1. Groundwater pumping to remediate groundwater pollution March 5, 2002

2. TOC  1) Squares  2) FieldTrip: McClellan  3) Finite Element Modeling

3. First: Squares  Oxford Dictionary says  “a geometric figure with four equal sites and four right angles”

4. Squares  Units within a flow net are curvilinear figures…  In certain cases, squares will be formed Constant head boundary…

5. Flownet

6.  No flow crosses the boundary of a flowline !  If interval between equipotential lines and interval between flowlines is constant, then volume of water within each curvilinear unit is the same…

7. Flow nets (rules)  Flowlines are perpendicular to equipotential lines  One way to assume that Q’s are equal is to construct the flownet with curvilinear squares  Streamlines are perpendicular to constant head boundaries  Equipotential lines are perpendicular to no-flow boundaries

8. Flow nets (rules 2)  In heterogeneous soil, the tangent law is satisfied at the boundary  If flow net is drawn such that squares exist in one part of the formation, squares also exist in areas with the same K K1 K2 11 22

9. Second: McClellan Airbase

11. Piping system

12. Groundwater extraction wells

13. Waste water treatment plant

14. How to determine the spacing of wells?  Determine feasible flow rates  Determine range of influence  Determine required decrease of water table  Calculate well spacings

15. Confined Aquifer  Well discharge under steady state can be determined using

16. Unconfined Aquifer  Well discharge under steady state can be determined using

17. Unconfined Aquifer  Well discharge under steady state WITH surface recharge can be determined using

18. What is optimal well design ?  In homogeneous soil:

19. In heterogeneous situation:  Wells have flow rate between 1 and 100 gpm  Some wells are in clay, others in sand

21. Finite Difference method  Change the derivative into a finite difference 

22. Approach to numerical solutions  1) Subdivide the flow region into finite blocks or subregions (discretization) such that different K values can be assigned to each block and the differentials can be converted to finite differences

23. Approach to numerical solutions  2) Write the flow equation in algebraic form (using finite difference or finite elements) for each node or block

24. Approach to numerical solutions  3) Use “numerical methods” to solve the resulting ‘n’ equations in ‘n’ unknowns for h subject to boundary and initial conditions

25. 1-D example  Boundaries: h left = 10, h right = 3  Initial conditions h = 0  K is homogeneous = 3  Delta x = 2