A comparison of fracture mixing models, 1. A transfer function approach to mass transport modeling

This paper develops a transfer function approach to mass transport modeling as a basis for comparing flowline routing or complete mixing models in two-dimensional fracture networks. The approach accounts for physical and chemical processes in the network, and for diffusion, retardation and kinetic decay in the matrix blocks. The fracture network is idealized in terms of fracture segments and intersections. By knowing the transfer function for each component, the response of the system can be evaluated by considering the interaction of all components. Mathematically, the transfer function for the single fracture is derived from an analytical solution for a single fracture, while the intersection component is approximated by either the complete mixing or the streamline routing model. In essence, the approach combines numerical and analytical approaches at the fracture scale to route mass through fracture segments and intersections. The analytical transfer function used in this application requires that mass diffusion not reach the centerline between fractures. Thus, there may be conditions where the transfer function may need to be modified to account for the geometry of the matrix blocks. The accuracy of the approach is examined through tests comparing results with an analytic solution and a simple network problem.