Plotting McCabe-Thiele Diagrams in Microsoft Excel for Non-Ideal Systems

John L. Gossage

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Conference: 2016 ASEE Annual Conference & Exposition
Location: New Orleans, Louisiana
Publication Date: June 26, 2016
Start Date: June 26, 2016
End Date: June 29, 2016
ISBN: 978-0-692-68565-5
ISSN: 2153-5965
Conference Session: New Pedagogical Approaches in Chemical Engineering
Tagged Division: Chemical Engineering
Page Count: 24
DOI: 10.18260/p.25913
Permanent URL: https://peer.asee.org/25913
Download Count: 22306

Paper Authors

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John L. Gossage Lamar University

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John L. Gossage is an Associate Professor in the Dan F. Smith Department of Chemical Engineering at Lamar University. His main research areas are simulation, applied probability, and engineering education. He currently teaches simulation and kinetics classes at both the undergraduate and graduate levels, as well as undergraduate advanced analysis. He holds a Ph.D. in chemical engineering from Illinois Institute of Technology in Chicago, IL.

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Abstract

Plotting McCabe-Thiele Diagrams in Microsoft Excel for Nonideal Systems

Although modern process simulation packages (such as Aspen Plus or Pro/II) can quickly and efficiently perform distillation column calculations, they often confuse students who are just beginning to learn distillation basics, leading to questions such as, “Why can’t the reflux ratio be smaller than the minimum reflux ratio?”, or “Why does increasing the product purity require a larger number of stages?”. Because of this, McCabe-Thiele diagrams are indispensable in teaching binary distillation, as they graphically demonstrate the relationships among key parameters (number of stages, feed location, reflux ratio, tops and bottoms purity, etc.) related to the design and operation of a distillation column.

The drawback to McCabe-Thiele diagrams is that they are difficult to draw freehand, and this difficulty is aggravated when the vapor-liquid equilibrium data for the system is represented not by a constant relative volatility but rather by a set of equilibrium data points, as then the necessary first step is to fit the equilibrium curve to the data. If this fitting is performed freehand, two problems arise: first, different hands will produce different curves, which will naturally alter the computed results (sometimes quite significantly); and second, the process is cumbersome and tedious, thereby consuming valuable class time.

This paper presents a method to automate the process of fitting binary equilibrium data to a smooth curve (using a cubic B-spline algorithm implemented via Visual Basic for Applications (VBA) in Microsoft Excel) and then drawing the McCabe-Thiele diagram in Microsoft Excel. In this way, the effect of changes to the operating conditions can be quickly and easily demonstrated to students in class. Furthermore, if the binary system in question contains an azeotrope, the spreadsheet will locate it. In addition, this paper provides the VBA code to find real roots of any cubic equation. If Excel’s Solver add-in is used, the method can also solve trial-and-error problems: for example, determine the necessary reflux ratio for a fixed number of stages in the column.

The inputs to the spreadsheet are the x-y equilibrium data, the feed composition and “q-value” (usually, the liquid mole fraction of the feed), the desired tops and bottoms purity, the reflux ratio, and the Murphree efficiency. The outputs are the location of the azeotrope (if present), the intersection point of the feed line with the equilibrium curve, the required number of stages, and the optimal feed stage location.

The cubic B-spline method presented in this paper can also be applied to smoothing any type of data where the endpoints are known.

Citation
Format

Gossage, J. L. (2016, June), Plotting McCabe-Thiele Diagrams in Microsoft Excel for Non-Ideal Systems Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.25913

TY  - CPAPER
AB  - Plotting McCabe-Thiele Diagrams in Microsoft Excel for Nonideal Systems

Although modern process simulation packages (such as Aspen Plus or Pro/II) can quickly and efficiently perform distillation column calculations, they often confuse students who are just beginning to learn distillation basics, leading to questions such as, “Why can’t the reflux ratio be smaller than the minimum reflux ratio?”, or “Why does increasing the product purity require a larger number of stages?”. Because of this, McCabe-Thiele diagrams are indispensable in teaching binary distillation, as they graphically demonstrate the relationships among key parameters (number of stages, feed location, reflux ratio, tops and bottoms purity, etc.) related to the design and operation of a distillation column.

The drawback to McCabe-Thiele diagrams is that they are difficult to draw freehand, and this difficulty is aggravated when the vapor-liquid equilibrium data for the system is represented not by a constant relative volatility but rather by a set of equilibrium data points, as then the necessary first step is to fit the equilibrium curve to the data. If this fitting is performed freehand, two problems arise: first, different hands will produce different curves, which will naturally alter the computed results (sometimes quite significantly); and second, the process is cumbersome and tedious, thereby consuming valuable class time.

This paper presents a method to automate the process of fitting binary equilibrium data to a smooth curve (using a cubic B-spline algorithm implemented via Visual Basic for Applications (VBA) in Microsoft Excel) and then drawing the McCabe-Thiele diagram in Microsoft Excel. In this way, the effect of changes to the operating conditions can be quickly and easily demonstrated to students in class. Furthermore, if the binary system in question contains an azeotrope, the spreadsheet will locate it. In addition, this paper provides the VBA code to find real roots of any cubic equation. If Excel’s Solver add-in is used, the method can also solve trial-and-error problems: for example, determine the necessary reflux ratio for a fixed number of stages in the column.

The inputs to the spreadsheet are the x-y equilibrium data, the feed composition and “q-value” (usually, the liquid mole fraction of the feed), the desired tops and bottoms purity, the reflux ratio, and the Murphree efficiency. The outputs are the location of the azeotrope (if present), the intersection point of the feed line with the equilibrium curve, the required number of stages, and the optimal feed stage location.

The cubic B-spline method presented in this paper can also be applied to smoothing any type of data where the endpoints are known.

AU  - John L. Gossage
CY  - New Orleans, Louisiana
DA  - 2016/06/26
PB  - ASEE Conferences
TI  - Plotting McCabe-Thiele Diagrams in Microsoft Excel for Non-Ideal Systems
UR  - https://peer.asee.org/25913
DO  - 10.18260/p.25913
ER  -