Multi-objective History Matching of a Deltaic Reservoir with Non-stationary Geostatistical Modelling

Abstract

History matching with a single objective function reflects only some global aggregated reservoir match quality and is not flexible enough to distinguish between local effects and provide a spread of diverse models for the forecast. On the contrary, multi-objective optimization (MOO) can distinguish between the contributions to the goodness to fit from some local parts of the model. History matching with MOO results in more diverse matched solutions and more robust prediction. Use of MOO in history matching also provides extra flexibility in matching local parts of the model especially in non-stationary cases. In this work we show how MOO improves the match quality of a non-stationary geostatistical model of a deltaic reservoir. Ensemble of multiple history match models achieved with MOO feature of better quality local matches. . Complex reservoirs descriptions with non-stationary characteristics are hard to match due to their high intrinsic heterogeneity and uncertainty associated with non-stationary description. Direct sequential simulation with local anisotropy correction (DSS-LA) provides a way to account for large scale trends, which are subject to uncertainty. The implementation of local anisotropy tackles the problem of non-stationary of the geostatistical model by imposing a trend in spatial correlation structure. The anisotropy change follows the trend in spatial correlation range and orientation across the reservoir model. While the uncertainty in the trend and spatial correlation is resolved through history matching using multi-objective optimisation. The proposed adaptive stochastic sampling framework integrates DSS-LA with the multi-objective history matching. Multiple optima matched models of porosity and permeability were obtained allowing the uncertainty assessment of the anisotropy model parameters.