SOLUTION 7
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1
2
5
3
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
​
​
​
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
17.43°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
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:
%
Stream 1
Heat gained by system
516.6 kJ/s
Temperature in
30°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
​
​
Heat capacity*Mass flowrate
12.6 kW/°C
Heat exchanger (3-5)
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
​
​
​
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
1519 kJ/s
Temperature Hot out
77.69°C
Log mean Temperature
36.84°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
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
1181.1 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
​
​
​
Cost
Cross sectional area
37.3 m²
Costs
17 535£
Variance on cost
±2 630£
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:
%
Overall cost
Money saved
806 000 ±5 100£
New total cost
444 000 ±5 100£
Utility cost (per year)
82 000£
Installation cost
34 300 ±5 100£
%
The total cost for this solution is the sum of the costs for utility over 5 years and the installation of the 2 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 37.69 °C
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Heating in this case (requires 2 heaters):
-
A phase change needs to occur in Stream 6 at 94.00 °C (requires 240 kJ/s)
-
The temperature of Stream 4 needs to be raised by 59.00 °C
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This gives rise to a total utility cost over 5 years of £410,000.
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