Boundaries and Superposition

1. Boundaries and Superposition Groundwater Hydraulics Daene C. McKinney

2. Introduction • Review • Continuity in Aquifers • Steady flow to a well in confined aquifer • Superposition • Two Wells in an Aquifer • Image Well • for an Impermeable Boundary • for a Constant Head Boundary • Multiple Wells in an Aquifer

3. Continuity in Aquifers • Confined aquifer • Unconfined aquifer • Linear equations • If h1 and h2 both satisfy a linear equation • Then another solution is h3 = Ah1 + Bh2 • where A and B are constants (For unconfined aquifer, everything is in terms of h2)

4. Steady Flow to a Well in a Confined Aquifer Q Ground surface Pre-pumping head Pumping well Drawdown curve Observation wells Confining Layer h0 r1 hw h2 b h1 Q Confined aquifer r2 Bedrock 2rw Point of interest (x,y) Well at = (xw,yw)

5. Superposition (2 wells pumping)

6. Superposition (n Wells pumping)

7. Steady Flow to a Well in an Unconfined Aquifer Q Ground surface Pre-pumping Water level Pumping well Water Table Observation wells h0 r1 hw h2 h1 Q Unconfined aquifer r2 Bedrock 2rw

8. Superposition (n Wells pumping)

9. Example y x

10. Example Q = 2x10-2 m3/s, T = 5x10-3 m2/s, Ho = 25 m, rw = 0.25 m y x 600 m

11. Well 1 pumping alone Well 2 pumping alone Both wells pumping together

12. Example • How much does the pumping in well 2 affect the head in well 1? • With both wells pumping • With only Well 1 pumping • Difference = 1.54 m x

13. Image Well to Simulate Impermeable Boundary y x

14. Drawdown Near Impermeable Boundary

15. Image Well to Simulate Constant Head Boundary y x Todd, 1980.

16. Example - Constant Head Boundary

17. Example – Impermeable Boundary

18. Pumping Near Parallel Boundaries

19. Location of a Boundary

20. Multiple Well Systems

21. Summary • Review • Continuity in Aquifers • Steady flow to a well in confined aquifer • Superposition • Two Wells in an Aquifer • Image Well • for an Impermeable Boundary • for a Constant Head Boundary • Multiple Wells in an Aquifer