Hydraulic Conductivity of MinnesotaMinnesota 

Confined Glacial Aquifers

R G SouleR. G. SouleMinnesota Department of Health

R. J. BarnesUniversity of Minnesota

OverviewOverview• Well by well comparison of  pumping test and 

ifi it t t ti t f h d lispecific capacity test estimates of hydraulic conductivity (K).

• Explore the additional information afforded by using specific capacity test K values.

• Consider the limitations of these tests.

Pumping and Specific Capacity Tests“Gold Standard” N = 239 N = 70,773

Pumping and Specific Capacity Test Pairs

• Must have the same unique well number*• Must have the same unique well number*, 

• Must have verified location*,

• Must be sufficient well construction and geologic information*, 

• Must be analyzed in a similar fashion.

*County Well Index (CWI) Minnesota Geological Survey

Estimating Specific Capacity  Test Transmissivity

Required Well Information

• Screened interval (L)Soil

r w

Screened interval (L)

• Radius (rw)

A if hi k (b)

Sand

Sandy Clay • Aquifer thickness (b)Sandy Clay

Clay

Sand &L Sand & Gravel

L b

Clay

Aquifer Thickness Problem

Soil• Many wells do not have l fi i l

Sand

Sandy Clay

lower confining layer information.

Sandy Clay

Clay

• Option 1: Use the observed “minimum” thickness.

Sand and Gravel

• Option 2: Estimate from the known thicknesses.

“b” or minimum estimate of “b”

Clay

Estimating Aquifer Thickness

400

Frequency of Known Aquifer ThicknessTotal = 8,000

300

350

200

250

eque

ncy

100

150

Fre

Average of

0

50

0 50 100 150 200 250 300

Average of Thickness > 20 ft. =   44 ft.

Minimum0 50 100 150 200 250 300

Aquifer Thickness [ft.]

MinimumThickness 20 ft.

Tests Requirements

Pumping TestsS F d l (USGS) St t (MDH DNR &– Sources:  Federal (USGS), State (MDH, DNR & MPCA), consultants, well drillers and publications.

– Analysts chosen Transmissivity

Specific Capacity

Analysts chosen Transmissivity.– Cooper‐Jacob or Theis methods.

Specific Capacity

– Source: CWI

Pumping rate (Q) N=100 Pairs– Pumping rate (Q)

– Duration (t)Drawdown (s)

N=100 Pairs

– Drawdown (s)

The Comparison SetAVERAGE WELL INFORMATION

YEAR BUILT 1985.4CASING DIAMETER [INCH] 11.9

WELL USE PERCENTPUBLIC WATER SUPPLY 60%

DEPTH [FT.] 174.5SCREEN LENGTH  [FT.]  29.3KNOWN AQUIFER THICKNESS  [FT.] (N=56) 50.5MINIMUM AQUIFER THICKNESS  [FT.] (N=44) 50.0

IRRIGATION & INDUSTRIAL 35%PUMP OUT 3%TEST & MONITORING 2%

AVERAGE TEST INFORMATION Pumping Test Specific CapacityDURATION [HOURS] 24 16DISCHARGE [GPM] 605 664TESTS WITH OBSERVATION WELLS [% ] 76% 0%TESTS WITH OBSERVATION WELLS [% ] 76% 0%ESTIMATED STORATIVITY 4.5E‐03 1.5E‐03

1600

Specific Capacity and Pumping Test ComparisonKnown Aquifer Thickness

1400

1600

Specific Capacity K (K sc)

Pumping Test K (K pt)

1000

1200

Test

R2 = 0.50

= 0.97

800

rom Pum

ping

 T R  0.50

31 Overestimates 25 Underestimates

400

600

K fr

0

200

0 200 400 600 800 1000 1200 1400 1600

K from Specific Capacity Test [ft. /day]

1600

Specific Capacity and Pumping Test ComparisonMinimum Aquifer Thickness

1400

1600

Specific Capacity K (K sc)

Pumping Test K (K pt)

1000

1200

Test

R2 = 0.48= 0.72

800

rom Pum

ping

  19 Overestimates 25 Underestimates

400

600

K fr

0

200

0 200 400 600 800 1000 1200 1400 1600

K from Specific Capacity Test [ft./day]

1600

Specific Capacity and Pumping Test ComparisonEstimated Aquifer Thickness

1400

1600

Specific Capacity K (K sc)

Pumping Test K (K pt)

1000

1200

Test R2 = 0.49

= 1.03

800

rom Pum

ping

 

27 Overestimates 21 Underestimates

400

600

K fr

0

200

0 200 400 600 800 1000 1200 1400 1600

K from Specific Capacity Test [ft./day]

1600

Specific Capacity and Pumping Test ComparisonKnown H Estimated H

1400Specific Capacity K (K sc)

Pumping Test K (K pt)

1000

1200

Test R2 = 0.50

= 0.99

800

rom

Pumping

 

58 Overestimates 46 Underestimates

400

600K fr

0

200

00 200 400 600 800 1000 1200 1400 1600

K from Specific Capacity Test [ft./day]

Additional Information from Specific Capacity Tests

• Apply the same methods to estimate K for theApply the same methods to estimate K for the remaining 70,673 specific capacity tests.

• Compare the local specific capacity tests to• Compare the local specific capacity tests to the pumping tests.

E l i l l i f K l• Evaluate spatial correlation of K values.

100%All Specific Capacity Tests Pumping Tests

Frequency Distributions of K

• Both test types have lognormal frequency distribution.80%

90%

100%

distribution.

• Not the same populations.

60%

70%

80%

cy of K

 [%]

40%

50%

60%

ve Frequ

enc

TestsMedian K [ft./day]

100 Pumping Test 13270 000 S ifi

• Heuristic for 50%  20%

30%

40%

Cumulativ 70,000 Specific 

Capacity Tests27

range:– Lower = mean/2

– Upper = mean * 2.50%

10%

20%

0%1 10 100 1000

K [ft./day]

Spatial Correlation of Pumping and Specific Capacity KS ifi C it T t N li b t

1500 m

Specific Capacity Tests Normalize between pumping test wells:

Specific Capacity K (K sc)

500 m

1000 m

500 m

1000 m

Excluding the Ksc of the Pumping Test Well

p p y ( sc)

Pumping Test K (K pt)

500 m500 m

PumpingFrom (ft.) To (ft.)

MeanKsp/Kpt

Pumping Test Well

Test0 500

500 1000

1000 1500

116%92%

49%1000 1500……. ……. …….

Spatial Correlation of Pumping and Specific Capacity TestsSpecific Capacity K / Pumping Test K 95% Confidence Boundary

100%

120%

Test K

p p y / p g y

Ksp > Kpt within 500 m. of pumping test wells

80%

100%

/ Pu

mping

 Te

Ksp / Kpt ≈ 90% between500 and 1000 m.

60%

Capa

city K /

Beyond 1000 m

20%

40%

age Specific  Beyond 1000 m 

Ksp / Kp ≈ 35 to 45 %.

0%

20%

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Avera

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Distance from Pumping Test Well [m]

Spatial Correlation of Specific Capacity TestsSource of Variability Amounty

Noise  41%

Small Scale Spatial Variability 20%

Large Scale  Spatial Variability 39%

Confined Glacial AquifersPermeability [ft./day] 

Conclusions for Confined Glacial Aquifers• A pumping test is more valuable than a specific capacity test.capacity test.

• Specific capacity K values are consistent with pumping test K values.p p g

• Specific capacity K values are “noisy”.

• Hydraulic conductivity is spatially related.Hydraulic conductivity is spatially related.– Change exponentially over a few kilometers.

– Change linearly over hundreds of kilometers.

• Pumping tests in this data set are located in higher hydraulic conductivity zones.