A productivity prediction model for multiple fractured horizontal wells in shale gas reservoirs

•Five-linear-flow model for MFHWs in dual-porosity shale formations.•Productivity decline behavior of a multi-fractured horizontal well was studied.•Fracture number, half-length, conductivity and SRV are the main influential factors.

Shale gas, as an unconventional gas resource that has great exploitation potential, is stored as absorbed gas and free gas. Development of shale gas by multi-stage hydraulic fracturing has become a key technology for releasing this stored gas. We considered several flow mechanisms through both the multi-scaled porous media and the complex fracture networks caused by stimulated reservoir volume (SRV) fracturing. We developed a five-linear-flow model for fractured horizontal wells in dual-porosity formations, considering adsorption-desorption, diffusion, and percolation behavior. An analytical solution was obtained by means of a Laplace transformation. The number of fractures, the fracture half-length, the fracture conductivity, the width of the SRV, the inter-porosity flow coefficient, the volume of adsorbed gas, and the Langmuir pressure were considered as sensitive factors having significant influences on the production behavior of gas wells. Our analysis shows that the number of fractures, fracture half-length, fracture conductivity, and the width of the SRV are the main influencing factors controlling well productivity. The longer the fracture half-length, the longer the stable production period will be. An increase in the number of fractures also leads to a longer stable production period, but there is an optimum value for a given well. The time of the stable production period will level out once the dimensionless fracture conductivity (the fracture conductivity times the distance from the well to the tip of the fracture divided by reservoir permeability) increases to 100. The optimum value of the dimensionless fracture conductivity is between 10 and 100. The stable production period increases as the width of the SRV approaches the half distance of two fractures.