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CENG0006: Coursework -1

Process Flowsheeting with Recycle, Linear Equations and Nonlinear Equations

Submission Deadline: 12 noon, 17th February 2021

Prepare a report (pdf) and submit via TurnItIn including a copy of the GAMS code (.gms), and output (.lst)
in the appendix of the report.

In addition to the TurnItIn submission, GAMS code (.gms) and output (.lst) files must be submitted as a
single zipped/compressed file folder via Moodle.

Each question carries marks distributed as shown below [ ].

Hints: See the two GAMS files for hints on the same tab.


Exercise – 1: Nonlinear Equations – van der Waals Equation of State
[15]

Using GAMS (as a programming language) solve for V the following van der Waals equation of state for
ammonia at 10 atm and 250°C by using Secant Method where two initial guesses for V are 2.50 and 2.51.

(P + a/V2) (V – b) = RT

a = (27/64) (R2Tc2/Pc)

b = RTc/(8Pc)

Given: R = 0.08206 atm l K-1 mol-1, P = 10 atm, T = 523 K, Tc = 407.5 K, Pc = 111.3 atm, a = 4.238448, b =
0.037556.

Provide the formulation of the problem and progress of the iterations in the report. Also upload the GAMS
(.gms and .lst) files.

Exercise – 2: Simulation of an Equilibrium Reactor

Consider the following reactor where stream 2 is pure ethane.

Ethane is dehydrogenated to ethylene and acetylene in the following pair of catalytic reactions:

26 ↔ 24 +2

26 ↔ 22 + 22

Let A represent ethane, B ethylene, C acetylene and D hydrogen. The reactions proceed such that the product
gas composition satisfies the following equilibrium conditions:




= 3.75


Reactor 2 3
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2

= 0.135

where y denotes mole fraction. Let 1and 2 denote extent of first and second dehydrogenation reactions
respectively. Assume 100 kmol/hr of ethane is entering the reactor.

(i) Write mass balance equations for the reactor in terms of component flowrates, and 1and 2.
[5]
(ii) Write equations for y, the mole fractions, in terms of the component flowrates, and 1and 2,
and substitute the equations obtained in to the equilibrium conditions given above to obtain
equations in terms of 1and 2. Formulate the resulting equations in GAMS and solve the
equations: (a) using the CNS solver to compute values of 1and 2, and (b) using Newton’s
method by using GAMS as a programming language to compute values of 1and 2.
[10]

Exercise – 3: Process Flowsheeting with Recycle
[30]

In this exercise you have to solve the mass balance for the following flowsheet:
The reactor considered in this flowsheet is the same as the reactor in the previous Exercise except that the
assumption of 100 kmol/hr of ethane entering the reactor does not hold due to the recycle (stream-5). A 100
kmol/hr feed (stream-1) of pure ethane is mixed with the recycle (stream-5) containing pure ethane, and the
mixed stream (stream-2) goes to the reactor where the dehydrogenation reactions as explained in the
previous Exercise take place. The outlet (stream-3) from the reactor goes to the separator which separates
95% of unreacted ethane from ethylene, acetylene, and hydrogen and recycles the separated ethane to the
reactor.

PART A: Write the mass balance for this problem and submit it as a part of the report. Carry out degrees of
freedom analysis and if it is not zero then make it zero by specifying some variables or removing some
specification. Submit degrees of freedom analysis in the report.

PART B: Equation Oriented Process Flowsheeting – using GAMS as a modelling tool

Formulate this problem in GAMS and solve it using the CNS solver. Submit the .gms and .lst files.

PART C: Sequential Modular Process Flowsheeting – using GAMS as a programming tool

Resolve the problem by using GAMS by using stream 5 as the torn stream. Plot , the error, as a function of
iteration counter k, where

=∑(5
+1() − 5
())
2
2
=1



Mixer

Separator

Reactor
Feed
1
2 3
4
5
Product
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where 5
() denotes the flowrate of component i in stream 5 computed in iteration number k.

In this case you could define the unknown variables as PARAMETERS in GAMS. To start the calculations,
guess initial values for stream 5 component flowrates and then sequentially calculate the remaining stream
component flowrates. Prepare a short report containing the plot mentioned above and the values of the
converged flowrates of all the components in all the streams. Decide a sensible value of  as the convergence
criteria – if you can not decide, then try different values and discuss your observations in the report.
Submit the .gms and .lst files.

Exercise – 4: Solving Nonlinear Equations by using GAMS
[20]

Consider the process flowsheet given in Figure 1 of the paper:

Process Optimization by Nonlinear Programming, C. W. Di Bella , W. F. Stevens, Ind. Eng. Chem. Process
Des. Dev., 1965, 4 (1), pp 16–20, DOI: 10.1021/i260013a005
http://pubs.acs.org/doi/pdf/10.1021/i260013a005

The process model is given by equations (22)–(30) consisting of 9 equations and 12 variables. Solve the system
of nonlinear equations when T = 654.219 Rankine, V = 60 cu. ft. and FR = 3.2689E+5 lb/hr by using GAMS.
The values of the model parameters are given in the Nomenclature section of the paper and the values of Ai
and Bi are given in the first column below Figure 1.

The GAMS input file must also contain adequate comment statements for ease of understanding. Submit your
GAMS input (.gms) file and output (.lst) file.

Exercise – 5: Linear Equations – a Chemical Separation System

Benzene, styrene, toluene and xylene are separated in a sequence of distillation columns (A, B, C) as shown
below. Stream 1 flowrate composition in mole % is 10% benzene, 15% styrene, 35% toluene and 40% xylene.






























A


B


C
1
2
3
4
5
6
7
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Column A: 80% benzene, 60% styrene, 30% toluene and 10% of xylene of stream 1 goes to stream 2 and the
remainder to stream 3.

Column B: 70% benzene, 65% styrene, 25% toluene and 5% xylene of stream 2 goes to stream 4 and the
remainder to stream 5.

Column C: 85% benzene, 65% styrene, 20% toluene and 10% xylene of stream 3 goes to stream 6 and the
remainder to stream 7.

Write the mass balance for this system as a set of linear equations in the form A x = b.
[10]

Solve the mass balance in the A x = b form by using GAMS for stream 1 flowrate of 100 moles/hr.
[10]

In the report provide the mass balance equations and the solution obtained. Also upload the GAMS code (.gms)
and output (.lst) files.


























































































































































































































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