Joint two-step inversion of porosity and saturation based on the Biot/squirt model with multiphase fluids

Abstract

It is of great importance to predict reservoir petrophysical properties, such as porosity and saturation based on elastic properties, including density and wave propagation velocity, through quantitative seismic interpretation. A joint two-step inversion (JoiTSI) method is proposed for predicting porosity and saturation with a forward petrophysical model. As the forward model, the Biot/squirt model with multiphase fluids (gas, oil, and water) describes the nonlinear relationships between petrophysical and elastic properties. The first step of the two-step inversion is to invert porosity and saturation via a semianalytical approximation approach. The second step is a joint inversion at high porosities where porosity and saturation are simultaneously optimized using a hybrid genetic algorithm. In these steps, maximum a posteriori estimations are performed based on normal prior distributions, where the posterior distributions may differ between two steps because of the potential variability in reservoir properties. The numerical tests indicate that this JoiTSI method is more efficient and more accurate than the traditional inversion methods. In addition, Poisson’s ratio, P-wave impedance, and S-wave impedance are found to give better inversion results than those based on more commonly used attributes (density, P-wave impedance, and S-wave impedance). In the oilfield seismic example, the inversion accuracy of porosity and saturation is verified by actual well logs, and the major oil and water layers are correctly identified.