I want to show you how to use the power of hydrogeological modeling You should be able to do more than just go through the motions of hydrogeological modeling, you should to be able to use the modeling process to further your understanding of the hydrogeological system that you are investigating. This will hinge on the development of a sound conceptual model, a concept in your mind of how the plumbing works and how it relates to the problem to be addressed We will use mathematical models (analytical and numerical) as tools to address these problems The next step is to learn how to convert your conceptual model into a mathematical model. This could be as simple as applying 1-D Darcy’s Law and as complex as setting up and calibrating a 3-D, transient numerical model. In any case the procedure is the same: 1) Define the problem in lay-terms (demonstrate the significance to your audience), 2) define the specific objectives in technical (hydrogeological) terms, 3) Develop a conceptual model [ site description and general hydrogeology ], 4) convert the conceptual model into mathematical models that will address the objectives [ methodology ] 5) determine specifically where you will get the information from to set up your model [more methodology ], 6) set up your model, calibrate and use it to address the objective [ results ] This will also help write the documentation which you should be writing all along
Majid Gw Final Ppt
Introduction to Groundwater Modelling Presented to : Dr.Zulfiqar Ahmed Presented by: MAJID KHAN M.Phil Geophysics Hydrogeologist Email: mkhidden@hotmail.
Presentation Outline Groundwater in Hydrologic Cycle Why Groundwater Modeling is needed? Mathematical Models Model Design Groundwater Flow Models
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Management of a groundwater system, means making such decisions as:• The total volume that may be withdrawn annually from the aquifer.• The location of pumping and artificial recharge wells, and their rates.• Decisions related to groundwater quality.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.
: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
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 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
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
Processes we might want to model Groundwater flow calculate both heads and flow Solute transport – requires information on flow (velocities) Calculate concentrations
MODELING PROCESSALL 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 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 transientproblems)
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
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)
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
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)
∆h∆h b S=V/A∆ h S = Ss b Confined aquifer Unconfined aquifer Specific yield Storativity Figures taken from Hornberger et al. (1998)
General 3D equation ∂ ∂h ∂ ∂h ∂ ∂h ∂h ( Kx ) + ( K y ) + ( Kz ) = Ss −R* ∂x ∂x ∂y ∂y ∂z ∂z ∂t ∂ ∂h ∂ ∂h ∂h2D confined: (Tx ) + (Ty ) = S −R ∂x ∂x ∂y ∂y ∂t2D 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
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)
Finite Difference Modelling3-D Finite Difference Models Requires vertical discretization (or layering) of model K1 K2 K3 K4
Model Design• Conceptual Model• Selection of Computer Code• Model Geometry• Grid• Boundary array• Model Parameters• Boundary Conditions• Initial Conditions.
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.
Conceptual ModelA descriptive representationof a groundwater system thatincorporates an interpretation of thegeological & hydrological conditions.Generally includes information aboutthe water budget. May includeinformation on water chemistry.
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
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.
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.)
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.
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 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
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
Boundary TypesSpecified 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 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 Parameters• Time• Space (layer top and bottom)• Hydrogeological characteristics (hydraulic conductivity, transmissivity, storage parameters and effective porosity)
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
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.
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
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)• 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 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.
Effective porosity• Required to calculate velocity, used mainly in solute transport 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 (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 2Dfluid density-coupled flow, contaminant mass (salinity) andheat transport in the subsurface.HST3D(3-D Heat and Solute Transport Model)The Heat and Solute Transport Model HST3D simulatesground-water flow and associated heat and solute transport inthree 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.