Lattice Boltzmann Simulation Of Flow In Porous Media

Fluid flow in complex geometries with complicated boundary conditions is widely encountered in petroleum, chemical and metallurgical processes. However, it also proposes a major difficulty in the scaling-up of related industrial equipments, which is not solved by traditional computational methods. As a mesoscopic physical model, the lattice Boltzmann method (LBM) is an alternative technique for computational fluid dynamics (CFD). It has many advantages including simplicity, adaptivity to complicated boundary conditions and explicit pressure solver, making it attractive to multiphase flows and flows in porous media. In this work, with increasing complexity, we investigate successively single-phase flow in artificial porous media, single-phase flow in natural porous media, multi-phase flow in natural porous media and finally coarse-grained computation on the single-phase flow in natural porous media.To study the interphase momentum transportation in heterogeneous gas-solid systems with multi-scale structures such as clusters, we carry out lattice Boltzmann simulations on GPUs to understand and hence predict the resistance behavior of the incompressible Newtonian flow in idealized particle clusters, and to validate the drag model in the Energy-Minimization Multi-Scale (EMMS) model under a wide range of particle Reynolds numbers, dense-phase fractions and dense-phase voidages. Furthermore, the critical condition for treating the cluster as homogenous suspension approximately is investigated and found that the critical condition is subject not only to particle Reynolds number but also to average solid fraction: it decreases with the increase of particle Reynolds number at constant average solid fraction or increases with average solid fraction at constant particle Reynolds number.The underground percolation in oil and gas production belongs to flow in natural porous media. The fluid flows in fractures of core sample in two-dimension are investigated by GPU-based multiple-relaxation-time (MRT) LBM simulations. Following that, to examine the permeabilities of real cores supplied by a petroleum company, we carried out LBM simulations on GPUs to understand and hence analysis the single phase flow in pore-scale matrixes from X-ray Micro-Computed Tomography (CMT). The computation gives related velocity fields and the permeability and they are compared with the experimental values and the numerical simulation of network model. The simulation results show that the computation of MRT-LBM performed on GPU is feasible for studying the transport property of fluid flow in porous media. This study provides basis for establishing the geological model and predicting the development index of oil-gas reservoir.In practice, however, multiphase flow is more often dealt with in natural porous media. To overcome the instability of multiphase interface, we improve the pseudo-potential multiphase LBM model and integrated some new development in this area with the introduction of an interfacial force, a equation of state and a multi-range interaction into pseudo-potential model. It is capable of simulating gas-liquid flow at high density ratio with stable interface, including the phase transition and the flooding process.To effectively investigate the flow in porous media at engineering scale, we carry out coarse-grained lattice Boltzmann simulations of single-phase flow in natural porous media. At present, although the speed of lattice algorithm is much faster than other algorithms of CFD, LBM simulation at pore-scale is computationally very demanding. For lower computational cost, we improved coarse-grained LBM with the averaging idea of lattice gas model to study the fluid flow in Berea sandstone and hence analyze its permeability. In the process of coarse graining, one needs to map the solid concentration converted from some pixels of CMT image into the collision step of LBM. The results indicate that the coarse-grained LBM is not only faster but also supply the information of fluid flow in more detail.To accelerate the computation, LBM simulations implemented on GPUs with CUDA are employed in most studies above, and are demonstrated as a promising approach for LBM simulations in industry.