A Singular Evolutive Interpolated Kalman Filter for Rapid Uncertainty Quantification

摘要

Inherent data and model uncertainties render the history- matching inverse problem extremely non-unique. Therefore, a reliable uncertainty quantification framework for predicting reservoir dynamic performance requires multiple reservoir models that match field production data. It has been previously demonstrated that the ensemble Kalman filter technique can be used for this purpose. In this technique, an ensemble of reservoir models is evolved by means of a stochastic nonlinear filtering procedure to agree with the observed production data. An efficient variant of the ensemble Kalman filter, namely, Singular Evolutive Interpolated Kalman Filter (SEIKF) is applied to the multi-model history- matching problem in this work. This novel technique operates in three steps: resampling, forecasting, and assimilation. Unlike the ensemble Kalman filter, where the members of the model ensemble are operated by forecasting and assimilation, in SEIKF, the members of the model ensemble are selected in the main orthogonal directions of a functional space described by an approximation to the error-covariance matrix. This enhanced sampling strategy, embedded into the resampling step, improves the filter stability and delivers rapid convergence. SEIKF is applied to a three-dimensional proof-of-concept waterflooding case where reservoir permeability is calibrated to production data. Accuracy and convergence of history match as well as the uncertainty of dynamic predictions yielded by the final model ensemble are used as criteria to evaluate the performance of SEIKF. The outcome of the proof-of-concept studies quantitatively demonstrates that SEIKF exhibits rapid convergence in the domain of model parameters. In terms of accuracy and uncertainty reduction, SEIKF performs comparable to a conventional ensemble Kalman filter. SEIKF promises a rapid and reliable framework for history matching and naturally lends itself to uncertainty quantification.