Modeling of Fluid Transfer from Shale Matrix to Fracture Network

Abstract

The objective of this paper is to incorporate a more detailed description of flow in shale matrix to improve modeling of production from fractured shale-gas reservoirs. Currently, most modeling approaches for shale-gas and -oil production are based on the dominance of Darcy flow in both natural fractures and matrix. We improve the description of matrix flow by considering diffusive (Knudsen) flow in nanopores. In our dual-mechanism approach, when Darcy flow becomes insignificant due to nanodarcy matrix permeability, Knudsen flow takes over and contributes, substantially, to the transfer of fluids from matrix to fracture network. Furthermore, we consider stress-dependent permeability in the fracture network. Therefore, incorporating Darcy and diffusive flows in the matrix and stress-dependent permeability in the fractures, we develop a dual-mechanism dual-porosity naturally fractured reservoir formulation and derive a new transfer function for fractured shale-gas reservoirs. The dual-mechanism dualporosity formulation presented in this paper can be used for numerical or analytical modeling purposes. We use the new formulation of matrix to fracture fluid transfer with an analytical model and demonstrate the differences from the conventional formulation. Introduction One of the major factors determining the productivity of shale reservoirs is the existence of a natural fracture network. In most cases, a question arises about the contribution of the shale matrix. Unfortunately, a complete understanding of fluid transfer from shale matrix to fracture network has not yet been achieved. Current studies, whether they model fluid flow in both fractures and matrix or incorporate the effect of fluid transfer from matrix to fractures with dual-porosity idealization, assume that the main contributor of the fluid transfer is the Darcy flow in the matrix induced by the pressure differential between the matrix and fracture. Fundamental considerations of Darcy flow, however, reveal that fluid movement in the nanodarcy shale matrix should be negligible for practical periods of time, unless exaggerated or unrealistic importance is assigned to other parameters to justify the sustained production levels observed in practice. Therefore, a more detailed look at the flow in the matrix is essential for better understanding of the contribution of shale matrix to production. In recent studies (Javadpour et al., 2007, Javadpour, 2009), gas flow in shale matrix has been described by Knudsen diffusion and slip flow in the nanopores, Darcy flow in the micropores, desorption from the surface of kerogen, and diffusion in solid kerogen. Our objective in this paper is to incorporate this more detailed description of flow in shale matrix to modeling of production from fractured shale-gas reservoirs. We limit our attention to Darcy and diffusive flow processes here. Desorption in shale reservoirs has been likened to that in coalbeds where gas desorbs from the surface of the coal matrix to the cleat system. The major difference in shale-gas reservoirs is in that desorption takes place from the surface of the organic content (kerogen) embedded in the shale matrix to nanopores. Therefore, to describe desorption in shale matrix, in addition to the standard parameters, such as the volume and maturity of the organic content and the Langmuir isoterms, the distribution of kerogen, pressure profile, and the exposed surface area of nanopores in the shale matrix should be considered. This information is currently nonexistent or incomplete and, thus, we defer incorporating desorption into our gas-flow model for shale matrix until later.