Bayesian Stochastic Inversion (A case study from an Iranian oil field)

Summary

We have implemented an estimation procedure whereby wireline data can be extrapolated away from existing well using geostatistical inversion of post-stack 3D seismic data. This procedure works directly in a fine-scale stratigraphic grid, and is conditioned by well and seismic data. It uses a Bayesian framework and a linearized, weak contrast approximation of the Zoeppritz equation to construct a joint log-Gaussian posterior distribution for Pwave impedances. Variograms are also estimated from well-log, seismic data and acoustic inversion results that define the expected degree of lateral smoothness away from the well. A sequential Gaussian Simulation algorithm is applied to sample the posterior PDF and generates multiple, high-resolution realizations of the acoustic impedance which can be utilized to generate stochastic realizations of petrophysical variables that not only honor the well-log data, but most importantly, that fully honor the 3D seismic.

Sensitivity analysis was also performed to find the optimum values for S/N ratio, Variogram ranges and prior standard deviation. We had just one well in the area and preferred to keep it to perform quality control of the inversion results. Without constraining with well, geostatistical inversion still can be used to estimate acceptable static reservoir model for the subsequent simulation and planning of in-fill drilling and/or enhanced-oil-recovery operations.