MAJID KHANM.Phil Geophysics Hydrogeologist

MAJID KHANM.Phil Geophysics Hydrogeologist

Introduction to Groundwater Modelling

Presented to :

Dr.Zulfiqar Ahmed

Presented by:

Email: mkhidden@hotmail.

Presentation Outline

Groundwater in Hydrologic Cycle

Why Groundwater Modeling is needed?

Mathematical Models

Model Design

Groundwater Flow Models

Groundwater in Hydrologic Cycle

Types of Terrestrial WaterTypes of Terrestrial Water

Ground waterGround water

SoilSoilMoistureMoisture

SurfaceWater

Unsaturated Zone / Zone of Aeration / Vadose (Soil Water)

Pores Full of Combination of Air and Water

Zone of Saturation (Ground water)

Pores Full Completely with Water

Groundwater

Important source of clean waterMore abundant than SW

Linked to SW systems

Sustains flows in streams

Baseflow

Why Groundwater Modelling is needed?

Groundwater

• An important component of water resource systems.

• Extracted from aquifers through pumping wells and supplied for domestic use, industry and agriculture.

• With increased withdrawal of groundwater, the quality of groundwater has been continuously deteriorating.

• Water can be injected into aquifers for storage and/or quality control purposes.

Management of a groundwater system, means making such decisions as:

• The total volume that may be withdrawn annually from the aquifer.

• The location of pumping and artificial recharge wells, and their rates.

• Decisions related to groundwater quality.

Groundwater contamination by:

Hazardous industrial wastes

Leachate from landfills

Agricultural activities such as the use of fertilizers and pesticides

MANAGEMENT means making decisions to achieve goals without violating specified constraints.

Good management requires information on the response of the managed system to the proposed activities.

This information enables the decision-maker, to compare alternative actions and to ensure that constraints are not violated.

Any planning of mitigation or control measures, once contamination has been detected in the saturated or unsaturated zones, requires the prediction of the path and the fate of the contaminants, in response to the planned activities.

Any monitoring or observation network must be based on the anticipated behavior of the system.

We should have a CALIBRATED MODEL of the aquifer, especially,we should know the aquifer’s natural replenishment (from precipitation and through aquifer boundaries).

Prior to determining the management scheme for any aquifer:

We should have a POLICY that dictates management objectives and constraints.

Obviously, we also need information about the water demand)quantity and quality, current and future ,(interaction with other

parts of the water resources system, economic information, sourcesof pollution, effect of changes on the environment---springs, rivers...,

The model will provide the response of the aquifer (water levels,concentrations, etc.) to the implementation of any managementalternative .

GROUND WATER MODELING

WHY MODEL?

•To make predictions about a ground-water system’s response to a stress

•To understand the system

•To design field studies

•Use as a thinking tool

Use of Groundwater models

Can be used for three general purposes:• To predict or forecast expected artificial

or natural changes in the system. Predictive is more applied to deterministic models since it carries higher degree of certainty, while forecasting is used with probabilistic (stochastic) models.

Use of Groundwater models

• To describe the system in order to analyse various assumptions

• To generate a hypothetical system that will be used to study principles of groundwater flow associated with various general or specific problems.

Ground Water Flow Modelling

A Powerful Tool

for furthering our understanding of hydrogeological systems

Importance of understanding ground water flow modelsConstruct accurate representations of hydrogeological systems

Understand the interrelationships between elements of systems

Efficiently develop a sound mathematical representation

Make reasonable assumptions and simplifications

Understand the limitations of the mathematical representation

Understand the limitations of the interpretation of the results

Introduction to Ground Water Flow Modelling

Predicting heads (and flows) and Approximating parameters

Solutions to the flow equationsMost ground water flow models are solutions of some form of the ground water flow equation

PotentiometricSurface

x

xx

ho

x0

h(x)

x

K q

“e.g., undirectional, steady-state flow within a confined aquifer

The partial differential equation needs to be solved to calculate head as a function of position and time, i.e., h=f(x,y,z,t)

h(x,y,z,t)?

Darcy’s Law Integrated

Processes we might want to model

Groundwater flow

calculate both heads and flow

Solute transport – requires information on flow (velocities)

Calculate concentrations

MODELING PROCESS

ALL IMPORTANT MECHANISMS & PROCESSES MUST BE INCLUDED IN THE MODEL, OR RESULTS WILL BE INVALID.

TYPES OF MODELS

CONCEPTUAL MODEL QUALITATIVE DESCRIPTION OF SYSTEM "a cartoon of the system in your mind"

MATHEMATICAL MODEL MATHEMATICAL DESCRIPTION OF SYSTEM

SIMPLE - ANALYTICAL (provides a continuous solution over the model domain)

COMPLEX - NUMERICAL (provides a discrete solution - i.e. values are calculated at only a few points)

ANALOG MODEL e.g. ELECTRICAL CURRENT FLOW through a circuit board with resistors to represent hydraulic conductivity and capacitors to represent storage coefficient

PHYSICAL MODEL e.g. SAND TANK which posses scaling problems

Mathematical Models

Mathematical model: simulates ground-water flow and/or

solute fate and transport indirectly by means of a set of governing equations thought to represent the physical processes that occur in the system.

(Anderson and Woessner, 1992)

Components of a Mathematical Model

• Governing Equation

(Darcy’s law + water balance equation) with head (h) as the dependent variable

• Boundary Conditions

• Initial conditions (for transient problems)

R x y Q

y

x

z

1. Consider flux (q) through REV2. OUT – IN = - Storage3. Combine with: q = -KK grad h

q

Derivation of the Governing Equation

Law of Mass Balance + Darcy’s Law = Governing Equation for Groundwater Flow ---------------------------------------------------------------

div q = - Ss (h t) (Law of Mass Balance)

q = - K grad h (Darcy’s Law)

div (K grad h) = Ss (h t)

(Ss = S / z)

0)()()(

z

hK

zy

hK

yx

hK

xzyx

General governing equationfor steady-state, heterogeneous, anisotropic

conditions, without a source/sink term

*)()()( Rz

hK

zy

hK

yx

hK

xzyx

with a source/sink term

*)()()( Rt

hS

z

hK

zy

hK

yx

hK

xszyx

General governing equation for transient, heterogeneous, and anisotropic conditions

Specific StorageSs = V / (x y z h)

Figures taken from Hornberger et al. (1998)

Unconfined aquifer

Specific yield

Confined aquifer

Storativity

S = V / A hS = Ss b

b

hh

*)()()( Rt

hS

z

hK

zy

hK

yx

hK

xszyx

Rt

hS

y

hT

yx

hT

xyx

)()(

Rt

hS

y

hhK

yx

hhK

xyx

)()(

2D confined:

2D unconfined:

Storage coefficient (S) is either storativity or specific yield.S = Ss b & T = K b

General 3D equation

Types of Solutions of Mathematical Models

• Analytical Solutions: h= f(x,y,z,t) (example: Theis equation)

• Numerical SolutionsFinite difference methodsFinite element methods

• Analytic Element Methods (AEM)

Finite Difference Modelling

3-D Finite Difference ModelsRequires vertical discretization (or layering) of model

K1K2

K3

K4

Model Design

MODELs NEED

GeometryMaterial Properties (K, S, T, Φe, R, etc.)

Boundary Conditions (Head, Flux, Concentration etc.)

Stress - changing boundary condition

Model DesignModel Design

• Conceptual Model• Selection of Computer Code• Model Geometry• Grid• Boundary array• Model Parameters• Boundary Conditions• Initial Conditions.

Concept DevelopmentConcept Development

• Developing a conceptual model is the initial and most important part of every modelling effort. It requires thorough understanding of hydrogeology, hydrology and dynamics of groundwater flow.

Conceptual Model

A descriptive representationof a groundwater system that incorporates an interpretation of the geological & hydrological conditions. Generally includes information about the water budget. May include information on water chemistry.

Selection of Computer CodeSelection of Computer Code

• Which method will be used depends largely on the type of problem and the knowledge of the model design.

• Flow, solute, heat, density dependent etc.• 1D, 2D, 3D

Model GeometryModel Geometry

• Model geometry defines the size and the shape of the model. It consists of model boundaries, both external and internal, and model grid.

BoundariesBoundaries

• Physical boundaries are well defined geologic and hydrologic features that permanently influence the pattern of groundwater flow (faults, geologic units, contact with surface water etc.)

BoundariesBoundaries

• Hydraulic boundaries are derived from the groundwater flow net and therefore “artificial” boundaries set by the model designer. They can be no flow boundaries represented by chosen stream lines, or boundaries with known hydraulic head represented by equipotential lines.

HYDRAULIC BOUNDARIES

A streamline (flowline) is also a hydraulic boundary because by definition, flow is ALWAYS parallel to a streamflow. It can also be said that flow NEVER crosses a streamline; therefore it is similar to an IMPERMEABLE (no flow) boundary

BUT

Stress can change the flow pattern and shift the position of streamlines; therefore care must be taken when using a streamline as the outer boundary of a model.

TYPES OF MODEL BOUNDARY

NO-FLOW BOUNDARYNeither HEAD nor FLUX isSpecified. Can represent aPhysical boundary or a flowLine (Groundwater Divide)

SPECIFIED HEAD ORCONSTANT HEAD BOUNDARYh = constantq is determined by the model.And may be +ve or –ve accordingto the hydraulic gradient developed

TYPES OF MODEL BOUNDARY (cont’d)

SPECIFIED FLUX BOUNDARYq = constanth is determined by the model(The common method of simulationis to use one injection well for eachboundary cell)

HEAD DEPENDANT BOUNDARYhb = constantq = c (hb – hm) and c = f (K,L) and is calledCONDUCTANCEhm is determined by the model andits interaction with hb

Boundary Types

Specified Head/Concentration: a special case of constant head (ABC, EFG)

Constant Head /Concentration: could replace (ABC, EFG)

Specified Flux: could be recharge across (CD)

No Flow (Streamline): a special case of specified flux (HI)

Head Dependent Flux: could replace (ABC, EFG)

Free Surface: water-table, phreatic surface (CD)

Seepage Face: pressure = atmospheric at ground surface (DE)

Initial ConditionsInitial Conditions

• Values of the hydraulic head for each active and constant-head cell in the model. They must be higher than the elevation of the cell bottom.

• For transient simulation, heads to resemble closely actual heads (realistic).

• For steady state, only hydraulic heads in constant head-cell must be realistic.

Model ParametersModel Parameters

• Time

• Space (layer top and bottom)

• Hydrogeological characteristics (hydraulic conductivity, transmissivity, storage parameters and effective porosity)

TimeTime

• Time parameters are specified when modelling transient (time dependent) conditions. They include time unit, length and number of time steps.

• Length of stress periods is not relevant for steady state simulations

GridGrid

• In Finite Difference model, the grid is formed by two sets of parallel lines that are orthogonal. The blocks formed by these lines are called cells. In the centre of each cell is the node – the point at which the model calculates hydraulic head. This type of grid is called block-centered grid.

GridGrid

• Grid mesh can be uniform or custom, a uniform grid is better choice when– Evenly distributed aquifer characteristics data– The entire flow field is equally important– Number of cells and size is not an issue

MODEL GRIDS

Grids It is generally agreed that from a practical

point-of-view the differences between grid types are minor and unimportant.

USGS MODFLOW employs a body-centred grid.

Boundary array (cell type)Boundary array (cell type)

• Three types of cells– Inactive cells through which no flow into or

out of the cells occurs during the entire time of simulation.

– Active, or variable-head cells are free to vary in time.

– Constant-head cell, model boundaries with known constant head.

Hydraulic conductivity and Hydraulic conductivity and transmissivitytransmissivity

• Hydraulic conductivity is the most critical and sensitive modelling parameter.

• Realistic values of storage coefficient and transmissivity, preferably from pumping test, should be used.

Effective porosityEffective porosity

• Required to calculate velocity, used mainly in solute transport models

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.

• It uses 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.

MODFLOW

USGS code Finite Difference Model

• MODFLOW 88• MODFLOW 96• MODFLOW 2000

MODFLOW

(Three-Dimensional Finite-Difference Ground-Water Flow Model)

• When properly applied, MODFLOW is the recognized standard model.

• 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.

MT3D

(A Modular 3D Solute Transport Model)

• MT3D is a comprehensive three-dimensional numerical model for simulating solute transport in complex hydrogeologic settings.

• 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.

FEFLOW

(Finite Element Subsurface Flow System)

FEFLOW is a finite-element package for simulating 3D and 2D fluid density-coupled flow, contaminant mass (salinity) and heat transport in the subsurface.

HST3D

(3-D Heat and Solute Transport Model)

The Heat and Solute Transport Model HST3D simulates ground-water flow and associated heat and solute transport in three dimensions.

SEAWAT

(Three-Dimensional Variable-Density Ground-Water Flow)

• The SEAWAT program was developed to simulate three-dimensional, variable- density, transient ground-water flow in porous media.

• The source code for SEAWAT was developed by combining MODFLOW and MT3D into a single program that solves the coupled flow and solute-transport equations.

SUTRA

(2-D Saturated/Unsaturated Transport Model)

• SUTRA is a 2D groundwater saturated-unsaturated transport model, a complete saltwater intrusion and energy transport model.

• SUTRA employs a two-dimensional hybrid finite-element and integrated finite-difference method to approximate the governing equations that describe the two interdependent processes.

• A 3-D version of SUTRA has also been released.

SWIM

(Soil water infiltration and movement model)

• SWIMv1 is a software package for simulating water infiltration and movement in soils.

• SWIMv2 is a mechanistically-based model designed to address soil water and solute balance issues.

• The model deals with a one-dimensional vertical soil profile which may be vertically inhomogeneous but is assumed to be horizontally uniform.

• It can be used to simulate runoff, infiltration, redistribution, solute transport and redistribution of solutes, plant uptake and transpiration, evaporation, deep drainage and leaching.

HAPPY MODELLING

THANKS