# Thermal Condition Q

Figure 2.8 Minimum number of trays.

4. Increasing product purities does not have a significant effect on the required reflux ratio.

5. Increasing the liquid to vapor ratio in a section of a column increases the separation that occurs in that section.

These effects apply to all types of separations and distillation columns.

Figure 2.9 Minimum reflux ratio.

2.2.5 Limiting Conditions

Before we go through a specific example, we need to discuss some of the limiting conditions. The minimum number of trays for a specified separation corresponds to total reflux operation. If the column is run under total reflux conditions, the distillate flowrate is zero. Therefore the reflux ratio is infinite, and the slope of the operating lines is unity. This is the 45° line. Thus the minimum number of trays can be determined by simply stepping up between the 45° line and the VLE curve (see Fig. 2.8).

The minimum reflux ratio for a specified separation corresponds to having an infinite number of trays. This usually occurs when the operating lines and the q line intersect exactly on the VLE curve. This is a "pinch" condition. It would take an infinite number of trays to move past this point. This is illustrated in Figure 2.9. The minimum reflux ratio is calculated from the slope of this limiting operating line.

### 2.2.6 Numerical Example using DISTIL

To illustrate this method on a numerical example, consider the separation of benzene and toluene. The column operates at atmospheric pressure. The feed is 100kmol/h of saturated liquid (q = 1) with composition z = 0.40 mole fraction (mf) benzene. The desired product compositions are xD = 0.95 and xB = 0.05. The flowrates of the two products are

The software DISTIL can perform the McCabe-Thiele analysis in a very convenient way. Start the program and use the Fluid Package Manager to define fluids property package and the components using the method described in Chapter 1. We use the Wilson fluids property method for the benzene/toluene system. Select the Separation Manager and Graphical Column Design on the top toolbar. The window shown at the top of Figure 2.10 opens with the Setup page tab selected, on which the fluid package and components are selected. Clicking Options under the Setup column on the left opens the window shown at the bottom of Figure 2.10, on which the pressure is specified.

Clicking the Configuration page tab opens the window shown at the top of Figure 2.11. We want a standard two-product column, so there is nothing to specify on this window. Clicking the Spec Entry page tab opens the window given at the bottom of Figure 2.11. This view is used to specify the feed conditions and the bottoms and distillate specification. First click the Feed button and give the feed composition (0.40 mf benzene) and the feed thermal condition (q = 1). Under the Internal Flow Specifications, we set a preliminary value of the reflux ratio to be 2. This will be changed later after the program calculates the minimum reflux ratio for us.

Clicking the Distillate button opens the window shown at the top of Figure 2.12, on which the distillate purity (0.95 mf benzene) is specified. Clicking the Bottoms button opens the window shown at the bottom of Figure 2.12, on which the bottoms impurity (0.05 mf benzene) is specified. Now the yellow message at the bottom of the window tells us that the program is Ready to Calculate.

Figure 2.10 Selecting fluid package and pressure.

Click Calculate to the right of the message. The message window turns green and says Calculations OK, as shown at the top of Figure 2.13. Note that the minimum reflux ratio has been calculated (RRmin = 1.489). The reflux ratio that has been specified is 2, which gives a ratio of the actual reflux ratio to the minimum of 2/1.489 = 1.34. The economic optimization of a distillation column is discussed in Chapter 4. Typical values of the RR to RRmin ratio are around 1.2, so our initial guess is a little high.

Clicking the Summary page tab gives the window shown at the bottom of Figure 2.13. The DISTIL program uses the stage numbering convention of starting at the top. The reflux drum is stage 0, and the partial reboiler is the last stage. For the specified reflux ratio and product purities, 13 stages plus a partial reboiler are required, with the feed

Figure 2.11 Selecting configuration, feed conditions, and reflux ratio.

fed on stage 7. If the reflux ratio is reduced to 1.2 RRmin [RR = (1.2)(1.389) = 1.67] and the calculations are redone, the number of stages increases to 17 with feed introduced on stage 9.

Various types of plots can be generated by clicking the Plots page tab and selecting one of the three types of plots listed under Plot Generation. Figure 2.14 gives the McCabe-Thiele xy diagram with the operating lines, the q line, the VLE curve, and the stages stepped off. Some of the features of this plot can be modified by right-clicking the plot and selecting Chart Control. Figure 2.15 gives the temperature profile and the benzene liquid and vapor mole fraction on all stages.

Figure 2.12 Specifying distillate and bottoms.

The DISTIL program can also be used to design columns in ternary systems, as we illustrate later in this chapter.