Pinch point in distillation

If an extended tie-line passes through the pole point P, an infinite number of stages will be needed. This condition sets the minimum flow of extraction-solvent required. It is analogous to a pinch point in distillation. 

The vapor-liquid equilibrium (VLB) and liquid-liquid extraction (LLE) correlations in Aspen Plus are not always as accurate as possible. This can cause significant errors, particularly near pinch points in distillation columns. If data is available, Aspen Plus will find values of the parameters for any of the VLB or LLE correlations by doing a regression against the data you input. This is illustrated to obtain an improved fit for the non-random two-liquid (NRTL) VLB correlation for the binary system water and isopropanol (IPA). VLB data for water and isopropanol is listed in Table B-1. This system has a minimum boiling azeotrope at 80.46°C. The Aspen Plus fit to the data with NRTL is not terrible, but can be improved. 

Felbab, N., D. IBldebrandt, and D. Glasser, A new method of locating all pinch points in nonideal distillation systems, and its application to pinch point loci and distillation boundaries. Computers and Chemical Engineering, 2011, 35(6) 1072 1087. 

The exact calculation procedure is dependent on how the feed species distribute between the distillate and the bottoms product. For multicomponent systems of class 1 type, all species in the feed are present in the distillate and the bottoms product. In such a system, we have a pinch point of the type represented by point B around the feed point in Figure 8.1.23(b) meant for a binary system. For multicomponent systems of class 2 type, either the distillate or the bottoms or both will not have one or more species present in the feed. One encounters two pinch points in these types of systems, one in the rectifying (enriching) section and the other in the stripping section due to the presence of the so-called nondistributing species which do not show up either in the distillate or the bottoms or both (Shiras et al, 1950). 

Figure 8.9 Vapor vs. liquid mole fractions at 1 atm for (a) chloroform (a)-n-hexane (b) and (b) acetone (a)-chloroform (b). A pinch point in the distillation process is illustrated.

The rectifying or stripping section of a column must operate somewhere between total reflux and minimum reflux conditions. The range of feasible operation of a column section can thus be defined for a given product composition. It can be seen in Figure 12.19 that these section profiles are bounded for a stage column by the distillation line and the pinch point curve. As noted previously, the pinch point curve provides a minimum reflux boundary for both staged and packed columns,... 

Also shown in Figure 12.19 is the residue curve projected from the same product composition. The area enclosed within the residue curve and the pinch point curve thus provides the feasible compositions that can be obtained by a packed column section from a given product composition. For any given product composition, the operation leaf of feasible operation for a column section can be defined by plotting the distillation line (or residue curve) and the pinch point curve1314. The column section must operate somewhere between the total and minimum reflux conditions. 

Bottom Product B with a straight line joining the Distillate D and Entrainer Feed E, as shown in Figure 12.24. Pinch point curves for the middle section can now be constructed by drawing tangents to the residue curves from the difference point (net overhead product). This is shown in Figure 12.25 for the system ethanol-water-ethylene glycol. The area bounded by the pinch point curves defines the middle section operation leaf. 

Figure 4.33 illustrates the PSPS and bifurcation behavior of a simple batch reactive distillation process. Qualitatively, the surface of potential singular points is shaped in the form of a hyperbola due to the boiling sequence of the involved components. Along the left-hand part of the PSPS, the stable node branch and the saddle point branch 1 coming from the water vertex, meet each other at the kinetic tangent pinch point x = (0.0246, 0.7462) at the critical Damkohler number Da = 0.414. The right-hand part of the PSPS is the saddle point branch 2, which runs from pure THF to the binary azeotrope between THF and water. 

It is possible to derive—roughly—the equations underlying the Underwood method (Underwood, 1946) from the above. The variable R represents the reflux ratio defined in terms of the liquid flow at the pinch point relative to the distillate top product flow i.e.,... 

Finally, from the results of these observations, we can prove that a pinch point is any point where a line emanating from the distillate composition is tangent to a residue curve. The vapor composition in equilibrium is on that same line. The reflux ratio to reach that pinch point is the ratio a/b. 

Thus, any point B that lies on a line passing through an inflection point of a residue curve with the same slope as the residue curve cannot have a pinch point trajectory emanating from it that crosses the distillation boundary. We draw a family of lines through every such inflection point. To the left of all these lines are the bottoms products, B, that can be bottoms products with a top product in the left-hand-side region. Points on and to the right of these lines are not candidates. 

Finally, we note with a similar set of arguments that no product in the left-hand-side region can have a pinch point curve that crosses the distillation boundary, thereby justifying the statement appearing in the literature that one cannot cross such boundaries from the convex side. 

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