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An Improved Heat Flux Theory and Mathematical Equation to Estimate Water Vapor Advection as an Alternative to Mechanistic Enhancement Factor

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An Erratum to this article was published on 27 February 2016

Abstract

The current study extended the theory of heat flux which was normally used to estimate the mechanistic enhancement factor. The current improved heat flux theory included three additional phenomena that were excluded from the simplified heat flux equation. Those three phenomena were the sensible heat by liquid water movement, the sensible heat by water vapor movement, and the partial derivative of matric pressure head effects on relative humidity with respect to temperature. The first phenomenon was found to be an important factor in relatively wet porous media, whereas the third phenomenon was found important near-dry porous media condition. Moreover, mathematical descriptions derived to allow direct conversion of mechanistic enhancement factor to water vapor advection term. The study used basic mass balance equation, ideal gas law, and air advection to describe the water vapor advection mechanism. The water vapor advection equation was found to be able to describe the influence of soil moisture content and air pressure.

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References

  • Abu-Hamdeh, N.H., Reeder, R.C.: Soil thermal conductivity effects of density, moisture, salt concentration, and organic matter. Soil Sci. Soc. Am. J. 64(4), 1285–1290 (2000). doi:10.2136/sssaj2000.6441285x

    Article  Google Scholar 

  • Bilskie, J.R., Horton, R., Bristow, K.L.: Test of a dual-probe heat-pulse method for determining thermal properties of porous materials. Soil Sci. 163(5), 346–355 (1998)

    Article  Google Scholar 

  • Burdine, N.: Relative permeability calculations from pore size distribution data. J. Pet. Technol. 5(03), 71–78 (1953)

    Article  Google Scholar 

  • Cahill, A.T., Parlange, M.B.: On water vapor transport in field soils. Water Resour. Res. 34(4), 731–739 (1998). doi:10.1029/97WR03756

    Article  Google Scholar 

  • Caldwell, M.M., Dawson, T.E., Richards, J.H.: Hydraulic lift: consequences of water efflux from the roots of plants. Oecologia 113(2), 151–161 (1998). doi:10.1007/s004420050363

    Article  Google Scholar 

  • Campbell, G.S.: Soil physics with BASIC: transport models for soil-plant systems. Developments in soil science, vol 14. Accessed from http://nla.gov.au/nla.cat-vn1895477. Elsevier, Amsterdam, New York (1985)

  • Cary, J.W.: Onsager’s relation and the non-isothermal diffusion of water vapor. J. Phys. Chem. 67(1), 126–129 (1963). doi:10.1021/j100795a030

    Article  Google Scholar 

  • Cary, J.W.: An evaporation experiment and its irreversible thermodynamics. Int. J. Heat Mass Transf. 7(5), 531–538 (1964). doi:10.1016/0017-9310(64)90050-X

    Article  Google Scholar 

  • Cary, J.W.: Water flux in moist soil: thermal versus suction gradients. Soil Sci. 100(3), 168–175 (1965)

    Article  Google Scholar 

  • Cary, J.W., Taylor, S.A.: The interaction of the simultaneous diffusions of heat and water vapor. Soil Sci. Soc. Am. Proc. 26, 413–420 (1962)

  • Cass, A., Campbell, G.S., Jones, T.L.: Enhancement of thermal water vapor diffusion in soil. Soil Sci. Soc. Am. J. 48(1), 25–32 (1984). doi:10.2136/sssaj1984.03615995004800010005x

    Article  Google Scholar 

  • Corey, A.T.: The interrelation between gas and oil relative permeabilities. Prod. Mon. 19(1), 38–41 (1954)

    Google Scholar 

  • Cunningham, R.E.: Diffusion in gases and porous media. R. E. Cunningham and R. J. J. Williams vol. Accessed from http://nla.gov.au/nla.cat-vn2596301. Plenum Press, New York (1980)

  • de Vries, D.A.: Simultaneous transfer of heat and moisture in porous media. Eos Trans. Am. Geophys. Union 39(5), 909–916 (1958). doi:10.1029/TR039i005p00909

    Article  Google Scholar 

  • Falta, R.W., Javandel, I., Pruess, K., Witherspoon, P.A.: Density-driven flow of gas in the unsaturated zone due to the evaporation of volatile organic compounds. Water Resour. Res. 25(10), 2159–2169 (1989)

    Article  Google Scholar 

  • Farouki, O.T.: Thermal properties of soils. In: vol. 81-1, pp. 151. CRREL Technical Information Analysis Center (TIAC) (1981)

  • Fick, A.: On liquid diffusion. J. Membr. Sci. 100(1), 33–38 (1995). doi:10.1016/0376-7388(94)00230-V

    Article  Google Scholar 

  • Heitman, J.L., Horton, R., Ren, T., Nassar, I.N., Davis, D.D.: A test of coupled soil heat and water transfer prediction under transient boundary temperatures. Soil Sci. Soc. Am. J. 72(5), 1197–1207 (2008). doi:10.2136/sssaj2007.0234

    Article  Google Scholar 

  • Hiraiwa, Y., Kasubuchi, T.: Temperature dependence of thermal conductivity of soil over a wide range of temperature (5–75 \(^{\circ }\text{ C }\)). Eur. J. Soil Sci. 51(2), 211–218 (2000). doi:10.1046/j.1365-2389.2000.00301.x

    Article  Google Scholar 

  • Ho, C.K., Webb, S.W.: A review of porous media enhanced vapor-phase diffusion mechanisms, models, and data: Does enhanced vapor-phase diffusion exist? In: Other Information: PBD: May 1996. p. Medium: ED; Size: 42 p. (1996)

  • Ho, C.K., Webb, S.W.: Enhanced vapor-phase diffusion in porous media—LDRD Final Report. In., p. Medium: ED (1999)

  • Jackson, R.D., Nielsen, D.R., Nakayama, F.S.: On Diffusion Laws Applied to Porous Materials, vol. 41–86. USDA-ARS, Washington, D.C. (1963)

  • Jury, W.A., Horton, R.: Soil Physics. Wiley, New York (2004)

    Google Scholar 

  • Kimball, B.A., Jackson, R.D., Reginato, R.J., Nakayama, F.S., Idso, S.B.: Comparison of field-measured and calculated soil–heat fluxes. Soil Sci. Soc. Am. J. 40(1), 18–25 (1976). doi:10.2136/sssaj1976.03615995004000010010x

    Article  Google Scholar 

  • Lu, S., Ren, T., Yu, Z., Horton, R.: A method to estimate the water vapour enhancement factor in soil. Eur. J. Soil Sci. 62(4), 498–504 (2011). doi:10.1111/j.1365-2389.2011.01359.x

    Article  Google Scholar 

  • Mason, E.A., Malinauskas, A.: Gas Transport in Porous Media: The Dusty-Gas Model, vol. 17. Elsevier Science Ltd, Amsterdam (1983)

    Google Scholar 

  • McInnes, K.J.: Thermal Conductivities of Soils from Dryland Wheat Regions of Eastern Washington. Washington State University, Pullman, WA (1981)

    Google Scholar 

  • Milly, P.C.D.: 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 (1982). doi:10.1029/WR018i003p00489

    Article  Google Scholar 

  • Mualem, Y.: A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12(3), 513–522 (1976)

    Article  Google Scholar 

  • Muskat, M., Wyckoff, R.D.: The flow of homogeneous fluids through porous media. International series in physics, vol. XIX, 763 p. J. W. Edwards, Ann Arbor, MI (1946)

  • Nakano, M., Miyazaki, T.: The diffusion and nonequilibrium thermodynamic equations of water vapor in soils under temperature gradients. Soil Sci. 128(3), 184–188 (1979)

    Article  Google Scholar 

  • Nassar, I.N., Horton, R.: Heat, water, and solution transfer in unsaturated porous media: I—Theory development and transport coefficient evaluation. Transp. Porous Media 27(1), 17–38 (1997). doi:10.1023/a:1006583918576

    Article  Google Scholar 

  • Noborio, K., McInnes, K.J.: Thermal conductivity of salt-affected soils. Soil Sci. Soc. Am. J. 57(2), 329–334 (1993). doi:10.2136/sssaj1993.03615995005700020007x

    Article  Google Scholar 

  • Noborio, K., McInnes, K.J., Heilman, J.L.: Two-dimensional model for water, heat, and solute transport in furrow-irrigated soil: II. Field evaluation. Soil Sci. Soc. Am. J. 60(4), 1010–1021 (1996). doi:10.2136/sssaj1996.03615995006000040008x

    Article  Google Scholar 

  • Parikh, R.J., Havens, J.A., Scott, H.D.: Thermal diffusivity and conductivity of moist porous media. Soil Sci. Soc. Am. J. 43(5), 1050–1052 (1979). doi:10.2136/sssaj1979.03615995004300050047x

    Article  Google Scholar 

  • Parlange, M.B., Cahill, A.T., Nielsen, D.R., Hopmans, J.W., Wendroth, O.: Review of heat and water movement in field soils. Soil Tillage Res. 47(1–2), 5–10 (1998). doi:10.1016/S0167-1987(98)00066-X

    Article  Google Scholar 

  • Penman, H.L.: Gas and vapour movements in the soil: I. The diffusion of vapours through porous solids. J. Agric. Sci. 30(03), 437–462 (1940). doi:10.1017/S0021859600048164

  • Philip, J.R., de Vries, D.A.: Moisture movement in porous materials under temperature gradients. Eos Trans. Am. Geophys. Union 38(2), 222–232 (1957). doi:10.1029/TR038i002p00222

    Article  Google Scholar 

  • Pruess, K.: TOUGH2: A general-purpose numerical simulator for multiphase fluid and heat flow. In: p. Medium: ED; Size: Pages: (102 p) (1991)

  • Riha, S.J., McInnes, K.J., Childs, S.W., Campbell, G.S.: A finite element calculation for determining thermal conductivity. Soil Sci. Soc. Am. J. 44(6), 1323–1325 (1980). doi:10.2136/sssaj1980.03615995004400060039x

    Article  Google Scholar 

  • Saito, H., Šim\(\mathring{\text{u}}\)nek, J., Mohanty, B.P.: Numerical analysis of coupled water, vapor, and heat transport in the vadose zone. Vadose Zone J. 5(2), 784–800 (2006). doi:10.2136/vzj2006.0007

  • Sakaguchi, I., Momose, T., Mochizuki, H., Kasubuchi, T.: Heat pipe phenomenon in soil under reduced air pressure. Eur. J. Soil Sci. 60(1), 110–115 (2009). doi:10.1111/j.1365-2389.2008.01095.x

    Article  Google Scholar 

  • Shokri, N., Lehmann, P., Or, D.: Critical evaluation of enhancement factors for vapor transport through unsaturated porous media. Water Resour. Res. 45(10), 1–9 (2009). doi:10.1029/2009wr007769

    Article  Google Scholar 

  • Shurbaji, A.-R.M., Phillips, F.M.: A numerical model for the movement of H2O, H218O, and 2HHO in the unsaturated zone. J. Hydrol. 171(1–2), 125–142 (1995). doi:10.1016/0022-1694(94)02604-A

    Article  Google Scholar 

  • van Genuchten, M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44(5), 892–898 (1980). doi:10.2136/sssaj1980.03615995004400050002x

    Article  Google Scholar 

  • Webb, S., Pruess, K.: The use of Fick’s law for modeling trace gas diffusion in porous media. Transp. Porous Media 51(3), 327–341 (2003). doi:10.1023/A:1022379016613

    Article  Google Scholar 

  • Winterkorn, H., Fang, H.-Y.: Soil Technology and Engineering Properties of Soils. In: Fang, H.-Y. (ed.) Foundation Engineering Handbook, pp. 88–143. Springer, US (1991)

    Chapter  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge the financial support from Meiji University, Japan and the Ministry of Higher Education Malaysia, and Universiti Malaysia Terengganu, Malaysia.

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Authors and Affiliations

  1. School of Agriculture, Meiji University, 1-1-1 Higashimita, Tamaku, Kawasaki, 214-8571, Japan

    Eng Giap Goh & Kosuke Noborio

  2. School of Ocean Engineering, Universiti Malaysia Terengganu, 21030, Kuala Terengganu, Terengganu, Malaysia

    Eng Giap Goh

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  1. Eng Giap Goh
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  2. Kosuke Noborio
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Correspondence to Eng Giap Goh.

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Goh, E.G., Noborio, K. An Improved Heat Flux Theory and Mathematical Equation to Estimate Water Vapor Advection as an Alternative to Mechanistic Enhancement Factor. Transp Porous Med 111, 331–346 (2016). https://doi.org/10.1007/s11242-015-0596-4

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  • DOI: https://doi.org/10.1007/s11242-015-0596-4

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