Well Test Analysis of Naturally Fractured Gas Condensate Reservoirs
Authors: Aguilera R. , Ng M.G. 
Published: March 2010

Abstract
Approximate equations are presented for evaluation of naturally fractured gas condensate reservoirs represented by dualporosity models in radial systems. The reader is cautioned that this work is in progress. Additional research will help to corroborate and refine these techniques. The solutions have not been published previously in the petroleum engineering literature.
The solutions are presented for drawdown and buildup tests. The model assumes flow of gas condensate from a tight matrix into permeable natural fractures. The fractures conduct the fluids to the wellbore.
Preliminary work shows that a conventional crossplot of m(p) vs. time on semilogarithmic coordinates results in approximately two parallel straight lines with a separation that is related to the storativity ratio between fractures and matrix. This plot allows determination of key parameters such as absolute permeability, effective permeabilities to oil and gas, skin, storativity ratio (ω), fracture porosity (Φ2), average distance between natural fractures (hm), radius of investigation, and extrapolated pressure (Pi or p*). In addition the method permits generating a liquid saturation profile and a general composition profile around the wellbore at shut-in.

Introduction
Naturally fractured reservoirs have been the object of intensive research during the last few years in the geologic as well as the engineering fields. Transient pressure analysis has received particular attention.
Barenblatt and Zheltov(1), and Warren and Root(2) handled naturally fractured reservoirs by assuming pseudo steady-state (restricted) interporosity flow in a model made out of cubes with spaces in between. Flow toward the wellbore was assumed to be radial via the natural fractures. Their work led to the conclusion that a conventional crossplot of pressure vs. log of time should result in two parallel straight lines with a transition period in between. The separation of the two straight lines allowed calculation of the storativity ratio omega, i.e., the fraction of the total storage within the natural fractures.
Kazemi(3) 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 due to the unsteady rather than pseudo steady-state interporosity flow assumption.
de Swaan(4) developed a diffusivity equation and analytical solutions to handle the first and last straight lines. His method, however, could not analyse the transition period. Najurieta(5,6) developed analytical solutions of de Swaan's radial diffusivity equation which could handle the transition period as well as the first and last straight lines.
Streltsova(7) used a gradient flow model and indicated that the transition period should yield a straight line with a slope equal to 1/2 the slope of the early and late straight lines. Her examples showing the 1/2 slopes gave values of storativity ratios approximately equal to 0.37, 0.26, and 0.48. Serra et al.(8) reached the same conclusion with the use of a stratum model for the cases in which the storativity ratio, omega, was smaller that 0.0099.
Various type curves have been developed to analyse naturally fractured reservoirs with transient(9, 10) and pseudo steady-state(11) interporosity flow.