Example 1 Stagnant Sweep Gas

When operating this distillation unit below the boiling temperature, the vapor space is partly filled with ambient air the watchglass must not perfectly seal the still. 

The concentrations at the condenser Xj,c are identical to the relative fluxes %j because of total condensation of the vapor escaping from the liquid surface. Schliinder [19] derived the following relationship between mole fractions of liquid in the still, Xj s, and the mole fractions of the condensed liquid in the receiver, ocjtc  

Equation (51) is based on the Stefan-Maxwell equations describing the mass transport in the gas phase. 

To illustrate the system behavior, the ternary mixture 1 = iso-propanol, 2 = water, and 3 = air is considered here. In order to obtain an algebraic solution, both the dif-fusivities of iso-propanol in air and iso-propanol in water vapor were assumed to be approximately the same, which is not far from reality. The liquid phase mass transfer resistance was negligibly small, as will be shown below. The phase equilibrium constants K/,c and Kjrs were calculated with activity coefficients from van Laar s equation. Water vapor diffuses 2.7-fold faster in the inert gas air than iso-propanol. The ratio of the respective mass transfer coefficients kj3 equals the ratio of the respective diffusivities to the power of 2/3rd according to standard convective mass transfer equations Sh =J Re, Sc). 

This example illustrates the distillation of a binary mixture in an open-batch distillery with flowing sweep gas, as shown in Fig. 4.17. The vapor emerging from the batch distillery is carried away by the sweep gas flow, thus keeping the partial vapor pressures above the gas-liquid interface at a constant value, depending on the magnitude of the sweep gas flow rate. 

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