STRIPA PROJECT 91413 Interpretation of Fracture System Geometry Using Well Test Data T.W. Doe J.E. Geier Golder Associates Inc. Redmond, Wash. USA November 1990 TECHNICAL REPORT An OECD/NEA International project managed by: SWEDISH NUCLEAR FUEL AND WASTE MANAGEMENT CO Division of Research and Development Mailing address: Box 5864, S-102 48 Stockholm Telephone: 08-665 28 00 INTERPRETATION OF FRACTURE SYSTEM GEOMETRY USING WELL TEST DATA T.W. Doe J.E. Geier Golder Associates Inc. Seattle, Washington November 1990 This report concerns a study that was conducted for the Stripa Project. The conclusions and viewpoints presented are those of the authors and do not necessarily coincide with those of the client. A list of other reports published in this series is attached at the end of this report. Information on previous reports is available through SKB. ABSTRACT This report presents three methods of determining fracture geometry and interconnection from well test information. Method 1 uses evidence for boundary effects in the well test to determine the distance to and type of fracture boundary. Method 2 uses the spatial dimension of the well test to infer the geometry of the fracture-conduit system. Method 3 obtains information on the spacing and transmissivity distribution of individual conductive fractures from fixed-interval-length (FIL) well tests. The three methods are applied to data from the Site Characterization and Validation (SCV) at the 360m level of the Stripa Mine. The focus of the technology development is the constant- pressure welltest, although the general approaches apply to constant-rate well tests, and to a much lesser extent slug or pulse tests, which are relatively insensitive to boundaries and spatial dimension. Application of the techniques to the N and W holes in the SCV area shows that there is little eviden. e for boundary effects in the well test results. There is, on the other hand, considerable variation in the spatial dimension of the well test data ranging from sub-linear (fractures which decrease in conductivity with distance from the hole) to spherical, for three-dimensional fracture systems. In some cases flow changes dimension over the course of the test. The absence of boundary effects suggests that the rock mass in the SCV area contains a well- connected fracture system. Major uncertainties in th* / a lysis of well test data limit the use of single borehole measurements. ft .out assuming the value of specific storage, one can reliably determine c / ;' ie spatial dimension, and, for two dimensional flow only, the transmiss * \j Among the uncertainties are the effective well radius, the degree to wi. h the fracture conduits fill the n-dimensional space in which flow occurs, and t > cross-sectional area of the conduits at the wellbore. This report presents a : nplete development of constant-pressure well test methods for cylindrica ow and flow of arbitrary dimension. Computer code listings for generation c typt curves are provided. 11 TABLE OF CONTENTS Page No. ABSTRACT i 1 INTRODUCTION 1 1.1 Basic Definitions for Well Testing 6 1.1.1 Permeability, Hydraulic Conductivity, Transmissivity 6 1.1.2 Storage 10 1.1.3 Wellbore Storage 12 1.1.4 Skin Effects 14 1.1.5 Flow Geometry 14 1.1.6 Outer Boundary Effects 16 1.2 Why Constant-Pressure Tests? 16 2 THEORY OF CONSTANT-PRESSURE WELL TESTING IN TWO DIMENSIONS 22 2.1 Conceptual Model of Hydrogeclogical System 24 2.2 Overview of Mathematical Approach 29 2.3 Analysis 30 2.3.1 Dimensionless Formulation 34 2.3.2 Laplace-Space Formulation 39 2.3.3 Laplace-Space Solution for Dimensionless Pressure 42 2.3.4 Laplace-Space Solution For Dimensionless Flowrate 46 2.4.5 Numerical Inversion of Laplace-Space Solutions 48 2.4 Computer Implementation 50 2.4.1 Calculation of the Laplace-Space Solutions 50 2.4.2 Verification of the Program CH-QP 51 2.5 Examples of Type Curves Produced Using CH-QP 55 3. GENERALIZED RADIAL FLOW MODEL FOR CONSTANT-PRESSURE WELL TESTS 60 3.1 Definition of Dimension 60 3.2 Space-filling Properties of Conduits 66 3.3 Generalized Geometry and Heterogeneous dimension 68 3.4 Linear Flow with Variable Material Properties 68 3.5 Generalized Solution for Constant-Pressure Well Tests 69 3.6 Dimen.sionless Formulation 72 3.7 Dimension n = 1: Linear Flow Solution 7t> 3.8 Dimension 2. Cylindrical Flow 7.s Ul TABLE OF CONTENTS (Cont) Page No. 3.9 Spherical Flow Tests 80 3.10 Response of Observation Wells to Constant-Pressure Well Tests 83 4. ANALYSIS OF WELL TEST DATA FROM SCV BOREHOLES 86 4.1 Background of Well Testing Program 86 4.2 Description of Data Analyses 89 4.3 N4 84.0-91.0 91 4.3 N4 84.0-85.0 94 4.4 Wl 38.1-39.1 96 4.6 Wl 110.4-111.4 104 4.7 W2 21.9-22.9 106 4.8 W2 28.8-31.8 108 4.9 W2 37.8-40.8 110 4.10 W2 49.8-50.8 113 4.11 W2 51.8-52.8 117 4.12 W2 53.8-54.8 117 4.13 W2 67.8-68.8 122 4.14 W2 69.8-70.8 126 4.15 W2 77.8-78.8 130 4.16 W2 83.8-84.8 133 4.17 W2 88.8-89.8 136 4.18 W2 111.8-112.8 138 4.19 W2130.7-131.7 142 4.20 W2137.7-138.7 145 4.21 W2137.7-140.7 148 4.22 Summary and Conclusions 151 5 DETERMINATION OF FREQUENCY AND CONDUCTIVITY OF FRACTURES FROM FIXED-INTERVAL-LENGTH WELL TESTS 153 5.1 Introductory Comments 153 5.2 Fixed-interval-length Versus Discrete Zone Sampling Approaches 153 5.3 Statistical Analysis of Fill Test Data 154 5.4 Fill Probabilistic Model 161 5.5 Application to SCV Well Test Data 163 IV TABLE OF CONTENTS (Cont) Page No. 6 SUMMARY AND CONCLUSIONS 165 7 ACKNOWLEDGEMENTS 168 8 NOTATION 169 9 REFERENCES 174 APPENDIX 1: CORRECTIONS FOR HEAD VARIATIONS - MULTIRATE ANALYSIS 179 APPENDIX 2: FRACDIMQ and FRACDIMH, GENERALIZED CONSTANT-PRESSURE WELL-TEST TYPE CURVES 183 APPENDIX 3: CH-QP, CYLINDRICAL FLOW WITH LEAKAGE, SKIN, AND BOUNDARY EFFECTS 187 APPENDIX 4: PROGRAM LISTINGS 191 LIST OF FIGURES 1-1 Fracture Sets 2 1-2 Examples of Closed and Open Boundaries 3 1-3 Examples of Linear, Radial, and Spherical Flow in Fractures and Porous Media 5 1-4 Physical Examples of Skin Effects 15 1-5 Pressure and Flow Versus Time for Constant Pressure, Constant Rate, and Pulse or Slug Tests 17 1-6 Slug/Pulse Test Boundary Effects 19 1-7 Slug Test Type Curves for Integral Dimensions 20 2-1 Conceptual Models for Radial Cylindrical Flow 26 2-2 Examples of Closed and Open Boundaries 28 2-3 Constant-Pressure Type Curves for Closed and Open Boundaries for Various Dimensionless Radii 56 2-4 Time to Observe Boundary Effects 57 2-5 Constant-Pressure Type Curves with Skin 59 3-1 Comparison of Radial and Linear Flow Calculations 61 3-2 Spatial Dimension - Integral Cases 62 3-3 Examples of Sublinear and Hyperspherical Conduits 65 3-4 Non-Space-Filling Conduits 67 3-5 Apparent Dimension in Linear, Heterogeneous Flow 70 3-6 Constant-Pressure Type Curves, Dimensions 0 to 4 73 3-7 General Type-Curve Analysis 75 3-8 Analysis of Linear Flow Data 77 3-9 Analysis of Cylindrical Flow Data 79 3-10 Analysis of Spherical Flow Data 82 3-11 Observation Well Response for a Constant Pressure Injection Test 84 4-1 Location of Boreholes and SCV Area 87 4-2 General Diagram of Testing Equipment 88 4-3 Well Test Data (Borehole N4, 84.0-91.0m) 90 4-4 Wei! Test Data (Borehole N4, 84.0-85.0m) 95 4-5 Well Test Data (Borehole Wl, 38.1-39.1 m) 97 4-6 MRATE-Corrected Data (Borehole Wl, 38.l-39.lm) 98 4-7 Well Test Data (Borehole Wl, 46.l-47.lm) 102 4-8 Well Test Data (Borehole Wl, 110.4-m.4m) 105 4-9 Well Test Data (Borehole W2, 21.9-22.9m) 107 4-10 Well Test Data (Borehole W2, 28.8-31.8m) 1O> 4-11 Well Test Data (Borehole W2, 37.8-40.8m) 1 ] I 4-12 Pseudo-Steady Flow Versus Injection Head (Borehole W2, 49.1-50.0m) 114 4-13 flow Versus time for Six Injection Heads (Borehole W2, 49.8-50.8m) i 15 VI LIST OF FIGURES (Cont) 4-14 Well Test Data (Borehole W2,49.8-50.8m) 116 4-15 Well Test Data (Borehole W2,51.8-52.8m) 118 4-16 Well Test Data (Borehole W2, 53.8-54.8m) 119 4-17 MRATE-Corrected Data (Borehole W2, 53.8-54.8m) 121 4-18 Well Test Data (Borehole W2, 67.8-68.8m) 124 4-19 MRATE-Corrected Data (Borehole W2, 67.8-68.8m) 125 4-20 Well Test Data (Borehole W2, 69.8-70.8m) 127 4-21 MRATE-Corrected Data (Borehole W2, 69.8-70.8m) 128 4-22 Well Test Data (Borehole W2, 77.8-78.8m) 131 4-23 MRATE-Corrected Data (Borehole W2, 77.8-78.8m) 132 4-24 Well Test Data (Borehole W2, 83.8-84.8m) 134 4-25 Well Test Data (Borehole W2, 88.8-89.8m) 137 4-26 Well Test Data (Borehole W2, lll.8-112.8m) 139 4-27 Well Test Data (Borehole W2,130.7-131.7m) 143 4-28 Type-Curve Matches (Borehole W2,130.7-131.7m) 146 4-29 Well Test Data (Borehole W2,137.7-138.7m) 147 4-30 Well Test Data (Borehole W2,137.7-140.7m) 149 5-1 Fixed-Interval-Length (FIL) Sampling Approach 155 5-2 Discrete Zone Sampling Approach 156 Al-1 Mulrirate Correction 181 A2-1 Accuracy of Numerically Integrated Bessel 186 Functions vn LIST OF TABLES 4-1 N4 84.0-91.0 93 4-2 N4 84.0-85.0 96 4-3 Wl 38.1-39.1 99 4-4 Wl 46.1-47.1 103 4-5 Wl 110.4-1145 104 4-6 W2 28.8-31.8 110 4-7 W2 37.8-40.8 112 4-8 W2 53.8-54.8 120 4-9 W2 67.8-68.8 123 4-10 W2 69.8-70.8 129 4-11 W2 77.8-78.8 133 4-12 W2 83.8-84.8 135 4-13 W2 88.8-89.8 138 4-14 W2 111.8-112.8 140 4-15 W2 130.7-131.7 144 4-16 W2 137.7-138.7 148 4-17 W2 137.7-140.7 150 5-1 Results of Osnes Maximum Likelihood Model for Conductive Fracture Frequency and Single Conduit Transmissivity 164 INTRODUCTION Where does the water move? How do we identify tine conduits that cany groundwater? How large are the conduits? How do they connect with one another to form flow paths? These are the essential questions for predicting the potential for contaminant movement by groundwater.