Well Tests to Characterize Idealized Lateral Heterogeneities by Vasi Passinos K 1,S 1 K 2,S 2

Faults Steeply Dipping Beds

Igneous Rocks Facies Change Reef Marine Clay Batholith Country rock Dike Channel sand Floodplain deposits

Confined Aquifer Unconfined Aquifer

Conceptual Models LocalNeighboring T1 S1T1 S1 T 2 S 2 LL 2-Domain Model3-Domain Model Matrix Strip T m S m LLw T s S s =S m

Analysis Governing Equation Initial Condition when Boundary Conditions

Analysis – 2-Domain Conditions at the contact L 1 2

Analysis – 3-Domain Conditions at the contact m m s Lw

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

Methods – Numerical Transient numerical model using MODFLOW 2-Domain – T r and S r were varied 3-Domain - T r 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 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 T r =10 T r = 1 T r =0.1 t dLA t dLB t dLC

2-Domain Model S Contrast S r = 10 S r = 1 S r = 0.1 t dLA t dLB t dLC

3-Domain Model T Contrast T r = 10 T r = 1 T r = 0.1 t dLB t dLC t dLD

2-Domain T Contrast – 0.125L

2-Domain T Contrast – 0.5L

2-Domain S Contrast – 0.125L

2-Domain S Contrast – 0.5L

Graphical Evaluation – 2-Domain Estimate Aquifer Properties t o = S =  s = 2.3 T = 1 t o = 0.42 S = 0.35  s = 4.1 T = 0.55

Graphical Evaluation – 2-Domain Estimate Aquifer Properties t o = 2.7 S =  s = 4.1 T = 0.55

T E =1 S E = T L =0.55 S L =0.25 T E =1 S E = T L =0.55 S L =0.136 T L =0.55 S L =0.06 T L =0.55 S L =0.27 T L =0.55 S L =0.021 T L =0.55 S L =0.068 T L =0.55 S L =0.029 T L =0.55 S L =0.021 L LL

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<t dL <2.5.

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 t c = 7.3 Streltsova, 1988

3-Domain T Contrast L

3-Domain T Contrast - 0.5L

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 & Conductance

Graphical Evaluation – 3-Domain Estimate Aquifer Properties t o = 0.09 S =  s = 2.3 T = 1 t o = S =  s = 2.3 T = 1

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 T ssd or C d of the layer. Solve for T ss or C

Non-Uniqueness s s Log (t) Dual Porosity Overlying Leaky Layer without storage Unconfined Aquifer w/delay yield from storage Overlying Leaky Layer with storage Streltsova, 1984 Streltsova, 1988 Streltsova, 1984 Neuman, 1975

Field Example 500 feet Down Up Ridge stream N fault

Field Case - Site Map N 500 feet BW-109 BW2 L B-4 Felsic Mafic

Drawdown from Pumping Well

Drawdown from Piezometers

Using Semi-Log Straight- Line Analysis : Minimum slope using the derivative curve is 0.5 T ssd =34=K s w/K a L T ss = 24 ft 2 /min w = 10 to 20 ft Determining Hydraulic Properties L = 280 ft Distance to fault b = 21.5 ft screened thickness T m = 0.05 ft 2 /min S m = 2x10 -4 ??? T s = 26 to 52 ft 2 /min T s /T m = 500 to 1000

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 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 Drawdown for low conductivity vertical layer controlled by conductance. C=K s /w Drawdown for high conductivity vertical layer controlled by strip transmissivness. T ss =K s *w Feasible to determine properties of a vertical layer from drawdown curves.

Conclusions Analyzing piezometers individually is a poor approach to characterizing heterogeneities. Drawdown curves non-unique. Require geological assessment.

Acknowledgments Funding –Geological Society of America –Brown Foundation –National Science Foundation Others…