A novel fracture dissolution model considering the nonlinear flow capacity of rough fractures

Existing research rarely considers the effects of rough fracture seepage on the progressive evolution processes of each physical field, and it primarily focuses on two-dimensional conditions. This study proposes a method to couple the Forchheimer equation with the Reynolds equation with time-varying apertures. The nonlinear flow of three-dimensional fractures under dissolution conditions is achieved. Then, the modified Reynolds equation under steady-state conditions is compared to the flow field governed by the Reynolds equation, and the validity of the modified Reynolds equation after coupling with the Forchheimer equation is verified. The results indicated that the maximum velocity of the flow field controlled by the modified Reynolds equation is slightly lower than that of the flow field controlled by the Reynolds equation, although the overall distribution trends are consistent. Under the control of the modified Reynolds equation, the pressure gradient of the flow field exhibits nonlinearity for the volumetric flow rate. When the fracture is rougher, the nonlinear coefficient increases, enhancing the nonlinearity between the pressure gradient and the volumetric flow. Therefore, the modified Reynolds equation can better represent the nonlinear seepage characteristics of fluids within rough rock fractures. The accuracy of the coupled model regarding the concentration field distribution within the three-dimensional parallel plate fracture and the evolution of the one-dimensional fracture inlet opening is verified using COMSOL multi-physical field coupling software. The theoretical analysis results closely align with numerical analysis, indicating that the model can effectively represent the concentration field distribution and aperture evolution. The research presented in this study can be a predictive method for the dissolution evolution of dam bedrock cracks.