Extended Probability Perturbation Method for Calibrating Stochastic Reservoir Models

Calibrating a stochastic reservoir model on large, fine-grid to hydrodynamic data requires consistent methods to modify the petrophysical properties of the model. Several methods have been developed to address this problem. Recent methods include the Gradual Deformation Method (GDM) and the Probability Perturbation Method (PPM). The GDM has been applied to pixel-based models of continuous and categorical variables, as well as object-based models. Initially, the PPM has been applied to pixel-based models of categorical variables generated by sequential simulation. In addition, the PPM relies on an analytical formula (known as the tau-model) to approximate conditional probabilities. In this paper, an extension of the PPM to any type of probability distributions (discrete, continuous, or mixed) is presented. This extension is still constrained by the approximation using the tau-model. However, when applying the method to white noises, this approximation is no longer necessary. The result is an entirely new and rigorous method for perturbing any type of stochastic models, a modified PPM employed in similar manner to the GDM.