It is widely recognized that predictions of hydrocarbon recovery are uncertain. In the area of reservoir engineering, the sources of uncertainty have three major causes: 1) the model, because it is an imperfect representation of reality, 2) geologic parameters, because of a limited sampling in space and/or time, and 3) measurement errors in the experiments performed to determine inputs. Thus, a statistical treatment that recognizes both the lack of knowledge and the uncertainty of the parameters involved in the forecast of reservoir performance is desirable. Current stochastic-modeling approaches (Monte Carlo simulation and geostatistics) require extensive computational effort for realistic problems. There are numerous reasons for this, but the one that seems to present the largest hurdle is that reservoir predictions require a large number of input parameters. The thrust of this work is to find ways to perform uncertainty predictions with fewer parameters.
This paper demonstrates several approaches that quantitatively estimate uncertainty in specific hydrocarbon-recovery predictions. These approaches include scaling, firstorder and second-order analyses, response surface, and the Taguchi and Box-Behnken experimental designs. Numerical reservoir simulations were performed in two hypothetical reservoirs using each of the above methods to estimate uncertainty in oil-recovery efficiency. Results from these techniques are compared to experimental design and Monte Carlo simulations. The combination of scaling and the Box-Behnken experimental design can provide a reasonably accurate uncertainty estimation of hydrocarbon recovery with fewer simulation runs than the Monte Carlo simulation. In addition, we successfully reduced the turnaround time of the Monte Carlo simulation runs by using clusters in parallel of personal computers instead of one computer (e.g., more than 10 times faster with a cluster of 16 PCs).
Experimental design and the use of multiple processors will reduce the computational effort in estimating uncertainty of a hydrocarbon-recovery prediction. This combination would also give rise to the possibility of exploring several existing methods in the design of experiments to lessen the burden of performing numerous large reservoir simulations.