Method for Automatic History Matching of Reservoir Simulation Models
Authors: Solorzano Luzbel Napoleon , Arredondo S.E. , Sergio Enrique 
Published: December 2007

This paper was prepared for the 48th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Las Vegas, Nev., Sept. 30-Oct. 3, 1973. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
The best methods published in the literature for automatic adjustment of reservoir simulation models to match field performance cannot be efficiently applied to reservoirs that include a large number of wells and/or a large number of pressure measurements in each well. As the size of the reservoir is increased, the number of zones and the number of errors are increased considerably so that adjustments by linear programming techniques becomes more and more time consuming.
In this paper, a method is presented that requires several random simulation runs, as proposed by Coats et al. and is applicable to proposed by Coats et al. and is applicable to large reservoirs. Furthermore, it offers the following advantages:it does not require a previous zonation of the parameters adjusted,it includes standardization of matrices of differences between calculated and observed values of the control variables as well as judicious weighting of the errors,it considers a nonlinear objective function andfor minimizing the objective function, a direct search method is used that hardly requires memory or computer time.
The proposed method has been applied to constructed and actual gas reservoirs where pressure was used as control variable. Also, pressure was used as control variable. Also, it was applied to a constructed two-dimensional three-phase reservoir where pressure and GOR were used as control variables. In all cases, very good agreement between actual and calculated values was obtained for porosity and permeability, the parameters considered in the permeability, the parameters considered in the matching process.

Introduction
Prediction of the behavior of an oil reservoir by numerical simulation is reliable only if the mathematical model reproduces the field-observed behavior. To accomplish this, the necessary adjustments should be made so that the model matches the production history. This phase of the simulation process is known as the match period.
When the matching process is not carried out within a reasonable period of time, the simulation costs may become prohibitively high. Hence, the necessity of substituting the usual procedure of trial and error for a more rapid procedure of trial and error for a more rapid and economic one.
Several investigators have developed methods for automating the matching process. Some of them make use of regression techniques in conjunction with the method of trial and error; others solve directly the flow equations, taking the petrophysical parameters as the unknowns.