Louis Mattar

Decline Curve Analysis for Naturally Fractured Gas Reservoirs: A Study on the Applicability of "Pseudo-time" and "Material Balance Pseudo-time"

This paper was selected for presentation by an IPTC Programme Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the International Petroleum Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the International Petroleum Technology Conference, its officers, or members. Papers presented at IPTC are subject to publication review by Sponsor Society Committees of IPTC. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the International Petroleum Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, IPTC, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract Robust techniques for analysis of production data of single porosity gas reservoirs have been developed and widely used for many years. These methods range from the traditional Arps decline method to modern type-curve matching. The more recent techniques are based on the use of pseudo-time for linearization of gas-flow equations, and material balance time to account for variable operating conditions. Whereas the governing equation for gas flow in a single porosity reservoir has been successfully linearized using pseudo-time evaluated at average reservoir pressure, the linearization of the governing equation in a double porosity reservoir is problematic due to pressure differences between the matrix and fracture systems. Similarly, the suitability of the material balance time concept, which has been successfully applied to a single porosity gas reservoir, has not been demonstrated for a double porosity gas reservoir. The purpose of this work is to suggest an appropriate pseudo-time and material-balance time functions when gas is produced from a naturally fractured gas reservoir. For this purpose, the resulting equations describing the matrix-fracture flow are cast in a form similar to those proposed by Warren and Root. These are then linearized, using appropriately-defined pseudo- time and material-balance pseudo-time functions. The results are compared against those of a commercial numerical simulator for two production scenarios, including constant rate and constant pressure production over some range of reservoir parameters. The results show that pseudo-time and material balance pseudo-time allow the accurate use of traditional double-porosity type-curves for naturally fractured gas reservoirs provided that the gas properties are evaluated at average reservoir pressure as determined from the material balance equation for double porosity systems.