# Modeling of a Distillation Column Using Bond Graphs

## Abstract

### 1.0 - Introduction

This thesis proposes using bond graphs as a way to model distillation columns. Bond graphs represent, graphically, the power flow in a system. This thesis will not discuss the explanation of, nor the justification for, bond graphs. Rather, this thesis will show the power of using bond graphs: bond graphs can provide a clear, graphical representation of a distillation column that systematically organizes the equations and possible approximations. Modeling and simulating distillation columns is not new. However, the typical models used for distillation columns are fairly complex and involve a number of approximations. The approximations used depend upon the components used.

This section will explain the operation and purpose of a distillation column and discuss in general the basic model used to describe a distillation column. The basic model includes equations for energy balance, mass balance, pressure, temperature, and vapor-liquid equilibrium.

### 2.0 - Modeling a Distillation Column

This section will discusses the numerous approximations that are used to implement the basic model. The main reason for these approximations is the fact that no one set of equations adequately describes the dynamic relation between variables for all combinations of components. The basic energy balance equations are well defined, for instance, but the enthalpy is always a function of temperature (and possibly other variables) that depends on the nature of the component. The vapor-liquid equilibrium equations are typically the most complex; they relate the molar fraction of a component in vapor with the molar fraction of that component in liquid. These equations depend on temperature, pressure, and the molar fractions of the other components. Several forms of these equations exist. Of course, just the term equilibrium calls into question the applicability of these equations to column dynamics. This idea will be explored.

### 3.0 - A Specific Example of a Distillation Model

This section will deal with the simulation of an existing comprehensive model of a specific distillation column using ACSL. This example is taken from the dissertation of Steven Gallun. Appendix A will contain the complete equations Gallun used and Appendix B will contain the ACSL program used to implement these equations. The simulation results of the ACSL program will be compared to those of Gallun. Included in this section will be a discussion of the specific choices made to assemble this model.

### 4.0 - Modeling the Gallun Model With Bond Graphs

This section will show how the same model presented in the previous section can be implemented using bond graphs. The discussion will begin with the specific transference of equations into bonds and then reveal a simpler graph using hierarchical bond graphs. The bond graph is then coded into DYMOLA and simulated using DESIRE. The results, when compared to the Gallun and ACSL implementations, should show the legitimacy of this approach. Appendix C will contain the DYMOLA code.

### 5.0 - Distillation Column Model with Chemical Reaction

This section will broaden the model of a distillation column by adding the possibility of chemical reactions to the model. Solvents are sometimes added to a distillation column to facilitate separation by reacting with some of the other components. Bond graphs can include these reactions (and the resulting equations) in a straight-forward way.

Only if there is time will this section include a simple example of a distillation column with a chemical reaction. (Taken from Chapter 8 of Holland, '81)

### 6.0 - Conclusion

This section will discuss the advantages of using bond graphs for modeling distillation columns. A comparison to commonly used techniques in chemical engineering will be made. The discussion will include applicability of using similar bond graph techniques to other chemical systems such as tubular reactors, and the power of using bond graphs for almost any system.

### Appendix A

- Gallun's equations for a comprehensive dynamic distillation column.

### Appendix B

- ACSL and DYMOLA code for Gallun's model.

### Appendix C

- DYMOLA code bond graph of Gallun's model.