1 INTRODUCTION
Rock pore-volume compressibility values are used chiefly by engineers as a factor for estimating the volume of oil reservoirs in the early stages of production. For volumetric (sealed) reservoirs producing above the bubble point (no free gas existing) the only forces driving the oil from the reservoir arise from the expansion of oil and water and the reduction of pore space resulting from the fluid pressure decline accompanying production. Rock pore-volume compressibility usually accounts for about one-fourth of the system compressibility, so the factors that significantly affect the magnitude of rock pore-volume compressibility also have an important influence on estimating reservoir size. One consideration is that compressibility measured using the conventional "hydrostatic stress" laboratory test can be almost double that occurring under the "uniaxial strain" conditions believed to exist in the reservoir. In the reservoir, with stress applied from above by the overburden and lateral deformation being prevented by surrounding rock, only vertical compaction occurs, which is a lesser change than the hydrostatic-stress compaction.
2 BACKGROUND
Rock pore-volume compressibility is a measure of the change in pore space which occurs when the rock is stressed and is related to both the physical properties and spatial arrangement of the constituent minerals. Most of the petroleum industry's pore-volume compressibility tests are hydrostatic tests. When measuring the hydrostatic compressibility of rock a liquid-saturated, jacketed sample is compressed equally from all directions in a pressure vessel. The volume of liquid produced, read using a calibrated receiver communicating with the pore space, is an essentially direct measure of the pore-volume change. The test is conducted by increasing pressure stepwise and reading the amount of fluid produced at each pressure step after equilibrium has been achieved. Van der Knaap (1959) predicted by theory and confirmed by experiment that pore fluid pressure opposed confining pressure to the full extent of the pore fluid pressure for hydrostatic loading, thus the frame stress on the rock is simply the difference between confining pressure and pore pressure. Uniaxial-strain tests are more complicated and time consuming so calculating uniaxial-strain response using data from the simpler hydrostatic test is desirable. Oniaxial-strain compressibility should be approximately one-half that measured in the hydrostatic test (Geertsma 1957). Teeuw (1971) described methods of carrying out uniaxial-strain tests and also pointed out the similarity in response of granular rock to that described by the Hertz sphere-packing model (Timoshenko & Goodier 1951) where compaction is shown to be a power function of stress.
3 NONLINEAR THEORY
Following the analysis of Teeuw (1971), Young's modulus E is assumed to contain the power-law dependence on stress O, given by (mathematical equation) (available in full paper)
