Transformations of fluxes and forces describing the simultaneous transport of water and heat in unsaturated porous media

Journal Article · Mon Dec 01 00:00:00 EST 1975 · Water Resour. Res.; (United States)

DOI:https://doi.org/10.1029/WR011i006p00938· OSTI ID:5384790

Raats, P A.C.

Balances of mass for the water in N distinct phases and a balance of heat for the medium as a whole were formulated. Following Philip and de Vries, it was assumed that the flux of water in each phase is proportional to the gradient of the pressure in that phase and that the diffusive component of the flux of heat is proportional to the gradient of the temperature. Clapeyron equations were used to express the gradient of the pressure in any phase in terms of the gradient of the pressure in a reference state and of the temperature. The reference state may be the water in one of the phases or the water in some measuring device such as a tensiometer or a psychrometer. Expressions for the total flux of water and for the diffusive flux of heat plus the convective flux of heat associated with the conversion from any phase to the reference state were shown to satisfy the onsager reciprocal relations. A theorem due to Meixner was used to delineate the class of fluxes and forces that preserves these relations. In particular, it was shown that if the gradients of water content and temperature are used as the driving forces, the onsager relations are no longer satisfied.

• Research Organization: Agricultural Research Service, Riverside, CA
• OSTI ID: 5384790
• Journal Information: Water Resour. Res.; (United States), Vol. 11:6
• Country of Publication: United States
• Language: English

Related Subjects

15 GEOTHERMAL ENERGY
POROUS MATERIALS
FLUID FLOW
HEAT TRANSFER
MASS TRANSFER
AQUIFERS
MATHEMATICAL MODELS
ONSAGER RELATIONS
PRESSURE DEPENDENCE
PRESSURE GRADIENTS
TEMPERATURE DEPENDENCE
TEMPERATURE GRADIENTS
WATER
ENERGY TRANSFER
HYDROGEN COMPOUNDS
MATERIALS
OXYGEN COMPOUNDS
150200* - Geology & Hydrology of Geothermal Systems