Joint inversion of the unified pore geometry of tight sandstones based on elastic and electrical properties

The prediction of the pore geometrical properties is important in the exploration and development of tight -sandstone hydrocarbon reservoirs. To investigate this topic, we have measured the porosity, permeability, P -and S-wave velocities, electrical conductivity, and axial and radial strains as a function of differential (confining minus pore) pressure of tight-sandstone samples, collected from the Zhongjiang gas field of Sichuan, in West China. The results show that the closure of cracks with pressure highly affects these properties. Then, we propose a multiphase reformulated differential effective-medium (R-DEM) model that employs the unified pore geometry (the same pores or cracks with different aspect ratios and volume fractions) for both elastic and electrical modeling. The model gives the pressure-dependence of the P-and S-wave velocities and electrical conductivity, and the experimental porosity and static moduli are used as constraints to estimate the pore geometry. The model describes the elastic properties of sandstones saturated with nitrogen gas, and the electrical conductivity when the pore fluid is brine. The prediction of the wet-rock S-wave velocities is less accurate, due to the presence of shear stiffening and weakening effects. Furthermore, we compare the results with those of the joint elastic -electrical inversion by using the dynamic instead of the static stiffness modulus. The results show that the latter provides a better agreement between theory and experiment. Subsequently, we show that the pore ge-ometry estimated from the elastic or the electrical measurements separately (unjoint inversion) present dis-crepancies, indicating that a joint inversion is required. The published experimental data are also used to illustrate the model, and the results are satisfactory.