H41D-1354
Pore-scale discretisation limits of multiphase lattice-Boltzmann methods

Thursday, 17 December 2015
Poster Hall (Moscone South)
Zhe Li1, Jill Middleton2 and Adrian Sheppard2, (1)Australian National University, Canberra, Australia, (2)Australian National University, Applied Mathematics, Canberra, Australia
Abstract:
Lattice-Boltzmann (LB) modeling is a popular method for the numerical solution of the Navier-Stokes equations and several multi-component LB models are widely used to simulate immiscible two-phase fluid flow in porous media. However, there has been relatively little study of the models’ ability to make optimal use of 3D imagery by considering the minimum number of grid points that are needed to represent geometric features such as pore throats. This is of critical importance since 3D images of geological samples are a compromise between resolution and field of view. In this work we explore the discretisation limits of LB models, their behavior near these limits, and the consequences of this behavior for simulations of drainage and imbibition.

We quantify the performance of two commonly used multiphase LB models: Shan-Chen (SC) and Rothman-Keller (RK) models in a set of tests, including simulations of bubbles in bulk fluid, on flat surfaces, confined in flat/tilted tubes, and fluid invasion into single tubes. Simple geometries like these allow better quantification of model behavior and better understanding of breakdown mechanisms.

In bulk fluid, bubble radii less than 2.5 grid units (image voxels) cause numerical instability in SC model; the RK model is stable to a radius of 2.5 units and below, but with poor agreement with the Laplace's law. When confined to a flat duct, the SC model can simulate similar radii to RK model, but with higher interface spurious currents than the RK model and some risk of instability. In tilted ducts with 'staircase' voxel-level roughness, the SC model seems to average the roughness, whereas for RK model only the 'peaks' of the surface are relevant. Overall, our results suggest that LB models can simulate fluid capillary pressure corresponding to interfacial radii of just 1.5 grid units, with the RK model exhibiting significantly better stability.