Stage calculations binary systems

McCabe-Thie/e Example. Assume a binary system E—H that has ideal vapor—Hquid equiHbria and a relative volatiHty of 2.0. The feed is 100 mol of = 0.6 the required distillate is x = 0.95, and the bottoms x = 0.05, with the compositions identified and the lighter component E. The feed is at the boiling point. To calculate the minimum reflux ratio, the minimum number of theoretical stages, the operating reflux ratio, and the number of theoretical stages, assume the operating reflux ratio is 1.5 times the minimum reflux ratio and there is no subcooling of the reflux stream, then ... 

In order to determine the packed height it is necessary to obtain a value of the overall number of transfer units methods for doing this are available for binary systems in any standard text covering distillation (73) and, in a more complex way, for multicomponent systems (81). However, it is simpler to calculate the number of required theoretical stages and make the conversion ... 

If the presence of the other components does not significantly affect the volatility of the key components, the keys can be treated as a pseudo-binary pair. The number of stages can then be calculated using a McCabe-Thiele diagram, or the other methods developed for binary systems. This simplification can often be made when the amount of the non-key components is small, or where the components form near-ideal mixtures. 

The classic papers by Lewis and Matheson [Ind. Eng. Chem., 24, 496 (1932)] and Thiele and Geddes [Ind. Eng. Chem., 25, 290 (1933)] represent the first attempts at solving the MESH equations for multicomponent systems numerically (the graphical methods for binary systems discussed earlier had already been developed by Pon-chon, by Savarit, and by McCabe and Thiele). At that time the computer had yet to be invented, and since modeling a column could require hundreds, possibly thousands, of equations, it was necessary to divide the MESH equations into smaller subsets if hand calculations were to be feasible. Despite their essential simplicity and appeal, stage-to-stage calculation procedures are not used now as often as they used to be. 

Operating Line and "Equilibrium" Curve. Both terms are of importance for the graphical solution of a separation problem, i.e., for the graphical determination of the number of stages of a cascade. This method has been developed for the design of distillation columns by MacCabe and Thiele and should be well known. For all cases, the operating line represents the mass and material balances. In distillation, the equilibrium curve represents the thermodynamical va-por/liquid equilibrium. For an ideal binary system, the equilibrium curve can be calculated from Raoult s law and the saturation-pressure curves of the pure components of the mixture. In all other cases, however, for example, for all membrane processes, the equilibrium curve does not represent a thermodynamical equilibrium at all but will represent the separation characteristics of the module or that of the stage. 

In this chapter, the Ponchon-Savarit graphical method for making stage-to-stage calculations is applied to distillation and extraction. Like the McCabe-Thiele procedure, the Ponchon-Savarit method is restricted to binary distillation and ternary extraction systems. The method does, however, obviate the need for the constant phase-ratio flow assumptions. 

Can we do the internal stage-by-stage calculations first and then solve the external balances To begin the stage-by-stage calculation procedure in a distillation column, we need to know all the conpositions at one end of the column. For ternary systems with the variables specified as in Table 5-1. these conpositions are unknown. To begin the analysis we would have to assume one of them. Thus, internal calculations for multiconponent distillation problems are trial and error. This is a second major difference between binary and multiconponent problems. 

Improper feed point location may require more theoretical stages than calculated. For a binary system, the feed point is located where the feed liquid composition matches the downflowing liquid composition in the column. With a multicomponent feed, the theoretical stage that matches the light-key concentration in the feed probably will not match the heavy-key concentration. In such a case, the feed stage should be selected so that the ratio of light key to heavy key in the liquid feed is the same as the ratio in the downflowing liquid within the column. 

The program uses two ASCII input files for the SCF and properties stages of the calculation. There is a text output file as well as a number of binary or ASCII data files that can be created. The geometry is entered in fractional coordinates for periodic dimensions and Cartesian coordinates for nonperiodic dimensions. The user must specify the symmetry of the system. The input geometry must be oriented according to the symmetry axes and only the symmetry-unique atoms are listed. Some aspects of the input are cumbersome, such as the basis set specification. However, the input format is documented in detail. 

In this chapter consideration is given to the theory of the process, methods of distillation and calculation of the number of stages required for both binary and multicomponent systems, and discussion on design methods is included for plate and packed columns incorporating a variety of column internals. 

As a first stage of this work, the comparison of our method with the result of MC calculation has been done for the system of binary monoatomic system. The set of parameters used is the same as used by Nakanishi et al.2)... 

The knowledge of the occurrence of azeotropic points in binary and higher systems is of special importance for the design of distillation processes. The number of theoretical stages of a distillation column required for the separation depends on the separation factor i.e. the ratio of the 7< -factors (7required separation factor can be calculated with the following simplified relation (Reference 1) ... 

This chapter introduces how continuous distillation columns work and serves as the lead to a series of nine chapters on distillation. The basic calculation procedures for binary distillation are developed in Chapter 4. Multicomponent distillation is introduced in Chapter 5. detailed conputer calculation procedures for these systems are developed in Chapter 6. and sinplified shortcut methods are covered in Chapter 7. More complex distillation operations such as extractive and azeotropic distillation are the subject of Chapter 8. Chapter 9 switches to batch distillation, which is commonly used for smaller systems. Detailed design procedures for both staged and packed columns are discussed in Chapter 10. Finally, Chapter 11 looks at the economics of distillation and methods to save energy (and money) in distillation systems. 

G3. Write a computer, spreadsheet, or calculator program to find the number of equilibrium stages and the optimum feed plate location for a binary distillation with a constant relative volatility. System will have CMO, saturated liquid reflux, total condenser, and a partial reboiler. The given variables will be F, Zp, q Xg, Xp, a, and Lq/D. Test your program by solving the following... 

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