Particle Transport Scheme for Embedded Discrete Fracture Models

Summary Embedded Discrete Fracture Models (EDFMs) for fractured porous media are preferable over Discrete Fracture Models if complex fracture geometries are to be fully resolved and the fractures and matrix discretizations are conformal. Lagrangian particle-tracking schemes offer convenient means for solute transport modeling because in EDFM frameworks, an orthogonal grid can be used irrespective of the fracture geometries. However, the absence of resolved fracture-matrix interfaces and different dimensionalities of the matrix and fracture continua motivate the use of a stochastic framework for particle-tracking. In this work, we developed a stochastic, time-adaptive particle-tracking scheme for EDFM models of fractured media with a permeable matrix. We formulated the probabilities of inter-continuum particle transfer, which have dependency on the particle travel time through the matrix/fracture control volumes. We showcase the conservative nature of the proposed particle-tracking scheme and additionally, illustrate the estimation of averaged solute concentration field. Such an illustration hints at the potential extensions of the tracking scheme, e.g., modeling of solute transport with kinetic reactions, and its incorporation into random walk models for dispersion in fractured media.