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Figure 6.2 Propane/isobutane sensitivity and SVD analysis.

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Figure 6.2 Propane/isobutane sensitivity and SVD analysis.

6.2.3 SVD Criterion

The lower graph in Figure 6.2 gives the U1 and U2 values from singular value decomposition (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 similar to the sensitivity results. They suggest that stage 8 can be controlled by reflux and stage 29, by heat input. The singular values of the steady-state gain matrix are s1 = 0.479 and s2 = 0.166, giving a condition number CN= s1/s2 = 2.88. This indicates that the two temperatures are fairly independent, so a dual-temperature control scheme should be feasible, at least from a steady-state perspective.

6.2.4 Invariant Temperature Criterion

Figure 6.3 gives the changes in the temperature profiles for two feed compositions on either side of the steady-state value (40 mol% propane). The solid lines represent 35 mol% propane and the dashed lines, 45 mol% propane in the feed. The product distillate and bottoms compositions are fixed at 98 and 2 mol%, respectively, for both feed compositions.

As expected in a binary constant-pressure system, fixing the composition fixes the temperature. So the temperatures at the top and at the bottom do not change. In theory, these end temperature could be controlled to achieve constant product purities. In practice, however, small amounts of other components or changes in pressure can render the use of temperatures at the very ends of the column ineffective. This will be demonstrated later when multicomponent systems are considered.

6.2.5 Minimum Product Variability Criterion

Figure 6.4 shows how product purities 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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Figure 6.3 Propane/isobutane; changes in temperature profile for feed composition changes with product purities fixed.

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Figure 6.3 Propane/isobutane; changes in temperature profile for feed composition changes with product purities fixed.

z (mf C3)

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