ABSTRACT FLUID FLOW THROUGH ROCK SALT UNDER VARIOUS STRESS STATES BY Chia-Shing Lai Concern for leakage of reactor fuel waste materials from underground salt cavities has prompted questions regarding the permeability of rock salt materials. To provide information on this question, the flow rate of kerosene through rock salt Specimens was studied for a range of normal and octahedral shear stresses. Kerosene was used as the fluid because of similarity to radioactive waste materials and its nonrusting properties when in contact with steel. Expressions for the permeability of the rock salt were developed in terms of the stress conditions and void ratios of the rock salt material. A high pressure triaxial cell was designed and constructed for permeability tests at various stress states. The cell permitted application of axial loads separate from lateral pressures. In- dependent hydraulic systems maintained axial and lateral pressures to about 1:5 psi of selected pressures. Fluid flow was permitted axially through the sample under a head differential of 125 psi. Rock salt from an underground formation in Louisiana was cut into cylindrical samples 3 inches high by 3 inches in diameter. Strain gages attached to the sides of the sample provided information Chia-Shing lai on tangential and axial strain. Overall axial deformation, obtained by means of a dial gage mounted outside the triaxial cell, provided a check on strain gage values. Kerosene flow through the sample was recorded at given time intervals. The experimental data provided the basis for developing empirical expressions for the rock salt permeability in terms of the mean normal stresses and octahedral shear stresses. Strain measurements permitted incorporating changes in void ratio into the permeability expressions. The flow of kerosene through the rock salt appears to obey approximately the same laws as developed for flow of water through soils. Laboratory permeabilities for the rock salt varied from 0.0036 to 40.6752 milli-darcy for various stress states. Very low permeabilities indicate that leakage of radioactive waste materials from underground salt cavities will be very small to almost negligible. FLUID FLOW THROUGH ROCK SALT UNDER VARIOUS STRESS STATES By Chia-Shing Lai A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil Engineering 1971 PLEASE NOTE: Some Pages have indistinct print. Filmed as received. UNIVERSITY MICROFILMS ACKNOWLEDGMENTS The writer wishes to express his sincere appreciation to Dr. Shosei Serata, who helped initiate this project, and to Dr. O.B. Andersland for his assistance and encouragement through- out the latter part of the writer's doctoral studies, and for his many helpful suggestions during the preparation of this thesis. The writer also wishes to express his sincere appreciation to Dr. C.E. Cutts, Dr. R.F. McCauley, and Dr. M. Fox for serving as members of his guidance committee. The writer acknowledges the U.S. Public Health Service and the Division of Engineering Research at Michigan State University for the financial aid that made this study possible. ii TABLE OF CONTENTS Page ACWOWIEDGMENTS ......0.0....0.................0...... ...... . ii LIST OF FIGURES ......00.0................................... v LIST OF TABIES ....... ............. ................O OOOOOOOOO Vii NOTATIONS ......O..0.. ............. 0............. ....... .0... Viii Chapter I 0 INTRODUCTION 0 O . . . ......... . O . O . . . . O . 000000000000000 1 II . LITERATURE STUDY ................................... 5 Underground DiSposal of Waste and Groundwater contamination I O . . . . . . . . . . . . . . . . . . . O . . . . . . . O . O . O O 5 Permeability of Underground Pbrous Media ........... 8 Effect of Stress and Strain Field Upon Porous Flow . 11 Leakage from an Underground Salt Cavity ............ 14 III. EQUIPMENT AND TEST PROCEDURES ............. ..... .... 16 High Pressure TriaXial Ce 11 . . . . . . . . . . 0 . . . . . . . O . O . O . 16 Specimen Preparation ............................... 19 Test Procedures and Pbrous Flow Measurements ....... 23 IV 0 EXERMNTAL RESULTS . O O . . . . . . . . O . . . .......... . . . . . . 26 Stress and Strain Measurements .. ............ . ...... 26 Flow Measurements ........... ... .................... 29 V. STRESS AND STRAIN EFFECTS ON PERMEABILITY 0F mEROCK SALT .........O......................O... 55 Stress Field .................................°..... 55 Strain Field ....................................... a‘ compreSSibility ............................ ..... ... 71 VI. FLOW FROM AN UNDERGROUND SAET CAVITY ........ ..... .. 82 iii Chapter VII. SUMMARY AND CONCLUSIONS 0.....0....U. High Pressure Triaxial Cell ........................ The Effect of Stress, Strain, and Compressibility upon Permeability OO0.0..........0.0.0.0...00000O. Feasibility of Radioactive Waste DiSposal .......... VIII. BIBLIOGRAHIY .0...OO..OOO APPENDIX --- DATA FUTURE RESEARCH ........ iv ................0........... 88 89 89 91 93 97 Figure 3-1 3-2 3-4 3-5 3-6 4-1 4-2 5-1 5-2 5-3 5-5 5-6 5-7 LIST OF FIGURES Page High Pressure TriaXial Cell ......OOOOOOOOOOOOOOOOO. 17 Schematic Diagram Showing Layout of Triaxial Pressure Cells and Automatic Pressure Control system .....................................O..... 20 Rock Salt Sample with Bronze Screens ............... 22 Two Finished Samples and Cover of High Pressure Triuial cell .0.................................. 22 High Pressure Triaxial Cell with Sample ............ 24 Test Set-up Showing Triaxial Cells, Pressure Gages, and Strain Gage EqUipmnt .........O0.0.... 24 Strain-Time Relationship at Various Stress Field ... 30 Flow-Time Relationship at Various Stress Levels .... 45 Typical Curve Showing Time Versus Accumulated Flow . 56 The Effect of Mean Stress upon Permeability for Various octahedral Shear Stress ......O........... 58 The Effect of Octahedral Shearing Stress upon Permeability for Various Mean Stress ............. 59 The Effect of Octahedral Shear Stress upon Permeability with Mean Stress Equal to Zero ...... 60 Permeability under Various Combinations of Mean Stress and octahedral Shear Stress ............... 61 Three Dimensional Plot of Mean Stress, Octahedral Shear Stress, and Permeability ................... 65 The Relationship between Taylor's Void Ratio Coefficient and Permeability..............,....... 68 The Effect of Product of cm and (ea/1+e) on Permability ................................O.... 69 Figure 5-9 5-10 5-11 5-12 5-13 5-14 5-15 6-1 6-2 Page The Relationship between Unit Volume Change and Pemability Of ROCR Salt .................OOO..OO 70 The Effect of Mean Stress on Void Ratio ............ 72 The Effect of Mean Stress on Taylor's Void Ratio coeffiCien-t ...................................... 73 The Effect Of Mean Stress upon Compressibility for Various Octahedral Shearing Stress (I) ....... 76 The Effect of Mean Stress upon Compressibility for Various Octahedral Shearing Stress (II) ...... 77 The Effect of Mean Stress upon Compressibility for Various Octahedral Shearing Stress (III) ..... 78 The Effect of Bulk Compressibility upon Perme- ability for Various Octahedral Shearing Stress ... 30 Hypothetical Storage Cavity in.a Salt Formation .... 83 Two Dimensional Configuration,ofWan Underground Formtion .0......OO.......................O00.... 86 vi Table 5-1 5-2 5-3 5-4 A-l A-2 A-3 LIST OF TABLES Page Stress levels for the TeSt Program ................. 28 Permeability as a Function of Mean Stress at Various Octahedral Shearing Stress ............... 62 Octahedral Shearing Stress as a Function of Permeability at Various Mean Stresses ............ 63 Compressibility as a Function of Mean Stress at Various Octahedral Shearing Stresses ............. 75 Compressibility as a Function of Permeability at Various Octahedral Shearing Stresses ............. 81 Strain-Rate, Deformation, and Flow-Test Data ....... 97 Flow-Rate, Permeability, Strain and Deformation .... 127 Stress, Taylor's Coefficient, Void Ratio, Void, and Bulk cmpreSSi-bility ......................... 128 vii 31332963 I 6L, 6L NOTATIONS cross-sectional area area of contact between solid particles arrangement of solid ratio of area of contact between soil solids to gross area inner radius of cylindrical cavity constants outer radius of cylinder compressibility' bulk compressibility (l/psi) grain compressibility (l/psi) average particle diameter particle size uniform diameter of straight parallel capillaries axial deformation measured by dial gage volume of flow void ratio major, intermediate, and minor principal strains tangential strain measured by strain gage, lateral strain based on dial gage readings axial strain obtained by dial gage Young's modulus initial unit weight at atmospheric pressure viii bulk density fluid density hydraulic gradient coefficient of permeability (cm/sec) physical permeability = R $- octahedral shear Strength 3? yield condition viscosity of fluid plastic radius porosity number of Spheres Poisson's ratio average fluid pressure uniform internal pressure uniform external pressure fluid pressure inside the cavity initial lateral underground pressure fluid pressure flow rate - fi§ radius of Sphere Bergelin's tube radius mean stress - %-(o1 + 02 +'o3) major, intermediate, and minor principal stress lateral stress total stress effective stress = (o - Pf) saturation of the sample specific internal area of model (Scheideggar, 1960) ix Carman's specific surface exposed to fluid (German, 1937) shape factor octahedral shearing stress tortuosity (Scheideggar, 1960) time discharge velocity pore pressure change crystal or solid volume void volume bulk volume depth of formation CHAPTER I INTRODUCTION The wide use of radioactive materials in the present era, necessitates safe disposal of reactor fuel waste because of its potential harmful effects upon human life. A variety of measures to safeguard such radioactive waste have been investigated; for example, storage in artificial containers on the ground, dumping wastes into the deep sea, shooting them into the Space or burying wastes in deep underground cavities (Kaufman, 1961). This study is concerned with the latter method, diSposal in underground cavities. Previous research has shown that underground burial of radioactive waste is the safest and the most efficient method for diSposal (Serata, 1959). Cavities provide thick Shielding, permit remote handling, and provide adequate cooling for high level radio- active waste. However, two problems related to underground disposal must be considered: one is structural stability of the under- ground cavity and the other is seepage of waste through the rock to ground water supplies or to the ground surface. More specifical- ly, the problem of structural stability relates to deformation of the underground structure, while the problem of seepage deals with the rock permeability and is a function of existing stresses. The problem of structural stability has been clarified to some extent. For example, the structural stability of salt cavities appears to be safe with regard to the high pressures associated with radioactive waste diSposal (Reynolds, 1960). The problem of seepage, however, still remains unanswered, and the degree of permeability under complex stress conditions is not yet known. In the decade following 1930, the state of stress in natural underground cavities was studied and experiments were carried out by many investigators (Dahir, 1964, Sakurai, 1966, Obert and Duvall, 1967). Sakurai (1966) and Dahir (1964) in- vestigated the theoretical and experimental behavior of under- ground stress fields and provided a theory for the rheological model of salt behavior. Since 1951, several experimental methods (Osoba, 1951; Fatt, 1952, 1953; Gray and Fatt, 1963; Douglas, 1953) have been developed for determination of the permeability of underground material with relation to stress states. These studies were con- cerned with hydrostatic compression. Gray and Fatt (1963) stated that permeability was a function of the ratio of radial to axial stress; i.e., triaxial stress conditions. Most of this research was conducted for the petroleum industry and for reservoir engineering. Preliminary studies of reactor fuel waste disposal in salt cavities were undertaken by Serata (1959). From his theoretical analysis and experimental investigations, Serata showed that the storage of radioactive waste in salt cavities was feasible. In 1960, Reynolds also reported to the Atomic Energy Commission on permeability of rock salt and creep of underground salt cavities. The purpose of this study is to determine the degree of seepage through a rock sample during a laboratory experiment, and to extrapolate the findings of this research to potential pollution. Because of test limitations imposed on the laboratory experiment, attention is focused on seepage through a typical Louisiana rock salt. The objectives of this thesis are to provide experimental data on flow of liquids through rock salt under various stress states and to prOpose a method for predicting the permeability of underground formations. Specifically, the objectives are as follows: (1) To design and construct a device Suitable for lab- oratory determination of permeability of rock salt under complex stress conditions. (2) To develop mathematical equations for prediction of permeability as a function of the complex stress conditions. (3) To evaluate the feasibility of radioactive waste diSposal in an underground formation and/or storage of other substances such as fuel and water. Rock salt has been chosen as the material for the under- ground formation in this study. From previous experience it has been demonstrated that rock salt shows isotropic and homogeneous qualities under static and dynamic loading and thatznxsproperties fall within a practical range for testing. A complete analysis of radioactive waste diSposal in under- ground salt formations requires a three dimensional stress loading scheme to determine seepage through a laboratory model for use in predicting the ultimate degree of pollution. This research has been undertaken to provide experimental data for three dimensional loading. For permeability tests under various stress states, a high pressure triaxial cell was designed and constructed. The test machines were equipped with coordinated loading in lateral and axial directions and could be controlled by using two independent hydraulic systems. Uniform flow was applied to the Specimen under a constant fluid pressure. The Specific permeability was obtained for several stress states including transient and steady state flow conditions. For this study, it was assumed that the rock salt is isotropic and homogeneous. Kerosene was used as the fluid repre- sentative of reactor waste. For convenience all tests were con- ducted at room temperatures. Since underground formations are warmer than room temperatures, corrections to the permeability can be made by allowing for changes in viscosity and density of the pore fluid. CHAPTER II LITERATURE STUDY Underground Disposal of Waste and Groundwater Contamination The treatment and diSposal of radioactive waste is one of the increasingly serious problems related to growth of the nuclear power industry. It is impossible to destroy or eliminate radio- activity by any known chemical or physical means, and the maximum permissible concentrations (U.S. Department of Health, Education, and Welfare, 1960) for radionuclides in air and in water are several orders of magnitude lower than those Specified for in- active contaminants. There are several alternatives in radio- active waste dISposal. These include: Storing in artificial con- tainers in or on the ground; dumping the waste into the deep sea; shooting it into the Space; or burying it in deep underground cavities. This study is concerned with the last of these diSposal measures because it is the most promising solution. Research has been in progress for a number of years on reducing radiation hazards to humans. An ultimate diSposal opera- tion is required that will insure that fission products are safely contained for centuries without requiring further monitoring. A unique property of these wastes is their intense radioactivity: they are capable of Spontaneous and prolonged boiling from absorp- tion of their own radiant energy. Unfortunately, the rate of heat released is not constant and violent surging can occur, leading to rapid fluctuations in pressure build-up (Burns, 1960). In con- structing waste diSposal facilities in underground formations it is necessary to consider the maximum pressure produced by the waste itself, and also to design for high external earth pressures in- cluding that from groundwater acting on the structures. During September 1955 the Committee on Waste DiSposal of the Division of Earth Science, National Academy of Science (1957) (consisting of leading scientists in inter-related fields such as chemistry, physics, geology, geophysics, economics, and sanitary engineering) discussed diSposal of radioactive waste in geologic formations. The committee then made a Specific recommendation on storage of radioactive waste (solid or liquid) in salt formations as perhaps the most promising method of diSposal. The major advantages of disposal in salt formations were (Serata, 1959): (1) Salt beds and domes are widely distributed and abundant throughout the country with an area of more than half a million square miles (Lang, 1957). The United States' salt reserves are estimated at greater than 6 x 1013 tons (Mineral Resources of the U.S., 1958); (2) Rock salt has a high thermal conductivity (2.5 BTU/hr-ft-OF at 2000F) (Birch and Clark, 1940) and a melting point sufficiently high for large quantities of heat to be dissipated during the storage of high level radioactive waste; (3) Rock salt has a compressive strength similar to that of concrete and lacks tensile strength. It flows plastically to relieve stress concentrations from mining and heating. However, under normal mining conditions, stress concentration and temperatures are low and supports are not needed. Due to plastic behavior, salt acts as a self sealer for the storage cavity as well as an absorber of higher stress concentration around the cavity opening; (4) The total Space created by mining rock salt during a period of 1934 to 1953 has been calculated as one billion cubic feet (National Academy of Science, 1957); (5) In the decade of the forties, hundreds of millions of gallons of liquid petrochemical products have been successfully stored in salt cavities by various oil companies (Reidel, 1952; Van Fossan, 1955). DiSposal studies on high level liquid and solid wastes initiated at Oak Ridge National Laboratory indicate that it is feasible to construct underground storage cavities. During 1954, over 1,000 gallons of acid waste, containing a liquid fission product with complexing agent and 1000 curies of Srgo, was successfully poured into a pit lined with limestone (Parsons, 1963) at 233 Lake, Ontario, Canada for the Clark River Project. It has been estimated that Sr90 will be released to the environment in about 130 years but that the rate of release into a nearby stream will not produce concentrations of these radio- nuclides above the normal drinking water tolerance. Hawkins demonstrated the value of Wyoming bentonite clay for preventing the seepage of rainwater into radioactive waste buried above the water table in a humid region. Other efforts to prevent this type of seepage had varied success at several sites (Hawkins and Horton, 1967). High level waste fission product solution containing 100 curies was incorporated into glass blocks and the blocks were buried for 3 years in sand beneath the water table. The experiment showed that even in saturated soil with low exchange capacity, this method of disposal was safe and the escape of hazardous radio- nuclides was within acceptable limits. An underground formation was shown to provide permanent radiation shielding and ion-exchange media for the anticipated suall.release (Meritt and Parsons, 1964). Fenimore (1964) reported on land burial of solid radio- active waste during a 10-year period. Since the initial land burial of solid radioactive waste in 1953 at the Savannah River Plant, 577,000 curies of fission product and induced radioactivity were buried. Routinesurveillancecfifthirteen test and observation wells indicated no migration of radioactive material. Geologic and hydrologic studies, radioassays of soil samples and measurements of ground water velocity using tritium as a tracer, indicated little probability of introducing this buried radioactivity into public zones. The studies and experiments in the literature show that underground burial of radioactive wastes in rock salt formations is feasible if these conditions are satisfied: (1) the rock salt is structurally stable; and (2) seepage is at a permissible rate. Permeability_g£_Underground Porous Media Since 1951 several experimental methods (Osoba, 1951; Fatt, 1952; Gray, 1963) have been developed for permeability measure- ment of rock materials under complex stresses. These experiments were conducted for the petroleum and reservoir engineering industry and used sandstone as the porous medium. They were conducted under hydrostatic compression or uniaxial compression. The most recent Study (Gray and Fatt, 1963) was concerned with the stress effect on permeability of sandstone cores and was undertaken primarily to develop methods for studying permeability of sandstone under simulated overburden preSSure. Findings demonstrate that the sandstone permeability decreases upon applica- tion of an overburden pressure and that this decrease is a function of the ratio of radial to axial stress. However, no extensive study on the relationship of radial to axial stress ratio upon permeability has been carried out. Osoba, Richardson, and Kerver (1951) made laboratory measurements on small core samples of reservoir rock to determine relative permeability to oil and gas by five methods. These tests included the Penn State Techniques, Single Core Dynamic Technique, Gas Drive Technique, Stationary Liquid Technique, and Hasseler Technique. Their study also included the influences of such factors as boundary effects, hysteresis, and rate of flow upon these measure- ments. Results indicated that four of the five methods yielded essentially the same relative permeability to gas; the Stationary Liquid Technique was applicable to oil only. Fatt and Davis (1952) worked on the reduction in permea- bility with increase in overburden pressure. Results showed that the Specific permeability of sandstone decreased with increase in overburden pressure, and that most of the decrease took place in 10 the range of zero to 3,000 psi. Wilson (1956) designed and constructed a useful apparatus for determination of relative permeability under simulated reser- voir conditions. Water-oil relative permeability data and water saturation vs. relative permeability were obtained. Results showed that the application of overburden pressure caused a reduction in the effective permeability to both water and oil in about the same proportion as for reduction of single-phase permeability. Fatt (1958) measured porosity and flow using packs of rubber Spheres under compression and showed that ideal Sphere packs did not model the flow porosity of consolidated sandstone. McLatchie, et. a1. (1958) reported the effective compress- ibility of reservoir rock and its influence on permeability. They concluded that the effective compressibility of the material could not be correlated with porosity and that other factors, such as the amount of clay material present, must be considered. Mann and Fatt (1960) studied the effect of pore fluids on the elastic properties of sandstone and found that the presence of an aqueous solution in the pore Spaces caused the elastic constant to change. For example: (1) Bulk compressibility increased by 10 to 30 percent; (2) Young's modulus decreased by 8 to 20 percent; and (3) Poisson's ratio increased by one hundred percent for Bandera sandstone and changed only a small amount for the two other sandstones. 11 Effect of Stress and Strain Field upon Porous Flow Although extensive studies have been carried out on the effect of stress fields upon porous flow under hydrostatic com- pression, few studies have been made on the effect of triaxial compression upon porous flow. To date, the studies have been con- cerned with the gross effect of overburden pressure on permeability, porosity, electrical resistance, and sonic velocity. The major conclusion drawn from these studies on porous flow are: (1) The permeability of sandstone decreases upon applica- tion of simulated overburden pressure, and (2) permeability re- duction of sandstone cores subjected to simulated overburden pressure is a function of the ratio of radial to axial stress. Secchi (1936) made experiments to study the dependence on permeability of a filter on external pressure and showed that such a dependence does exist, and is subject to hysteresis. A series of experiments published by Ruth (1946) and Tiller (1953) showed that the relationship of permeability k to fluid pressure p and the total pressure 0 can be represented as follows: -m k = K(o - p) (where m is constant) This relationship was deduced from largely empirical investigations. The relationship is valid only if (c - p) is larger than some lower limiting value. Athy (1930) found that the variation of clay porosity, with depth, can be represented by 12 where no is the average porosity of surface clay, a is a con- stant, and z is depth below the surface. Bergelin (1949), Pbrkhaev (1949), and Templeton (1953, 1954) studied the use of capillaric models to investigate the flow of several phases in a single capillary. These investigations were mainly experimental, since techniques had been devised for the observation of gas-liquid or liquid-liquid diSplacement in uniform capillaries with diameters as small as four microns. The concepts of diSplacement in single capillaries repre- sented as a bundle of capillaries have been studied by Gates and Lietz (1950), Fatt and Dykstra (1951), Burdine (1953), Hassan and Nielson (1953), and Irmay (1954). As is usual for capillaric model theories it was assumed that the sample could be represented by a bundle of capillary tubes in which the fluid path length was not the same as the bulk length. In addition, the fluid path length was considered to vary with saturation. The following equations list the relationships of perme- ability to porosity and the other factors proposed by different investigators: nr2(l-l-b) (1) Fatt and Dykstra (1951) dk -.————§———.d3' 8a where, k = permeability n - porosity r I tube radius 8' I saturation of the sample a,b constants 13 (2) Hagen-Poiseuille (Scheidegger, 1960) n 62 n3 k"'32 0’ k"=22 where, 6 = uniform diameter of straight parallel capillaries v-J ll tortuosity S = specific internal area of the model n = porosity (as in (1) above) (3) Kozeny Theory (Scheidegger, 1960) 3 on TS2 where Symbols are as identified in (2) above k: (4) Modified Kozeny Theory (Kozeny-Carman Equation) (Carman, 1937, 1938, 1939) n3 k=2 2 55 (1 - n ) 0 with symbols as in (2) above, and so is Carman's "specific" surface exposed to the fluid (5) Brinkman's Theory (Happel and Byrne, 1954) 2 k=11‘—8(3+-1-‘_‘—n-3 fi'” where g'n NR3 = l-n = Total volume of Spheres k = permeability R = radius N = number of Spheres :3 ll porosity l4 (6) Taylor's Theory (Taylor, 1948) 2 1!. e3 k=I)S p, 1+8 where DS diameter of particle U = fluid viscosity e = void ratio C = constant yw = fluid density From these relationships, it is noted that permeability is primarily affected by porosity of the media. Change of porosity for a material is, however, directly affected by external pressure. Leakage from 22 Underground Salt Cavity In 1960 the U.S. Atomic Energy Commission, in reSponse to the urgent need for practical solution to reactor fuel diSposal, supported research by Reynolds at the University of Texas on perme- ability of rock salt and creep of underground salt cavities. From theoretical analysis and experimental studies the following conclusions resulted: 1. Storage of radioactive wastes in salt cavities is feasible. 2. Though rock salt is relatively plastic and elastic when it is mined, localized fractures occur. 3. No flow can occur through the solid salt crystals. 4. Superficial cracks in a cavity can be sealed by the use of a diatomaceous earth SuSpension. 5. The non-reactive liquid permeability K can be estimated: 15 -10 -0.212 physical permeability in cm2 where K = om = mean confining stress in psi Pf = average fluid pressure in psi PrOper selection of the piezometric head in a cavity (internal pressure) can provide an additional safety factor for assuring that no leakage from a cavity will occur. Data and analysis from the University of Texas work has suggested that wastes could be confined in salt cavities for over 500 years. It should be noted, however, that creep decreased with age and creep rate increased when temperature was increased. CHAPI‘ER III EQUIPMENT AND TEST PROCEDURES The equipment used in this research includes standard items except for the Specially designed high pressure triaxial cell and the hook-up of hydraulic pumps and pressure shock absorbers. A detailed description is given for the high pressure triaxial cell. Details of the test procedures are given in two parts: Specimen preparation and porous flow measurements. High Pressure Triaxial Cell A high pressure triaxial cell, designed to permit applica- tion of uniform confining pressures and axial loads, was fabri- cated. Two independent hydraulic load systems, were used to apply confining pressures and axial loads. The triaxial test simulated the complex stress conditions existing in an underground formation adjacent to the diSposal cavity. The triaxial cell used to measure rock properties at high pressure is shown in Fig. 3-1. It was designed so that pressure could be maintained on the internal fluid (kerosene) and external fluid (hydraulic oil) independently. This cell consisted of a base, an outer cylinder, cover plates, neoprene high pressure hoses, gages, and an axial pressure ram. Stainless steel tubes were used for the collector, distributor, and accessories. The 16 17' To Capillary Tube Air Outlet r H ‘ /’///,/.// / / / / /; / / -/ f . // 7” v/ 5/ // I 45:. / Mb reg—A * v 7 ‘ F Fluid Collect- / j ing cap Bronze Wire Screens ;,w' (Three Layers) { \K\\\ I \ To Strain Gage Strain Gage Channel Selector ijzj Lateral ‘_ PresSure System Spe cimen / F lex ib 1e Epoxy _/VA/ ’ Coating With Fiber-r”’ Glass Reinforcement \ If =I=: fiirz _|_ \\l\.\\\\ r/ I u 1 \ \ \ ‘ —w«~—Axial Pressure \\\ \\ \\ \ i\\ \\ \\ \ \\\ \m; Ram Fluid Distributing \\ \\\\ ~\ ‘x \\ ~\\ \ \ ‘“-———o-Ring Cap (Honey Comb g \_\ \ \ . \ Cylinder) “ \ \ \\ A ‘ \ / / J / . Q 5// £77 ' 13 Axial Pressure J System “j‘ 3 \\ Keros ene Air Out let Pressure System Dial Gage Fig. 3-1. High Pressure Triaxial Cell (Scale 1 : 2) 18 base, cover, and cylinder were made of stainless steel. One of the stainless steel tubes was attached to the pressure ram, an- other tube was attached to the collector cylinder. The apparatus was designed to Operate at confining pressures up to 10,000 psi. All other parts and appurtenances were capable of similar high pressure Operation. Both top and base were drilled with small holes for attaching the air release valve with a ball bearing at the opening. The major problem was prevention of leakage in order to maintain different pressures in the internal fluid (kerosene) and the external fluid (hydraulic oil). This requirement was accomplished by sealing with neoprene O-rings (see Fig. 3—1). Strain gages, placed in hard epoxy cement to prevent leakage, were attached to the sample with wires passing through Openings in the cell. The load capacities of the hydraulic pumps were 10,000 psi for both axial and lateral stress directions with pressures measured by a separate hydraulic pressure gauge in each system. Stresses could be controlled independently or simultaneously. Axial and lateral deformations were measured by strain gauges placed on the sample with an accuracy of :10-6 inch per inch. A mechanical dial gauge, mounted outside the cell, provided an accurate reading on the axial deformation in terms of the movement of the ram piston relative to the cell body with an accuracy of i 10'4 inch. 19 The pressure applied to a test Specimen was held reasonably constant by the automatic control System in both the lateral and axial stress directions. A shock absorber, used in each hydraulic system, reduced the shock impulse produced by the strating of automatic pump during the loading cycle. The sensitive pressure switch attached to the automatic pump maintained pressures at close to 1:5 psi in both pressure systems. Specimen Preparation Rock salt used in this research was Obtained from Louisiana. The salt was mined at a depth of about 700 ft., was white in color, and consisted of crystalline grains of approximately 0.1 to 0.7 inches in diameter. Cylindrical Specimens, 3 inches in diameter and 3 inches in height (see Fig. 3-3), were prepared with a band saw, grinder, and lathe, and then smoothed with sand paper finishing. Small cavities on the sides of the specimen (which could permit a development of a puncture in the epoxy coating) were filled with Gypsum cement, then coated with a very thin layer of hard epoxy coating to prevent fluid leakage along the wall. Variation in Specimen size was within 1 1/32 inch for the height and diam- eter. Three bronze screens placed between the Specimen and the steel caps separated the specimen from.the fluid distributor and collector. The caps were drilled with 1/8" holes to provide openings for fluid movement. Strain gages were attached along the periphery at midheight of the Specimen and vertically along the sides with thin epoxy cement. 20 Fig. 3—2 SCHEMATIC DIAGRAM SHOWING LAYOUT OF TRIAXIAL PRESSURE CELLS AND AUTOMATIC PRESSURE CONTROL SYSTEM 10. ll. 12. 13. 14. 15. 21 Component Designations for Fig, 3-2 High Pressure Triaxial Cell (Fig. 4-1) Specimen Strain Gauges Fluid Collector Fluid Distributor Axial Pressure Rams Dial Gages Capillary Tube or Burettes Shock Absorbers Automatic Pumps with Pressure Switches Hand PUmps Hydraulic Oil-Kerosene Transformers Channel Selector Strain Gage Recorder Pressure Gages 22 Fig. 3-3. Rock Salt Sample with Bronze Screens Fig. 3-4. Two Finished Samples and Cover of High Pressure Tri- axial Cell 23 Gage and lead wires were embedded in the epoxy cement (see Fig. 3-4). The Specimen and caps were coated with flexible epoxy cement (REN product) and with two layers of fiber glass cloth for reinforcement. Test Procedures and Porous Flow Measurements The laboratory tests provided information on the deforma- tion and permeability of rock salt Specimens at various stress levels. The specimens in which stress and strain distributions are examined were under non-plastic conditions. The base, with triaxial cell and axial pressure ram, was set on the table of the testing machine. Next, hydraulic lines were connected for application of axial and lateral pressures. A dummy gage ring was placed on the top of the pressure ram to compensate for the fluid effect on the acting gage and a specimen was then placed in the cells. After connecting the strain gage wires, the cell was filled with hydraulic Oil to the top (see Fig. 3-5). A Small tube for collecting fluid was connected directly to the top cap as Shown in Fig. 3-6. A cotton ball, soaked with kerosene, was placed at the top of the tube to prevent evaporation of the fluid. Assembly was finally completed by installation of the top cap and connection to the hydraulic system. Kerosene was used for all porous flow measurements because of its similarity to water and its nonrusting properties. The air release valve was kept open and hydraulic pressure was gradually increased by means of a hand pump until the cell was completely filled with oil. The air release valve was then 24 Fig. 3-5. High Pressure Triaxial Cell with Sample (see Fig. 4-1) Fig. 3-6. Test Set-up Showing Triaxial Cells, Pressure Gauges, and Strain Gauge Equipment 25 closed and axial pressure was gradually increased up to 10 psi to obtain perfect contact between the cover, Specimen, and ram. Approximately 50 pound preSSure increments were applied for both axial and lateral pressure until the calculated working stress was reached. Strain gage readings were recorded for each stress increment. After the pressures had reached the working value, the automatic pumps were turned on to maintain a constant pressure. Shock absorbers, inserted between the automatic pump and pressure cell, limited sudden increases of pressure to not more than i’10 pSi. Seepage pressures and confining pressures were held con- stant throughout the experiment except for the high T-value working stress (T = 1000 psi). The high-rate of flow which occurred under this T-value required that the seepage pressure be reduced. The strain reading and accumulated flow were recorded at selected time intervals until a constant flow rate was Obtained. Data are given in the appendix. CHAPTER IV EXPERIMENTAL RESUDTS Stress and Strain Measurements The flow properties of porous media usually depend upon material characteristics such as bulk density or void ratio and particle size, shape, and arrangement. These characteristics vary from one material to another. They may also vary within the same material if it is Subjected to factors such as strain hardening due to the stress applied upon the material or to chem- ical reaction, i.e., heat. However in this study only strain effects due to the Stress change were included as an object of the research. In order to study flow prOperties, temperature and chemical reaction were considered constant for the laboratory conditions. Permeability of materials subjected to different strain conditions depended on the stress conditions and permeability measurements in this study were obtained under constant stress levels and recorded as a time function until a constant flow rate was observed. The mean stress, om, applied to the material was calculated as gm = 1/3 (51 +’02 + 03) psi, where 01, 02, 03 are principal stresses. The octahedral shearing stress, T, was equal to ’- A2 - -2_~“-u -- 2 1/3J/(ol ' oz) +(o'2 - 03) + (03 - ol) . Since no tectonic forces were considered, 02 = 03 = o and cm becomes L 26 27 1/3 (20L + 01) and T =,/2/3 (01 - o for the triaxial test L) conditions. The axial and tangential strains were Obtained by and 3 strain gage as The temperature was assumed constant €1 L' and equal to room temperature. The test was designed to control stresses in the range of cm equal 1,000 psi to 5,000 psi which approximates the actual overburden pressure at depths of 1,000 ft. to 5,000 ft. below the ground Surface. The range of octahedral shearing stresses were 100 psi to 1,000 psi. Rock salt has an ultimate octahedral Shear- ing strength close to 1,000 psi. The stress levels for each test condition are tabulated in Table 4-1. Since a five inch piston was used to apply pressure on a three inch cylindrical Specimen, P1 and PL were computed to obtain cm and T. P1 and PL are the vertical and lateral pressures, respectively. Constant stress conditions were maintained throughout each experiment by using the automatic hydraulic pump equipment. A minimum of 10,000 minutes was allowed for the flow rate to reach a steady state flow condition for each experiment. Dial gage readings provided accurate data on axial deforma- tions. SR-4 strain gages attached to the external Specimen surface provided data on the ratio of axial to tangential strain. An apparent error in the Strain gage readings Should cancel when these data are used as a ratio. Lateral strain was calculated by multi- plying this ratio of tangential to axial Strain by the axial de- formation. For example, consider test 1 where total axial strain 31 equals 615 X 10.6 in/in and total lateral strain 6L = 145 X 10- in/in based on strain gage readings. Since the total axial 6 T (psi) 100 300 500 700 1000 U m Table 4-1. (psi) 28 Stress Levels for the Test Program 1000 P1: 1006 P : 929 1017 788 1028 823 1040 505 1057 293 1350 1356 1280 1367 1138 1378 997 1390 855 1407 643 1700 1706 1629 1717 1538 1728 1347 1740 1205 1757 993 3000 3006 2898 3017 2788 3028 2823 3040 2505 3057 2293 4000 4006 3929 4017 3788 4028 3647 4040 3505 4057 3293 5000 5006 4929 5017 4788 5028 4647 5040 4505 5057 4293 29 deformation 6 based on the dial gage, equals 109 X 10"4 in. 1’ 1 - (Si = -%2 X 10 4 in/in) the computed tangential strain a I- - e£=eiX—L=36X%%X104=8.7Xloain/in. (See Table 91 A-1 and A-2) All strain readings were recorded at selected time intervals until a constant flow of liquid was obtained. The results from strain measurements are plotted against time as shown in Fig. 4-1-1 to 4-1-30. Flow Measurements Flow meaSurementS were Obtained for selected stresses while strains were measured in the axial and tangential directions. This represents a simulation of the stress conditions on an element of salt material in an underground formation. The flow of kerosene was measured by capillary tube, burette, or graduate cylinder according to the flow rate. The flow preSSure was maintained constant by use of the automatic pump control System. The kerosene flow was vertical from the external Supply into and through the salt Specimen. The accumulated effluent was collected in the receiver and recorded at selected time intervals until a steady state flow rate was Obtained. The pressure differential between entrance and exit locations, AP, should be equal to the gage pressure reading, P. Because the pressure at the outlet was equal to atmospheric pressure, it was assumed that AP was dissipated during flow through the Specimen. Accumulated flow EV is plotted against time in Fig. 4-2-1 to Fig. 4-2-10 for the selected stress conditions. -4 in/in) '2 in/in) Strain Strain Gage (x 10 Dial Gage (x 10 -4 in/in) Dial Gage (10.2 in/in) Strain Strain Cage (10 30 Legend [JAxial Strain (dial gage) initial point = 0 CDAxial Strain (strain gage) initial point = 0 C>Latera1 Strain (strain gage) initial point I 0 J I I I I l I I I Time (1000 min.) Fig. 4-1-1. Strain-Time Relationship at o - 1000 psi T = 100 psi m o . 0 g 0 O O 0 . ° . . O C . O o 1... [3 I.P. = 0 r <3 I.P. - 315 x 10'6 in/in <3 I.P. = 0 (See legend on Fig. 4-1-1) C) o . ‘ ‘ ‘ ‘ A é_e_e_=_e_e—g-g-glg_: : Em r’ 1 1 1 1 1 L 1 1 1 1 0 l 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-2. Strain-Time Relationship at o = 1350 psi m T B 100 psi Strain Strain Strain Gage (x 10"4 in/in) in/ in) -4 '2. . Dial Gage (x 10 1n/1n) Strain Gage (x 10 in/ in) -2 Dial Gage (x 10 31 ”' 1:1 I.P. = 1195 x 10'6 in/in C) I.P. = 0 - r o (3 I.P. = 0 . (See legend on Fig. 4-1-1) . 0 . I I " . I _ O I O . O l.— I . I ,I . . g I II I I I I ' ' ' ' ' e I ' ‘ 1A A II I.A A A a. A. n A A .n a A . 01_‘E‘ % I I I, I I I I I L 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-3. Strain-Time Relationship at gm = 1700 psi T = 100 psi T' I I I I I II I —%D . I r I __ I ... . ‘ ‘ ‘ ‘ A A A A A 4.3 ‘ A 1.- A : . I I I I I I I I I I I {j T‘ Q -‘- DI.P. = 5273 x 10'6 in/in _ / OLP. = 1835 x 10'6 in/in ’_ £31.P. = 0 L__ . (See legend on Fig. 4-1-1) 1 1 I 1. .I I I I I I J 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Strain-Time Relationship at o = 3000 psi m T ' 100 psi Strain Strain Cage (10.4 in/in) Dial cage (10'2 in/in) 32 Strain Strain Cage (10.4 in/in) Dial Gage (10.2 in/in) O I . o I I . . O O I ' -6 . CJI.P. I 5722 X 10 in/in O - 2 . OI.P. - 2057 x 10 6 in/in . . ALP. I 302 x 10..6 in/in (See legend on Fig. 4-1-1) I 43 A A, ‘ .A it A A. ‘ A ‘ ‘_4§TJNJ\ To 1 - . A A I . I . . . . I. l I I I I I II I #437 4‘%3 I O I 1 1 1 1 I I 1 1 I I 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-5. Strain-Time Relationship at o I 4000 psi T I 100 psi m A A..A ‘ ‘ ‘ ‘ £5 A ‘ ‘ A A 2 I— ‘ . I I . T. I 9 . . . I . CII.P. I 5940 X 10"6 in/in ' O I.P. - 1834 x 10"6 in/in 1 __ ALP. 672 x 10'6 in/in ‘ (See legend on Fig. 4-1-1) I I II I I I I I II I 514* l I D O__.. I I 0 l 2 3 4 5 8 9 10 Time (1000 min.) Fig. 4-1-6. Strain-Time Relationship at am a 5000 p31 T I 100 psi Strain Strain Strain Gage (10-4 in/in) Dial Cage (10.2 in/in) Strain Gage (10-4 in/in) Dial Gage (10"2 in/in) 33 OLP. - 2321 x 10"6 in/in 5 _ OLP. - 999 x 10'6 in/in ' -6 I 4 L ALP. 11x10 in/in . . , (See legend on Fig. 4-1-1) . 0 O . O O . A . ‘ ‘ A 2 I— ‘ A A I ‘ I A A ‘ ‘ A A A 1 P— 0. 7 I I I " ' I I I I I I I I I o~— . D D I 1 I l 1 I 1 1 1 l I 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-7. Strain-Time Relationship at cm I 1000 psi T I 300 psi -6 3 C]I.P. I 2790 X 10 in/in OLP. - 856 x 10‘6 in/in ALP. - 168 x 10'6 in/in . ° (See legend on Fig. 4-1-1). . ° 0 . I 2 . I I . I C ‘ ‘ T a A A A ‘ A 1 P" C) A ‘ ‘ a A A :/,:l‘% I I I I I II I I I I I I I 7' O—I— O I I I I l l I I I I l 0 l 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-8. Strain-Time Relationship at o I 1350 psi m T I 300 psi Strain Strain Gage (10-4 in/in) Dial Gage (10.-2 in/in) Strain Strain Gage (10-4 in/in) Dial Gage (10"2 in/in) 34 O C I I . I I I I I 3 s . ‘ I . . A A M 2 _ ‘ ‘A A I A ‘ ‘ - . ‘ C]I.P. - 4020 x 10 6 in/in ‘ 01.17. - 658 x 10"6 in/in l —- / ALP. I 95 X 10.6 in/in (See legend on Fig. 4-1-1) . .. I II I I I I: I I I I I I 0-4 ' r I I I I I I I I I L I 0 1 2 3 4 5 6 7 8 9 110 Time (1000 min.) Fig. 4-1-9. Strain-Time Relationship at o I 1700 psi r - 300 psi m 4 L— . O A’: \ /. . I I I I I I I I I5; ‘I I I I I 3 I." I - . ‘2’. - I 7’.“ -6 . q‘llk ‘ CJI.P. I 3908 X 10 in/in OLP. - 1810 x 10'6 in/in 2 —' c>I.P. - 0 (See legend on Fig. 4-1-1) 1 I. o.__ I I I I J, I 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-10. Strain-Time Relationship at o I 3000 psi r - 300 psi m Strain Strain Gage (10-4 in/in) Dial Gage (10.2 in/in) Strain Strain Gage (1.0-4 in/in) Dial Gage (10"2 in/in) 35 4 I— . . I I I I I I II I e I l *{} —{3 C) I I I 3 _ I ' I . . I 9 . I I -6 . I ' ULP. I 4305 X 10 in/in 2 ’ OLP. - 2002 x 10'6 in/in ’ ALP. - 0 I (See legend on Fig. 4:1- ‘ 1 ‘ A A ‘ ‘ A A ‘ ‘ ‘ A I ‘ A A O—I I I I I I l I L I L I I 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-11. Strain-Time Relationship at o I 4000 psi 7 - 300 psi m 0 4 (3 O #_ I N Strain Strain Gage (10.4 in/in) 0181 Gage (10'2 in/in) H 38 I- oLP. - 2439 x 10'6 m/m OI.P. = 1727 x 10'6 in/m . - ALP. - 314 x 10'6 in/in . (See legend on Fig.4:l:l I— I .0 r- . A A A I A A ‘ ‘ ‘ F— . “A‘ ‘ A A _. I .IIIIIIIIIII I I I‘D ..AA I I I I I I I II II_ I 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-17. Strain-Time Relationship at am I 4000 psi T I 500 psi I. OI.P. - 2878 x 10'6 in/in OI.P. - 1574 x 10"6 in/in ._ ALP. - 369 x 10'6 in/in (See legend on Fig. 4-1-1) . . h- . O . . . '0 I ’ . ‘. C .— O I _' I A A A A 1A A A I ‘1 ‘ ‘ ‘ ‘ ‘ A __ A . . I I I I I II I I I I I I I ' ... O I III I 1 I I I I I I O 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-18. Strain-Time Relationship at am - 5000 p31 T I 500 psi Strain Strain Gage (10-4 in/in) Dial Gage (10-2 in/in) Strain Strain Gage (10"4 in/in) Dial Gage (10.2 in/in) 39 2.0 *— A A AA A : t 9 . ‘ ‘ A A . O . 1.5 P— A . I I 9 I . -6 ‘/ D I.P. - 6536 x 10 in/in :" 0 LP. - 3950 x 10'6 in/in 1'0 *— 3 ALP. - 319 x 10"6 in/in ‘// (See legend on Fig. 4-1-1) 0 .. ./ I / ... . I ' . . . . . . I I I I ' I 0+- ‘ I I I I I I, II I I I I 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-19. Strain-Time Relationship at am I 1000 psi T I 700 psi 4 I . . . . II I .9 . . . I . -6 3 __ . OI.P. "‘ 6672 X 10 1n/in - OI.P. - 3122 x 10"6 in/in ' ALP. - 333 x 10'6 in/in 2 L_ . (See legend on Fig. 4-1-1) 11. AAAAAAA‘AI“‘ “ ‘ A A I I I I I II I I I I I I I I I I I I o.._,. I L I I I J I I I I 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-20. Strain-Time Relationship at T I 700 psi cm I 1350 psi 4O Fig. 4-1-22. Strain-Time Relationship at cm I 3000 psi T I 700 psi 25 __ 0 LP. - 6255 x 10"6 in/in 0 LP. - 3416 x 10'6 in/in OI.P. - 0 . I A 20 I— (See legend on F1-..4- - . 0 ' ' ° . of: A . . . - a I .5. S o a fit 0'4 15 h. I ‘ c> ‘ A .5 ctro . ‘ ‘ ‘ ‘ A A A A A I H A u I ~/ __ A 4.: OO 10 A cm I m U DO A m .5 w . u H h .2 5 _ I I - I I I I I I I I I I I I I a: c: I I ' I A 0 —-II—- A I I I I I I I I O 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-21. Strain-Time Relationship at o I 1700 psi T I 700 psi m 2.0 I— I I I O O A I :3 'E‘ 1'5 I— I . . . A A. A ‘ I ‘7‘“: fl: EJ I.P. - 6590 x 10'6 1.1/1.1 :3 :3 'o 1.0 _ :0‘ OI.P. - 361 x 10'6 in/in H - g 3.: . ALP. - 496 x 10 6 in/in I: go /’ (See legend on Fig. 4-1-1) A .3 H 0.5 '" .l u I u H a. c: / _ I I I I III- I 3 I ' ' ' ' ' . I O—II— A I I I I L I I l I I TV_ 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Strain Strain cage (10-4 in/in) Dial Gage (10’2 in/in) Strain Strain Gage (10.4 in/in) Dial Gage (10’2 in/in) 41 _. r3 I.P. - 6700 x 10'6 in/in 0 LP. - 8 x 10"6 in/in ALP. - 486 x 10'6 in/in __ (See legend on Fig. 4-1-1) ‘ A ‘ A A A A ‘ Q I . ‘ A I 9 I— I ‘ .A . . I ‘ I I I £5 I - I - I I I l. I I - D - I I —-u-— I I J I I I I L I L L 0 1 2 3 4 5 7 8 9 10 Time (1000 min.) Fig. 4-1-23. Strain-Time Relationship at o I 4000 psi '1' - 700 psi m 5 a I.P. - 7017 x 10’6 1.1/1.“ 0 I.P. I 42 X 10.6 in/in I 4 ALP. - 534 x 10'6 in/in . 0 r’ I (See legend on Fig. 4-1-1). I 9 . I . I 3 ._ I . I I 2 I A A A ‘I A. ‘ I ‘ ‘ ‘ ‘ A 1 I- . z . I I I I I I I I II I I 0-4 0 I I I I I I I I I 0 1 2 3 4 5 7 8 9 10 Time (1000 min.) Fig. 4-1-24. Strain-Time Relationship at am I 5000 psi T I 700 psi Strain Strain Strain Gage (10-4 in/in) Dial Gage (10.2 in/in) in/in) -4 Strain Gage (10 Dial Gage (10.2 in/in) 42 D I.P. - 5806 X 10-6 in/in 5 - OI.P. - 140>.<1'0'6 in/in A OI.P. - 0 ‘ ‘ ‘ (See legend on Fig. 4-1-1) ‘ . A 4 L ‘ ,. . A ‘A A 3 r- A‘A A . C 2 _ A . . . . . I A . . I .. O 1 — I". C I .. I II I I I I I I I I I I I O—«I— I . l I 0 1 2 3 4 5 6 7 8 9 1o Time (1000 min.) Fig. 4-1-25. Strain-Time Relationship at am - 1000 psi T I 1000 p81 0‘: [MP 7754 x 10"6 111/111 . A OI.P. 4330 x 10'6 in/in ALP. - 0 (See legend on Fig. 4-1-1) 1 1 I I 1 I I 1 I I I 0 1 2 3 4 S 6 7 8 9 10 Time (1000 min.) Fig. 4-1-26. Strain-Time Relationship at o - 1350 psi m T - 1000 psi Strain Strain Strain Cage (10-4 in/in) Strain Cage (10"4 in/in) Dial Cage (10'2 Ila/in) Dial Gage (10'2 in/in) 43 OI.P. - 8060 x 10'6 in/in 3 OI.P. I 4964 X 10”6 in/in .- O ALP. - 249 x 10 6 in/in . (See legend on Fig. 4-1-1) 2 - ‘ . . O I . A ‘ I-— . . O ‘ ‘ ‘ A I ‘ A ‘ :. 4 ‘ 1 >— I/‘ III-.... "' .- L—- /; l 0 —-n—- O I I l I I, I I L I, I, I, 0 1 2 3 4 5 6 7 8 9 10 Time (1000 min.) Fig. 4-1-27. Strain-Time Relationship at oh I 1700 psi T I 1000 psi 25 '- 20 _ OI.P. = 6220 x 10'6 in/in o I.P. - 1370 x 10'6 in/in OI.P. I 0 15 —' (See legend on Fig. 4-1-1) 10 *— 5 Time (1000 min.) Fig. 4-1-28. Strain-Time Relationship at o I 3000 psi 'r - 1000 psi m Strain Strain Cage (10-4 in/in) Dial Gage (10’2 in/in) Strain Strain Cage (10-4 in/in) Dial Gage (10’2 in/in) 44 T I 1000 p81 3 _ ULP. - 5198 x 10"6 in/in OI.P. - 784 x 10"6 in/in F’ ALP. - 420 x 10'.6 in/in . ' . (See legend on Fig. 4-1-1) . . .A ‘ I I A ‘ ‘ 2 #— an: : ‘ ‘ /. . . _. 3’:/' ‘x’ l r— 6/, A I I I I I I I II I I I I ' I. ' ' ' ' O‘”‘ ‘ I I l I I I I I l l l J O 1 2 3 4 S 6 7 8 9 10 Time (1000 min.) Fig. 4-1-29. Strain-Time Relationship at o I 4000 psi T - 1000 psi m 18 F . O 15 —' . . .. I 0 . . . -6 . ' ULP. - 7912 x lo ill/in 12 +— ’ O I.P. I 2013 x 10.-6 in/in CSI.P. I O 9 ~— (See legend on Fig. 4-1-1) I 6 __ ‘ ‘ ‘ ‘h ‘ 4‘ g .A A A : E a: I I I I I I I {3 43 3 __ A A 0.“. a I I I I I J 1 I I I 0 l 2 3 4 S 6 7 8 9 10 Time (1000 min.) Fig. 4-1-30. Strain-Time Relationship at cm a 5000 p31 45 396a mawuum 2.3.5; as 3533333“ IEHHIROHm .HuNuq .wwm éfia 83V as; S m w n o n q n N H o _ fi fi _ _ _ _ J _ _ t 0‘0 To 0 O O O t I l, I I I I I . I I I I I II III I I I \ . Sin“ -3 x 9.: u 2E4 . o . \\x . \ N :3 8: u on .28 2: u b . . . . . \ I I I I \ Q I I I \ o . 58:8 S x 93 u 2:2 . \ I MI I\ a . 8 Us 82 u o in 02 u k . \ O \ I \ w 0 .\ . S O O . S Sana $3 x 35 n 2:2 E $8 83 u o :3 2: u k S .0 3 w." 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IIO I I I I I I I I I I I III III I E :Ha\Ha_m-oH x o.N a ua\>2 .Hma coon u o .Hma cos n I I. m ...IIIIIIII I I OH cHa\Ha moH x o.m u “2\>2 .HII oooq u an .Hma ooN a I I nH O I II J ON 0 I \\\R.. mu ..\\\ I\\\I\ I On I I I I .II I .1 mm a I 5838 mIOH x mo.mH n u4\>< IHmm coon n 0 JR 005 I ... I o.» I m.» L on (IE 01) «018 53 £33 835m 2 3.123832 33....on .m-N-2 .me AéHa Soc 25 S I m N o m I m N H oH H 2 7 H H H H H H H H 531. NS x 0.22 a 2:2 .HII 8: u so .38 So... I IIIIII\.\H - I I I I I I I I I I I I I\\\\\\I OIIIIAVI I-\\II\\ I I I I I I I I I I I I I I I I I I I I E \ cHEHa TS x oi: a 2:2 .23 82 u 8 :3 82 u L. I \ 8 I 5828 m-oH x omNN a 2:2 :3 83 u 8 Jan 82 u I NH cH 0N .NN wN Nm (1111 E:01) mom 54 me>QH mmouum um QHSIIOHuIHom uaHHnath .oHINuq .me H.=Ha oooHv IaHa oH m w I m I m H m _ 1 _ H H a H _ _ _ .1. «hr 8 u I I I a. I I I I It I astHa m-OH x N.m u u2\>2 .HII coon u as .HIN oooH u a I I I H I I I I I - O \\ aHaxHa m-oH x N NH 82\>2 I \xx\\.\\\\¢»t“\\nu N I I \\ Hma oooq u 8 Han oooH u e I I .uxxxi -\\\\x I I \\ I I I I I I. I I I I I I I\ x \ I m I I I I .1 q I I I aHa\Ha m-oH x m.mm n 82\>2 I .H88 coon a as .HII oooH u I (III] 301) MOIJ CHAPTER V STRESS AND STRAIN EFFECTS ON PERMEABILITY OF THE ROCK SAET Stress Field The flow of kerosene through rock salt decreased with time until steady state flow was reached. The rate of decrease was highest for the early stages of transient flow. As shown by Fig. 4-2-1 to Fig. 4-2-10, time periods greater than about 5,000 minutes were required to reach constant flow rates for all the stress con- ditions. Individual tests were run for 10,000 minutes to obtain the coefficient of permeability. The coefficient of permeability, R, was determined by observing the rate of flow equal to AV/At. Then, according to Darcy's law, the flow rate is: q=AV/At=vA=kiA 5.1 where AV = volume of flow At = time v = discharge velocity k = permeability, ft/sec A = cross-sectional area of sample, ft2 i hydraulic gradient The value of iA was constant and equal to 57 ft2 for all experi- ments with one exception for the test using the highest pressure 55 56 2 condition, cm = 5000 psi, where iA equals 32 ft . At: AV =M. k M l A PSI“ Accumulated Flow (ml.) V: 8-< 3 t: time (103 min.) Fig. 5-1. Typical Curve Showing Time Versus Accumulated Flow. The pore Space in the rock salt contains kerosene at a pressure denoted by P. If the 'total' stress acting in a given direction at any point in the rock salt is a, the problem is to know in what manner the 'effective' stress, denoted by 0', is related to P and a. The effective stress is, by definition (Skempton, 1961) the stress controlling changes in volume of soil. Change in total volume changes the volume of the pore space which is directly related to permeability. The common opinion (Skempton, 1961) is that the effective stress is actually the intergranular stress acting between the 57 particles comprising the porous material. Skempton (1961) shows that this stress is C'=o‘-(1-a)P 5.2 where a is the area of contact between the particles, per unit gross area of the material. For soils, in the stress range for practical problems, the value a is very small and can be ne- glected. For rock salt and the larger stresses used in this pro- ject the value of a is unknown. In the permeability tests reported, the seepage pressure decreases to almost zero at the exit end of the sample. For P 7 O, the total stress will approximately equal the effective stress. For this case total stresses can be used for strain calculations. For this research, total stresses are much larger than fluid pressures and therefore will approximate the effective stresses. For field problems where P can be quite large this assumption may not be tenable and actual effective stresses will be required for stress-strain relationships. The relationship between coefficient of permeability, mean stress, and octahedral shearing stress is summarized in Figs. 5-2, 3, 4, and 5. The experimental data show that the coefficient of perme- ability of rock salt decreases with increasing mean stress and increases with increasing octahedral shearing stress. The data summarized in Fig. 5-1 can be formulated into an equation for pre- dicting the permeability for a range of different stress conditions. Using the method of least-squares analysis and the computer the experi- mental points,curvesl.through 6, can be expressed by the relationship 58 mmmuum uuosm Huuwmsuuoo msoHum> now muHHHLUQEHNm coma mmwuum numz_uo uoomwm mph .Num .me AHma oooHV mauuum sum: ”as m a m N H m H q H H d H 1- .13 m B I I . a o oeooo.o-we o u u on Has ooH u a m L 8 m o msooo.o-mm.o u x on .Hma com a k .e m-OH N so ocooo.0um~.H u M on .Hma oom u e .m H o noooo.0uwo.H u M wOH .Hma so» a e .N o 8 ll N: H o “sooo.o-~o.~ u u on Han ooOH u k H-oH H OH OH (Kalap E_oI) Kltttqaamaaa :x 59 r 3.00 2.88 L 2.77 2.66 2.55 2.44 (18d) 888138 Jaaqs {alpaqenoo 2.33 r 2.22 :1 ‘L 201 2.11 2.00 1'- 102 10 K: Permeability (10.3 darcy) The Effect of Octahedral Shearing Stress upon PErmeability for Various Mean Stress Figo 5-30 60 Hum oumN cu Hmacm mmwuum cam: :25 muHHHnmoHFHom some mmmuum .825 Hun—69330 mo 33me m5. .qnm .me 9.23 25 s OH w o c N kmfl+$5uxw£ OH OCH )1 (£01199 8 01) finnqeamaa 61 mmmpum ummnm kuvmnwuoo can wmmpum cam: mo mcoHumcflnaou msoHum> puma: huHHHnwmaumm .mum .me AHma oooav mmmuum ado: "so m ¢ m N H _ A. H Amoudvaawav x %UHHHnmmEpmm c.Hu OH .1. (19d 001) 999133 Jeaqs {expaqenoo 62 log K = K +-m o 5.3 o o =0 m m m where K = permeability in milli-darcy at cm = constant cm Kc =0 = constant permeability in milli-darcy at cm = 0 psi m To = octahedral shearing stress in psi m: slope of curve = A log K/Aom Table 5-1 gives the equations for five different T-value as follows: Table 5-1. Permeability as a Function of Mean Stress at Various Octahedral Shearing Stress Significance Simple T (psi) Equations of F Correlation 100 log K = 0.78-0.00070 cm 0.001 0.979 300 log K = 0.99-0.00065 am < 0.0005 0.985 500 log K = 1.23-0.00066 am < 0.0005 0.990 700 log K B 1.68-0.00067 am < 0.0005 0.982 1000 log K = 2.02-0.00067 am ‘< 0.0005 0.984 From statistical analysis the simple correlation of K and cm fall within the range of 0.978 to 0.989. The average slope of the curve is found to be 0.00067. An attempt was made in Fig. 5-3 to observe the correla- tion between octahedral shear stress and permeability when using mean stress as a parameter. Again a least square computer analysis was applied. The equations are listed in Table 5-2. 63 Table 5-2. Octahedral Shearing Stress as a Function of Permeability at Various Mean Stresses Significance Simple om (psi) Equations of F Correlation 1000 T = 1.94 KO'71 0.19 0.913 1350 T = 2.31 K0°68 < 0.0005 0.917 1700 T = 2.58 KO°73 0.01 0.956 3000 T = 3.25 x°°72 0.011 0.958 4000 T = 3.52 KO'66 0.028 0.975 5000 T = 3.91 KO'71 0.030 0.936 The simple correlation of T and K fall within the range of I 0.913 to 0.974 with general equation, To = me . A higher m correlation exists between K and cm than between T and K. In order to observe the correlation between octahedral shear stress and mean stress using permeability as a parameter, Fig. 5-5 is constructed. Consequently, as the result of estimating flow through media under various stresses, Eq. 5-3 appears to be most accurate. Fig. 5-4 is constructed to study the relationship between octahedral shear stress and permeability. This curve shows that permeability increases with increasing octahedral shear stress, which can be expressed with the relationship: log K = 0.62 + at c = 0 5-4 __1_ 720 T ’ m This increase in K is probably due to dilatancy of the salt grains with the resulting small increase in pore volume. 64 A general equation of permeability as a function of mean stress and octahedral shear stress can be obtained as: l = ‘——— - , 5-5 log K 0.62 + 720 T 0 00067 Cm by substituting equation 5-4 in equation 5-3, assuming that the solution is linear with mean value m in Eq. 5-3. To describe the correlation between permeability, mean stress, and octahedral shear stress, a three dimensional plot is constructed in Fig. 5-6, which proves to be more descriptive than earlier figures. Permeability can be predicted according to any one of the empirical equations given previously. However, the coefficient of permeability is not directly affected by stress itself, but is affected by porosity changes due to deformation of the rock from applied stresses. The following section presents experimental strain results and a discussion about how permeability is related to porosity and deformation. Strain Field Axial and tangential strain changes were measured through- out the experiments. The rate of strain change decreased with time along with the reduction of pore space when stress was applied to the Specimen. The rate of decrease was much higher for the early stage of the experiment before it approached a constant value. The results show that a constant value was approached at times greater than about 5,000 minutes. 2 Yw 3 ' ' = I_I—e— ' Taylor 8 equation Q (DS “ 1+e C) 1A can be used for studying the strain effect on permeability, where: 65 ’7 I 7 I I I I I I 0 1 2 3 4 S 6 7 8 am (1000 psi) Fig. 5-6. Three Dimensional Plot of Mean Stress, Octahedral Shear Stress, and Farmesbility 66 Q = flow rate = AV/At D = diameter of particle Yw = fluid density n = fluid viscosity e = void ratio C = constant i = hydraulic gradient A = cross-section area Kerosene was used as the fluid with specimen size, pressure, and temperature constant. This means that D8, Yw’ u, C, i, and A all have constant values in this study. Laboratory determination of porosity change was computed from experimental strain data as follows: Assume that the salt crystals are incompressible. The total volume of Specimen V (V = rzn - 2r = 2nr3 where V is initial volume of sample) equals the Crystal or Solid Volume, Vs’ plus the Void Volume, V After a given axial compression, V. ei, of the sample a new total volume is calculated using the lateral strain 61 based on dial gage readings and 2nre' I = L _ V (r + 211 )2 n 2r (1 61) 516 =2Trr3 (1+6L2) (1'61) _ I The unit volume change is represented by EV!—-= e!- 3 3 , 2 , A1,. 2nr ' 2V? (1 + 6L) (1 ' 61) V 2nr 1-(1+e£)2(1-3i ) l - (l + 26L ' 61 + (e I’ll (e£}3/:'0- /;%f/1)H 67 where higher order terms are very small and can be neglected. AV I I I I —=1-1+2 - =2 - 5-8 V ( 6L 61) 6L 61 Vv ' (Zei - ei)V Therefore, the new void ratio is: e = V 5-9 8 To examine Taylor's (1948) equation, permeability k is plotted against e3/(l+e) in Fig. 537. The results show that per- meability increased with an increase in e3/(l+e). By using least square analysis, the result can be expressed by equation as follows: 3 e TIE = 0.21 log K - 8.19 5-10 log The simple correlation is 0.843 and F is significant < 0.0005. The mean stress, Om’ was included with the data as shown3 in Fig. 5-8. Log permeability K is plotted against log cm(l§;§° The plot showed that product of cm and e3/(l+e) remained nearly constant for all K values. This indicated that a given rock salt had almost a constant value of the product of Cm and e3/(1+e) and its permeability appeared to be independent of this value. The equation obtained by using least square analysis was 3 e log (om 1+e) = 0.027 log K - 1.93 5-11 with a significance of F of 0.473 and a simple correlation of 0.136: this indicates a high degree of dependence between these two variables. The effect of unit volume change on permeability was studied by plotting the unit volume change (Zei - ei) against permeability K in Fig. 5-9. From Fig. 5-7 it is observed that the correlation of permeability K and the unit volume change 68 huHHHnmoEumm pom ucmHonmmoo oHumm wHo> m.uoH%mH ammsuun aHnmaoHumHmm ssh .mnm .me AuouwouHHHHav quHHnmosuom "M o 0 OH 0H OH H HIOH N. H m- H q- 1 H 4 q q 1 ioHuoH nu mIOH O O OO O .. wIOH mH.m - e on Hm.o n Aw+Hv\mm on 1 NIOH (MU/Ea nuarorggaoo 01388 PICA $.101A91 69 %uHHHnmoEumm so am”! mHv val Eb mo uosvoum mo uomwmm may .wum .me m AzoumpHHHHav huHHHnuusuwm “M 0 NS H H H-oH ~-cH m-oH ¢-oH H H] H J—I H d H m-OH O a mo mm.H - e on KNo.o u .mwm . be on x m L7 my my M9Wc. O o O O O O O .. o|ol|olo o Imo18 ...- H ) .0 no no AonxU no no mu m. o no ,\ O O l H-0H 70 uHmm xoom mo huHHHnmmauwm new owcmco mEDHo> UHGD cmmsumn aHnmaoHuwHom 65H .mum .me AsouueHHHHav HuHHHnwmaumm we o oH OH H H-OH N..oH m- H a- JV 1 H m H H Ir 0 m- H H H¢.o - mm.m- u H w~_+ va on q-oH n-0H 1 N.oH (ur/ur) ES - ?sz :aSuan amnIoA arun 71 (Zei - 31) can be expressed as: log (zei - .1) = -3.88 - 0.41 log K 5-12 with significance of F < 0.0005 and a simple correlation of 0.885. An attempt was made to show the correlation between mean stress cm and void ratio e. The plots in Fig. 5-10 suggest that there is a relationship, Om = 9150 - 366e 5-13 with significance of F < 0.0005 and simple correlation of 0.842. The equation indicates that void ratio should approach zero when mean stress approaches 10,000 psi. Taylor's (1948) coefficient was also examined against mean stress in Fig. 5-11. The equation obtained was Cm = 5396 - 0.45 e3/(14e) 5-14 with significance of F less than 0.005 and simple correlation of 0.864. Compressibility Compressibility is the volume change per unit volume of the material per unit change in pressure. Compressibility of the rock salt was studied from the stress and strain observation of the tests. Three types of compressibility were considered (1) solid grains of rock salt, (2) fluid kerosene, and (3) bulk. 72 NN om oHumm wHo> so mmmuum emu: mo uommmm was H¢-oHv oHumm eHo> no wH 0H ¢H NH .oH-m .me OH db 4 H H H a moon I omHm I o 111 D (ted 0001) 989133 uaaw 73 ucmHonmoou oHumm 30> w.uoH%w,.H. co mmmpun sum: mo uowmwm or; .HHIm .me Ho-oH Xv uamHUHummoo m.uonma "H0+Hv\mm 0H m w H o m s m H H o L a H H HI H H H J H H a no 8 97H m lex mq.o I ommn n D H m : D m (18d 0001) 889139 uaan 74 Rock formations surrounding a cavity are subject to external stresses from adjacent rocks and from the hydrostatic pressure of fluid in the pores. The external stress generally has the largest value in the vertical direction (overburden weight) and smaller values in the lateral directions. When a cavity is created in a salt formation, the stress around the cavity changes with respect to distance from the cavity center. Normal stresses at the cavity walls may be reduced to zero. This section is concerned with the change of pore volume associated with this change in stress condition. The rock reSponse to the change can be divided into the three compressibility categories. (1) The change in solid grain volume (Knutson, C.F., B.F. Bohor, 1963) is _.l_ .___ _ c —V( dc dpi 0 515 where Cg “ grain compressibility (1/psi) = O by assuming no volume change of salt crystal VS = volume of solid rock material, in P1 = internal fluid pressure, psi 0 = active external mean stress, psi m (2) The change in fluid or liquid unit weight is expressed as Y=Yoe where Yo initial unit weight at atmospheric pressure "U ll pressure measured above the standard atmoSpheric pressure 6' = compressibility of fluid 75 (for water l-'= 300,000 psi) w (3) The change in bulk volume can be expressed as Vb acm Ti where Cb = bulk compressibility, l/psi Vb = bulk volume, in Since the solid volume is assumed constant and the fluid is assumed incompressible throughout this discussion, the com- pressibility is limited to change in pore volume only. Bulk com- pressibilities computed for all the experimental reSults are summarized in Table 5-3. Figs. 5-12, 13, and 14 Show the relation- ship between bulk compressibility and mean stress for different 7 values. From Fig. 5-13 the results show a reduction of com- pressibility with change in mean stress for each different octahedral shearing stress value. These equations are listed in Table 5-3. Table 5-3. Compressibility as a Function of Mean Stress at Various Octahedral Shearing Stress T (psi) Equations Significance Simple of F Correlation 100 log ch = 1.29-1.45 log am < 0.0005 0.984 300 log ab = 1.75-1.31 18g °m < 0.0005 0.998 500 log ch = 1.51-1.38 log % < 0.0005 0.995 700 log Cb = 1.91-1.25 log am < 0.0005 0.996 1000 log Cb = 2.42-1.09 log am < 0.0005 0.998 76 AHV mmmuum wcHuwonm Hmuumsmuuo mSOHuo> haw muHHHAHmmouano con: muwuum duo: mo uoommm 05H .NHIm .an AHma OOOHV mmouum and: "so 0 m a m N H _ 1 H H H H O“ IN I." Hma oooH m H88 ooh u b .q H48 oom u 4 .m Hma com a k .N H H88 ooH u t . q 0 ) T ‘ ' ( 89 A X? 11 (rad/9-01) £3111q18891dm00 : AHHV mmmhum waHumonm Hmuwosmuoo 77 msoHum> you muHHHnHmmmuano con: mmmuum duo: mo uoowwm use .mHIm .me AHmav mmmuum duos“ "so .86 on oo.¢ ww.m hm.m oo.m nm.m ¢¢.m mn.m -.m HH.m oo.m H H H H H d H H H H . H-8H Av H 0 I’ll!!!" > I bwmmmmmmmw 1 o OI H u, , ;flWUm a a . o moH m¢.H - mH.H- I o on H48 ooH u 4 .m E o moH Hm.H - m~.H- I so on .Hma com a 4 .8 a b on mm.H I Hn.HI I no on .Hma com I k .m a no . o moH m~.H - Hm.H- u on H48 ooh I 8 .N J oH so on mo.H I ~¢.NI I no on .Hma oooH n e .H o>u=o mI (led/1) Knlthlssaldmoo AHHHV mmmuum wawuumnm Huuvmnuuuo unawuw> new huwHHnfimmouaaoo con: mmmuum saw: no uommwm may .qaum .me 78 a 3% 83v 38.5 :32 u o L h.S m 1 enoa Hum ooH u k .m Hum com a H .q Hun com a k .m H3 85 u H. .N H3 83 u H. .H «5:6 “I A q --= D I IL 9 = (959) (ISd/I) KQIIIquandmog 79 It is observed that the rate of compressibility is reduced approx- imately the same for different octahedral shearing stresses. Skempton (1961) has presented a theory for compressibility of saturated materials where the unit volume change is AV _ _ — V- —- CEAP - (l-8)Au], a — AS/A 5'18 and Ap' = Ap - (l-a)Au where C compressibility Ap - applied preSSure Au = pore pressure change A = area of contact between soil solids A = gross area In this study, pore pressure was held constant at 125 psi at the entrance and zero at the exit (average of 63 psi) where Ap was in the range of 1,000 psi to 5,000 psi. If the area AS were approximately equal to gross area A, the effect of pore pressure, (l-a)Au, would be small in comparison to the applied pressure, Ap. In other words, the effective stress for this study is approximately equal to the applied stress. However, for the practical solution, it may be necessary to consider pore pressures and their reduction of effective stresses. Bulk compressibility effect on permeability is shown in Fig. 5-15. Here, permeability increases with increasing com- pressibility and compressibility increases with increasing octahedral shearing stress. Summarizing, the experimental points, curves 1 through 5, can be expressed as shown in Table 5-4. 80 mmmuum waHuamnm Hmuvosuuoo msoHuw> you AUHHHnmeuom Goa: huHHHaHmmmuaaoo stm mo uommwm may .mHum .th AmouavHHHHav »UHHHnuuaumm "x o NoH OH H HuoH N- H muoH euoH A d1 d 4 d a on a~.o .Hma oooH e M on mm.o u o on .Hma can u e . e m mo.o - q «m.m - m on om.o u o on .Hma con u .m H mm.m - x on «m.o u o on .Hma com a e .N - o~.m - x on mm.o u o on .Hma ooH u t .H mpuso N.oH in . A_T. 0\1 Jon I.- 1.. no 2 m o- m a 8 3 I. a. I. T. .l. 3 .A ) T.— 0— o, / .d S hu OH m- 81 Table 5-4. Compressibility as a Function of Permeability at Various Octahedral Shearing Stresses, Significance Simple T (psi) Equations of F Correlation 100 log C B 0.35 log K - 5.70 0.001 0.979 300 log C = 0.34 log K - 5.88. 0.0005 0.997 500 log C = 0.36 log K - 5.94. 0.0005 0.992 700 log C = 0.32 log K - 6.08 0.0005 0.997 1000 log C = 0.27 log K - 6.13 0.0005 0.995 It is shown in Fig. 5-15 that the s10pe is approximately the same except for the octahedral shearing stress at 1,000 psi. In general, the flow pattern, under different octahedral shearing stress and compressibility, can be constructed. With experimental data on the relationship between stress, strain, and compressibility to permeability one can construct a nomograph or set of general equations for different conditions. The prediction of flow through the rock salt formation can be calculated using known values of the stress or strain distribution surrounding the cavity and the experimental constants discussed. CHAPTER VI FLOW FROM AN UNDERGROUND SALT CAVITY The principle of flow from a cavity can be illustrated using information from the previously described experimental study. Because of the variables involved, i.e., the geometry of salt formation, the various levels of piezometric head, and the location of a cavity in a formation, it is not within the scope of this study to present an exact solution. However, in order to illustrate a typical solution, a hypothetical salt cavity has been chosen as shown in Fig. 6-1. Although some degree of permeability was measured in the test samples, it is recognized that these specimens were recon- solidated and may only approximate a medium which has been sub- jected to consolidation over a geological time period. Based on mining operations and experience (Brown and Gloyna, 1959) in the storage of liquid petroleum products in salt cavities, it is recognized that massive salt structures are almost impervious to the flow of water. Consequently, any computation using the lab- oratory results may include a substantial safety factor. Assume that a salt cavity exists in an underground forma- tion as shown in Fig. 6-1 with the following conditions given: Lateral underground pressure = PL psi Fluid pressure = P1 psi 82 83 i; Ground Surface Aflxflflé Z I k::p// ' Stream‘f //// 1 l ne Salt // /////// // Formation // / / / , / //"‘ / I / // , / Equipotential line gg///f" [I //:}//i;/ Underground Water Formation Fig. 6-1. Hypothetical Storage Cavity in a Salt Formation Cavity radius I ao ft Octahedral shear strength - KO psi Assume that the salt formation lies above the ground water level. The problem concerns flow from the cavity through an element r feet from the cavity. The condition for plastic flow in the rock salt may be examined by computing the plastic radius, p0, by the equation (Serata and Gloyna, 1960) PL - P K o .. ' 1 i 9. aoexp<7?—-z> 6-1 84 If this radius is less than the cavity radius, only elastic con- ditions need be considered. For this example assume that po < a0. The stress distribution adjacent to natural underground cavities can be obtained by the established methods. For design and stability problems it is generally assumed that rock is an isotropic, homogeneous, linear-elastic material, and that the deformational reSponse of a rock body to an applied force can be determined from elastic theory. In 1964, Dahir presented a solu- tion of the general stress distribution for completely elastic thick-walled cylinders using rock salt and found that the theo- retical results compared reasonably well with the experimental results. Recently, Obert and Duvall (1967) happened to encounter the identical solution on the determination of stress distribution in a thick-wall cylinder subjected to a triaxial stress field. Sakurai (1966) derived the general stress distribution in the elastic and plastic regions for a circular cylindrical cavity with infinite thickness of the formation. The stress distribution around a cavity can be obtained from any one of the studies mentioned above. The cavity has to be carefully chosen at the location where a uniform media and a sound formation exists. The size of the cavity is also limited so that the entire formation around the cavity behaves as an elastic material. Construction of a cavity causes a change in stresses in the vicinity of the cavity and for that region the stress dis- tribution will not be hydrostatic. For this reason, it is 85 concluded that the best correlation can be obtained by using these stresses as a parameter. The expression for the permeability K is assumed to be: K = f(0m3 Ta Yb: 3: d9 CS, Ar) where cm is the mean stress, T is the octahedral shear stress, Yb is bulk density, e is void ratio, d is particle size, CS is shape, and Ar refers to the geometry of a certain waste cavity. Since bulk density and void ratio are dependent upon stress and strain and assuming that d, CS, and Ar are constant, the equation can be reduced to K = f(om, T) for a specific formation. Because strain is function of stress the equation can be also expressed as a function of strain. A definite correlation between permeability and effective porosity for a given medium under different strain distribution exists (Knutson and Bohor, 1963; Taylor, 1948) which is useful in deter- mining one of the two quantities when the other is unknown. Permeability is found by using the experimental results correSponding to each stress condition as shown in Fig. 5-6. Finally, radial flow away from the cavity may be computed using the equation (Muskat, 1946) for flow given as ZfikN_1[Pe - pWJ/u kN log re/r0 log ro/rw + 86 [N] Region Fig. 6-2. Two Dimensional Configuration of an Underground Formation where Q is the rate of fluid flow, U is the viscosity of fluid, kN and kN-l are coefficients of permeability at two adjacent concentric annular regions (N) and (N-l), pw is fluid pressure inside the cavity, pe is fluid pressure at radius re, and rw, r0, re are radii as shown in Fig. 6-2. When the wastes are placed in the cavity, a frontal zone of the liquid waste will penetrate through the formation outward with a flow rate of Q. For practical engineering purposes, the distance between the cavity floor and the underground water forma- tion, and the cavity radius should be selected so that it is within the safety range. To obtain the entire flow pattern and pressure difference such as Apl, and Apz, as shown in Fig. 6-1, the stream lines away from the cavity must be constructed. Due to the non- homogeneous permeability, numerical methods would be most applicable 87 for a solution to the flow net. Since Q is the function of rw in equation 6-2, the safety dimension of rw can be selected as a cavity radius within a range of permissible leakage. It is noted from the experimental results that permeability decreases when mean stress increases. If the cavity is constructed in a deeper formation (i.e. increase the overburden pressure) then the possibility of leakage will be considerably reduced. Based upon the experimental investigations in this thesis, the permeability, under mean stress in the range of 1000 to 5000 psi and octahedral shear stress of 100 to 1000 psi, was in the range of 0.0036 to 40.6752 milli-darcy. This low permeability indicates that leakage of radioactive waste materials from under- ground salt cavities will vary from small to almost negligible. As a result the waste liquid in the cavities can be confined in salt beds for a long period of time. Furthermore, due to plastic behavior (Sakurai, 1966), rock salt acts as a self sealer for the storage cavity and the high density of an underground formation provides permanent shielding and ion-exchange media for any re- lease of radioactivity. CHAPTER VII SUMMARY AND CON CLUS IONS The conclusions are summarized under three headings: (1) high pressure triaxial cell, (2) the effect of stress, strain, and compressibility upon permeability, and (3) feasibility of radioactive waste diSposal in an underground formation. High Pressure Triaxial Cell A high pressure triaxial cell was constructed to permit the application of uniform confining pressures and axial loads to simulate the complex stress conditions existing in an under- ground formation adjacent to the diSposal cavity. Pressure con- trol was maintained reasonably constant for the various stress conditions by the automatic control system. The measurement of fluid flow and strain of the Specimen were recorded prOperly. Cylindrical specimens of rock salt were prepared so that the flow and strain properties could be obtained accurately. The experiment showed that the high pressure triaxial cell can be used to study the deformation and/or flow property of rock salt without modifying the parts of cell. The results revealed that the accuracy of the equipment would be adequate for research projects on similar materials. 88 89 The Effect gf Stress, Strain, and Compressibility upon Permeability Data showing the effect of mean stress and octahedral shear- ing stress upon permeability of the rock salt was obtained. By statistical analysis, empirical equations were derived,which pre- dict the permeability in terms of mean stress and octahedral shear- ing stress. A high degree of correlation with the experimental data was obtained. Observations of strain changes were converted into void changes within the Specimen to study the relationship to perme- ability. The effect of change in void ratio upon permeability was expressed by empirical equations with high correlations re- sulting. The effect of mean stress on void ratio was studied in the same manner. A high correlation was found between permeability and com- pressibility (with T as a parameter). Empirical equations were also derived for permeability in terms of compressibility and octahedral shearing stress. From the results of the data analysis, it was concluded that pore volume reduction is the main factor in decreasing per- meability. Pore volume reduction again depends upon the combina- tion of mean stress and octahedral shearing stress. Feasibility gf Radioactive Waste Disposal Based upon the experimental investigation of permeability in this study it is concluded that leakage of radioactive waste from salt cavities will be almost negligible. Laboratory perme- abilities for the rock salt varied from 0.0036 to 40.6752 milli- 90 darcy for various stress states. A procedure for predicting the degree of leakage was proposed for a given cavity and assumed boundary conditions. This research also Suggests that underground storage cavities may also be utilized to store other substances such as fuel. CHAPTER VIII FUTURE RESEARCH Further research is needed in certain areas to find solu- tions for related problems. In particular, future research would be useful: (1) (2) (3) To study the effect of temperature on sample compressibility and related effect on flow. The storage cavity temperature may rise above the temper- ature of the surrounding formation as a result of radioactive decay of the fission products in the stored wastes. Structural stability and permeability should be studied for various temperatures. In order to extend the theory and techniques presented in this study, other rocks should be investigated to determine the possibility of applying this technique to different materials. To modify the experimental approach. For the purpose of substantiating the flow equations de- rived in this study the experimental set-up could be modified. Various sizes of cavities can be drilled at the center of cylindrical sample. Flow through the media toward the center can then be measured using the external fluid pressure as the confining pressure and flow pressure. 91 BIB LIOGRAPHY 92 This set-up is advantageous because the flow effect can be studied, and the stress-strain effect due to the cavity existence can also be checked. BIBLIOGRAPHY Athy, L.F. "Density Porosity, and Compaction of Sedimentary Rocks", American Association of Petroleum Geologist (Bulletin), Vol. 14, No. 1, Jan. 1930, pp. 1-24. Bergelin, O.P. "Flow of Gas-Liquid Mixtures", Chemical Engineering, Vol. 56, No. 5, May 1949, pp. 104-7. Birch, F. and H. Clark. "Thermal Conductivity of Rock and Its Dependence Upon Temperature and Composition", American Journal of Science, Vol. 238, Aug. 1940, p. 552. Brown, K., and B.F. Gloyna. "Pressure Temperature Effect on Salt Cavities and Survey of Liquified Petroleum Gas Storage", The University of Texas Sanitary Engineer Research Laboratory Technical Rggort to U.S. Atomic Enegy Conmission, Austin: Univ. of Texas Press, Jan. 15, 1959. Burdine, N.T. "Relative Permeability Calculations from Pore Size Distribution Data", AIME: Transactions, Vol. 198, Mar. 1953, pp. 71-8. Burns, R.H. "The Treatment of Radioactive Liquid Effluent", Radioactive Wastes: Their Treatment and Diaposal, 1960, pp. 114-5. Carman, P.C. "Fluid Flow through Granular Beds", Transactions of the Institute of Chemistry, Vol. 15, May 1937, pp. 150-66. . "Foundamental Principles of Industrail Filtration", Transactions of the Institute of Chemistry, Vol. 16, Oct. 1938, pp. 168-88. . Journal of Agricultural Science, Vol. 29, 1939, p. 262. Dahir, A.G. "Continuous Medium Analysis of Elastic, Plastic and Viscoelastic Behavior of a.Model Salt Cavity", Unpublished Ph.D. dissertation, Michigan State University, E. Lansing, 1964. Douglas, J., Jr., P.M. Blair, and R.J. Wagner. "Calculation of Linear Waterflood Behavior Including the Effect of Capillary Pressure", AIME: Transactions, Vol. 213, June 1953, pp. 96-102. 93 94 Fatt, I. and D.H. Davis. "Reduction in Parmeability with Over- burden Pressure", AIME: Transactions, Vol. 195, Dec. 1952, p. 329. Fatt, I. and H. Dykstra. "Relative Permeability Studies", AIME: Transactions, Vol. 192, Sept. 1951, pp. 249-56. Fatt, I. "Effect of Overburden PreSSure on Relative Permeability", AIME: Transactions, Vol. 198, Oct. 1953, pp. 325-6. . "Pore Structure in Sandstones by Compressible Sphere- Pack Models", American Association of Petroleum Geologists: Bulletin, Vol. 42, July 1958, pp. 1914-23. Fenimore, J.W. "Land Burial of Solid Radioactive Waste During a lO-Year Period", Health Physics, Vol. 10, April 1964, pp. 229-36. Gates, J.I. and W.T. Lietz. American Petroleum Industry Drilling Procedures and Practices, 1950. Gray, Donald and I. Fatt. "The Effect of Stress on Permeability of Sandstone Cores", AIME: Transactions, Vol. 228, 1962-1963, pp. 95-100. Happel, J. and B.J. Byrne. "Motion of a Sphere and Fluid in a Cylindrical Tube", Industrial and Engineering Chemistry, Vol. 46, June 1954, pp. 1181-6. Hassan, M.E. and R.F. Nielsen. "How to Calculate Relative Permeability of Bradford Sand from Capillary Pressure Data", Petroleum Engineering, Vol. 25, No. 3, Mar. 1953, pp. B61-2. Hawkins, R.H. and J.H. Horton. "Bentonite as a Protective Cover for Buried Radioactive Wastes", Health Physics, Vol. 13, Marc. 1967, pp. 287-920 Inman, A.E. "Salt, An Industrial Potential for Kansas", Univ. of Kansas Research Foundation, 1951. Irmay, S. Transactions of American Geophysics, Vol. 35, 1954, p. 463. Kaufmann, W.J., et. a1. "DiSposal of Radioactive Waste into Deep Geological Formation", Journal: Water Pollution Control Federation, Vol. 33, 1961, p. 73. Knutson, C.E. and B.F. Bohor. "Reservoir Rock Behavior Under Moderate Confining Pressure", Rock.Mechanics Proceedings of 5th Symposium, 1963. Lang, W.B. "Annoted Bibliography and Index Map of Salt DepositS' in the United States", Bulletin of Geological Survey, No. 1019-j, Washington, D.C.: Government Printing Office, 1957. 95 McLatchie, A.S., R.A. Hemstock and J.W. Young. "The Effective Compressibility of Reservoir Rock and Its Effects on Permeability", AIME: Transactions, Vol. 213, June 1958, pp. 386-88. Mann, R.L. and I. Fatt. "Effect of POre Fluids on the Elastic Properties of Sandstone", Geophysics, Vol. 25, No. 2, April 1960, pp. 433-44. Merritt, W.F. and P.J. Parsons. "Safe Burial of High-level Fission Product Solution Incorporated into Glass", Health Physics, Vol. 10, Sept. 1964, pp. 655-64. Mineral Resources of the United States, Washington: Public Affairs Press, 1958. Muskat, M. The Flow of Homogeneous Fluids Through Porous Media, Ann Arbor: J.W. Edwards, Inc., 1946. National Petroleum Council. "Feasibility of Underground Storage", World Patroleum Report, Vol. 23, No. 7, 1952, p. 40. National Research Council of National Academy of Science, Th2 Disposal of Radioactive Waste on Land, The Committee on Waste DiSposal of the Division of Earth Science, National Academy of Science, 1957. Obert, L. and W.I. Duvall. Rock Mechanics and the Design of Structures in Rock, New York: John Wiley & Sons, Inc., 1967. Osoba, J.S., J.G. Richardson and J.K.Kerver. "Laboratory Measure- ments of Relative Permeability", AIME: Transactions, Vol. 192, Feb. 1951, pp. 47-56. Parsons, P.J. "Migration From a Di3posal of Radioactive Liquid in Sands", Health Physics, Vol. 9, Mar. 1963, pp. 333-42. Pbrkhaev, A.P; Kolloid Zhur, Vol. 11, 1949, pp. 346-52. Reidel, J.G. "LPG Goes Underground", The Oil and Gas Journal, Vol. 51, No. 10, July 14, 1952, pp. 70-o. Reynolds, T.D. "Reactor Fue1.Waste Diaposal Project: PErmeability of Rock Salt and Creep of Underground Salt Cavitiesfl Atomic Energy Commission Report UUnpublished), Dec. 30, 1960. Ruth, B.F. "Correlation Filtration Theory with Industrial Practice", Industrial and Engineering Chemistry, Vol. 38, No. 6, June 1946, pp. 564-71. 96 Sakurai, S. "Time-Dependent Behavior of Circular Cylindrical Cavity in Continuous Medium of Brittle Aggregate", (Ph.D. Thesis) E. Lansing: Michigan State University, 1966. Scheidegger, A.E. The Physics of Flow Through Porous Media, New York: The MacMillan Co., 1960. Secchi, I.M. Chimica e Industria, Vol. 18, 1936, pp. 514-63. Serata, S. "Development of Design Principle for DiSposal of Reactor Fuel Waste into Underground Salt Cavities", Un- published Ph.D Dissertation, Univ. of Texas, Austin, 1959. Serata, S. and E.G. Gloyna. "Principles of Structural Stability of Underground Salt Cavities", Journal of Geophysics Research, Vol. 65, No. 9, Sept. 1960, pp. 2979-87. Skempton, AHW. "Effective Stress in Soils, Concrete and Rocks", Pore Pressure and Suction in Soil, Butterworth, London, 1961, pp. 4-160 Taylor, D.W. Fundamentals of Soil.Mechanics, New York: John Wiley & Sons, 1948. Templeton, C.C. "A Study of DiSplacements in Microscopic Capillaries", AIME: Transactions, Vol. 201, July 1953, pp. 162-8. . Bulletin of American Physics Society, Vol. 29, No. 2, 1954, p. 16. Tiller, F.M. "Role of Porosity in Filtration", Chemical Engineering Progress, Vol. 49, No. 9, Sept. 1953, pp. 467-79. U.S. Department of Health, Education, and'Welfare. Radiological Handbook, Washington, D.C.: Government Printing Office, 1960. Van Fossan, N.E. "Underground Storage", The Oil and Gas Journal, Vol. 54, April 1955, pp. 80-93. Wilson, J.W. "Determination of Relative Permeability Under Simulated Reservoir Conditions", American Institute of Chemical Engineers Journal, Vol. 2, No. 1, Mar. 1956, pp. 94-100. APPENDIX DATA * Table A-1. Strain-rate, Deformation, and Flow-Test Data Test 10 T 100 psi 0 1000 ps i at time = 0 ll 0 't‘al Ini 1 51 Initial 6L = 0 Initial ' = 0 61 Total 61 = 615 x 10'6 in/in Total 6L = 145 X 10.6 in/in Total ei = 36 X 10.4 in/in Computed SL = 8.7 X 10-4 in/in Time 31 3L 31 Time EV (min.) -6 -6 _4 (min.) Gnl.) (10 in/in) (10 in/in) (10 in/in) 0000 000 000 000 0000 0000 0058 324 020 006 411 96 0411 454 052 016 458 107 0458 464 060 016 954 220 0945 509 085 019 1369 306 1369 534 095 022 1903 410 1903 546 105 024 2383 498 2383 552 112 024 2672 546 2672 554 115 024 3339 656 3339 574 120 027 3825 730 3825 569 122 030 4154 782 4154 575 129 129 4773 874 4773 584 132 030 5270 948 5270 574 131 027 5766 1019 5766 582 142 028 6218 1086 6218 584 140 029 6708 1153 6708 586 138 031 7250 1229 1250 604 132 034 9258 1497 9258 614 147 036 9435 1522 9435 615 145 036 * Data listed as e = Axial strain gage observation, 6 = Lateral Strain gage observation, 3i = Axial dial gage reading, 2% = Accumulated . I flow reading, 61, = Si X eL/el, and constant flow rate was obtained from plotting. 97 98 Test 2. T = 100 ps i o = 1350 psi at time = 0 Initial 61 = 315 X 10”6 in/in Initial 6L = 0 Initial 6i = 0 Total 31 = 1200 X 10.6 in/in Total 6L = 100 X 10.-6 in/in Total 3; = 67 x 10'4 in/in Computed 61 = 5.7 X 10-4 in/in Time 6 8 (min.) -61 _2 (10 in/in) (10 in/in) 0000 000 000 0005 000 005 0210 225 030 0585 400 050 1074 750 059 1560 778 061 2052 785 062 2510 787 066 3001 795 068 3404 797 070 3956 805 070 4430 808 075 4755 815 077 5399 820 078 5879 827 080 6392 840 083 6832 845 086 7320 846 088 7706 855 089 9034 870 098 9999 885 100 I 61 (10‘4in/in) 000 036 048 053 053 055 056 056 057 058 059 058 059 060 061 063 063 ' 063 064 066 067 Time (min. 0000 0210 0585 1074 1560 2052 2510 3001 3404 3956 4430 4755 5399 5879 6392 6832 7320 7706 9034 9999 Onl.) 0000 0021 0055 0094 0136 0174 0208 0230 0266 0286 0314 0312 0342 0359 0376 0392 0415 0433 0482 0523 99 Test 3. T = 100 psi 0 = 1700 pSi at time = 0 Initial 31 = 1195 x 10'6 in/in Initial 6L = 0 Initial 31 = 0 Total 31 = 1448 X 10.6 in/in Total 6L = 28 X 10"6 in/in Total 6i = 82 x 10'4 in/in Computed ei = 1.7 X 10-4 in/in Time 61 6L (min.) -6 -6 (10 in/in) (10 in/in) 0000 000 000 0005 005 003 0254 073 009 1059 142 017 1544 144 019 1942 146 020 2502 149 021 2991 147 021 3298 165 022 3948 173 023 4432 178 023 4848 184 023 5386 193 024 5872 200 024 6182 202 024 6827 213 025 7315 220 025 7678 225 026 8767 235 027 9785 253 028 61 (lo-Ain/in) 000 024 048 067 070 069 069 070 071 076 074 075 076 075 076 079 079 081 082 082 Time (min. 0000 0254 1059 1544 1942 2502 2991 3298 3948 4432 4842 5386 5872 6182 6827 7315 7678 8767 9785 9785 Onl.) 0000 0011 0041 0056 0068 0086 0102 0109 0130 0143 0153 0168 0170 0175 0182 0194 0199 0208 0222 0222 100 Test 4. T = 100 psi 0 = 3000 pSi at time = 0 5273 x 10'6 in/in Initial 31 Initial 1835 x 10'6 in/in eL Initial 3i = 0 Total 5977 x 10‘6 in/in 61 Total 6L = 2280 x 10.6 in/in Total 6i = 303 x 1074 in/in Computed €£ = 116 X 10-4 in/in Time 6l 6L (min.) -6 -6 (10 in/in) (10 in/in) 0000 000 000 0396 261 230 0440 259 237 0941 456 323 1370 549 361 1885 626 401 2377 669 417 2656 686 429 3321 696 432 3809 697 440 4133 698 439 4767 699 445 5248 700 446 5753 701 442 6202 702 440 6692 702 443 7236 703 447 9243 704 445 9243 704 445 9243 704 445 61 (10-4in/in) 000 216 229 280 292 295 297 299 300 301 301 301 302 303 302 303 303 303 303 303 Time @nin. 0000 0040 0440 0941 1370 1885 2377 2656 3321 3809 4133 4767 5456 5602 5795 6202 6692 7236 9243 9424 Onl.) 0000 0026 0178 0528 0813 1118 1325 1501 1722 2997 2010 2302 2505 2550 2655 2675 2780 2855 3160 3185 101 Test 5. T = 100 psi 0 = 4000 psi at time = 0 Initial 33 = 5722 X 10.6 in/in Initial 6L = 2057 X 10"6 in/in Initial 31 = 302 X 10'4 in/in Total 81 = 6015 x 10‘6 in/in ' Total 6L = 2182 X 10“6 in/in Total 31 = 355 X 10.4 in/in Computed ei = 129 X 10.4 in/in Time el 6L (min.) -6 -6 (10 in/in) (10 in/in) 0000 000 000 0205 090 060 0572 131 096 1058 163 113 1546 180 115 2045 195 113 2495 210 115 2987 220 117 3395 233 115 3941 237 115 4416 245 113 4746 245 115 5380 253 116 5864 256 116 6379 262 116 6817 261 123 7306 266 124 7602 268 124 9035 284 135 9999 293 125 61 (10'4in/in) 000 027 039 043 044 044 046 046 046 048 050 050 050 050 050 050 050 051 053 053 Time (min. 0000 0205 0572 1058 1546 2045 2495 2987 3395 3941 4416 4746 5380 5864 6379 6817 7306 7692 9035 9999 Gal.) 0000 0149 0264 0468 0637 0786 0945 1004 1123 1206 1245 1251 1276 1301 1319 1340 1376 1381 1400 1451 102 Test 6. T = 100 psi 0 = 5000 psi at time I 0 Initial 31 = 5940 X 10-6 in/in Initial 6L = 1834 X 10'.6 in/in Initial 61 = 672 X 10"4 in/in Total $1 = 6129 X 10-6 in/in Total 6L = 2123 X 10.6 in/in Total 3i = 733 X 10.4 in/in Computed €£ = 254 X 10.4 in/in T ime e e . L (min.) -61 '6 (10 in/in) (10 in/in) 0000 000 000 0005 001 003 0233 052 067 1040 135 186 1523 158 221 1930 170 233 2481 179 246 2972 182 256 3280 183 251 3926 179 258 4411 178 258 4829 182 259 5363 184 270 5850 184 268 6166 186 266 6805 187 267 7291 185 273 7660 187 269 8751 189 286 61 (IO-ain/in) 000 000 018 018 057 057 058 056 057 057 058 058 058 058 059 059 060 060 061 Time Gain. 0000 0233 1040 1523 1930 2481 2972 3280 3926 4411 4829 5363 5850 6805 7291 7660 8751 9767 97 67 9767 2V Onl.) 0000 0031 0106 0146 0154 0204 0229 0246 0251 0254 0275 0284 0300 0316 0325 0345 0350 0375 0375 0375 103 Test 7. T = 300 psi 0 = 1000 psi at time = 0 Initial 61 = 2321 x 10'6 in/in Initial 6L = 999 x 10'6 in/in Initial Si 11 x 10" in/in Total 61 = 2790 x 10'6 in/in Total 6L = 1210 X 10-6 in/in Total 6i = 68 x lo‘4 in/in Computed ei = 29.3 X 10.4 in/in Tittle 31 6:1. (min.) -6 '6 (10 in/in) (10 in/in) 0000 000 000 0536 O86 069 1052 170 111 1541 219 134 1925 246 150 2492 271 160 2992 289 171 3304 299 173 3933 314 181 4418 321 190 4824 339 189 5372 349 199 5856 369 201 6333 379 206 6811 396 211 7332 401 216 7863 409 217 8451 431 221 9999 469 231 1 (IO-Ain/in) € 000 010 016 054 058 060 061 061 061 062 064 052 052 053 053 053 053 055 057 Time (min. 0000 0187 0536 1052 1541 1925 2492 2992 3304 3933 4418 4824 5372 5856 6333 6811 7332 7863 8451 9999 Onl.) 0000 0144 0350 0620 0850 1010 1248 1443 1550 1776 1921 2027 2175 2292 2402 2515 2632 2746 2876 3211 Test 8. T = 300 psi 0 = 1350 pSi at time = 0 2790 x 10'6 104 Initial 61 = in/in Initial 6L = 856 X 10.6 in/in Initial 3i = 168 X 10.4 in/in Total 91 = 3047 X 10.6 in/in Total 3L = 1018 x 10'6 in/in Total 61 = 82 X 10"4 in/in Computed e; = 27.7 X 10.4 in/in Time 31 3L (min.) -6 -6 (10 in/in) (10 in/in) 0000 000 000 0005 001 002 0417 082 072 0905 101 086 1398 165 087 1708 174 099 2350 186 102 2835 190 104 3205 190 099 3724 201 104 4280 202 108 4697 205 117 5233 215 127 5708 216 129 6050 220 129 6669 229 143 7154 228 135 8487 240 154 9999 257 162 e' 1 -4. . (10 ln/ln) 000 056 070 079 082 082 082 082 082 082 082 082 082 082 082 082 082 082 082 Time (min.) 0000 0417 0905 1398 1708 2350 2835 3105 3724 4280 4697 5233 5708 6050 6669 7154 8487 9999 (ml.) 0000 0050 0097 0154 0186 0244 0290 0312 0374 0410 0441 0483 0518 0547 0592 0626 0692 0798 Test 9. T = 300 psi 0 = 1700 psi at time = 0 Initial 31 't'al Inl 1 6L Initial 61 = Total 61 = 4417 x 10'6 Total SL = 887 x 10"6 Total 91 = 95 x 10'4 Computed 61 = 19 X 10-4 Time 3 1 Gain.) -6 (10 in/in) 0000 000 0914 160 1403 218 1719 239 2355 280 2844 295 3179 310 3793 315 4284 329 4661 331 5238 341 5724 348 6109 348 6679 360 7168 360 8979 385 98 97 3 97 105 4020 x 10‘6 in/in 658 x 10‘6 in/in 64 x 10'4 in/in in/in in/in in/in in/in eL (10'6in/in) 000 144 175 188 204 208 210 211 213 209 217 217 217 227 227 227 229 I e 1 (10'4in/in) 000 024 026 027 030 030 031 031 031 031 031 031 031 031 031 031 031 Time 0min.) 0000 0914 1403 1719 2355 2844 3179 3793 4284 4461 5283 5724 6109 6679 7168 8979 9897 (ml.) 0000 0043 0063 0073 0098 0116 0125 0147 0162 0172 0194 0208 0217 0235 0249 0297 0322 106 Test 10. T = 300 psi 0 = 3000 psi at time = 0 Initial 3908 X 10.6 in/in 61 = Initial 6L = 1810 x 10'6 in/in Initial 31 = 0 Total 61 = 4293 x 10'6 in/in Total 6L = 2210 X 10'.6 in/in 314 x 10"4 in/in Total ei Computed ei = 161.7 X 10“4 in/in Time 61 6L I 3 Time 1 (min.) _4 (10 in/in) (min.) (ml.) (10'6in/in) (10'6in/in) 0000 000 000 0176 060 050 0533 115 098 1040 165 142 1531 190 176 1922 210 185 2478 230 210 2980 242 225 3300 244 231 3922 260 248 4406 269 258 4818 280 270 5360 291 287 5845 298 298 6329 310 309 6799 322 322 7319 331 330 7857 340 347 8441 350 360 9999 385 400 000 279 288 297 303 306 308 309 309 310 311 312 312 311 311 312 313 313 314 314 0000 0176 0260 0533 1040 1531 1922 2478 2980 3300 3922 4406 4818 5360 5845 6329 6799 7319 7857 8441 0000 0295 0826 1380 2186 2767 3122 3690 3993 4154 4589 4804 4975 5185 5316 5515 5725 5801 6076 6211 107 Test 11. T = 300 psi 0 = 4000 psi at time = 0 Initial 61 = 4305 X 10'.6 in/in Initial 6L = 2002 X 10-6 in/in Initial 61 = 0 Total 61 = 4665 x 10'6 in/in Total 9L = 2152 X 10"6 in/in Total 31 = 390 x lo‘4 in/in Computed SI = 180 X 10.4 in/in Titne 31 3L (min.) -6 -6 (10 in/in) (10 in/in) 0000 000 000 0005 145 002 0401 190 020 0888 220 038 1382 238 050 1697 248 053 2331 256 060 2818 265 068 3120 270 070 3766 280 076 4262 285 080 4685 290 088 5216 300 099 5692 305 106 6037 310 105 6650 318 116 7137 320 118 8467 342 133 9946 360 150 61 (10'4in/in) 000 359 354 377 381 383 385 385 385 386 385 386 387 387 387 388 388 389 390 Time 0min.) 0000 0401 0888 1382 1697 2331 2818 3120 3133 3766 4262 4685 4750 5216 5692 6037 6650 7137 8467 9946 Onl.) 0000 0251 0484 0715 0806 1004 1143 1203 1205 1306 1394 1485 1488 1557 1655 1711 1784 1851 1994 2185 Test 12. T = 300 psi 0 = 5000 psi at time U 0 Initial cl = 3771 X 10.6 in/in Initial 6L = 1900 X 10-6 in/in Initial 61 = 355 X 10.4 in/in Total 61 = 4155 X 10.6 in/in Total 6L = 2088 X 10-6 in/in Total 61 = 406 x 10'4 in/in Computed ei = 204.3 X 10.4 in/in Time s 8 (min.) -61 -6L (10 in/in) (10 in/in) 0000 000 000 0005 055 005 0894 270 098 1385 295 112 1402 243 115 2335 325 128 2826 340 139 3166 345 138 3774 359 145 4265 370 152 4650 378 150 5218 388 162 5704 400 162 6098 410 162 6659 420 170 7150 428 172 8966 368 181 9884 384 188 108 61 (lo-ain/in) 000 002 036 041 041 045 046 046 047 047 048 049 049 049 049 050 051 051 Time (min. 0000 0005 0894 1385 1702 2335 2826 3166 3774 4265 4650 5218 5704 6098 6659 7150 8966 9884 Onl.) 0000 0007 0107 0153 0184 0235 0275 0291 0331 0342 0363 0379 0405 0419 0441 0465 0429 0580 109 Test 13. T = 500 psi 5 = 1000 psi at time = 0 Initial 61 = 3350 X 10.6 in/in Initial 6L = 634 x 10'6 in/in Initial 31 = Total 91 = 3854 X 10.6 in/in Total 6L = 800 x 10'6 in/in Total 61 = 27 10’4 in/in Computed 61 = 5.7 X lO-Ain/in Time 81 6L (min.) -6 -6 (10 in/in) (10 in/in) 0000 000 000 0169 135 033 0396 205 059 0872 280 089 1366 340 101 1521 355 106 1768 375 111 2312 405 126 2807 419 132 3193 435 139 3753 444 140 4246 448 144 4859 453 151 5193 455 150 5683 462 150 6639 463 152 7114 475 154 8395 487 161 8987 489 162 9999 504 166 6' 1 (10-4in/in) 000 001 005 012 016 016 018 019 019 019 020 021 022 023 023 024 024 024 025 027 Time (min.) 0000 0169 0189 0396 0872 1366 1521 1756 1784 2312 2807 3193 3753 4246 4859 5193 5683 5967 5972 5982 6639 7114 8395 8987 9999 (ml.) 0000 0275 0300 0545 1015 1415 1535 1690 2035 2380 2645 2840 3105 3330 3605 3742 3937 4047 4052 4062 4312 4477 4902 5102 5422 110 Test 14. T = 500 psi 0 = 1350 psi at time = 0 Initial 4025 X 10.6 in/in 61 Initial 6L = 80 X 10..6 in/in Initial ti = 0 Total 31 = 4310 X 10-6 in/in Total 3L = 224 x 10'6 in/in Total 31 = 40 X 10.4 in/in Computed ei = 2 X 10”4 in/in Time (min.) -6 -6 (10 in/in) (10 in/in) 0000 000 000 0005 025 005 0389 130 065 0924 116 094 1415 209 112 2363 244 126 2895 250 127 3389 257 128 3804 257 129 3300 255 133 4623 263 136 5244 265 138 5738 266 136 6217 271 130 6680 275 134 7180 275 132 7630 275 130 9010 281 135 9999 285 144 (10'4in/in) 000 000 000 011 021 031 034 036 036 036 039 036 036 036 037 038 038 039 040 Time 0min.) 0000 0389 0924 1415 2363 2859 3389 3304 4623 5244 5738 6217 6680 7180 7363 9010 9999 Onl.) 0000 0100 0210 0300 0465 0545 0628 0698 0817 0903 0973 1036 1093 1153 1208 1369 1421 Test 15. T = 500 psi 0 = 1700 psi at time = 0 Initial 91 = 4916 Initial 6L = 513 Initial 61 = 0 Total 31 = 5230 X Total 6L = 615 x Total ti = 60 x Computed 61 = 7.0 Time 61 (min.) 0000 0450 0945 1394 1890 2385 2839 3330 3825 4223 4770 5260 5676 6210 6705 7061 8638 9418 9418 (10'6in/in) 000 093 130 155 174 185 196 204 213 217 230 241 246 256 265 273 297 314 314 111 x 10'6 in/in x 10"6 in/in 10‘6 in/in 10.6 in/in 10-4 in/in x 10'4 in/in 6L 000 035 055 067 071 076 079 081 082 084 087 088 089 089 092 094 101 102 102 (10-6in/in) e1 (10"4in/in) 000 027 036 041 044 046 046 046 047 049 051 051 053 054 056 056 057 060 060 Time (min. 0000 0450 0945 1394 1890 2385 2839 3330 3825 4223 4770 5260 5676 6210 6705 7061 8638 9418 (ml.) 0000 0040 0075 0105 0138 0168 0197 0225 0255 0276 0305 0330 0349 0370 0390 0400 0505 0530 112 Test 16. T = 500 psi 0 = 3000 psi at time = 0 in/in Initial e 2360 x 10"6 l 't’al Ini 1 6L 1880 x 10'6 in/in Initial ei - 0 Total 61 = 2709 x 10"6 tal TO 6L in/in 1980 x 10'6 in/in Total 265 X 10.4 in/in I 61 Computed 61 = 194 X 10.4 in/in Time a a (min.) -61 L (10 in/in) 0000 000 000 0379 079 031 0852 126 059 1345 153 072 1503 160 073 1752 169 075 2290 195 083 2785 211 087 3178 214 081 3790 221 082 4225 224 086 4840 228 089 5173 225 090 5664 230 092 5950 231 093 6618 232 093 7094 235 091 8384 241 096 8973 245 099 9989 249 100 (10-6in/in) e1 _4 . (10 in/ln) 000 229 246 253 254 255 259 259 261 262 262 262 262 262 262 263 266 263 264 265 Time (min.) 0000 0159 0379 0852 1345 1503 1752 2290 2785 3178 3710 4225 4840 5173 5664 5950 6628 7094 8384 8973 9989 (ml.) 0000 0095 1800 0325 0435 0475 0520 0610 0670 0730 0775 0825 0865 0885 0915 0930 0975 0995 1075 1115 1180 113 Test 17. T = 500 psi 0 = 4000 psi at time = 0 2439 x 10'6 in/in Initial 31 Initial 1727 X 10"6 in/in eL Initial 61 = 314 x 10'6 in/in Total 61 = 2717 X 10.6 in/in Total 61 = 1855 x 10‘6 in/in Total 3i = 348 X 10-4 in/in Computed 61 = 238 X 10.4 in/in Time 61 8 (min.) L (10'6in/in) 0000 000 000 0374 052 000 0907 100 067 1397 133 078 2347 178 095 2841 182 098 3376 202 100 3788 208 101 4282 212 108 4609 213 098 5227 220 107 5722 227 108 6203 238 110 6667 240 114 7152 241 115 7608 251 116 8996 268 122 9999 278 128 (10'6in/in) e1 (10'4in/in) 000 010 019 008 028 030 030 030 030 031 031 032 033 032 032 033 033 034 Time Quin.) 0000 0374 0907 1397 2347 2841 3376 3788 4282 4609 4722 5227 5722 6203 6667 7152 7608 8996 EV (ml.) 0000 0405 0785 1005 1500 1652 1806 1923 2089 2157 2206 2294 2304 2491 2549 2641 2754 3002 114 Test 18. T = 500 psi 0 = 5000 psi at time - 0 2878 X 10 in/in Initial 31 Initial e 1574 x 10'6 L in/in ' = 369 x 10'4 Initial 31 in/in Total 3097 X 10.6 in/in e1 -6 = 1655 x 10 Total 6L in/in Total 3i Computed 61 = 212 X 10-4 397 x 10"4 in/in in/in ' e Tim e1 6 (min.) L (10'6in/in) 0000 000 000 0435 054 032 0930 093 054 1385 129 062 1875 151 072 2371 169 072 2830 177 072 3316 179 073 3810 184 074 4212 184 075 4756 188 075 5248 192 076 5667 194 076 6195 199 077 6690 200 078 7054 204 079 8631 216 080 9408 219 081 (10‘6in/in) 1 (10‘4in/in) 6 000 013 019 021 022 023 023 024 024 024 025 024 024 025 026 026 027 028 Time 0min. 0000 0435 0930 1385 1875 2371 2830 3316 3810 4212 4756 5248 5667 6195 6690 7054 8631 9408 Onl.) 0000 0205 0378 0464 0569 0636 0700 0701 0702 0745 0791 0802 0803 0870 0899 0902 1003 1005 115 Test 19. T = 700 psi 0 = 1000 psi at time = 0 Initial 6536 x 10'6 in/in e1 3950 x 10'”6 in/in Inltlal 6L Initial 31 Total 61 = 6710 x 10'6 in/in 319 X 10 4 in/in Total 4140 x 10'6 in/in 6L 339 X 10.4 in/in Total 31 Computed 3' = 209 X 10.4 in/in Time e1 6 (min.) L (10'6in/in) 0000 000 000 0029 002 002 0337 040 045 0706 070 075 1202 096 102 1500 111 118 1695 120 125 2273 138 138 2942 143 152 3587 148 158 4081 152 159 4556 152 162 5026 154 163 5527 161 170 5845 162 170 6471 164 171 6967 166 178 7389 168 179 8282 172 183 (10'6in/in) e1 (10'4in/in) 000 002 007 010 013 014 014 014 014 017 017 017 018 019 019 019 020 020 020 Time Gain.) 0000 0029 0037 0039 0102 0106 0337 0706 1202 1365 1417 1500 1520 1695 2273 2942 2955 3587 4081 4556 5026 5527 5845 5895 6471 7389 7523 8282 8882 9931 EV Onl.) 00000 00100 00135 00141 00341 00350 00982 01884 02938 03588 03687 03839 03877 04214 04876 05919 05938 06840 07477 08088 08692 09285 09278 09738 10417 10914 11075 11929 12608 14912 116 Test 20. T = 700 psi 0 = 1350 pSi at time = 0 Initial 31 = 6672 X 10.6 in/in Initial 6L = 3122 X 10"6 in/in Initial ei = 333 X 10”4 in/in Total 61 = 7035 x 10'6 in/in Total 6L = 3240 x 10"6 in/in Total 3i = 350 X 10'.4 in/in Computed 61 = 161 X 10.4 in/in 311:.) 61 SL (10-6in/in) (10-6in/in) 0000 000 000 0005 008 001 0860 223 065 1345 250 081 1791 278 093 2295 303 097 2785 318 100 3184 326 103 3734 337 105 4224 338 104 4692 339 105 5167 343 113 5668 348 104 6011 348 107 6542 347 111 7007 350 113 7309 351 112 8476 357 115 8918 358 116 9874 363 118 1 (10-4in/in) G 000 000 012 015 015 015 015 015 016 016 017 016 016 016 017 017 017 017 017 017 Time (min. 0000 0860 1345 1791 1808 2295 2785 3184 3734 4224 4692 5167 5668 6081 6612 7077 7379 8546 8988 9944 (ml.) 0000 1725 2468 3050 3059 3827 4316 4567 4989 5206 5478 5625 5801 5891 6013 6202 6365 6687 6897 7164 Test 21. T = 700 psi 0 = 1700 psi at time = 0 Initial e 1 Initial 6L Initial 31 Total 31 Total 6L Total 31 Computed 61 = 215 X 10'-4 Time (min.) 0000 0085 0974 1469 1943 2410 2905 3307 3790 4280 4692 5236 5721 6085 6670 7150 7488 8361 9191 9957 6255 x 10' 3416 x 10'6 0 -6 8360 x 10 4797 x 10"6 375 x 10"4 e1 (10'6in/in) 0000 0183 1184 1452 1600 1690 1757 1804 1845 1857 1885 1900 1934 1944 1955 1985 1990 6036 2082 2105 6 117 in/in in/in in/in in/in in/in in/in eL (10'6in/in) 0000 0079 0660 0803 0933 1034 1084 1120 1137 1164 1184 1197 1215 1235 1244 1264 1280 1300 1335 1381 61 (10-4in/in) 0000 0270 0341 0357 0369 0369 0370 0370 0369 0371 0376 0374 0375 0377 0374 0375 0374 0374 0375 0375 Time (min. 0000 0085 0974 1469 1943 2410 2905 3307 3790 4280 4692 5236 5721 6085 6670 7150 7488 8361 9191 9957 (ml.) 0000 0036 0790 1354 1402 1864 2003 2215 2247 2379 2386 2404 2518 2525 2630 2737 2783 2799 2932 3084 118 Test 22. T = 700 psi 0 = 3000 psi at time = 0 Initial 31 = 6590 X 10-6 in/in Initial 6L = 361 X 10"6 in/in Initial 3i = 496 X 10-4 in/in Total ,1 = 6788 x 10'6 in/in Total 6L = 509 X 10.6 in/in Total 3i = 518 X 10.4 in/in Computed gi = 39 X 10-4 in/in T158 61 6L 61 (min.) -6 -6 _4 (10 in/in) (10 in/in) (10 in/in) 0000 000 000 000 0326 043 056 007 0689 067 080 010 1185 094 102 013 1364 100 110 013 1487 102 111 014 1683 105 115 015 2260 122 126 015 2926 133 128 016 3570 137 130 016 4065 141 132 017 4541 145 132 017 5010 151 134 017 5509 155 136 017 5832 158 137 018 6455 165 138 019 6948 165 142 020 7355 167 142 020 8266 179 143 020 9817 198 148 022 Time (min. 0000 0017 0029 0098 0326 0689 1185 1364 1420 1487 1506 1683 2260 2926 3077 3570 4065 4541 5010 5509 6455 6948 7355 7511 8266 8868 9817 EV Onl.) 0000 0005 0010 0018 0065 0105 0167 0190 0195 0200 0202 0235 0251 0275 0281 0296 0308 0320 0325 0331 0346 0350 0357 0361 0373 0386 0395 119 Test 23. T = 700 psi 0 = 4000 p81 at time = 0 Initial 31 = 6700 x 10'6 in/in Initial 6L = 8 X 10"6 in/in Initial 61 = 486 x 10’4 in/in Total 61 = 6943 X 10-6 in/in Total 6L = 314 X 10-6 in/in Total 3i = 531 X 10.4 in/in Computed 61 = 25 X 10“4 in/in T158 8l 6L (min.) '6 -6 (10 in/in) (10 in/in) 0000 000 000 0081 040 020 0958 194 095 1457 240 112 1947 272 130 2398 296 133 2894 312 140 3298 321 138 3779 326 150 4269 339 144 4682 347 147 5224 356 148 5709 367 150 6077 374 151 6658 383 152 7138 392 154 7480 401 156 8350 422 157 9186 436 162 9959 451 164 61 (lo-ain/in) 000 004 023 028 031 033 034 036 036 037 037 038 038 038 039 039 039 042 044 045 Time 0min.) 0000 0081 0958 1457 1947 2398 2894 3298 4269 4682 5224 5709 6077 6658 7138 7480 8350 9186 9959 (ml.) 0000 0040 0380 0515 0600 0650 0720 0740 0815 0830 0865 0890 0905 0925 0955 0970 1005 1045 1080 120 Test 24. T = 700 psi 6 = 5000 psi at time 0 Initial 61 = 7017 X 10'-6 in/in Initial 6L = 42 X 10.6 in/in Initial 31 = 534 X 10-4 in/in Total = 7468 X 10-6 in/in Total = 206 x 10'6 in/in Total = 594 X 10-4 in/in -4 Computed 61 = 16.3 X 10 in/in Time 61 6L (min.) -6 -6 (10 in/in) (10 in/in) 0000 000 000 0002 001 119 0850 110 ' 149 1336 143 169 1783 159 188 2285 166 195 2775 172 200 3195 173 210 3725 181 218 4215 186 230 4688 190 232 5760 193 239 5660 199 250 6071 206 259 6605 211 268 7070 216 267 7378 221 270 8545 231 290 8950 233 300 9941 243 314 I S 1 (10'4in/in) 000 035 043 047 050 051 054 055 055 055 054 057 057 057 058 058 057 058 050 060 Time (min. 0000 0850 1336 1783 2285 2775 3175 3725 4215 4688 5160 5660 6071 6605 7070 7378 8545 8950 9941 2V (ml.) 0000 0050 1052 1250 1449 1647 1751 1900 1951 2002 2053 2149 2301 2350 2400 2450 2601 2699 2901 Test 25. 121 T = 1000 psi 0 = 1000 pSi at time = 0 Initial Initial Initial Total Total Total Computed Time (min.) 0000 0301 0629 1118 1390 1625 2076 2556 2750 3517 4012 4503 5178 5753 6391 6880 7376 8186 8649 9999 5806 x 10'6 in/in 61 6L = 140 x 10'6 in/in ' = 61 O = 8315 x 10'6 in/in =+4835 X 10.6 in/in e' = 171 x 10'4 L 61 (10'6in/in) 0000 0520 0759 0986 1120 1221 1373 1532 1586 1770 1856 1906 1986 2049 2119 2166 2221 2300 2371 2509 ' = 294 x 10'4 in/in in/in eL (10'6in/in) 0000 1850 2242 2648 2840 2085 3201 3415 3511 3747 3865 3985 4085 4165 4238 4305 4378 4485 4525 4695 61 (lo-ain/in) 0000 0052 0099 0145 0169 0186 0210 0223 0238 0240 0240 0241 0257 0260 0262 0260 0273 0277 0285 0294 Time (min. 0000 0301 0629 0806 1118 1390 1625 2076 2556 2750 3005 3517 4012 4503 5178 5753 6391 6880 7146 7376 8186 8649 9631 Onl.) 00000 01568 03193 04048 05496 06715 07749 09695 11559 12296 13242 14763 16263 17227 19084 20513 22004 23084 23673 24184 25984 26966 29139 Test 26. T = 1000 psi 0 = 1350 psi at time = 0 Initial 31 = 7754 Initial 6L = 4830 Initial 61 = 0 Total 31 = 8125 x Total 3L =+5085 X Total 61 = 310 X Computed 61 = 194 Time 31 (min.) 0000 0454 0949 1376 1894 2389 2910 3334 3804 4177 4773 5269 5656 6214 6709 7140 8089 8401 9555 9971 (10'6in/in) 000 067 120 154 181 210 230 233 244 252 263 271 280 294 307 314 330 337 362 371 122 in/in in/in in/in in/in in/in in/in eL (10'6in/in) 000 048 070 088 102 108 126 138 140 146 155 165 175 185 192 201 219 223 242 255 I 61 (10-4in/in) 000 288 295 298 301 303 305 305 305 306 306 306 306 306 307 308 308 308 309 310 Time Quin.) 0000 0454 0949 1376 1894 2389 2910 3334 3804 4177 4773 5269 5656 6214 6709 7140 8089 8401 8640 9555 9971 EV Onl.) 0000 0643 1229 1720 2288 2774 3265 3627 4020 4341 4823 5212 5519 5944 6315 6636 7493 7718 7893 8511 8770 123 Test 27. T = 1000 psi 0 = 1700 psi at time = 0 8060 x 10'6 in/in Initial 61 Initial e 4964 x 10'6 in/in L Initial 61 = 249 x lo‘4 in/in Total 61 = 8325 X 10..6 in/in Total 3L =+5135 x 10‘6 in/in Total ,1 = 322 x 10'4 in/in Computed 61 = 198.7 X 10-4 in/in Time s 8 (min.) -61 -6L (10 in/in) (10 in/in) 0000 000 000 0005 001 008 0580 060 058 1044 087 080 2232 118 108 2540 127 112 2925 135 114 3429 145 119 3924 154 122 4309 163 128 4869 173 132 5354 185 139 6309 202 145 6799 213 150 7258 218 154 8739 247 165 9578 265 171 el (lo-4in/in) 00 36 51 57 66 66 66 67 68 69 69 69 71 72 73 74 73 Time (min. 0000 0580 1044 2232 2540 2925 3420 3924 4309 4869 5354 6309 6799 7258 8739 9578 (ml.) 0000 0371 0625 0886 1204 1333 1479 1618 1707 1859 1986 2222 2333 2440 2795 2995 124 Test 28. T = 1000 psi 0 = 3000 psi at time I 0 Initial 6220 X 10.6 in/in e1 1370 X 10"6 in/in Initial 6L Initial 31 = 0 Total 61 = 7590 x 10'6 in/in Total =+890 X 10.6 in/in eL Total 3i = 411 x 10'4 in/in Computed ei = 48.3 X 10"4 in/in Time a e finin.) 1 L (10'6in/in) (10‘6in/in) 0000 0000 0000 0001 0030 1200 0008 0050 1350 0216 0498 1600 0659 0790 1801 1140 0948 1915 1331 0994 1945 1598 1050 1981 2099 1120 2025 2594 1200 2042 3091 1230 2100 3770 1272 2145 4339 1280 2160 4974 1300 2160 5464 1310 2170 5972 1230 2170 6769 1335 2215 7236 1342 2225 8218 1350 2248 8829 1370 2260 61 (10'4in/in) 0000 0065 0093 0240 0332 0362 0373 0383 0396 0399 0401 0403 0403 0405 0405 0405 0407 0408 0411 0411 Time (min.) 0000 0008 0216 0659 1140 1331 1598 2099 2594 3091 3770 4339 4974 5464 5972 6769 6804 7236 8218 8829 Onl.) 0000 0005 0035 0101 0155 0165 0185 0223 0251 0278 0309 0333 0354 0373 0388 0412 0414 0431 0460 0480 125 Test 29. T = 1000 psi 0 = 4000 psi at time = 0 Initial 61 = 5198 x 10'6 in/in Initial 6L = 784 X 10.6 in/in Initial 61 = 420 X 10.6 in/in Total 61 = 7930 x 10'6 in/in Total 6L =+1020 X 10..6 in/in Total 61 = 451 x 10'4 in/in Computed ei = 58 X 10-4 in/in Time 61 8L (min.) -6 -6 (10 in/in) (10 in/in) 0000 000 000 0443 073 075 0939 107 108 1370 123 125 1883 137 141 2379 145 152 2920 155 161 3324 160 168 3794 170 170 4168 175 172 4764 185 180 5259 192 185 5659 197 190 6205 205 195 6699 205 201 7128 226 206 8081 240 213 8392 245 215 9552 267 231 9965 273 236 SI 1 -4. C (10 in/in) 000 008 013 017 018 018 018 019 020 020 021 022 023 025 027 031 029 029 030 031 Time (min. 0000 0443 0939 1175 1370 1883 2379 2920 3324 3794 4168 4764 5259 5649 6205 6699 7128 8081 8392 8635 9552 9965 (ml.) 0000 0051 0102 0119 0129 0159 0178 0201 0218 0230 0238 0252 0254 0262 0268 0271 0279 0289 0293 0296 0304 0311 30. Test '1' II C att Init Init Init Tota Total 6L =+2745 x 10' Total 3i = 501 X 10-4 Computed ei = 144 X 10 4 Time 31 (min.) -6 (10 in/in) 0000 0000 0005 0055 0570 0514 1034 0780 2223 1224 2535 1300 2915 1380 3419 1430 3914 1453 4303 1472 4860 1485 5344 1503 6299 1530 6790 1551 7251 1555 8735 1609 9572 1648 1000 psi 5000 psi ime = 0 ial 31 131 6L 131 31': 0 l e = 9560 x 10'6 l 7912 x 10'6 2013 x 10'6 126 in/in in/in in/in in/in in/in in/in eL (10'6in/in) 0000 0020 0235 0345 0530 0531 0600 0601 0621 0625 0631 0642 0665 0671 0685 0714 0732 I 6l (10'4in/in) 0000 0401 0457 0480 0501 0497 0498 0499 0499 0499 0499 0499 0499 0499 0500 0501 0501 Time (min° 0000 0570 1034 2223 2535 2915 3419 3914 4303 4803 4860 5344 6299 6790 7152 8735 9572 (ml.) 000 085 126 205 212 227 251 266 283 295 297 313 348 366 382 435 480 127 0H0 000 0H0 0m 0s 00 ~00 H00 000 00 00 on H00 5H0 000 N00 05H 00H 000 N00 0H0 00 mm NHH 000 000 ~00 ~00 0H5 ~00 Hm NH 0H0 000 000 N0 00 00 H00 N00 000 000H NO0H 000H N00 000 N00 00NH 000H 000H 0NHH HO0H NHOH NmHH 000H 0mm 00H 00H H0 mHNH ONHH N00 000 000 000 0mH~ 000H 000 N00 HON 00H 00n~+ 0000+ 000 + 00Hm+ 0000+ 0000+ 000 + 0H0 + 000 + nmn0+ 0000+ 00H0+ 000H 000H 000H 0H0 000 000 0000 NOHN 0HNN n00 0HOH 0HNH 0~HN NOHN 00mm 00 00H 00H HaH\cH0 0| 40 000m 0000 0000 0000 0~H0 0H00 000m 0000 0050 0000 0000 0Hn0 0000 NHNN 0050 0000 0H00 0000 00H0 0000 0000 0H00 0000 00mm 0NHO 0H00 0000 000H 000H 0H0 HaH\aHV 0000.0 0NHN.0 0000.0 0500.0 0000.0H 0000.00 0000.0 0000.0 0000.0 0000.0 0000.0 Nm0~.mH ~0H0.0 0000.0 NOHH.0 0000.0 0000.0 0000.0 0000.0 0000.0 0000.0 0000.0 00NN.H 0000.0 0000.0 0000.0 0000.0 0000.0 00Hn.0 0mH0.N Hmonoo-HHHHav M 05.0 0~.NH 00.00 00.000 00.000 00.0000 00.0 00.0 00.0H 00.00H 00.000 00.000H 00. 0H.N 00.0 00.00 00.0HH 00.000 00. 0N.H 00.0 00.00 00.00 00.nmm 00. 00. N0.H 00.0H 00.00 00.00H HaHa\Hav 00H 0 coHumEpowmn can .chuum .muHHHQmmEuom .muduualo 0000 0000 0000 000H 000H 000H 0000 0000 0000 000H 000H 000H 0000 0000 0000 000H 000H 000H 0000 0000 0000 000H 000H 000H 0000 0000 0000 000H 000H 000H Haoav 000H 000 000 000 00H AHoav e .Nu< mHan 128 mom.o oHa.H mHNo omoam aoa.o oooo.o ooon ooa.o Noa.H ammo onmmm maa.m oHH~.o oooa ooo.o NHo.H mHmo oooHH omo.m omoo.o ooom ao~.H ono.~ oaoo owoaH aao.o oaon.o ooHH oooH on.H Nmo.~ oaoo oHoHH -o.o oooo.mH oAMH ooo.~ ooo.~ oaoo aaooo mam.o ~n~o.oa oooH oom.o ooa.H aNoo oNooH ~om.m ammo.o ooon Hom.o mNm.H Hooo omHoH oom.m ~ooo.o oooa on.o omm.H oomo oNHoH mam.m moo~.o ooom H-.H mao.~ mmoo omHmH mHo.o oaoo.N ooaH ooh omn.H ooH.~ ouoo oooNH Ha~.o omoo.o oan moo.N oao.~ aaoo oomoo oum.o ~5o~.aH oooH Ho~.o mom.H HNoo ooHHH mH~.~ HoHo.o ooon Non.o ao~.H aHoo omoao ooH.H ammo.o oooa Hoa.o mHa.H mnoo oamoo HaH.m NaHH.o ooom oo~.H mmo.~ maoo ooaaH moo.» mmaa.o ooaH oon aom.H amo.~ aaoo ooNNH Hmo.a ammo.~ ommH ooo.~ ooo.~ omoo aoHoo ooH.o oaoN.o oooH moN.o mHm.H HHoo oomHH oau.~ oooo.o ooom aam.o ohm.H omao ooaoH Hoo.~ m-o.o oooo ooo.o oo6.H omoo oooao oo~.m aooo.o ooom maH.H aaa.H mmHo omomH Hma.a Nmmn.o ooaH oom ma8.H Hoo.H omHo ooooH mam.a mo-.H oan oHo.~ oHo.~ HHHo oooao ooo.a oomo.o oooH HHH.o mow.o ooNH oamHo Nao.o omoo.o ooom man.o mHm.H mHoo ooomH Hma.m mooo.o oooo Hmm.o Nom.H ammo ooHNH amo.a aouo.o ooom NoN.H moo.~ mooo omaoH oom.o oaa~.o ooAH ooH on.H omo.~ oaoo mNamH aom.o omHa.o oan mao.~ mao.~ mmoo mHaoo mHo.o maHa.~ oooH Hma CH ca H a I a A. 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