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
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
This gives rise to a total utility cost over 5 years of £410,000.
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