Application of Inverse Simulation to A Complex Multireservoir System
Authors: Boberg T.C. , Woods E.G. , McDonald W.J. , Stone H.L. , Abib Osmar 
Published: December 2007

Boberg, T.C., SPE-AIME, Esso Production Research Co. Woods, E.G., SPE-AIME, Esso Production Research Co. McDonald Jr., W.J., SPE-AIME, Esso Production Research Co. Stone, H.L., SPE-AIME, Esso Production Research Co. Abib, Osmar, Arabian American Oil Co.
A technique for automatically matching pressure history has been applied successfully to a complex multireservoir field in Saudi Arabia. The technique, called inverse reservoir simulation, obtained an excellent match for all wells in the field by computer-guided adjustment of reservoir variables (permeability and porosity) specified by the engineers.

Introduction
History matching to determine reservoir description often is the most time-consuming and costly part of a reservoir study. Depending on the complexity of the situation, from 20 to 40 complete history simulations may be required to achieve an acceptable match of pressure performance. This paper describes the history-matching phase of a large Mid-East reservoir study in which nonlinear regression techniques were used. To study the effectiveness of these newly developed techniques, manual adjustments of reservoir parameters were avoided. parameters were avoided. Numerous automatic history-matching techniques have been described in the literature. The procedure used here was similar to that described by Thomas et al. in that it employs a modified Gauss-Newton least-squares technique to minimize the sum of the squared differences between observed and calculated pressure data. The major difference from the method pressure data. The major difference from the method of Thomas et al. is that a rotational discrimination technique is employed to improve stability when null-effect variables are encountered. This procedure is described by Law and Farris.Calculated pressures were derived from numerical models of the combined reservoir-aquifer system. During the course of this investigation, two numerical models were used to simulate reservoir behavior. Mathematical details of the numerical models employed are given in Refs. 5 and 6. The major advantages of the techniques employed in this study are1. Excellent stability of the nonlinear regressionprocedure, even when constrained variablesand variables having little effect on thepressure solution were manipulated.2. Use of techniques to permit a largenon-core-contained reservoir simulationproblem to be solved efficiently with goodstability.The first advantage was most important. At the outset of the study, a reasonable amount of knowledge of the reservoir system already existed. Core analysis provided a basic average zonation and an areal provided a basic average zonation and an areal variation for porosity and permeability. There had been previous reservoir studies, although they had the previous reservoir studies, although they had the disadvantage of yielding limited pressure history data. Therefore, it was important to constrain certain parameters such as porosity within reasonable limits. parameters such as porosity within reasonable limits. Less reliable were the initial estimates of permeability, and those were not constrained during the investigation. The situation was so complex that frequently it was not apparent which variables would have little effect on the solution. Ordinary Gauss-Newton procedure is susceptible to divergence when variables having little effect on the pressure solution are chosen; the procedure used here pressure solution are chosen; the procedure used here circumvents that problem.
JPT
P. 801