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

Abstract

[1] 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 largescale (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.

Upscaling of a dual-permeability Monte Carlo simulation model for contaminant transport in fractured networks by genetic algorithm parameter identification

“…The corresponding networks are sparsely fractured domains dominated by a few long fractures connecting their boundaries [22]. Moreover, the following correction is applied to the sampled value of the conductivity in order to account for the "stair step" pattern of the velocity field, which causes an apparent decrease of the hydraulic gradient from cell to cell in MODFLOW [22]: in the vertical direction. These dimensions are comparable to those adopted in [6].…”

“…Assuming that the individual properties are not correlated [22], fractures are generated in two groups, of fixed orientation ( 1  , 2  ), with position uniformly distributed in a two-dimensional domain, and length ( f L ) and conductivity ( f K ) distributed according to power laws, such as: [22].…”

“…By choosing a small power law exponent for the fracture length distribution, the following criterion can be adopted to control maximum spatial density [22] The lower limit is not computed by evaluating the percolation threshold; rather, here, in analogy with [22], it is instead determined indirectly by carrying out trial numerical simulations on the flow field in order to determine a value which guarantees a certain degree of connectivity and allows for a flow in the fractures from one side of the domain to the other.…”

“…Different realizations of fracture fields are generated on small sub-domains by random sampling from the assigned distributions and by mapping into continuum grids with constant cell size, according to a recently suggested methodology [5] [22]. Then, the MODFLOW and MT3DMS solvers [23] [24] are employed to get detailed flow and transport solutions over these sub-domains [5].…”

“…In fact, the shape of the peak predicted by the detailed MODFLOW and MT3DMS is mainly due to the fastest tracer particles which are transported by advection along the main fractures and rarely interact with the matrix nor change their fracture direction. To intuitively describe this process, we can assume that, in a sparsely fractured domain dominated by a few long fractures connecting its boundaries, as the one under consideration [22], the advective transport is driven by a single fracture, e.g. with orientation ; then, we can write the average time  one of these particles takes to exit the domain boundary as:…”