Factorial Design Analysis of Wet-Combustion Drive
Authors: Sawyer D.N. , Cobb W.M. , Stalkup F.I. , Braun P.H. 
Published: December 2007

Abstract
This paper illustrates the application of a statistical experimental design technique (factorial design) to the study of a computer model of a physical process (the wet-combustion drive). physical process (the wet-combustion drive). Factorial design has been used successfully for many years in experimental work to allow investigators to study systematically and efficiently the interactions of important variables and their effects on physical processes. It can also be applied to great advantage processes. It can also be applied to great advantage to computer models of physical processes. The mathematical model in this illustration was programmed to simulate the wet-combustion process programmed to simulate the wet-combustion process in a previously waterflooded confined five-spot. The model couples basic energy and mass balance equations to approximate heat and fluid-flow phenomena. Application of the factorial design phenomena. Application of the factorial design technique to this computer model has allowed us to study individually and collectively, in a relatively short time, the effects that nine important variables exert on the economics of this process. These nine variables are measures of time, reservoir pressure, heat loss, oil burned as fuel, waterflooded residual oil, steam front sweep, oil bank sweep, air co st, and oil price. The final result is a simple equation containing these variables that can be used by the reservoir analyst quickly to screen reservoirs as candidates for the wet-combustion process and perform a sensitivity analysis to determine how perform a sensitivity analysis to determine how uncertainties in the variables will affect the economics.

Introduction
Since it is extremely difficult, if not impossible in most cases, to simulate reservoir performance in the laboratory, the oil production industry has been in the forefront of developing mathematical models of various recovery processes. As the models become more sophisticated, the computer run time per case -- and hence the cost of simulation - increases rapidly. Since it is desirable to minimize the number of computer runs, we very seldom simulate every field or make a completely general study of how the variables in our computer model (and their interactions) affect the process. The prohibitive cost of screening all fields with the computer simulator and then performing a complete sensitivity analysis involving a large number of variables often forces us to arbitrarily limit the scope of our study. For example we might first screen reservoirs by limiting our simulator runs tothose two or three fields in which we own the largest working interestthose that constitute our major sources of production, andthose that will very soon be production, andthose that will very soon be depleted by primary recovery or by waterflooding.
The simulation is for the best-estimate set of conditions for each field. After picking the best prospects, we may run a sensitivity analysis, prospects, we may run a sensitivity analysis, possibly by choosing a few of the variables possibly by choosing a few of the variables considered to be most important and changing them, one variable at a time, about the best-estimate conditions. Factorial design is a statistical technique developed m assist experimentalists in dealing with some of the same problems faced by the users of reservoir simulators - namely, how to study systematically and efficiently the effects of a large number of variables on a complicated process and how to reduce the results to a reasonably simplified form. To our knowledge, factorial design has been used little, if at all, in reservoir analysis. We believe it can be valuable in reservoir simulation to obtain a simplified equation that can be used to screen reservoirs rapidly and to perform sensitivity analysis. The concepts and applications of factorial design and its variations, along with details of the calculations, are found in abundance in the literature and thus will not be presented in great detail here. Refs. 1 and 2 are particularly recommended for details on calculations Ref. 3 through 7 are recommended as practical examples of the use of the technique and as general reviews of As application. Likewise, the concepts of the wet-combustion process are well discussed in the literature. Details of our particular mathematical model (computer simulator) of the wet-combustion process can be found in Appendix A. In particular, process can be found in Appendix A. In particular, we will discuss only those details of factorial design and of the computer model that point out major advantages and major limitations of each.
SPEJ
P. 25