Rayleigh distillation equation

Equation 14.7 is known as the Rayleigh Equation and describes the material balance around the distillation pot. 

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),... 

Derive and apply Rayleigh equation to relate the compositions of the residue and composited distillate to the fraction of the feed differentially distilled. 

If the reflux ratio R or distillate rate D is fixed, instantaneous distillate and bottoms compositions vary with time. For a total condenser, negligible holdup of vapor and liquid in the condenser and the column, equilibrium stages, and constant molar overflow, the Rayleigh equation can now be written as... 

Rayleigh distillation Fractional separation of isotopes in accordance with the Rayleigh equation for fractional distillation or condensation. For any condensation process... 

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. ... 

Dtotai is calculated from the Rayleigh equation calculation procedure, with F set either by the size of the still pot or by the charge size. For an existing apparatus the distillate flow rate, D in kmol/h, cannot be set arbitrarily. The column was designed for a given maximum vapor velocity, Uf]ood> which corresponds to a maximum molal flow rate, Vj ax (see Chapter 101. Then, from the mass balance around the condenser,... 

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 At the bottom of the column bottoms are continuously withdrawn and part of the stream is sent to a total reboiler, vaporized and sent back up the column.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. 

During the distillation, at any time, the molar content of the distillation still is B with mole fraction x of the key component. After distilling a partial amount dB with mole fraction y of the key component, the residue in the still becomes B - dB with mole fraction x - dx. Neglecting the product dB dx and separating the variables x and y in the mass balance, a differential equation for the discontinuous simple distillation is derived. This equation was first introduced by Lorx> Rayleigh and is called the Rayleigh equation... 

F. Fractionation. We have referred several times to the buildup of NCI3 concentration due to fractionation. This occurs when a small fraction of a chlorine stream condenses, as in a suction chiller reboiler, or when liquid chlorine is vaporized or is allowed to boil down in a vessel. Here, we attempt to quantify the latter situation. It is a case of simple differential distillation of a two-component mixture. We start by assuming a constant relative volatility. The Rayleigh equation [108] becomes... 

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... 

The integration of Eq. (11.3-10) can be done graphically by plotting l/(y — x) versus X and getting the area under the curve between Xj andxz- The equilibrium curve gives the relationship between y and x. Equation (11.3-10) is known as the Rayleigh equation. The average composition of total material distilled, y, can be obtained by a material balance. 

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. 

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 ... 

In 1937, Bogart [41] presented the first analysis of the variable reflux policy for a binary system. The steps involved in the calculation procedure for the variable reflux mode are similar to those in the case of the constant reflux mode however, in the variable reflux case, the reflux ratio is varied instead of the distillate composition at each step. Moreover, the Rayleigh equation, though valid for the variable reflux condition, takes a simplified form. Since the distillate composition remains constant (remember that we are considering binary systems here) throughout the operation, the Rayleigh equation reduces to the following equation. 

Solution Since the distillate composition is held constant throughout the variable reflux mode of operation, the distillate composition xp = xpav = 0.85. For the various iterates of R, we obtain the corresponding values of xb - The value of the amount of product distilled at each xb is also calculated using the Rayleigh equation for the variable reflux condition (Equation 4.9). 

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. 

The holdup effects can be neglected in a number of cases where this model approximates the column behavior accmately. This model provides a close approximation to the Rayleigh equation, and for complex systems (e.g., azeotropic systems) the synthesis procedures can be easily derived based on the simple distillation residue curve maps (trajectories of composition). However, note that this model involves an iterative solution of nonlinear plate-to-plate algebraic equations, which can be computationally less efficient than the rigorous model. 

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