Hyperparameter inversion of well logs for the simultaneous estimation of volumetric and zone parameters

Abstract

We develop a new alternative for the joint inversion of well logs to predict the volumetric and zone parameters in hydrocarbon reservoirs. Porosity, water saturation, shale content, kerogen, and matrix volumes are simultaneously estimated with the tool response function constants with a hyperparameter estimation assisted inversion of the total and spectral natural gamma-ray intensity, neutron porosity, and resistivity logs. We treat the zone parameters, i.e., the physical properties of rock matrix constituents, shale, kerogen, and porefluids, as well as some textural parameters, as hyperparameters and estimate them in a metaheuristic inversion procedure for the entire processing interval. The selection of inversion unknowns is based on parameter sensitivity tests, which indicate that the automated estimation of several zone parameters is favorable, and their possible range can also be specified in advance. In the outer loop of the inversion procedure, we use a real-coded genetic algorithm for the prediction of zone parameters, and we update the volumetric parameters in the inner loop in addition to the fixed values of the zone parameters estimated in the previous step. We apply a linearized inversion process in the inner loop, which allows for the quick prediction of volumetric parameters along with their estimation errors from point to point along a borehole. The derived parameters, such as hydrocarbon saturation and total organic content, indicate good agreement with core laboratory data. The significance of the inversion method is that the zone parameters are extracted directly from the wireline logs, which improves the solution of the forward problem and reduces the cost of core sampling and laboratory measurements. In a field study, we demonstrate the feasibility of the inversion method using real well logs collected from a Miocene tight gas formation situated in the Derecske Trough, Pannonian Basin, East Hungary.