Constant Relative Volatilities

Figure 1 shows the schematic of a MultiVBD Column. A dynamic model based on constant relative volatility, constant molar liquid holdup on the stages, total condenser and constant pressure is considered here and are shown in Figure 2. Note, the simple model for the conventional column is taken from Mujtaba (2004) and therefore is not presented here.

The chemical equilibrium constant at 366 K [(Feq)366] and the relative volatilities (constant or temperature dependent) are specified for each case. Equimolal overflow is assumed in the distillation columns, which means that neither energy balances nor total balances are needed on the trays for steady-state calculations. Other assumptions are isothermal operation of the reactor, theoretical trays, saturated hquid feed and reflux, total condensers, and partial reboilers in the columns. Additional assumptions and specifications are the following ... 

Example This equation is obtained in distillation problems, among others, in which the number of theoretical plates is required. If the relative volatility is assumed to be constant, the plates are theoretically perfect, and the molal liquid and vapor rates are constant, then a material balance around the nth plate of the enriching section yields a Riccati difference equation. 

It is sometimes permissible to assume constant relative volatility in order to approximate the equilibrium curve quickly. Then by applying Eq. (13-2) to components 1 and 2,... 

A system with constant relative volatility can be handled conveniently by the equation of Smoker [Trans. Am. Inst. Chem. Eng., 34, 165 (1938)]. The derivation of the equation is shown, and its use is ihustrated by Smith (op. cit.). 

This term is analogous to relative volatility or its reciprocal (or to an equilibrium selectivity). Similarly, the assumption of a constant sepa-... 

In distillation work for binary systems with constant relative volatility, the equilibrium between phases for a given component can be expressed by the following equation ... 

For a binary mixture with constant relative volatility the following expression applies ... 

Relative volatility is the volatility separation factor in a vapor-liquid system, i.e., the volatility of one component divided by the volatility of the other. It is the tendency for one component in a liquid mixture to separate upon distillation from the other. The term is expressed as fhe ratio of vapor pressure of the more volatile to the less volatile in the liquid mixture, and therefore g is always equal to 1.0 or greater, g means the relationship of the more volatile or low boiler to the less volatile or high boiler at a constant specific temperature. The greater the value of a, the easier will be the desired separation. Relative volatility can be calculated between any two components in a mixture, binary or multicomponent. One of the substances is chosen as the reference to which the other component is compared. 

When temperature is constant and at equilibrium for a homogeneous mixture (such as azeotrope), the composition of the liquid is identical with the composition of the vapor, thus xj = y, and the relative volatility is equal to 1.0. 

For a binary system with constant relative volatilities ... 

X = mol fraction of a component in liquid phase y = mol fraction of a component in vapor phase a = relative volatility P = constant in Equation 8-43 K = total pressure, psia L = total mols in liquid phase... 

For systems of high (above approximately 3.0) constant relative volatility the Raleigh equation can be expressed ... 

Most batch distillations/separations are assumed to follow the constant relative volatility vapor-liquid equilibrium curve of... 

This system for evaluating multicomponent adjacent key systems, assuming constant relative volatility and constant molai overflow, has proven generally satisfactory for many chemical and hydrocarbon applications. It gives a rigorous solution for constant molai overflow and volatility, and acceptable results for most cases which deviate from these limitations. 

The direct-solution method of Akers and Wade [1] is among several which attempt to reduce the amount of trial-and-error solutions. This has been accomplished and has proven quite versatile in application. The adaptation outlined modifies the symbols and rearranges some terms for convenient use by the designer [3]. Dew point and bubble point compositions and the plate temperatures can be determined directly. Constant molal overflow is assumed, and relative volatility is held constant over sections of the column. 

Mols of component, i, at start of distillation Total mols of liquid in bottoms of still at time, Tj Total mols liquid (not including any steam) in bottom of still at start time Tq (batch charge) y intercept of operating line or constant at fixed pressure for Winn s relative volatility Mols of component, i, in bottoms No. components present, phase rule or no. components, or constant... 

Ol = Relative volatility of components lighter than light key at feed tray temperature P = Constant of fixed pressure in Winn s relative volatility. Equation 8-43... 

Equilibrium data correlations can be extremely complex, especially when related to non-ideal multicomponent mixtures, and in order to handle such real life complex simulations, a commercial dynamic simulator with access to a physical property data-base often becomes essential. The approach in this text, is based, however, on the basic concepts of ideal behaviour, as expressed by Henry s law for gas absorption, the use of constant relative volatility values for distillation and constant distribution coeficients for solvent extraction. These have the advantage that they normally enable an explicit method of solution and avoid the more cumbersome iterative types of procedure, which would otherwise be required. Simulation examples in which more complex forms of equilibria are employed are STEAM and BUBBLE. 

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. 

A batch still corresponding to a total separation capacity equivalent to eight theoretical plates (seven plates plus the still) is used to separate a hydrocarbon charge containing four (A, B, C, D) simple-hydrocarbon components. Both the liquid and vapour dynamics of the column plates are neglected. Equilibrium data for the system is represented by constant relative volatility values. Constant molar overflow conditions again apply, as in BSTILL. The problem was originally formulated by Robinson (1975). 

The relative volatility will change as the compositions and (particularly for a vacuum column) the pressure changes up the column. The column pressures cannot be estimated until the number of stages is known so as a first trial the relative volatility will be taken as constant, at the value determined by the bottom pressure. 

Estimates of the flows of the combined keys enable operating lines to be drawn for the equivalent binary system. The equilibrium line is drawn by assuming a constant relative volatility for the light key ... 

Hengstebeck shows how the method can be extended to deal with situations where the relative volatility cannot be taken as constant, and how to allow for variations in the liquid and vapour molar flow rates. He also gives a more rigorous graphical procedure based on the Lewis-Matheson method (see Section 11.8). 

Winn (1958) has derived an equation for estimating the number of stages at total reflux, which is similar to the Fenske equation, but which can be used when the relative volatility cannot be taken as constant. 

Propane is separated from propylene by distillation. The compounds have close boiling points and the relative volatility will be low. For a feed composition of 10 per cent w/w propane, 90 per cent w/w propylene, estimate the number of theoretical plates needed to produce propylene overhead with a minimum purity of 99.5 mol per cent. The column will operate with a reflux ratio of 20. The feed will be at its boiling point. Take the relative volatility as constant at 1.1. 

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