An equivalent model for grout flow along rough dissolution fractures in carbonate formations

• A novel equivalent model is proposed for grout flow along rough dissolution fractures in carbonate formations. • Dissolution effects delay the non-Darcy transition and enhance permeability. • Grouting in 3D rough dissolution fracture networks is simulated with effects of complex fracture geometries. Rough-walled and dissolution fractures are widely developed in carbonate formations, and the flow behavior of Bingham cement grout within their complex geometric surfaces is difficult to characterize accurately, which hinders a reliable evaluation of the grouting process. Therefore, this study innovatively examines the coupled effects of rough-walled and dissolved geometries along fractures and the rheological properties on the grout flow behavior, based on an established numerical grouting model verified by analytical solutions and experimental results. Numerical results show that in rough fractures, the equivalent permeability coefficient exhibits a non-monotonic variation with increasing Reynolds number, first increasing and then decreasing. In dissolution fractures, dominant channels can significantly enhance the equivalent permeability, while larger apertures tend to weaken the channel effect. A critical Reynolds number is further defined to characterize the transition of fracture flow from a shear plug flow-dominated regime to an inertia-dominated regime. On this basis, an equivalent grout flow model is established by comprehensively considering the effects of fractal dimension, dissolution patterns, yield stress, and Reynolds number, and is then applied to grouting simulations in three-dimensional rough dissolution fracture networks. The results indicate that increasing fractal dimension enhances the spatial heterogeneity of fractures and shortens the grout penetration distance, whereas dissolution enlarges the flow channels and thereby extends the penetration distance. These findings provide a theoretical basis for analyzing grout flow in rough dissolution fractures.