Bubble point calculation efficiency

The highly interactive nature of the balance and equilibria equations for the distillation period are depicted in Fig. 3.66. An implicit, iterative algebraic loop is involved in the calculation of the boiling point temperature at each time interval. This involves guessing the temperature and calculating the sum of the partial pressures, or mole fractions. The condition required is that Zyi + yw = 1. The iterative loop for the bubble point calculation is represented by the five interconnected blocks in the lower right hand corner of Fig. 3.66. The model of Prenosil (1976) also included an efficiency term E for the steam heating, dependent on liquid depth L and bubble diameter D. 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

In principle, a solution to the bubble-point T problem is possible because the number of unknowns is equal to the number of independent equations. However, since the equations are strongly nonlinear, simultaneous solution of N + 3 equations is not trivial, even if N is small. Fortuantely, efficient and robust compeler programs for such calculations have been prepured by sevem] authors, including the authors of... 

In another study, Grayson examined the effect of K-values on bubble-point, dew-point, equilibrium flash, distillation, and tray efficiency calculations. He noted a wide range of sensitivity of design calculations to variations in K-values. 

A distillation unit consists of a partial reboiler, a bubble cap column, and a total condenser. The overall plate efficiency is 65%. The feed is a liquid mixture, at its bubble point, consisting of 50 mole% benzene in toluene. This liquid is fed to the optimum plate. The column is to produce a distillate containing 95 mole% benzene and a bottoms of 95 mole% toluene. Calculate for an operating pressure of 1 atm ... 

Bubble points or dew points can be determined by flash calculations with yr in Equations 2.7 or 2.13 set to either zero or one. Although the general flash calculation method described in the previous section may be applied to bubble points and dew points, phase boundary calculations are handled more efficiently by other methods. At the bubble point, the liquid composition equals the feed composition since all the feed remains in the liquid phase. The composition of a vapor bubble at equilibrium with the liquid is given by Equation 2.13b, which reduces to... 

The problems of phase transition always deeply interested Ya.B. The first work carried out by him consisted in experimentally determining the nature of memory in nitroglycerin crystallization [8]. In the course of this work, questions of the sharpness of phase transition, the possibility of existence of monocrystals in a fluid at temperatures above the melting point, and the kinetics of phase transition were discussed. It is no accident, therefore, that 10 years later a fundamental theoretical study was published by Ya.B. (10) which played an enormous role in the development of physical and chemical kinetics. The paper is devoted to calculation of the rate of formation of embryos—vapor bubbles—in a fluid which is in a metastable (superheated or even stretched, p < 0) state. Ya.B. assumed the fluid to be far from the boundary of absolute instability, so that only embryos of sufficiently large (macroscopic) size were thermodynamically efficient, and calculated the probability of their formation. The paper generated extensive literature even though the problem to this day cannot be considered solved with accuracy satisfying the needs of experimentalists. Particular difficulties arise when one attempts to calculate the preexponential coefficient. 

A vaiue for the Murphree vapor-phase efficiency E v is then calculated for the overall tray by adjusting the point efficiency Eqc to take into account the effects of liquid mixing and entrainment. A summary of the AIChE design procedure for bubble-cap trays and an example of its application are given by King. A very approximate estimate of the overall efficiency of bubble-cap columns used for absorption can be obtained from Fig. 6.4-13. This simple correlation was proposed by O Connell. ... 

Integrating consecutively above equation from b = 0 at the tray deck to h = hi for the bubble formation zone and from hi to 2 for the dispersed bubble zone, the yout can be found for calculating the point efficiency. The trial and error method for stepwise calculation is employed to obtain the solution. The equations needed for computation of each zone are given below. 

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