Abstract: The effective stress principle of Terzaghi, the foundation of soil mechanics, is widely used in reservoir stress-sensitive research for pore volume and permeability. However, its applicability to the pore volume strain of rock is controversial. Force analysis on porous media with incompressible grains and compressible grains are conducted, and expressions of effective stress for total volume, grain skeleton and pore volume are deduced, which are further compared with effective stress equations proposed by Biot and Skepmton. Then, a new effective stress equation for pore volume strain is established. Finally, the experimental demonstration and application are conducted. The results show that the effective stress is the macroscopic equivalent stress of intergranular beyond the pore pressure in the porous media with incompressible grains. While the effective stress is equivalent stress for the same strain in the porous media with compressible particles. There are three kinds of effective stress equations for total volume strain, particle volume strain and pore volume. The new effective stress for pore volume is related to porosity, compression coefficient of total volume and particles, total stress and pore fluid pressure. The deviations between four theoretical calculations and experimental tests on three kinds of pore media are within 5%. With increasing the total stress quantitatively, the coefficients of pore volume effective stress can be used for equivalently simulating reservoir production with pore pressure dropping. The calculation of the three compressibility equations is convenient and accurate.

Key words: effective stress equation, compressibility coefficient, grain deformation, pore volume strain, total volume strain, stress sensitive effect