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EER= Qc = cooling capacity (Btu/hr) Q cooling capacity (Btu/hr) T COP = sink EER= wc = e electrical input wattage electricalinputwattage (Tsink −Tsource) Q cooling capacity (Btu/hr) we COP = Carnot 48,000Btu / hr HPonly 48,000Btu / hr = 3.35 COPHPonly = ⎡4200⎤ watt × 3.413 Btu / hr ⎡⎣4200⎤⎦ watt × 3.413 watt c EER= w = electrical input wattage = 3.35 In this example, th⎣e net⎦COP is aboButu1/3h%r lower than the Wheree: COP of the heat pump as a standalonweatdt evice. Assume that an air-to-water heat pump has an output of Es = energy savings (MMBtu/yr) ER = seasonal space heating energy required by building 48,000 Btu/hr, with a corresponding electrical input of 5.5 = 3.35 COP = seasonal averageBctuo/ehffircient of performance of COP = 48,000Btu / hr = 2.92 net 48,000Btu / hr L ⎡4200⎤ watt × 3.413 ⎣⎦ KW. The load side circulator requires 180 watts. Calculate lower-performing heat pumpwatt COP = seasonal average coefficient of performance of COPnet =⎡(2×220)+4200+180⎤watt×3.413Btu/hr =2.92 Btu / hr the COP of this⎣ heat pump alone a⎦nd the net COP of the ⎡⎣(2×220)+4200+180⎤⎦watt×3.413 watt H higher-performing heat pump heat pump and its load side circulator. The COP of the air-to-water heat pump alone is: watt 48,000Btu / hr (Tsink −Tsource) COPnet = 2 Btu / hr = 2.92 heating load of 15 Btu/hr/ft . The design heating load The net COP of the heat pump and its load side circulator is: cold 6000oF•day climate. It’s estimated annual space w electrical input wattage In this example, the net COP is only about 3% lower than e 48,000Btu / hr COP of 3.4. Another simulation for a low ambient air- the COP of th⎡e air-to-wate⎤r heat pump as a standalone E=E1−1 device. Es venR t⎢⎡hou1gh the1air-⎥⎤to-water heat pump draws an COP = =2.48 Es =ER⎣⎢COPL −COPH ⎦⎥ additional 1.3 CkiOloPwattCsOoPf electrical power compared to net to-water heat pump systemBtup/rhorjects a seasonal COP ⎣LH⎦ the geothermal heat pump, its ne4t 8C,O00P,0iBntuth/isherxample, ⎡⎣5500+180⎤⎦watt×3.413 watt of 2.5. Estimate the annual energy saved by using the COP = is only about 12% lHoPwonelyr than that of the geothermal heat geothermal heat pump rather than the air-to-water heat ⎡4200⎤watt×3.413Btu/hr pump. It’s also important to remember that the COP of any = 3.35 pump. Also estimate the cost savings assuming that the ⎡11⎤⎡11⎤ E =E ⎡ 1 − 1 ⎤ local c⎢ost of electri⎥city is $0.11 per kilowatt-hour. ⎣ =39.⎦9 − =4.22MMBtu/seasons R s R⎢⎡1 1⎥⎤ ⎢⎡1 1⎥⎤ watt E =E − ⎣COPL COPH⎦ The energy saved is easily calculated using Formula 3-1: COP COP 2.5 3.4 heat pumEp=isEhighly de−penden=t o3n9.9it⎣s op−eratin⎦g=c4o.2n2dMitMioBntsu,/ season sR⎣⎢L H⎦⎥⎢⎥ ⎣COPL COPH ⎦ ⎣2.5 3.4⎦ and thus, there are scenarios where the net COP of an air-to-water heat pump could exceed the net COP of a geothermal water- to-water heat pump. 6. Savings decCreOaPse as=loads decrease: 48, 000 Btu / hr = 2.92 If the air-to-water heat pump was used, the additional 4.22 MwMaBttu/season required would have to be supplied by electricity. At a flat rate of $0.11 per KWHR the additional energy would cost: net Btu / hr As the design heat loss of buildings decreases, so do the ⎡⎣(2×220)+4200+180⎤⎦watt×3.413 energy cost savings associated with a heat pump system having a “high” seasonal COP relative to those of a heat pump system with a “lower” COP. The seasonal COP of a heat pump is a weighted average COP = 48,000Btu / hr = 2.56 value that accounts for the wide range of operating conditions HPonly ⎡5500⎤ watt × 3.413 Btu / hr that a specific heat pump undergoes during an entire heating ⎣⎦ watt season, in a specific system at a specific location. Seasonal COP is typically estimated using computer simulation and is discussed in more detail in section 5. This is certainly a non-trivial savings, especially considering that it is a recurring annual cost that could escalate if the Formula 3-1 can be used to calculate the annual heating several thousands of dollars more to install the geothermal heat pump earth loop, especially after installation subsidies COP = 48,000Btu / hr energy reduction realized when a heat pump with a higher = 2.48 Btu / hr seasonal coefficient of performance is used instead of a net are no long⎛er availa⎞ble. Based on a previously mentioned sd in ⎡⎣5500+180⎤⎦watt×3.413 watt heat pump with a lower seasonal coefficient of performance. T=T−T (T−T)+T cost estsima⎜te, a ve⎟rticinal eoautrth lionop for a 2.5-ton rated Formula 3-1 26 ⎝Tin −Tod ⎠ geothermal heat pump would cost between $5,000 and (MMBtu/hr) 48,000Btu / hr COP = HPonly 48,000Btu / hr Consider a 2,000 square foot house with a design ⎡⎣(2×220)+4200+180⎤⎦watt×3.413 watt is 30,000 Btu/hr. Assume that this load corresponds to an interior temperature of 70oF and an outdoor design temperature of 5oF. The house is located in a relatively COP = 48,000Btu / hr = 2.56 heating energy requirement is 39.9 MMBtu/yr (1 MMBtu temperature hydronic heating distribution system. A computer simulation of a geothermal water-to-water heat pump systems indicates an average seasonal ⎡⎣5500⎤⎦ watt × 3.413 Btu / hr = 1,000,000 Btu). The house is equipped with a low- HPonly watt L =Qd(T−T)−Q price ofbledglectricity iincroeutases.i However, this energy cost ∆Td should also be considered in the context of spending $8,750. At an average estimated cost of $6,875, an annual savings of $136 would yield a simple 2 payback of 50.6 Q=⎡k+k(T)⎤+k(T )+k(T ) years. That is about twice the life expectancy of current h⎣12s⎦3out 4out generation geothermal heat pumps. E = E ⎡ 1 − 1 ⎤=39.9⎡ 1 − 1 ⎤=4.22MMBtu/season s R ⎢⎣COPL COPH ⎥⎦ ⎢⎣2.5 3.4⎥⎦ 95% of load by heat pump C O P = ⎡⎣ c 1 + c 2 ( T s ) ⎤⎦ + c 3 ( T a m b ) + c 4 ( T a m b ) 2 COPHPonly = 48,000Btu / hr = 2.56 COPHPonly =⎡5500⎤watt×3.413Btu/hr =2.56 ⎣ ⎦ Btu / hr ⎡5500⎤ watt × 3.413 ⎣ ⎦ T watt COPCarnot = sink watt COP = 48,000Btu / hr = 2.48 net 48,000Btu / hr Btu / hr COPnet =⎡⎣5500+180⎤⎦watt×3.413Btu/hr =2.48 Q cooling capwacaitty (Btu/hr) ⎡⎣5500+180⎤⎦watt×3.413 EER= c = watt E = E ⎡ 1 − 1 ⎤=39.9⎡ 1 − 1 ⎤=4.22MMBtu/season s R⎢⎣COPL COPH⎥⎦ ⎢⎣2.5 3.4⎥⎦ 4.22 MMBtu ⎛ 293KWHR ⎞ ⎛ $0.11 ⎞ = $136 / season ⎜⎝ M M B t u ⎟⎠ ⎜⎝ K W H R ⎟⎠ E=E⎡1−1⎤ s R ⎢⎣COPL COPH ⎥⎦PDF Image | Heat Pump Systems 2020
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