Page 35 - gas transport in porous media

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Gas Ho

Liquid

Figure 3.1. Illustration of molecular states of liquid and gas

system. As the temperature increases, the vapor pressure of a liquid increases sig-
nificantly. At a molecular level, the energy associated with the molecules increases
with increasing temperature. At higher temperatures, molecules have greater kinetic
energy (they become more “active”) and begin to break free of the van der Waals
forces that attract the molecules to one another. The process of molecules break-
ing free from one another is known as evaporation, and the rate of evaporation
increases with increasing temperature. The separation distance between vapor-phase
molecules is large relative to the separation distance between liquid-phase molecules
(Figure 3.1).
The vapor pressure is the pressure that the vapor-phase molecules exert on each
other and on the walls of a container. In a closed container partially filled with liquid,
evaporation of the liquid will continue until the pressure exerted by the vapor-phase
molecules equals the saturated vapor pressure determined by the system temperature
for that compound. When this saturated (or equilibrium) vapor pressure is reached, the
rateofevaporationisbalancedbytherateofcondensationattheliquid/vaporinterface.
Compounds that are more readily evaporated have a higher vapor pressure at a given
temperature. Figure 3.2 shows the vapor pressure as a function of temperature for
water and trichloroethylene (TCE). For any given temperature, the saturated vapor
pressure of TCE is greater than the saturated vapor pressure of water. Therefore, TCE
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is more volatile than water. Another interesting note is that at 100 C, the saturated
vapor pressure of water is 101 kPa, which is equal to the atmospheric pressure at sea
level. Thus, the boiling point of water is simply the temperature at which the saturated
vapor pressure equals the surrounding pressure. Therefore, according to Figure 3.2,
◦
the boiling point of TCE at sea level (101 kPa) is approximately 87 C. At higher
elevations, the atmospheric pressure is lower, so the boiling point for liquids is also
lower. Expressions relating vapor pressure to temperature for various compounds can
be found in Reid et al. (1987).
The concentration of a vapor in equilibrium with its liquid can be calculated using
the ideal gas law and the vapor pressure of the compound at the system temperature.
◦
For example, if water is poured into a container at 20 C, and then sealed with an
amount of head space above the liquid water, the liquid water will evaporate until
enough water vapor exists in the head space to exert a pressure equal to the vapor
pressure at the system temperature.