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. Over the past two years of my PhD project, I have developed a parallelised GPU code to implement two commonly used multiphase LB models: Shan-Chen pesudo-potential model and Rothman-Keller colour-gradient model, and I explored 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 those two models in a series of simple geometry 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 this mid-term review, I will present the results of various characterisation tests and point out what are the corresponding implications to the large scale drainage/imbibition simulations in realistic porous media.