A comprehensive study of the effect of Brinkman flow on the performance of hydraulically fractured wells

The most recent study shows that a rigorous Darcy flow does not exist in hydraulic fractures due to the effect of viscous shear from fracture walls, and the Brinkman equation can be a more accurate method to characterize the fracture flow (Teng et al., 2020). For Darcy flow, the fracture permeability is equivalent to the proppant-pack permeability, whereas, for the Brinkman flow, the fracture permeability is related to the fracture width as well as to the proppant-pack properties. In this work, the authors conducted a comprehensive study of the effect of Brinkman flow on the performance of fractured wells by use of a proposed semi-analytical model. In addition to the Brinkman flow, this proposed semi-analytical model also can account for the geomechanical effect to describe the stress-dependent proppant-pack properties and fracture width. The calculated results in this work show that the fracture permeability is lower than the proppant-pack permeability ascribing to the effect of Brinkman flow. As the production proceeds, the Brinkman flow will play a more important role in influencing the fluid transport within propped fractures. The effect of Brinkman flow on the well performance is significant only if the geomechanical effect is considered. If the fracture volume is sufficiently large or the proppant-pack permeability is sufficiently high, a longer fracture can be more favorable for improving the well productivity. If the Darcy parameter (defined in Eq. (22)) of the hydraulic fracture is less than 0.001, the long-term cumulative production of the fractured wells will not be influenced by the Brinkman flow. If the Darcy parameter is larger than 0.001, the effect of Brinkman flow cannot be neglected unless the Darcy-flow dimensionless conductivity is sufficiently large.