The range of influence of the poroelastic effects in terms of dimensionless complexes for the radial hydraulic fracturing model

In our previous work the fully coupled model of the planar hydraulic fracture propagation in a poroelastic medium was developed. In present paper we simplify this model to the case of axisymmetric fracture propagation in order to find the conditions whereby the poroelastic effects are essential. We consider two dimensionless complexes responsible for the transition from 1D to 3D filtration and for the poroelastic influence on the fracture geometry. Analyzing a large set of case studies, we find the critical values for these parameters below which the aforementioned physical effects are not important. Particularly, we demonstrate that 1D pressure diffusion is preserved until the diffusion length scale is 2.4 times smaller than the fracture size. In turn, the diffusion scale plays a central role in the poroelastic stress influence on the fracture propagation. Also, we show that in case of low closure stress the pressure diffusion is dominated not by the filtration process but by the rock deformation with a slight impact on the fracture geometry. We believe that this study will become useful for the appropriate model selection in engineering practice.