Simultaneous integration of pressure, water cut,1 and 4-D seismic data in geostatistical reservoir modeling

A geostatistically-based inverse technique, the sequential-self calibration (SSC) method, is used to update reservoir models so that they match observed pressure, water cut and time-lapse water saturation derived from 4-D seismic. Within the SSC, a steady-state genetic algorithm (GA) is applied to search the optimal master point locations, as well as the associated optimal permeability perturbations at the master locations. GA provides significant flexibility for SSC to parameterize master point locations, as well as to integrate different types of dynamic data because it does not require sensitivity coefficients. We show that the coupled SSC/GA method is very robust. Integrating dynamic data can significantly improve the characterization of reservoir heterogeneity with reduced uncertainty. Particularly, it can efficiently identify important large-scale spatial variation patterns (e.g., well connectivity, near well averages, high flow channels and low flow barriers) embedded in the reservoir heterogeneity. Using dynamic data, however, could be difficult to reproduce the permeability values on the cell-by-cell basis for the entire model. This reveals the important evidence that dynamic data carry information about large-scale spatial variation features, while they may be not sufficient to resolve the individual local values for the entire model. Through multiple realization analysis, the large-scale spatial features carried by the dynamic data can be extracted and represented by the ensemble mean model. Furthermore, the region informed by the dynamic data can be identified as the area with significant reduced variances in the ensemble variance model. Within this region, the cell-by-cell correlation between the true and updated permeability values can be significantly improved by integrating the dynamic data.