Multiple-Rate Analysis for Pressure-Buildup Tests in Reservoirs With Tectonic, Regional, and Contractional Natural Fractures

Abstract

Summary. Approximate solutions of radial flow theory are presented for pressure-buildup analysis in naturally fractured reservoirs with tectonic, pressure-buildup analysis in naturally fractured reservoirs with tectonic, regional, and contractional fractures. The solutions allow handling of variable rates before shut-in, as well as unsteady-state interporosity flow. Although approximations, these solutions are apparently satisfactory for most cases of practical interest. Introduction Approximate solutions of radial-flow problems are presented for analyzing pressure-buildup tests in presented for analyzing pressure-buildup tests in reservoirs with tectonic, regional, and contractional natural fractures when there are variations in flow rates he fore shut-in and unsteady-state interporosity flow. The conclusion is reached that a conventional plot of Pws vs. on Cartesian coordinates should result in two parallel straight lines with a transition period that depends on the shape of the matrix blocks. The methods, illustrated with a step-by-step example, allow calculation of pi or p*, transmissibility, storativity ratio, matrix storage, fracture storage, average distance between fractures, fracture porosity, fracture thickness, skin, and radius of investigation. Values of transmissibility calculated by conventional constant-rate methods in a variable-rate case could be considerably in error, especially in the case of naturally fractured reservoirs. The methods presented in this paper help obtain more accurate transmissibilities. Furthermore, the equations can he easily used for matching real pressure data in new or old wells. State of the Art Naturally fractured reservoirs have been studied intensively during the last 10 years in the geologic and engineering fields. Transient-pressure analysis has received particular attention. Barenblatt and Zheltov assumed pseudosteady-state interporosity flow in a model made of orthogonal, equally spaced fractures. Warren and Root used the same assumption and concluded that a conventional semilog plot of pressure vs. time should result in two parallel straight lines with a transition period in between. The separation between the two parallel straight lines allowed calculation of the storativity ratio-i.e., the fraction of the total storage within the fracture system. Kazemi used a numerical model of a finite reservoir with a horizontal fracture under the assumption of unsteady-state interporosity flow and substantiated Warren and Root's conclusion with respect to the two parallel straight lines. The transition period, however, was different because of the unsteady-state rather than pseudosteady-state interporosity flow assumption. A breakthrough in the analysis of naturally fractured reservoirs was provided by de Swaan, who developed a diffusivity equation and analytic solutions to handle unsteady-state interporosity flow. This method, however, could not analyze the transition period between the two parallel straight lines. Najurieta developed approximate parallel straight lines. Najurieta developed approximate analytic solutions of de Swaan's radial diffusivity equation that could handle the transition period, as well as the first and last straight lines. More recently, Streltsova used a gradient-flow model and indicated that the transition period yielded a straight line with a slope equal to one-half the slope of the early and late straight lines. Serra et al. reached the same conclusion using a stratum model for the cases in which the storativity ratio was smaller than 0.0099. Various type curves have been developed to analyze naturally fractured reservoirs with unsteady-state and pseudosteady-state interporosity flow. These curves, pseudosteady-state interporosity flow. These curves, including the pressure derivative, are valuable but must be used carefully to avoid potential errors resulting from multiple matches. This paper presents equations for evaluation of build-up tests in reservoirs with tectonic, regional, and contractional fractures when there are variations in flow rates before shut-in. This problem has not been treated in previous petroleum engineering literature. Geologic Models A classification of naturally occurring fractures has been presented by Stearns and Friedman an Nelson. presented by Stearns and Friedman an Nelson. SPEFE P. 253