Lattice-Boltzmann Simulations of Heterogeneous Porous Media: A Comparison Between Three Approaches

Lattice-Boltzmann simulations provide a method for modeling fluid flow through complex pore spaces, such as those commonly encountered in many geofluid applications. However, simulating this level of detail comes at a cost -- these explicit, high resolution models often require large amounts of computational resources. An alternative approach, suggested by Dardis and McCloskey (1998), is to introduce a meso-scale Lattice- Boltzmann model that incorporates the porosity of the medium as a model parameter. Rather than a lattice comprising nodes that are either solid or fluid, this approach uses a probabilistic or partial bounce-back model where node properties are varied to reflect the local permeability of the material. These types of models have great potential in a range of geofluids simulations; examples of particular interest to the Geofluids group at the University of Minnesota include the study of pumice permeability, karst formation and well pumping tests. However, there are several different methods for formulating these partial-bounce-back models and little has been done to examine their validity. This presentation compares the predictions of different partial-bounce-back lattice-Boltzmann models under conditions from laminar to turbulent flow. In particular, three models are examined: Dardis and McCloskey (1998), Sukop and Thorne (2004) and an in-house model developed by the Geofluids group at the University of Minnesota. The models' predictions are compared with results from finite element simulations, data from well efficiency experiments and permeability measurements.