Write a vba macro to calculate the material balance over

Question

General description

The project focuses on material balance of ammonia production. The chemical reaction is:

3/2H₂ + 1/2N₂ ↔ NH₃

The process employs two "plug flow" reactors in series with a cold-shot strategy for temperature control to increase the conversion. A simplified flow diagram shown in Figure 1 represents the process. The syngas contains mainly hydrogen and nitrogen with an exact ratio of 3 to 1. The syngas also contains a small percentage of Argon. The fraction of "cold-shot" stream is denoted as ?1. The fraction of the recycled gas, ?2 , is also purged from the process to remove excessive argon.

The specific data (Argon fraction, ?1 and ?2 ) for each group is given in Table 3

Question 1. Material balance with Excel/VBA

Figure 1. Ammonia production

The single-pass conversion rate for both reactors can be approximately modelled by the following formula:

if x < 50%: c = 0.17 - 0.156x - 0.38x²

if x > 50%: c = 0

Where c the hydrogen-based conversion, x is molar fraction of NH₃ in the reactor input stream.

Question 1a. Write a VBA macro to calculate the material balance over the reactor.

Question 1b. Use tear-analysis to find the feasible material balance for the process. What is the overall conversion?

Question 2. HYSYS simulation

In this part, the conversion rates are calculated from reaction constant and reactor size by HYSYS. The reactors consist of series of elementary tubes. Each elementary tube has a length of 1 m and diameter of 0.2 m. For these particular reactors, the net rate of reaction (forward rate minus reverse rate) is given in kgmole/(m3.s) and the parameters are:

Forward: A₁ = 10⁴ kgmole/m³ s^-1,

E₁ = 9.1×10⁴ kJ/kgmole,

Reverse: A2 = 1.3 ×10¹⁰ kgmole/m³ s^-1,

E₂ = 1.4×10⁵ kJ/kgmole

Note that this rate equation applies in the vapour phase and is based on partial pressure (atm).

The process also involved heaters and coolers, as showed in Figure 2. The properties and constraints are given in Tables 1 and 2, respectively.

Figure 2. PFD for ammonia plant (for HYSYS simulation).

Table 1. Properties of components.

Item	Value	Comment
Property package	SRK	Peng-Robinson?
Synthesis gas (syngas)	Nitrogen/hydrogen ratio: 1/3 The balance is Argon: specified in Table 3. Pressure: specified in Table  3.	Temperature is 250oC. Contain only N2,H2  and Ar
Mix-100 and 101	Mixers	No pressure drop
Tee-100	Ratio between S-4 and S-2, specified in Table 3.	Fraction of S-2 (?1)
Heater-(or Cooler) 100	Heat up, or cool down, S-3 to 275oC	delP is zero, heating duty is NOT specified
Reactors R-1 and R-2	PFRs with fixed tube dimensions.	Other parameters are at default. The numbers of tubes are n1 and n2, respectively. Start both reactors with 1 tube.
Cooler-1	Drop temperature to -20oC.	Condenses ammonia. Pressure drop is zero.
Separator	50% liquid volume
Tee-101	Purge percentage, specified in Table 3.	Purge from 2% to 8%  vapour
Heater-101	Heat recycle stream to  285oC	delP is zero, heating duty is NOT specified

Table 2. Technical constraints.

Item	Value	Comment
NH3  purity in product	> 98% (mass fraction)	Product quality
Argon entering reactors	< 2% (mole fraction)	Constraint for catalysts

Question 2a. Develop a HYSYS simulation of the process with the details in Table 1. Please use the same unit and stream names as given in Figure 2. For your report, provide the following:

(a) HYSYS PFD printout: aim for a neat arrangement of the flow-sheet.

(b) Input Summary.

(c) Stream tables: Showing material stream, energy stream and composition information; must be easy to read.

Question 2b. What is the maximal production of the process with n1 and n2 =1? What is the overall conversion at this condition?

Questions 3. Optimization with HYSYS

Question 3a is dependent on your group number. For odd group numbers:

Question 3a. What is the minimal n1 to obtain a production of 20,000 ton of ammonia/day?

For even group numbers:

Question 3a. What is the minimal n2 to obtain a production of 20,000 ton of ammonia/day?

Question 3b is the same for all groups.

Question 3b. What is the minimal sum of n1 and n2 to obtain a production of 20,000 ton of ammonia/day?

Question 4. Discussion on the results

- Any technical problems encountered and how you solved them
- Any checks you performed to give you confidence that the simulations are right, with evidence
- Compare Excel and simulations results on a single reactor
- Any observations you would like to make on the simulation results
- A discussion of how your simulation might differ from reality and the top three things you would do to improve the fidelity of the work.

Presentation of the report/HYSYS/Excel/VBA

For the report:
(a) State what you are going to study and why.
(b) Clearly outline your assumptions and methodology.
(c) Present evidence of your work: modified PFD(s), Input Summary file(s) and stream table(s); manual calculations; and similar as needed.
(d) Present and discuss the results, including comments on their implications for the process. Please draw on your knowledge gained in other units to help answer this question.

Report and simulation file
Please use a standard report format, with an Executive Summary and a Conclusions and Recommendations section. All files generated, including HYSYS simulations, spreadsheets and the final report document itself, have to submit to BB. In the report, please very briefly describe the contents of each simulation and spreadsheet file.

First advice: for the sensitivity study, you can convert a number of small tubes into 1 tube with a larger diameter (e.g. a system of 4 tubes of 0.2 m diameter is equivalent to 1 tube of 0.4 m diameter).

Last advice: be aware of the possibility of multiple steady state solutions.

Table 3. Group-specific data.

Group #	?1	Purge, ?2	Ar (%)	Pressure (atm)
1,10,19,28,37,46	0.6	0.03	0.7	150
2,11,20,29,38,47	0.4	0.04	0.8	160
3,12,21,30,39,48	0.5	0.03	0.6	150
4,13,22,31,40,49	0.6	0.05	0.4	140
5,14,23,32,41,50	0.7	0.04	0.7	135
6,15,24,33,42	0.6	0.03	0.5	155
7,16,25,34,43	0.5	0.03	0.6	145
8,17,26,35,44	0.4	0.03	0.8	150
9,18,27,36,45	0.7	0.06	0.7	150