11. Response of Confined Aquifers to Pumping

Steady Flow to WellsGroundwater Hydraulics

Daene C. McKinney

1SummarySteady flow to a well in a confined aquiferto a well in an unconfined aquiferUnsteady flow to a well in a confined aquiferTheis methodJacob methodto a well in a leaky aquiferto a well in an unconfined aquifer

Steady Flow to Wells in Confined Aquifers3Steady Flow to a Well in a Confined Aquifer2rwGround surfaceBedrockConfined aquiferQh0Pre-pumping headConfining Layerbr1r2h2h1hwObservation wellsDrawdown curveQPumping well

Theim EquationIn terms of head (we can write it in terms of drawdown also)

4Example - Theim EquationQ = 400 m3/hrb = 40 m. Two observation wells, r1 = 25 m; h1 = 85.3 mr2 = 75 m; h2 = 89.6 mFind: Transmissivity (T)

2rwGround surfaceBedrockConfined aquiferQh0Confining Layerbr1r2h2h1hwQPumping wellSteady Flow to a Well in a Confined Aquifer5Steady Radial Flow in a Confined AquiferHead

Drawdown

Steady Flow to a Well in a Confined AquiferTheim EquationIn terms of drawdown (we can write it in terms of head also)

6Example - Theim Equation1-m diameter well Q = 113 m3/hr b = 30 mh0= 40 m Two observation wells, r1 = 15 m; h1 = 38.2 mr2 = 50 m; h2 = 39.5 mFind: Head and drawdown in the well2rwGround surfaceBedrockConfined aquiferQh0Confining Layerbr1r2h2h1hwQPumping wellDrawdownAdapted from Todd and Mays, Groundwater Hydrology

Steady Flow to a Well in a Confined Aquifer7Example - Theim Equation2rwGround surfaceBedrockConfined aquiferQh0Confining Layerbr1r2h2h1hwQDrawdown @ wellAdapted from Todd and Mays, Groundwater Hydrology

Steady Flow to a Well in a Confined AquiferDrawdown at the well 8Steady Flow to Wells in Unconfined Aquifers9Steady Flow to a Well in an Unconfined Aquifer

2rwGround surfaceBedrockUnconfined aquiferQh0Pre-pumping Water levelr1r2h2h1hwObservation wellsWater TableQPumping well

Unconfined aquifer

10Steady Flow to a Well in an Unconfined Aquifer2rwGround surfaceBedrockUnconfined aquiferQh0Prepumping Water levelr1r2h2h1hwObservation wellsWater TableQPumping well2 observation wells: h1 m @ r1 m h2 m @ r2 m

11Given: Q = 300 m3/hr Unconfined aquifer 2 observation wells, r1 = 50 m, h = 40 m r2 = 100 m, h = 43 m

Find: K

Example Two Observation Wells in an Unconfined Aquifer2rwGround surfaceBedrockUnconfined aquiferQh0Prepumping Water levelr1r2h2h1hwObservation wellsWater TableQPumping wellSteady Flow to a Well in an Unconfined Aquifer12Unsteady Flow to Wells in Confined Aquifers13Unsteady Flow to a Well in a Confined Aquifer Two-Dimensional continuity equationhomogeneous, isotropic aquifer of infinite extentRadial coordinatesRadial symmetry (no variation with q) Boltzman transformation of variables

Ground surfaceBedrockConfined aquiferQh0Confining Layerbrh(r)QPumping wellUnsteady Flow to a Well in a Confined Aquifer Continuity

Drawdown

Theis equation

Well function

Ground surfaceBedrockConfined aquiferQh0Confining Layerbrh(r)QPumping well

Unsteady Flow to a Well in a Confined Aquifer15Well FunctionU vs W(u)1/u vs W(u)

Unsteady Flow to a Well in a Confined Aquifer16Example - Theis EquationQ = 1500 m3/dayT = 600 m2/dayS = 4 x 10-4

Find: Drawdown 1 km from well after 1 year

Ground surfaceBedrockConfined aquiferQConfining Layerbr1h1QPumping wellUnsteady Flow to a Well in a Confined Aquifer17Well Function

Example - Theis EquationQ = 1500 m3/dayT = 600 m2/dayS = 4 x 10-4

Find: Drawdown 1 km from well after 1 year

Ground surfaceBedrockConfined aquiferQConfining Layerbr1h1QPumping well

Unsteady Flow to a Well in a Confined Aquifer19Pump Test in Confined AquifersTheis Method20Pump Test Analysis Theis Method

Q/4pT and 4T/S are constantRelationship betweens and r2/t is similar to the relationship betweenW(u) and uSo if we make 2 plots: W(u) vs u, and s vs r2/tWe can estimate the constants T, and S

constants

Ground surfaceBedrockConfined aquiferQConfining Layerbr1h1QPumping well21Example - Theis MethodPumping test in a sandy aquiferOriginal water level = 20 m above mean sea level (amsl)Q = 1000 m3/hr Observation well = 1000 m from pumping well Find: S and TGround surfaceBedrockConfined aquiferh0 = 20 mConfining Layerbr1 = 1000 mh1QPumping wellBear, J., Hydraulics of Groundwater, Problem 11-4, pp 539-540, McGraw-Hill, 1979.Pump Test Analysis Theis MethodTheis MethodTimeWater level, h(1000)Drawdown, s(1000)minmm020.000.00319.920.08419.850.15519.780.22619.700.30719.640.36819.570.431019.450.556018.002.007017.872.1310017.502.50100015.254.75400013.806.20

Pump Test Analysis Theis MethodTheis MethodTimer2/tsuW(u)(min)(m2/min)(m)00.001.0E-048.6333333330.082.0E-047.9442500000.153.0E-047.5352000000.224.0E-047.2561666670.305.0E-047.0271428570.366.0E-046.8481250000.437.0E-046.69101000000.558.0E-046.5530003335.858.0E-010.3140002506.209.0E-010.26

s vs r2/t

W(u) vs u

Pump Test Analysis Theis Methodr2/tsuW(u)r2/tsW(u)uMatch PointW(u) = 1, u = 0.10s = 1, r2/t = 20000 Theis MethodPump Test Analysis Theis MethodTheis Method

Match PointW(u) = 1, u = 0.10s = 1, r2/t = 20000Pump Test Analysis Theis Method26Pump Test in Confined AquifersJacob Method27Jacob ApproximationDrawdown, s

Well Function, W(u)

Series approximation of W(u)

Approximation of s

Pump Test Analysis Jacob Method28Jacob Approximation

t0

Pump Test Analysis Jacob Method29Jacob Approximation

t0

t1t2s1s2Ds

1 LOG CYCLE

1 LOG CYCLEPump Test Analysis Jacob Method30Jacob Approximation

t0t1t2s1s2Dst0 = 8 mins2 = 5 ms1 = 2.6 mDs = 2.4 m

Pump Test Analysis Jacob Method31Unsteady Flow to Wells in Leaky Aquifers32Radial 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 Aquifers33

Leaky Well Function

r/B = 0.01r/B = 3cleveland1.cive.uh.edu/software/spreadsheets/ssgwhydro/MODEL6.XLSUnsteady Flow to Wells in Leaky Aquifers34Leaky Aquifer ExampleGiven:Well pumping in a confined aquiferConfining layer b = 14 ft. thickObservation well r = 96 ft. form wellWell Q = 25 gal/minFind:T, S, and KFrom: Fetter, Example, pg. 179t (min)s (ft)50.76283.3413.59604.08754.392445.474935.966696.119586.2711296.411856.42

Unsteady Flow to Wells in Leaky Aquifers35

Theis Well Function= 0.15= 0.20= 0.30= 0.40r/BMatch PointW(u, r/B) = 1, 1/u = 10s = 1.6 ft, t = 26 min, r/B = 0.15Unsteady Flow to Wells in Leaky Aquifers36Leaky Aquifer ExampleMatch PointWmp = 1, (1/u)mp = 10smp = 1.6 ft, tmp = 26 min, r/Bmp = 0.15Q = 25 gal/min * 1/7.48 ft3/gal*1440 min/d = 4800 ft3/dt = 26 min*1/1440 d/min = 0.01806 d

Unsteady Flow to Wells in Leaky Aquifers37Unsteady Flow to Wells in Unconfined Aquifers38Unsteady Flow to a Well in an Unconfined Aquifer Water is produced byDewatering of unconfined aquiferCompressibility factors as in a confined aquiferLateral movement from other formations2rwGround surfaceBedrockUnconfined aquiferQh0Prepumping Water levelr1r2h2h1hwObservation wellsWater TableQPumping wellUnsteady Flow to Wells in Unconfined Aquifers39Analyzing Drawdown in An Unconfined AquiferEarlyRelease of water is from compaction of aquifer and expansion of water like confined aquifer. Water table doesnt drop significantlyMiddleRelease of water is from gravity drainageDecrease in slope of time-drawdown curve relative to Theis curveLateRelease of water is due to drainage of formation over large areaWater table decline slows and flow is essentially horizontal

Unsteady Flow to Wells in Unconfined Aquifers40

EarlyLateUnconfined Aquifer (Neuman Solution)

Early (a)Late (y)Unsteady Flow to Wells in Unconfined Aquifers41Procedure - Unconfined Aquifer (Neuman Solution)Get Neuman Well Function CurvesPlot 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/ua, and W(ua, )Solve for T and S

Match late-time points with y-type curve with the same as the a-type curveSelect the match point (y) on the two graphs. Note s, t, 1/uy, and W(uy, )Solve for T and Sy

Unsteady Flow to Wells in Unconfined Aquifers42Procedure - Unconfined Aquifer (Neuman Solution)From the T value and the initial (pre-pumping) saturated thickness of the aquifer b, calculate Kr

Calculate Kz

Unsteady Flow to Wells in Unconfined Aquifers43Example Unconfined Aquifer Pump TestQ = 144.4 ft3/minInitial aquifer thickness = 25 ftObservation well 73 ft awayFind: T, S, Sy, Kr, Kz

Ground surfaceBedrockUnconfined aquiferQh0=25 ftPrepumping Water levelr1=73 fth1hwObservation wellsWater TableQ= 144.4 ft3/minPumping wellUnsteady Flow to Wells in Unconfined AquifersPump Test data

Unsteady Flow to Wells in Unconfined Aquifers

Early-Time Data

Unsteady Flow to Wells in Unconfined AquifersEarly-Time Analysis

Unsteady Flow to Wells in Unconfined Aquifers

Late-Time Data

Unsteady Flow to Wells in Unconfined AquifersLate-Time Analysis

Unsteady Flow to Wells in Unconfined AquifersSummarySteady flow to a well in a confined aquiferto a well in an unconfined aquiferUnsteady flow to a well in a confined aquiferTheis methodJacob methodto a well in a leaky aquiferto a well in an unconfined aquifer

K

b

h(r)

ground surface

bedrock

aquitard

confined

aquifer

initial head

Well

s(r)

aquifer

unconfined

r

Q

leakage

R

h0

Cone of

Depression

K

b

h(r)

ground surface

bedrock

aquitard

confined

aquifer

initial head

Well

s(r)

aquifer

unconfined

r

Q

leakage

R

h0

Cone of

Depression