ASSISTED HISTORY MATCHING OF A WATERFLOODED RESERVOIR USING EXTENDED AND UNSCENTED KALMAN FILTERS

Petroleum industry has been widely using reservoir simulation to predict the fluid flow in subsurface reservoirs. The challenge to using these simulators is to obtain the input parameters for the reservoir models e.g. porosity and permeability. Once the spatial variability of these parameters is known, a system of nonlinear equations could be solved to predict the flow in the porous media. The challenge in doing so is that these parameters are not known in the whole domain of the reservoir. What is usually known is the production data such as the well bottom‑hole pressures, production and injection rates. Inferring the parameters from the observations would require solving an inverse problem. In this study, a five Spot waterflooding pattern in a two dimensional reservoir has been investigated by applying the two Kalman filtering techniques to estimate the essential parameters needed for the reservoir simulation. Kalman Filters are stochastic minimum mean square error estimation tools that have been widely used in the control theory. The objective of this paper is to prove the applicability, the shortcomings and the advantages of two of the most famous Kalman filters for assisted history matching. Extended Kalman filter relies heavily on the linearization of the complex system of partial differential equations. Unscented Kalman filter generates a set of probable reservoir models and uses the available observations and the covariance matrices to improve their performance and predictability. The results obtained from these methods have been compared to one other in the paper. It was observed that Unscented Kalman filter outperforms extended Kalman Filter owing to the fact that the fluid flow calculations in reservoir is highly non linear and linearization of such a problem can lead to erroneous results. Both methods could become computationally expensive as the size of the model size gets larger.