An Effective Equation Governing Convective Transport in Porous Media

The fine structure of disordered porous media (e.g., fully saturated randomly packed beds) causes microscopic velocity fluctuations. The effect of the spatial and temporal randomness of the interstitial velocity field on the convective transport of a scalar (heat or mass) is investigated analytically. For a uniform mean velocity profile, the effective heat transport equation is obtained as the equation governing the transport of the ensemble average of the scalar under conditions of steady or unsteady random fields (with given statistics). In both cases, it is shown that the effective transport coefficient is enhanced by a hydrodynamic dispersive component, which is an explicit function of the mean filtration velocity. The agreement with experiments is encouraging. The effective transport equation is then generalized to three-dimensional mean velocity fields for isotropic media.