## Stepping Off Trays

Tray-to-tray calculations involve the solution of vapor liquid equilibrium relationships and component balances. These tray-to-tray calculations can be solved graphically by stepping back and forth between the operating line (y -- mx + b) and the VLE curve (y (*)), as shown in Figure 2.24. For example, let us start at the bottom of the column with known values of xB and Ls Vs. Our VLE relationship gives us yB if we know xB. Graphically,

## Stripping Section

A light component balance around the wth tray in the stripping section yields (see Figure 2.20) * (tK1 + (> )** (228) This is called the operating-line equation. It has the form of a straight line y mx + b. The slope of the line is the ratio of liquid to vapor flow rates in the stripping section. This straight line can be plotted on an x-y diagram (see Figure 2.21). The intersection of the operating line with the 45 line (where x y) occurs at xB. This is easily proved by letting the point of...

## Increasing Relative Volatility

Minimum reflux ratio is also reduced. Relative volatility has a strong effect on the cost of separation. Therefore, columns are usually designed to operate at the lowest economical pressure, since lower pressure means lower temperatures and higher relative volatilities in most systems. The lowest economical pressure is usually the pressure that provides a temperature in the overhead condenser that is high enough to permit cooling water or air to be used for heat...

## Design Problem

We are now ready to summarize the graphical design technique for determining the number of trays required to achieve desired product purities, given a reflux ratio. As we will show later, the lower the reflux ratio specified, the more trays are required. Since increasing reflux ratio increases energy costs F La D , while increasing trays increases investment costs, distillation design involves a classical engineering trade-off between the two design variables reflux ratio and number of trays....

## Xy diagram showing both stripping and rectifying operating lines

We simply move vertically up a line through xB until the VLE curve is intersected, and then read off the yB value. A component balance around the reboiler gives This is the stripping operating line equation 2.28 applied to the reboiler stage. We know yB. We could plug into equation 2.31 and solve analytically for Jii. Alternatively, we can solve graphically for xx simply by moving horizontally on a straight line through yB until the operating line is intersected. Then this McCabe-Thiele diagram...

## Feed Thermal Condition

The feed to a distillation column can be liquid or vapor, or both, depending on the temperature, pressure, and composition of the feed. To quantify the thermal condition of the feed, the parameter q is defined as the fraction of the feed that is liquid. It follows that 1 q is the fraction of feed that is vapor If the feed is a saturated liquid at its bubble point, q 1. If the feed is a saturated vapor at its dew point, q 0. If the feed is a vapor liquid mixture, q is a fraction. Values of q...

## Thermodynamic Basis

The second law of thermodynamics tells us that the chemical potential of each component must be equal in both liquid and vapor phases at phase equilibrium. A somewhat simplified equation representing this condition is Xj mol fraction of th component in liquid yj mol fraction of th component in vapor PT total system pressure Bubble point and dew point at constant pressure Pj vapor pressure of _ th component at the temperature of the system yy activity coefficient of thej'th component in the...

## Minimum Number of Trays

The minimum number of trays to make a specified separation is found when an infinitely large reflux ratio is used. The L V ratios in both sections of the column become unity and lie on the 45 line Figure 2.29 . This situation actually takes place in a column when it is operated under total reflux conditions. No feed is introduced and no products are withdrawn, but heat is added in the reboiler and all the overhead vapor is condensed and returned to the column as liquid reflux. Since D 0, R D...

## Minimum Reflux Ratio

The minimum reflux ratio for specified product purities and feed conditions occurs when an infinite number of trays are required to make the separation. Figure 2.27 shows the normal minimum reflux ratio situation. It occurs when the operating lines just intersect on the VLE curve. An infinite number of trays are required to step past the feed plate because of the pinch condition the converging operating and VLE lines . The actual reflux ratio used must be higher than the minimum. Increasing...

## System

Figure 2.19 summarizes the system and nomenclature to be considered. Liquid and vapor rates in the section above the feed rectifying section are called Lr and VR in mols minute. Liquid and vapor rates below the feed in the stripping section are called Ls and Vs. These are assumed to be constant on all trays throughout each individual section. This constancy of molar flow rates is what we call equimolal overflow. Primarily it assumes that the molar heats of vaporization of the components are...

## Material balance on stripping section

From a total mass balance around the system in Figure 2.20, Ls Vs B. Therefore, Ls Vs B. Substituting into equation 2.29 gives Therefore, the operating line can be easily placed on an x-y diagram by simply drawing a straight line with slope Ls Vs , starting at xB on the 45 line see Figure 2.21 .

## Nonideality

In most distillation systems, the predominant nonideality occurs in the liquid phase because of molecular interactions. Equation 2.4 contains yv the liquidphase activity coefficient of the yth component. When chemically dissimilar components are mixed together for example, oil molecules and water molecules , there can be repulsion or attraction between dissimilar molecules. If the molecules repel each other, they exert a higher partial pressure than if they were ideal. In this case the activity...

## Relative Volatility

Relative volatility is a very convenient measure of the ease or difficulty of separation in distillation. The volatility of component j relative to component k is defined as A large value of relative volatility ajk implies that components j and k can be easily separated in a distillation column. Values of ajk close to 1 imply that the separation will be very difficult, requiring a large number of trays and high energy consumption. For binary systems relative volatility of light to heavy...

## Bubble Point Calculations

In all bubble-point calculations, we know the composition of the liquid x s are all given . In addition we must be given either the pressure or the temperature of the system. The problem is to calculate the unknown temperature or pressure and the composition of the vapor phase j gt y . Bubble-Point Temperature Calculation. This is by far the most common type of calculation encountered in distillation work because column pressure is usually known. The calculation procedure is iterative 2....

## FIGURE 212 Isothermal flash

1 V F P Pt - 1 1 2-13 The only variable that is unknown in this equation is the V F ratio since the P s are functions of temperature only. Therefore, another iterative, trial-and-error solution is required. One guesses a V F and sees whether equation 2.13 is satisfied. The left-hand side of equation 2.13 is a nonmonotonic function see Figure 2.13 . A value of zero for V F always satisfies the

## Experimental VLE Data for Binaiy Systems

The VLE data for binary systems are obtained experimentally by mixing two components and allowing the vapor liquid system to equilibrate. Then temperature and pressure are measured. Samples of the vapor phase and liquid phase are taken and analyzed. Liquid compositions are usually expressed as mol fraction of light component and the symbol x is used. Vapor composition is expressed as mol fraction light component, using the symbol y. Mixture composition is then changed and the procedure...

## Fundamental Manipulated Variables

Two of the four manipulated variables listed above must be used to maintain liquid inventories in the reflux drum and in the column base. Therefore, we are left with just two manipulated variables that can be used to control compositions in the column. No matter what manipulated variables are chosen to control what controlled variables, there are basically two fundamental manipulated variables that affect compositions. These are feed split and fractionation. Feed split means the fraction of the...

## C xy Diagrams

Either isothermal or isobaric data can be represented by simply plotting liquid composition x versus vapor composition y. This a versus y curve see Figure 2.9 is called the equilibrium line. This type of diagram is the most widely used on distillation. Both T-xy and P-xy are useful in illustrating the concepts of bubble point, dew point, superheated vapor, and subcooled liquid. Consider the P-xy diagrams sketched in Figure 2.10. Suppose we have a mixture with composition z, and we hold it at...

## Nomenclature

Figure 2.1 summarizes the nomenclature conventions that will be used throughout this book. At this point we will consider only a simple single-feed, two-product column separating a binary two-component mixture. Feed rate is F mois per minute. Feed composition is zF mol fraction of the more volatile component. The column trays are numbered from the base upward, with feed introduced on the NF tray. The total number of trays in the column is Nt. Products removed from the top and bottom of the...