UMASS AMHERST Continuing & Professional Education GeoScience Series Geothermal Heat Pumps: Concept...
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GeoScience Series Geothermal Heat Pumps: Concept to Completion
Basic Review Energy Budget Physics Behind Heat Pumps Definitions
and Terminology 1
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GeoScience Series Geothermal Heat Pumps: Concept to Completion 2
The Energy Budget All bodies emit characteristic energy spectrum
Energy Emitted Proportional to Temperature 4 Energy emitted drops
as the square of the distance Emission governed by the
Stefan-Boltzman Law I = T 4
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Suns Emission Rate 6000K I = (5.67 x 10 -8 ). (6000 4 ) = 73.5 x 10
6 W/m 2 W = (energy per square meter) x (area of photosphere) =
(73.5 x 10 6 ) x (4r 2 ); where r = 647 x 10 6 m = 3.865 x 10 26 W
Energy Flux: Total Energy:
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Energy Received by Earth W 1/r 2 r = 150 x 10 9 m A sphere = 4r 2 =
2.83 x 10 23 m 2 Energy Flux to Earth: W/m 2 = 3.865 x 10 26 Watts
/ 2.83 x 10 23 m 2 = 1367 W/m 2 Solar Constant (S o )
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Energy Received by Earth
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GeoScience Series Geothermal Heat Pumps: Concept to Completion 6
Earths Disk Energy Received By Earth W = (S o ) ( r 2 ),
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Albedo 30% of incoming radiation is reflected
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Energy Emitted by Earth Short Wave Radiation in Peak = 0.47 m
Visible Light Heat Earth Long Wave Radiation out Peak = 10 m
Infrared = heat 239 in = 239 out
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Equilibrium Temperature of Earth
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GeoScience Series Geothermal Heat Pumps: Concept to Completion 10
Effects of an Atmosphere
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Effects of an Atmosphere
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Effects of an Atmosphere Equivalent to Equilibrium T of 58C or 136F
Too Hot!
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Transfer Mechanisms Conduction - transfer of energy by neighboring
molecules across a temperature gradient Convection - transfer of
energy through larger scale motion of currents warm air rises, cool
air sink convection Thermals and create weather Latent Heat
transfer of energy through a change in state evapotranspiration
(feeds our weather) Advection Same as convection but
horizontal
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14
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Energy In = Energy Out The Energy Balance Top of Atmosphere W/m 2
Sunlight Absorbed + IR Back = IR emitted + Thermals + ET (163)
(340) (398) (18) (86) Sunlight In = Sunlight reflected (atmos &
land) + IR emission (340) (99.5) (239.7) At Earths Surface In
Atmosphere Sunlight Absorbed + IR Absorb + Thermals + ET = IR space
+ IR ground (77) (358) (18) (86) (200) (340)
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NASA
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Earths Other Energy Source Radioactive decay of three elements 238
U, 232 Th and 40 K produce most of Earths internal heat Equivalent
to 38 trillion Watts (U.S uses 0.3 trillion Watts) Spread over
earths surface average heat flow to surface from radioactive decay
produces 0.075 W/m 2 Enough to light a single 75 Watt bulb on 1000
m 2 lot (approximately an area = 100 x 100 ft) Energy absorbed from
sun about 2200 times larger than heat flow Davies and Davies,
2010
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The Real World - Insolation NASA
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Long-Wave Radiation Out NASA
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Absorbed Energy NASA
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Average Surface Temperatures NASA
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Temperature Variation with Depth TTeTemperature Variation in F VT
Dept Mines, Mineral & Energy
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Boutt et al., 2010
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Mean Earth Temperatures in U.S. VT Dept Mines, Mineral &
Energy
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Energy absorbed by the earth is renewable It is stored by the soil,
rock and water GSHP systems borrow this heat temporarily
Summary
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Physics of Heat Pumps 1060 Btu to evaporate 1 lb of water (at 60F)
1060 Btu is released when that 1 lb of water condenses
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Closed system Heat Source (Ground) Heat Distribution (Structure)
Expansion Valve Compressor Evaporator Hot Gas, High PressureCool
Gas, Low Pressure Hot Liquid, High Pressure Condenser Cooler
Liquid/Vapor Mix Low Pressure Heating
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GeoScience Series Geothermal Heat Pumps: Concept to Completion
Ground Exchanger(GHEX) Interior Air Distribution 28 Coupling the
Heat Pump Three main components to the System Heat Pump
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GSHP Vocabulary BTU British Thermal Unit: energy required to raise
1 lb water 1 F Therm 1 Therm = 100,000 BTU Ton 12,000 BTU/h: the
amount of heat required to melt 1 ton of ice in 24 hours So,
288,000 BTU to melt 1 ton of ice
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Thermal Conductivity Thermal Conductivity equivalent to Hydraulic
Conductivity D constant head reservoir L Sand Darcys Experiment
(1857) Q h Q L Q A h Q Q ( h/L) A
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Q/A gradient slope = K = Hydraulic Conductivity Rewrite, Q = Darcys
Law K h/L) A For heat flow: Q = heat flow in Btu/hr h/L =
temperature gradient = T/L (F/ft) A = cross sectional area of flow
= L 2 (ft 2 ) K = thermal conductivity = (Btu/hr/F/ft)
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Pulling terms together, Q = (T/L) A = QL/TA Units are: Btu/hr/F/ft
1 Unit Volume 1 1 Conceptually, Temperature Gradient = 1 1 1 = Heat
Flow in Btu/hr through a unit length of material per unit area
under a unit temperature gradient
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Specific Heat Capacity c p - Specific heat capacity is the amount
heat energy a unit mass of material takes into storage or releases
from storage per unit change in T 1Btu/lb/F This is equivalent to
specific storage in hydrogeology
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Conceptual Meaning of Specific Heat Capacity 1 unit Mass Earth Heat
Out or In 1 unit in T
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Volumetric Heat Capacity is also equivalent to specific storage s
is the amount of heat energy a unit volume of material takes into
storage or releases from storage per unit change in T. s has units
of Btu/ft 3 /F s = c p Volumetric Heat Capacity Specific and
Volumetric Heat Capacity are related by
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Conceptual Meaning of Volumetric Heat Capacity Heat Capacity 1 unit
Volume earth Heat Out or In 1 unit in T
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Heat Capacity Heat Capacity is equivalent to Storage used in
hydrogeology C = Q/ T C = Heat Capacity in Btu/F Q = heat energy in
Btu T = temperature in F
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Heat Capacity and Specific Heat Capacity Two important
relationships: C = c p x total mass of material being heated C = s
x total volume of material being heated
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Thermal Diffusivity Thermal Diffusivity equivalent to
Transmissivity D = / c p D is a measure of the rate at which a
temperature disturbance at one point in a body travels to another
point in the body similar to transmissivity English Units are: ft 2
/hr Thermal conductivity / volumetric heat capacity
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GSHP Efficiency Terminology Coefficient of Performance COP energy
in or energy output (Btu/h) electrical energy needed (Btu/h) at a
specific T Energy Efficiency Ratio EER (steady state cooling eff.)
cooling capacity (BTU/h) electrical energy input (Btu/h) at a
specific T Seasonal Energy Efficiency Ratio (SEER) total cooling
over entire cooling season (BTU/h) electrical energy used over
cooling season (Btu/h) EER = 0.875 x SEER
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GSHP Acronyms EAT Entering Air Temperature EWTEntering Water
Temperature LWTLeaving Water Temperature HCTotal Heating Capacity
TCTotal Cooling Capacity CFMCubic Feet per Minute GPMGallons per
Minute GSHPGround Source Heat Pump
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Important Conversions & Calculations 1 Watt = 1 Joule/sec 1
Watt = 3.412 BTU/hr 1 Btu = heat to raise 1 lb of water 1 degree
Farenheit 12,000 Btus per hour = 1 ton
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GeoScience Series Geothermal Heat Pumps: Concept to Completion 43 A
Useful Calculation Flow (gpm) x T difference (F) x 500 = Q (Btu/hr)
Eg., ((1 gpm x 60 min/hr)/7.481 gal/ft 3 ) x 62.4 lbs/ft 3 = 498
lbs water/hr (~500 lbs/hr) In a closed loop system: for a 10 degree
temperature difference 1 gpm x 500 lbs/hr x 10 F temp diff. = 5000
Btu/hr Therefore, 1 gpm adds 5000 Btus of heat per hour 5000 Btu/hr
/ 12,000 Btu/hr/ton = 0.42 tons or 1 gpm flow needed per 0.42 tons
or 2.4 gpm required per ton of heating or cooling when you have a
10 temp. diff.
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GeoScience Series Geothermal Heat Pumps: Concept to Completion The
Thermodynamics of it All: Do GSHPs Work in Cold Climates?
Coefficient of Performance (COP) = Heat Energy Output Electric
Energy Input Industry claims COP ranging from 3 to 6 From the
Second Law of Thermodynamics and the Carnot cycle: COP theoretical
limit = Indoor Temperature (Indoor Temperature - Temperature of
Heat Source/Sink) 44
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GeoScience Series Geothermal Heat Pumps: Concept to Completion
Thermodynamics (continued) Degrees Farenheit to degrees Kelvin
conversion: K = 5/9 (F - 32) + 273 Example: Heat a dwelling to 70 F
~ 294 K Ambient groundwater temperature in Massachusetts is
typically about 54 F ~ 285 K From the Carnot cycle: COP theoretical
limit = 294 K = 33 294 K 285 K 45
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GeoScience Series Geothermal Heat Pumps: Concept to Completion
Thermodynamics (continued) What happens to the theoretical
efficiency toward the end of the heating season if the entering
water temperature has dropped to 35 F? 35 F ~ 275 K COP theoretical
limit = 294 K = 15 294 K 275 K 46
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Thermodynamics (continued) Why is the theoretical heat pump
efficiency many times greater than the actual COP? No heat pump is
100% efficient - Not all of the energy put into the heat pump is
converted into the work of pumping heat some energy lost as waste
heat It takes energy to pump the heat transfer fluid through the
ground coupled part of the system and the air or water through the
buildings heating ducts 47
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Ground Exchange vs. Air Exchange Heating season Cooling season
FF
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Entering Heat Pump Temperature vs. Theoretical Maximum COP Entering
Temperature F Theoretical Coefficient of Performance