Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation

Abstract

This paper investigates whether particle ensembles in a fractured rock domain may be adequately modeled as an operator‐stable plume. If this statistical model applies to transport in fractured media, then an ensemble plume in a fractured rock domain may be modeled using the novel Fokker‐Planck evolution equation of the operator‐stable plume. These plumes (which include the classical multi‐Gaussian as a subset) are typically characterized by power law leading‐edge concentration profiles and super‐Fickian growth rates. To investigate the possible correspondence of ensemble plumes to operator‐stable densities, we use numerical simulations of fluid flow and solute transport through large‐scale (2.5 km by 2.5 km), randomly generated fracture networks. These two‐dimensional networks are generated according to fracture statistics obtained from field studies that describe fracture length, transmissivity, density, and orientation. A fracture continuum approach using MODFLOW is developed for the solution of fluid flow within the fracture network and low‐permeability rock matrix, while a particle‐tracking code, random walk particle method for simulating transport in heterogeneous permeable media (RWHet), is used to simulate the advective motion of conservative solutes through the model domain. By deterministically mapping individual fractures onto a highly discretized finite difference grid (1 m × 1 m × 1 m here), the MODFLOW “continuum” simulations can faithfully preserve details of the generated network and can approximate fluid flow in a discrete fracture network model. An advantage of the MODFLOW approach is that matrix permeability can be made nonzero to account for any degree of matrix flow and/or transport.