Using the EnKF for Assisted History Matching of a North Sea Reservoir Model

Abstract

Abstract The ensemble Kalman filter (EnKF) has been used for history matching a simulation model of a North Sea reservoir. Parameters such as initial fluid contacts, vertical transmissivity multipliers and fault transmissivity multipliers have been estimated as well as 3D fields of porosity and permeability. It is shown that for several of the parameters a large initial uncertainty is reduced to an acceptable level by the assimilation of well-log measurements and production rates of oil, gas and water. The result is an ensemble of history matched realizations which can be used to predict the uncertainty in future production. It is also shown that the formulation used in the EnKF reduces a nonlinear minimization problem in a huge parameter space, involving the minimization of an objective function with multiple local minima, to a statistical minimization problem in the ensemble space. Thus, by searching for the mean rather than the mode of the posterior pdf, the method avoids getting trapped in local minima and is thus promising for history matching reservoir simulation models. Furthermore, the EnKF provides an ideal setting for operational reservoir monitoring and prediction, including proper representation and prediction of uncertainty. Introduction Recently, there has been a growing interest in more mathematical and statistical methods for history matching. These involve both brute force direct minimization techniques and gradient methods based on the use of adjoints. Common for these is that they have all considered a pure parameter estimation problem. This differs from the combined parameter and state estimation problem which is considered when using the Ensemble Kalman Filter (EnKF) introduced by Evensen (1994, 2006). The EnKF has recently been taken into use with simulation models for oil and gas reservoirs, with the purpose of estimating poorly known parameters and to improve the predictive capability of the models. Traditional methods for assisted history matching minimize a cost function which measures the difference between simulated and observed production rates. The methods use the following loop:The flow simulator is run for the complete production period;the cost function is evaluated based on the difference between historical and simulated production rates;the static parameters are updated, and the and the simulator is rerun. These methods solve a so called strong constraint formulation where the model errors are assumed to be accounted for by the set of parameters included in the cost function. The search for the solution is conducted in a space with dimension equal to the number of parameters and the problem becomes highly nonlinear leading to a cost function which typically will contain many local minima. This effectively limits the number of parameters which can be included in the optimization. Consequently the parameterization used becomes critical and the major uncertainty in the model must be represented by as few parameters as possible (Evensen, 2006).