Equilibrium stages minimum number

Damkohler number (-) feed flow rate (mol- s ) chemical equilibrium constant (-) reaction rate constant (mol-m -s ) liquid flow rate (mol- s ) total number of stages (-) minimum number of stages (-) reaction order (-)... 

After condensation in a total condenser and separation of the two liquid layers, the water layer is withdrawn as product and the diisopropyl ether layer is returned as reflux. We operate at an external reflux ratio that is 2.0 times the minimum external reflux ratio. Operation is at 1.0 atm. Find the minimum external reflux ratio, the actual L/D, the distillate flow rate and mole frac water, the bottoms flow rate and mole frac water, and the number of equilibrium stages required (number the top stage as number 1). Use an expanded McCabe-Thiele diagram to determine the number of stages. Data for the azeotropic conposition fProblem 8.D81 can be used to find the mole fracs of water in the two layers in the separator and the relative volatility of water with respect to ether at low water concentrations. The weight fractions have to be converted to mole fracs first. 

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. 

An estimate of the minimum absorbent flow rate for a specified amount of absorption from the entering gas of some key component K for a cascade with an infinite number of equilibrium stages is obtained from Eq. (13-40) as... 

From Fenske s equation, the minimum number of equilibrium stages at total reflux is related to their bottoms (B) and distillate or overhead (D) compositions using the average relative volatility, see Equation 8-29. 

Occasionally the minimum reflux calculated by this method comes out a negative number. That, of course, is a signal that some other method should be tried, or it may mean that the separation between feed and overhead can be accomplished in less than one equilibrium stage. 

A short-cut design method for distillation is another subroutine. This method is based upon the minimum reflux of Underwood (17, 18, 19, 20), the minimum stages of Fenske (21) and Winn (22), and the reflux vs stages correlation of Erbar and Maddox (23) and Gray (24). In SHORT, which uses polynomial K and H values, the required number of equilibrium stages may be found for a specified multiple of minimum reflux, or alternatively, the reflux ratio may be found for a given multiple of minimum stages. 

The condition where the reflux and stripping ratios approach infinity is termed total reflux. No feed enters the column and no product leaves. Both component balance lines coincide with the 45° diagonal line and are therefore furthest away from the equilibrium curve. Total reflux sets the minimum number of stages required for the separation. For Example 2,1, Fig. 3,lid shows that the minimum number of stages required for the separation is 6. 

Chemical equilibrium constant for dimerization Liquid-liquid distribution ratio Liquid flow rate Number of equilibrium stages Number of relationships Number of design variables Minimum number of equilibrium stages Number of phases Number of repetition variables Number of variables Rate of mass transfer Molar flux... 

The variable that has the most significant impact on the economics of an extractive distillation is the solvent-to-feed flow rate ratio S/F. For close-boiling or pinched nonazeotropic mixtures, no minimum-solvent flow rate is required to effect the separation, as the separation is always theoretically possible (if not economical) in the absence of the solvent. However, the extent of enhancement of the relative volatility is largely determined by the solvent composition in the lower column sections and hence the S/F ratio. The relative volatility tends to increase as the S/F ratio increases. Thus, a given separation can be accomplished in fewer equilibrium stages. As an illustration, the total number of theoretical stages required as a function of S/F ratio is plotted in Fig. 13-95a for the separation of the nonazeotropic mixture of vinyl acetate and ethyl acetate using phenol as the solvent. 

For the separation of a minimum-boiling binary azeotrope by extractive distillation, there is clearly a minimum-solvent flow rate below which the separation is impossible (due to the azeotrope). For azeotropic separations, the number of equilibrium stages is infinite at or below (S/F) i and decreases rapidly with increasing solvent feed... 

If the equilibrium ratios are functions of phase compositions as occurs in liquid extraction or extractive distillation, it is necessary to include more variables in the iterative process. It was later shown (3) that for liquid extraction problems with known stage temperatures, the minimum number of iteration variables for quadratic convergence is nm, the n vapor flow rates, and n(m — 1) of the phase compositions. The total number of variables is n(2m + 2) because the temperatures are known. The iteration sequence is completely different for this case as compared with the previous case with composition independent equilibrium ratios. 

Calculate the minimum number of equilibrium stages, Nm, from the Fenske equation. Equation 6.27.2. 

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