A leak of 5 mm has been detected in the compressed air distribution lines. Determine the payback period for repairing the leak. Assume an isothermal compression. Use the following information: • The total cost of the leak repair is $150.

Question

A leak of 5 mm has been detected in the compressed air distribution lines. Determine the payback period for repairing the leak. Assume an isothermal compression. Use the following information:
• The total cost of the leak repair is $150.
• The annual average compressed air temperature and absolute pressure are 20°C and 900 kPa, respectively.
• The compressor is operating 3,000 hours per year with an average load factor of 70 percent.
• The annual average ambient air temperature and pressure are 15°C and 100 kPa, respectively.
• The electrical motor efficiency is 90 percent.
• The cost of electricity is $0.05/kWh.

Accepted Answer

Using Eq. (11.7), the waste in the compressed mass flow rate through the leak can be estimated:

[latex]Δ \dot{m}_{a}=\sqrt {\frac {2}{R_{a}}}.C_{L}.A_{L}.P_{o}.T^{\frac {1}{2}}_{o}[/latex] (11.7)

[latex]Δ\dot{m}_{a}=\sqrt {\frac {2}{287}}*0.65*00000196*800000.(273+20)^{\frac {1}{2}}=0.050kg/s[/latex]

For an isothermal compression, the annual electrical energy waste by the leak is calculated using Eq. (11.10):

[latex]ΔkWh_{comp}=\frac {Δ\dot{m}_{a}.N_{h,comp}.LF_{comp}.R_{a}.T_{i}.Ln(\frac {P_{o}}{P_{i}})}{η_{M}}[/latex] (11.10)

[latex]ΔkWh_{comp}=\frac {(0.050kg/s)*3000hrs/yr*0.70*287J/kg.K.(273+15)*Ln(\frac {800}{100})}{0.90}=20050k Wh/yr[/latex]

Therefore, the simple payback period for the piping system that connects the intake of the compressor to the outside air is:

[latex]SPB=\frac {\$150}{20050k Wh/yr*\$0.05/kWh}=0.15 years=2 months[/latex]

Question 11.5: A leak of 5 mm has been detected in the compressed air distr...

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