Vapor-liquid equilibrium differential distillation

Measurements of binary vapor-liquid equilibria can be expressed in terms of activity coefficients, and then correlated by the Wilson or other suitable equation. Data on all possible pairs of components can be combined to represent the vapor-liquid behavior of the complete mixture. For exploratory purposes, several rapid experimental techniques are applicable. For example, differential ebulliometry can obtain data for several systems in one laboratory day, from which infinite dilution activity coefficients can be calculated and then used to evaluate the parameters of correlating equations. Chromatography also is a well-developed rapid technique for vapor-liquid equilibrium measurement of extractive distillation systems. The low-boiling solvent is deposited on an inert carrier to serve as the adsorbent. The mathematics is known from which the relative volatility of a pair of substances can be calculated from the effluent trace of the elutriated stream. Some of the literature of these two techniques is cited by Walas (1985, pp. 216-217). 

A simple application for batch distillation is what is known as differential distillation. It consists of a boiler containing a load of liquid. The liquid is progressively vaporized, with the vapor flowing to a condenser, producing a liquid distillate. There is no reflux, so the only stage with vapor-liquid equilibrium is the boiler. 

Note that this equation is not easily integrated, for two reasons. First, the activity coefficient is a function of the liquid-phase composition, which continually changes as additional liquid is vaporized. Second, differential distillations are usually done at constant pressure (in particular, open to the atmosphere), so that as the composition changes, the equilibrium temperature of the liquid changes (following the bubble point temperature curve), and the pure component vapor pressures are a function of temperature. 

In the simple differential distillation process, the vapor product is in equilibrium with the liquid in the reboiler at any given time but changes continuously in composition. The mathematical approach must therefore be differential. Assume that at any time during the course of the distillation there are L moles of liquid in the still of composition x mole fraction of A and that an amount dD mole of distillate is vaporized, of mole fraction y in equilibrium with the liquid. Then we have the following differential material balances ... 

EXAMPLE 113-2. Sirttple Differential Distillation A mixture of 100 mol containing 50 mol % n-pentane and 50 mol % -heptane is distilled under differential conditions at 101.3 kPa until 40 mol is distilled. What is the average composition of the total vapor distilled and-the composition of the liquid left The equilibrium data are as follows, where x and y are mole fractions of n-pentane. 

Simple Distillation. Distillation without rectification can be carried out by several methods. The two most generally considered cases are (1) continuous simple distillation and (2) differential distiUor tion. In continuous distillation, a portion of the liquid is vaporized under conditions such that all the vapor produced is in equilibrium with the unvaporized liquid. In differential vaporization, the liquid is vaporized progressively, and each increment of vapor is removed from contact with the liquid as it is formed and, although each increment of vapor can be in equilibrium with the liquid as it is formed, the average composition of all of the vapor produced will not be in equilibrium with the remaining liquid. 

For such an operation to approach even approximately the theoretical characteristics of a differential distillation, it would have to proceed infinitely slowly so that the vapor issuing from the liquid would at all times be in equilibrium with the liquid. All entrainment would have to be eliminated, and there could be no cooling and condensation of the vapor before it entered the condenser. Despite the fact that these conditions are substantially impossible to attain, it is nevertheless useful to study the limiting results which a differential distillation could produce as a standard for comparison. 

Figure 7.6 shows the variables involved in a differential distillation process. For a binary system, there are four the moles liquid in the still or boiler at any instant W and its mole fraction the rate of vapor withdrawal D (moles/s) and the instantaneous vapor composition The mass balances and the equilibrium relation yg = /(x ) provide only three of the required equations. For the fourth we must draw on an energy balance. This stands to reason, because the rate of vapor production D will evidently depend on... 

The second way to effect these separations is staged distillation. In staged distillation, the column internals are completely different than those normally used for gas absorption. Now these internals consist of a series of compartments or trays, where liquid and vapor are contacted intimately, in the hope that they will approach equilibrium. Now, the liquid and vapor concentrations in the column do not vary continuously, but discretely, jumping to new values on each tray. Staged distillation was an innovation for commodity chemicals a century ago, and was the standard during the rapid growth of the chemical industry. While it is still the standard in universities, it has been eclipsed by differential distillation in many areas of industrial practice. 

A batch still contains 100 kmol of a benzene-toluene solution at 85°C and 100 kPa. The mixture is distilled with no reflux in the column, in a differential batch distillation process. Determine the equilibrium liquid and vapor compositions at 5°C increments up to 105°C. It is also required to find at each time interval the amount of solution in the still and the total distillate composition. 

In the mode of minimum reflux adiabatic sections trajectories intersect reversible distillation trajectories in points Therefore, the separation process between product point and point can be carried out in principle, maintaining phase equilibrium between meeting flows of vapor and liquid in the cross-section at the height of the colunm by means of differential input or output of heat. We call such a separation process, with the same product compositions as at adiabatic distillation, a partially reversible one. A completely reversible process is feasible only for the preferable split that is rarely used in practice. Nonadiabatic distillation used in industry is a process intermediate between adiabatic and partially reversible distillation. Summary input and output of heat at nonadiabatic and adiabatic distillation are the same, and the energetic gain at nonadiabatic distillation is obtained at the transfer of a part of input or output heat to more moderate temperature level, which uses cheaper heat carriers and/or coolants. 

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