The next separation system examined is a ternary mixture of benzene, toluene, and ortho-xylene. The feed flowrate is 1 kmol/s, and the design feed composition is 30 mol% benzene, 30 mol% toluene, and 40 mol% orthoxylene. The operating objective is to separate the light-key component benzene from the heavy-key component toluene. Of course, the heavier-than-heavy-key component orthoxylene goes out the bottom with the toluene. Column pressure is set at 1 atm. The column has 32 stages and is fed on stage 16. Distillate impurity is specified to be 0.1 mol% toluene. Bottoms impurity is specified to be 0.1 mol% benzene. The reflux ratio required to achieve these purities is 1.908.
The upper graph in Figure 6.5 gives the temperature profile at design conditions. The lower graph shows the difference between the temperatures on adjacent trays. There is large change right at the feed stage. Because of the introduction of the feed, this is not a good location for temperature control. There is also a large change in temperature near the bottom of the column, which is due to the buildup of the heavier-than-heavy-key component orthoxylene. This is also not a good location for temperature control since we are trying to infer the compositions of benzene and toluene. The slope analysis suggests the use of stage 21 for temperature control.
The upper graph in Figure 6.6 gives the openloop steady-state gains between tray temperatures and the two manipulated variables. These curves show that stage 21 is sensitive to changes in heat input and stage 22 is sensitive to changes in reflux.
The lower graph in Figure 6.6 gives the U and U2 values from SVD analysis. The first is the solid line and is associated with reflux. The second is the dashed line and is associated with heat input.
The SVD results are the similar to the sensitivity results. They suggest that stage 21 can be controlled by reflux and stage 23, by heat input. The singular values of the steady-state gain matrix are o-j = 9.14 and s2 = 0.518, which gives a condition number
CN = o-j/o-2 = 17.6. This indicates that the two temperatures are not nearly as independent as in the propane/isobutane system, so a dual-temperature control scheme may not be as effective. This makes sense because stages 21 and 23 are too close together to be independent.
Figure 6.7 gives the changes in the temperature profiles for three different feed compositions in the ternary system. The design feed composition is 30/30/40 mol% benzene/toluene/xylene (BTX). The impurities in the bottoms and in the distillate are kept constant at 0.1 mol% benzene and 0.1 mol% toluene, respectively. The solid lines represent 25/35/40 mol% BTX feed composition; the dashed lines, 35/25/ 40 mol% BTX feed composition; and the dotted lines, 25/25/50 mol% BTX feed composition.
For changes in the benzene to toluene ratio in the feed, the results show that the temperature on stage 27 does not change for constant product impurities. So, if this is the type of feed composition disturbance expected, controlling stage 27 should provide effective control.
However, for the change in the xylene concentration of the feed, stage 27 changes by almost 3 K.
Figure 6.8 shows how product impurities change when the temperature on a specific tray is held constant and feed composition changes. The second control degree of freedom that is fixed in this figure is the reflux flowrate.
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