Multicomponent Hydrocarbon System

The next separation system examined is a five-component hydrocarbon mixture. The feed flowrate is 1 kmol/s, and the design feed composition is 1 mol% ethane (C2), 40 mol% propane (C3), 29 mol% isobutane (iC4), 29 mol% normal butane (nC4) and 1 mol% isopentane (iC5). The operating objective is to separate the light-key component propane from the heavy-key component isobutane. Of course, the heavier-than-heavy-key components nC4 and iC5 go out the bottom with the iC4. The lighter-than-light key component C2 goes out the top with the propane. Column pressure is set at 13.5 atm. The column has 37 stages and is fed on stage 18. Distillate impurity is specified to be 2 mol% iC4. Bottoms impurity is specified to be 2 mol% C3. The reflux ratio required to achieve these purities is 2.168.

6.4.1 Slope Criterion

The upper graph in Figure 6.9 gives the temperature profile at design conditions. The lower graph shows the differences between the temperatures on adjacent trays. The largest change occurs on stage 31. There is also a large change in temperature at the top of the column due to buildup of the lighter-than-light-key component C2. There is also a smaller peak at stage 8.

6.4.2 Sensitivity Criterion

The upper graph in Figure 6.10 gives the openloop gains between tray temperatures and the two manipulated variables. These curves show that stage 30 is sensitive to changes in heat input and stage 8 is sensitive to changes in reflux. In this system, the slope criterion and the sensitivity criterion give identical results.

6.4.3 SVD Criterion

The lower graph in Figure 6.10 gives the U and U2 values from SVD analysis. The SVD results are similar to the sensitivity results. They suggest that stage 8 can be controlled by reflux and stage 30, by heat input. The singular values of the steady-state gain matrix are ctj = 0.4066 and s2 = 0.1637, giving a condition number CN = ctj/ct2 = 2.48. This indicates that the two temperatures are quite independent, so a dual-temperature control scheme may be effective if it is required.

Figure 6.9 Multicomponent temperature profile and slope.

6.4.4 Invariant Temperature Criterion

Figure 6.11 gives the changes in the temperature profiles for four different feed compositions. The design feed composition is 1/40/29/29/1 mol% C2/C3/iC4/nC4/iC5. The

Figure 6.11 gives the changes in the temperature profiles for four different feed compositions. The design feed composition is 1/40/29/29/1 mol% C2/C3/iC4/nC4/iC5. The

Figure 6.10 Multicomponent sensitivity and SVD analysis.
Figure 6.11 Multicomponent changes in temperature profile for C2 C3, and iC5 feed composition changes with product purities fixed.

impurities in the bottoms and in the distillate are kept constant at 2 mol% C3 and 2 mol% iC4, respectively. The solid line shows a feed composition in which the propane composition is decreased from 40 to 35 mol% C3 and the isobutane composition is increased from 29 to 34 mol% iC4. The dashed line represents a feed composition in which the propane composition is increased from 40 to 45 mol% C3 and the isobutane composition is decreased from 29 to 24 mol% iC4. The dotted line shows a feed composition in which the ethane composition is increased from 1 to 2 mol% C2, while the iC4 and nC4 are both reduced from 29 to 28.5 mol%. The dashed-dotted line indicates a feed composition in which the isopentane composition is increased from 1 to 10 mol% iC5, the isobutane composition decreased from 29 to 25 mol% iC4 and the n-butane composition decreased from 29 to 24 mol% nC4.

For changes in the propane to isobutane ratio in the feed or for changes in the C2 in the feed, the results show that the temperature on stage 34 does not change for constant product impurities. So if these are the types of feed composition disturbance expected, controlling stage 34 should provide effective control.

However, for a change in the iC5 concentration of the feed, stage 34 changes by ~2K. Therefore, controlling stage 34 will not handle changes in the composition of the heavier-than-heavy-key component in the feed.

6.4.5 Minimum Product Variability Criterion

Figure 6.12 shows how product impurities change when the temperature on a tray is held constant and feed composition changes. The second control degree of freedom that is fixed in this figure is the reflux flowrate. Table 6.1 shows that the required changes in reflux flowrate are much smaller than the required changes in the reflux ratio in this multi-component system. The reflux flowrate is fixed at 0.8816 kmol/s.

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