Four compressibilities are defined for porous rock, relating changes in the bulk and pore volumes to changes in the pore and confining pressures. Using a micromechanical theory based on classical linear elasticity, three relations are found between these compressibilities. Two of these relations are verified experimentally for Berea and Bandera sandstone. Bounds are derived for these compressibilities, involving only the porosity and the elastic moduli of the rock‐forming minerals. For the strains to be unique functions of the stresses the compressibilities must be functions only of the difference between the confining and pore pressures. This dependence is verified for Berea, Bandera, and Boise sandstone. While the strains cannot be expressed as functions of an “effective stress,” regardless of how it is defined, the (elastic) volumetric behavior of porous rocks can be studied through tests conducted at zero pore pressure.

Thermal conductivities of unconsolidated oil sands have been measured and the results correlated with physical properties of the sand-fluid system. Saturation of the wetting fluid has a dominant effect on thermal conductivity values. Water-saturated sands were found to have thermal conductivities six to eight times greater than values for the same sand packs air saturated. For correlation purposes, the porosity of a sand pack is an adequate indicator of matrix structure. Other quantities needed to develop a satisfictory equation for predicting thermal conductivity are the conductivities of the wetting fluid and of the rock solids. The effects of changes in temperature on the thermal conductivity of unconsolidated oil sands are relatively small and can be evaluated with a simple linear equation. The effects of changes in pressure on the thermal conductivity of liquid-saturated unconsolidated sands are also small and for practical purposes can be ignored. Results of the present work are believed to have direct application to calculations relating to thermal processes in underground reservoirs. Core-analysis and well-log data can be used to evaluate the thermal properties of unconsolidated oil sands required for such calculations. INTRODUCTION The most successful thermal recovery operations are those that have been applied to relatively shallow producing formations consisting mostly of unconsolidated sands. Necessary in designing such projects is a knowledge of the thermal properties and behavior of the sand-fluid system under reservoir conditions of saturation, pressure, and temperature. A great deal of literature has been published on the thermal properties of granular materials, and several models and correlations for predicting thermal properties have been proposed.1–5 Unfortunately, most test data have been obtained for systems or conditions much different from those found in petroleum reservoirs. Most models or prediction equations do not cover ranges of variables of importance to subsurface applications and, in addition, often require knowledge of system parameters that normally are not readily available from common sources such as core analyses and well logs. The purpose of this work was to establish relationships between laboratory measurements of thermal properties and other more easily measurable properties of unconsolidated sands. Simple systems consisting of uniform-grain-size quartz sands saturated with single fluids were first studied. The work then progressed to more complex systems, including actual oilfield cores containing substantial portions of their original fluids. RELATIONSHIP OF THERMAL CONDUCTIVITY TO OTHER PHYSICAL PROPERTIES The thermal conductivity of fluid-saturated, unconsolidated sand is strongly dependent upon the saturation and thermal conductivity of the wetting phase fluid. Air- or gas-saturated sands characteristically have low thermal conductivities. This is because the contact areas between grains, through which heat must flow, are small. Introduction of a wetting-phase liquid greatly increases the thermal conductivity by increasing the effective grain contact area and thus enlarging the effective area through which heat can flow. Present experimental results show that the thermal conductivity of brine-saturated unconsolidated sands increases sixfold to eightfold over that of the same sand packs air saturated. This effect is considerably less pronounced in consolidated sandstones; Anand's data6 show a twofold to threefold increase between brine-saturated and air-saturated sand packs.

ifeasuying~})e~hertnal properties o! rocks and rock-fluid

Published in Petroleum Transactions, AIME, Volume 213, 1958, pages 375–378. Abstract Results of experimental measurements of heat capacities and thermal conductivities of some typical porous rocks are presented. Measured heat capacities agree closely with values calculated from known chemical compositions of the rocks. On the basis of this agreement, heat capacities of fluid-saturated rocks were calculated. Thermal conductivities of the rock samples were measured under various conditions of fluid saturation. From these data thermal diffusivities were calculated. A significant variation of thermal diffusivity with temperature is indicated. Introduction Knowledge of the thermal characteristics of fluid-bearing porous rocks has become increasingly important with the development of thermal oil-recovery processes. Reliable thermal data for petroleum reservoir rocks are not available and approximate values are generally assumed for reservoir calculations. The effects of temperature, pressure and fluid saturation on thermal properties of porous rocks have not been carefully studied. The purpose of the present work was to measure and report the thermal characteristics of some typical porous rocks. A group of eight sedimentary rock samples, including limestone, shale, sandstone and siltstone, was selected for the study. Properties reported include heat capacities, thermal conductivities and thermal diffusivities. The effect of fluid saturation on these properties was also considered. Determinations of thermal properties require precise measurements which are time consuming and difficult to reduce to a routine basis. Methods have not been developed for measurement of thermal properties under conditions of pressure, temperature, and fluid saturation, which may be encountered in thermal recovery processes. As one approach to these problems, some preliminary work on methods of estimating thermal properties from other more readily measurable characteristics of the rock-fluid system is reported.

Simultaneous measurement of pore and elastic properties of rocks under a wide range of triaxial stress conditions may be made with equipment and methods developed in this paper. Tests were run on three outcrop sandstones at several confining pressures and axial stresses up to approximately 80 percent of failure stress. The greater reduction in porosities and permeabilities occurred in the hydrostatic loading portion of the stress cycle, but substantial reductions in both properties did occur upon application of deviator (triaxial) stress. Triaxial elastic moduli were calculated from strain gauge measurements. Both Young's moduli and shear moduli were found to increase with increasing confining pressure. Poisson's ratios increased with axial stress but showed no consistent change with confining pressure. Only very general relations were observed between pore and elastic properties. The lesser decrease in porosity and permeability at higher stress values is related to increase in rigidity of rocks at higher stresses. Introduction Many investigators have studied the effects of hydrostatic stress on the properties and behavior of rocks. A few have studied the effects of triaxial stress fields on individual physical properties of rocks. To our knowledge no one has measured simultaneously pore and elastic properties of rocks under a wide range of triaxial stress conditions. This is the purpose of this work. Rocks exist in the subsurface under what Jaeger refers to as "polyaxial" stress conditions (all principal stresses unequal). When two of the three principal stresses are equal, this is referred to as triaxial loading. The triaxial method of loading is most commonly used in modern testing work because experimental difficulties in measuring physical properties of rocks are greatly reduced over polyaxial testing. Although triaxial loading may not reproduce subsurface conditions precisely, subsurface stress conditions are never known precisely anyway. Triaxial testing would seem to be more realistic than testing under hydrostatic loading (all principal stresses equal) for application of results to subsurface problems. The objectives of this work were threefold:to develop methods of measuring simultaneously pore and elastic properties of rocks under triaxial stress conditions,to determine whether changes in these properties are of sufficient magnitude to be considered in subsurface calculations andto attempt to relate changes in pore properties and elastic properties since they will have been measured at the same time under identical loading conditions. REVIEW OF EARLIER WORK PORE PROPERTIES Several investigators have studied the effects of stress on the physical properties of rocks. Fatt and Davis showed the reduction of permeability of rock with hydrostatic loading. McLatchie et al. and Knutson and Bohor related permeability reduction to compressibility of reservoir rock, again under hydrostatic loading. Wyble, and later Redmond, evaluated the effects of applied radial pressure on conductivity, porosity and permeability of sandstones. In this latter work, no axial stress was applied. Dobrynin reviewed much of the previous work done on the effects of overburden pressure on physical properties of rocks. He concluded that changes in physical properties are controlled to a large extent by pore compressibility of the rock. Several sets of curves developed from empirical relations am presented. These curves permit estimation of change of properties with net overburden pressure, knowing the pore compressibility and porosity of the rock. SPEJ P. 283ˆ