Groundwater Pollution Remediation

1. Groundwater PollutionRemediation NOTE 4 Superposition

2. Principle of Superposition • If Φ1 = Φ1 (x, y, z, t) and Φ2 = Φ2 (x, y, z, t) are two general solutions of a homogenous linear partial differential equation L(Φ) = 0, then any linear combination Φ = C1 Φ1 + C1 Φ2 where C1, C2 are constants is also a solution of L(Φ) = 0. • Applications: multiple well systems, non-steady pumpage, boundary problems

3. Image Well Theory (1) Barrier Boundary Q d Pumping Well x dA/dX = 0 (no flux B.C.) at X =0

4. No barrier aquifer Q r X

5. Image Well Theory • Barrier Boundary: How to compute • drawdown at the observation well? Q Q d d Pumping Well Image Well r2 r1 Observation Well x dA/dX = 0 (no flux B.C.) at X =0

6. Unsteady state confined aquifer GW solution When u is smaller than 0.01, then, In which conditions is the u small? Radius of Influence (u < 0.01)

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

8. Image Well Theory (2) Recharge Boundary Fully penetrating stream Q d Pumping Well x Constant head at X =0

9. Image Well Theory (2) Recharge Boundary: Find drawdown at the observation well. Fully penetrating stream Q Q d d Pumping Well Image Well r2 r1 Observation Well x Constant head at X =0

10. Image Well Theory (3) Between Barrier Boundaries Q Pumping Well

11. Image Well Theory (4) Barrier-Recharge Boundaries Fully penetrating stream Q Pumping Well