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 simula- tors, 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 strate- gies 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 geolog- ical 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.

Accelerating Physics-Based Simulations Using End-to-End Neural Network Proxies: An Application in Oil Reservoir Modeling

“…State of the art techniques can be classified in two categories: 1) reducing the complexity of the PDEs while providing an acceptable loss of prediction accuracy (e.g., reduced order modeling [9] can accelerate the simulations by factors of 10 2 and has been found useful in optimization and control [12], and upscaling which achieves acceleration with coarser reservoir models [6]), and (2) simple polynomial interpolation techniques computing the objective function (e.g. Net Present Value, or NPV) or to characterize the uncertainty [23]. It is important to note that while the latter techniques are fast their accuracy tends to be poor.…”

“…Accelerating reservoir simulations has a wide literature. State of the art techniques can be classified in two categories: (1) reducing the complexity of the PDEs while providing an acceptable loss of prediction accuracy [e.g., reduced order modeling (ROM) (He and Durlofsky, 2015 ) can accelerate the simulations by factors of 10 2 and has been found useful in optimization and control (Jansen and Durlofsky, 2016 ), and upscaling which achieves acceleration with coarser reservoir models (Durlofsky, 2005 )], and (2) simple polynomial interpolation techniques computing the objective function (e.g., Net Present Value, or NPV) or to characterize the uncertainty (Valladao et al, 2013 ). It is important to note that ROM techniques typically target optimization of certain variables, such as well controls, for fixed well locations (in contrast, our task is to accelerate across different sequences of well locations).…”

Assisted history matching using pattern recognition technology

“…Response surface models have been frequently used in petroleum engineering. There are number of articles available in uncertainty analysis of reservoir behavior (Damsleth, Hage and Volden 1992, Friedmann, Chawathe and Larue 2003, Cheong and Gupta 2005, well optimization (Zabalza, et al 2000, Landa and Güyagüler 2003, Valladao, et al 2013, and history matching (Eide, et al 1994, White and Royer 2003, Alessio, Bourdon and Coca 2005, Gupta, et al 2008, Cheng, Dehghani and Billiter 2008, Arwini and Stephen 2011).…”

Profit and Risk Measures in Oil Production Optimization∗∗This research project is financially supported by the Danish Research Council for Technology and Production Sciences. FTP Grant no. 274-06-0284 and the Center for Integrated Operations in the Petroleum Industry at NTNU.

“…This was used in structural engineering problems by Rockafellar and Royset (2010). In the oil community, CV aR α has been used by Valladao et al (2013) as a deviation measure. They used a λ parameter as a weight to find Pareto solutions with different expected profit -profit deviation trade-offs.…”