1.3 Mass Transfer
In the vapor-liquid contacting system shown in Figure 1-2 the vapor and liquid will not be initially at equilibrium. By transferring mass from one phase to the other we can approach equilibrium. The basic mass transfer equation in words is
In this equation the mass transfer rate will typically have units such as kmol/h or lbmol/h. The area is the area across which mass transfer occurs in m2 or ft2. The driving force is the concentration difference that drives the mass transfer. This driving force can be represented as a difference in mole fractions, a difference in partial pressures, a difference in concentrations in kmol/L, and so forth. The value and units of the mass transfer coefficient depend upon which driving forces are selected. The details are discussed in Chapter 15.
For equilibrium staged separations we would ideally calculate the mass transfer rate based on the transfer within each phase (vapor and liquid in Figure 1-2) using a driving force that is the concentration difference between the bulk fluid and the concentration at the interface. Since this is difficult, we often make a number of simplifying assumptions (see Section 15.4 for details) and use a driving force that is the difference between the actual concentration and the concentration we would have if equilibrium were achieved. For example, for the system shown in Figure 1-2 with concentrations measured in mole fractions, we could use the following rate expressions.
In these equations Ky and Kx are overall gas and liquid mass transfer coefficients, yA* is the mole fraction in the gas in equilibrium with the actual bulk liquid of mole fraction xA, xA* is the mole fraction in the liquid in equilibrium with the actual bulk gas of mole fraction yA, and the term "a" is the interfacial area per unit volume (m2/m3 or ft2/ft3).
By definition, at equilibrium we have yA* = yA and xA* = xA. Note that as yAyA* and xAxA* the driving forces in Eqs. (1-5) approach zero and mass transfer rates decrease. In order to be reasonably close to equilibrium, the simplified model represented by Eqs. (1-5) shows that we need high values of Ky and Kx and/or "a." Generally speaking, the mass transfer coefficients will be higher if diffusivities are higher (details are in Chapter 15), which occurs with fluids of low viscosity. Since increases in temperature decrease viscosity, increasing temperature is favorable as long as it does not significantly decrease the differences in equilibrium concentrations and the materials are thermally stable. Mass transfer rates will also be increased if there is more interfacial area/volume between the gas and liquid (higher "a"). This can be achieved by having significant interfacial turbulence or by using a packing material with a large surface area (see Chapter 10).
Although some knowledge of what affects mass transfer is useful, we don't need to know the details as long as we are willing to assume we have equilibrium stages. Thus, we will delay discussing the details until we need them (Chapters 15 through 18).