INTRODUCTION GROUNDWATER FLOW MODELS Groundwater models are computer models of groundwater flow systems. They are used by hydro geologists. They are used to simulate and predict aquifer conditions. They may be a scale model or an electric model of a groundwater situation or aquifer. A groundwater model is meant to be a (computer) program for the calculation of groundwater flow and level. Some groundwater models include (chemical) quality aspects of the groundwater.

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used to predict the effects of hydrological changes (like groundwater abstraction or irrigation developments) on the behaviour of the aquifer and are often named groundwater simulation models. based on groundwater flow equations which are differential equations, solved only by approximate methods . For the calculations, one needs inputs like: hydrological inputs, operational inputs, external conditions: initial and boundary conditions, (Hydraulic) parameters. The model may have chemical components like water salinity, soil salinity and other quality indicators of water and soil, for which inputs may also be needed.

Hydrological inputs:

Hydrological inputs may consists of hydrological data like rainfall, evapo-transpiration and surface runoff which determine the recharge. They may vary from time to time and from place to place.

Operational inputs :

Operational inputs They concern human interferences with the water management like irrigation, drainage pumping from wells, water table control, and the operation of retention or infiltration basins. hydrological nature. also vary in time and space. Many groundwater models are made for the purpose of assessing the effects hydraulic engineering measures .

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Fig. 2 Boundary conditions

Boundary and initial conditions:

Boundary and initial conditions Boundary conditions: – -related to levels of the water table -Artesian pressures - hydraulic head along the boundaries of the model on the one hand (the head conditions ), or to groundwater inflows and outflows along the boundaries of the model on the other hand (the flow conditions ).

Initial conditions:

Initial conditions refers to initial values of elements. that may increase or decrease in the course of the time inside the model domain. they cover largely the same phenomena as the boundary conditions do.

Fig. 3 Example of parameters of irrigation cum groundwater model :

Fig. 3 Example of parameters of irrigation cum groundwater model

Parameters :

Parameters usually concern the geometry of and distances in the domain to be modelled and physical properties of the aquifer that are more or less constant with time but that may be variable in space . Important parameters are:- Topography thicknesses of soil layers permeability for water aquifer transmissivity and resistance aquifer porosity storage coefficient capillarity of the unsaturated zone.

Applicability :

Applicability depends on the accuracy of the input data and the parameters. Determination of these requires considerable study.

Types of groundwater models:

Types of groundwater models Groundwater models can be one dimensional, two dimensional, three dimensional, semi three dimensional.

One, two and three dimensional models:

One, two and three dimensional models One-dimensional models can be used for the vertical flow in a system of parallel horizontal layers. Two dimensional models apply to a vertical plane while it is assumed that the groundwater conditions repeat themselves in other parallel vertical planes. Spacing equations of subsurface drains and the groundwater energy balance applied to drainage equations are examples of two-dimensional groundwater models. Three dimensional models like MODFLOW require discretization of the entire flow domain.

Semi three-dimensional model :

Semi three-dimensional model In semi 3-dimensional models:- the horizontal flow is described by 2-dimensional flow equations (i. e. in horizontal x and y direction). vertical flows (in z-direction) are described with a 1-dimensional flow equation, or derived from a water balance of horizontal flows. Two classes of semi 3-dimensional models are- Continuous models or radial models Discretized models or prismatic models .

Two classes of semi 3-dimensional models are-:

Two classes of semi 3-dimensional models are- Continuous models or radial models consisting of 2 dimensional sub models in vertical radial planes intersecting each other in one single axis. The flow pattern is repeated in each vertical plane fanning out from the central axis. Discretized models or prismatic models consisting of sub models formed by vertical blocks or prisms for the horizontal flow combined with one or more methods of superposition of the vertical flow.

MODEL DEVELOPMENT:

MODEL DEVELOPMENT A groundwater model application can be considered to be two distinct processes. the first process is model development resulting in a software product. the second process is application of that product for a specific purpose. developed in a logical sequence .

Model development:

Model development

MODELLING OF GROUNDWATER FLOW AND MASS TRANSPORT:

MODELLING OF GROUNDWATER FLOW AND MASS TRANSPORT Groundwater modelling begins with a conceptual understanding of the physical problem. The next step in modelling is translating the physical system into mathematical terms. In general, the results are the familiar groundwater flow equation and transport equations. The governing flow equation for three-dimensional saturated flow in saturated porous media is:

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where, Kxx, Kyy, Kzz = hydraulic conductivity along the x,y,z axes which are assumed to be parallel to the major axes of hydraulic conductivity; h = piezometric head; Q = volumetric flux per unit volume representing source/sink terms; Ss = specific storage coefficient defined as the volume of water released from storage per unit change in head per unit volume of porous material.

transport of solutes in the saturated zone:

transport of solutes in the saturated zone The transport of solutes in the saturated zone is governed by the advection-dispersion equation which for a porous medium with uniform porosity distribution is formulated as follows:

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where, c = concentration of the solute R c = sources or sinks; Dij = dispersion coefficient tensor; V i = velocity tensor. Basic processes, that are considered, include groundwater flow, solute transport and heat transport. Most groundwater modelling studies are conducted using either deterministic models , based on precise description of cause-and-effect or input-response relationships or stochastic models reflecting the probabilistic nature of a groundwater system.

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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 most used approaches 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.

GROUNDWATER FLOW MODELS :

GROUNDWATER FLOW MODELS The most widely used numerical groundwater flow model is MODFLOW which is a three-dimensional model , originally developed by the U.S. Geological Survey (McDonald and Harbaugh, 1988). It uses block-centred finite difference scheme for saturated zone. 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, 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 .

Various models used are:-:

Various models used are:- 1. 3DFEMFAT (3-D Finite-Element Model of Flow and Transport through Saturated-Unsaturated Media) 2. AQUA3D (3-D Groundwater Flow and Contaminant Transport Model) 3. AT123D (Analytical Groundwater Transport Model for Long-Term Pollutant Fate and Migration) 4. BIOF&T 2-D/3-D (Biodegradation, Flow and Transport in the Saturated/Unsaturated Zones) 5. Chemflo (Simulates Water and Chemical Movement in Unsaturated Soils) 6. ChemFlux (Finite Element Mass Transport Model) 7. FEFLOW (Finite Element Subsurface Flow System) 8. FLONET/TRANS (2-D cross-sectional groundwater flow and contaminant transport modelling)

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9. FLOWPATH (2-D Groundwater Flow, Remediation, and Wellhead Protection Model) 10. GFLOW (Analytic Element Model with Conjunctive Surface Water and Groundwater Flow and a MODFLOW Model Extract Feature) 11. GMS (Groundwater Modelling Environment for MODFLOW, MODPATH, MT3D, RT3D, FEMWATER, SEAM3D, SEEP2D, PEST, UTCHEM, and UCODE) 12. Groundwater Vistas (Model Design and Analysis for MODFLOW, MODPATH, MT3D, RT3D, PEST and UCODE) 13. HST3D (3-D Heat and Solute Transport Model) 14. MicroFEM (Finite-Element Program for Multiple-Aquifer Steady-State and Transient Groundwater Flow Modelling) 15. MOC (2-D Solute Transport and Dispersion in Groundwater) 16. MOCDENSE (Two-Constituent Solute Transport Model for Groundwater Having Variable Density) 17. MODFLOW (Three-Dimensional Finite-Difference Ground-Water Flow Model),etc.

MODFLOW:

(Three-Dimensional Finite-Difference 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 program that can be readily modified, 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 MODFLOW report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation 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 Sub routines 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. MODFLOW

CONCLUDING REMARKS:

CONCLUDING REMARKS Mathematical models are tools, which are used in studying groundwater systems. In general, mathematical models are used to simulate (or to predict) the groundwater flow and in some cases the solute and/or heat transport. Predictive simulations must be viewed as estimates, dependent upon the quality and uncertainty of the input data. Models may be used as predictive tools; however field monitoring must be incorporated to verify model predictions. The best method of eliminating or reducing modelling errors is to apply good hydro geological judgement and to question the model simulation results. If the results do not make physical sense, find out why.

REFERENCES :

REFERENCES 1. Anderson, M.P. and W.W. Woessner, 1992, Applied Groundwater Modelling . Academic Press, Inc., San Diego, CA., 381 p. 2. American Society for Testing and Materials, 1993, Standard Guide for Application of a Ground-Water Flow Model to a Site-Specific Problem . ASTM Standard D 5447-93, West Conshohocken, PA, 6 p. 3. American Society for Testing and Materials, 1995, Standard Guide for Subsurface Flow and Transport Modelling . ASTM Standard D 5880-95, West Conshohocken, PA, 6 p. 4. Bear, J., and A. Verruijt, 1987, Modelling Groundwater Flow and Pollution . D. Reidel Publishing Company, 414 p. 5. Franke, O.L., Bennett, G.D., Reilly, T.E., Laney, R.L., Buxton, H.T., and Sun, R.J., 1991, Concepts and Modelling in Ground-Water Hydrology -- A Self-Paced Training Course . U.S. Geological Survey Open-File Report 90-707. 6. Kashyap, Deepak, 1989, Mathematical Modelling for Groundwater Management– Status in India . Indo-French Seminar on Management of Water Resources, 22- 24 September, 1989, Festival of France-1989, Jaipur, pp. IV-59 to IV-75. 7. Kinzelbach, W., 1986, Groundwater Modelling: An Introduction with Sample Programs in BASIC . Elsevier, New York, 333 p. 8. Kumar, C. P., 1992, Groundwater Modelling – In. Hydrological Developments in India since Independence. A Contribution to Hydrological Sciences, National Institute of Hydrology, Roorkee, pp. 235-261. 9. Kumar, C. P., 2001, Common Ground Water Modelling Errors and Remediation. Journal of Indian Water Resources Society, Volume 21, Number 4, October 2001, pp. 149-156. 10. McDonald, M.G. and A.W. Harbaugh, 1988, A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model , USGS TWRI Chapter 6-A1, 586 p. .

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