Transient pressure responses of vertical fracture with finite conductivity in shale gas reservoir

• A trilinear flow model for vertical fracture in shale gas reservoir was presents.
• Large adsorption coefficient results in strong adsorption capacity, with low desorption capabilities.
• Large dimensionless fracture conductivity factor tends to shorten early flow period.
• Inter-porosity transfer coefficient determines the appearance, time and height of the transition stage.
• Storativity ratio determines the extent of crossflow time.

Shale gas reservoirs usually have extremely low permeability and relatively low porosity. Horizontal wells with massive multi stage hydraulic fracturing treatment has been performed on these reservoirs to achieve economic breakthrough. This paper considered shale gas dispersion and desorption in the matrix, presents a trilinear flow model for finite conductivity on vertical fracture in shale gas reservoir. We applied the Laplace transformation on this model and solved it with the Stehfest numerical inversion method. Typical pressure test curves were plotted, and the effects of sensitive parameters on the dimensionless wellbore pressure were also studied. Adsorption coefficient reflects the adsorption capacity of the matrix on shale gas, which implies the larger adsorption coefficient rate, the higher adsorption capacity, with low desorption capabilities. Fracture conductivity factor denotes the conductivity of fractures; the larger the fracture conductivity factor, the stronger the fracture conductivity capacity, which means limited flow rate within a short time. Inter-porosity transfer coefficient determines the appearance, time and height of the transition stage. If the inter-porosity transfer coefficient became smaller, the transition stage will occur early. Storativity ratio determines the extent of crossflow time; the smaller the storativity ratio is, the earlier the appearance time will be, and crossflow time will be longer.

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