Distillation constant-pressure equilibrium

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

When does a liquid boil Clearly, boiling at constant pressure—say, atmospheric pressure—begins when we increase the temperature of a liquid or solution and the vapor pressure reaches a pressure of one atmosphere. Alternatively, the pressure over a liquid or solution at constant temperature must be reduced until it reaches the vapor pressure at that temperature (e.g., vacuum distillation). Yet it is well known that liquids can be superheated (and vapors supersaturated) without the occurrence of phase transfer. In fact, liquids must always be superheated to some degree for nucleation to begin and for boiling to start. That is, the temperature must be raised above the value at which the equilibrium vapor pressure equals the surrounding pressure over the liquid, or the pressure must be reduced below the vapor pressure value. As defined earlier, these differences are called the degree of superheat. When the liquid is superheated, it is metastable and will reach equilibrium only when it breaks up into two phases. 

A residue curve map (RCM) consists of a plot of the phase equilibrium of a mixture submitted to distillation in a batch vessel at constant pressure. RCM is advantageous for analyzing ternary mixtures. More exactly, a residue curve shows explicitly the evolution of the residual liquid of a mixture submitted to batch distillation. 

With a constant value for a this equation provides a simple, approximate expression for representing the equilibrium y = x diagram. Doherty and Malone Conceptual Design of Distillation Systems, McGraw-Hill, 2001, sec. 2.3) discuss this approximation in greater detail and give a selection of binary mixtures for which the approximation is reasonable. At a constant pressure of 1 atm these include benzene + toluene, a = 2.34 benzene -I- p-xylene, a = 4.82 and hexane + p-xylene, a = 7.00. 

As a mixture of volatile liquids is distilled, the compositions of both the liquid and the vapor, as well as the boiling point of the solution, change continuously. At constant pressure, we can represent these quantities in a boiling point diagram, Figure 14-12. In such a diagram the lower curve represents the boiling point of a liquid mixture with the indicated composition. The upper curve represents the composition of the vapor in equilibrium... 

So far the discussion has been specific to systems at constant temperature equivalently, pressure could be fixed and temperature and liquid phase composition taken as the variables. Although much experimental vapor-liquid equilibrium data are obtained in constant-temperature experiments, distillation columns and other vapor-liquid separations equipment in the chemical process industry are operated more nearly at constant pressure. Therefore, it is important that chemical engineers be familiar with both types of calculations. 

While the design of distillation columns can be quite complicated, we will consider only the simplest case here. The simplificadons we will use are that vapor-liquid equilibrium will be assumed to exist on each tray (or equilibrium stage) and in the reboiler, that the column operates at constant pressure, that the feed is liquid and will enter the distillation column on a tray that has liquid of approximately the same composition as the feed, that the molar flow rate of vapor V is the same throughout the column, and that the liquid flow rate L is constant on all trays above the feed tray, and is constant and equal to L -b F below the feed tray, where F is the molar flow rate of the feed to the column, here assumed to be a liquid. The analysis of this simplified distillation column involves only the equilibrium relations and mass balances. This is demonstrated in the illustration below. 

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. 

A batch distillation column with three theoretical stages (the first stage is the still pot) is charged with 100 kmol of a 20 mol% n-hexane in n-octane mixture. At a constant reflux ratio R - 1.0, how many moles of the charge must be distilled if an average product composition of 70 mol% n-hexane is required If the boilup ratio is 10 kmol/h, calculate the distillation time. The equilibrium distribution curve at column pressure is given in Figure 6.27. 

Let s consider the following experiment a ternary mixture of composition x, Xg, Xq is submitted to simple differential distillation at constant pressure, as depicted in Figure 9.1-left. The time-evolution of the liquid composition describes a residue curve. Suppose that at the time t, the pot contains L moles of liquid of composition x/. If the vapour with the equilibrium composition y/ is removed at the rate V, then the component material balance over the time dt gives ... 

While we have studied the properties of binary mixtures at constant temperature so far we shall now examine the behaviour of these mixtures at constant pressure. The conditions are those found in distillation, which is normally an isobaric process tending to establish equilibrium between the liquid and vapour phases. A boiling point diagram shows the boiling points and the equilibrium compositions of binary mix-... 

In order to obtain a single equilibrium curve, we have to specify enough variables that only one degree of freedom remains. For binary distillation this can be done by specifying constant pressure. For absorption, stripping, and extraction we specified that pressure and tenperature were constant, and if there were several solutes we assumed that they were independent. In general, we will specify that pressure and/or temperature are constant, and for multisolute systems we will assume that the solutes are independent. 

The reaction is exothermic and requires a reactor design (adiabatic fixed bed with recycle or tubular) that keeps the temperature essentially constant. The equilibrium constant for this reaction is about 100 (Voloch et al, 1986). The reaction takes place below 100 C and at a high enough pressure to assure its occurrence in the liquid phase (about 200psig). In most commercial units, the catalyst is a cation exchange resin which limits the MTBE reaction temperatures due to catalyst stability constraints. The methanol/isobutene ratio is kept close to 1 to avoid the formation of oligomers at too low a methanol concentration or excess methanol in the C4 overhead stream. The upper limit in the methanol/isobutene ratio is due to the formation of an azeotrope with the C4 s in the distillation process which is about 4% methanol in the overhead stream. Typical yields from an MTBE unit at 1/1 methanol to isobutene ratio over a resin catalyst are shown in Table 22 (Miller and Piel, 1989). 

At z in the curve, however (the minimum of vapour pressure), the solution and vapour are in equilibrium and the liquid at this point will distil without any change in composition. The mixture at z is said to be azeotropic or a constant boiling mixture. The composition of the azeotropic mixture does vary with pressure. 

The calculational base consists of equilibrium relations and material and energy balances. Equilibrium data for many binary systems are available as tabulations of x vs. y at constant temperature or pressure or in graphical form as on Figure 13.4. Often they can be extended to other pressures or temperatures or expressed in mathematical form as explained in Section 13.1. Sources of equilibrium data are listed in the references. Graphical calculation of distillation problems often is the most convenient... 

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