Inversion of effective pore aspect ratio based on DEM analytical model and Gassmann equations

Abstract

By integrating Gassmann equations with the DEM analytical model of dry-rock frame derived from the differential effective medium theory, this paper presents a method for pore structure evaluation and shear wave velocity prediction from the effective pore aspect ratios inverted from the P-wave (and S-wave) velocity. First, we build a link among P-wave and S-wave velocity, density, porosity, saturation and mineral compositions through Gassmann equations and the DEM analytical model. Then, by assuming that the porous rock contains spheroidal pores with a single aspect ratio, we apply nonlinear global optimization algorithm to find the best estimate for the effective pore aspect ratio in terms of minimizing the error between theoretical predictions and experimental measurements. Finally, we estimate the S-wave velocity from the inverted effective pore aspect ratios. The results show that the inverted aspect ratio can be used to accurately indicate the pore structure of the reservoir. Comparison of the inversion of pore aspect ratio between only from Pwave and from both P-wave and S-wave is made; the pore aspect ratios from these two methods are almost the same. And, the predicted shear-velocity only from P-wave is in good agreement with the measured one. These results show that our method of the shear-velocity prediction by using the pore aspect ratio inverted from P-wave is effective.