Multicomponent Separation Calculations

Given the then each assumed value V/F (or L/f) has a unique solution for V . This is a variation on the single-stage flash calculation for a vapor-liquid separation. 

The calculation for a multicomponent system is, in general, trial and error, establishing the values of and the y, along with a corresponding value for V . In turn, given the feed rate F and the specified ratio V/F, the absolute value of the permeate rate V with respect to F follows similarly for determining an absolute value for the reject rate L relative to F. 

Given the value of (x )-, these calculations establish the respective values of V for each of the limiting conditions, along with the respective compositions x, and y,. These limiting bubble-point and dew-point type determinations were previously described. 

In the parlance used for distillation calculations, the two key components can be designated as those whose distribution behavior is closest to unity, with one key component showing a R-value less than 1 and the other greater than 1. The latter would exhibit the greater volatility or activity, in this case, would have a greater value for K. 

That is, if P- P-, then component would have the greater permeability and have the higher volatility or activity. 

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As a special case of multicomponent separation calculations, the double trial-and-error type calculations involved for two components are best done utilizing spreadsheet techniques as set forth in Appendix 3 of Hoffman (2003). However, it is possible to obtain an analytic solution for two components, albeit involved and unwieldy. For the record, this latter procedure is as follows. 

Naphtali, L.M. and Sandholrn, DT. (1971) Multicomponent separation calculations by linearization. AIChEJ, 17,148. 

The program is rather slow in execution and therefore the model is limited to an eight-plate column, which is rather unrealistic for this multicomponent separation. The program is therefore given only for example purposes and a real simulation should involve rather more plates. As in BSTILL, the speed of calculation is also very sensitive to the magnitude of the liquid holdup on the plates, which again are large compared to normal practice. 

Inside-Out Algorithms for Multicomponent Separation Process Calculations... 

In this chapter, the fundamental principles and relationships involved in making multicomponent distillation calculations are developed from first principles. To enhance the visualization of the application of the fundamental principles to this separation process, a variety of special cases are considered which include the determination of bubble-point and dew-point temperatures, single-stage flash separations, multiple-stage separation of binary mixtures, and multiple-stage separation of multicomponent mixtures at the operating conditions of total reflux. 

ChemSep is a suite of programs for performing multicomponent separation process calculations on PCs. It was created specifically for use by students in university courses on stagewise separation processes, but it is also used by professionals in industry. It includes ChemProp, a program that allows estimation of physical properties such as densities, viscosities, heat capacities and conductivities, and surface ten-... 

In general, feedforward control systems can be designed for multicomponent separations almost as easily as for binary separations. The first relevant question is how many product streams there are. If there are only two, distillate flow can be calculated as the sum of those components which pass overhead ... 

Occasionally there is a need to perform some preliminary but rapid estimates for a specific separation without resorting to the tedious graphical or plate by plate calculations. In such instances one can turn to some of the short-cut methods that have been developed specifically for multicomponent separations in the chemical process industry but which also work reasonably well with binary and multicomponent separations at low temperatures. These are the Fenske-Underwood method for obtaining the minimum number of plates at total reflux, the Underwood method for obtaining the minimum reflux, and the Gilliland correlation to determine the theoretical number of plates based on the information provided by the two prior methods. 

In the calculations for multicomponent separations, it is often necessary to estimate the minimum reflux ratio of a multistage distillation column. A method developed for this purpose by Underwood [ 1 ], and described in detail by Treybal [2], requires the solution of the equation... 

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. 

Van Vlimmeren, B.A.C., Fraaije, J.G.E.M. Calculation of noise distribution in mesoscopic dynamics models for phase-separation of multicomponent complex fluids. Comput. Phys. Comm. 99 (1996) 21-28. 

Distillation Columns. Distillation is by far the most common separation technique in the chemical process industries. Tray and packed columns are employed as strippers, absorbers, and their combinations in a wide range of diverse appHcations. Although the components to be separated and distillation equipment may be different, the mathematical model of the material and energy balances and of the vapor—Hquid equiUbria are similar and equally appHcable to all distillation operations. Computation of multicomponent systems are extremely complex. Computers, right from their eadiest avadabihties, have been used for making plate-to-plate calculations. 

Flash distiUations are widely used where a cmde separation is adequate. Examples of flash multicomponent calculations are given in standard distiUation texts (30). 

Simple analytical methods are available for determining minimum stages and minimum reflux ratio. Although developed for binary mixtures, they can often be applied to multicomponent mixtures if the two key components are used. These are the components between which the specification separation must be made frequendy the heavy key is the component with a maximum allowable composition in the distillate and the light key is the component with a maximum allowable specification in the bottoms. On this basis, minimum stages may be calculated by means of the Fenske relationship (34) ... 

In concentrated wstems the change in gas aud liquid flow rates within the tower and the heat effects accompanying the absorption of all the components must be considered. A trial-aud-error calculation from one theoretical stage to the next usually is required if accurate results are to be obtained, aud in such cases calculation procedures similar to those described in Sec. 13 normally are employed. A computer procedure for multicomponent adiabatic absorber design has been described by Feiutnch aud Treybal [Jnd. Eng. Chem. Process Des. Dev., 17, 505 (1978)]. Also see Holland, Fundamentals and Modeling of Separation Processes, Prentice Hall, Englewood Cliffs, N.J., 1975. 

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. 

Although the methods developed here can be used to predict liquid-liquid equilibrium, the predictions will only be as good as the coefficients used in the activity coefficient model. Such predictions can be critical when designing liquid-liquid separation systems. When predicting liquid-liquid equilibrium, it is always better to use coefficients correlated from liquid-liquid equilibrium data, rather than coefficients based on the correlation of vapor-liquid equilibrium data. Equally well, when predicting vapor-liquid equilibrium, it is always better to use coefficients correlated to vapor-liquid equilibrium data, rather than coefficients based on the correlation of liquid-liquid equilibrium data. Also, when calculating liquid-liquid equilibrium with multicomponent systems, it is better to use multicomponent experimental data, rather than binary data. 

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