Well tests to characterize idealized lateral heterogeneities
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K 1 ,S 1. K 2 ,S 2. Well Tests to Characterize Idealized Lateral Heterogeneities. by Vasi Passinos. Faults. Steeply Dipping Beds. Facies Change. Floodplain deposits. Marine Clay. Channel sand. Reef. Dike. Country rock. Batholith. Igneous Rocks. Confined Aquifer.

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Well Tests to Characterize Idealized Lateral Heterogeneities

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Well tests to characterize idealized lateral heterogeneities

K1,S1

K2,S2

Well Tests to Characterize Idealized Lateral Heterogeneities

by

Vasi Passinos


Well tests to characterize idealized lateral heterogeneities

Faults

Steeply Dipping Beds


Well tests to characterize idealized lateral heterogeneities

Facies Change

Floodplain

deposits

Marine Clay

Channel

sand

Reef

Dike

Country rock

Batholith

Igneous Rocks


Well tests to characterize idealized lateral heterogeneities

Confined Aquifer

Unconfined Aquifer


Conceptual models

Local

Neighboring

Matrix

Matrix

Strip

T1S1

Tm Sm

T2 S2

Tm Sm

Ts

Ss=Sm

L

w

L

L

L

Conceptual Models

2-Domain Model

3-Domain Model


Analysis

Analysis

Governing Equation

Initial Condition

Boundary Conditions

when


Analysis 2 domain

1

2

L

Analysis – 2-Domain

  • Conditions at the contact


Analysis 3 domain

m

m

s

L

w

Analysis – 3-Domain

  • Conditions at the contact


Method analytical

Method – Analytical

  • Transient analytical solution using Method of Images (Fenske, 1984)


Methods numerical

Methods – Numerical

  • Transient numerical model using MODFLOW

  • 2-Domain – Tr and Sr were varied

  • 3-Domain - Tr and w of the strip were varied.

  • Grid optimized for small mass balance errors

  • The properties of the model were selected so that the drawdown and time from the numerical model were dimensionless


Dimensionless time

Dimensionless Time

  • Drawdowns were evaluated at three dimensionless times to illustrate effects during development of drawdown fields.

  • Dimensionless time used for type curves

  • Dimensionless time used in drawdown fields


2 domain model t contrast

2-Domain Model T Contrast

tdLA

tdLC

tdLB

Tr=10

Tr = 1

Tr=0.1


2 domain model s contrast

2-Domain Model S Contrast

tdLA

tdLC

tdLB

Sr = 10

Sr = 1

Sr = 0.1


3 domain model t contrast

3-Domain Model T Contrast

tdLB

tdLC

tdLD

Tr = 10

Tr = 1

Tr = 0.1


2 domain t contrast 0 125l

2-Domain T Contrast – 0.125L


2 domain t contrast 0 5l

2-Domain T Contrast – 0.5L


2 domain s contrast 0 125l

2-Domain S Contrast – 0.125L


2 domain s contrast 0 5l

2-Domain S Contrast – 0.5L


Graphical evaluation 2 domain estimate aquifer properties

to = 0.42 S = 0.35

Ds = 4.1 T = 0.55

to = 0.029 S = 0.017

Ds = 2.3 T = 1

Graphical Evaluation – 2-DomainEstimate Aquifer Properties


Graphical evaluation 2 domain estimate aquifer properties1

to = 2.7 S = 0.136

Ds = 4.1 T = 0.55

Graphical Evaluation – 2-DomainEstimate Aquifer Properties


Well tests to characterize idealized lateral heterogeneities

TL=0.55

SL=0.029

TL=0.55

SL=0.021

L

TE=1

SE=0.0179

TL=0.55

SL=0.25

TE=1

SE=0.0179

TL=0.55

SL=0.136

TL=0.55

SL=0.27

TL=0.55

SL=0.068

TL=0.55

SL=0.06

TL=0.55

SL=0.021

L

L


Critical region

Critical Region

  • An early semi-log straight line can be determined by

  • The second derivative was compared to plots with a variety of curves. An early SLSL could be identified by a second derivative of 0.2 or less from 0.3<tdL<2.5.


Critical region1

Critical Region

  • Observation points confined to a region that is within 0.3 to 0.5 of the distance between the pumping well and the linear discontinuity


Distance to the contact

Distance to the Contact

Streltsova, 1988

tc = 7.3


3 domain t contrast 0 125l

3-Domain T Contrast - 0.125L


3 domain t contrast 0 5l

3-Domain T Contrast - 0.5L


Strip transmissivness conductance

Strip Transmissivness & Conductance

  • Hydraulic properties of the strip depend on strip conductivity and width

  • Strip K greater than matrix

  • Strip K less than matrix


Strip transmissivness conductance1

Strip Transmissivness & Conductance


Graphical evaluation 3 domain estimate aquifer properties

to = 0.09 S = 0.054

Ds = 2.3 T = 1

to = 0.028 S = 0.017

Ds = 2.3 T = 1

Graphical Evaluation – 3-DomainEstimate Aquifer Properties


Determine properties of strip

Determine Properties of Strip

  • SLSL analysis on the first line will give T and S of the area near the well.

  • Take the derivative of time and determine the maximum or minimum slope.

  • Using equations from curve fitting determine Tssd or Cd of the layer.

  • Solve for Tssor C


Non uniqueness

Non-Uniqueness

Overlying Leaky Layer without storage

Dual Porosity

s

Streltsova, 1988

Streltsova, 1984

Overlying Leaky Layer with storage

Unconfined Aquifer w/delay yield from storage

s

Neuman, 1975

Streltsova, 1984

Log (t)

Log (t)


Field example

Field Example

stream

N

Up

Down

Ridge

fault

stream

500 feet


Field case site map

500 feet

Field Case - Site Map

Felsic

N

Mafic

B-4

BW2

BW-109

L


Drawdown from pumping well

Drawdown from Pumping Well


Drawdown from piezometers

Drawdown from Piezometers


Determining hydraulic properties

Determining Hydraulic Properties

Tm = 0.05 ft2/min

Sm = 2x10-4 ???

  • Using Semi-Log Straight-Line Analysis :

  • Minimum slope using the derivative curve is 0.5

  • Tssd=34=Ksw/KaL

  • Tss = 24 ft2/min

    w = 10 to 20 ft

Ts = 26 to 52 ft2/min

Ts/Tm = 500 to 1000

L = 280 ft Distance to fault

b = 21.5 ft screened thickness


Conclusions 2 domain model

Conclusions 2-Domain Model

Using the Jacob method to analyze well tests:

  • Piezometers r < 0.25L gives T, S of local region.

  • Piezometers r > 0.25L gives average T of both regions.

  • Piezometers r > 0.25L unable to predict S


Conclusions 2 domain

Conclusions – 2-Domain

  • Piezometers in neighboring region also give average T of both regions.

  • L can be determined from intersecting SLSLs using a piezometer within the critical region


Conclusions 3 domain model

Conclusions 3-Domain Model

  • Drawdown for low conductivity vertical layer controlled by conductance.

    C=Ks/w

  • Drawdown for high conductivity vertical layer controlled by strip transmissivness.

    Tss=Ks*w

  • Feasible to determine properties of a vertical layer from drawdown curves.


Conclusions

Conclusions

  • Analyzing piezometers individually is a poor approach to characterizing heterogeneities.

  • Drawdown curves non-unique. Require geological assessment.


Acknowledgments

Acknowledgments

  • Funding

    • Geological Society of America

    • Brown Foundation

    • National Science Foundation

  • Others…


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