16

CHAPTER 2

LITERATURE REVIEW

2.1 GENERAL

Considerable number of studies has already been done on effluent

disposal and its effect on ground water quality. In this chapter, a review of

literature on these aspects is presented including the concepts used in earlier

studies which can provide a link with the present approaches. It helps one to

adopt, modify and improve the conceptual framework used to analyze the

groundwater remediation techniques and the methodology. The literature

reviewed is grouped under different categories dealing with the estimation of

the surface water potential, characterization of aquifer, estimation of

contaminated soil parameters, column experiments and recovery of

contaminated soil, groundwater flow and contaminant transport modelling,

pump and treat remediation system with multiple stages and barriers,

optimization techniques and treatment methods.

2.2 ESTIMATION OF RUNOFF FROM SMALL WATERSHEDS

A model called SCS-CN was developed by the Soil Conservation

Service (SCS) of the U.S. Department of Agriculture (USDA) and described

in the National Engineering Handbook Section 4 of Hydrology (NEH-4).

When SCS became Natural Resources Conservation Service (NRCS), the

model was renamed as NRCS-CN.

17

SCS-CN (or NRCS-CN) model is the product of more than 20 years

of studies of rainfall–runoff relationships from small rural watersheds. Based

on annual flood data collected at a number of study watersheds with drainage

areas of 1 sq. miles (2.6 sq. km) or less and with a uniform basin hydrologic

soil–cover complex, the SCS developed the CN tables (Bales and Betson,

1981). It is a simple procedure for estimating stream flow volume (exclusive

of base flow) generated by large rainstorms. Further, this SCS-CN model is

basically empirical and provided a consistent basis for estimating the amount

of runoff under varying land use and soil types.

Sherman (1942, 1949) was the first to propose the plotting of direct

runoff against storm rainfall leading to the origin of the SCS-CN

methodology. Mockus (1949) proposed later that the estimates of surface

runoff for ungauged watersheds could be based on soil, landuse, antecedent

rainfall, storm duration and average annual temperature.

In the past three decades, the SCS-CN methodology has been used

by a number of researchers for runoff estimation worldwide, which in turn,

lead to intensive and extensive exploration into its formation, rationality,

applicability and extendibility, pros and cons, and physical significance

among others. Consequently, its applicability to field data was reviewed

(Hjelmfelt et al 2002), and the hand book was significantly revised several

times (SCS 1993).

2.3 ESTIMATION OF DISPERSION COEFFICIENT

Dispersion is a fundamental physical process which occurs in many

or most groundwater flow related problems, such as pollution from a

concentrated and distributed source, sea water intrusion, seepage of polluted

surface water through rivers or lakes or changes in water quality due to

18

artificial recharge. It is a property of an aquifer, which takes into account the

spreading or mixing of particles. Estimation of inherent flow and dispersion

parameters such as lateral and longitudinal dispersion coefficients of a porous

medium are crucial for the description of groundwater flow and contaminant

movement. These two classes of parameters describe the physical process

governing the movement of a non-reactive solute through a saturated porous

medium. Generally, the dispersivity is higher in longitudinal direction than in

transverse direction. This means that particles will disperse more in the

longitudinal direction than in the transverse direction. The phenomenon of

dispersion is shown in the Figure 2.1 Two fluid particles starting at B and C

are dispersed to locations farther apart at B1 and C1 during transport through

soil pores. While parcels from A and B are brought close together, resulting in

mixing of water in two regions.

1A

C

A

1B

B

C1

Figure 2.1 Dispersion Phenomenon

Cirpka et al (2006) have analyzed reactive transport controlled by

transverse dispersive mixing and presented the expressions for calculating

concentration distributions of compounds undergoing quasi-instantaneous

reactions and proposed a new method to evaluate transverse dispersion

coefficients. These coefficients determine the length of the reactive plume

under steady-state conditions. It is possible to infer the transverse mixing

coefficients from the length of a plume under well-controlled experimental

conditions. In this study, they relate the plume length to the transverse

dispersion coefficient and apply the resulting expression to experimental data

19

of alkaline plumes in ambient flow of acidic water. They also showed that the

plume length essentially is inversely proportional to the transverse dispersion

coefficient. They have presented a new laboratory method for quantification

of transverse mixing and analytical expressions relating the length of the

reactive plumes to transverse dispersion coefficients.

Garcia et al (2006) have derived the ability of an artificial neural

network (ANN) to provide a data-driven approximation of the explicit relation

between transmissivity and hydraulic head as described by the groundwater

flow equation. This approximation can easily be solved for the inverse

problem and is capable of simulating aquifer response to additional stresses.

The first task is to successfully train the ANN to approximate the relationship

between any possible transmissivity field of the aquifer being modified and

the hydraulic head values as described by a water flow model. The second

task is to invert this model to solve the inverse problem so as to produce a

transmissivity field. This paper also explains the ANN training, the inversion

process and demonstrates that the process works using a hypothetical two

dimensional aquifer problem where the input and outputs are known.

Therefore, performance of the inversion process can be quantified. An ANN

was successfully trained to produce a data driven approximation of the

implicit relationship between transmissivity and hydraulic head under steady

state condition.

Halford et al (2006) have presented an approach for field scale

estimation of the hydraulic properties of a geohydrologic column. Techniques

for defining the geohydrology, well construction, pumping history, drawdown

and initial estimates of hydraulic conductivity are described in multiple

aquifer tests in different aquifers can be interpreted with a single simulation.

A new approach has been presented for consistently estimating the hydraulic

properties of a geohydrologic column using a moving MODFLOW model and

20

data from multiple aquifer tests. Vertical hydraulic conductivity estimated is

directly comparable to properties in a regional ground water flow model,

which makes the results more applicable than individual analysis from

multiple analysis solutions.

A study by Hunt (1997) indicated two approximate analytical

solutions which have been obtained for groundwater contaminant transport

with variable density flows. The first solution is for the steady downward

movement of a dense contaminant from a line source on an impermeable

boundary and the second problem is for the analogous problem of a point

source on the impermeable boundary. These similarity solutions assume that

the distances from the source are large compared with both the lateral

dispersivity and a characteristic dimension of the contaminant release region.

In addition molecular diffusion is considered relative to mechanical

dispersion.

Massabo et al (2007) have introduced a quick method for

estimation of laboratory-scale transverse dispersion coefficient. This method

is based on the analytical solution of the advection dispersion equation where

a pulse like injection of non reactive solute is introduced in a soil column

packed with homogeneous porous medium. This method takes into account

the effect of boundary conditions such as no flux on the column wall and zero

concentration at a large distance limit. Solving the advection dispersion

equation transverse dispersion coefficient was obtained. The local sensitivity

was analyzed. The goodness of the method was verified. This method gives

accurate results. The main draw back is, it can suffer from low accuracy if

accurate estimate of velocity is not available.

Rai et al (2007) have estimated the dispersion coefficient from soil

column test. In this, two methodologies viz., summation distribution graph

21

and Z-transform of transfer function of the process have been proposed for

estimating the dispersion coefficient from the data of soil column test.

Application of the methodologies has been demonstrated on the published

data. The proposed methods have better potential to estimate the dispersion

coefficient with reliable accuracy. The summation distribution graph

approach can be easily performed on a simple scientific calculator whereas

the latter one needs linear optimization technique and hence it is complicated.

2.3.1 Laboratory Column Study

Laboratory column tests are useful in determining contaminant

removal rates under conditions that more closely approximate the operating

conditions anticipated in the field, such as flow velocity. The laboratory

column study test is used to determine dispersion coefficient and the recovery

coefficient to remove the contaminants.

Govindaraju et al (1996) have conducted a study in which

cumulants are proposed as a tool for determining the relevant information

contained in. A method for computing cumulants in terms of moments is

proposed using ideas from combinatories theory. This method was applied to

effluent concentration data from soil column study. Analyzing effluent

concentration from soil column is the most common laboratory method for

calculating solute transport properties.

Lin et al (1996) have conducted soil column experiments to study

the distribution of Preferential Flow Paths resulting from removal of fine size

clay particles. The analysis of the effluent during the experiments indicated

that the clay particles were removed from the soil column, accompanied by an

increase in porosity and hydraulic conductivity. The detachment of clay

particles in either natural or compacted soils is important in predicting the

22

permeability of such media and the associated contaminant transport. The

colloidal clay particles provide an additional mobile solid phase for

movement of adsorbed contaminants. This study has useful application in

contaminant migration in sub surface and soil remediation issues. This paper

presents the concept and relevant theory that is necessary for finding

expressions of conductivity of soil exhibiting preferential flow paths.

Mon et al (2005) have conducted the column experiments that have

been proposed as an alternative method for measuring sorption isotherms. No

shaking is required and the flow-through system represents natural flow

conditions more closely. The column technique was promising to determine

sorption characteristic of dyes. This study was to compare the sorption

characteristic of four Triarylmethane dyes and investigated the suitability of

column experiments for measuring the sorption isotherms. The four dyes used

were Erio Floxine 2G, Pyranine, Lissamine Yellow FF and Brilliant Blue

FCF. They concluded that the column technique is a useful method to screen

dyes as hydrological tracer. The technique is faster and thus allows a more

efficient screening of dyes. The column techniques allow assessment of the

colouring ability of dyes in porous media and may also represent the natural

condition.

Robbins (1989) has proposed a method for determining transverse

dispersion coefficients of porous media in laboratory column experiments. In

this work, the Continuous Point Source method was presented for determining

transverse dispersion coefficient of saturated porous media in laboratory

column experiments. The method entails injecting a conservative tracer from

an injector embedded in a porous medium, monitoring concentration

variations with time within the column upgradient where the tracer impinges

on the column wall, and extracting longitudinal and transverse dispersion

coefficient values from relative concentration-time data using three-

23

dimensional advection dispersion formulations. The method was tested in a

column packed with glass beads for comparison with flow tank tests. The

transverse dispersion coefficient values calculated using column test agrees

closely with flow tank results. The method presented offers new approach for

determining transverse dispersion coefficient especially in undisturbed core

samples.

Skouras et al (2005) have reported high-resolution single-source

solute transport experiment in glass-etched pore networks for quantifying the

hydrodynamic dispersion as a function of Peclet number (Pe). The

hydrodynamic dispersion coefficients are estimated by matching the spatial

and temporal distributions of the solute concentration over various regions of

the network with the numerical solution of the advection dispersion equation

and using a parameter space analysis to ensure well conditioning of the

parameters. The estimated longitudinal dispersion coefficients are in close

quantitative agreement with literature data for dispersion in porous media.

The extracted transverse dispersivity values indicate an apparent decrease of

transverse dispersivity with increasing flow velocity.

Cirpka et al (2006) have presented a study for the determination of

transverse dispersion coefficient from reactive plume lengths. In this study,

reactive transport controlled by transverse dispersive mixing was analyzed

and the expression for calculating concentration distributions of compounds

undergoing quasi-instantaneous reactions was presented. Using this, an

expression for length of the reactive plume was derived. Solving this

expression the transverse dispersion coefficient was found out. This method

was applied to two experimental setups of different dimensions. The

computed transverse dispersion coefficients were small. They concluded that,

even though the transverse dispersion coefficients were small, they cannot be

neglected.

24

Singh (2006) has given a simple optimization method for the

explicit estimation of dispersivity and injected mass from breakthrough curve

due to instantaneous source. The proposed simple method yields successive

estimates of specific dispersivity and injected mass and also the time after

which the test may be terminated as the collection of data beyond this time

would not improve the estimates. In this method, Partial Differential Equation

governing the one-Dimensional advection-dispersion process describing

transport of ideal solute with adsorption in a homogeneous isotropic soil

medium was used. The proposed simple method was applicable only for low

values of specific dispersivity but the optimization method can be used for

any value of specific dispersivity. The proposed optimization method used a

derivative based technique in which the analytical derivatives were derived.

The parameters estimated in this method were compared with those obtained

from other methods. It was shown that the simple method suggested was a

shorter duration test and the peak concentration can be estimated using only a

few data points.

Ratha et al (2007) have given a solution for the advection

dispersion equation using a finite volume model. This study is concerned with

the modelling of conservative as well as non conservative solute transport in

ground water. The model is based on an operator split approach which uses an

Eulerian frame work with finite volume method for advective transport and

fully implicit central difference method for dispersive transport. This

formulation helps in accurately simulating both highly advective and

dispersive transport cases with less restriction on the grid size and time step.

The numerical solution is compared with exact as well as the approximate

analytical solution and the maximum error as percentage of peak

concentration is presented for different values of decay constant at varying

distances. The finite volume method provides accurate solutions of both

conservative and non-conservative solutes for both advection and dispersion

dominated situations.

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2.3.2 Scale Effect on Dispersion Coefficient

In the literature presented so far, dispersion coefficient found in the

laboratory on a small scale did not match with the field dispersivity values.

The following literature describes the scale effect on dispersivity.

Pickens et al (1981) have modelled scale-dependent dispersion in

hydro-geologic systems. They illustrate a practical method of handling scale

dependent dispersion using a finite element solute transport model. Various

scale dependent dispersivity relationships were presented including types

which approach gradually to a maximum or asymptotic value. The model

using scale-dependent dispersivity functions was verified by comparison to

theoretical results for variances of the solute distributions. The finite element

model was applied successfully to tracer test results which exhibited a scale

effect. The effect of early time scale dependent dispersion may be, in some

cases, of little consequence in predictions at a large mean travel distances. For

such situations the system can be adequately simulated with the classical

advection dispersion equation. However this method is not certainly

universal.

Wierenga et al (1989) have analyzed solute transport through small

and large unsaturated soil columns. This study was carried out to determine

how the parameters in the convection-dispersion equation are determined

from short column experiments and applied to long column experiments filled

with the same soil material. Unsaturated solute transport experiments were

conducted using several small and one large column packed with the same

sandy soil material. Comparing small column effluent concentration

distribution with data from a large column showed grater diameter values for

the large column. Dispersivity was about 5cm in large column but only about

1cm in small column. While dispersivity value was about 5 times in large

26

column than the small column, the retardation factor was essentially the same.

Hence a scale effect is observed here.

2.3.3 Estimation of Recovery Rate

Jin et al (2001) have evaluated the water quality of the aquifers and

the travel time of pollutant in the aquifer. A series of simulations performed

by them showed on a controlled hypothetical landfill to evaluate error in the

leachate calculation that the error in the calculation was due to inaccurate

input data rather than the mechanism of calculation in the Hydrologic

Evaluation of Landfill Performance (HELP) programs. Performance of

several variable input including precipitation, time, present runoff,

groundcover, lateral drainage, slope and leakage function were considered, in

the process it was concluded that the HELP model can estimate leachate

percolation.

Lowry et al (2006) have presented an assessment of aquifer storage

recovery using groundwater flow model. The term recovery efficiency

describes the percentage of water that can be recovered after injection. In this

research hydro geologic condition controls the recovery efficiency, which was

evaluated using particle tracking models and solute transport models. This

includes the effects on both advection and dispersion when simulating purely

advective transport with a particle tracking code. The objective of this

research was to investigate the hydraulic controlling factors on aquifer storage

recovery as they relate to recovery efficiency of a fresh water aquifer. The

research demonstrated that the hydraulic factors play a key role in physical

and operational condition and recovery efficiency of an aquifer can be

evaluated using groundwater model.

27

Minsker et al (1998) presented a methodology for using

optimization methods to assist in designing in-situ bioremediation of

groundwater. Aerobic in-situ bioremediation of contaminants such as fuels is

rapidly becoming a widely accepted technology. Given the complexity of in-

situ bioremediation, computer modelling provides a valuable screening tool

for exploring various preliminary site designs without large expenditures in

field testing. The results given for the hypothetical site also demonstrated that

exploiting the natural transport and degradation processes in the aquifer

through longer cleanups may significantly reduce bioremediation and

pumping cost. The results also indicated the importance of the pre specified

potential well locations on the model results.

Rainey et al (1998) have conducted two experiments on the column

contact time and superficial velocity of water, and percolation of tracer

element and benzoic acid through sand column. Column contact time of water

equals the elapsed time (seconds) versus column length (inches). Superficial

velocity of water is the volumetric flow rate (ml/sec) Vs column length

(inches). The amount of benzoic acid that was leached through the various

size columns has been measured. They concluded that the flow rate of leached

water moves towards zero as the column length approached infinity and

volumetric flow rate of water would decrease with increases column length.

Clarke et al (2005) have developed a step-by-step approach to

estimate the travel times for contaminated front and for a plume. They

discussed the reasoning behind their methods and described in detail, how to

develop the travel time equation could be developed. First they have

considered a contaminant front where dispersion is modelled by the standard

Advection Dispersion Equation (ADE) for which the breakthrough curve of a

front expands as the contaminant disperses. The fractional travel distance/time

relationships have been developed by Wheatcraft (2000).

28

Sidauruk et al (1997) have presented an inverse method based on

analytical solutions of contaminant transport problems. The initial step in a

groundwater contamination remediation process is to identify the extent of the

plume. The problems differ from the analytical solution-based algorithms in

that they only require a planned set of concentration data and no other prior

information It produces a complete estimate of mass transport parameters like

dispersion coefficients and flow velocity as well as source characteristics like

amount of pollutants and its initial location. The paper explored two simple

scenarios of groundwater pollution namely plumes caused by instantaneous

and continuous point sources in a two-dimensional uniform ground water

flow. The present algorithms use explicit formulae, eliminating the need for

an initial guess and the subsequent interactions to determine the unknown

parameters.

Wheatcraft (2000) has studied the travel time for contaminant

fronts or plumes which are often obtained using estimates of average pore

velocity from Darcy’s equation. These estimates provide information only

about the travel time of the average concentration (or the peak). He developed

equations for other portions of the breakthrough curve for a nonreactive

contaminant. These travel time equations provide a method for calculating

early arrival times for low concentrations.

2.4 GROUND WATER FLOW MODELLING

2.4.1 Groundwater Flow Models Review

Groundwater models are used by the environmental scientists to

predict the transport of contaminants for risk evaluation under a wide variety

of hydro-geologic conditions. In general, these models are classified as

conceptual descriptions and approximations that describe physical systems

29

using mathematical equations. They are not exact descriptions of physical

systems or processes. The models are represented using set of mathematical

equations to simplify the hydro-geological system for reasonable prediction

alternative, scenarios, their testing and comparison. The applicability or

usefulness of a model depends on how closely the mathematical equations

approximate the physical system being modelled. In order to evaluate the

applicability or usefulness of a model, it is necessary to have a thorough

understanding of the physical system and the assumptions embedded in the

derivation of the mathematical equations.

These assumptions typically involve the direction of flow,

geometry of the aquifer, the heterogeneity or anisotropy of sediments or

bedrock within the aquifer, the contaminant transport mechanisms and

chemical reactions. Because of the simplifying assumptions embedded in the

mathematical equations and the many uncertainties in the values of data

required by the model, a model must be viewed as an approximation and not

an exact duplication of field conditions. Groundwater models, however, are a

useful investigation tool even as approximations, that groundwater

hydrologist may use for a number of applications.

Applications of existing groundwater models include water balance

(in terms of water quantity), gaining knowledge about the quantitative aspects

of the unsaturated zone, simulation of water flow and chemical migration in

the saturated zone including river-groundwater relations, assessing the impact

of changes of the groundwater regime on the environment, setting

up/optimising monitoring networks, and setting up groundwater protection

zones.

It is important to understand general aspects of both groundwater

flow and transport models so that application or evaluation of these models

30

may be performed correctly. The governing equations for groundwater

systems are usually solved either analytically or numerically. Analytical

models contain analytical solution of the field equations, continuously in

space and time. In numerical models, a discrete solution is obtained in both

the space and time domains by using numerical approximations of the

governing partial differential equation. Various numerical solution techniques

are used in groundwater models. Among the approaches mostly used in

groundwater modelling, three techniques can be distinguished: Finite

Difference Method, Finite Element Method, and Analytical Element Method.

All techniques have their own advantages and disadvantages with respect to

availability, costs, user friendliness, applicability and required knowledge of

the user.

Salient features of the frequently used groundwater models have

been presented below.

2.4.1.1 3DFEMFAT

This is Three Dimensional Finite-Element Model of Flow and

Transport through Saturated-Unsaturated Media. Typical applications of this

model are for the study of infiltration, wellhead protection, pollution from

agricultural pesticides, sanitary landfill, radionuclide disposal sites, hazardous

waste disposal sites, density-induced flow and transport and salt water

intrusion. It can simulate combined sequential flow and transport, or coupled

density-dependent flow and transport. In comparison to conventional finite-

element or finite-difference models, the transport module of 3DFEMFAT

offers several advantages. It completely eliminates numerical oscillation due

to advection terms it can use a very large time step size to greatly reduce

numerical diffusion. The hybrid Lagrangian-Eulerian finite-element approach

is always superior to and will never be worse than its corresponding upstream

31

finite-element or finite-difference methods. It is flexible and versatile in

modelling a wide range of real world problems.

2.4.1.2 AQUA3D

It is a Three Dimensional Groundwater Flow and Contaminant

Transport Model. This model solves transient groundwater flow with

inhomogeneous and anisotropic flow conditions. Boundary conditions may be

prescribed as nodal head and prescribed flow as a function of time or head-

dependent flow. It also solves transient transport of contaminants and heat

with convection, decay, adsorption and velocity-dependent dispersion.

Boundary conditions may be either prescribed nodal concentration

(temperature) or prescribed dispersive mass (heat) flux.

2.4.1.3 FEFLOW

This is a finite-element package for simulating 3D and 2D fluid

density coupled flow and contaminant mass (salinity) and heat transport in the

subsurface. It is capable of computing: groundwater systems with and without

free surfaces (phreatic aquifers, perched water tables or moving meshes);

problems in saturated and unsaturated zones; both salinity-dependent and

temperature-dependent transport phenomena (thermohaline flows); and

complex geometric and parametric situations.

The package is fully graphics-based and interactive. Pre-, main- and

post processing are integrated. There is a data interface to GIS (Geographic

Information System) and a programming interface. The implemented

numerical features allow the solution of large problems and adaptive

techniques are incorporated.

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2.4.1.4 FLOWPATH

It is a comprehensive modelling environment specifically designed

for simulating 2-D groundwater flow and contaminant transport in

unconfined, confined and leaky aquifers with heterogeneous properties,

multiple pumping wells and complex boundary conditions. Some typical

applications of FLOWPATH include: determining remediation well capture

zones; delineating wellhead protection areas; designing and optimizing

pumping well locations for dewatering projects; and determining contaminant

fate and exposure pathways for risk assessment

2.4.1.5 GFLOW

It is a Windows 95/98/NT program based on the analytic element

method. It models steady-state flow in a single heterogeneous aquifer using

the Dupuit-Forchheimer assumption. While GFLOW supports some local

transient and three-dimensional flow modelling, it is particularly suitable for

modelling regional horizontal flow. To facilitate detailed local flow

modelling, it supports a MODFLOW-extract option to automatically generate

MODFLOW files in a user-defined area with aquifer properties and boundary

conditions provided by the GFLOW analytic element model. It also supports

conjunctive surface water and groundwater modelling using stream networks

with calculated baseflow.

2.4.1.6 GMS

This is a sophisticated and comprehensive groundwater modelling

software. It provides tools for every phase of a groundwater simulation

including site characterization, model development, calibration, post-

processing, and visualization. GMS supports both finite-difference and finite-

33

element models in 2D and 3D including MODFLOW 2000, MODPATH,

MT3DMS/RT3D, SEAM3D, ART3D, UTCHEM, FEMWATER and

SEEP2D. The programme modular design enables the user to select modules

in custom combinations, allowing the user to choose only those groundwater

modelling capabilities that are required.

2.4.1.7 Groundwater Vistas

Groundwater Vistas (GV) is a sophisticated windows graphical user

interface for 3-D groundwater flow and transport modelling. It couples a

model design system with comprehensive graphical analysis tools. It is a

model-independent graphical design system for MODFLOW MODPATH

(both steady-state and transient versions), MT3DMS, MODFLOWT,

MODFLOWSURFACT, MODFLOW2000, GFLOW, RT3D, PATH3D,

SEAWAT and PEST, the model-independent calibration software. The

combination of PEST and GV's automatic sensitivity analysis makes GV a

good calibration tool. The advanced version of Groundwater Vistas provides

the ideal groundwater risk assessment tool. Groundwater Vistas is a

modelling environment for the MODFLOW family of models that allows for

the quantification of uncertainty. Stochastic (Advanced) Groundwater Vistas

includes, Monte Carlo versions of MODFLOW, MODPATH and MT3D,

Geo-statistical Simulators, SWIFT support advanced output options and more.

GV displays the model design in both plan and cross-sectional views using a

split window (both views are visible at the same time). Model results are

presented using contours, shaded contours, velocity vectors, and detailed

analysis of mass balance.

34

2.4.1.8 MOC

This model is both general and flexible in that it can be applied to a

wide range of problem types. It is applicable for one- or two-dimensional

problems involving steady-state or transient flow. MOC computes changes in

concentration over time caused by the processes of convective transport,

hydrodynamic dispersion, and mixing (or dilution) from fluid sources. The

model assumes that gradients of fluid density, viscosity and temperature do

not affect the velocity distribution. However, the aquifer may be

heterogeneous and/or anisotropic. The MOC model is based on a rectangular,

block-centered, finite-difference grid. It allows the specification of injection

or withdrawal wells and of spatially-varying diffuse recharge or discharge,

saturated thickness, transmissivity, boundary conditions, and initial heads and

concentrations. This model incorporates first-order irreversible rate-reaction;

reversible equilibrium controlled sorption with linear, Freundlich, or

Langmuir isotherm; and reversible equilibrium-controlled ion exchange for

monovalent or divalent ions.

2.4.1.9 MODFLOW

MODFLOW is the name given to the United State of Geological

survey (USGS) Modular Three- Dimensional Ground-Water Flow Model.

Because of its ability to simulate a wide variety of systems, its extensive

publicly available documentation, and its rigorous USGS peer review,

MODFLOW has become the worldwide standard ground-water flow model.

MODFLOW is used to simulate systems for water supply, containment

remediation and mine dewatering. When properly applied, MODFLOW is the

recognized standard model. The main objectives in designing MODFLOW

were to produce a programme that can be readily modified, is simple to use

and maintain, can be executed on a variety of computers with minimal

35

changes, and has the ability to manage the large data sets required when

running large problems. The MODFLOW report includes detailed

explanations of physical and mathematical concepts on which the model is

based and explanations of how those concepts were incorporated in the

modular structure of the computer program. The modular structure of

MODFLOW consists of a Main Program and a series of highly-independent

subroutines called modules. The modules are grouped in packages. Each

package deals with a specific feature of the hydrologic system which is to be

simulated such as flow from rivers or flow into drains or with a specific

method of solving linear equations which describe the flow system such as the

Strongly Implicit Procedure or Preconditioned Conjugate Gradient. The

division of MODFLOW into modules permits the user to examine specific

hydrologic features of the model independently. This also facilitates

development of additional capabilities because new modules or packages can

be added to the program without modifying the existing ones. The

input/output system of MODFLOW was designed for optimal flexibility.

Ground-water flow within the aquifer is simulated in MODFLOW

using a block centered finite-difference approach. Layers can be simulated as

confined, unconfined, or a combination of both. Flows from external stresses

such as flow to wells, areal recharge, evapotranspiration, flow to drains, and

flow through riverbeds can also be simulated.

2.4.1.10 MODFLOW SURFACT

A new flow and transport model, MODFLOW SURFACT, is based

on the USGS MODFLOW code, the most widely-used ground-water flow

code in the world. It attempts to overcome certain limitations of MODFLOW

in simulating complex field problems. Additional computational modules

have been incorporated in MODFLOW SURFACT to enhance the simulation

36

capabilities and its robustness to achieve a seamless integration of flow and

transport modules.

2.4.1.11 MODFLOWT

MODFLOWT is an enhanced version of the USGS MODFLOW

model which includes packages to simulate advective-dispersive contaminant

transport. Fully three-dimensional, MODFLOWT simulates transport of one

or more miscible species subject to adsorption and decay through advection

and dispersion.

This model performs groundwater simulations utilizing transient

transport with steady-state flow, transient flow, or successive periods of

steady-state flow. Groundwater flow data sets created for the original

MODFLOW model function without alteration in MODFLOWT. Thus

extension of modelling projects to simulate contaminant transport is very easy

using MODFLOWT. It is thoroughly tested and has been bench-marked

against other transport codes including MT3D, SWIFT and FTWORK. A

comprehensive and pragmatic approach to contaminant transport has been

incorporated into MODFLOWT which allows for three distinct directional

dispersivity values, multiple chemicals and a rigorous treatment of the

hydrodynamic dispersion tensor.

2.4.1.12 MODFLOWwin32

This has all the features of other MODFLOW versions including

the newest packages added over the years since MODFLOW's original release

by the USGS. These new packages include the Stream Routing Package,

Aquifer Compaction Package, Horizontal Flow Barrier Package, BCF2 and

BCF3 Packages, and the new PCG2 solver. In addition, MODFLOWwin32

37

will create files for use with MODPATH (particle-tracking model for

MODFLOW) and MT3D (solute transport model). MODFLOWwin32, as its

name implies, is a 32- bit program designed to address all the memory

available to Windows. It will run in all versions of Windows including

Version 3.1, 3.11, Windows 95, 98 and Windows NT.

2.4.1.13 MODPATH

This Particle Tracking Post-Processing Package for the USGS 3-D

Finite-Difference Ground-Water Flow Model (MODFLOW) is a widely-used

particle-tracking program.

2.4.1.14 MOFAT

This model for Windows includes a graphical preprocessor, mesh

editor and postprocessor with on-line help. It is possible to simulate

multiphase (water, oil and gas) flow and transport of up to five non-inert

chemical species in MOFAT. It is useful to model flow of light or dense

organic liquids in three fluid phase systems and to simulate dynamic or

passive gas as a full three-phase flow problem. It can model water flow only,

oil-water flow, or water-oil-gas flow in variably-saturated porous media. By

solving flow equations at each node (on the finite-element mesh) only for

phases that are undergoing changes in pressures and saturations above

specified tolerances MOFAT achieves a high degree of computational

efficiency using a new adaptive solution domain method. Therefore, if NAPL

is absent or exists at a residual saturation, MOFAT will locally eliminate

those flow equations. It analyzes convective-dispersive transport in water,

NAPL, and gas phases by assuming local equilibrium or nonequilibrium

partitioning among the fluid and solid phases.

38

This model considers interphase mass transfer and compositional

dependence of phase densities. A concise but accurate description of soil

capillary pressure relations is used which assures natural continuity between

single-phase, two-phase and three-phase conditions.

2.4.1.15 MT3D

This is a comprehensive three-dimensional numerical model for

simulating solute transport in complex hydro-geologic settings. It has a

modular design that permits simulation of transport processes independently

or jointly. It is capable of modelling advection in complex steady-state and

transient flow fields, anisotropic dispersion, first-order decay and production

reactions, and linear and nonlinear sorption. It can also handle bioplume-type

reactions, monad reactions, and daughter products. This enables MT3D to do

multi-species reactions and simulate or assess natural attenuation within a

contaminant plume. MT3D is linked with the USGS groundwater flow

simulator, MODFLOW, and is designed specifically to handle advectively

dominated transport problems without the need to construct refined models

specifically for solute transport.

2.4.1.16 PEST

This is a nonlinear parameter estimation and optimization package.

It can be used to estimate parameters for just about any existing model

whether or not one has the model's source code. The package is able to "take

control" of a model, running it as many times as it needs while adjusting its

parameters until the discrepancies between selected model outputs and a

complementary set of field or laboratory measurements is reduced to a

minimum in the weighted least-squares sense.

39

2.4.1.17 Processing MODFLOW (PMWIN)

Processing MODFLOW for Windows (PMWIN) is a complete

simulation system. It comes with a professional graphical preprocessor and

postprocessor, the 3-D finite-difference ground-water models MODFLOW-

88, MODFLOW-96, and MODFLOW 2000; the solute transport models

MT3D, MT3DMS, RT3D and MOC3D; the particle tracking model

PMPATH 99; and the inverse models UCODE and PEST-ASP for automatic

calibration. A 3D visualization and animation package and a 3D Groundwater

Explorer, are also included.

2.4.1.18 SUTRA

This is a 2D groundwater saturated-unsaturated transport model, a

complete saltwater intrusion and energy transport model. SUTRA simulates

fluid movement and transport of either energy or dissolved substances in a

subsurface environment. It employs a two-dimensional hybrid finite-element

and integrated finite-difference method to approximate the governing

equations that describe the two interdependent processes that are simulated:

(1) fluid density dependent saturated or unsaturated groundwater flow and

either (2a) transport of a solute in the groundwater, in which the solute may

be subject to equilibrium adsorption on the porous matrix and both first-order

and zero-order production or decay, or (2b) transport of thermal energy in the

groundwater and solid matrix of the aquifer. A 3-D version of SUTRA has

been recently released.

2.4.1.19 Visual MODFLOW

Visual MODFLOW provides professional 3D groundwater flow

and contaminant transport modelling using MODFLOW-2000, MODPATH,

40

MT3DMS and RT3D. Visual MODFLOW Pro seamlessly combines the

standard Visual MODFLOW package with WinPEST and the Visual

MODFLOW 3D-Explorer to give the most complete and powerful graphical

modelling environment available. This fully-integrated groundwater

modelling environment allows to:

• Graphically design the model grid, properties and boundary

conditions, Visualize the model input parameters in two or

three dimensions,

• Run the groundwater flow, pathline and contaminant transport

simulations,

• Automatically calibrate the model using WinPEST or manual

methods, and

• Display and interpret the modelling results in three-

dimensional space using the Visual MODFLOW 3D-Explorer

2.4.1.20 Beyond MODFLOW

Together FEFLOW and MIKE SHE cover virtually all groundwater

related applications. MODFLOW is the trusted workhorse for thousands of

groundwater modellers around the world. For a range of applications,

MODFLOW is a sufficient and well proven technology. However,

groundwater issues are becoming more complex. Today, many real-world

problems require more advanced tools. Ever tighter project budgets and

schedules require the most cost-effective tools available. Beyond

MODFLOW, DHI has wide rage of applications such as unsaturated seepage

analysis, mining and tunnelling, complex geology, thermal and density flow,

heat transport in groundwater, salt water intrusion, multi-species reactive

transport, conjunctive use of groundwater and surface water, environmental

41

river flows, irrigation and drought management, wetland management and

restoration, floodplain management, integrated catchment management and

land use and climate change.

2.4.2 The Governing Groundwater Flow Equation

The governing groundwater flow equation below is restricted to

fluids with a constant density or in cases where the differences in density or

viscosity are extremely small or absent (Barends and Uffink 1997). This

equation is derived by mathematically by combining a water balance equation

with Darcy’s law (Anderson and Woessner 1992).

∗−∂∂

=⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂ W

thS

zhK

zyhK

yxhK

x szyx (2.1)

where,

Kx, Ky and Kz are components of the hydraulic conductivity tensor [LT-1]

Ss is the specific storage [L-1]

W* is the general sink/source term that is intrinsically positive

and defines the volume of inflow to the system per unit

volume of aquifer per unit of time [T-1]

h is the groundwater head [L]

x, y and z are the Cartesian coordinates [L]

t is time [T]

In order to obtain the groundwater head solution, the simulation

models are based on the mathematical models with certain simplifying

assumptions for the flow domain and its boundaries. At present, a large

number of mathematical models are available, which are capable of handling

fresh and saline groundwater flow in aquifer systems. They are subdivided

into analytical and numerical models (Essink 1996).

42

When it is simplified, groundwater flow equation might be solved

analytically. The simplifications usually involve assumption of homogeneity

and one- or two-dimensional flow. Except for applications to well hydraulics,

the analytical solutions for flow problems are not widely used in practical

application. Numerical solutions are much more versatile and with the

widespread availability of computers, they are easier to use than some of the

more complex analytical solutions (Anderson and Woessner 1992).

2.5 SOLUTE TRANSPORT MODELLING

When the problems involve miscible fluids, it is necessary to solve

the solute transport equation. In order to solve the solute transport problem,

one has to solve the two equations: the first one is the governing equation of

groundwater flow and another is solute transport equation.

2.5.1 Governing Equation for Solute Transport

The advection-dispersion equation can be solved analytically only

after several simplifying assumptions (e.g,) a homogeneous aquifer and a

uniform groundwater flow. The analytical solutions are obtained in either one

dimensional (Kreft and Zuber 1978, Bear 1979) or two-dimensional models

of point injection (Barends and Uffink 1997).

( )tccv

xxcD

x iij

iji ∂

∂=

∂∂

−⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

∂∂

(2.2)

is also known as the advection-dispersion equation.

where,

Dij is the dispersion coefficient [L2/T]

c is concentration[M/L3]

43

vi is the Darcian groundwater velocity [L/T ], ( vi = qi /n)

qi is the specific volume flux and [L/T ]

n is the porosity

The programme code for a solute transport model typically consists

of two sub models: a model to solve the flow equation and another to solve

the advection- dispersion equation. The solution of the flow equation yields

the distribution head, from which the velocity field is calculated. Velocities

are input to the transport sub model, which predicts the concentration

distribution in time and space. This holds true, when the groundwater density

is constant and it is also valid for water with low concentrations of total

dissolved solids (TDS) and/or temperature in range of most shallow aquifers.

2.6 GROUND WATER MANAGEMENT MODELS

Management of ground water pollution problem often requires the

use of non-linear optimization models due to the complexity of the governing

equations. The difference in the concentration between ground water and

effluent serves as a significant driving force for the migration of solute. In

such cases, the groundwater velocity field is a function of solute

concentrations. Hence non-linearties appear in advective and dispersive

transport terms. The combined simulation optimization studies were generally

based on embedded method of response matrix approach. The embedded

method (Wills and Finney 1998, Das and Datta 1999) directly incorporates

the numerical equations as constrains in an optimization framework. This

approach results in a very large constraint set especially for large aquifer

systems or for transient problems. On the other hand, in the response matrix

approach an external groundwater simulation model is used to develop unit

responses (Hallaji and Yazicigil 1996). This approach can be applied only

when the system is linear. An alternative to these methods is a linked

44

simulation-optimization approach (Gorelick et al 1984, Emch and Yeh 1998).

Linkage of nonlinear simulation model within the management model would

take considerably large computational time to achieve optimal solution.

Another alternative is response surface method (Gosavi 2003) and in this

method an approximate solution for the flow and transport processes could be

linked within the management model (Alley 1986, Aly and Peralta 1999,

Bhattacharjya and Datta 2005, Rao et al 2005).

Mahar and Datta (2001) have used an optimization-based

methodology for identifying unknown sources of ground-water pollution. The

main advantage of using optimal source identification models, in which flow

and transport equations are embedded as constraints, is to simultaneously

estimate unknown pollution sources as well as flow and transport parameters.

A nonlinear programming algorithm is used to obtain the optimal estimates of

unknown source characteristics. The input to this model includes measured

pollutant concentration at observation sites. The source identification

methodology is further extended to the simultaneous estimation of aquifer

parameters as well as identification of unknown pollutant sources.

Performance of the developed methodology is evaluated for illustrative

examples considering two-dimensional flow and advective-dispersive solute

transport. These performance evaluations demonstrate that the proposed

methodology performs satisfactorily in identifying the locations, determining

the magnitudes and specifying duration of the unknown ground-water

pollution sources, even when the aquifer parameters are unknown.

Four major methods that solve the solute transport equation are: 1)

the finite difference method; 2) the finite element method; 3) the random walk

method and 4) the method of characteristics (Konikow and Bredehoeft 1978).

In the last method, the particle tracking technique is also employed to solve

45

the advective transport and either the finite difference or finite element

approach is used to solve the dispersive equation.

Bouwer et al (2005) represents a process of generating numerical

grids with appropriate property distributions from geologic conceptual

models, thus making the entire process easy to implement with fewer user-

induced errors. The series of grids of various resolutions are used to assess the

level at which increasing resolution no longer influences the flow and solute

transport results. Grid resolution if found to be a critical issue for groundwater

flow and solute transport. The resolution required in a particular instance is a

function of the feature size of the model, the intrinsic properties of material

and the specific physics of the problem and boundary conditions.

Mehl and Hill (2001) compared five common numerical techniques

for solving the advection-dispersion equation (finite difference, predictor

corrector, total variation diminishing, method of characteristics and modified

method of characteristics) using simulation of a controlled conservative tracer

test experiment through a heterogeneous and two-dimensional sand tank. This

study demonstrated that the choice of assigned dispersivity and the amount of

numerical dispersion present in the solution technique, estimates the hydraulic

conductivity values to a high degree of accuracy.

Thirumalaivasan (2001) has made an attempt to assess the aquifer

vulnerability using Analytic Hierarchy Process and Geographical Information

System (GIS) for upper Palar watershed using DRASTIC MODEL. The

drastic model uses the following seven thematic maps namely depth to water,

recharge, aquifer media, soil media, topography, impact of vadose zone and

hydraulic conductivity. Analytic Hierarchy Process (AHP) is used to arrive

the weights and ranks of the criteria of the seven layers. He has developed

46

user friendly VB software interfaced with GIS for estimation of weights and

ranks of the thematic layers for aquifer vulnerability assessment.

Bauer et al (2004) have used an integral groundwater investigation

method for the quantification of Polychloroethylene (PCE) and

Tetrachloroethane (TCE) mass flow rates at an industrialized urban area in

Linz, Austria. In this approach, pumping wells positioned along control

planes perpendicular to the groundwater flow direction are operated for a time

period on the order of days and sampled for contaminants. The concentration

time series of the contaminants measured during operation of the pumping

wells are then used to determine contaminant mass flow rates, mean

concentrations and the plume shapes and positions at the control planes. By

use of the integral investigation method, it is possible to identify active

contaminant sources, quantify the individual source strength in terms of mass

flow rates at the control planes and estimate the contaminant plume position

relative to the control planes. The source zones emitting the highest PCE and

TCE mass flow rates could be determined, representing the areas where

additional investigation and remediation activities will be needed.

Jason et al (2007) have proposed a methodology to quantify the

prediction uncertainty associated with ground water vulnerability models that

were developed through and approach that coupled multivariate logistic

regression with a geographic information system (GIS). This method uses

Latin Hypercube Sampling (LHS) to illustrate the propagation of input error

and estimate uncertainty associated with the logistic regression predictions of

ground water vulnerability. Central to the proposed method is the assumption

that prediction uncertainty in ground water vulnerability models is a function

of input error propagation from uncertainty in the estimated logistic

regression model coefficients and the values of explanatory variables

represented in the GIS (data error). Input probability distributions that

47

represent both model and data error sources of uncertainty were

simultaneously sampled using a Latin Hypercube approach with logistic

regression calculations of probability of elevated non point source

contaminants in groundwater. The resulting probability distribution represents

the prediction intervals and associated uncertainty of the ground water

vulnerability predictions. The method is illustrated through a ground water

vulnerability assessment of the high plains regional aquifer. Results of LHS

simulations reveal significant prediction of uncertainties that vary spatially

across the regional aquifer. Additionally, the proposed method enables a

spatial deconstruction of the prediction uncertainty that can lead to improved

prediction of ground water vulnerability.

Hunt (2006) suggested that it is powerful and easy to use

applications of analytic element method but are not as widespread as finite-

difference or finite-element models partly because they are relatively new.

Although reviews that focus primarily on the mathematical development of

the method have appeared in the literature, a systematic review of applications

of the method is not available. While not fully encompassing, the applications

described here cover areas where the method has been historically applied (

regional, two-dimensional steady state models, analyses of ground water-

surface water interaction, quick analyses and screening models and wellhead

protection studies) as well as more recent applications (grid sensitivity

analyses, estimating effective conductivity and dispersion in highly

heterogeneous systems). The review of applications also illustrates the areas

requiring more methods of development (three-dimensional and transient

simulations).

Lin et al (2007) have concluded that Groundwater Model (GWM)

brings new management modelling capabilities to the USGS MODULAR

three-dimensional ground water model MODFLOW-2000. GWM uses a

48

response matrix approach to solve several types of linear, nonlinear, and

mixed-binary linear GWM formulations, and can be applied to a wide range

of groundwater flow (GWF) management problems. In spite of the lack of

capabilities for ground water quality and variable-density flow problems, it is

a powerful and free tool for researchers, professionals, and decision makers

who are involved in GWF management.

Chrisian et al (2006) have presented an approach for coupling

MODFLOW and MT3DMS for simulation of ground water flow.

MODFLOW routines were modified to solve a variable-density form of the

ground water flow equation in which the density terms were calculated using

an equation of state and the simulated MT3DMS solute concentrations.

Changes to MODFLOW and MT3DMS input files were kept to a minimum

and thus existing data files and data files created with most pre-and post-

processors can be used directly with the SEAWAT code. The approach was

tested by simulating the Henry problem and two of the saltpool laboratory

experiments (low-and high –density cases) for the Henry problem. The

comparison of simulated results showed the good agreement with the steady-

state semi-analytic solution and also the transient isochlor movement as

simulated by a finite-element model. For the saltpool problem, the simulated

breakthrough curve compared better with the laboratory measurements or

low-density case than for the high- density cases but showed good agreement

with the measured salinity isosurfaces for both cases. Results from the test

cases presented here indicate that the MODFLOW/MT3DMS approach

provides accurate solutions for problems involving variable-density ground

water flow and solute transport.

Pitrak et al (2007) suggested that the borehole dilution techniques

use repeated fluid column profiling after establishment of an initial uniform

condition to monitor the rate at which ambient ground water moves into a

49

bore hole. Application of the dilution technique in a monitoring well makes it

possible to estimate the horizontal Darcy flow velocity of ground water in the

aquifer surrounding the bore hole. Previous investigators have demonstrated

the technique using either relatively concentrated saline solutions or deionized

water to produce a fluid column with properties distinctly different from those

of local ground water; they presented a new dilution technique using the food

colour brilliant blue FCF (euro code E-133) to mark the fluid column and

using a specially constructed photometric sensor to characterize the dilution

of this dye over time. The effective application of this technique is

documented by two practical examples.

Kraemer (2007) have suggested the Analytic Element Method

(AEM) for solving problems of regional ground water flow may be

considered a community, and this community can be studied from the

perspective of history and philosophy of science. Applying the methods of the

Hungarian philosopher of science Imre Lakatos (1922 to 1974), the AEM

“research program” is distinguished by its hard core theoretical basis

protective belt (auxiliary assumptions), and heuristic (problem solving)

machinery. Analytic Element Method has emerged relatively recently in the

scientific literature and has a relatively modest number of developers and

practitioners compared to the more established finite-element and finite-

difference methods. Nonetheless, there is evidence to support the assertion

that the AEM research program remains in a progressive phase. The evidence

includes an expanding publication record, a growing research strand

following professor Otto Strack’s book Groundwater Mechanics (1989), the

continued placement of AEM researchers in academic institutions, and the

further development of innovative analytical solutions and computational

solvers/models.

50

Leake et al (1998) have evaluated the methods that can be used to

interpolate smaller-scale model-boundary flows and heads from large scale

block-centered finite-difference model such as MODFLOW. The scope of this

analysis includes horizontal interpolation of horizontal-flow components.

Methods presented in this analysis have been successfully used in the past for

problems such as particle tracking, and are modified here for the application

of computing boundary conditions for smaller-scale model. Interpolation

methods are to allow the calculation of flow and head values for boundary

conditions in smaller scale ground water flow models embedded in larger

block-centered finite-difference flow model.

Eaton et al (2007) have formulated and tested a 3D conceptual

model of ground water flow and hydrochemistry in a fractured sedimentary

rock aquitard to show that flow dynamics within the aquitard are more

complex than previously believed. This conceptual model for control of

hydraulic head and hydro-geochemistry in rock aquitards potentially is

applicable to a broad area within 10 km of the subcrop of the aquitard

formation. It was concluded that the results presented here provides a baseline

for evaluation of predevelopment conditions or intrinsic properties of the

aquitard and therefore may be useful for isolating the effects of the multi-

aquifer wells.

Fogila et al (2007) have tested alternative ground water models

using cross-validation and other methods. The methods are able to rank

alternative models and identify observations important to parameter estimates

and predictions. It was concluded that the results indicate that for model

selection, the information criteria produce similar results at much smaller

computational cost than cross-validation.

51

Gotovac et al (2006) have presented a multi-resolution adaptive

modelling of ground water flow and transport problems. The numerical

procedure is the Adaptive Fup Collocation Method (AFCM), based on Fup

basis functions. The numerical procedure was tested and verified by few

characteristic ground water flow and transport problems, the Buckley-

Leverette multiphase flow problem, 1-D vertical density driven problem and

standard 2-D sea water intrusion benchmark-Henry problem. The results

demonstrate that the method is robust and efficient.

Pelham et al (2000) have focused on the regulation and use of

injected tracers. Groundwater tracers are increasingly being used to estimate

subsurface flow and transport parameters. Injection of tracers falls under the

federal Underground Injection Control (UIC) programme. UIC limits the

introduction of substances into groundwater sources of drinking water as a

part of the Safe Drinking Water Act. UIC program requires that underground

sources of drinking water are not endangered, and that will be provided to

tracer injection.

Chesnaux et al (2005) have developed a new analytical solution for

the problem of transit time within an unconfined horizontal aquifer and with

constant recharge across the water table. This study considered a vertical

section through a saturated flow system within an unconfined aquifer

underlain by an impervious boundary. The soil was assumed homogeneous,

while the flow system was assumed at steady state. The aquifer was bounded

by either two fixed head boundaries or a fixed head boundary on down

gradient and no-flow boundary in upstream. The flow in this aquifer was

considered horizontal and one dimensional according to the Dupuit

approximation. This ignores unsaturated flow and is essentially a one-

dimensional approach to solve vertical two-dimensional plane problems in an

52

unconfined aquifer. They developed a new analytical solution for transit time

within Dupuit type systems.

2.7 PUMP-TREAT-INJECT (PTI) REMEDIATION SYSTEM

Atwood and Gorelick (1985) have developed two-stage planning

procedure to select the best wells and their optimal pumping and recharge

schedules to contain the plume while a well or system of wells within the

plume removes the contaminated water. In stage-1, a combined groundwater

flow and solute transport model is used to simulate contaminant removal

under an assumed velocity field. The result is the approximate plume

boundary location as a function of time. In stage-2, a linear program, which

includes a groundwater flow model as part of the set of constraints,

determines the optimal well selection and their optimal pumping and recharge

schedules by minimizing total pumping and recharge.

Ahlfeld et al (1988) have developed contaminated groundwater

remediation system using hydraulic control. Two nonlinear optimization

formulations were proposed, which model the design process for the location

and pumping rates of injection and extraction wells in an aquifer cleanup

system. The formulations were designed to find a pumping system which

removes the most contaminant over a fixed time period and reduces the

contaminant concentration to specified levels by the end of a fixed time

period at least cost. The formulations employ a two dimensional Galerkin

Finite Element Simulation Model of steady state groundwater flow and

transient convective-dispersive transport. To make the optimization problems

computationally tractable sensitivity theory is used to derive a general

relationship simulation outputs with respect to model inputs.

53

Andricevic and Kitandis (1990) have formulated the methodology

for optimizing the pumping schedule for a groundwater remediation, when the

available information does not allow deterministic predictions. The

information is based on the minimization of the cost function over all possible

values of the uncertain parameters weighed by the probability that they are

correct ones. They have shown that the cost function can be regarded as the

sum of two terms. The first one is the cost of the deterministic optimization

problem formed, if all the parameters would assume their mean values. The

second term varies with estimation error and it was calculated using

asymptotic approximations. The optimal solution under uncertainty is

obtained through the minimization of the sum of two terms. A comparison has

shown that this method performs better than deterministic approach.

McKinney and Lin (1996) have optimized the pump and treat

ground water remediation system. In this study, a groundwater management

model using a non linear programming algorithm was developed to find the

minimum cost design of the combined pumping and treatment components of

a pump and treat remediation system. Results of applying this model to an

aquifer with homogeneous hydraulic conductivity shows that well installation

cost has a significant impact on the total cost of the system so the total cost

can be reduced by using fewer wells of large flow rate. In this case study,

optimal injection concentration was found to be 70% to 80% of the cleanup

standard and designs with remediation period around 5 to 6 years had the

minimum cost. Air stripping tower was used to treat contaminated water by

mainly removing volatile organic compounds. The height of air stripping

tower was selected based on influent rate, and contaminant concentration in

the influent and effluent standard.

Eldho (2003) has made an attempt to study the scope of onsite

pump and treat method for the remediation of a contaminated aquifer. In this

54

study, the parameter estimation is done through field tests. Pumping tests

were carried out in 20 wells including bore wells to determine the aquifer

parameters. A contaminant transport model based on finite element method

was used to determine the exact plume position. The contaminant plume was

spread approximately over a length of 3000 m, a width of 750 m and to a

thickness of 30 m in the top aquifer layer. The pump and treat remediation of

the plume was targeted for a period of 5 years. The pump and treat system

proposed consisted of 5 pumping wells, 7 infiltration wells, and the above

ground treatment plant. In this case study, to find an optimal pump and treat

system, a trial and error procedure of testing various possibilities of pumping,

treating and recharging were done by considering various quantities of

pumping at the possible locations to achieve the targeted remediation. Totally

192.9 m3/h contaminated water had to be pumped, treated and recharged to

achieve the five year target of remediation of the contamination plume.

2.7.1 Pump-Treat-Inject System Design with Multiple Stages

Bear and Sun (1998) have developed a hierarchical optimization

model for solving multi-stage Pump-Treat-Inject (PTI) remediation design

problem. The main advantage of this technology is that the PTI strategy can

be adjusted and modified from stage to stage and this will make PTI

optimization more realistic. In this model the total cleanup time is given as a

constraint and it is divided into several stages for generating flexible optimal

solution. The upper level module takes the minimization of total cost as the

objective and uses the maximum contaminant level standards as the main

constraint. In each of the stages the number of wells is given by the upper

level module. The basic level module optimizes the well locations and

pumping / injection rates. The solutions to both the upper and basic module

are limited to local optimal. To get global optimal solution, it is necessary to

repeat the running optimization program with various initial solutions.

55

Spilitopoulous et al (2000) have developed a new optimization

technique for the optimal design of groundwater remediation system. The

remedial action involves pump and treat techniques and they have focused on

the design of the pumping scheme and the treatment components at least cost

so that the treatment process is part of the optimal remediation design. The

treatment process consists of air stripping towers and granular activated

carbon units. Two scenarios were examined, one for high concentration

source and one for low concentration source. Based on these two scenarios

the pumping rate and location of pumping well were determined. The

treatment plant is designed based on the pumping field.

Saez and Harmon (2006) have focused on improving pump and

treat remediation system by optimizing a two-stage operational scheme to

reduce volume extracted when confronted with non equilibrium desorption,

low permeability units and continuous contaminant sources such as non-

aqueous phase liquids (NAPL). In this system, two pumping rates used, Q1

and Q2, were the initial short-term high pumping rate and later long-term low

pumping rate. The optimal time to switch from a Q1 to Q2 was found by

analyzing mass transfer rate. By adopting two-stage operational scheme, the

extracted volume can be reduced than in single operating policy. In this, the

effectiveness of a two-stage operation scheme was measured for various types

of aquifers.

2.7.2 Pump-Treat-Inject System with Barriers

Bayer et al (2004) have examined the potential of partial

containment strategies to reduce the pumping rate required for the pump and

treat measure, by the installation of physical barriers such as slurry walls or

sheet piles. Different barrier settings (specified by location, shape and length

of the barrier) were analyzed with respect to their effect on the pumping rate

56

within the framework of a modelling study on a simplified contamination

scenario. The results showed that physical barriers are appropriate means to

decrease expected pumping rates as well as the variance of corresponding

pumping rate distribution at any given degree of heterogeneity.

Bayer and Finkel (2006) have investigated the performance of

vertical barriers in combination with extraction wells for the partial hydraulic

isolation of contaminated areas. In this study, they have analyzed the flow

direction and distribution of aquifer transmissivity by the introduction of a

barrier. The spatial distribution of aquifer transmissivity is considered by

means of Monte Carlo simulations. The hydraulic efficiency of the scenarios

was rated based on the expected reduction of the pumping rate that was

required to achieve contaminant capture. The pumping rate required for

various barrier-well combinations was determined to achieve robust systems.

They have concluded that the barrier-supported approach generally yielded

savings in the pumping rate compared to well system. The efficiency of the

barrier supported system was highly dependent on the interaction of variance

and integral scale of transmissivity distribution, well and barrier position as

well as direction of background flow.

2.8 OPTIMIZATION TECHNIQUES

McKinney and Lin (1994) have incorporated Genetic algorithm

into groundwater simulation model to solve three groundwater management

problems: (i) maximum pumping from an aquifer; (ii) minimum cost water

supply development; and (iii) minimum cost aquifer remediation. The results

showed that Genetic Algorithm can effectively and efficiently be used to

obtain globally optimal solutions to these groundwater management

problems. It provides solutions, which are as good as or better than those,

obtained by linear and nonlinear programming. Constraints can be

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incorporated into the formulation and do not require derivatives with respect

to decision variables as in nonlinear programming. The computational time

required for solution of GA groundwater management models increases with

the complexity of the problem.

Hilton and Culver (2000) have developed two new methods for

constraint handling within the GA framework. The first method, Additive

Penalty Method (APM) is a commonly used penalty function approach in

which a penalty cost proportional to the total constraint violation is added to

the objective function. The second method, Multiplicative Penalty Method

(MPM), multiplies objective function by a factor proportional to the total

constraints violation. The APM and MPM using constant and generation

varying weights are applied to pump and treat design examples. Overall, the

application of APM resulted in infeasible solution with small to moderate

total constraints violation. With the MPM, a set of feasible and near optimal

policies was readily identified for both examples. Additionally MPM

converges to the solution faster than the APM. These results demonstrate that

the MPM is a robust method, capable of finding feasible and optimal

solutions while using a range of weights.

Maskey et al (2002) have developed Groundwater remediation

strategy using Global Optimization Algorithms. In this study, four Global

Optimization (GO) algorithms (Genetic Algorithm, Multistart Clustering,

Adaptive Cluster covering and Controlled Random Search) were used to

minimize both cleanup time and cleanup cost taking pumping rates and well

locations as decision variables. Groundwater flow and particle-tracking

models MODFLOW and MODPATH were used. Cleanup time is a function

of pumping rate, number of pumping and recharge wells and then location.

Cleanup cost includes well installation cost and operational cost. In this paper,

real and hypothetical contaminated aquifers are considered for application and

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four algorithms are compared on its effectiveness and efficiency criteria. In all

cases Adaptive Cluster Covering was the fastest to reach the solution with

minimum model runs but the results obtained through Genetic Algorithm

gives optimum value. This paper also concluded that the cleanup time

estimated by particle tracking method, may be very high due to some particles

which may enter cells with very low or no outflow or travel through very long

paths and excluding the effect of few such particles can significantly reduce

the cleanup time.

Hilton and Culver (2005) have developed a robust GA approach

that takes into account the uncertainty of hydraulic conductivity values for

determining the best groundwater remediation design. In this study, robust

GA is applied to two cases of varying heterogeneity of a contaminated aquifer

remediated by a pump-and-treat system. For the same cases, basic GA and

noisy GA were used and the results were compared. The designs identified by

the robust GA and noisy GA performed better in constraint feasibility and

reliability than the solution found by basic GA. This work shows that

assuming a deterministic description of the aquifer either homogeneous or

heterogeneous can result in significant under-design and poor remediation

performance.

Ren and Minsker (2005) compared the performance of different

cost functions using two case studies. The findings show that the results are

more accurate for more complex cost functions, but the degree of loss in

accuracy varies substantially for the two case studies and for different

parameter settings with in each case study (such as cleanup length, risk level

or mass remaining). Overall, the realistic cost functions are able to identify

more and better solutions than simplified cost function.

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Shieh and Peralta (2005) presented a simulation/optimization

model, which used a new hybrid method combining genetic algorithm and

simulated annealing to search for an optimal design. This hybrid method is

parallel recombinative simulated annealing, which is a general-purpose

optimization approach that has good convergence of simulated annealing and

the efficient parallelization of a genetic algorithm optimization. Results show

that parallel recombinative simulated annealing performs better than

simulated annealing and genetic algorithms for optimizing system design

when including installation costs.

Mohan and Sreeram (2005) have developed an Artificial Neural

Network (ANN) model to obtain the optimal pumping policy for the

containment of groundwater contamination and validated the model by

applying it to a case study. Neural network was made up of three layers

namely, input layer, hidden layer and output layer. The number of nodes in

each layer was determined by analyzing the problem to be solved. In this

study two-optimization models, namely, a linear programming model and a

nonlinear programming model, depending on the relationship considered

between drawdown and the pumpage were used to develop optimal pumping

strategies. To simulate the groundwater flow, a finite element model was

used. For this purpose AQUI with quadrangular elements was used. For

developing neural network 49 patterns of inputs and corresponding outputs

were derived. In 49 patterns, 45 sets were used for training the neural network

model and the remaining four were used for testing the model. In this study,

back propagation algorithm was used to reduce the sum of square error. For

testing trained neural network, a program was written in “C” language using

MATLAB. Finally, they have concluded that nonlinear programming is viable

tool to obtain optimal pumping patterns for the containment of groundwater

contamination.

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Sinha et al (2007) have presented multiscale island injection genetic

algorithm in which the optimization algorithms had different multiscale

population working on different islands (groups of processors) and

periodically exchanging information. The performance of several variations

of this approach was compared with the results of a simple genetic algorithm.

The new approach found the same solution as much as 81% faster than the

simple genetic algorithm and 9 to 53% faster than other previously formulated

multiscale strategies.

Gotovac et al (2007) have presented a multi resolution adaptive

approach applicable to ground water flow and transport problems with sharp

gradients, fronts and narrow transition zones. The results demonstrate that

AFCM is robust and efficient having significant advantages over conventional

numerical methods. The multi-resolution adaptive approach implemented in

AFCM provides a different modelling opportunity in many areas of complex

groundwater flow and transport problems.

Karen et al (2006) addressed the uncertainty in the groundwater-

flow model while taking into account the standard deviation of the uncertain

parameter (hydraulic conductivity). The application Robust Optimization

(RO) used in this work can be used to develop a design that accounts for

variable degrees of risk. Convergence of the solutions determined through the

application of RO was easily observed when applying equal area sampling to

the truncated lognormal distribution and to the beta distribution. A pump-

and-treat groundwater remediation design was developed for contaminant

containment whereby groundwater flow constraints have been placed upon

this system. This optimization model can also accommodate the examination

of multiple hydrostratigraphic units in the ground water model.

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Babbar and Minsker (2006) have proposed multiscale strategies for

GAs that evaluates the design on different spatial grids at different stages of

algorithm. The strategies were initially tested on a hypothetical groundwater

remediation problem and then the best approach was used to solve a field

scale groundwater application at Umatilla Chemical Depot in Oregon. In the

Umatilla case, the multiscale GA was able to save as much as 80% of the

computational costs (relative to GA that used only the fine grid) with no loss

of accuracy.

Karen et al (2006) have developed mathematical based

groundwater flow models. These mathematical models were most effective as

predictive tools when the parameters that govern groundwater flow were

known with a high degree of certainty. The hydraulic conductivity of an

aquifer, however, is uncertain, and so remediation designs developed using

models employing one realization of the hydraulic conductivity field have an

associated risk of failure of plume contaminant. This method of optimization

is a multi scenario approach whereby multiple hydraulic conductivity fields

are examined simultaneously.

Kumar et al (2005) have compared several popular optimization

methods for solving a simple groundwater source identification problem and

showed that hybrid GA- Local Search (GA-LS) approaches were generally

more effective than using stand alone versions of each method. Some variants

of the GA-LS approaches were then implemented on a parallel supercomputer

to solve a more complex three dimensional problems. Supercomputer

implementation enabled solution to complex 3D source identification

problems in a few hours. The same size problems may take in the order of

several months if a MATLAB PC implementation is used. Even though only

source identification problems were tested by these authors, the approaches

studied by them could be readily extended to other groundwater inverse

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problems such as contaminant zone and hydraulic conductivity zone

identification problems.

David and Lund (2006) have derived the balancing rules to inform

short term draw down and recharge of water in multiple, unconnected

aquifers. Optimization formulations used either a specified target delivery rate

(for withdrawals) or available surface water supply (to recharge). Aquifers

were modelled as separate, single celled basins with lumped parameters

representing key physical, institutional, and financial characteristics. The

results showed how cost characteristics, fraction of recharged water available

for withdrawal, initial storage, maximum recharge and pumping rates, and

uncertainties regarding the future availability of water for extraction influence

recharge and withdrawal decisions.

Espinoza and Minsker (2005) have presented the new Self Adaptive

Hybrid Genetic Algorithm (SAHGA) and compared its performance to a

Nonadaptive Hybrid Genetic Algorithm (NAHGA) and Simple Genetic

Algorithm (SGA) on a ground water remediation problem. Of the two hybrid

genetic algorithms, SAHGA is shown to be far more robust than NAHGA,

providing fast convergence across broad ranges of parameter settings. For the

test problems SAHGA needs 75% fewer function evaluations than SGA, even

with an inefficient local search method. These findings demonstrate that

SAHGA has substantial promise for enabling solution of larger scale

problems than was previously possible.

Hilton and Teresa (2005) have developed a robust genetic

algorithm approach that takes into account the uncertainty of hydraulic

conductivity values when determining the best remediation design possible.

While the robust GA is a multiple realization method minimal additional

computation effort over the basic GA was required to identify robust designs.

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Mohan et al (2007) have studied the opencast mines operating in an

area with dominant groundwater features and facing hydrology-related

problems such as heaving and bursting of the mine floor due to excessive

uplift pressure. An optimization-based development of the groundwater

control system was adopted to ensure that local and regional hydro-geological

impacts were within acceptable limits. For this case study, an optimization

program based on the simulated annealing technique was developed and

applied to a three-dimensional seven-layer groundwater model. The calibrated

groundwater flow model, based on MODFLOW, was used as the simulation

component in the linked simulation optimization model. The combined model

was then used to identify the optimum depressurization strategy. The results

show that this combined simulation and optimization methodology is a viable

approach for solving large-scale groundwater management problems. But one

can use this for optimization of pumping well locations.

2.9 APPLICATION OF MODULAR GENETIC ALGORITHM

(ModGA) FOR OPTIMIZATION OF FLOW AND

TRANSPORT

In recent years, researchers have actively sought to couple aquifer

simulation models with mathematical optimization techniques to address

important groundwater quantity and quality management issues (e.g.,

Gorelick 1983, Ahlfeld et al 1988, Wagner and Gorelick 1989, Andricevic

and Kitanidis 1990, Dougherty and Marryott 1991, McKinney and Lin 1994).

The coupled simulation-optimization approach is appealing because it can

account for the complex behaviour of the groundwater flow system and

identify the best management strategy under consideration of the management

objectives and constraints. Comprehensive reviews of the simulation-

optimization approach can be found in Gorelick (1983 and 1990), Willis and

Yeh (1987), Yeh (1992), and Gorelick et al (1993). Wagner (1995) outlines

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some of the more recent advances in simulation-optimization groundwater

management modelling.

While significant progress has been made in the theoretical

development of the simulation-optimization approach for groundwater

hydraulic control and quality management, the application of simulation-

optimization models to large, field-scale problems has remained very limited.

Several factors may have contributed to this lack of practical applications.

First, the use of a simulation-optimization model requires intensive computing

capabilities, thus making many complex three-dimensional field problems

intractable. Second, there are currently very few general-purpose and easy-to-

use simulation-optimization codes available to practitioners at the field

project level. Finally, the advantages of the simulation-optimization approach

over the conventional trial-and-error approach in solving real-world problems

have not been adequately demonstrated since most studies presented in the

literature use simple hypothetical examples.

In spite of these shortcomings, however, it is believed that the

simulation-optimization models has become a widely accepted and used tool

in groundwater hydraulic control and remediation system designs, as

increasingly more powerful desktop computers and a new generation of

software packages become available.

A simulation-optimization model, referred to as ModGA, can be

used for optimal design of groundwater hydraulic control and remediation

systems under general field conditions. The model couples genetic algorithms

(GA), a global search technique inspired by biological evolution, with

MODFLOW (McDonald and Harbaugh 1988) and MT3D (Zheng 1990 and

1997), two commonly used groundwater flow and solute transport codes. The

coupled simulation-optimization model is capable of finding the global

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optimum when multiple local optima are present for certain complex

problems. It allows for multiple management periods in which optimal

pumping rates and schedules vary with time to adapt to the changing flow and

transport conditions during the remediation process.

The objective function of the model is general enough to

accommodate many different types of optimization problems with multiple

cost terms such as the capital costs associated with drilling and installation,

and the operational costs associated with pumping and treating the

contaminated groundwater. Most constraints that are commonly encountered

in hydraulic control and remediation system design can be incorporated,

including hydraulic gradients, pumping capacities, head and concentration

limits, and the maximum number of active wells allowed at any time out of all

candidate wells.

ModGA is fully compatible with the MODFLOW and MT3D

simulators and supports all the discretization and simulation capabilities of

these codes. After flow and/or transport models have been constructed and

calibrated for a specific site, they can be used directly by ModGA in the

remediation design phase without any modification to the MODFLOW and

MT3D input files. If the user-specified constraints involve the flow conditions

only, ModGA will automatically skip transport simulation. One of the key

features of ModGA is the simplicity and ease with which it can be applied to

field problems.

This is made possible by the choice of GA as the optimization

technique in the coupled simulation-optimization code. As one of the global

optimization techniques that seek to optimize the objective function by

mimicking a natural selection process, GA is simple to implement because it

is independent of the form of the objective function and the nature of the

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simulation code. Using GA, there is no need to calculate the derivatives

(gradients) of the objective function with respect to the variables to be

optimized, thus eliminating a primary source of numerical difficulty

associated with the simulation-optimization approach. As a result, GA based

optimization model is generally more robust and stable than a gradient based

model, especially when the flow and/or transport models are complex and

highly nonlinear.

The most significant limitation of ModGA, as with any other

optimization code based on a global search technique, is the intensive

computational requirement due to the large number of forward flow and/or

transport simulation runs needed. While this limitation will be mitigated to a

large extent with the rapid advances in computer powers, it should be kept in

mind that the most effective use of ModGA is to identify a near-optimal

solution generally with a much smaller number of forward simulation runs

than that would be required to identify the absolute optimum. Although a

near-optimal solution may be slightly different from the global optimum,

reaching the global optimum may require so much more computational time

that it is neither practical nor necessary.

Groundwater flow and solute transport modelling using

MODFLOW and MT3D is a prerequisite to the application of ModGA. Thus,

it is assumed that the user of ModGA is already familiar with MODFLOW

and MT3D, and groundwater modelling in general.

2.10 ANT COLONY OPTIMIZATION

The Ant Colony Optimization (ACO) method is inspired by the fact

that ants are able to find the shortest route between their nest and a food

source. This is accomplished by using pheromone trails as a form of indirect

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communication. Ant colony simulation techniques are adapted to minimize

the number of monitoring locations in the sampling network without

significant loss of information. They can decide the optimal movement of

pumping wells location to achieve maximum concentration removal from the

contaminated plume using the prior information. More recently, ACO algorithms

have been applied to solve a wide range of engineering and science problems such

as random number generators, autonomous decentralized shop floor routing,

bandwidth minimization problem in a large-scale power transmissions system

redundancy apportionment problem in electrical and mechanical systems and

capacitated minimum spanning tree problems applied to telecommunication

networks. To date, a limited number of studies have been published in which

ACO or swarm intelligence has been used to solve water resources and

hydrology problems but these do not focus on groundwater management and

remediation design optimization problems in general and optimization of

pumping well location in particular. Among water resources related studies

Maier (2003) used ACO to optimize water distribution systems designs and

Wegley (2000) used particle swarm optimization to determine pump speeds to

minimize the total costs in water distribution systems. Abbaspour (2001) used

ACO to solve an inverse modelling problem of identifying unsaturated soil

parameters.

2.11 SUMMARY

The growing body of the literature indicates that many models have

been developed so far to study the groundwater flow and contaminant

movement. The behaviour of contaminant movement and its remediation

have been investigated by large number numerical models developed after

1970s. The three dimensional solute transport codes have been developed but

the increased computation effort required to solve them has limited most

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solutions to two-dimensional vertical cross sections. There are a few ready-

to-use, user-friendly software packages that can deal effectively, and

efficiently, with real world problems of groundwater remediation. One such is

MODFLOW and has become the worldwide standard three-dimensional

ground-water flow model, originally developed in the U.S.A., because of its

ability to simulate a wide variety of systems, it’s extensive publicly available

documentation, and its rigorous USGS peer review (McDonald and Harbaugh

1988). The advantages of MODFLOW include numerous facilities for data

preparation, easy exchange of data in standard form, extended worldwide

experience, continuous development, availability of source code, and

relatively low price. However, surface runoff and unsaturated flow are not

included in the package and hence in case of transient problems, MODFLOW

can not be applied if the flux at the groundwater table depends on the

calculated head and the function is not known in advance. It is simple to use

and maintain, can be executed on a variety of computers with minimal

changes, and has the ability to manage the large data sets required when

running large problems. The division of MODFLOW into modules permits

the user to examine specific hydrologic features of the model independently.

This also facilitates development of additional capabilities because new

modules or packages can be added to the program without modifying the

existing ones. The input/output system of MODFLOW was designed for

optimal flexibility. Visual MODFLOW package with WinPEST and the

Visual MODFLOW 3D-Explorer gives the most complete and powerful

graphical modelling environment available MODFLOW.

This user-friendly combined three dimensional simulation-

optimization model, however, has its own limitation. Therefore, there is a

need to develop a combined simulation optimization approach using

evolutionary algorithm, which is suitable for nonlinear and transient problems

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in order to optimize the pumping well locations for different management

periods whereas this module is not available in any of the models described

above including the recent model Beyond MODFLOW. The sensitivity of

pumping well location for pumping and recharge rate is not yet fully analyzed

and remains as one important topic which need to be addressed.