Nonlinear flow and permeability anisotropy characteristics in hydraulic fracturing-induced rock fractures subjected to various normal compressive stresses

Abstract Well productivity after hydraulic fracturing is strongly affected by the flow behaviors in created fracture complexity. In this study, gas flow tests were conducted in splitting fractures (induced by Brazilian splitting) and hydraulic fractures (created by hydraulic fracturing) to study the nonlinear fluid flow behaviors in rough fractures. 3D fracture surfaces were first digitally reproduced with a scanner and then the fracture geometry parameters (roughness profile index $$R_{p}$$ R p , the root mean square of the fracture profile wall slope $$Z_{2}$$ Z 2 ), aperture distributions were computed for both fractures. The influence of the fracture geometry characteristics on the nonlinear flow behaviors were systematically analyzed. The permeability anisotropy was numerically examined in detail. The results show that $$R_{p}$$ R p , $$Z_{2}$$ Z 2 and mean aperture of hydraulic fractures are relatively smaller, indicating that the fracture surfaces are smoother. The transmissivity of splitting fracture is relatively higher than that of hydraulic ones, and the ratio of splitting to hydraulic one varies from 2.51 at $$\sigma_{c}$$ σ c = 1 MPa to 60.95 at $$\sigma_{c}$$ σ c = 40 MPa. By contrast, splitting fractures have larger critical Reynolds number and lower critical pressure gradient, implying that nonlinearity is easier to occur in splitting fractures. The average Forchheimer coefficient for splitting fractures is 0.00577, which is 1.5 times larger than that (0.0041) for hydraulic ones. In addition, the fractures exhibit strong permeability anisotropy and this anisotropic effect is significantly dependent on the loading stress. In general, the permeability anisotropy in hydraulic fracture is more significant, showing that their permeability anisotropy ratios $$K$$ K are larger and more sensitive to the loading. The obtained results confirm that there exist some discrepancies in flow behaviors between splitting and hydraulic fractures and for more accurate evaluation in engineering practice, hydraulic fractures should be fully considered.