A Brief Introduction to Groundwater Modeling Karl Payne

Groundwater Modeling Ø What is a groundwater model? A groundwater model is a mathematical or analogue simulation of a groundwater flow or transport process. “ As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. ” A. Einstein

Analytical Models & Numerical Models Ø Analytical models are mathematically exact solutions to the governing equations.

Hypothetical Aquifer

Questions

Mathematical Model

Analytical Solution

Answers

Analytical Models Ø Simple to implement Ø Require little input Ø Computationally undemanding VERY LIMITED- simple homogeneous and isotropic systems simple boundary conditions

Numerical Methods Ø Approximate solutions to the governing equations. Ø Most widely used are finite-difference and finite-element methods. Ø These methods rely on discretization of the solution domain.

Finite Difference Method

Numerical Solution

Applications of Groundwater Models Ø Groundwater Contamination: Model could be used to estimate expected travel times of contaminant plume. Ø Design of remedial program: Model could be used determine optimum pumping rates and placement of pumping wells of pump-and-treat system. Ø Assessment of climate change impact on water resources.

Modeling Protocol • Establish the Purpose • Develop a Conceptual Model • Selection of Computer Code • Model Design • Calibration • Model Verification

Model Purpose Is the model being used for prediction or is it interpretive? Ø Example of predictive model would be a model used to investigate impact of climate change on water resources. One wants to predict how the freshwater/saltwater interface responds to changes in stresses. Ø Example of interpretation would be a sensitivity analysis-Identification of important system parameters. Ø

Conceptual Model Ø A conceptual model is a pictorial representation of the groundwater system in the form of a block diagram or cross sections. Ø Hydrostratigraphy Ø System Boundaries Ø Hydrologic Stresses Ø Aquifer Parameters

Selection of Code

Model Design Ø The conceptual model is put into a form suitable for modeling. This step includes: Ø Ø Designing the grid Selecting time steps Setting boundary and initial conditions Selection of values for aquifer parameters and hydrologic stresses

Model Calibration

Model Verification Ø Establish greater confidence in the model. Ø Verify the ability of the calibrated model to reproduce a second set of field data.

A Three-dimensional Saline Intrusion Model of Barbados using Hydro. Geo. Sphere Karl Payne 07/09/2011

Introduction Fig 1: Map of the Caribbean

Geology and Hydrogeology of Barbados • Barbados is composed of Pleistocene reef deposits up to 100 m thick A • The Pleistocene limestone aquifer is underlain by low -permeability Tertiary sediments B Fig 2: Geology Map of Barbados

Fig 3: Cross-section through the line AB • Recharge to the Pleistocene limestone aquifer can take place by diffuse infiltration through the soil or by discrete infiltration through drainage wells and some sinkholes

The aquifer is divided into two hydrologic zones: (1)The streamwater zone which is the upland portion of the aquifer characterized by gravityflow along the base of the limestone. Fig 4: Hydrogeologic map of Barbados (2)The sheetwater zone which is the freshwater lens portion of the aquifer that occurs in low-lying parts of the island.

Conceptual Model Ø Homogeneity and isotropy Ø Unsaturated/Saturated Flow Ø Flow is three-dimensional Ø No vertical flow component across the contact between the Pleistocene limestone and the Tertiary stratum Ø Neglect the flux contribution from the Scotland District

Aquifer Parameters Hydraulic conductivity (K) of 10 -4 m/s Porosity – 0. 3 Recharge was taken to be 15% of average annual rainfall (1500 mm/yr)

Model Selection Ø Hydro. Geo. Sphere(HGS)Jointly developed by groundwater scientist at the University of Waterloo and Laval University, Canada. Ø A Three-dimensional numerical model describing fully-integrated subsurface and surface flow and solute transport.

HGS Features 2 D overland/stream flow including stream/surface drainage network genesis. Ø 3 D variably-saturated flow in porous media. Ø 3 D variably-saturated flow in fractures and karst conduits. Ø Advective-dispersive transport, reactive solute/thermal transport in all continua. Ø Fully-coupled, simultaneous solution of surface/ subsurface flow and transport Ø

Mesh Design Fig 5: Discretization of model domain Fig 6: Land Surface Elevation

Saturation Animation

Results Fig 7: Freshwater lens in plan view Fig 8: Pressure head distribution

Results

Model Calibration PEST (Parameter Estimation) is the industry standard software package for parameter estimation and uncertainty analysis of complex environmental and other computer models.

Model Calibration Fig 9: Delineation of model into K zones Fig 10: Sinkhole map of Barbados

Model Calibration Fig 6: Calibration results

Modeling Approaches to Simulate Seawater Intrusion Ø Sharp interface vs Diffuse Interface

Density-dependent Transport Ø In coastal areas, there exists a body of sea water, often in the form of a wedge, underneath the freshwater lens. Ø Fresh water and salt water are miscible fluids and the zone of contact between them takes the form of a transition zone. (We saw this from geophysics)

t=0 yrs t=50 yrs Fig 8: Time evolution of the salinization process t=100 yrs

Salinization Animation (Plan)

Salinization Animation (Crosssection)

Telescopic Mesh Refinement: Creating a LSM from RSM Ø Regional scale model used as BC to local scale

Example: Spring Hall Model

Questions?