Geophysical and production data history matching based on ensemble smoother with multiple data assimilation

Abstract

The Ensemble Kalman Filter (EnKF), as the most popular sequential data assimilation algorithm for history matching, has the intrinsic problem of high computational cost and the potential inconsistency of state variables updated at each loop of data assimilation and its corresponding reservoir simulated result. This problem forbids the reservoir engineers to make the best use of the 4D seismic data, which provides valuable information about the fluid change inside the reservoir. Moreover, only matching the production data in the past is not enough to accurately forecast the future, and the development plan based on the false forecast is very likely to be suboptimal. To solve this problem, we developed a workflow for geophysical and production data history matching by modifying ensemble smoother with multiple data assimilation (ESMDA). In this work, we derived the mathematical expressions of ESMDA and discussed its scope of applications. The geophysical data we used is P-wave impedance, which is typically included in a basic seismic interpretation, and it directly reflects the saturation change in the reservoir. Full resolution of the seismic data is not necessary, we subsampled the P-wave impedance data to further reduce the computational cost. With our case studies on a benchmark synthetic reservoir model, we also showed the supremacy of matching both geophysical and production data, than the traditional reservoir history matching merely on the production data: the overall percentage error of the observed data is halved, and the variances of the updated forecasts are reduced by two orders of the magnitude.