McCabe-Thiele method minimum reflux

The reduction in the required number of plates as R is increased beyond Rm will tend to reduce the cost of the column. For a column separating a benzene-toluene mixture, for example, where Xf = 0.79, xd = 0.99 and xw = 0.01, the numbers of theoretical plates as given by the McCabe-Thiele method for various values of R are given as follows. The minimum reflux ratio for this case is 0.81. 

The feed, at a flow rate of 100 kmol/h, is sent as saturated vapor to the distillation column. The column is equipped with a partial condenser with a vapor product, and a reboiler. For a solvent rate of 500 kmol/h, it is required to determine the required number of equilibrium stages and the optimum feed location for a reflux ratio of 1.5 times the minimum. The McCabe-Thiele method may be used on a solvent-free basis. 

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...

Total reflux corresponds to a situation where there is no feed, distillate, or bottoms and where the minimum number of stages is required to achieve a desired separation. It will be recalled that in the McCabe-Thiele method this situation corresponded to having the operating line coincide with the y = x line. 

According to the McCabe-Thiele method, the system for separation is considered on a quasi-binary basis. In this approach, it must be possible to neglect the influence of the solvent, which is acceptable if the phase boundary lines (solubilities) do not change much with concentration during separation. In this case, the number of theoretical stages, the minimal reflux (ratio), the minimum number of theoretical stages, and their mutual dependence can be determined. 

A modified McCabe-Thiele method employed in extractive distillation has been described by Nagel and Sinn [78]. Kortiim and Faltusz [79] have dealt with a variety of problems involved in selective separating processes ranging from the design of an automatic apparatus of special steel for continuous operation to the calculation of the minimum reflux ratio and the required amount of additive. 

FIGURE 5.3-11 Minimum reflux by McCabe-Thiele method (a) normal equilibrium curve and (b) equilibrium curve with concavity. 

For a given rectification problem the minimum reflux ratio v ,jn and the minimum number of separation stages may be determined by the McCabe-Thiele method or calculated by Eqs. (2-74) and (2-77). With these, the required number of theoretical stages for any chosen reflux ratio V is found from the Gilliland diagram. The best economic operating range of rectification columns is... 

C Total and Minimum Reflux Ratio for McCabe-Thiele Method... 

Figure 11.4-10. Total reflux and minimum number of trays by McCabe-Thiele method. 

Minimum reflux, by definition, is that condition whereby a zone of an infinite number of stages exists immediately on each side of the feed location. In the McCabe-Thiele method of graphical representation and calculation, both operating lines intersect with the locus of the feed partitioning, all at a point on the fC-value plot (or equilibrium curve). It is therefore impossible to calculate away from this point of intersection, in either direction. 

The operation of a binary distillation has two important limiting cases minimum and maximum stages for a given separation. Minimum stages occur when the column is operated with total reflux (i.e., no top product is withdrawn). This situation, when applied to the McCabe-Thiele method, uses the y = x line as the mass balance for both rectifying and stripping. The situation is depicted in Figure 12-11. 

Figure 12-11. Total reflux and minimum stages with McCabe-Thiele method. (Reproduced with permission from reference 18. Copyright 1997, American Chemical Society.)...

If graphical methods are used for binary systems, the minimum reflux ratio may be estimated directly. For McCabe-Thiele, it can be determined from the minimum slope of the upper operating line, which can be found graphically and often represents coincidence with the intersection of the line with the equilibrium curve, as shown in Fig. 5.3-11. Unusual curvature of the equilibrium relationship can limit the minimum reflux ratio to a higher value as also shown in Fig. 5.3-11. In stepping off stages, starting at the top, a... 

The end of each sub-task is detected as the following violation takes place. At some point the reflux ratio used approaches the actual minimum value for the corresponding composition in the vessel. At this point a new reflux ratio has to be used. The limiting composition at the end of the sub-task is found using the simple graphical method of McCabe-Thiele. The distillate amount and the amount remaining in the vessel are calculated from simple mass balance equations. The operating time of the sub-task is found from the overall material balance around the top of the column. This procedure is repeated until the desired yield is achieved. 

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