A review of recent solute transport models and a case study

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

http://www.envirocomp.org/

mailto:[email protected]

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,


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].


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.


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.

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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


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


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


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.


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.


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).


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A review of recent solute transport models and a case study

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