Critical Evaluation of the Ensemble Kalman Filter for Reservoir Parameter Estimation under Incorrect and Uncertain Prior Models

摘要

depends on the representativeness of the initial ensemble of reservoir properties. The initial ensemble is commonly constructed by assuming a known geological continuity model such as a variogram. However, since geologic continuity models are derived from incomplete data and imperfect modeling assumptions they are subject to uncertainty. Neglecting this important source of uncertainty can lead to systematic errors and questionable estimation results. In this paper, we evaluate the performance of the EnKF under varying levels of uncertainty in the variogram model parameters. We first attempt to directly estimate variogram parameters from flow data and show that the complex and non-unique relation they have with the flow data provides little sensitivity for an effective inversion with the EnKF. We then assess the performance of the EnKF for estimation of gridblock permeability values under uncertain and incorrect initial variogram parameters and show that any bias in specifying variogram parameters tends to persist throughout the EnKF analysis although locally reasonable permeability updates may be obtained near observation points. We consider the uncertainty in the variogram model parameters and account for the full range of structural variability in the initial permeability ensemble. We show that under this assumption the EnKF update results are quite promising. We conclude that, in applying EnKF to realistic problems where the level of prior uncertainty may not be known, it is preferable to overestimate the uncertainty in geologic continuity and initialize the EnKF with a wide range of variability in property description than to overlook the variogram uncertainty at the risk of introducing systematic bias that cannot be corrected by the EnKF updates.