Abstract

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, first-order 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.

Introduction

Reservoir uncertainty analysis seems to be important to achieving good reservoir management. Reservoir simulation studies play a significant role in the evaluation of different scenarios (i.e., geological or reservoir description) that affect the production forecast and the final oil recovery. These scenarios are the manifestation of the lack of information on or uncertainty about reservoir features. However, evaluating uncertainty involves effort and this is simply unjustifiable for many projects. Therefore, a practical procedure must reduce the effort in evaluating the uncertainty and yet retain a satis factory accuracy.

The development of a method that can model and quantify uncertainty in reservoir simulation in an efficient and practical way is clearly needed. In this paper, we investigate a variety of approaches—scaling analysis, first-order and second-order analyses, experimental design, and response surface analysis—to estimate the uncertainty in a recovery prediction. These procedures are measured against experimental-design simulations and the traditional Monte Carlo procedure to compare their efficiency.

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