A common pitfall in history matching is to falsely generalize the learning from local data to the entire field, which can lead to radical over-estimation of uncertainty reduction and bad reservoir management decisions. This problem is referred to as the local-global problem and in this paper a methodology is proposed to quantify and correct for the error arise from this problem.
Most performance metrics in an oil field, such as estimated ultimate recovery (EUR), are field-level ob jective functions that depend on properties (e.g., porosity) over the entire field. On the other hand, most measurement data (e.g., BHP) are sensitive only to a local area around the wells and are thus susceptible to local variation of geological properties. Calibrating field-level objective functions and multipliers of global properties (e.g., porosity) to local well data over-estimates the reduction of global uncertainties. In this paper, we derived the formula to quantify error in the calibrated posterior distribution (S-Curve) resulted from the local-global problem, as well as a correction factor to recover the true posterior S-Curve.
Through theoretical derivation, it is shown that the model error arise from the local-global problem is dependent on the magnitude of the global and local variation of the uncertain properties (e.g., porosity). The larger the local variation relative to the global variation, the larger the error is in the estimated posterior S-Curve. The error also depends on the variogram of the local variation, and the detection range of the data. The error is larger for case with long variogram for the local variation and short data detection range. In addition, this model error can be highly correlated for different measurement data points even when the measurement error for these data were independent. To address this local-global modeling error, a series of analytical and empirical formula is proposed, which has successfully corrected the error and greatly improve the posterior S-Curve for a series of cases.
To the best of our knowledge, this is the first time the error from the local-global problem is quantified and corrected. The methodology proposed could help improve the reliability of the result from probabilistic history matching.