8. Modeling Energy and Mass Transport

The chapter deals with modeling non-isothermal mass momentum, and energy transport. Here, an additional variable is added-the temperature. To obtain the temperature distribution in the fluid and solid phases that occupy the porous medium domain, we have to write and solve the energy balance equation, obviously with appropriate initial and boundary conditions, as well as with temperature-dependent constitutive relationships. This equation, with appropriate initial and boundary conditions are considered in this chapter. The assumption that underlies this chapter is that thermal equilibrium exists between all phases present at point in the porous medium domain. The presentation in Chaps. 5, 6, and 7, focused on flow and transport under isothermal conditions. Under non-isothermal conditions, all constitutive relations involve also temperature an additional variable, and the complete model should also include the energy balance equation. The solute transport models considered in Chap. 7, may now involve exogenic and endogenic reactions. Within a porous medium domain, thermal energy may be transported by four mechanisms: (1) Advection by a fluid (or fluids) moving in the void space, (2) conduction in all solid and fluid phases (overlooking advection in a deformable solid), (3) mass diffusion in the fluid phases, and (4) thermal dispersion in the fluid phase(s). All these modes of energy transport are discussed in this chapter. The effects of natural thermal gradients, produced by solar radiation at ground surface, on water and water vapor movement, as well as on the chemical and biological behavior in the subsurface, may serve as examples of interest to soil scientists. In dealing with contaminated groundwater, a number of remediation techniques are associated with heating the soil, and injection of steam. Other interesting cases that require knowledge of heat and mass transport in porous media are the storage of energy in aquifers, or in the unsaturated zone, the production of geothermal energy, the disposal of \(\text {CO}_{2}\) in deep geological formations, the geological storage of high-level nuclear waste, and the thermally enhanced production of petroleum. Finally, in the chemical industry, most processes that take place in reactors occur under non-isothermal conditions. Because of its importance, we have added an appendix (App. A) that presents and discusses modeling of phenomena of transport that take place in chemical reactors. Coupling between the transport of mass and heat is also due to the fact that both the fluid’s density and its viscosity are temperature dependent. Most partitioning and equilibrium coefficients, discussed in Chaps. 6 and 7, are strongly temperature dependent.