On the stochastic response surface methodology for the determination of the development plan of an oil & gas field

Abstract

The economical performance of an oilfield operation is uncertain and highly influenced by strategic and operational decisions variables such as well placement, scheduling and control. Based on numerically intensive reservoir simulators, the evaluation of an extensive list of possible decisions across all possible realizations becomes computationally intractable and additional mathematical techniques are required. A common approach to dealing with this problem is the Response Surface Methodology (RSM) coupled with Design of Experiments (DoE) and sampling techniques. Existing approaches to construct surrogates depend on specific statistical/risk measures such as expected value and standard deviation. For example, in order to construct a surrogate for the standard deviation of NPV, one would compute the standard deviation associated with the simulation results over the selected geological realizations for each candidate production strategy and then fit a mathematical model to it. In this case, the idiosyncratic response of each geological realization with respect to the production strategy is lost, which may lead to a bad risk assessment and, consequently an inappropriate decision making process. In this paper, we propose Stochastic Response Surface Methodology (SRSM) to enhance the decision-making process over the determination of oil & gas production strategies while properly taking into consideration geological uncertainty. The SRSM does not depend on any pre-defined risk measure providing the necessary flexibility to evaluate the intrinsic risk-return trade-off associated with the economical performance of the reservoir. Our approach is based on the construction of surrogates for each geological realization selected by sampling procedure. We argue that constructing a different surrogate for each selected realization captures the idiosyncratic behavior of each representative geological setting and provides the flexibility of choosing any set of risk measures after the surrogate construction has been done. Based on the Brugge field, an SPE benchmark case study, we provide a numerical example to illustrate our methodology. Copyright 2013, Society of Petroleum Engineers.