Tangent pinch

Extractive distillation is defined as distillation in the presence of a miscible, high boiling, relatively nonvolatile component, the solvent, that forms no azeotropes with the other components in the mixture (23). It is widely used in the chemical and petrochemical industries for separating azeotropic, close-boiling, and other low relative volatiUty mixtures, including those forming severe tangent pinches. 

FIGURE 11 Graphic illustrations of minimum solvent rate, (a) Pinch at the bottom, (b) pinch at the top, (c) tangent pinch. 

As can be seen from Fig. 4.7, the kinetic tangent pinch point at the critical Damkohler number Dar = 0.166 has an important role for the topology of the maps. This is also reflected by the feasibility diagrams given in Fig. 4.8(a-c). In Fig. 4.8(c), the stable node branch at positive Damkohler numbers are collected from the singular point analyses of the reactive condenser (Fig. 4.8(a)) and the reactive reboiler... 

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. 

At minimum reflux, the pinch occurs at the intersection of the component balance line and the g-line when the equilibrium curve has no inflection points (Fig. 2,11c), This would be expected because the component balance lines intersect on the q-line. When the equilibrium curve has a point of inflection (Fig. 2.12), the pinch between the equilibrium curve and the component balance line may occur at the point of tangency instead of the intersection of the g-line and the component balance line. This condition is termed tangent pinch. 

To determine minimum reflux, construct the q-line and identify its point of intersection with the equilibrium curve. Then draw a line from the product composition point on the 45° diagonal line to this intersection point, From Eq. (2,29), the slope of the line is RmiJ (/ min + 1), and the intercept of this line on they axis is XrJ(RmiT. + 1). Minimum reflux can be determined from either of these. If minimum reflux occurs at a tangent pinch, the minimum reflux is independent of the q-line and the feed composition, It can then be determined from the equilibrium curve alone (13). 

Neither minimum reflux nor a tangent pinch is an operable condition. Either will require an infiuite number of stages in the column, and this is physically impossible. Nevertheless, operation can some-... 

Figure 2.12 Tangent pinch. (From C, J, King, Separation Processes. 2d ed,. Copyright by McGraw-Hill, Inc. Reprinted by permission.)...

One useful limit for a stripping column is the maximum L/G ratio, which corresponds to the minimum stripping gas flowrate (minimum G/L ratio) required for a desired separation. The maximum L/G is the slope of the line which begins at the point (To, Xi) and intersects the equilibrium line. As shown in Figure 6.7, the (L/G)max occurs as one rotates the operating line clockwise around (Xi, Tq) until it intersects the equilibrium line. This can occur at a tangent pinch point and not necessarily at the end of the column Xm, Ym). 

Many industrially important liquid systems are difficult or impossible to separate by simple continuous distillation because the phase behavior contains an azeotrope, a tangent pinch, or an overall low relative volatility. One solution is to combine distillation with one or more complementary separation technologies to form a hybrid. An example of such a combination is the dehydration of ethanol using a distillation-membrane hybrid, as shown in Figure 6.30. 

Figure 16.2 McCabe-Thiele method for mixtures showing equilibrium curves with tangent pinch. Left Position of tangent pinch and critical distillate composition. Right Minimum reflux and feed composition A - feed pinch control, B - tangent pinch control...

At the inflection point, designated by tangent pinch, the composition is x,p, and the tangent intersects the diagonal at (Fig. 16.2-left). This composition is the... 

Pinching (either due to a mislocated feed, proximity to minimum reflux, or a tangent pinch) is commonly implicated by the above insensitivity. A McCabe-Thiele diagram and a key ratio plot can help identify the cause application of these techniques for this purpose is described elsewhere (193). Any scale-up of such efficiency data must be conservatively performed. 

To study the behavior of the singular points in the vicinity of the MTBE vertex, Thiel et al. [8] used a continuation method with the Damkbhler number as continuation parameter. The results computed at p = 0.8 MPa are shown in Fig. 5.17. It can be observed that a stable node branch beginning from pure MTBE in the absence of chemical reaction moves away from MTBE vertex with rising Da. As the Damkohler number Da = 1.49 X 10 is reached, the stable node branch turns into a saddle branch. This point is called the kinetic tangent pinch [9]. The saddle branch arrives at Da = 0.0 in the binary azeotropic point between MeOH and MTBE. 

Fig. 5.20. Singular point curves in the TAME system at different operating pressures and branch of kinetic tangent pinches ([8], reprinted from Chem. Eng. Sci., Vol 52, Thiel, Sundmacher and Hoffmann, Pages 993-1005, Copyright 1997, with permission from Elsevier Science)...

At an operating pressure p below 1.0 MPa, the curves have a qualitative shape similar to those computed for the MTBE example a stable node branch moves from the TAME vertex to the kinetic tangent pinch and reaches its maximum Damkhhler number Da here. Then, the stable node branch turns into a saddle branch and runs into the binary azeotropic point between MeOH and TAME. A second saddle branch develops if an operating pressure p = 0.8 MPa at the starting point of pure lA is chosen. This saddle branch moves away from the lA vertex and reaches the line of chemical equilibrium at Da —y oo. This point is marked with a diamond in Fig. 5.20. If p is set to 1.0 MPa the stable node branch does not turn into a saddle branch that ends in the binary azeotropic point between MeOH and TAME, but which runs into pure lA. Consequently, at p = 1.0 MPa a second saddle branch, which starts at the binary azeotropic point between MeOH and TAME and arrives in the line of chemical equilibrium at Da —y oo, can be computed. In addition, in Fig. 5.20 the branch of kinetic tangent pinches is also plotted. 

Distillation of the product will be complicated by the existence of azeotropes between ethanol and ethyl acetate, water and ethanol, and water and ethyl acetate. And the acetic acid-water and acetone-water mixtures are famous for their tangent pinches. Rigorous distillation simulations with thermodynamics that accurately predict each of these azeotropes and pinches will be required to have confidence in the design. 

Detecting pinched regions (Sec, 2.2.5) Pinching and its cause (minimum reflux, mislocated feed, tangent pinch, etc.) are readily visible on an x-y diagram. Figure 2.22 compares a well-located fe point in the depropanizer example with a mislocated feed point. The pinch is clearly seen in Fig. 2.226, while no pinch exists in Fig. 2.22a. 

Figure 4-26. Miiiimum reflux (A) pinch at feed stage, (B) tangent pinch, (C) concentration profile...

Generate the y-x curves for each binary pair. If all separations are relatively easy (reasonable relative volatilities and no inflection points causing tangent pinches for one of the pure conponents) use the ideal heuristics in Section 11. S. 

If one of the binary pairs has a small relative volatility or a tangent pinch, determine if this separation is easier in the presence of the third conponent. This can be done by generating distillation curves or y-x binary equilibrium at different constant concentrations of the third component. If the presence of the third conponent aids the separation, separate the difficult pair first. The concentration of the third conponent can be adjusted by recycling it from the column... 

It can be noticed that the PRAz is an intermediate boiling reacting mixture and behaves like a tangent pinch that prohibits designing the separation sequence towards pure MTBE. 

Levy, S. G., Doherty, M. F. (1986). A Simple Exact Method for Calculating Tangent Pinch Points in Multicomponent Nonideal Mixtures by Bifurcation Theory. Chem. Eng. Sci,4, 3155-. ... 

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