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Numerical Ground WaterModeling

By:- Pankaj Khanna

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Numerical Ground water model

Computer model

Recharge Discharge

Natural conditions Man made conditions

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S teps Involved

U nderstanding physical behavior of system

Translation of physical properties into mathematical terms

Calibration and verification

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Groundwater Recharge Rain and snow Natural Water which Infiltrates is used by plants and is subject to

evaporation ; if infiltration rate exceeds these two process, waterpercolates down

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Groundwater Discharge

Discharges groundwater naturally to stream, rivers, springs etc. Pumpage from wells

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Modeling of groundwater flow and masstransport

The governing flow equation for three-dimensional saturatedflow in saturated porous media is:

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

where,c = concentration of the solute;Rc = sources or sinks;Dij = dispersion coefficient tensor;vi = velocity tensor.

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C hanges in chemical concentration

A dvective transport, in which dissolved chemicals are moving with theflowing groundwater;

hydrodynamic dispersion, in which molecular and ionic diffusion andsmall-scale variations in the flow velocity through the porous media cause

the paths of dissolved molecules and ions to diverge or spread from theaverage direction of groundwater flow

fluid sources, where water of one composition is introduced into andmixed with water of a different composition

reactions, in which some amount of a particular dissolved chemicalspecies may be added to or removed from the groundwater as aresult of chemical, biological, and physical reactions in the water or between the water and the solid aquifer materials or other separateliquid phases.

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Numerical Methods to solve equations

A rea divided into grids

finite-difference methods finite-element methods

approximate the firstderivatives in the partialdifferential equations asdifference quotients

use assumed functions of the dependent variablesand parameters toevaluate equivalentintegral formulations of

the partial differentialequations

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E ach grid has nodes at corners E ach node has a associated basis function

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Matrix S olution Technique

Direct Iterative

a sequence of operations isperformed only once to solve

the matrix equation

process of successiveapproximation

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Boundary and initial conditions

S teady state: onlyboundary conditionsrequired

Transient conditions:Boundary and initialconditions required

The boundary conditions are generally of three types:1) specified value (head or concentration),2) specified flux (corresponding to a specified gradient of heador concentration), or3) value-dependent flux (or mixed boundary condition, inwhich the flux across a boundary is related to both the normalderivative and the value)

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Groundwater flow models

The most widely used numerical groundwater flow model is MODFLOW which isa three-dimensional model, originally developed by the U. S . Geological S urvey(McDonald and Harbaugh, 1988). Because of its ability to simulate a wide varietyof systems,Other examples are:

3DFEMFAT (3-D Finite-Element Model of Flow and Transport throughS aturated-Unsaturated Media): Typical applications are infiltration, wellheadprotection, agriculture pesticides, sanitary landfill, radionuclide disposalsites, hazardous waste disposal sites, density-induced flow and transport,saltwater intrusion, etc.

AQUA3D (3-D Groundwater Flow and C ontaminant Transport Model): solvestransient groundwater flow with inhomogeneous and anisotropic flow conditions

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References

Use of numerical models to simulate groundwater flow andtransport: L.F. KONIKOW, U. S .A Geological survey

Groundwater flow models, C . P. Kumar, National Institute of Hydrology, Roorkee 247667 (Uttaranchal)

What is a numerical groundwater model? by william meyer and

edward w. wolfe, april 10, 2011

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Thank you