Equal-molar overflow

The effective top and bottom section temperatures are used to determine Kj and KV These are used along with the effective top and bottom section molar liquid and vapor rates to determine S and S. Section temperatures are the average of the top and feed design temperatures for the top section and bottom and feed design temperatures for the bottom section, or averaged column profile data, if available. The molar flows can be obtained assuming equal molar overflow or with averaged column profile data, if available. 

Here we are interested in modeling a typical tray in a binary distillation column, as shown in Figure 5.14. The major assumption we usually make for binary distillation is that of equal-molar overflow, namely that the molar vapor flow rate entering the tray is equal to the molar vapor flow rate leaving the tray, Vn+i = K-... 

The main effect of the equal-molar overflow assumption is that the energy balance is not required in the solution model for a tray. 

After heat recovery, via HXl and HX2, the reactor effluent is fed into a distillation column. The two reactants, A B, are light key (LK) and intermediate boiler (IK), respectively, while the product, X, is the heavy component (HK). The Antoine constants of the vapor pressure equation are chosen such that the relative volatilities of the components are ttA = 4, ttB = 2, and Oc=l for this equal molar overflow system (Table 1). Only one distillation column is sufficient to separate the product (C) from the unreacted reactants (A B). Ideal vapor-liquid equilibrium is assumed. Physical property data and kinetic data are given in Table 1. 

The constant-molar-overflow assumption represents several prior assumptions. The most important one is equal molar heats of vaporization for the two components. The other assumptions are adiabatic operation (no heat leaks) and no heat of mixing or sensible heat effects. These assumptions are most closely approximated for close-boiling isomers. The result of these assumptions on the calculation method can be illustrated with Fig. 13-28, vdiich shows two material-balance envelopes cutting through the top section (above the top feed stream or sidestream) of the column. If L + i is assumed to be identical to L 1 in rate, then 9 and the component material balance... 

The system is ideal, with equilibrium described by a constant relative volatility, the liquid components have equal molar latent heats of evaporation and there are no heat losses or heat of mixing effects on the plates. Hence the concept of constant molar overflow (excluding dynamic effects) and the use of mole fraction compositions are allowable. 

The number of molecules passing in each direction from vapour to liquid and in reverse is approximately the same since the heat given out by one mole of the vapour on condensing is approximately equal to the heat required to vaporise one mole of the liquid. The problem is thus one of equimolecular counterdiffusion, described in Volume 1, Chapter 10. If the molar heats of vaporisation are approximately constant, the flows of liquid and vapour in each part of the column will not vary from tray to tray. This is the concept of constant molar overflow which is discussed under the heat balance heading in Section 11.4.2. Conditions of varying molar overflow, arising from unequal molar latent heats of the components, are discussed in Section 11.5. 

Thus, the assumptions of enthalpy additivity and equality of heats of vaporization of the two components in a binary lead to the approximation of constant molar overflow of liquid and vapor in a column section. The implication is that for each mole of component 1 vaporizing at a given stage, one mole of component 2 condenses. Substituting V=Vj= and L = I.., = Lj in Equation 5.1 yields the following ... 

Assuming constant molar overflow, LjV is constant and the assumption of equimolar counterdiffusion is valid, so that the flux of one component across the vapor-liquid interface is equal and opposite to the flux of the other component = -Nb)-For a diffeential height dz in a packed column, the mass transfer rate is ... 

This is called pseudo-molar overflow. Only when the heats of evaporation of the eomponerrts are equal, the equation can be simplified further to molar overflow. This does not happen... 

If this process is carried out in a distillation column, the minimum energy required may be determined from the heat Qk supplied in the reboiler/gmol of feed at Tg if we may assume that the total heat supplied at the reboiler is equal to that withdrawn in the condenser (i.e. Qc) at Tc-Further, this minimum will occur at the minimum reflux ratio, which means that there will be an infinite number of plates. Following Humphrey and Keller (1997), we aissume the fallowing complete separation of feed into two pure products constant relative volatility i2 constant molar overflow feed at bubble point minimum reflux ratio single reboiler and condenser liquid feed at bubble point. Consider now the distillation column shown in Figure 10.1.5(a). The overall and component material balance equations are ... 

The restriction to dilute solution is less serious than it might first seem. While correlations of mass transfer coefficients like those in Chapter 8 are often based on dilute solution experiments, these correlations can often be successfully used in concentrated solutions as well. For example, in distillation, the concentrations at the vapor-liquid interface may be large, but the large flux of the more volatile component into the vapor will almost exactly equal the large flux of the less volatile component out of the vapor. There is a lot of mass transfer, but not much diffusion-induced convection. Thus constant molar overflow in distillation implies a small volume average velocity normal to the interface, and mass transfer correlations based on dilute solution measurements should still work for these concentrated solutions. 

Then, every mole of condensing vapor vaporizes exactly 1 mole of liquid. Since it is the molar latent heats that are presumed to be equal, the flows must be specified in terms of moles, and the concentrations in terms of mole fractions for use with the constant molal overflow assumption. 

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