TEAMS: This project can be completed in teams of up to 4 students.
DISTILLATION COLUMN COMPOSITION CONTROL
Over 40,000 distillation columns operate today in the U.S. in petrochemical processing facilities and
cumulatively consume 40‐60% of all of the total energy used in the petrochemical industry and more
than 6% of the TOTAL U.S. energy usage. Reducing distillation energy usage can have a major impact on
energy independence, greenhouse gas emissions, and give a competitive advantage to any
manufacturer that is better able to implement improvements.

Task
Design a control system for a binary (cyclohexane / n‐heptane) distillation column and
maintain the distillate composition above 0.95 mole fraction cyclohexane (C6H12) and the bottoms
composition below 0.05 mole fraction in cyclohexane so that both streams can be sold commercially. If
the distillate composition is above 0.95, it indicates that energy was wasted to exceed the target
specification limit. If the distillate composition is too low, energy is also wasted because the product
must be recycled through the distillation column. If the bottoms composition is below 0.05
cyclohexane, then energy has been wasted to boil‐up more material than was needed to achieve the
desired purity specification. In order to meet the target specifications, two key column variables can be
manipulated: (1) the reflux rate (in [mol/min] flowrate) that is fed back onto the top tray in the column
can be modulated via a control valve and (2) the reboiler boil‐up rate (in [mol/min] units) can be
adjusted by means of a control valve feeding steam to the reboiler. A distillation column is a highly
coupled non‐linear system that inherently leads to interacting controllers. Your overall task is to
develop a control scheme that can provide good compositional control of both the overhead and
bottoms product streams in the face of disturbances of both feed flow, composition, and quality.
A fully non‐linear model of the cyclohexane/n‐heptane distillation column has been developed and is
supplied in the associated MATLAB file. You can use this model to both (1) empirically develop linear
system models for the column around a desired steady‐state operating point and (2) test your proposed
control schemes on the fully non‐linear process to determine how well the control scheme will work in
practice in the plant. The model provided is based on a steady‐state operating point of: (1) a feed
flowrate of 1 [mol/min] to the column that is 50 mol% cyclohexane and 50 mol% n‐heptane, (2) a reflux
flowrate from the total condenser back into the top of the column is 2.706 [mol/min], (3) a bottoms
boil‐up vapor flowrate in the reboiler of 3.206 [mol/min], (4) a column containing 41 stages including
the reboiler and total condenser (which produces saturated liquid distillate), (5) feed being introduced
on the 21 stage in the column where stage #1 is at the top of the column, (6) a relative volatility
between cyclohexane and n‐heptane of 1.5. You can assume that the control valve on the reflux return
line to the column is fast and can modulate the reflux rate between 0 [mol/min] and 5 [mol/min].
Likewise, you can assume the steam line control valve to the reboiler is sized so that it can deliver boilup
vapor flowrates from 0 [mol/min] to 5 [mol/min].
You should at a minimum complete the following tasks as a part of your control system design and
verification:
1. Empirically determine a linear system model that describes the distillation column and relates
changes in feed flowrate, composition, or quality to the distillate composition and bottoms
composition around the desired operating point of feed flowrate of 1 [mol/min], feed
composition of 50 mol% cyclohexane, 95 mol% cyclohexane in the distillate and 5 mol%
cyclohexane in the bottoms product. Implement that linear system model in SIMULINK.
2. Perform an analysis to determine what manipulated variables (i.e. reflux flowrate or reboiler
boil‐up vapor flowrate) should be paired with each regulated output variable (i.e. distillate
composition and bottoms composition).
3. If one assumes that the composition analyzers used on the column are on‐line gas
chromatographs that are properly calibrated but act as a time delay element in the
measurement of 10 minutes (i.e. due to the time required to elute material through the GC
column), use at least two different methods including IMC to design and tune controllers for the
system that do not utilize decouplers. Test your control system on the nonlinear column model
and discus how effective the control system performs in the face of +/‐ 10% disturbances to
feed flowrate, composition, and quality.
4. Redesign/retune controllers for the system in a case where static decouplers are used to allow
for better control of the system. Test your control system on the nonlinear column model and
discus how effective the control system performs in the face of +/‐ 10% disturbances to feed
flowrate, composition, and quality.
5. Redesign/retune controllers for the system in a case where dynamic decouplers are used to
allow for better control of the system. Test your control system on the nonlinear column model
and discus how effective the control system performs in the face of +/‐ 10% disturbances to
feed flowrate, composition, and quality.
6. Design a control system which implements feedforward control as a means to mitigate the
effect of feed flowrate changes on column performance. Test your control system on the nonlinear
column model for +/‐ 10% changes in feed flowrate.
7. Design a control system which implements a Smith Predictor structure to better deal with time
delays in the system. Test your control system on the nonlinear column model and discus how
effective the control system performs in the face of +/‐ 10% disturbances to feed flowrate,
composition, and quality.
8. BONUS: Show use of any other methods and approaches in the course to develop and effective
control system for the column.
DELIVERABLES:
Your report must be submitted in two parts: (1) a single PDF file containing all of the report addressing
the required tasks and any optional tasks undertaken and (2) a SIMULINK model file containing what you
deem as the best control system configuration implemented on the non‐linear column model supplied
with the project documentation.
Your design report should focus on what methods you apply to developing the response to each task,
what the outcome of those efforts are, and to what degree effective control is achieved for the column.
Effective use of tables, figures, and diagrams (e.g. SIMULINK diagrams, time domain response plots, etc.)
in addition to text are expected in the final report.

Sample Solution

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.

God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.