Comparison of Xu-White, Simplified Xu-White (Keys & Xu) and Nur’s critical porosity in shaley sands

Along with applicability to the specific reservoir scenario, calibrability is an indispensable criterion for selection of the optimum rock-physics model. Calibration becomes of an underdetermined nature and suffers from non-uniqueness when the parameters in the model outnumber the measured data which is typically limited to sonic and density. In this article, the calibration method proposed by Amini (2018) was used to address this challenges by comparing three different models for dry rock elastic moduli (Xu&White, Keys&Xu, Nur’s critical porosity) on sand-shale mixtures. The performance of these models in predicting the wireline log velocities and their corresponding fitting parameters were compared. It was observed that, once calibrated, all the three models could reasonably model the elastic moduli log data. The optimised critical porosity for high porosity sands were about 0.35–0.4 and the increase in clay content reduces this value. The critical porosities optimised separately for shear modulus were slightly higher than the ones for the bulk modulus. The optimised effective aspect ratio from Xu-White model for high porosity sands were about 0.2 and the increase in clay content reduces this value. The aspect ratios from Keys-Xu model show a large scatter and do not agree well with Xu-white model.