Use of Ensemble Kalman Filter for Bounded Reservoir

The Ensemble Kalman Filter (EnKF) has been used for history matching of the reservoir models. The methodology can be used to estimate the correlation between reservoir properties (permeability, porosity) and reservoir response (pressure, flow rate). Recent studies show that the methodology is promising, however the methodology is novel to reservoir simulation, and further research of the filter is needed for practicing community. The main scope of this paper is to explore the applicability of the EnKF to estimate the reservoir properties in constant rate inner boundary no flow outer boundary reservoir models. The radial flow of the reservoir is modeled using diffusivity flow equation. The analytical solution was derived using Laplace transform, and its inverse was derived using complex residual theorem. The analytical solution is used to develop a nonlinear state space model where the analytical solution is the forward model. In practice, the analytical solution is replaced by the reservoir simulator (numerical solution of flow equation). An EnKF sequential updating is proposed to estimate the reservoir properties based on pressure observations of a well testing experiment. The case study supports the expectation that the methodology is applicable for reservoir simulation environment