Combined mechanistic and machine learning method for construction of oil reservoir permeability map consistent with well test measurements

Abstract

We introduce a novel method for estimating the spatial distribution of absolute permeability in oil reservoirs, consistent with well logging and well test measurements. The primary objective is to create a permeability map, incorporating the well test interpretation results and achieving hydrodynamic similarity to the actual permeability distribution around each well. This enhancement aims to improve the accuracy of reservoir modeling outcomes in reproducing real data. We utilize Nadaraya-Watson kernel regression to parameterize the two-dimensional spatial distribution of rock permeability. The kernel regression parameters are optimized by minimizing the discrepancies between actual and predicted values of permeability at well locations, the integral permeability of the reservoir domain around each well, and skin factors. This inverse optimization problem is addressed by repeatedly solving forward problems, where an artificial neural network (ANN) predicts the integral permeability of the formation surrounding a well and skin factor. The ANN is trained on a physics-based dataset generated through a synthetic well test procedure, which includes the numerical modeling of the bottomhole pressure decline curve in a reservoir simulator and its interpretation using a semi-analytical reservoir model. The proposed method is tested on the “Egg Model”, a synthetic reservoir with significant heterogeneity due to highly permeable channels. The permeability map created by our approach demonstrates hydrodynamic similarity to the original map. Numerical reservoir simulations, corresponding to the constructed and original permeability maps, yield comparable pore pressure and water saturation distributions at the end of the simulation period. Additionally, we observe a notable match in flow rates and total volumes of produced oil, water, and injected water between simulations. The developed approach outperforms kriging in terms of numerical reservoir modeling outcomes. This research advances existing geostatistical interpolation techniques by fusing well logging and well test data to build the reservoir permeability map through an optimization framework coupled with machine learning. Unlike traditional variogram-based geostatistical simulation algorithms, our method provides a permeability distribution that is hydrodynamically similar to the actual one, enhancing initial guess in the history matching process. The novel incorporation of well test interpretation results into the permeability map represents a significant improvement over existing methods, offering an innovative approach that can benefit the petroleum industry. We also provide recommendations for further developing the proposed algorithm to account for geological realism.