Energy Equation for Volatile Liquid Transport in Porous Media
Publication: Journal of Engineering Mechanics
Volume 130, Issue 3
Abstract
Two energy balance equations widely used to describe simultaneous transfer of heat and mass in porous media are inconsistent with control volume energy conservation. Potential energy, enthalpy, and internal energy terms are involved in the discrepancies. Energy within a volume is properly counted as the sum of internal, potential, and kinetic energy. However, one equation uses enthalpy where internal energy should have been used. In the other, potential energy and shifts in internal energy associated with heat of wetting are not included. Energy conservation for a control volume dictates summing convective fluxes of internal, potential, and kinetic energy at the control volume surface along with conducted heat and work crossing the boundary. The pressure–volume (pv) work at the volume surface may be combined with internal energy convection so that flow of enthalpy is used in the flux term. Examples of energy change versus work input in adiabatic processes illustrate the error introduced when enthalpy rather than internal energy is used to compute control volume energy content. For porous media flows kinetic energy can be dropped. A consistent equation based on the control volume approach is presented. It includes effects due to internal energy, potential energy, heat of wetting, conducted heat, non-pv work, enthalpy, and mass flow. Substantial temperature changes due to heat of wetting have been found experimentally in a separate work. A comparison is needed of the experiments and a numerical simulation based on the new equation.
Get full access to this article
View all available purchase options and get full access to this article.
References
Benjamin, J. G., Gaffarzadeh, M. R., and Cruise, R. M.(1990). “Coupled water and heat transport in ridged soils.” Soil Sci. Soc. Am. J., 54(4), 963–969.
de Vries, D. A.(1958). “Simultaneous transfer of heat and moisture in porous media.” EOS Trans. Am. Geophys. Union, 39(5), 909–916.
Edlefsen, N. E., and Anderson, A. B. C.(1943). “Thermodynamics of soil moisture.” Hilgardia, 15(2), 31–288.
Fayer, M. J. (2000). “UNSAT-H Version 3.0: Unsaturated soil water and heat flow model—Theory, user manual, and examples.” Report No. PNNL-13249, Pacific Northwest National Laboratory, Richland, Wash.
Hartley, J. G. (1977). “An analysis of the thermal stability of the soil environment of underground electrical cables.” PhD dissertation, Georgia Institute of Technology, Atlanta, Dissertation Abstract 77-29,213.
Hillel, D. (1980). Fundamentals of soil physics, Academic, New York.
Irvine, T. F., and Liley, P. E. (1984). Steam and gas tables with computer equations, Academic, New York.
Jury, W. A. (1973). “Simultaneous transport of heat and moisture through a medium sand.” PhD dissertation, Univ. of Wisconsin, Madison, Wis., Dissertation Abstract 73-27,109.
Milly, P. C. D.(1982). “Moisture and heat transport in hysteretic, inhomogeneous porous media: A matric head-based formulation and a numerical model.” Water Resour. Res., 18(3), 489–498.
Milly, P. C. D.(1984). “A simulation analysis of thermal effects on evaporation from soil.” Water Resour. Res., 20(8), 1087–1098.
Moran, M. J., and Shapiro, H. N. (1992). Fundamentals of engineering thermodynamics, 2nd Ed., Wiley, New York.
Parlange, M. B., Cahill, A. T., Nielsen, D. R., Hopmans, J. W., and Wendroth, O.(1998). “Review of heat and water movement in field soils.” Soil Tillage Res., 47(1), 5–10.
Pruess, K. (1987). “TOUGH user’s guide.” Rep. No. NUREG/CR-4645, Earth Sciences Division, Lawrence Berkeley National Laboratory, Univ. of California, Berkeley, Calif.
Pruess, K., and Narasimhan, T. N.(1985). “A practical method for modeling fluid and heat flow in fractured porous media.” SPEJ, 25(1), 14–26.
Pruess, K., Oldenburg, C., and Moridis, G. (1999). “TOUGH2 user’s guide, version 2.0.” Rep. No. LBNL-43134, Earth Sciences Division, Lawrence Berkeley National Laboratory, Univ. of California, Berkeley, Calif.
Prunty, L. (2002). “Spatial distribution of heat of wetting in porous media.” Paper 023119, American Society of Agricultural Engineers, St. Joseph, Mich.
Salzmann, W., Bohne, K., and Schmidt, M.(2000). “Numerical experiments to simulate vertical vapor and liquid water transport in unsaturated non-rigid porous media.” Geoderma, 98(3–4), 127–155.
Information & Authors
Information
Published In
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Jan 15, 2003
Accepted: Aug 22, 2003
Published online: Feb 19, 2004
Published in print: Mar 2004
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.