Optimizing Reservoir Performance Under Uncertainty with Application to Well Location

Abstract

Abstract Stochastic parameters representing geological uncertainties in reservoir modeling may be classified in 2 types:Continuous stochastic variables (e.g., degree of communication through a fault); andDiscrete stochastic variables representing different geological interpretations (e.g., same/different channel observed in different wells) each with a given probability. A method for optimizing reservoir performance is presented, which may take into account both these types of uncertainties in a consistent and simple way by finding values of reservoir management variables that optimize the expected performance over the population of possible reservoirs. The method is based on response surfaces and experimental design and is implemented in a user-friendly computer program which may be used together with any reservoir simulator or analytical flow model. In this paper, the method is illustrated through 3 examples of optimizing well locations under uncertainty. Introduction The optimal field development strategy depends on reservoir geometry and petrophysical parameters. Often there is considerable uncertainty in these parameters, and this should be accounted for in the optimization. We present a method for incorporating uncertainty via the probability distribution of input parameters or by the use of several realizations from a stochastic model. The method is implemented in a user friendly computer program, Decision, and may in principle be used to optimize any reservoir response variable (or a combination of variables) with respect to any reservoir management parameter, such as well locations, allocation of well rates, etc. The number of simulations needed is reduced using multiple regression and kriging together with methods for experimental design. Decision may also be used to perform uncertainty analysis without optimization by running Monte Carlo simulations on reservoir response surfaces generated as functions of stochastic variables (see Refs. 1 through 3). In this paper, the method is illustrated through 3 examples of optimizing well locations under uncertainty. One of the examples is a synthetic model with uncertainties related to the location and transmissibility of small, sub-seismic faults, while the other two are from two real North Sea fluvial reservoirs with uncertainties related to channel deposition. One example uses a large number of reservoir realizations coupled with a simple analytical flow model, while the other reservoir is modelled with a full dynamic reservoir simulator using 8 reservoir realizations. Well locations corresponding to maximum expected production as well as locations that minimizes the risk are considered. P. 67