Experimental study on nonlinear flow behavior in smooth and rough sandstone fractures subjected to various injection pressure and normal compressive stress

The presence of fracture roughness and the occurrence of nonlinear flow complicate the fracture flow process. In the present study, water flow tests were conducted to comparatively study the flow behavior in smooth (Joint Roughness Coefficient (JRC) = 0–2) and rough (JRC = 18–19) fractures. The confining stress is in the range of 2–60 MPa and the injection pressure is in the range of 0.1–12 MPa to ensure obtaining a wide range of experimental data points. Surface roughness parameters (R_p, Z₂, JRC) based on a single fracture surface and aperture distribution based on both surfaces were calculated and their effect on the flow behavior was explored. Transmissivity, flow regimes and the Forchheimer coefficient β were analysed in detail. The results show that the mean aperture size of tensile fracture is lightly smaller than that of cut fracture, with a much smaller standard deviation. Tensile fracture also has a higher peak frequency, indicating that the two fracture surfaces match more perfectly. The intrinsic transmissivity ratio of cut to tensile fracture increases from 1.6 under 2 MPa to 9740.7 under 60 MPa, which may be attributed to the fact that cut fracture has an about \(1/30\) $1/30$ stress-dependence coefficient λ of the tensile fracture. Flow data for cut fracture scatter in transition and turbulent flow regions while scatter in laminar and transition flow regions in tensile fracture, and it is supposed to be quite difficult for flow in tensile facture to enter into turbulent flow. For tensile fracture, a linear relationship exists between Forchheimer coefficient β and mean aperture size η ( \(\beta = a_{1} \eta + b_{1}\) $\beta =a_1\eta +b_1$ ) and the correlation coefficients is up to 0.988, while for cut fracture, an exponential model relating β with both confining stress and mean aperture size η was proposed ( \(\beta = a_{2} e^{{\left( {b_{2} - c_{2} \eta } \right)^{\sigma } }}\) $\beta =a_2{e}^{{\left(b_2-c_2\eta \right)}^{\sigma }}$ ) and the correlation coefficients is up to 0.978.