Distillation constant molar overflow

The McCabe-Thiele Method is restricted in its application because it only applies to binary systems and involves the simplifying assumption of constant molar overflow. However, it is an important method to understand as it gives important conceptual insights into distillation that cannot be obtained in any other way. 

If the feed is partially vaporized, the vapor flow below the feed will be lower than the top of the column. For above ambient temperature separations, the cost of operating the distillation will be dominated by the heat load in the reboiler and the vapor flow in the bottom of the column. For below ambient temperature separations, the cost of operating the column will be dominated by the cost of operating the refrigerated condenser and hence the vapor flow in the top of the column. If constant molar overflow is assumed, the vapor flow in the bottom of the column V is related to the vapor flow in the top of the column by... 

This method is one of the most important concepts in chemical engineering and is an invaluable tool for the solution of distillation problems. The assumption of constant molar overflow is not limiting since in very few systems do the molar heats of vaporisation differ by more than 10 per cent. The method does have limitations, however, and should not be employed when the relative volatility is less than 1.3 or greater than 5, when the reflux ratio is less than 1.1 times the minimum, or when more than twenty-five theoretical trays are required(13). In these circumstances, the Ponchon-Savarit method described in Section 11.5 should be used. 

The HETP of a column, valid for either distillation or dilute-gas absorption and stripping systems in which constant molar overflow can be assumed, and in which no chemical reactions occur, is related to the height of one overall gas-phase mass-transfer unit, HQG, by the equation ... 

Underwood s method (36). This method solves an equation which relates feed composition, thermal condition of the feed, and relative volatility at the average temperature of the column for a factor 6 which lies numerically between the relative volatilities of the keys. This factor is substituted in a second equation which relates minimum reflux to relative volatility and distillate composition. The method assumes constant relative volatility at the mean column temperature and constant molar overflow (Sec. 2.2.2). This method gives reasonable engineering accuracy for systems approaching ideality (28). The Underwood method has traditionally been the most popular for minimum reflux determination, When no distributed key components are present, the method is... 

Steam stripping is to be used to remove a solvent from contaminated soil. An enriching colunm will be used to recover the solvent from the stream. A vapor feed of 40 mol/hr with a composition of 20 mol% solvent and 80 mol% water enters an enriching column. The distillate stream is to have a flow rate of 5 mol/hr and a concentration of 90 mol% solvent. The internal reflux ratio is 0.875 and constant molar overflow (CMO) may be assumed. Graph the operating line to predict the number of equilibrium stages in this enriching column. 

We desire to use a distillation column to separate an ethanol-water mixture. The column has a total condenser, a partial reboiler, and a saturated liquid reflux. The feed is a saturated liquid of composition 0.10 mole fraction ethanol and a flow rate of 250 mol/hr. A bottoms mole fraction of 0.005 and a distillate mole fraction of 0.75 ethanol is desired. The external reflux ratio is 2.0. Assuming constant molar overflow, find the flowrates, the number of equilibrium stages, optimum feed plate location, and the liquid and vapor compositions leaving the fourth stage from the top of the column. Pressure is 1 atm. 

These assumptions, referred to as the McCabe-Thiele assumptions, lead to the condition of constant molar overflow. For constant molar overflow, the analysis of a distillation column is greatly simplified because it is not necessary to consider energy balances in either the rectifying or stripping sections only material balances and a VLE curve are required. 

A distillation column with a partial reboiler and a total condenser is being used to separate a mixture of benzene, toluene, and 1,2,3-trimethylbenzene. The feed, 40 mol% benzene, 30 mol% toluene, and 30 mol% 1,2,3-trimethylbenzene, enters the column as a saturated vapor. We desire 95% recovery of the toluene in the distillate and 95% of the 1,2,3-trimethylbenzene in the bottoms. The reflux is returned as a saturated liquid, and constant molar overflow can be assumed. The column operates at a pressure of 1 atm. Find the number of equilibrium stages required at total reflux, and the recovery fraction of benzene in the distillate. Solutions of benzene, toluene, and 1,2,3-trimethylbenzene are ideal. 

If the reflux ratio R or distillate rate D is fixed, instantaneous distillate and bottoms compositions vary with time. For a total condenser, negligible holdup of vapor and liquid in the condenser and the column, equilibrium stages, and constant molar overflow, the Rayleigh equation can now be written as... 

For constant molar overflow and negligible liquid holdup, the rate of distillation is given by the rate of loss of charge, or... 

A logical question that arises at this point is whether CPM theory can be applied to other separation systems. In an effort to illustrate this, we will consider membrane permeation because of its striking difference from distillation. By the nature of its operation, membrane separation is fundamentally different while in distillation, the separation is achieved by differences in boiling points, the driving force in membrane permeation is a difference between chemical potentials in the two phases. One of the most important consequences of this is that the constant molar overflow assumption, in general, cannot be employed in membrane permeating systems. 

Subsequently, t arek (9) used his procedure to predict conditions in a 30-plate bubble-cap column used for simultaneous reaction and distillation of the mixture water-acetic acid-acetic anhydride at a pressure of 400 mm Hg. Additional assumptions included absence of vapour-phase reaction, introduction of reflux and feed at their boiling points and constant molar overflow. Provided plate efficiency was around 50% for each component, reasonable agreement was clairiied between theory and experiment. 

On the other hand, calculation of diffusion in distillation columns tends to be easier if the molar average reference velocity v gf moi is used. In distillation, constant molal overflow is often valid or close to valid fSection 4.2T The resulting equimolar counterdiffusion results in = -Ng, and there is no convection in the reference frame with v,.pf mni = 0. If we choose the reference velocity as the molar average velocity, then Eq. ri5-16ei becomes... 

C7. For binary distillation with constant molar overflow (CMO),Vi.ef oi = 0. If CMO is valid, show that Vref niass 0 if MW MWBy, and calculate the functional form for Vi.ef,mass that make convection zero in this reference frame. Do this for diffusion in the vapor assuming an ideal gas. 

We now go back to the distillation column, shown in Figure 7. Also for this system a degree of freedom analysis will be performed. The assumptions for this degree of freedom analysis are that there are only two components, and that there is constant molar overflow (so the energy balance is neglected). The system then contains the following 7n+l variables, where n is the number of trays ... 

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. 

The Underwood Equation is based on the assumption that the relative volatilities and molar overflow are constant between the pinches. Given that the relative volatilities change throughout the column, which are the most appropriate values to use in the Underwood Equations The relative volatilities could be averaged according to Equations 9.47 or 9.49. However, it is generally better to use the ones based on the feed conditions rather than the average values based on the distillate and bottoms compositions. This is because the location of the pinches is often close to the feed. 

Since in an extractive distillation process based on this ternary system the extractive agent is nonvolatile and remains in the liquid phase, and since because of the similarity of the molar latent heats of nitric acid and water there is substantially constant molar liquid overflow, the mole fraction of magnesium nitrate remains almost constant throughout the process. It is appropriate to represent the equilibrium situation as a pseudo-binary system for each magnesium nitrate concentration, and Figure 7 shows vapor-liquid equilibria on a nitric acid-water basis at a series of magnesium nitrate concentrations from zero to 0.25 mole fraction in the liquid phase. 

The actual variations in the V and L streams in a distillation column depend on the enthalpies of the vapor and liquid mixtures. The limitations imposed by assuming constant molal overflow can be removed by enthalpy balances used in conjunction with material balances and phase equilibria. The enthalpy data may be available from an enthalpy-concentration diagram, such as the one in Fig. 18.24. Since benzene-toluene solutions are ideal, this diagram was constructed using molar average heat capacities and heats of vaporization. Some... 

As a footnote, considerable simplification in the mathematical separation representations could result by assuming that the respective molar flow rates remain constant throughout the membrane unit. Such is the practice in distillation calculations, where there is mass transfer in both directions. The assumption is similarly made in absorber or stripper calculations, where only one key component is involved. This condition, called constant molal overflow in distillation and absorber and stripper derivations and calculations, may also be accommodated in the case of multistage or cascade membrane calculations, as derived and utilized... 

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. 

---