An efficient time-domain approach for simulating Pe-dependent transport through fracture intersections

摘要

In the subsurface, fractures commonly provide dominant pathways for fluid flow and solute transport. However, mechanisms responsible for dispersion in large-scale fracture networks are not completely understood. Scalable models of flow and transport in discrete fracture networks that accurately represent the small-scale physics controlling transport can provide a means for improving understanding of the large-scale dispersion mechanisms. Within fracture networks, mixing within fracture intersections can play an important role in mass transport. This mixing process results from a combination of advection and diffusion within fracture intersections. A number of high-resolution computational studies involving direct solution of the Stokes equations in fracture intersections show that mixing exhibits a strong dependence on Peclet number, Pe =(V(b))/(D_m), where V is the mean fluid velocity, (b) is the mean fracture aperture and D_m is the molecular diffusion coefficient. However, such high-resolution techniques are not feasible in large-scale network simulations, so it is common to model mixing using either stream-tube routing (Pe →∞) or complete mixing (Pe → 0). We present a novel probabilistic method that allows accurate and efficient calculation of the Pe-dependent solute transport through fracture intersections. Fundamental to our approach is a simplified approximation to the Stokes velocity field within fracture intersections based upon local application of the cubic law in each fracture entering and exiting the fracture intersection. In addition, we use a time domain approach to route particles across the fracture intersection in a single step; using this approach the influence of both advection and diffusion are represented explicitly. Results show that our new model accurately represents the trajectory and travel times of particles passing through a fracture intersection. Furthermore, the proposed algorithm is two to three orders-of-mag-nitude faster than comparable simulations relying upon detailed simulation of the Stokes velocity field.