Why Transmissivity Values from Specific Capacity Tests Appear

Unreliable

Rich SouleJustin Blum

Steve Robertson

Wellhead Protection in Minnesota

•State Wellhead Protection Rule specifies the use of groundwater flow models to determine wellhead protection areas.

•Transmissivity is typically the most sensitive and uncertain parameter in these models.

•There are over 900 community water supply systems covered by the Rule.

•There are six of us to do the work.

Transmissivity Information

Pumping TestsObservation WellsMultiple AnalysisPreferred T Values

Specific Capacity TestsDriller DataLocation CheckedObvious errors removed.

⎥⎦

⎤⎢⎣

⎡=

SrtT

sQT

w 25.2ln

4 2π

⎥⎦

⎤⎢⎣

⎡=

SrtT

TQs

w 25.2ln

4 2πCooper and Jacob, 1946 Assume

S = Specific StorageCalculateT = Transmissivity

Iterate

Estimating T from a Specific Capacity Test

MeasuredQ= discharges = drawdownt = time since startrw = radius of well

t2

Q

st1

Test Differences

Discharge

High

Low

Duration

Days

Hours

WaterLevelsVery Many

Two

ObservedWells

Several

One

AnalysisMethods

TooMany

Few

TestType

Pumping

Specific Capacity

T S Bounds Leakage Number

489

127,834

TestType

Pumping

Specific Capacity

Information Available from Test

What’s the Difference?Frequency Distributions of T Estimates

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

1 10 100 1000 10000 100000 1000000 10000000

Ln (T) ft^2/day

Fre

quen

cy %

RawSpecificCapacityTests

PumpingTests

LognormalDistribution

ButNot the SamePopulations

Pumping Tests v. Specific Capacity (Ft̂ 2/day)

10

100

1000

10000

100000

10 100 1000 10000 100000

Pumping Test Preferred T

Spec

ific

Cap

acity

ScatteredR2=.25

ButUnbiased

Direct Comparison of Methods-Same WellsSp

ecifi

c C

apac

ity T

T (ft2/day)

ScatteredR2=.20

Butalso

Unbiased

Pumping Tests Preferred v. Other Analysis Methods

10

100

1000

10000

100000

10 100 1000 10000 100000

Pumping Test Preferred Method

Pum

ping

Tes

t Oth

er M

etPumping Tests – Different Analysis Methods

Conventional WisdomFrequency Distributions of T Estimates

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

1 10 100 1000 10000 100000 1000000 10000000T ft 2̂/day

%

SpecificCapacityTests

PumpingTests

Specific Capacity

Pumping Test

•Measurement Bias.•Limited Data•Limited Analysis•Just wrong.

•No Measurement Bias.•Lots of Data•Unlimited Analysis•Always right.

LOCATION LOCATION LOCATION

•Pumping tests are done in wells located and designed for high production.

•Specific capacity tests are done in domestic wells located randomly and designed to meet a minimum demand.

Population Bias

Population Bias: Spatial Variation

(meters)

Within 6 km variability is due to small scale effects or measurement error.

Beyond 6 km morethan half of the variability is due to location.

•Find all specific capacity tests within 2 km of the pumping tests.

•Determine the average values for these tests.

•Check for bias.

•Correlation should improve with the number of specific capacity tests.

Pumping Tests

Confirming the Location Bias

Meak K of Specific Capacity within 2 km v. Pumping Test K

1

10

100

1000

10000

1 10 100 1000 10000

K (ft/day) Pumping Test

Mea

n K

(ft/d

ay) S

peci

fic C

apac

ity

Scattered But UnbiasedCheck for Bias

Meak K of Specific Capacity within 2 Km v. Pumping Test KN>20

1

10

100

1000

10000

1 10 100 1000 10000

K (ft/day) Pumping Test

Mea

n K

(ft/d

ay) S

peci

fic C

apac

ity

Correlation improves with N

Sources of Specific Capacity Bias:

•Measurement Error•Partial Penetration•Aquifer Heterogeneity•Casing Storage •Well Efficiency

Would be unbiased

Measurement Bias: Partial Penetration•114,452 Quaternary Wells•75% have unknown H•Average known H = 25 ft.

⎥⎦

⎤⎢⎣

⎡=

SrtT

sQT

w 25.2ln

4 2π

Clayey TillSand & Gravel

H =

L =

? ? ? ?

⎥⎦

⎤⎢⎣

⎡+= p

w

sSr

tTs

QT 2

25.2ln 4 2π

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−= HLG

HLHLsp /

rHln

)/()/(1

w

Brons and Marting (1961)Where

32 )/(675.4)/(447.11)/(363.7948.2)/(

HLHLHLHLG

−+

−=

Bradbury and Rothschild (1985)

Frequency Distributions of T Estimates

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

1 10 100 1000 10000 100000 1000000 10000000

Ln (T) ft^2/day

Fre

quen

cy %

RawSpecificCapacityTests

PumpingTests

Frequency Distributions of T Estimates

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

1 10 100 1000 10000 100000 1000000 10000000

Ln (T) ft^2/day

Fre

quen

cy %

RawSpecificCapacityTests

PumpingTests

PartialPenetration

Maybe but Low Q…..

Mean K v. Screen Length

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25 30

Screen Length (ft)

K (F

t/day

)

95% Confideinceof the Mean

Measurement Bias: Isotropic Aquifer

Lucky StrikeZone

AverageJoe Zone

InterestingZone

If the Aquifer is Isotropic K is constant for different screen lengths

Average Joes' Percentiles 5 ft.Screens

1

10

100

1000

10000

100000

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Percentile

T (f

t^2/

day)

Interesting Like the Chinese Curse

15 ft. 4406606

20 ft. 9600 480

10 ft. 13713701370

4807420 1379

348 947 2134 6171

ScreenLength

Tft2/day

Kft/day

A Statistical Model

Heterogeneous Aquifer: Interesting ZoneMean K v. Screen Length

0

100

200

300

400

500

600

700

800

900

1000

10 15 20 25 30

Scren Length (ft)

K (F

t/day

)

95% Confideinceof the Mean

Modeled K

May be an Important Measurement Bias

Casing Storage Effects?

Log Time

1 10 100 1000 10000

Dra

wdo

wn

(s)

10

0

20

30

40

T1

T2

tc

sQdd

t pcc /

)( 6.0 22 −=

dc = casing diameter (in)dp = riser diameter (in)Q in gpm, s in feet

Schafer (1978) from Popadoplus-Cooper Equation

Transmissivity v. Test Duration

0

100

200

300

400

500

600

0 10 20 30 40

Duration (Hrs)

Geo

Mea

n T

(Ft^

2/da

y)

Probably not. Wells might be fairly efficient too……

1

2

4TTE = Schafer (1978)

Conclusions

•Pumping tests are essential to evaluate aquifer hydraulics in the vicinity of the well. However, the selection of the well locationoften ensures that it is not representative of the aquifer.

•Specific capacity tests generally provide unbiased estimates oftransmissivity. However, they often are highly variable and may Require many tests to provide a good estimate of transmissivity.

Meak K of Specific Capacity within 2 Km v. Pumping Test KN < 5

1

10

100

1000

10000

1 10 100 1000 10000

K (ft/day) Pumping Test

Mea

n K

(ft/d

ay) S

peci

fic C

apac

ity T

ests

Meak K of Specific Capacity within 2 Km v. Pumping Test K10>N>5

1

10

100

1000

10000

1 10 100 1000 10000

K (ft/day) Pumping Test

Mea

n K

(ft/d

ay) S

peci

fic C

apac

ity T

ests

Meak K of Specific Capacity within 2 Km v. Pumping Test K20>N>10

1

10

100

1000

10000

1 10 100 1000 10000

K (ft/day) Pumping Test

Mea

n K

(ft/d

ay) S

peci

fic C

apac

ity T

ests

Meak K of Specific Capacity within 2 Km v. Pumping Test KN>20

1

10

100

1000

10000

1 10 100 1000 10000

K (ft/day) Pumping Test

Mea

n K

(ft/d

ay) S

peci

fic C

apac

ity T

ests