Designing Better Decisions

Abstract

Abstract The computer may be considered a laboratory and experiments performed on the computer (like running ECLIPSE) may be designed and analyzed in much the same way as non-computer experiments. Experimental design methods replace traditional sensitivity studies where one input variable is varied at the time. The basic idea is to vary several input variables simultaneously and intelligently. Damsleth, Hage and Volden demonstrate that the number of simulations may be reduced 30-40% without loosing information. Based on the output from ECLIPSE a relation between the response variable (‘Production after 4 years’ in our example) and the input variables (Lobes, STOOIP,…) is estimated. This relation is used as a surrogate simulator: The values of the input variables are sampled from assigned probability distributions to produce a large number of Monte Carlo simulated values for the response variable. We extend and discuss the results of the mentioned paper. In particular we investigate the impact of dependence between the input variables. Moreover, the relevance of Geostatistical methods (kriging) are documented. By modeling dependence between different computer runs, the precision of predictions are significantly proved. The methods are demonstrated on the case study discussed in (1). 1 Introduction: Description of the Problem Reservoir simulations have a profound effect on important decisions regarding evaluation and planning of reservoir development. Obviously, it is important to design - and analyze reservoir simulations properly. The computer may be considered a laboratory and the experiments performed on the computer (running ECLIPSE is but one example) can be designed and analyzed in much the same way as non-computer experiments. Basically, the theory of experimental design was developed and applied in agriculture in the 1920's. Since 1984-85 ‘computer experiments’ denote a branch of statistics, see Sacks et. al. The application of experimental design in petroleum is convincingly demonstrated in Damsleth, Hage and Volden by means of a case study. The present paper extends on the aforementioned paper in several ways; mainly by focusing on methods. To compare results and methods we use the same data set. The general background and motivation is provided in the mentioned paper. A computer experiment is performed simply by assigning values to input variables x1, x2, (like STOOIP, Lobes,…) and running a computer program (like ECLIPSE) to provide a value for the response variable y (like Production after 4 years or Net Present Value). The relation between the response variable and the input variables is estimated based on the data. This relation may be used as a surrogate simulator simply by assigning probability distributions to the input variables and performing Monte Carlo simulations. Experimental design methods replace traditional sensitivity studies where one input variable is varied at the time. P. 143^