Flow Consistency Between Non-Darcy Flow in Fracture Network and Nonlinear Diffusion in Matrix to Gas Production Rate in Fractured Shale Gas Reservoirs

Document Type



Springer Netherlands


School of Engineering




Originally published as: Liu, J., Gao, F., Ju, Y., Zhang, X., & Zhang, L.-C. (2016). Flow consistency between non-darcy flow in fracture network and nonlinear diffusion in matrix to gas production rate in fractured shale gas reservoirs. In Transport in Porous Media. 111(1). 97-121. Available here.


Due to complex pore structures and ultra-low permeability in unconventional gas reservoirs, the flow consistency between the macro-flow in fracture network and the micro-flow or gas diffusion in matrix may significantly impact the production rate of fractured gas reservoirs. This study investigated the impact of this flow consistency on the production rate through the development of a numerical simulation model and its application to a shale gas reservoir. In this model, a fractured gas reservoir consists of fracture network and matrix. In the fracture network, gas flow was assumed to follow the non-Darcy law. In the matrix, a nonlinear diffusion model was proposed for the gas micro-flow through a non-empirical apparent permeability. This nonlinear diffusion model considered the advection and diffusion of the free-phase gas in nanoporous channels as well as the gas desorption in matrix. Further, the mass exchange rate between fracture network and matrix was calculated via a diffusion time which comprehensively considers both the diffusion capability and the size of matrix block. This numerical model was verified through history matching of the production data from two shale wells and then applied to a typical production well to investigate the effects of pore size in matrix, fracture spacing, and initial fracture permeability on production curve (i.e., production rate versus time). It is found that the production curve is significantly affected by this flow consistency. Pore size and initial fracture permeability play the key roles in this flow consistency. Fracture spacing and fracture permeability can alter the production curve. In this sense, the production curve can be designable through this flow consistency. Production efficiency can be improved through appropriate control of the fracturing degree of shale reservoir. Meanwhile, accurate measurement of shale pore size distribution provides an important parameter to the design of this flow consistency. © 2015, Springer Science+Business Media Dordrecht.