Presented in M.Phil class during course work in front of Dr. Zulfiqar Ahmad Chairman Department of Earth sciences and class fellows as well

1. Introduction to Groundwater Modelling
Presented to :
Dr.Zulfiqar Ahmed
Presented by:
MAJID KHAN
M.Phil Geophysics
Hydrogeologist
Email: mkhidden@hotmail.

2. Presentation Outline
Groundwater in Hydrologic Cycle
Why Groundwater Modeling is needed?
Mathematical Models
Model Design
Groundwater Flow Models

3. Groundwater in Hydrologic Cycle

5. Types of Terrestrial Water
Surface
Water
Soil
Moisture
Ground water

6. Pores Full of Combination of Air and Water
Unsaturated Zone / Zone of Aeration / Vadose
(Soil Water)
Zone of Saturation (Ground water)
Pores Full Completely with Water

7. Groundwater
Important source of clean water
More abundant than SW
Baseflow Linked to SW systems
Sustains flows
in streams

9. Why Groundwater Modelling is needed?

10. 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.

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• The total volume that may be withdrawn annually from the aquifer.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

12.  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.

13. :Prior to determining the management scheme for any aquifer
We should have a CALIBRATED MODEL of the aquifer, especially,
we should know the aquifer’s natural replenishment (from
precipitation and through aquifer boundaries).
,The model will provide the response of the aquifer (water levels
concentrations, etc.) to the implementation of any management
. alternative
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, sources
,...of pollution, effect of changes on the environment---springs, rivers

14. 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

15. 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.

16. 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.

17. Ground Water Flow Modelling
A Powerful Tool
for furthering our understanding
of hydrogeological systems
Importance of understanding ground water flow models
Construct 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

18. Introduction to Ground Water Flow Modelling
Predicting heads (and flows) and
Approximating parameters
h(x,y,z,t)?
Poten
Solutions to the flow equations tiome
tri
Most ground water flow models are Surfa c
ce
solutions of some form of the ground
water flow equation
x
The partial differential equation needs
to be solved to calculate head as a q
function of position and time, K
i.e., h=f(x,y,z,t)
“e.g., undirectional, steady-state flow ho x x h(x)
x
within a confined aquifer
Darcy’s Law Integrated 0 x

19. Processes we might want to model
 Groundwater flow
calculate both heads and flow
 Solute transport – requires information
on flow (velocities)
 Calculate concentrations

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

21. 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

22. Mathematical Models

23. 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)

24. 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)

25. Derivation of the Governing Equation
R ∆x ∆y Q
q
∆z
∆x
∆y
1. Consider flux (q) through REV
2. OUT – IN = - ∆Storage
3. Combine with: q = -K grad h

26. 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)

27. General governing equation
for steady-state, heterogeneous, anisotropic
conditions, without a source/sink term
∂ ∂h ∂ ∂h ∂ ∂h
( K x ) + ( K y ) + ( Kz ) = 0
∂x ∂x ∂y ∂y ∂z ∂z
with a source/sink term
∂ ∂h ∂ ∂h ∂ ∂h
( Kx ) + ( K y ) + ( Kz ) = − R *
∂x ∂x ∂y ∂y ∂z ∂z

28. General governing equation for transient,
heterogeneous, and anisotropic conditions
∂ ∂h ∂ ∂h ∂ ∂h ∂h
( Kx ) + ( K y ) + ( Kz ) = Ss −R*
∂x ∂x ∂y ∂y ∂z ∂z ∂t
Specific Storage
Ss = ∆V / (∆x ∆y ∆z ∆h)

29. ∆h
∆h
b
S=V/A∆ h
S = Ss b Confined aquifer
Unconfined aquifer
Specific yield Storativity
Figures taken from Hornberger et al. (1998)

30. General 3D equation
∂ ∂h ∂ ∂h ∂ ∂h ∂h
( Kx ) + ( K y ) + ( Kz ) = Ss −R*
∂x ∂x ∂y ∂y ∂z ∂z ∂t
∂ ∂h ∂ ∂h ∂h
2D confined: (Tx ) + (Ty ) = S −R
∂x ∂x ∂y ∂y ∂t
2D unconfined: ∂ ∂h ∂ ∂h ∂h
( hKx ) + ( hKy ) = S −R
∂x ∂x ∂y ∂y ∂t
Storage coefficient (S) is either storativity or specific yield.
S = Ss b & T = K b

31. Types of Solutions of Mathematical Models
• Analytical Solutions: h= f(x,y,z,t)
(example: Theis equation)
• Numerical Solutions
Finite difference methods
Finite element methods
• Analytic Element Methods (AEM)

32. Finite Difference Modelling
3-D Finite Difference Models
Requires vertical discretization (or layering) of model
K1
K2
K3
K4

33. Model Design

34. MODELs NEED
Geometry
Material Properties (K, S, T, Φe, R, etc.)
Boundary Conditions (Head, Flux, Concentration etc.)
Stress - changing boundary condition

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

36. Concept 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.

37. Conceptual Model
A descriptive representation
of 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.

38. Selection 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

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

40. Boundaries
• 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.)

41. Boundaries
• 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.

42. 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.

43. TYPES OF MODEL BOUNDARY
NO-FLOW BOUNDARY
Neither HEAD nor FLUX is
Specified. Can represent a
Physical boundary or a flow
Line (Groundwater Divide)
SPECIFIED HEAD OR
CONSTANT HEAD BOUNDARY
h = constant
q is determined by the model.
And may be +ve or –ve according
to the hydraulic gradient developed

44. TYPES OF MODEL BOUNDARY (cont’d)
SPECIFIED FLUX BOUNDARY
q = constant
h is determined by the model
(The common method of simulation
is to use one injection well for each
boundary cell)
HEAD DEPENDANT BOUNDARY
hb = constant
q = c (hb – hm)
and c = f (K,L) and is called
CONDUCTANCE
hm is determined by the model and
its interaction with hb

45. 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)

46. Initial 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.

47. Model Parameters
• Time
• Space (layer top and bottom)
• Hydrogeological characteristics
(hydraulic conductivity, transmissivity,
storage parameters and effective porosity)

48. Time
• 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

49. Grid
• 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.

50. Grid
• 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

51. MODEL GRIDS

52. 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.

53. 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.

54. Hydraulic conductivity and
transmissivity
• Hydraulic conductivity is the most critical
and sensitive modelling parameter.
• Realistic values of storage coefficient and
transmissivity, preferably from pumping
test, should be used.

55. Effective porosity
• Required to calculate velocity, used mainly
in solute transport models

56. Groundwater Flow Models

57. 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.

58. MODFLOW
√ USGS code
√ Finite Difference Model
• MODFLOW 88
• MODFLOW 96
• MODFLOW 2000

59. 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.

60. 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.

61. 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.

62. 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.

63. 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.

64. 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.

65. THANKS
HAPPY MODELLING