1. Groundwater Pollution Remediation NOTE 3 2D Analytical Solutions

2. Two-Dimensional GW Flow Equations Assume horizontal flow (Dupuit approximation) => vertical equipotentials Confined Aquifer Unconfined Aquifer N: recharge rate

3. Flow to a well in a confined aquifer Q r Assumptions: Ф(r) q zt q zb

4. After the assumptions are considered, the equations can be simplified as the following equation.

5. Boundary conditions?

6. Incorporating BCs

7. Here σ = Ф o – Ф (draw down) RADIUS OF INFLUENCE: distance beyond which drawdown is negligible. Thiem Equation (1906)

8. Steady flow to a well in an unconfined aquifer Q r Assumptions: Ф(r)

9. Boundary conditions?

10. Dupuit-Forchheimer Well Discharge equation. Confined-Unconfined Comparison

11. Unsteady flow to a well (confined aquifer) BCs & ICs

12. Theis Solution

13. Papadopulos Solution (Extensions to anisotropic media)

14. Cooper-Jacob Solution (For a small u) When u is smaller than 0.01, then, In which conditions is the u small? Radius of Influence (u < 0.01)

15. Unsteady flow to a well (unconfined aquifer) Corrected drawdown