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SOLUTION 1

Total savings over 5 years

Total cost over 5 years

Required equipment

Click on a heat exchanger to get more info on the calculations around it

Configuration B Plant Diagram (2).png

6     3

3'     4

1

5

3''

2

Preexisting 

heat exchanger

Heat exchanger (1-2)

Heat capacity

10.1

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

Stream 2

Heat capacity*Mass flowrate

10.1 kW/°C

Heat gained by system

-545.4 kJ/s

Temperature in

94°C

Temperature out

40°C

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

​

We then calculate the temperature difference to plug into the equation

​

 

We find that 

​

​

​

render.png
Stream 2.png
render.png

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

Heat exchanger

Remaining heat 

28.8 kJ/s

Temperature Hot out

42.85°C

Log mean Temperature 

17.44°C

We now seek to find the maximum amount of heat that can be exchanged between stream 1 and stream 2. This maximal amount corresponds to the lowest value of the absolute value of heat gained by the system between stream 1 and 2. Namely the lowest value between 516.6 kJ/s and 545.4 kJ/s which is 516.6 kJ/s.

​

​

From that we calculate the remaining heat that needs to be removed

​

​

 

And the effective temperature out of Stream 1 

​

​

 

Finally, we calculate the log mean temperature using the formula 

render.png
1,2.png
28.8.png
2,1.png

Cost

Cross sectional area 

34.45m²

Costs

16 700£

Variance on cost

±2 510£

We first calculate the area required for the heat exchanger based on this equation:

​

​

where U represents the overall heat transfer coefficient

and Q represents the actual amount of heat tranferred between the two streams above.

 

We then calculate the cost using the following formula:

render.png

%

Overall formula for areea.png
Formula for cost .png
1,2.png
2,1.png
Heat exchanger (1-2)

Stream 1

Heat gained by system

516.6 kJ/s

Temperature in

30°C

Temperature out

71°C

render.png
render.png

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

Stream 1.png

Heat capacity*Mass flowrate

12.6 kW/°C

Heat exchanger (3-6)

Stream 6

Latent heat of vaporisation

2000 kJ/kg

In stream 6, the substance goes through a phase change whilst remaining at 94°C. We thus use the formula: 

​

​

 

We know that the massflowrate is 12kg/s. Additionally, we know that the specific latent heat of vaporisation is 2000kJ/kg. 

​

We thus plug in the numbers and find that

​

​

 

​

​

Heat gained by system

240 kJ/s

Mass flowrate

0.12 kg/s

render.png
render.png

 

Phase Change

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

Stream 3

Heat capacity*Mass flowrate

40.3 kW/°C

Heat gained by system

-2700.1 kJ/s

Temperature in

107°C

Temperature out

40°C

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

​

We then calculate the temperature difference to plug into the equation

​

 

We find that 

​

​

​

render.png
Stream 3.png
Streaam 3.png

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

Heat exchanger

Remaining heat 

2460.1 kJ/s

Temperature Hot out

101.04°C

Log mean Temperature 

9.72°C

We now seek to find the maximum amount of heat that can be exchanged between stream 3 and stream 6. This maximal amount corresponds to the lowest value of the absolute value of heat gained by the system between stream 3 and 6. 

​

​

From that we calculate the remaining heat that needs to be removed

​

​

 

And the effective temperature out of Stream 3 

​

​

 

Finally, we calculate the log mean temperature using the formula on the page for counter current flows and find

3,6.png
3,6.png
2460.1.png
16.69.png

Cost

Cross sectional area 

28.7m²

Costs

14 992£

Variance on cost

±2 249£

We first calculate the area required for the heat exchanger based on this equation:

​

​

where U represents the overall heat transfer coefficient with

and Q represents the actual amount of heat tranferred between the two streams above.

 

We then calculate the cost using the following formula:

render.png
Overall formula for areea.png
Formula for cost .png

%

3,6.png
3,6.png
Heat exchanger 3-6

Heat exchanger (3'-4)

Stream 3'

Heat capacity*Mass flowrate

40.3 kW/°C

Heat gained by system

-2474.1 kJ/s

Temperature in

101.04°C

Temperature out

40°C

render.png

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

delta T 3'.png
Q dot 3'.png

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

Stream 4

Heat capacity*Mass flowrate

2.2 kW/°C

Heat gained by system

129.8 kJ/s

Temperature in

40°C

Temperature out

99°C

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

​

We then calculate the temperature difference to plug into the equation

​

 

We find that 

​

​

​

render.png
Stream 4.png
Stream 4.png

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

Heat exchanger

Remaining heat 

2330.3 kJ/s

Temperature Hot out

97.82°C

Log mean Temperature 

16.69°C

We now seek to find the maximum amount of heat that can be exchanged between stream 3' and stream 4. This maximal amount corresponds to the lowest value of the absolute value of heat gained by the system between stream 3' and 4. 

​

​

From that we calculate the remaining heat that needs to be removed

​

​

 

And the effective temperature out of Stream 3' 

​

​

 

Finally, we calculate the log mean temperature for a counter current flow and find:

3'4.png
Q3'4.png
2330.3.png
9.72.png

Heat exchanger (3''-5)

Stream 3'' 

Heat capacity*Mass flowrate

40.3 kW/°C

Heat gained by system

-2330 kJ/s

Temperature in

97.82°C

Temperature out

40°C

render.png

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

delta T 3''.png
Q dot 3''.png

Heat capacity

10.1

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

Stream 5

Heat capacity*Mass flowrate

38.1 kW/°C

Heat gained by system

1181 kJ/s

Temperature in

40°C

Temperature out

71°C

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

​

We then calculate the temperature difference to plug into the equation

​

 

We find that 

​

​

​

render.png
Streqm 5.png
Stream 5.png

We first calculate the heat gained by the system with the heaters in the plant using the formula:

​

 

We then calculate the temperature difference to plug into the equation 

​

 

We find that 

 

​

​

Heat exchanger

Remaining heat 

1 149 kJ/s

Temperature Hot out

68.5°C

Log mean Temperature 

27.7°C

We now seek to find the maximum amount of heat that can be exchanged between stream 3'' and stream 5. This maximal amount corresponds to the lowest value of the absolute value of heat gained by the system between stream 3'' and  5. 

​

​

From that we calculate the remaining heat that needs to be removed

​

​

 

And the effective temperature out of Stream 3'' 

​

​

 

Finally, we calculate the log mean temperature using the formula 

Q3''5.png
3'',5.png
27.66.png
1149.2.png

Cost

Cross sectional area 

49.6m²

Costs

20 825£

Variance on cost

±3 124£

We first calculate the area required for the heat exchanger based on this equation:

​

​

where U represents the overall heat transfer coefficient

and Q represents the actual amount of heat tranferred between the two streams above.

 

We then calculate the cost using the following formula:

render.png

%

Formula for cost .png
Overall formula for areea.png
3'',5.png
3'',5.png

Overall cost

Money saved

960 000 ±9 000£

New total cost

291 000 ±9 000£

Utility cost (per year)

46 200£

Installation cost

60 000 ±9 000£

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Avenir Light is a clean and stylish font favored by designers. It's easy on the eyes and a great go to font for titles, paragraphs & more.

​

The total cost for this solution is the sum of the costs for utility over 5 years and the installation of the 4 heat exchangers.

Utility costs arise from the requirement for further heating or cooling once a stream has passed through a heat exchanger. If no exchanger is installed on a stream, utility costs for that flow will remain unchanged.

​

Cooling in this case (requires 2 coolers):

  • The temperature of Stream 2 needs to be reduced by 2.85°C

  • The temperature of Stream 3 needs to be reduced by 28.52°C

​

There are no heating requirements in this case.

​

This gives rise to a total utility cost over 5 years of £231,000.

​

%

Year 1 Costs Solution 1 (B).png
5 Year Costs Solution 1 (B).png
Heat exchanger 3'-4
Heat exchanger 3''-5
Overall cost

Cost

Cross sectional area 

9.04m²

Costs

7 496£

Variance on cost

±1 124£

We first calculate the area required for the heat exchanger based on this equation:

​

​

where U represents the overall heat transfer coefficient with

and Q represents the actual amount of heat tranferred between the two streams above.

 

We then calculate the cost using the following formula:

We first calculate the area required for the heat exchanger based on this equation:

​

​

where U represents the overall heat transfer coefficient

and Q represents the actual amount of heat tranferred between the two streams above.

 

We then calculate the cost using the following formula:

3',4.png
3'4.png
Formula for cost .png
Overall formula for areea.png

%

render.png
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