1. Dr. James M. Martin-Hayden Associate Professor Dr. James M. Martin-Hayden Associate Professor (419) 530-2634 Jhayden@Geology.UToledo.edu

2. Ground Water Flow Modeling 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 (a necessity) Understand the limitations of the mathematical representation Understand the limitations of the interpretation of the results

3. 3-D Darcy’s Law (cont.) Horizontal and Vertical Hydraulic Gradients 284 282 286 h 1 =286.11 h 2 =284.87 h 3 =282.68 m Horizontal Component, in field applications: Represented as a single vector perpendicular to flow lines Approximated* using a 3 point problem or a contour map of the piezometric surface (horizontal component only) vhvh VzVz h s = 291.26m h d = 290.74  s =385m  h =4.00m  z =-5.84m  h = 0.52m *Finite difference approximation 0.0104 Vertical component Often taken as positive downward Can be approximated* using a well nest =-0.0890 m

4. Introduction to Ground Water Flow Modeling Predicting heads (and flows) and Approximating parameters Solutions to the flow equations Most ground water flow models are solutions of some form of the ground water flow equation Potentiometric Surface x x x hoho x 0 h(x) x K q “e.g., unidirectional, 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 LawIntegrated

5. Flow Modeling (cont.) Limitations of Analytical Models Closed form models are well suited to the characterization of bulk parameters However, the flexibility of forward modeling is limited due to simplifying assumptions: Homogeneity, Isotropy, simple geometry, simple initial conditions… Geology is inherently complex: Heterogeneous, anisotropic, complex geometry, complex conditions… This complexity calls for a more powerful solution to the flow equation  Numerical modeling

6. Finite Difference Modeling (cont.) 3-D Finite Difference Models Requires vertical discretization (or layering) of model K1K1 K2K2 K3K3 K4K4

7. Case Study An unconfined sand aquifer in northwest Ohio Conceptual Model

8. An Overview Water Table  Boreholes: our primary method of collecting subsurface data  Geological data does not change much, but  Groundwater geochemistry is always changing  Enter, groundwater monitoring wells:  screen sediments out and allow groundwater in to be sampled  provide continuous access to the subsurface (i.e. allow groundwater monitoring)