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.