DIRECT COMPUTATION OF STOCHASTIC FLOW IN RESERVOIRS WITH UNCERTAIN PARAMETERS

A direct method is presented for determining the uncertainty in reserv oir pressure, flow, and net present value (NPV) using the time-depende nt, one phase, two- or three-dimensional equations of flow through a p orous medium. The uncertainty in the solution is modelled as a probabi lity distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an ex pansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input pa rameters. Hierarchical equations that define approximations to the mea n solution at each point and to the field covariance of the pressure a re developed and solved numerically. The procedure is then used to fin d the statistics of the flow and the risked value of the field, define d by the NPV, for a given development scenario. This method involves o nly one (albeit complicated) solution of the equations and contrasts w ith the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems mo delled by linear or nonlinear partial differential equations with unce rtain data. (C) 1997 Academic Press.