Question

Air stored underground at 500 psia and 200 deg.F is first heated by natural gas combustion to 2,340 deg.F at constant pressure, then expanded in an 89% efficient turbine to atmospheric (14.7 psia) pressure. Part of the work of the turbine is used to compress ambient air at 70 deg.F and 14.7 psia to store it underground with an 85% efficient compressor. The air that is stored underground loses heat to the surroundings. The turbine powers an electric generator that is 93% efficient converting mechanical power to electrical power. Mass flow of air is 100 lb/s.
a. How much heat is added by the combustion of natural gas to the air stored underground that enters the turbine? [Answer: 513.6 Btu/lb]
b. What is the work produced by the turbine? [Answer: 379.7 Btu/lb]
c. What is the work of compression? [Answer: 260.2 Btu/lb]
d. At what temperature does the air exit the compressor? [Answer: 1154 deg.F]
d. Natural gas costs $3 per million Btu (MMBtu) and the electricity that is generated by this storage system is sold at $50/MWh. The system produces electricity from the stored compressed air for 5 hours per day. Calculate the net income from the system from electricity sales. [Answer: $2931 electricity sold, $2773 cost of natural gas, $158 net income from producing electricity 5 h/day.]

These compressed air storage systems are not practical if the stored compressed air loses too much heat underground. In this example compressed air lost 230 Btu/lb underground, which is far too much loss to make the system practical.

Answer 1

- Also, P. = 14.7 Psia Given: het Tie Temperature of air at Entry of compressor 70°F = 529.67°R ta - Temperature at exit of compressor T3: Temperature of air at entry of gas combustion 200° F = 659.67°R P₂ = P4 = 500psia Chamber 1 chamber Tu- Temperature at exit combustion of = 2340F = 2799.67°R lisen, of = 89 %. = 0.89 (p = 0.24 Btu lbo R 0.85 lisen, I 8501: chamber the combustion Sol" Heat added in - Tz) Cp (Tu 0-24 ( 2799.67-659.67) =513.6 Btuleb Answer 5 the Ts Para Temperature at of exit turbine 10.2857 500 14.7 Tu 2799.67 کوتم ܟܐ Ts T5 = 1022.15 °R lisen, t= Actual work I sentropic work Ty Ts' » 0.89 2799:67 – Ts! 2799.67 - 1022.15 = 0.89 тч - Ts UP SUW MY INSTAD

Ts' =1217.68 OR work produced by the turbine =Cpl Tu - Ts') = 0.24(2799.67-1217.68) 379.7 Btuleb Answer 0.2857 Y-7 500 Tg Та د) ( 14.7 Pi 529.67 Tg = 1450.770R lisen, c = I sentropic work Actual work Ty-TI 1450.77 - 529.67 0.85 = ► 0.85 = Tol-Ti T,- 529.61 TA'=1613-32 compression = G (Ta -Ti)=0-2461613-32 - 529.6 = 260.1 Btullld Answer erature air exit of compressor = 11 16 13.32R work q Ô Temp q = 1153.68 F Answer