Hydraulic fracturing with leakoff in a pressure-sensitive dual porosity medium

Hydraulic fracturing is a key method in the stimulation of shale gas reservoirs. Shale gas formations often contain natural fractures which are fluid-pressure sensitive and dilate in response to the inflation of the fracture, increasing fluid loss and slowing down and potentially prematurely arresting fracture propagation. Models typically assume 1-D single-porosity/permeability (Carter) leakoff perpendicular to the hydraulic fracture. However, the leakoff process in naturally fractured formations is considerably more complex. In this study, we present an hydraulic fracturing model based on the PKN-formalism which accommodates leakoff into a pressure-sensitive dual porosity medium. Proppant transport is accommodated by introducing empirical constitutive equations to determine the proppant distribution during the hydraulic fracturing treatment. The model is solved numerically and is validated against known small and large time asymptotic solutions. The model is capable of providing a rapid estimation of the morphology of hydraulic fractures in naturally fractured formations and the corresponding proppant distribution. The simulation results illustrate that the leakoff into a dual porosity medium, where fracture permeability is a strong function of applied fluid pressure, results in a reduced length of the propagating fracture due to the fugitive fluid leakoff from the fracture into the surrounding formation and that this in turn results in a reduced maximum width during the treatment. The ability to infuse proppants in fluid-driven fractures penetrating large distances from the injection wellbore is further limited by premature screen-out. This may compromise the ultimate efficiency of the final hydraulic fracture regarding gas recovery. Reduced propagation and premature screen-out are limited by low permeability and large spacing of the natural fractures. The presence of an existing network of natural fractures, including those adjacent to the hydraulic fracture that may become propped, aids in the recovery of the resource by reducing diffusion lengths of the hydrocarbon to the main fracture.