A Method for Determining Reservoir Parameters From Early Drawdown Data

Abstract

This paper was prepared for presentation at the 47th Annual Fall Meeting of the Society of Petroleum Engineers held in San Antonio, Tex., Oct. 8–11, 1972. 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 who the paper is presented. Publication elsewhere after publication in the JOURNAL 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. 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 Least Squares Differential Algorithm (LSDA) automatically determining reservoir description parameters in an optimal manner is described. in contrast to current reservoir history matching schemes, LSDA provides for: Pseudo-linearization of the relationships between Pseudo-linearization of the relationships between performance data and reservoir description performance data and reservoir description parameters; Description of the system transfer parameters; Description of the system transfer function as a second order polynomial trend; and Least squares reduction as the criterion for optimizing the description parameters. These provisions eliminate the problems associated with provisions eliminate the problems associated with applying linear approximations to non-linear systems and analyzing error-corrupted data. LSDA is tested using a mathematical model of a single well, radial, gas reservoir which provides for the inclusion of nondarcy and provides for the inclusion of nondarcy and Klinkenberg effects as well as the properties of real gases. The results of LSDA are compared with those obtained by the Least Squares Linear Programing (LSLP) method. Programing (LSLP) method Introduction Estimation of future reservoir performance from past reservoir history is usually accomplished by employing an appropriate mathematical model to match past history and, having done so within acceptable limits, to compute future performance. The matching procedure is the critical performance. The matching procedure is the critical phase of this process and requires the phase of this process and requires the determination of an optimal (and hopefully unique) set of reservoir parameters which enables the mathematical model to successfully describe the reservoir performance data during the match period. The performance data during the match period. The quest for a better procedure for automatically determining this optimal set of reservoir description parameters is the basis for this paper. Green, et al., present a good discussion of the various methods for using computer modeling to predict reservoir performance. Coats, et al., have developed a method for automatically determining the optimal reservoir description parameters using Least Squares Linear Programming parameters using Least Squares Linear Programming (LSLP). LSLP assumes that the performance data and the description parameters are linearly related (although the authors of LSLP pointed out that transforming performance data and description parameters to more nearly assure this assumption parameters to more nearly assure this assumption would probably improve the method's ability to determine optimal description parameters). LSLP also uses a first order trend to describe the system transfer function and makes no claim as to its abilities to handle error-corrupted data.