Analytical solution of coupled stress-flow-transport processes in a single rock fracture

A closed-form solution is presented for modeling the coupled stress-flow-transport processes along a single fracture embedded in a porous rock matrix. Necessary assumptions were made to simplify the subject into a two-dimensional (2D) problem, considering the changes of fracture aperture and matrix porosity under various stress conditions. The cubic law was assumed to be valid for the fluid flow in the fracture, with an impermeable rock matrix. For transport mechanisms, advective transport along the fracture, longitudinal hydrodynamic dispersion in the flow direction, and the matrix diffusion were considered in three different transport models under constant concentration or constant flux (Danckwerts') inlet boundary conditions. This analytical solution can be used as a constitutive model, or as an example for validation of similar constitutive models, for modeling the coupled hydro-mechanical-chemical (HMC) processes in fracture networks of crystalline rocks. The influences of stress/deformation processes on different transport mechanisms in a single fracture under different inlet boundary conditions were studied for the first time. The results show that changes of fracture, as controlled by a combination of normal closure and shear dilatancy, have a significant influence on the solute concentration distribution both along the fracture and in the rock matrix, as well as on the solute residence/breakthrough time, especially when shear-induced dilatancy occurs. Under compressions, the decreasing matrix porosity slightly increases the solute concentration along the fracture and in the rock matrix.