification and applicability to field scale problems, were
reviewed by [6]. This review reported that many of the models were developed for
specific purposes, and thus were only as complex as required. The review of hydro-
geochemical transport models by [8] and [9] shows that there are a number of different
approaches to modeling the transport of chemical species involved in multiple
equilibrium - controlled reaction and discusses the computational effort required to solve
the governing equations and the types of reactions considered. A number of multiple
component reactive transport models that handle aqueous complexation and
precipitation/dissolution reactions was reviewed by [10] and [11]. The capabilities of
solute transport models that require use of supercomputers was reviewed by [12]. A
theoretical framework for assessing the capabilities of models of contaminant transport
was presented by [13].
The purpose of this chapter is threefold: First to update earlier reviews mentioned
above. Second to focus more specifically on developing a framework for assessing
capabilities based on geochemical requirements and third to present a case study that
utilises the modeling framework described in the second aim. Basic descriptions of recent
physical and chemical models are also included in this chapter.
5 A Review of Recent Solute Transport Models and a Case Study 3
2 Chemical Solute Transport Models
A solute transport model usually consists of a physical and a chemical component or sub-
model. Basic descriptions of various physical and chemical equilibrium models are given
later.
2.1 The Physical Model Component
The physical model is defined as a mathematical description of flow and transport
phenomena in the saturated or unsaturated zone of the soil or aquifer system. The
description of the water flux in the transport equation is expressed in one of three ways
(a) mass transport based on the governing mass balance equations (e.g. Darcy’s law), (b)
as mixing cell models, or (c) as preferential flow models.
Most physical models designed to simulate the transport of soil-moisture and/or
solutes in groundwater are generally one or two-dimensional [6]. Many of the proposed
models can easily be extended to two or three dimensions. This may be necessary when
dealing with modelling sub-surface contaminant transport problems in the saturated zone
[14-16].
2.1.1 Mass Transport Models
The mass balance equation for a certain chemical entity and for a certain given space
domain of the porous media has been extensively cited e.g. [17]. Typically, all chemical
reactions are classed into two groups; one group with sufficiently fast and reversible
reactions and the other group with slower and /or irreversible reactions. The first group
models the equilibrium reactions and the second group characterise the kinetically
dominated reactions. In [17] these are referred to as tenads. The tenads are usually
equivalent of the chemical elements that remain as elements during chemical reactions.
The coupled transport of mass and energy into snowpacks was presented by [28]. The
combined effects of infiltration rate, repository head and reactive transport processes on
migration of 237
Neptunium from potential repositories to the water table was developed
by [29]. The process of evolution of oxidation and generation of acidity of the pyrite
overburden spoil pile was developed by [30]. A coherent and numerical framework
integrating hydrodynamics at pore and aggregate/matrix block scales was developed by
[31]. A series of recent experiments quantifying the leaching of reactive and non-reactive
tracers, nutrients, pesticides and contaminants in the vadose zone using an 1D
convection-dispersion method are described in [32–66].
2.1.2 Mixing Cell Models
Mixing cell models have been used widely (e.g., [13], [18-19]) to simulate a variety of
reactive chemical transport processes. A brief survey of published applications of mixing
cell models given by [19] is shown in table 1.
Two types of mixing cell models are in common use. In the first type, the advective
transport is simulated by moving the cell solution down-flow by one cell at the beginning
of each time step [24]. In the second type, used by [21], the physical dispersion is
4 ESEC II
simulated by controlling the numerical dispersion introduced by the solute. Mixing cell
models are simple to code and fast to compute [19]. Recent implementations of this
method include, for example, mixed convection process to simulate a saline disposal
basin [67], mixing of cells by modeling the nitrate leaching from arable land into
unsaturated zone [68] and one-dimensional, vertical, advective dispersive transport using
compartmental mixing cells (CMC) to simulate the transport of hydrochemical species in
regional groundwater systems [69].
Table 1. Application of mixing cell models (adapted from [19]).
Source Application Chemicals
[20] Data from field experiments at the Borden K, Mg, Na
landfill site analysed. Chemical interactions Ca, Cl
explained using 1-D and 2 -D mixing cell models.
[21] 1-D mixing cell model used to analyse data K, Ca
from laboratory experiments, and for
estimating model parameters.
[22] Transport with ion exchange from the field Ca,Mg,Na
experiment of [23] analysed Cl
with 1-D mixing cell model.
[24] 1 -D field application showing the interactions Ca,Mg,Na
of chemicals in a Dutch polder Cl
[25] 3 -D field application to explain the changes Cl
of fluid phase concentrations due to pumping
[26] 1-D mixing cell model applied to data from Cd,Cu, Zn
laboratory experiments to explain ion Ca,Mg, Cl,
exchange behaviour. SO4
[27] 2-D mixing cell model, simulated results Cl
compared with the field data.
2.1.3 Preferential Solute Transport Models
Modelling and monitoring transport of solutes in the vadose (unsaturated zone) is
difficult due to the complicated networks of interconnected pathways in the soil which
can transmit water, contaminants, and nutrients at varying velocities [36, 37]. Preferential
pathways resulting from biological and geological activity, such as sub-surface erosion,
faults and fractures, shrink-swell cracks, animal burrows, worm holes, decaying roots,
etc., may transmit water and solutes at very much higher rates than those anticipated by
current theory. The preferential flow mechanism in heterogeneous soils is well known.
Recent studies modelling preferential solute flow include [33, 36–40, 70–76]. These
studies include one dimensional preferential transport of water and solute in sandy soils,
finite element models to describe the solute transport in multi-layer subsurface systems,
5 A Review of Recent Solute Transport Models and a Case Study 5
flow in water-repellent soils, preferential solute transport in large laboratory lysimeters,
and analytical expressions for flushing solutes from residues in aquifers in a rectangular
source area and as highlighted the application buffer in groundwater protection.
2.2 Chemical Model Component
The chemical model component of geochemical models based on equilibrium theory
assumes that all chemical reactions proceed instantaneously to equilibrium and is often
referred to as the Local Equilibrium Assumption. (LEA).
2.2.1 Local Equilibrium Assumption (LEA)
The equilibrium approach to a groundwater transport system relies on the so-called “local
equilibrium” approach; the assumption being that the distribution of the chemical species
may be approximated by the equilibrium distribution at every point in space and time
[17]. The reactions are considered homogeneous involving at least two phases, such as
precipitation, dissolution and ion exchange. Other researchers assessed the impact of
physical and chemical parameters on the validity of the LEA and except for [76], all
attempts in defining criteria for the validity of the LEA have only considered surface
reactions e.g., sorption and ion exchange [96].
2.2.2 Equilibrium Transport Systems
A complete solute transport model must account for multiple species chemical and
transport processes. A decision whether a chemical process should be formulated
kinetically or assume a local equilibrium state needs to be made. The models reported in
the literature using LEA are more numerous than those assuming kinetically control
reactions, mainly due to two reasons; first, the chemical literature contains relatively
abundant data on equilibrium parameters and second, the algebraic formulation of the
equilibrium solutions is faster to solve than the differential equation system of the kinetic
formulation [1, 97].
2.2.3 Multiple Equilibrium - Controlled Chemical Reactions
The problem of modelling solute transport accompanied by many chemical reactions is
also of current interest. There are a number of different approaches to modelling the
transport of species involved in multiple equilibrium-controlled reactions eg. [8, 9]. A
solute transport model coupled with multiple equilibrium-controlled or kinetically-
controlled chemical reactions by applying a new approach based on the concentration and
reaction vector spaces was developed by [77].
3 Chemical Equilibrium Reactions
Chemical substances transported in the groundwater react with other chemicals or with
the soil matrix. A general geochemical transport model must be able to handle the various
6 ESEC II
classes of reactions. These include cation exchange, adsorption, complexation,
precipitation/dissolution, redox, the open/closed carbonate systems and biodegradation.
Very few models include all major types of geochemical reactions. Redox and
precipitation /dissolution are known to often play a major role relating the mobility of
various species in a given system [10, 11].
3.1 Cation Exchange
Cation exchange between water and solid material becomes important when water with
ion concentrations different from the parent soil is either infiltrated or injected into a soil
[78, 79]. When groundwater of a particular composition moves into a cation exchange
zone, the cation concentrations will adjust to a condition of exchange equilibrium [80].
Cation exchange is usually modelled according to a constant charge or a constant
potential model [81]. The constant potential model is usually considered a more realistic
treatment of natural sorbing porous media whose surface charge is not constant but a
function of pH. This is the preferred approach by most researchers [94, 95].
3.2 Adsorption
The relationship between solid and liquid phase solute concentrations at equilibrium is
given by the adsorption isotherm. Adsorption is the process where solutes adhere to the
surface of soil particles. The incorporation of various adsorption isotherms and transport
models was comprehensively reviewed by [3]. A list of the most common adsorption
isotherms is presented in Table 2. The linear and Freudlich isotherms are characterised by
having no maximum adsorption capacity. All isotherms are single-species except the
competitive Langmuir isotherm, which resembles the ion exchange process, where
adsorption of one ion must be accompanied by desorption of the other ion.
3.3 Precipitation/Dissolution
Precipitation-dissolution and oxidation-reduction reactions may cause special problems
when dealing with multiple species transport and chemical reactions. Precipitation-
dissolution reactions often lead to the formation of sharp concentration fronts in both
aqueous and the solid phases often creating instabilities in numerical solutions and failure
to correctly predict the solute concentration. Several investigators have worked on sharp
front or precipitation-dissolution problems. For example, [81,82] considered dissolution
problems with only diffusion in the aqueous phase. The nature of the precipitation-
dissolution process makes it almost impossible to infer anything about the rates of
reaction and time to react equilibrium in real soils. Many authors indicate that observed
levels of super-saturation may be caused by slow kinetics [85–93].
5 A Review of Recent Solute Transport Models and a Case Study 7
Table 2. Various ion exchange equations and equilibrium adsorption isotherms (adapted from [3]).
Ion exchange equations Equilibrium Adsorption isotherms
Kerr Linear
Vanselow Freundlich
Gaines - Thomas Langmuir
Davis Langmuir, two - surface
Davis-Krishnamorthy-Overstreet Competitive Langmuir
Gapon Langmuir
________________________________________________________________________
3.4 Redox Reactions
Oxidation and reduction (redox) reactions play an important role in geological as well as
in environmental processes. Processes that are controlled by redox reactions include
diagenesis of sedimentary rocks, contaminant transport, formation of oil and gas, etc.
Redox reactions may often be key mechanisms controlling the migration of toxic organic
and inorganic waste in the groundwater. Most numerical models dealing with reactive
chemical transport either exclude the redox reactions [97–99] or limit their models to
one-dimensional transport [93]. Redox reactions were interpolated into the geochemical
models developed by [10, 11, 102, 103].
3.5 Biodegradation
The microbial mediated oxidation of organic compounds such as benzene or toluene,
inorganic aqueous species such as oxygen [104], nitrate [105], sulphate or minerals such
as Fe (OH) 3 may act as terminal electron acceptors while changing their redox-state [eg.
104, 105]. Biodegradation of petroleum hydrocarbons in groundwater was most recently
and comprehensively described by a one-dimensional reactive multiple component
transport model coupled with microbial metabolism and geochemistry in [33].
3.6 DNAPL Transport
Dense Non-Aqueous Phase Liquid (DNAPL) solvents are immiscible with and denser
than water. They migrate downward through aquifers as a separate phase, travelling
under the combined influence of gravity and capillary forces. Recent one dimensional
and two-dimensional flow experiments in columns that allowed with water bypass around
the contaminant zone were conducted by [105]. Generic simulations coupled with two-
dimensional models to show that mass transfer tends to be an equilibrium process for
homogeneous systems and a kinetic process for heterogeneous systems were described by
[106]. Analytical solutions characterizing the dissolution/ mass transfer mechanism of a
single-component NAPL source were presented by [107].
8 ESEC II
4 Current Models’ Descriptions and Classifications
Table 3 summarises the physical components for a broad range of selected recent models
that function in either the saturated or the unsaturated zone. The finite difference method
(FDM) and finite element method (FEM) are most commonly used to solve the
underlying transport equations. Finite difference techniques are perhaps the simplest
among the numerical methods in solving the continuity system. These techniques have
been used by [93, 100, 101, 108 – 110]. The physical transport model using a
combination of finite difference techniques coupled with differential algebraic equations
and Newton-Raphson iteration by described by [10, 11]. Finite element techniques were
adopted by [78 – 81, 111], to name just a few. Most of the geochemical transport models
included in Table 3 are based on the mass balance equation approach. However, [24, 93,
112, 113] applied mixing cell models. The preferential solute transport models are
restricted to application only in the vadose (unsaturated zone) of the soil matrix. Most
models are limited to one spatial dimension [108, 109, 111, 113]. Two - dimensional
models have been applied for example by [78–81] and in three dimensions by [28].
Models that can be applied to more than one dimension are indicated in the table with the
symbols MD.
Table 4 presents a description of functional model characteristics, descriptions of
chemical processes and validation for selected models. In most cases, the geochemical
model was developed for a specific purpose. Certain geochemical processes were often
neglected. Only in a few cases does the geochemical model include all types of chemical
processes. In one case, [17] a useful methodological framework was introduced, by
which a more general model could be formulated using the governing equations for
multiple component one-dimensional transport where ion exchange is the sorptive
mechanism and described by a mass action or a Gapon equation. In other cases ion
exchange, complexation and precipitation/dissolution of calcium sulphate were explicitly
incorporated. However, dispersion was neglected. The exchangeable concentrations (ion
exchange) were calculated with the help of Gapon equation [114]. A model that
considered macrosolute and microsolute chemistry was developed to predict the potential
movement of trace solutes in soil systems by [113]. Sorption, ion exchange,
complexation, dissolution and precipitation were included in the macro-model chemistry.
Solute transport models for nitrogen transformations in the soil were developed by 86 –
89]. These models also account for variable saturated conditions.
5 A Review of Recent Solute Transport Models and a Case Study 9
Table 3. Description of physical components for each selected model.
Reference Physical Spatial Computational
/Source Transport Dimension Solution Method
[17, 111] MBE 1 FEM
[94] MBE 1 FDM
[23, 78] MBE 2 FEM
[108] MBE 1 FDM
[76] MBE 1 FEM
[20] MIX 1 MIX
[101] MBE 1 FDM
[93] MIX 1 FDM
[113] MIX 1 FDM
[28] MBE 3 IFDM
[24] MIX 1 IFDM
[10] MBE MD IFDM/NR
[109] MBE 1 FDM
[8, 9] MBE 2 FEM
[102, 103] MBE 1 MBE
[110] MBE 1 FDM
[114] MBE 2 FEM
[120] MBE 2 FEM
[36, 40] PREF 1 FDM
[72] PREF 1 FDM/OTHER
Key:
FDM = Finite Difference Method MBE = Mass Balance Approach
FEM = Finite Element Method MIX = Mixing Cell Model
NR = Newton – Raphson PREF = Preferential Flow Approach
IFDM = Integrated Finite Difference 1 = One Dimension
OTHER = other method (e.g. algebraic) 2 = Two Dimensions
3 = Three Dimensions
MD = Any Dimension.
10 ESEC II
Table 4. Description of Chemical Processes and Validation for Selected Models
Reference/
Source
Aqueous activity
correlation
Complexation Precipitation
/Dissolution
Redox
reaction
Ion exchange /
adsorption
Validation Comments
[17] - - -* - Gaines - Thomas - * Can be induced
[94]
Davies + + - Gapon SC* * Synthetic
[113] Davies + - - Rothmund - Kornfeld
SC Carbonate System - Open
[4] _ + + - Mass action -
[23] (Davies)*
- - - Gaines - Thomas A-SC *Can be induced
[108] - - - - Mass action -
[76] - + - - Surface Complexation -
[20] - + + - Gaines - Thomas Field
[100, 101] Debye Huckel
+ + - Mass action
SC Field
[93] + + + + - -
[113] Davies - - - Gapon/Kerr A-Field
[24] -* -* - - Gapon * Field** *From MICROQL
**From Valochi
[28] - - + - - Field *From PHREEQE
[10, 11] - + + + - Field
[109] - - - - Freundlich A-SC
[8, 9] - + + + Freundich A-SC
[6, 103] Davies + + + - A-E-N Carbonate system - Open
[114] - + + - Gapon Field
[120] - + + + Gaines-Thomas Field
Key :
A = Analytical SC = Soil Column Experiment Batch = Batch Experiment - = not included
Field = Field Experiment N = Numerical E = Example Application + = included
5 A Review of Recent Solute Transport Models and a Case Study 11
Transient solute models that include both water and salt transport and an approximate
solution to the equilibrium problem were developed by [4, 115, 116]. In the latte case, the
chemical calculations in the model included complexation, lime and gypsum solubility
and exchange equilibria. A constant charge model was developed by [80, 81] to model
the transport of ion exchanging solutes in groundwater. The numerical technique in this
case, previously developed by [17] was used to simulate the two dimensional transport of
cations in a field experiment with the direct injection of municipal effluent into an
aquifer. The model developed by [98] considers ion exchange, aqueous complexation and
dissociation of water. This model was validated on the field experiment conducted by
[23]. A one-dimensional transport model to estimate clean-out times for the
decontamination of Strontium-90 in an unconfined aquifer was developed by [108].
However, this model only considers ion exchange and decay. A similar model was
developed by [100, 101] but also included Langmiur and Freundlich adsorption, and this
model was verified with analytical solutions.
A model comprising of ion exchange and also soluble complexation in a multiple
component system was developed by [76, 116, 117]. The model, however, was not
validated against any experiments. A similar model that included processes ion exchange,
complexation and closed calcite dissolution/precipitation was developed by [20] to study
the migration of cations in the well-known Borden aquifer in Ontario, Canada. One
dimensional flow was assumed at the test site. The ion exchange process was described
by a Gaines-Thomas equation and complexation was allowed between all ion pairs of
calcium, magnesium, sodium and potassium with sulphate and carbonates. Another
similar model, developed by [16] combined a simple one-dimensional flow, chemical
model, with lateral and longitudinal dispersion. The authors however, attempted to
simulate the physical transport of solutes more closely than compared to [20]. The results
of the model were compared with field results for the Border test site.
A model for ion-exchange, precipitation / dissolution and complexation was
developed by [100, 101]. Mg-Ca exchange and Na-Ca exchange were described by a
mass action and Davis-Krinshamoorthy equation, respectively. A mixing cell model
coupled to a comprehensive equilibrium chemistry model was developed by [113]. Their
model, based on the computer programme EQ 3/6 [119], included cation exchange and
used to simulate composition changes in saltwater when it enters a fresh water aquifer.
Simulations with this model showed that during dispersive flow, characteristic
concentrations of sodium, calcium and magnesium develop in both time and space as a
result of the cation exchange. A model considering aqueous complexation and either
sorption or ion exchange was developed by [99]. This model is limited to few simple, but
important chemical reactions. The chemical component of the model accounts for
complexation, precipitation/dissolution, redox process and adsorption. Another model by
[92] included ion exchange of an arbitrary number of both insoluble exchanges and the
combined effects of ion exchange, precipitation / dissolution waves in alkaline flooding
associated with oil recovery [93]. The ion exchange calculations were validated by
simulating a sodium-calcium exchange experiment and the model was finally applied to
alkaline flooding in an oil-bearing core. A study of the contamination of a shallow
aquifer as a result of the infiltration of uranium mine tailings led to the development of a
three-stage model by [28]. Time-dependent fluid potentials, fluid saturations and
infiltration rates were calculated at the first stage. The results of the first stage were then
12 ESEC II
input to the second stage which consisted of the chemical species migration in the
unsaturated zone and of a dynamic mixing of the infiltrating water and the groundwater.
A program, DYNAMIX, was used for this stage, where a multiple-species, advective-
dispersive transport model was coupled to an existing geochemical equilibrium model
PHREEQE [118]. A non-reactive, single species transport was calculated at the third
stage, in order to predict plume migration.
The computer program DYNAMIX was first developed by [28]. The model
considered only acid-base reactions and precipitation / dissolution of minerals. The
current version of DYNAMIX model includes acid-base reactions, aqueous
complexation, redox reactions, precipitation-dissolution reactions and kinetic mineral
dissolution. However, they focused on oxidation-reduction reactions and on mineral
precipitation and dissolution that control the movement of many heavy metals in
groundwater systems.
Models combining a physical non-equilibrium transport model with a chemical
equilibrium model were first developed by [1, 22]. The concept of two-region and later
multiple region solute transport models have been successfully used by many researchers
to study the effects of preferential flow e.g. [36, 40, 72]. However, these models are
generally only applicable to vadose zone experiments and have only simple descriptions
of geochemical processes. A model to predict the transport and transformations of
pesticides and their metabolites in the unsaturated zone of the soil was developed by [42].
Physical, chemical and biological processes considered include convection, dispersion,
ionic exchange, biodegradation and hydrolysis. The model predicted, with good
agreement, the movement of various chemicals such as fungicides, nitrogen fertilisers
and radionuclides in the soil improving understanding of different mechanisms affecting
their transport. Finally, the proposed analytical models can be used to verify the accuracy
of numerical models used for predicting chemical transport in the sub-surface
environment.
HYDROGEOCHEM, a two–dimensional, finite–element, hydro-geochemical
transport model for simulating transport of reactive multiple species was developed by
[8]. This model accounts for complexation, dissolution-precipitation, oxidation-reduction,
adsorption and ion exchange. A prototype geochemical transport model including
complexation, precipitation -dissolution and oxidation – reduction was also developed by
[102, 103]. Sorption and ion exchange reactions are excluded. The model was validated
by comparisons with the geochemical transport model CHMTRNS. With field
applications, their model was able to simulate transport of nitrate and chemical reduction
by pyrite oxidation and resultant pyrite dissolution at the Rabis Creed aquifer
denitrification site in Denmark. A large-scale and long-term field experiment on cation
exchange in a sandy aquifer was studied by [95] with a three-dimensional geochemical
transport model, which is a part of the European Hydrological System (SHE) program,
along with a cation exchange submodel. The geochemical model included cation-
exchange processes using a Gaines-Thomas equation, a closed carbonate system and the
effects of ionic strength. The variation and the goodness of the selected chemical process
parameters were discussed in detail.
SALTFLOW is a three dimensional model for simulating complex density-
dependant groundwater flow and mass transport problems [121]. The model can be used
to solve one, two, or three dimensional mass transport problems within a variety of
5 A Review of Recent Solute Transport Models and a Case Study 13
hydrogeological systems. A finite element method is employed on deformable domain
geometry. The model includes preconditioned conjugate gradient solver to solve the
matrix equation. The IRRIGATION BAY MODEL (1997) was developed by the
Cooperative Research, Centre for Catchment Hydrology Australia to provide a
framework for investigating questions of irrigation practice and bay design for different
site characteristics [122]. An optimisation algorithm is provided to permit decision
support for irrigation management. This model couples a wide range of physical
processes, such as overland flow, groundwater flow, evapotranspiration and soil water
movement between irrigation events. PHTRAN is a model for hydrological transport,
with inorganic equilibrium chemistry and microbial activity during kinetically controlled
biodegradation in groundwater [33]. SMART (Streamtube Model for Advective and
Reactive Transport), a multicomponent transport model was developed to investigate the
use of surfactants to enhance the in situ remediation of polycyclic aromatic hydrocarbons
(PAH) contamination in the subsurface (SMART) [123]. SMART employs a Lagranian
approarch to describe three-dimensional reactive transport in heterogeneous porous
aquifers with emphasis on the effect of hydraulic and physico-chemical aquifer properties
on the coupled transport of PAH and surfactants.
A model for the simulation of solute transport in aggregated porous media was
developed by [110]. The model considers transport by convection and dispersion in the
mobile phase, diffusion of solute inside aggregates of arbitrary shapes and sizes. External
mass transfer resistance and linear adsorption are also considered. The main advantage of
this model is that it incorporates, in a unique way, the whole variety of models so far
proposed for transport modelling in aggregated porous media. This model also provides
an accurate solution using very little computer time. UNSARCHEM-2D, a 2-D finite
element code for modelling major ion equilibrium and kinetic nonequilibrium chemistry
in variably saturated porous media developed by [114], accounts for equilibrium
chemical reactions such as complexation, cation exchange, and precipitation-dissolution.
Model utility was illustrated with two dimensional simulations of surface and subsurface
irrigation from a line source. MINTRAN, a model for simulating multiple
thermodynamically reacting chemical substances in groundwater systems consists of two
main modules, a finite element transport module (PLUME 2D) and an equilibrium
geochemistry module (MINTEQ A2) [120]. The module is based on thermodynamic
equilibrium equations, and is potentially capable of handling chemical speciation, acid-
base, oxidation-reduction, non-linear ion exchange, adsorption and precipitation-
dissolution reactions. The model is primarily targeted for studying groundwater
contamination due to acid mine tailing effluents.
5 Modeling Fluoride Transport in an Aluminium Smelter: A Case
Study
The Portland Aluminium smelter discharges approximately 73 ML of process waste
water each year, with the paved areas of the site adding an additional 640 ML of storm
water run off [125]. The Portland Aluminium smelter is situated approximately 15 km
south-east of the town of Portland on the south-west coast of Victoria, Australia (Figure
1). The total area of the site is approximately 440 hectares, of which the smelter occupies
14 ESEC II
approximately 25%. The site is gently undulating, varying in elevation from about 25m in
the east to a maximum elevation of about 40 meters above sea level in the west.
Calcareous dunes of calcarinite sands, weathered basalt and limestone are the dominant
geological feature on Portland Aluminium’s property [135].
Figure 1. The site of the Portland Aluminium Smelter.
Portland Aluminium’s water research began in 1993 with the aim of developing
strategies for economically achieving zero wastewater discharge. A large part of this has
been about maximising efficiency within existing processes and minimising stormwater
contamination to enable harvest, treatment and use within the facility. However given
Portland’s climate it is recognised that the site will probably produce more water than can
be used and research has also been directed toward wetland and dry land use and
conditioning of mildly contaminated water (fluoride, phosphorus and nitrogen) followed
by shallow aquifer recharge. At Portland these aquifers have a diffused discharge to the
ocean. Modeling has shown that the combination of crop and wetland processes and the
ion exchange capacity of the clays in subsoils have an almost infinite capacity to
immobilise fluoride and utilise or immobilise nutrients.
In common with many other smelters, the waste water stream is currently
discharged to the ocean. However, this mode of release is unlikely to be acceptable in the
near future, and alternative disposal options for the water are required. Options being
considered include the discharge of water either directly onto the land or into wetlands
where the water will evaporate or infiltrate into the soil, use for irrigation of tree
plantations, or discharge via evaporation in constructed ponds [125].
Fluoride occurs naturally in rocks, soil, plants and water. The average dissolved
fluoride content of major rivers of the world is 0.01 to 0.02 mg/L and for the ocean of the
order of 1.5 mg/L [125]. The smelter buys in potable drinking water for use as process
water, and this contains approximately 0.1 mg/L fluoride. Tertiary treated sewage water
5 A Review of Recent Solute Transport Models and a Case Study 15
discharged from the nearby Portland Coast Water sewage treatment works contains
approximately 0.5 mg/L fluoride. Portland Aluminium waste water, on the other hand,
has much elevated levels of fluoride from between 5 to 15 mg/L. Accumulation of
fluoride can alter the structure and function of the plant cells and terrestrial plants
growing near fluoride emitting sources can accumulate high levels of this ion. When
fluoride is emitted by smelters, it travels only a relatively short distance, and its effects
can be observed in vegetation only a few kilometres from its source [125]. The purpose
of this study was to investigate the leaching and transport of fluoride through the surficial
aquifers and measure the potential of fluoride contamination on deeper groundwater
aquifers that are important source of drinking water for the Portland region.
Using MODFLOW as a platform for groundwater flow, a complex three
dimensional solute model that accounts for environmental and others parameters in the
subterranean environment has been developed. Mathematical constructs, incorporated at
a cellular level, allow the modeling of water movement and solute transport over time.
Modeling accuracy in areas of interest is improved by increasing the number of
discretisational elements at those locations. This increases the accuracy of local hydro-
lithological heterogeneity and water movement with chemical interaction The model has
been calibrated to in situ observations and is being used as a predictive tool to determine
locations for the safe disposal of wastewater with high concentrations of fluoride. Figure
2 shows the results of an investigation into the hydraulic head resulting in aquifer shape,
for the southwest region of the Portland site. Water moves perpendicular to isobars of
topographic continuity. Figure 3 shows the excellent agreement between the observed
head and modelled head for 25 observation bores.
Figure 2. Hydraulic head and aquifer shape, for the southwest region of the Portland site.
Calibration statistics are included in red. Iso-potentials in grey indicate the hydraulic head.
16 ESEC II
Observed versus computed target values
R2 = 0.9709
20
22
24
26
28
30
32
34
36
38
40
20 22 24 26 28 30 32 34 36 38 40
Observed value (m)
Mo
delle
d v
alu
e (m
)
Figure 3. Observed and model calibrated hydraulic head for 25 observation wells.
The area around southern outflow of Grants Creek (Figure 2) is a dominant
groundwater exit point. Figures 4 and 5 are the results of two transient simulations in
which terraced wetlands have been used as fluoride-laden, process water loading zones.
The load consists of 300 cubic meters of water with a fluoride concentration of 12 mg/L,
dosed daily as at 5 years (Figure 4) and as at 10 years (Figure 5). The model does not
include the removal of the contaminant by the physical process of adsorption, in which
recent laboratory results have shown to be extremely high. Thus these figures represent
the “worst-case”scenario.
5 A Review of Recent Solute Transport Models and a Case Study 17
Transient model simulation: 5 years
Dose: 300 kL
Dose regularity: Daily.
Contaminant species: [F-] = 12mg/L.
Dose location: Terraced wetlands.
Figure 4. Predicted fluoride contaminant plume after 5 years of regular daily application of 300 kL
[12] ppm Fluoride in the terraced wetlands.
Transient model simulation: 10 years (observation = final iteration)
Dose: 300 kL
Dose regularity: Daily.
Contaminant species: [F-] = 12mg/L.
Dose location: Terraced wetlands.
Figure 5. Predicted fluoride contaminant plume after 10 years of regular daily application of 300 kL
[12] ppm Fluoride in the terraced wetlands.
18 ESEC II
Chemical results from laboratory analysis, and fluoride inputs from airborne sources, are
currently being included in the digital modelling environment. Figure 6 shows the
preliminary results of a fluoride adsorption experiment conducted on the aquifer clays.
This experiment has been conducted on all aquifer mediums found on site.
Approximately 5g of clay was equilibrated with 50 mL of a gradation of various
concentrations of fluoridated water, ranging from 0 mg/L thru to 1000 mg/L. Clearly
even at high concentrations (500-1000mg/L F-), the clays show a remarkable ability to
adsorb fluoride. Preliminary analysis indicates the clays show a potential to adsorb
approximately 177g of fluoride per cubic meter of clay.
Figure 7 is a schematic representation of the micro or sub catchments based on a
topographical assessment. Disposal zones would be selected to maximise the residence
time of surface applied water thus allowing for maximum evapotranspiration, utilisation
of nutrients by crops or wetland vegetation and adsorption of fluoride by aquifer clays.
Concentration of fluoride remaining after 50mL of a gradation of
concentrations were equilibrated with 5g of aquifer clays.
0
50
100
150
200
250
0 200 400 600 800 1000
Initial concentration of fluoride (mg/L)
Co
nce
ntr
ation o
f fluori
de (
mg/L
)
afte
r e
quili
bri
um
wa
s a
chie
ved
Figure 6. Fluoride adsorption on the aquifer clays. About 5g of clay was equilibrated with 50 mL of
fluoridated water ranging from 0 mg/L thru to 1000 mg/L.
5 A Review of Recent Solute Transport Models and a Case Study 19
Figure 7. Schema of the micro-catchments based suitable for disposal of fluoride.
The following data was found to be critical in the model development :
1. Digital surface maps particularly wetlands, soils, and vegetation.
2. Digital elevation maps
3. Aerial photography
4. Bore locations and bore logs
5. Piezometer records
6. Biological surveys
7. Neighbouring land use
8. Meteorological records
Important information that was generated by the model include :Surface and groundwater
hydrology, ion exchange capacity of topsoils and subsoils and nutrient uptake in local
farmland practice or in especially developed crops, particularly the ability to utilise
stormwater and process effluent The model is able to predict the increase in groundwater
recharge with time, resulting from land disposal of waste water, determine the maximum
acceptable loadings of waste water irrigation and fluoride concentrations in accordance
with EPA criteria, determine what proportion of the surface applied fluoridated waste
water migrates to deep groundwater and to the sea-ward boundary, predict the net
migration, concentration and residence times of the surface applied chemicals in surficial,
shallow and deep aquifers, and in the ocean surrounding the Smelter site, and describe the
temporal and spatial variations in groundwater levels and geochemistry resulting from
land disposal of waste water and seasonal fluctuations in rainfall.
20 ESEC II
6 Conclusion
An overview of recent groundwater models capable of simulating solute transport and
equilibrium chemistry has been presented in this chapter. A specific case study is also
illustrated. The models vary considerably in complexity with regard to descriptions of the
water flux and geochemical processes. The essential key elements for model development
and selection based on a representative class of solute transport models have also been
described. A framework that classes models according to functional characteristics was
proposed. There is no one universal model that is capable of simulating solute transport
for every conceivable situation and consequently many models have been purpose built,
often with assumptions reflecting the context of the experiment (e.g. acid mine tailings
effluent, surface application of pesticides, subsurface nutrient flows, biochemical
remediation, preferential flow, etc). As a result any adopted model requires extensive
validation and verification with actual field data. This has been illustrated in the Portland
Smelter fluoride study. Future research into geochemical model development would
benefit from better descriptions of geochemical reactions, with more emphasis placed on
cation exchange and redox reactions.
Acknowledgments
The authors wish to thank The Council of Scientific and Industrial Research, New Delhi for grant support
and the help of Mr. M. Senthilkumar, Research Fellow under the All India Council for Technical Education
sponsored project for assistance in the preparation of this manuscript. This research was in part also funded
by Portland Smelter, the Australian-India Council grant for collaborative research and the Australian
Research Council’s Large Grant Scheme (Grant Nos. A89701825 and A10014154) and Australian
Research Council Industry Linkage grant (C00002301).
5 A Review of Recent Solute Transport Models and a Case Study 21
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