Modeling conservative tracer transport in fracture networks with a hybrid approach based on the Boltzmann transport equation

Abstract

Fractures often represent the primary transport pathways within low-permeability rock. Continuum models based on the advective-dispersion equation have difficulty representing the complex transport phenomenology observed in field studies. Discrete fracture network models can represent a greater range of transport behavior at the price of being computationally intensive, which restricts their application to small rock volumes. The linear Boltzmann transport equation from the kinetic theory of gases includes additional dependencies on the particle speed and direction of travel and can thus represent a greater range of transport behavior compared with the advective-dispersion equation. The capability of the Boltzmann equation for modeling more complex transport behaviors of conservative tracers was evaluated. Parameters appearing in the Boltzmann equation were calibrated using small-scale discrete fracture networks. The calibrated Boltzmann model can simulate at spatial/temporal scales that would be prohibitively expensive with a discrete fracture network. This hybrid approach successfully reproduced the results of discrete fracture network simulations in two dimensions.