Conduction and Convection
As we discussed in Chapter 8, our knowledge of the pore-level fluid mechanics in two-phase flow through porous media is rather incomplete. In this chapter, we discuss thermal dispersion, i.e., convective heat transfer at the pore level, using the available knowledge about the subject. This knowledge is even more inconclusive. We begin with the local volume averaging of the energy equation, and then we arrive at the effective thermal conductivity tensor and the thermal dispersion tensor for the three-phase system (liquid-gas-solid). The same closure conditions used in the single- phase flow treatments are used. Then we examine the various features of these tensors such as their anisotropy, and we discuss some of the available models and empirical relations for the various elements of these tensors. We conclude by noting that near the bounding surfaces, the phase distribution nonuniformities lead to substantial variations in the magnitude of the components of the effective thermal conductivity and the dispersion tensors.
KeywordsPorous Medium Representative Elementary Volume Phase Distribution Thermal Dispersion Dispersion Tensor
Unable to display preview. Download preview PDF.
- Hashimoto, K., Muroyama, K., Pujiyoshi, K., and Nagata, S., 1976, “Effective Radial Thermal Conductivity in Co-current Flow of a Gas and Liquid Through a Packed Bed,” Int. Chem. Eng., 16, 720–727.Google Scholar
- Matsuura, A., Hitcka, Y., Akehata, T., and Shirai, T., 1979a, “Effective Radial Thermal Conductivity in Packed Beds with Gas-Liquid Down Flow,” Heat Transfer-Japanese Research, 8, 44–52.Google Scholar
- Matsuura, A, Hitake, Y., Akehata, T., and Shirai, T., 1979b, “Apparent Wall Heat Transfer Coefficient in Packed Beds with Downward Co-Current Gas- Liquid Flow,” Heat Transfer-Japanese Research, 8, 53–60.Google Scholar
- Saez, A. E., 1983, Hydrodynamics and Lateral Thermal Dispersion for Gas-Liquid Cocurrent Flow in Packed Beds, Ph.D. thesis, University of California-Davis.Google Scholar
- Saez, A. E., Carbonell, R. G., and Levee, J., 1986, “The Hydrodynamics of Trickling Flow in Packed Beds, Part I: Conduit Models,” AIChE J., 32, 353–368.Google Scholar
- Somerton, W. H., Keese, J. A., and Chu, S. C., 1974, “Thermal Behavior of Unconsolidated Oil Sands,” SPE J., 14, 513–521.Google Scholar
- Specchia, V. and Baldi, G., 1979, “Heat TVansfer in TVickle-Bed Reactors,” Chem. Eng. Commun., 3, 483–499.Google Scholar
- Udell, K. S- and Fitch, J. S., 1985, “Heat and Mass TVansfer in Capillary Porous Media Considering Evaporation, Condensation and Noncondensible Gas Effects,” in Heat Transfer in Porous Media and Particulate Flows, ASME HTD 46, 103–110.Google Scholar