Practical Solutions for Pressure Transient Responses of Fractured Horizontal Wells in Unconventional Reservoirs

Abstract

Abstract This paper presents an analytical trilinear flow solution to simulate the pressure transient and production behavior of fractured horizontal wells in unconventional reservoirs (Ozkan et al., 2009). The model is simple, but versatile enough to incorporate the fundamental petrophysical characteristics of unconventional reservoirs, including the intrinsic properties of the matrix and the natural fractures. Special characteristics of fluid exchange among various reservoir components may also be considered. This practical solution provides an excellent alternative to rigorous solutions, which are cumbersome to evaluate. One of the advantages of the trilinear flow solution is its convenience in deriving asymptotic approximations. Though linear and bilinear flow regimes have been noted for fractured horizontal wells in the literature based on their diagnostic features, they have not been associated with particular reservoir characteristics and flow relationships. The solutions documented in this work provide insight about potential flow regimes and the conditions leading to these flow regimes. Identification of these flow regimes is important for the characterization of unconventional reservoirs from pressure transient tests. Because of its relative simplicity, the trilinear flow solution does not require special expertise to compute and apply. Introduction Although it is possible to develop detailed analytical (Chen and Raghavan, 1997, and Raghavan et al., 1997) and numerical (Medeiros et al., 2008) models to represent transient fluid flow toward a multiply fractured horizontal well in tight, unconventional reservoirs such as shale, the downside of these models is the increased computational requirements, the implicit functional relationships of key parameters, and the inconvenience in their use in iterative applications. Despite the complex interplay of flow among matrix, natural fractures, and hydraulic fractures, the key characteristics of flow convergence toward a multiply fractured horizontal well may be preserved in a relatively simple, trilinear flow model (Ozkan et al., 2009). The basis of the trilinear flow model is the premise that the productive lives of fractured horizontal wells in tight formations are dominated by linear flow regimes (Medeiros et al., 2008). To derive a practical solution, the trilinear flow model includes some idealizations and simplifying assumptions. The model is for single-phase flow of a constant compressibility fluid and is applicable to single-phase gas flow through pseudopressure transformation. Identical hydraulic fractures are assumed to be equally spaced along the horizontal well, which is a common field practice. Dual-porosity idealization (Warren and Root, 1963, Kazemi, 1969, de Swaan-O, 1976, and Serra et al., 1983) is used to simulate the naturally fractured porous medium. The solution is derived in the Laplace-transform domain because we consider a naturally fractured inner reservoir. The results are then numerically inverted to the time domain using the algorithm proposed by Stehfest (1970). One-dimensional linear flow, akin to flow in vertical-well fractures, is assumed in the hydraulic fractures because wellbore storage normally masks the very early-time (radial) flow convergence toward the well within the hydraulic fractures (Soliman et al., 1990, Mukherjee and Economides, 1991, and Larsen and Hegre, 1991, 1994). However, the impact of radial flow convergence at the fracture-horizontal well intersection is taken into account by a flow choking skin, and the wellborestorage effect is incorporated into the model by convolution.