Geometry-Based Prediction of Solute Transport Process in Single 3D Rock Fractures Under Laminar Flow Regime

Subsurface substance migration in the fractured rock aquifer is mainly controlled by fractures, and prediction of solute transport in fractures is important to many geophysical processes and engineering activities. This study explores the possibility of predicting transport process in single rock fractures from measurable physical properties. For this purpose, we conducted a large number of pore-scale simulations of solute transport in single 3D rock fractures with different apertures and various degrees of roughness. The numerically-obtained breakthrough curves under laminar flow regime were reproduced with high fidelity by the classic analytical solution within the framework of macroscopic advection-dispersion theory. The fitted transport coefficients (hydrodynamic dispersion coefficient and transport velocity) were normalized by the parallel-plate model's values, and were further parameterized by aperture b and roughness parameter sigma/b in form of omega e(b/psi) + lambda(m(sigma/b) - 1)/b(n) and 1 - alpha(sigma/b)/beta(b), respectively. By incorporating these parameterized transport coefficients and the modified cubic law into the classic analytical solution, we proposed a new transport predictive model. This model was adaptively degenerated into the classic analytical solution of parallel-plate model, and was proved to be capable of predicting macroscopic solute transport only relying on arithmetic-mean mechanical aperture and its standard deviation, without solving the velocity and concentration fields. By the established model, we quantitatively revealed the impacts of aperture and roughness on the breakthrough curve under laminar flow regime. This study puts a step toward predicting solute transport process in fractured rock aquifers with measurable geometric properties.