Validating the Use of Experimental-Design Techniques in Exploratory Evaluations
Authors: Denney Dennis 
Published: February 2015

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 107441, "Validating the Use of Experimental-Design Techniques in Exploratory Evaluations," by T. Amorim, SPE, and B. Moczydlower, SPE, Petrobras, prepared for the 2007 SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, 15–18 April.
This work presents a validation of the use of experimental-design techniques in exploratory evaluations. The results indicated that the quadratic technique showed the best cost/benefit ratio and suggested that the proposed methodology generates reliable results in most cases. The most influential parameter on the quality of the results was the range of possible results emulated by the proxy model. The quality of the risk analysis performed with these experimental-design techniques was influenced by the ability of the proxy model to emulate the flow-simulator response. The efficiency of different experimental-design techniques in different reservoirs was analyzed, and the reliability and limitations of this evaluation methodology were assessed.

Introduction
When evaluating exploratory prospects, a large number of variables are considered, each with a certain degree of uncertainty. Therefore, probabilistic approaches have long been used to quantify the effects of those uncertainties in the economic evaluation of these prospects.
The authors recommend use of flow simulators together with experimental-design techniques and response-surface methods to obtain a better understanding of the effect of dynamic uncertainties in the prediction of the cumulative production and the production profile. The experimental-design technique was used to plan a certain number of flow simulations and attempt to build a response surface (i.e., a proxy model of the objective function being studied). Use of this proxy model made it possible to run thousands of simulations quickly and perform risk analysis with the Monte Carlo method.
The quality of the risk analysis will be influenced greatly by the ability of the proxy model to emulate the flow-simulator's response. Three cases were studied: a nonassociated-gas reservoir and two oil reservoirs. The 10,000 results of the proxy model used to make the risk analysis were compared with 10,000 flow simulations. Thereby, it was possible to compare the efficiency of different experimental-design techniques and to assess the reliability and the limitations of the evaluation methodology proposed by the authors.

Methodology
One limitation in this process is that it can handle only parameters that vary continuously. Therefore, parameters that can assume only discrete values [e.g., pressure/volume/temperature (PVT) tables] were not used. The authors used commercial software to make a risk analysis of the proposed models. First, this software planned a certain number of simulations with experimental-design techniques. After those simulations were completed, it gathered information from the simulations (e.g., 20-years' cumulative production) and generated a proxy model of the objective function being studied with the response-surface method. Then the Monte Carlo method was used on this proxy model to develop a risk analysis. To enrich this study, two designs were used: quadratic and full.