Transport in Porous Media 30: 323–344, 1998. 323 © 1998 Kluwer Academic Publishers. Printed in the Netherlands. Dispersion Phenomena in Thermal Diffusion and Modelling of Thermogravitational Experiments in Porous Media DANIEL FARGUE 1 , PHILIPPE JAMET 1 and PIERRE COSTES ` EQUE 2 1 Ecole Nationale Sup´ erieure des Mines de Paris, 35 rue Saint-Honor´ e, 77305 Fontainebleau Cedex, France 2 Laboratoire M´ ecanismes de Transfert en G´ eologie (UMR 55.63), Universit´ e Paul Sabatier, All´ ees Jules Guesde, 31000 Toulouse, France (Received: 24 February 1997; in final form: 28 October 1997) Abstract. In a TIPM paper published in 1992, the authors presented a simple model of thermograv- itational diffusion in packed columns (TPC). Though qualitatively in agreement with the experi- mental results, this model exhibited a systematic discrepancy with respect to the magnitude of the permeability of maximum separation in the TPC experiments. Here, the results of a re-examination of the classical phenomenology of irreversible thermodynamics in porous media, applied to TPC, are described. Through the interpretation of additional TPC experiments, we show that the effective thermal diffusion coefficient in TPC includes a dependency upon the fluid velocity. This depen- dency is consistent with a nonlinear extension of irreversible thermodynamics, and the model so amended accounts for a correct re-interpretation of the experiments. Key words: thermal diffusion, dispersion in porous media, effective transport coefficients, irre- versible thermodynamics, transport model, phenomenological equations. Notations a isothermal plates spacing in the thermal diffusion column c 1 mass fraction of the solute c 2 mass fraction of the solvent D effective molecular (isothermal) diffusion coefficient for the solute in TPC experiments D ′ effective thermal diffusion coefficient for the solute in TPC experiments d molecular (isothermal) diffusion coefficient of the solute in the packing (at rest) d ′ thermal diffusion coefficient of the solute in the packing (at rest) d 0 molecular (isothermal) diffusion coefficient of the solute g gravity h 1 massic enthalpy of the solute h 2 massic enthalpy of the solvent i,j,k,l space indices J l 1 mass flux of the solute relative to the fluid phase k intrinsic permeability of the column packing k m value of the optimum intrinsic permeability of the column packing L length of the thermal diffusion column L ab second-order phenomenological coefficients (a,b = 1,w,q )