Numerical modelling of colloid transport in sets of parallel fractures with fracture skin

A numerical model is developed to describe the transport of colloids in sets of parallel fractures with fracture skin. The model accounts for transport along the fracture, irreversible deposition onto fracture surfaces, penetration into the rock formation, irreversible deposition onto the fracture skin surfaces and irreversible deposition onto the rock matrix surfaces. The impact of kinetic colloid deposition in a fractured formation is investigated for constant flux boundary and constant concentration boundary conditions at the inlet. A triple continuum approach, with fracture; fracture skin and rock matrix, is utilized for modelling the system. The resulting set of governing partial differential equations is solved using a fully implicit numerical formulation based on the finite difference method. Simulations for both the boundary conditions indicate that colloid migration along the fracture increases with increase in flow velocity and increase in fracture aperture. Furthermore, it is shown that the increase in colloid penetration depth along the fracture with increase in flow velocity is higher at large flow velocities compared to smaller flow velocities. Sensitivity analyses are also performed to investigate the effect of various colloid properties on the evolution of colloid concentration in the fractured formations with fracture skin.