Validating the Use of Experimental Design Techniques in Exploratory Evaluations

Abstract

This work presents a validation of the use of Experimental Design (ED) techniques in exploratory evaluations. The results generated by a commercial software, which uses ED techniques combined with the Monte Carlo method, have been compared with 10,000 equivalent actual flow simulations. Several oil and gas real reservoirs were studied. The static and dynamic variables were selected from real prospect studies, as well as their respective range of variation. For each case studied, the commercial software planned a small number of flow simulations to run, applying different ED techniques. Based on the simulation results, a proxy model was generated using the Response Surface Method (RSM). Making use of this proxy model, it was possible to quickly simulate 10,000 experiments and to perform statistics calculations with the Monte Carlo method. In order to verify the quality of the proxy, 10,000 simulation files were generated, with the exact same combinations of parameters used in the Monte Carlo method. A script was written to run automatically all the files and to register their results. Besides comparing the statistics generated by these two methodologies, it was possible to compare the actual results of each one of the 10,000 simulations. The results indicate that the quadratic technique is the one with the best cost-benefit ratio and suggest that the proposed methodology generates reliable results in most cases. This reliability decreases when there are complexities in the flow model, such as well and group controls, water and/or gas reinjection, etc. However, results show that the range of possible results to be emulated by the proxy model is the most influential parameter in the quality of the results generated by it. The quality of the risk analysis performed with these ED techniques is obviously influenced by the ability of the proxy model to emulate the flow simulator response. The efficiency of different ED techniques, in different reservoirs, was analyzed and the reliability and limitations of this evaluation methodology has been accessed. Introduction In the evaluation of exploratory prospects in the petroleum industry, one must deal with a large number of variables, each one of them with a certain degree of uncertainty. Therefore, probabilistic approaches have long been used in order to quantify the impact of those uncertainties in the economic evaluation of these prospects. Nowadays, exploration studies have already incorporated an uncertainty analysis in the most influential static variables, but they still tend to translate all the dynamic uncertainties into a single variable (usually the recovery factor). From this point on, simple programs or even electronic spreadsheets are used to generate production profiles, based on the estimated accumulated production. The authors hereby recommend using flow simulators together with experimental design techniques and response surface methods, to have a better understanding of the impact of dynamic uncertainties in the prediction of both the accumulated production and the production profile. The experimental design technique is used to plan a certain number of flow simulations and to try to build a response surface, i.e., a proxy model of the objective-function being studied. With this proxy model, it is possible to run thousands of simulations almost instantaneously and perform a risk analysis using the Monte Carlo method.1,2 The quality of the risk analysis will be greatly influenced by the ability of the proxy model to emulate the flow simulator's response.3 The authors have studied three different cases: a non-associated gas reservoir and two oil reservoirs, and compared the 10,000 results of the proxy model used to make the risk analysis and 10,000 actual flow simulations. By doing that, it is possible to compare the efficiency of different experimental design techniques and to access the reliability and the limitations of the evaluation methodology proposed by the authors.