Batch distillation Rayleigh equations

Rayleigh equation An equation that relates the quantity to the concentration of the more volatile component in batch distillation. The equation is formulated from an unsteady-state material balance in which vapour leaving the still is in equilibrium wrtth the liquid. As the vapour is richer in the more volatile component, the composition of the Rquid and vapour are not constant ... 

Equations relating the flow rates and compositions of feed and product streams in differential separation processes, first derived by Lord Rayleigh [Rl] for batch distillation, are often called the Rayleigh distillation equation. We shall derive some of these relationships for type B differential stage separation, using the nomenclature shown in Fig. 12.11. 

A simple alternative to the Rayleigh equation can be derived for an ideal mixture based on the relative volatility. Although the temperature in the still increases during a batch distillation, the relative volatility, which is the ratio of vapor pressures, does not change much and an average value can be used. From Eq. (18.34),... 

Multistage batch distillation (i.e., batch rectification) is governed by the Rayleigh equation... 

The minus sign comes from switching the limits of integration. Equation (9=7) is a form of the Rayleigh equation that is valid for both simple and multistage batch distillation. Of course, to use this equation we must relate Xp, to x and do the appropriate integration. This is covered in sections 9.2 and 2. ... 

Derive and use the Rayleigh equation for sinple batch distillation... 

E3. In inverted batch distillation the charge of feed is placed in the accumulator at the top of the column fFigure 9-8). Liquid is fed to the top of the column. At the bottom of the column bottoms are continuously withdrawn and part of the stream is sent to a total reboiler, vaporized and sent back up the column. During the course of the batch distillation the less volatile component is slowly removed from the liquid in the accumulator and the mole fraction more volatile component increases. Assuming that holdup in the total reboiler, total condenser and the trays is small compared to the holdup in the accumulator, the Rayleigh equation for inverted batch distillation is. 

One form of separation is differential distillation, in which a batch of liquid vaporizes until a certain amount is left as residue. The Rayleigh equation [2] for such an operation is... 

Batch Distillation Example. As an illustration of the use of this equation, consider the experiment performed by Rayleigh. 1,010 g. of a 7.57 mol per cent solution of acetic acid in water was distilled until the stUl contained 254 g. whose com-... 

Residue curves in batch distillation The illustrated forms of the Rayleigh equations (6.3.87) and (6.3.91) allow one to relate the change in the total number of moles in the residual liquid phase with the liquid-phase composition change in simple batch distillation with no reflux and total condensation. One would like to know how the liquid-phase composition changes with time. Visualization of this composition change pathway is going to be quite illustrative. For ternary systems, such visualizations are likely to be particularly useful. The topic of residue curve maps is briefly introduced here to that end. 

Remember we are using the same batch and the same column for this operation. Since in this case neither distillate composition nor reflux ratio is constant, the following procedure is used for integration of the Rayleigh equation. 

As stated earlier, the basic batch distillation column satisfies the Rayleigh equation. Therefore we can use the same equation to calculate the total amount of distillate, as was done for the constant reflux condition. Values of xb,xd— b, f/xn — xb are obtained for each operating line. Values of xb versus 1/xd — xb are plotted from which the right hand side of the Rayleigh equation is obtained as the area under the curve and is found to be 0.5108, which corresponds to ln[ ]. Hence the total amount of distillate given by (1 — is equal to 40 moles, which is what we obtained in the variable reflux and constant reflux operations in Examples 4.2 and 4.3. 

This equation is the exact analog of the Rayleigh equation relating the amount and composition of the still-pot liquid in a batch distillation. By choosing values for fi and calculating the corresponding Fi s with (12.11), the integral may be evaluated to obtain a relation between the monomer composition and conver-... 

Batch Dehydration of Benzene. As another example of the use of Rayleigh s equation, consider the dehydration of benzene. Benzene saturated with water at 20 0. contains 0.25 mol per cent water, and it is to be given a simple differential distillation at a constant pressure of 1 atm. The operation is to proceed until the mol per cent water in the liquid remaining in the still is 0.00025. The following data and simplifying assumptions will be used in the calculations ... 

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