Shale gas production is effectively enhanced by multi-staged hydraulic fracturing from horizontal wells. The characteristics of the generated fracture networks are crucial to estimating shale gas production rate and consequently determine the economics of shale gas projects. The location and geometry of hydraulic fractures are reasonably well known; whereas the secondary fractures, generated during the fracturing process, are numerous and can only be described by a stochastic framework. We thus propose three groups of fractures to be modeled: (1) hydraulic fractures whose location and geometry can be deterministically approximated, (2) smaller induced/natural fracture subset connected between hydraulic fractures, and (3) disconnected small scale (natural or induced) fractures. As the permeability contrast between fractures and micro or nano pores in shale is very large, the gas production rate will be controlled by the diffusion process that feeds gas from shale to fracture networks and by the pressure-drop propagation mechanism in the formation. The transport of gas from micro or nano pores to the fracture network comprises two mechanisms: (1) molecular (or density) diffusion and (2) convective flow due to gas compressibility. We derive a simple numerical solution for the advection/diffusion equation, coupled with statistical distribution of micro and nano pores.


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