McCabe-Thiele method feed line

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

The McCabe-Thiele method can be used for the design of columns with side streams and multiple feeds. The liquid and vapour flows in the sections between the feed and take-off points are calculated and operating lines drawn for each section. 

The McCabe-Thiele method will be used. The side draw is more concentrated in acetone than either feed and should therefore be located above the feeds. Calculate the internal liquid and vapor flow rates and the slope of the operating line between the condenser and the side draw ... 

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. 

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. 

And we define a function to optimize including the McCabe-Thiele method for the number of trays assuming constant relative volatility. We compute the operating lines as a function of the compositions of the feed, the distillate, and the residue. Next, we use a while statement to compute the number of theoretical trays. Finally, we compute the cost of the vessel and that of the energy required at the boiler. 

To design such a process, the McCabe-Thiele method may be used to determine the number of theoretical separation stages, as examined in Sections 3.3.2-3.3.4 for distillation, absorption (gas scrubbing), and liquid-liquid-extraction. Thus, we obtain the number of theoretical extraction stages of a countercurrent extraction column based on the equilibrium curve (solubility of extract in the solvent for a given content in the solid) and the operating line. The latter depends on the extract content of the solid feed and residue, and on the in- and outlet extract concentration in the solvent The extract content of the feed is fixed, and the value of the residue is specified by the required degree of extraction. The inlet content of the extract in the solvent is also fixed, as either pure solvent is used or the value is specified by separation of the extract from the used solvent after the extraction. Therefore, the only parameter that is left is the outlet concentration of the extract in the solvent, which depends on the ratio of the solvent flow to the feed rate of the solid feedstock (mass balance). 

Figure 8.1.20. Vapor-liquid equilibrium curve, operating lines for enriching section and stripping section and construction of ideal stages and q Une for a feed consisting of vapor and liquid in a multistage distillation column having ideal equilibrium stages the McCabe-Thiele method.

The McCabe-Thiele graphical method uses three important types of line the operating lines, an equilibrium line and a g-line (feed line). 

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