General

A detailed description of MD principle is given by Banat (1994) [27] and a summary of that is provided here. Conventionally, MD is a thermally driven process in which a microporous hydrophobic membrane separates a warm solution from a cooler chamber, which contains either a liquid or a gas. As the process is nonisothermal, vapor molecules migrate through the membrane pores from the high to the low vapor pressure side, that is, from the warmer to the cooler compartment. It is also possible to lower the vapor pressure isothermally by using concentrated solutions or applying vacuum in the downstream side. The separation mechanism of MD is based on vapor-liquid equilibrium. The principle of MD is illustrated in Fig. 4. The transport mechanism of MD involves four steps [27]:

1. Movement of the volatile components from the bulk of the feed stream to the membrane surface

2. Evaporation of the volatiles in the warm feed at the membrane surface

Membrane

Warm feed

Pore

Membrane

Warm feed

Cold permeate

Figure 4 Membrane distillation concept. Adapted from Ref [27].

Cold permeate

Figure 4 Membrane distillation concept. Adapted from Ref [27].

3. Migration of the vapor through the nonwetted pores

4. Condensation of the vapor at the cold permeate side either in a liquid or in a condenser

The nature of the driving force, in synergy with the hydrorepellent character of the membrane, allows the complete rejection of nonvolatile solutes such as macromolecules, colloidal species, ions, and so on. Typical feed temperatures vary in the range of30-60 °C, thus permitting the efficient recycle of low-grade or waste heat streams, as well as the use of alternative energy sources (solar, wind, or geothermal). If compared to RO process, MD does not suffer from limitations arising from concentration polarization phenomenon and can be preferentially employed whenever elevated permeate recovery factors or high retentate concentrations are requested.

The main requirement of this process is that the membrane must not be wetted and only vapor is present in the pores. When used for desalination, saltwater is the hot feed solution. Pure water vapor passes through the membrane pores while the salts and other nonvolatiles remain on the warm side of the membrane. When volatile components are to be removed from water, the separation depends on their relative volatilities. As in ordinary distillation, the relative volatilities ofcompounds at the operating conditions determine their presence in the recondensed phase. When used for ethanol, acetone, or benzene removal, these compounds and some water vapor migrate through the membrane pores.

Vapor pressure gradient. A detailed discussion of MD transport can be found elsewhere [26], and only a summary is provided here. Heat and mass transport through membranes occur only if the overall system is not in thermodynamic equilibrium. In membrane processes, two homogeneous subsystems (with defined chemical potentials of mi and m/0 are separated by a membrane. For small changes of the number of moles in the two phases (caused by the mass transfer across the membrane), the variation of the Gibbs free energy (G) is:

Relation (8) expresses a general concept: the driving force for the mass transport of a component from one phase to the other is given by the difference in the chemical potential of the two phases caused by changes in temperature, pressure, and activity. In Eq. (8), ni' is the mole of i-th component transferred and is related to transmembrane flux Ji by:

where t indicates the time and A the membrane area. The hydrostatic pressure gradient across the membrane is negligible in MD, and the driving force of process is the partial pressure difference across the membrane, established by a temperature difference between the two contacting solutions, or by vacuum, air gap, or sweep gas in the permeate side. In the frequent case of nonideal mixtures, the vapor-liquid equilibrium is mathematically described in terms of partial pressure (pi), vapor pressure of pure i (po), and activity coefficient Zi, according to the thermodynamic relationship:

In Eq. (10), P is the total pressure, a the activity, and xi and yi are the liquid and vapor mole fractions, respectively. The vapor pressure po of a pure substance varies with temperature according to the Clausius-Clapeyron equation:

where l is the latent heat of vaporization (l — 9.7cal/mol for water at 100 °C) [26], R the gas constant, and T the absolute temperature. At the pore entrance, the curvature of the vapor-liquid interface is generally assumed to have a negligible effect on the equilibrium; however, possible influences on the vapor pressure value can be estimated by the

Kelvin equation:

where r is the curvature radius, gL the liquid surface tension, and c the liquid molar density. Activity coefficients Z can be deduced by a large variety of equations aiming to evaluate the excess Gibbs function of mixtures; the most popular of them are reported in elsewhere [26,28].

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