# SAP 19CGA007 process balances assignment

PROCESS BALANCES SAP 19CGA007 SAP 2020 Loughborough University

## SECTION A

Q1. Gas containing 20% methane, 60% propane and 20%carbon dioxide is fed to a boiler where it is burnt with 100% excess air. Gas is supplied to the boiler at 25ÂºC and the combustion air enters at a temperature of 225ÂºC. The boiler stack temperature is 425ÂºC. The state of all reactants and products is gaseous.

Relevant data are provided overleaf.

- Draw a schematic diagram of the process and calculate the standard combustion enthalpies for methaneand propane.[6marks]
- Calculate mole balance of the inlet and outlet of the boilerand use tables to show the results.[6marks]
- Calculate the energy balance of the combustion reactions taking place inside the boiler and use tables toshow the results.[6marks]
- The boiler is used to evaporate water at 100ºC to steam at the same temperature. Assuming that there are no other heat losses, determine the mass of steam produced for each mole of gas fed to the boiler.Write down clearly all the assumptions used to solve the problem.[7marks]

**Relevant Data:**

Air consists of 21% O_{2} and 79% N_{2 }on a volume basis

*C _{p}*(O

_{2}) = 30 J mol

^{-1}K

^{-1 }

*C*(N

_{p}_{2}) = 30 J mol

^{-1}K

^{-1}

*C _{p}*(H

_{2}O) = 35 J mol

^{-1}K

^{-1 }

*C*(CO

_{p}_{2}) = 39 J mol

^{-1}K

^{-1 }

*C _{p}*(CH

_{4}) = 35.7 J mol

^{-1}K

^{-1 }

*C*(C

_{p}_{3}H

_{8}) = 73.6 J mol

^{-1}K

^{-1}

Latent heat of vaporisation of water at 100ºC = 2257 kJ kg^{-1 }

Energies of formations refer to each mole formed at a datum temperature of 25ºC.

▵*H ^{o}_{f}*(CH

_{4}) = -74.5 kJ mol

^{-1 }▵

*H*(C

^{o}_{f}_{3}H

_{8}) = -103.8 kJ mol

^{-1}

▵*H ^{o}_{f}*(CO

_{2}) = -393.5 kJ mol

^{-1 }▵

*H*(H

^{o}_{f}_{2}O) = -241.8 kJ mol

^{-1}

**Q2** A chemical laboratory with a volume of 500 m^{3} is equipped with a ventilation system. The volumetric flow rate of the ventilation air is 0.6 m^{3} s^{-1}. A polymerisation reactor is housed within the laboratory. In the event of a reactor seal failure, the reactor would release a maximum of 1 mol of vinyl chloride monomer (C_{2}H_{3}Cl), which is a gas at ambient conditions, occupying a volume of 22.4 L at 1 atm and 0^{o}C. The molecular weight of vinyl chloride is 62.498 g mol^{-1}. The ideal gas constant is 0.082 L atm K^{-1} mol^{-1}. A mole fraction of C_{2}H_{3}Cl (1 mol) in the room air greater than 10^{-6} constitutes a health hazard.

Suppose that the reactor seal ruptures at a time t = 0 and the maximum amount of C_{2}H_{3}Cl is emitted and spreads uniformly throughout the room almost instantaneously.

- Write a differential balance for C
_{2}H_{3}Cl, using*N*to denote the total number of moles of gas in the room (assume constant) and*x*to denote the mole fraction of C_{2}H_{3}Cl in the laboratory air. Convert the balance into an equation in terms of d*x*/d*t*and provide an initial condition. [8 marks] - Integrate the balance to obtain an expression for
*x*(*t*) and verify your solution.[8 marks] - Convert the expression for
*x*(*t*) into an expression for the concentration of C_{2}H_{3}Cl in the room,*C*(mol C_{C2H3Cl }_{2}H_{3}Cl L^{-1}). Calculate the following:- the concentration of C
_{2}H_{3}Cl in the room 5 minutes after the rupture occurs; 4 marks] - the time required for the C
_{2}H_{3}Cl concentration to reach the safe level. 5 marks]

- the concentration of C

## SECTION B

**Q3**

A number of stages are involved in the manufacture of bars of white chocolate.

The production of 1 kg of chocolate requires 0.3 kWh of electricity (at 9 p kWh

^{-1}), 0.5 kWh of gas (at 5 p kWh^{-1}) and 0.2 m^{3}of water (at 25 p m^{-3}). White chocolate contains: 50% cocoa butter, 15% milk solids, 5% milk fat and the remainder is sugar.Calculate the variable cost per 100 g bar of chocolate based on the following costs:

sugar £0.30 per kg, milk solids £1.50 per kg, milk fats £0.50 per kg, wrapper £0.02 per chocolate bar, cocoa beans £2200 per tonne and 2.25 kg of beans are converted to 1 kg of cocoa butter. [5 marks]

- Without calculating the ‘fixed capital cost’, give five examples of costs that are included in it. marks]
- The current facility, built in 2005 at a battery limit cost of £2,500,000, can produce up to 2 million of 100 g chocolate bars per year. There are plans to open a new facility set to double production capacity. The cost index in 2005 was 450 and is now 550. Estimate the fixed capital cost of the new plant, assuming a scale up index of 0.7 and allowing an extra 20% for offsite costs. marks]
- The new plant will be run on a three-shift rota. Each shift will require four operators, each paid £24,500 per year, five packers, each paid £26,000 per year and one supervisor, paid £37,000 per year. Maintenance and overheads are estimated at 5% and 3% of the fixed capital, respectively. Work out the annual fixed operating costs of the new plant. marks]
- Based on the variable cost per bar of chocolate calculated in part (a) and assuming depreciation of £400,000 per annum, work out the break-even production rate for the new plant if each chocolate bar is sold to stores for £0.65. Discuss your result. marks]

**Q4** Methanol is produced by the reaction of carbon dioxide and hydrogen as follows:

CO_{2} + 3 H_{2} → CH_{3}OH + H_{2}O

The fresh feed to the process contains hydrogen, carbon dioxide and 0.5 mol% of inerts (I). The reactor effluent passes to a condenser that removes essentially all of the methanol and water formed. The unconsumed reactants and the inerts (I) are recycled and mixed with the fresh feed before entering the reactor. To avoid buildup of the inerts in the system, a purge stream is withdrawn from the recycle. The feed to the reactor (not the fresh feed to the process) contains 28 mol% CO_{2}, 70 mol% H_{2}, and 2 mol% inerts. The single-pass conversion of hydrogen is 66%. Use a basis of 100 kmolh^{-1} for the feed to the reactor.

- Draw and label a flowchart of the process. marks]
- Using a stream table determine the molar composition of the recycle stream. [10 marks]
- Calculate the flow rate of the fresh feed. marks]
- Find the flow rate of the purge stream and complete the stream table. marks]

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