THE EFFECT OF PORE STRUCTURE ON THE PORE AND BULK COMPRESSIBILITIES OF CONSOLIDATED SANDSTONES (ROCK MECHANICS, POROUS MATERIALS)

A theory for the volumetric behavior of porous rocks is developed, based on classical elasticity. Three relations, which are independent of the pore structure, are derived among the four porous rock compressibilities (which relate the pore and bulk strains to the pore and confining pressures). A mathematical proof is given that a necessary condition for the differential stress-strain relations to be integrable is that the compressibilities be functions only of the differential pressure, which is the difference between the confining and pore pressures. A physical explanation of why this is to be expected is put forward in terms of the closure of microcracks.; The compressibilities of two-dimensional cracks of various shapes is studied in detail. It is shown that the compressibility of a crack is governed primarily by its aspect ratio. Tubular pores with polygonal cross-sections are studied using complex variable methods, and it is seen that the compressibilities of such pores are only slightly greater than that of a tubular pore with circular cross-section. An exact expression for the compressibility of a three-dimensional spheroid is derived, and it is seen that the asymptotic expression for pennyshaped cracks is in fact extremely accurate for aspect ratios as high as about 0.30.; Various theories for analyzing the effect of stress-field interactions between pores are discussed, and compared to data from the literature on the elastic moduli of materials with spherical pores. Of the existing theories, the Kuster-Toksoz method is seen to be superior to either the self-consistent approach or the no-interaction approach. A modification of the self-consistent method is shown to be nearly as accurate as the Kuster-Toksoz method.; Using the oblate spheroid as the model for pores in a sandstone, an integral equation is derived which relates the compressibility-pressure curve to the crack aspect ratio distribution. This equation can be used in conjunction with any theory relating crack density to bulk compressibility.; Pore compressibility tests were run on three consolidated sandstones. It is verified that the compressibilities depend only on the differential pressure. Comparison with bulk compressibility data verifies that the pore and bulk compressibilities are related in the manner predicted by the theory. The new self-consistent theory, along with the integral equation, is used to determine the aspect ratio distributions of the three sandstones (Boise, Berea, and Bandera).