Garey A. Fox, Ph.D., P.E., Derek M. Heeren, Michael A. Kizer, Ph.D. Oklahoma State University Evaluation of Alluvial Well Depletion Analytical Solutions

Garey A. Fox, Ph.D., P.E., Derek M. Heeren, Michael A. Kizer, Ph.D.Oklahoma State University

Evaluation of Alluvial Well Depletion Analytical Solutions from a Stream-Aquifer

Analysis Test

OKLAHOMA STATE UNIVERSITYBiosystems and Agricultural Engineering

Funding for this work provided by a FY 2010 Oklahoma Water Resources Research Institute (OWRRI) through the USGS 104(b) Program.

• Streams and Alluvial Aquifers– Hydraulically Connected/Single Resource– Alluvial Well Depletion– Protection of base flow currently not addressed in

water law systems of many states (OK)

Introduction

OKLAHOMA STATE UNIVERSITYBiosystems and Agricultural Engineering Department

Stream Depletion by Ground Water PumpingStream Depletion by Ground Water Pumping

Source: Winter et al., 1998, USGS Circular 1139



Introduction• Rapid development of analytical solutions for

alluvial well depletion…• Suggested as alternative means of deriving

streambed conductivity, Ksb

Objectives



• Evaluation of analytical solutions using field data from multiple geologic conditions is needed– Assessment of applicability and predictive capability

• Stream-Aquifer Analysis Test:– Pumping well adjacent to a

stream/river – North Canadian River in Oklahoma

– Drawdown response measured in multiple observation wells

– Stream depletion estimated not measured

Field Site



• North Canadian River: – Sand bed, partially

penetrating stream – Connects Canton Lake in

the north and Lake Overholser in the south

• North of El Reno, OK in Canadian County

Field Site



Site Characteristics



• Surface geology is Quaternary alluvial sands and gravels (aeolian and fluvial in origin)

• Characterized as 15-20 m in thickness with widths of 1.6 km from the river

• Drillers’ logs report mostly fine sand with interdispersed clay

• Previous aquifer tests by Ryder (1996):• Specific yield = 0.29• Hydraulic Conductivity = 48 m/d

Streambed Sediment Sampling



• Five streambed sediment samples…• Thalweg and near-bank sand bars• Sieve analysis for grain-size distribution

Particle Size (mm)

0.010.11

Per

cent

Fin

er (

%)

0

20

40

60

80

100

Sieve Analysis of Five Sediment SamplesBest Fit Trendline

d10 = 0.19 mm

d30 = 0.28 mm

d50 = 0.37 mm

d60 = 0.41 mm

d90 = 0.65 mm

Ksb = 30 m/d

(Alyamani and Sen, 1993)

Streambed Conductivity, Ksb



• Falling-head permeameter tests:

Time (s)

0 50 100 150 200 250 300

He

ad

Dis

pla

cem

en

t a

bo

ve I

niti

al

Wa

ter

Le

vel (

m)

0.00

0.05

0.10

0.15

0.20

MeasuredPredicted (Darcy Equation)

tH

H

tt

dK sb

0

0

ln

Streambed Conductance, OKLAHOMA STATE UNIVERSITYBiosystems and Agricultural Engineering Department


• Streambed Conductivity, Ksb:• Average = 16.5 m/d• Standard Dev. = 3.1 m/d

• Width of River, W = 20-25 m

• Streambed Thickness, M = minimal restriction

dmOM

WK sb 1000

NCR - Falling-Head Permeameter

Sa

tura

ted

Hyd

rau

lic C

on

du

ctiv

ity,

Ksb

(m

/d)

0

5

10

15

20

25

Installation of Well Field



• Observation wells installed using GeoProbe– Installed to 8 m depth with 5 m

of screened section at base

• Drawdown and temperature measured every 5 minutes using water level loggers (HoboWare)– Installed logger in river to

monitor stream stage and temperature

Long-Term Monitoring



Date

10/3/09 10/7/09 10/11/09 10/15/09 10/19/09 10/23/09

Ele

vati

on

(m

)

102

103

104

105

106

107

Stream

F

G

H

Stream/Aquifer Analysis Test



• Attempted to use several analytical solutions…– Hunt (1999) solution solved in Maple:

– Hunt (2003) solution for semiconfined aquifers

Tt

SL

ST

terfc

T

L

ST

t

Tt

SLerfc

Q

Qs4424

exp4

2222

0

22

1

22

1 /4

)/2(

/4

)(

4),,(

dSTt

yTxLEe

STt

yxLE

T

Qtyxsw

Stream/Aquifer Analysis Test



Date

10/3/09 10/7/09 10/11/09 10/15/09 10/19/09 10/23/09

Ele

vati

on

(m

)

102

103

104

105

106

107

Stream

F

G

H

Stream-Aquifer Analysis Test



(a) Observation Well F

Time, t (min)

10 100 1000 10000

Dra

wd

ow

n, s

w (

m)

0.0

0.2

0.4

0.6

0.8

1.0

ObservedTheis (1941) and Hunt (1999) SolutionsTheis (1935) Solution - No Stream

T = 860 m2/dSy = 0.28

> 600 m/d

Delayed-Yield Effects

Well Identification (Figure 1)

SSE n STDD Xa NOF

F 0.09 891 0.01 0.73 0.01 G 0.07 891 0.01 0.35 0.02 H 0.07 891 0.01 0.34 0.02





SSE n STDD Xa NOF

F 0.09 891 0.01 0.73 0.01 G 0.07 891 0.01 0.35 0.02 H 0.07 891 0.01 0.34 0.02

(c) Observation Well H

Time, t (min)

10 100 1000 10000

Dra

wd

ow

n, s

w (

m)

0.0

0.1

0.2

0.3

0.4

0.5

ObservedTheis (1941) and Hunt (1999) Solutions

T = 950 m2/dSy = 0.28

> 1500 m/d





Time, t (min)

100 1000 10000

Str

eam

Dep

leti

on

, Q

s/Q

(%

)

0.0

0.2

0.4

0.6

0.8

1.0

Tt

SLerfc

Q

Qs4

2

Tt

SL

ST

terfc

T

L

ST

t

Tt

SLerfc

Q

Qs4424

exp4

2222

Conclusions



• Stream-aquifer analysis test able to derive reach-scale conductance

• North Canadian River - fully penetrating stream with little to no hydraulic resistance– Estimated stream depletion of 60 to 70% of Q

after only 5 days of pumping• Advantages of earlier solutions:

– Considerably simplifies the mathematical complexity

– Reduced the number of parameters to parameterize the stream-aquifer interaction

Questions?

E-mail: [email protected]

Research Website: http://biosystems.okstate.edu/Home/gareyf







SSE n STDD Xa NOF

F 0.09 891 0.01 0.73 0.01 G 0.07 891 0.01 0.35 0.02 H 0.07 891 0.01 0.34 0.02

(b) Observation Well G

Time, t (min)

10 100 1000 10000

Dra

wd

ow

n, s

w (

m)

0.0

0.1

0.2

0.3

0.4

0.5

ObservedTheis (1941) and Hunt (1999) Solutions

T = 790 m2/dSy = 0.19

> 1500 m/d


Documents

Garey A. Fox, Ph.D., P.E., Derek M. Heeren, Michael A. Kizer, Ph.D. Oklahoma State University Evaluation of Alluvial Well Depletion Analytical Solutions