Groundwater Hydraulics: Well Pumping and Superposition Analysis

This content delves into various aspects of well pumping in groundwater hydraulics. It covers topics such as boundaries, superposition, confined and unconfined aquifers, pumping near streams, and practical examples. The visuals aid in understanding concepts like drawdown at wells and the effects of pumping on aquifers.

• Groundwater
• Hydraulics
• Well Pumping
• Superposition Analysis
• Aquifers

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1. Flow to Wells - 6 Boundaries and Superposition Groundwater Hydraulics Daene C. McKinney 1

2. Introduction Wells pumping near boundaries for an Impermeable Boundary for a Constant Head Boundary Multiple wells systems Partially penetrating wells 2

3. Pumping a Well in a Confined Aquifer Steady Flow y ? ? ? ( , ) x y ? = 2???? Well pumping Q r Unsteady Flow Theis x (xw, yw)=(-a, 0) Q s u ( ) = 4pTW u ( ) Jacob (u small) ? =2.3? 2.25?? ?2? 4??log10 3

4. Superposition (2 Wells pumping)

5. Superposition (2 Wells pumping) y Q ( , ) x y Q 2r 1r (w ) 0 , x x ( ) 0 , w x ? = ?1+ ?2 ?2 ?1?2 ? ? ?1 ? ? ?2 ? ? = 2???? + 2???? = 2???? ? ? ?? ??= 2???? ? ? ? ? ? = 4??? ?1 + 4??? ?2 = 4??? ?1 + ? ?2 ??= 4??? ?? ? =2.3? 2.25?? ?1 +2.3? 4????? 2.25?? ?2 4????? ??=2.3? 2.25?? ?? 2? 2? 4????? 2? 2 =2.3? 4????? 2.25?? ? 1 2?2 2 ?1 5

6. Well Pumping in an Unconfined Aquifer Q Ground surface Pre-pumping Water level Pumping well y Observation well ( , ) x y h Well pumping Q r h0 r x R (xw, yw)=(-a, 0) Q Unconfined aquifer Bedrock ? ???? ? ? 2 2= 0 ?2= ? ?? 2+ ? ?? 2 6

7. Flow to a Well Near a Stream (Constant Head Boundary) 7

8. Well Pumping in an Unconfined Aquifer Near a Stream (Constant Head Boundary) y Image well Real well ( , ) x y Q Q 2r 1r (w ) 0 , x x ( ) 0 , w x Image region Real region Stream 2 2=(+?) ? ?1 +( ?) ?? ? ?2 0 ?? ?? ?? Image injection well Real pumping well ?2 ?1 ? ???? 2 2= 0 ? ???? ?2 ?1 2 2= 0 8

9. Example A well of radius 0.2 m produces 550 m3/day from an unconfined aquifer with K = 10 m/day. The well is located 250 m from a river and the saturated thickness at the river is 30 m. What is the drawdown at the well? y Image well Real well ( , ) x y Q Q 2r 1r (w ) 0 , x x ( ) 0 , w x Image region Real region Stream ? ???? ? ???? ?2 ?1 ?2 ?1 2 2 2= 0 2= 0 ? ? ???? ?2 ?1 550 ?(10)?? 500 0.2 302 2 ?= 0 = = 27.6 ? 9

10. Effect on Drawdown When Pumping Near a Stream y Image well Real well ( , ) x y Q Q 2r 1r (w ) 0 , x x ( ) 0 , w x Image region Real region Stream 10

11. Flow to a Well Near an Impermeable Boundary 11

12. Image Well to Simulate Impermeable Boundary y Image well Real well ( , ) x y Q Q 2r 1r (w ) 0 , x x ( ) 0 , w x Image region Real region Boundary 2 2=(+?) ? ?1 +(+?) ?? ? ?2 0 ?? ?? ?? Image pumping well Real pumping well ?2 ?2?1 ? ???? 2 2= 0 12

13. Effect on Drawdown When Pumping Near an Impermeable Boundary y Image well Real well ( , ) x y Q Q 2r 1r (w ) 0 , x x ( ) 0 , w x Image region Real region Boundary 13

14. Pumping in a Confined Aquifer Near an Impermeable Boundary y Image well Real well ( , ) x y Q Q 2r 1r (w ) 0 , x x ( ) 0 , w x Image region Real region Boundary Steady Flow ? ? ?? ? ? ?? ? ? ?? ? ?? ? = 2???? + 2???? = 2???? + ?? ?2 ???? ? ? = 2???? 14

15. Pumping in a Confined Aquifer Near an Impermeable Boundary y Image well Real well ( , ) x y Q Q 2r 1r (w ) 0 , x x ( ) 0 , w x Unsteady Flow Theis Image region Real region Boundary ? ? ? ? = 4??? ?? + 4???(??) = 4??? ?? + ?(??) 2? ??=??2? ??=?? 4?? 4?? 15

16. Pumping in a Confined Aquifer Near an Impermeable Boundary y Image well Real well ( , ) x y Q Q 2r 1r (w ) 0 , x x ( ) 0 , w x Unsteady Flow Jacob Image region Real region Boundary ? =2.3? 2.25?? ??2? +2.3? 4??log10 2.25?? ?? 4??log10 2? ? =2.3? 2.25?? ??2? 2.25?? ?? log10 + log10 2? 4?? 2 ? =2.3? 2.25?? ? 1 4??log10 ??2?? 2 16

17. Example Impermeable Boundary Find the drawdown in the observation well after 10 hours of pumping 2402(3?10 5) 4(6.4?10 3)(36,000)= 1.88?10 3< 0.01 ??=??2? 4??= Q = 0.03 m3/s T = 6.4x10-3 m2/s S = 3x10-5 t = 36,000 s 4102(3?10 5) 4(6.4?10 3)(36,000)= 5.47?10 3< 0.01 2? ??=?? 4??= u < 0.01, use Jacob 17

18. Example Impermeable Boundary Q = 0.03 m3/s T = 6.4x10-3 m2/s S = 3x10-5 t = 36,000 s 2 ? =2.3? 2.25?? ??2? ?2.25?? ?? =2.3? 4????? 2.25?? ? 1 4????? 2? ??2?? 2 2 2.25(6.4?10 3)(36000) 3?10 5 2.3(0.03) 4?(6.4?10 3)??? 1 ? = 24024102 ? = 3.85 ? 18

19. Drawdown Near Impermeable Boundary 19

20. Superposition (n Wells pumping) Q 2 Q 2r 1 ? = ?1+ ?2+ ?3+ +?? ( , ) x 2y 2 1r ( , ) x y ( , ) x 1y ? 1 ? = ?? ?=1 Q 3r 3 ( , ) x 3y ? ? ? ?? 3 ? ? ?? ? = 2???? ??= 2???? ?=1 ? ? ? ? = 4??? ?? ??= 4??? ?? ?=1 ? 2.3? 4????? 2.25?? ?? ??=2.3? 2.25?? ?? ? = 4????? 2? 2? ?=1 20

21. Example - Multiple Well System 200 m 200 m Find the steady-state pumping rate for each well so that the drawdown in each well will not exceed 2 m. ?1= ?11+?12+?13 ?2= ?21+?22+?23 ?3= ?31+?32+?33 T = 27.8x10-3 m2/s rw = 0.2 m b = 40 m R = 800 m sij = drawdown in well i due to pumping in well j 21

22. Example - Multiple Well System ? ? ?? ???= 2???? ? ? ??? ???= 2???? ? 800 0.2 ?11= 2?(27.8?10 3)?? = 47.48? ? 800 200 ?12= 2?(27.8?10 3)?? = 7.94? ? 800 400 ?13= 2?(27.8?10 3)?? = 3.97? 22

23. Example - Multiple Well System ?1= ?3= 47.48? + 7.94? + 3.97? = 59.39? ?23= ?21=?12= 7.94? ?22= ?11= 47.48? ?2= 7.94? + 47.48? + 7.94? = 63.36? So more drawdown at middle well for given Q 63.36 > 59.39 ?2< 2 ? ?? 63.36? < 2 ? < 3.16?10 2?3/? ? < 113?3/ ? 23

24. Partially Penetrating Wells ??= ? + ? 24

25. Partially Penetrating Wells ??= ? + ? ?? 2?? 1 ? ? 1 ? ? 2?? ?? 2?? 1 ? ? 1 ? ? ?? ? = ?? ? = ?? 25

26. Partially Penetrating Wells ? ? ?? ? 150 0.5 = 0.9078? rw = 0.5 m b = 28 m R = 150 m ??= 2???? = 2???? ? Compare Q/s for each case 26

27. Partially Penetrating Wells ?? 2?? 1 ? ? 1 ? ? ?? ??= ?? ??= ??+ ??= 0.9078? ? 1 0.5 0.5 1 0.5 14 0.5 = 1.3278? ?+ ?? 2?? ? 27

28. Partially Penetrating Wells ?? 2?? 1 ? ? 1 ? ? 2?? ??= ?? ??= ??+ ??= 0.9078? ? 1 0.5 0.5 1 0.5 14 2(0.5) = 1.2175? ?+ ?? 2?? ? 28

29. Partially Penetrating Wells ??= 0.9078? ??= 1.3278? ??= 1.2175? ? ? ? ?/??= 0.7531? ?/??= 1.1016? ?/??= 0.8214? ?? 68% ?? (?) ?? 75% ?? (?) 29

30. Summary Wells pumping near boundaries for an Impermeable Boundary for a Constant Head Boundary Multiple wells systems Partially penetrating wells 30