Estimation of the thermal dispersion in a porous medium of complex structures using a lattice Boltzmann method

The thermal dispersion in a porous medium of complex structure is investigated by using the lattice Boltzmann method. The media under consideration include two-dimensional arrays of uniformly distributed circular and square cylinders, and uniformly distributed spherical and cubical inclusions. Upon validating the procedure, calculations have been performed for flows of various Prandtl and Reynolds number combinations. The porosity and the fluid–solid diffusivity ratio have been varied to investigate their effects on the dispersivity. For both 2D and 3D cases, the dispersivity is found to increase with the Peclet number raised to the same constant exponent regardless of the medium structures. The in-line arrangement yields higher dispersivity than the staggered arrangement, however, the dispersivity is independent of the inclusion shape except for the 3D staggered cases. New correlations for dispersivity for 2D and 3D cases are then proposed in terms of Peclet number, porosity, and the fluid–solid diffusivity ratio.