Substituting petro-elastic model with a new proxy to assimilate time-lapse seismic data considering model errors

Abstract

Dynamic data from oil and gas reservoirs (such as well-production or 4D seismic data) have been used often to reduce uncertainty in reservoir simulation models. These data are assimilated in the simulation models separately or jointly. Assimilation of 4D seismic data conventionally involves with a petro-elastic model (PEM) to transform outputs from the simulation models to elastic properties. The PEM is a set of different equations with uncertain parameters and its inclusion in assimilation algorithms calls on multidisciplinary teams of geoscientists and engineers. Moreover, PEM requires extraction of different outputs from the simulation models for the seismic forward model calculations. The extraction process can be costly for large-scale simulation models of giant reservoirs. This research presents a new petro-elastic proxy model (named DAI-Proxy) with a novel formulation to substitute the PEM and integrate 4D seismic data. DAI-Proxy relates time-lapse acoustic impedance to a summation of saturation and pressure changes with two coefficients which are functions of porosity. As the proxy is an approximation of the PEM, its application is affected by model error. We introduce two approaches to account for the proxy model error: (1) considering uncertain coefficients for the DAI-Proxy and (2) using fixed coefficients in the proxy while estimating model errors statistics from the prior ensemble of models. We incorporate these two approaches with a data assimilation algorithm to assimilate simultaneously 4D seismic and well-production data. A benchmark case is used with different cases of data assimilation to compare the DAI-Proxy and the PEM applications. Results show that data match quality for 4D seismic and well-production have similar responses for the PEM and DAI-Proxy implementations. In terms of production forecast, using fixed coefficients in the proxy with its model error treatment create a data assimilation framework comparable to the PEM case. Our results indicate that the traditional PEM application to integrate jointly 4D seismic and well-production data can be replaced with our new DAI-Proxy application. Given the degree of uncertainty in the PEM, related to the rock and fluid models, our proxy provides similar results with fewer uncertain inputs. The proxy offers further advantage as it needs less outputs from the simulation models for seismic forward model calculations. In addition, it helps petroleum engineers to use a computationally less expensive model (light model) as a substitute for the PEM to assimilate 4D seismic data.