Rate Transient Analysis in Naturally Fractured Shale Gas Reservoirs

Abstract

Abstract Shale gas reservoirs have been observed to exhibit a half slope on a log-log plot of rate against time. This indicates transient linear behavior and is believed to be caused by drainage from matrix surfaces into the adjoining fractures. A standard test case for the slab matrix transient dual porosity model is presented in this paper. It is shown in this paper that various shape factor formulations can be used in the transient dual porosity model provided that corresponding appropriate changes are made in the solution parameters and the interporosity flow parameter. It is also shown in this paper that different matrix geometry exhibit the same transient linear response when the area-volume ratios are similar. This paper also presents a procedure incorporating a rectangular geometry dual porosity model to analyze the transient linear flow regime obtained in naturally fractured shale gas reservoirs. This procedure allows the use of different matrix geometries. Introduction Naturally fractured reservoirs such as shale and coalbed have been traditionally modeled using the dual porosity concept proposed by Warren and Root.1 The dual porosity model consists of matrix blocks, which provide storage of the hydrocarbon, separated by fractures which provide permeability. Different matrix geometries - slab, cylinder, sphere - have generally been utilized with the slab being the most widely used. The cylinder and sphere geometry are used as approximations to the two-dimensional (columns) and three-dimensional (cubes) cases. Initial applications of the dual porosity model were limited to solving problems related to constant rate pressure-transient analysis.1–9 Ozkan et al.10 present analysis of flow regimes associated with flow of a well at constant pressure in a closed cylindrical reservoir. The slab matrix model similar to deSwaan5 and Kazemi2 is used in their paper. Unsteady matrix-fracture transfer is inherent in the model. Five flow regimes are presented in Ozkan et al.10. Flow regimes 1, 2 and 3 were previously described described in Serra et al.7 Two new regimes are presented in Ozkan et al.10 Flow regime 4 reflects unsteady linear flow in the matrix system and occurs when the outer boundary influences the well response and the matrix boundary has no influence. Flow Regime 5 occurs when the response is affected by all the boundaries. Most of the problems previously considered were for the incompressible fluid case. Some authors11–16 have also considered the gas case. Gatens et al.14 analyzed production data from about 898 Devonian shale wells in four areas. They present three methods of analyzing production data - type curves, analytical model and empirical equations. The empirical equation correlates cumulative production data at a certain time with cumulative production at other times. This avoids the need to determine reservoir properties. Reasonable matches with actual data were presented. The analytical model is used along with an automatic history matching algorithm and a model selection procedure to determine statistically the best fit with actual data. Watson et al.15 also present an analytical model for naturally fractured reservoirs with history matching and model selection. They incorporate the use of a normalized time in the analytical model to account for changing gas properties with pressure. Spivey and Semmelbeck16 present a method for predicting production from dewatered coal and fractured gas shale reservoirs. Their method incorporates the slab matrix transient radial model, adjusted time, adjusted pressure and a total compressibility term accounting for desorption. Shale gas production data from a sample well is plotted against time on a log-log plot as shown in Fig. 1. A half-slope is obtained on the plot. This indicates a transient linear regime analogous to Regime 4 described in Ozkan et al.10 The transient linear behavior shown in Fig. 1 occurs for a duration of almost two log cycles.