Abstract
This paper presents a nonlinear optimization technique that automatically varies reservoir parameters to obtain a history match of held parameters to obtain a history match of held performance. The method is based on the classical performance. The method is based on the classical Gauss-Newton least-squares procedure. The range of each parameter is restricted by a box-type constraint and special provisions are included to handle highly nonlinear cases. Any combination of reservoir parameters may be used as the optimization variables and any set or sets of held data may be included in the match.
Several history matches are presented, including examples from previous papers for comparison. In each of these examples, the technique presented here resulted in equivalent history matches in as few or fewer simulation runs.
Introduction
The history matching phase of reservoir simulations usually requires a trial-and-error procedure of adjusting various reservoir parameters procedure of adjusting various reservoir parameters and then calculating field performance. This procedure is continued until an acceptable match procedure is continued until an acceptable match between field and calculated performance has been obtained and can become quite tedious and time consuming, even with a small number of reservoir parameters, because of the interaction between the parameters, because of the interaction between the parameters and calculated performance. parameters and calculated performance. Recently various automatic or semiautomatic history-matching techniques have been introduced. Jacquard and Jain presented a technique based on a version of the method of steepest descent. They did not consider their method to be fully operational, however, due to the lack of experience with convergence. Jahns presented a method based on the Gauss-Newton equation with a stepwise solution for speeding convergence; but his procedure still required a large number of reservoir simulations to proceed to a solution. Coats et al. presented a proceed to a solution. Coats et al. presented a workable automatic history-matching procedure based on least-squares and linear programming. The method presented by Slater and Durrer is based on a gradient method and linear programming. In their paper they mention the difficulty of choosing a step paper they mention the difficulty of choosing a step size for their gradient method, especially for problems involving low values of porosity and problems involving low values of porosity and permeability. They also point out the need for a permeability. They also point out the need for a fairly small range on their reservoir description parameters for highly nonlinear problems. Thus, parameters for highly nonlinear problems. Thus, work in this area to date has resulted either in techniques based on a linear parameter-error dependence or in nonlinear techniques which require a considerable number of simulation runs.
The method presented here is a nonlinear algorithm that will match both linear and nonlinear systems in a reasonable number of simulations.
HISTORY MATCHING
In a reservoir simulation, various performance data for the field, such as well pressures, gas-oil ratios, and water-oil ratios, are used as the basis for the match. During the matching of these performance data certain reservoir and fluid performance data certain reservoir and fluid parameters are assumed to be known while other parameters are assumed to be known while other less reliable data, forming the set (x1, x2...xn), are varied to achieve a match.
The objective of the history-matching procedure presented in this paper is to minimize, in a presented in this paper is to minimize, in a least-squares sense, the error between the set of observed and calculated performance data, Fk(x1, x2... xn).
SPEJ
P. 508
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