Estimation of Fracture Effective Permeability by Upscaling Using Ensemble Kalman Filter and Streamline Simulation

Abstract

Abstract As naturally fractured reservoirs (NFRs) present a wide range of geological characteristics and complex flow mechanisms between fracture and matrix, reservoir simulation is highly necessary to properly evaluate reservoir performance. Modeling and simulation of NFRs are conducted commonly with two alternative approaches, the dual-porosity model and the discrete fracture model. The single-continuum approach, where fracture systems are represented by effective permeability, is often more effective and flexible for NFRs simulation. In this paper, we present an upscaling approach to estimate the effective permeability for NFRs based on flow calculations. We used the local-global upscaling (LGU) method as the first step to calculate effective permeability for the discrete fracture model. As the second step, the ensemble Kalman filter (EnKF) approach was applied to assimilate an ensemble of the upscaled models to the production history from the reference model. Although the EnKF has been successfully applied in recent years to inversion problems for inferring parameters from the core scale to the reservoir scale, it is difficult to estimate channel-like high permeability parts because the EnKF works well under the assumption of the Gaussian distribution. We demonstrate and confirm accomplishments and limitations of the LGU and EnKF applied to the discrete fracture model. In order to overcome the limitation, we refined the effective permeability distribution with the velocity field that is calculated by a streamline model. We demonstrate two cases describing different types of NFRs for which we could obtain satisfactory upscaling and inversion results. In each case, a reference model was set up initially with a fine grid explicitly including discrete random fractures, and 40 realizations were constructed, upscaled to a coarse grid, and processed by the EnKF. The effective permeability fields updated by the EnKF could match the production history, but the streamline and water saturation distributions did not resemble the those of the reference model. The velocity fields that were obtained from the reference model could refine the upscaled models with and without the EnKF assimilation. For all flow simulation, we used our streamline-based simulation model.