Presentation is loading. Please wait.

Presentation is loading. Please wait.

Steady Flow to Wells Groundwater Hydraulics Daene C. McKinney.

Similar presentations


Presentation on theme: "Steady Flow to Wells Groundwater Hydraulics Daene C. McKinney."— Presentation transcript:

1 Steady Flow to Wells Groundwater Hydraulics Daene C. McKinney

2 Summary Steady flow – to a well in a confined aquifer – to a well in an unconfined aquifer Unsteady flow – to a well in a confined aquifer Theis method Jacob method – to a well in a leaky aquifer – to a well in an unconfined aquifer

3 Steady Flow to Wells in Confined Aquifers

4 Steady Flow to a Well in a Confined Aquifer r w Ground surface Bedrock Confined aquifer Q h0h0 Pre-pumping head Confining Layer b r1r1 r2r2 h2h2 h1h1 hwhw Observation wells Drawdown curve Q Pumping well Theim Equation In terms of head (we can write it in terms of drawdown also)

5 Example - Theim Equation Q = 400 m 3 /hr b = 40 m. Two observation wells, 1.r 1 = 25 m; h 1 = 85.3 m 2.r 2 = 75 m; h 2 = 89.6 m Find: Transmissivity ( T ) r w Ground surface Bedrock Confine d aquifer Q h0h0 Confining Layer b r1r1 r2r2 h2h2 h1h1 hwhw Q Pumping well Steady Flow to a Well in a Confined Aquifer

6 Steady Radial Flow in a Confined Aquifer Head Drawdown Steady Flow to a Well in a Confined Aquifer Theim Equation In terms of drawdown (we can write it in terms of head also)

7 Example - Theim Equation 1-m diameter well Q = 113 m 3 /hr b = 30 m h 0 = 40 m Two observation wells, 1.r 1 = 15 m; h 1 = 38.2 m 2.r 2 = 50 m; h 2 = 39.5 m Find: Head and drawdown in the well r w Ground surface Bedrock Confine d aquifer Q h0h0 Confining Layer b r1r1 r2r2 h2h2 h1h1 hwhw Q Pumping well Drawdown Adapted from Todd and Mays, Groundwater Hydrology Steady Flow to a Well in a Confined Aquifer

8 Example - Theim Equation r w Ground surface Bedrock Confine d aquifer Q h0h0 Confining Layer b r1r1 r2r2 h2h2 h1h1 hwhw Q Drawdown @ well Adapted from Todd and Mays, Groundwater Hydrology Steady Flow to a Well in a Confined Aquifer Drawdown at the well

9 Steady Flow to Wells in Unconfined Aquifers

10 Steady Flow to a Well in an Unconfined Aquifer r w Ground surface Bedrock Unconfined aquifer Q h0h0 Pre-pumping Water level r1r1 r2r2 h2h2 h1h1 hwhw Observation wells Water Table Q Pumping well Unconfined aquifer

11 Steady Flow to a Well in an Unconfined Aquifer r w Ground surface Bedrock Unconfined aquifer Q h0h0 Prepumping Water level r1r1 r2r2 h2h2 h1h1 hwhw Observation wells Water Table Q Pumping well 2 observation wells: h 1 m @ r 1 m h 2 m @ r 2 m

12 Given: – Q = 300 m 3 /hr – Unconfined aquifer – 2 observation wells, r 1 = 50 m, h = 40 m r 2 = 100 m, h = 43 m Find: K Example – Two Observation Wells in an Unconfined Aquifer r w Ground surface Bedrock Unconfined aquifer Q h0h0 Prepumping Water level r1r1 r2r2 h2h2 h1h1 hwhw Observation wells Water Table Q Pumping well Steady Flow to a Well in an Unconfined Aquifer

13 Unsteady Flow to Wells in Confined Aquifers

14 Unsteady Flow to a Well in a Confined Aquifer Two-Dimensional continuity equation homogeneous, isotropic aquifer of infinite extent Radial coordinates Radial symmetry (no variation with ) Boltzman transformation of variables Ground surface Bedrock Confined aquifer Q h0h0 Confining Layer b r h(r) Q Pumping well

15 Unsteady Flow to a Well in a Confined Aquifer Continuity Drawdown Theis equation Well function Ground surface Bedrock Confined aquifer Q h0h0 Confining Layer b r h(r) Q Pumping well Unsteady Flow to a Well in a Confined Aquifer

16 Well Function U vs W(u) 1/u vs W(u) Unsteady Flow to a Well in a Confined Aquifer

17 Example - Theis Equation Q = 1500 m 3 /day T = 600 m 2 /day S = 4 x 10 -4 Find: Drawdown 1 km from well after 1 year Ground surface Bedrock Confined aquifer Q Confining Layer b r1r1 h1h1 Q Pumping well Unsteady Flow to a Well in a Confined Aquifer

18 Well Function

19 Example - Theis Equation Q = 1500 m 3 /day T = 600 m 2 /day S = 4 x 10 -4 Find: Drawdown 1 km from well after 1 year Ground surface Bedrock Confined aquifer Q Confining Layer b r1r1 h1h1 Q Pumping well Unsteady Flow to a Well in a Confined Aquifer

20 Pump Test in Confined Aquifers Theis Method

21 Pump Test Analysis – Theis Method Q/4 T and 4T/S are constant Relationship between – s and r 2 /t is similar to the relationship between – W(u) and u – So if we make 2 plots: W(u) vs u, and s vs r 2 /t – We can estimate the constants T, and S constants Ground surface Bedrock Confin ed aquifer Q Confining Layer b r1r1 h1h1 Q Pumpin g well

22 Example - Theis Method Pumping test in a sandy aquifer Original water level = 20 m above mean sea level (amsl) Q = 1000 m 3 /hr Observation well = 1000 m from pumping well Find: S and T Ground surface Bedrock Confined aquifer h 0 = 20 m Confining Layer b r 1 = 1000 m h1h1 Q Pumping well Bear, J., Hydraulics of Groundwater, Problem 11-4, pp 539-540, McGraw-Hill, 1979. Pump Test Analysis – Theis Method

23 Theis Method Time Water level, h(1000) Drawdown, s(1000) minmm 020.000.00 319.920.08 419.850.15 519.780.22 619.700.30 719.640.36 819.570.43 1019.450.55 … 6018.002.00 7017.872.13 … 10017.502.50 … 100015.254.75 … 400013.806.20 Pump Test Analysis – Theis Method

24 Theis Method Timer2/tsuW(u) (min)(m2/min)(m) 0 0.001.0E-048.63 33333330.082.0E-047.94 42500000.153.0E-047.53 52000000.224.0E-047.25 61666670.305.0E-047.02 71428570.366.0E-046.84 81250000.437.0E-046.69 101000000.558.0E-046.55 … 30003335.858.0E-010.31 40002506.209.0E-010.26 s vs r 2 /t W(u) vs u Pump Test Analysis – Theis Method r2/tr2/t s u W(u) r2/tr2/ts u

25 Match Point W(u) = 1, u = 0.10 s = 1, r 2 /t = 20000 Theis Method Pump Test Analysis – Theis Method

26 Theis Method Match Point W(u) = 1, u = 0.10 s = 1, r 2 /t = 20000 Pump Test Analysis – Theis Method

27 Pump Test in Confined Aquifers Jacob Method

28 Jacob Approximation Drawdown, s Well Function, W(u) Series approximation of W(u) Approximation of s Pump Test Analysis – Jacob Method

29 Jacob Approximation t0t0 Pump Test Analysis – Jacob Method

30 Jacob Approximation t0t0 t1t1 t2t2 s1s1 s2s2 s 1 LOG CYCLE Pump Test Analysis – Jacob Method

31 Jacob Approximation t0t0 t1t1 t2t2 s1s1 s2s2 s t 0 = 8 min s 2 = 5 m s 1 = 2.6 m s = 2.4 m Pump Test Analysis – Jacob Method

32 Unsteady Flow to Wells in Leaky Aquifers

33 Radial Flow in a Leaky Aquifer When there is leakage from other layers, the drawdown from a pumping test will be less than the fully confined case. Unsteady Flow to Wells in Leaky Aquifers

34 Leaky Well Function r/B = 0.01 r/B = 3 cleveland1.cive.uh.edu/software/spreadsheets/ssgwhydro/MODEL6.XLS Unsteady Flow to Wells in Leaky Aquifers

35 Leaky Aquifer Example Given: – Well pumping in a confined aquifer – Confining layer b = 14 ft. thick – Observation well r = 96 ft. form well – Well Q = 25 gal/min Find: – T, S, and K From: Fetter, Example, pg. 179 t (min)s (ft) 50.76 283.3 413.59 604.08 754.39 2445.47 4935.96 6696.11 9586.27 11296.4 11856.42 Unsteady Flow to Wells in Leaky Aquifers

36 Theis Well Function = 0.15 = 0.20 = 0.30 = 0.40 r/B Match Point W(u, r/B) = 1, 1/u = 10 s = 1.6 ft, t = 26 min, r/B = 0.15 Unsteady Flow to Wells in Leaky Aquifers

37 Leaky Aquifer Example Match Point W mp = 1, (1/u) mp = 10 s mp = 1.6 ft, t mp = 26 min, r/B mp = 0.15 Q = 25 gal/min * 1/7.48 ft 3 /gal*1440 min/d = 4800 ft 3 /d t = 26 min*1/1440 d/min = 0.01806 d Unsteady Flow to Wells in Leaky Aquifers

38 Unsteady Flow to Wells in Unconfined Aquifers

39 Unsteady Flow to a Well in an Unconfined Aquifer Water is produced by – Dewatering of unconfined aquifer – Compressibility factors as in a confined aquifer – Lateral movement from other formations r w Ground surface Bedrock Unconfined aquifer Q h0h0 Prepumping Water level r1r1 r2r2 h2h2 h1h1 hwhw Observation wells Water Table Q Pumping well Unsteady Flow to Wells in Unconfined Aquifers

40 Analyzing Drawdown in An Unconfined Aquifer Early – Release of water is from compaction of aquifer and expansion of water – like confined aquifer. – Water table doesnt drop significantly Middle – Release of water is from gravity drainage – Decrease in slope of time- drawdown curve relative to Theis curve Late – Release of water is due to drainage of formation over large area – Water table decline slows and flow is essentially horizontal Unsteady Flow to Wells in Unconfined Aquifers

41 Early Late Unconfined Aquifer (Neuman Solution) Early (a) Late (y) Unsteady Flow to Wells in Unconfined Aquifers

42 Procedure - Unconfined Aquifer (Neuman Solution) Get Neuman Well Function Curves Plot pump test data (drawdown s vs time t) Match early-time data with a-type curve. Note the value of Select the match point (a) on the two graphs. Note the values of s, t, 1/u a, and W(u a, ) Solve for T and S Match late-time points with y-type curve with the same as the a-type curve Select the match point (y) on the two graphs. Note s, t, 1/u y, and W(u y, ) Solve for T and S y Unsteady Flow to Wells in Unconfined Aquifers

43 Procedure - Unconfined Aquifer (Neuman Solution) From the T value and the initial (pre-pumping) saturated thickness of the aquifer b, calculate K r Calculate K z Unsteady Flow to Wells in Unconfined Aquifers

44 Example – Unconfined Aquifer Pump Test Q = 144.4 ft 3 /min Initial aquifer thickness = 25 ft Observation well 73 ft away Find: T, S, S y, K r, K z Ground surface Bedrock Unconfined aquifer Q h 0 =25 ft Prepumping Water level r 1 =73 ft h1h1 hwhw Observation wells Water Table Q= 144.4 ft 3 /min Pumping well Unsteady Flow to Wells in Unconfined Aquifers

45 Pump Test data Unsteady Flow to Wells in Unconfined Aquifers

46 Early-Time Data Unsteady Flow to Wells in Unconfined Aquifers

47 Early-Time Analysis Unsteady Flow to Wells in Unconfined Aquifers

48 Late-Time Data Unsteady Flow to Wells in Unconfined Aquifers

49 Late-Time Analysis Unsteady Flow to Wells in Unconfined Aquifers

50 Summary Steady flow – to a well in a confined aquifer – to a well in an unconfined aquifer Unsteady flow – to a well in a confined aquifer Theis method Jacob method – to a well in a leaky aquifer – to a well in an unconfined aquifer


Download ppt "Steady Flow to Wells Groundwater Hydraulics Daene C. McKinney."

Similar presentations


Ads by Google