Permeability estimation using rock physics modeling and variational Bayes inversion

Permeability estimation is pivotal in reservoir characterization; however, prevailing methods lack a standardized approach. Traditionally reliant on core samples, permeability assessment encounters limitations across diverse thicknesses and wells. An innovative core-independent two-step rock physics template (RPT) can be designed to estimate elastic and conductive properties. The suggested RPT employs the T-matrix method to leverage well-log data encompassing porosity, fluid saturation, and various textural parameters. The estimation process for textural parameters involves addressing uncertainties through the fixed form variational inference (FFVB) with the trust region reflective optimization algorithm. These uncertainties span estimated textural parameters, seismic wave propagation velocity, electrical resistivity, and hydraulic permeability. Micro and macro voids, micro-spherical pores porosity, and their semi-axis are modeled using Beta distributions for both prior and variational families. The noise in the model assumes an inverse gamma distribution for sonic travel time and true formation resistivity. Validation of the proposed method is achieved by comparing the FFVB results with Metropolis Hasting's sampling method in three depths and also through geological observations and experimental analyses on available core samples. The inverse problem, involving the determination of textural parameters through sonic travel time and resistivity, is solved. Subsequently, the forward problem is addressed to estimate permeability. The robustness of the inverse problem is underscored by minimal discrepancies between measured sonic travel times, true formation resistivity values, and the results of the forward problem. The method demonstrates its effectiveness in permeability estimation, even in regions lacking core data, thereby emphasizing its reliability and applicability in diverse geological settings.