A new particle‐tracking approach to simulating transport in heterogeneous fractured porous media

Abstract

[1] Particle-tracking methods are often used to model contaminant transport in fractured porous media because they are straightforward to implement for fracture networks and are able to take into account the matrix effect without mesh generation. While classical methods assume infinite matrix or regularly spaced fractures, we have developed a stochastic method adapted to solute transport in complex fracture networks associated with irregular matrix blocks. Diffusion times in the matrix blocks are truncated by the finite size of the blocks. High ratios of matrix diffusion to fracture advection, small fracture apertures, and small blocks favor the transfer of particles to nearby fractures through matrix diffusion. Because diffusion occurs on both sides of the originating fracture before particles reach one of the neighboring fractures, transfer times to both neighboring fractures are strongly affected by the network configurations on both sides of the fracture. This new particle-tracking method is able to deal with complex fracture networks by considering heterogeneous configurations on both sides of the fracture. We finally show on simple Sierpinski lattice structures that neglecting the finite size of the matrix blocks may lead to orders of magnitude overestimations of the transfer times.Citation: Roubinet, D., H.-H. Liu, and J.-R. de Dreuzy (2010), A new particle-tracking approach to simulating transport in heterogeneous fractured porous media, Water Resour.

Analytical models of heat conduction in fractured rocks

“…The latter step will rely on the Green's functions derived in this study. Heat transfer in fracture networks. Multiscale modeling approaches to flow and transport in fractured rocks [e.g., Dershowitz and Miller , ; Cvetkovic et al , ; Roubinet et al , , ] combine a discrete fracture network (DFN) representation at the field scale with analytical solutions at the fracture scale. We will embed our analytical solutions into particle‐tracking DFN models to represent rock conduction effects at the field scale with optimized computational cost and representation accuracy.…”

“…Such models are amenable to the same mathematical treatment as their counterparts developed for mass transport in discrete fracture networks. Examples of the latter include analytical [ Tang et al , ], semianalytical [ Roubinet et al , ; Sudicky and Frind , ], and numerical [ Roubinet et al , ] models of solute transport due to advection and diffusion in fractures and pure diffusion in the host matrix. A key difference between heat and mass transfer in fractured environments is that heat readily diffuses through both solid and fluid phases, whereas solutes spread largely in the fluid phase.…”

Semi‐analytical solutions for solute transport and exchange in fractured porous media

“…Their solution was extended by Sudicky and Frind [1982] to account for the presence of neighboring parallel fractures. These analytical solutions are routinely used to interpret field and experimental observations [ Callahan et al , 2000; Maloszewski and Zuber , 1993; Moreno et al , 1985; Zhou et al , 2007] and to simulate transport in fractured media with complex fracture geometries [ Liu et al , 2007; Roubinet et al , 2010].…”

Random walk simulation of miscible flow through heterogeneous 2D porous media considering dispersion tensor

“…Also, the RW algorithm can be combined with classical numerical or analytical solutions. For example, Roubinet et al (2010) modeled flow through a fracture network by RW approach and used an analytical solution for matrix-fracture interactions. Recently, Stalgorova and Babadagli (2012) developed a RW algorithm to simulate miscible flooding of light and heavy oil in fractured porous media at the laboratory scale.…”