Development of transport equations for multiphase system—I: General Development for two phase system

TL;DR: In this paper, a theoretical study of thermal dispersion in porous media is presented, where the contribution of pore level velocity distributions on dispersion is captured in an analysis of thermal transport in a thickwalled tube containing a flowing fluid.

TL;DR: An insight is offered into the impacts of heterogeneity on the scaling of effective transport parameters in heterogeneous reservoir models and a key finding is that spatial heterogeneity models with similar univariate and bivariate statistics may exhibit different scaling characteristics because of the influence of higher order statistics.

TL;DR: In this paper, the authors applied the results obtained in Part II of this paper to the analysis of heat transfer processes in packed beds and developed an explicit constraint to determine the applicability of the thermal equilibrium assumption between solid and fluid phases.

TL;DR: In this paper, a new model was developed for the transient thermal response of a packed bed, using the method of spatial averaging, and it was found that after a sufficiently long time has elapsed, the temperature pulses for the fluid and solid phases will be separated by a constant distance and will spread or disperse about their centroids at an equal rate.

TL;DR: In this paper, the theorems of local volume averaging which relate averages of derivatives to derivatives of averages are presented. And the proofs demonstrated are intended to be simpler than those found in the literature.

TL;DR: In this article, a new model for porous media comprised of monosized, or nearly-monosized grains, is developed, where the problem of flow through each unit cell is reduced, subject to reasonable assumptions, to the determination of the flow in an infinitely long periodically constricted tube.

TL;DR: The apparent diffusion coefficient is the sum of the molecular and Taylor diffusion coefficients in the two phases and a term due to the finite rate of partition between them as discussed by the authors, and it is shown how the Taylor diffusion coefficient depend on the ratio of amounts of solute held in two phases, and how this gives a connexion between the coefficient a 2 U 2 /48 D found by Taylor (1953) for viscous flow in a circular tube and the 11 a 2U 2/48 D in his analysis of the distillation column.

TL;DR: In this article, the axial effective thermal conductivity in the one-phase model and the heat transfer coefficient in the twophase model were derived without assuming that the solid and gas temperatures are equal.