Probabilistic history matching with the capacitance–resistance model in waterfloods: A precursor to numerical modeling

Abstract Several equally probable sets of uncertain reservoir parameters can normally match a production history. Such equiprobable history-matched solutions (EPHMS) are a way to estimate the uncertainty in hydrocarbon-recovery predictions. In most cases, time and resource limitations permit evaluation of only few of the EPHMS, thereby reducing reliability of predictions of numerical models. As a precursor to comprehensive numerical simulations in a probabilistic frame, we suggest the use of capacitance–resistance model or CRM. In CRM only injection and production rates are needed. The CRM is a fast analytic tool for history matching and optimizing waterfloods. In this study, we used CRM and a Buckley–Leverett-based fractional-flow model to rapidly generate many EPHMS. The EPHMS represent a unique combination of major reservoir variables, such as residual saturations, endpoint mobility ratio, oil and water in-place volumes, and recoverable oil. We used production data from two matured waterfloods and a synthetic field (Synfield) to evaluate the EPHMS. For most cases, one thousand EPHMS and the consequent cumulative distribution functions (CDFs) for several uncertain variables, including recoverable oil, were developed. We compared the CDFs obtained from EPHMS to that of 200 finite-difference simulations performed on the Synfield by changing porosity and residual saturations. EPHMS mimicked the same uncertain range of production forecasts used earlier in the finite-difference model. This approach attested to the goodness of CRM solutions and its ability to quantify reservoir uncertainty. Two field examples illustrated applications of the proposed approach at the field and pattern levels, and provided clues about the remaining oil and its monetary value.

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