Integration of Well-Test Pressure Data Into Heterogeneous Geological Reservoir Models

This paper presents the application of the ensemble Kalman filter (EnKF) method to the integration of well-test data into heterogeneous reservoir models generated from geological and geophysical data. EnKF does not require computing the gradient of an objective function and, hence, can be applied easily with any reservoir simulator, and more importantly, it is far more efficient than a gradient-based history-matching procedure when the forward model is represented by a reservoir simulator. In the procedure for integrating pressure-transient data considered here, the static geological/geophysical data are assumed to be encapsulated in a multivariate probability-density function (pdf) characterized by a prior mean and covariance for the joint distribution of the porosity and permeability fields. Because the prior mean of the property fields obtained from the core and log data can sometimes be erroneous, a partially doubly stochastic model is applied to account for the uncertainty of the prior mean. In the doubly stochastic model, a correction to the prior mean is adjusted together with the heterogeneous field during history matching. The method is tested with synthetic heterogeneous single-layer and two-layer reservoirs. Excellent data matches are obtained with EnKF in a small fraction of the time that would be required for a gradient-based history-matching process, and the observed data fall within the uncertainty bounds of the ensemble data predictions. In the layered-reservoir case, the uncertainty in rock-property fields is reduced further by integration of production-log data (layer flow rates). We show that problems of statistical inconsistency and poor data matches that are sometimes encountered when matching production data with EnKF do not occur when matching pressure data with the EnKF implementation used here. This undoubtedly occurs because the dynamical system (reservoir-simulator equations) is much more nearly linear for the single-phase-flow problems considered here than for multiphase-flow cases.