Quantification of uncertainty for fluid flow in heterogeneous petroleum reservoirs

Detailed description of the heterogeneity of oil/gas reservoirs is needed t o make performance predictions of oil/gas recovery. However, only limited m easurements at a few locations are usually available, This combination of s ignificant spatial heterogeneity with incomplete information about it leads to uncertainty about the values of reservoir properties and thus, to uncer tainty in estimates of production potential. The theory of stochastic proce sses provides a natural method for evaluating these uncertainties. In this study, we present a stochastic analysis of transient, single phase flow in heterogeneous reservoirs. We derive general equations governing the statist ical moments of flow quantities by perturbation expansions. These moments c an be used to construct confidence intervals for the flow quantities (e.g., pressure and flow rate). The moment equations are deterministic and can be solved numerically with existing solvers. The proposed moment equation app roach has certain advantages over the commonly used Monte Carlo approach. ( C) 1999 Elsevier Science B.V. All rights reserved.