CSIRO Computational Modelling, Private Bag 10, Clayton South, 3169, Australia.
CSIRO Energy, Private Bag 10, Clayton South, 3169, Australia.
Phys Rev E. 2017 Dec;96(6-1):063108. doi: 10.1103/PhysRevE.96.063108. Epub 2017 Dec 12.
We develop a gray-scale lattice Boltzmann (LB) model to study fluid flow combined with heat transfer for flow through porous media where voxels may be partially solid (or void). Heat transfer in rocks may lead to deformation, which in turn can modulate the fluid flow and so has significant contribution to rock permeability. The LB temperature field is compared to a finite difference solution of the continuum partial differential equations for fluid flow in a channel. Excellent quantitative agreement is found for both Poiseuille channel flow and Brinkman flow. The LB model is then applied to sample porous media such as packed beds and also more realistic sandstone rock sample, and both the convective and diffusive regimes are recovered when varying the thermal diffusivity. It is found that while the rock permeability can be comparatively small (order milli-Darcy), the temperature field can show significant variation depending on the thermal convection of the fluid. This LB method has significant advantages over other numerical methods such as finite and boundary element methods in dealing with coupled fluid flow and heat transfer in rocks which have irregular and nonsmooth pore spaces.
我们开发了一种灰度格子玻尔兹曼（LB）模型，用于研究通过多孔介质的流体流动与传热，其中体元可能部分为固体（或空隙）。岩石中的传热可能导致变形，这反过来又会调节流体流动，因此对岩石渗透率有重要贡献。LB 温度场与通道中流体流动的连续偏微分方程的有限差分解进行了比较。泊肃叶通道流和 Brinkman 流都得到了极好的定量一致性。然后，该 LB 模型应用于模拟多孔介质，如填充床和更真实的砂岩岩样，并且在改变热扩散率时可以恢复对流和扩散两种状态。结果发现，尽管岩石渗透率可能相对较小（毫达西量级），但温度场可能会根据流体的热对流而发生显著变化。与有限元和边界元等其他数值方法相比，这种 LB 方法在处理具有不规则和不光滑孔隙空间的岩石中耦合的流体流动和传热方面具有显著优势。
