Chen C.J. Physics of Solar Energy

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6.6 Ground Source Heat Pump and Air Conditioning  133

6.6 Ground Source Heat Pump and Air Conditioning

In Section 5.3, we discussed solar energy stored in the ground: At a depth of about

10 meters, the temperature of Earth is cooler than the average in the summer and

warmer than the average in the winter. Tapping into that stored solar energy could

greatly reduce the use of energy for space heating and cooling as well as water heating.

Although direct use of the stored energy for space cooling in the summer has been

practiced for centuries in some places on the world, it allows very little control. The

modern method of tapping into that stored solar energy is to use vapor compression

heat pump and refrigeration systems [5, 53, 75]. This enables full control to the desired

temperature. The energy saving can be as great as 50%.

Table 6.1 shows the accumulated wattage and number of ground source heat-pump

installations in several countries up to 2004. Although the United States has the largest

installation wattage and number of systems, Sweden has the largest percentage of heat

pump installations. This is simply due to economics. In Sweden, the weather is cold,

and there are no fossil fuel resources. Nevertheless, most of the electricity in Sweden is

from hydropower, which is relatively inexpensive. The combination of cheap electricity

and the high eﬃciency of geothermal systems makes perfect economic sense.

6.6.1 Theory

A schematic of a ground source heat pump is shown in Fig. 6.5. Several meters un-

derground, the temperature is basically constant over the entire year, for example, at

=15

◦

C. In winter, the ambient temperature can be as cold as 0

◦

C. To maintain a

comfortable temperature, heat should be supplied into the house. In summer, the am-

bient temperature can be as hot as 30

◦

C. Heat should be extracted from the house. In

Section 6.3.1, we showed that, by supplying mechanical work, heat can be transferred

from a cold reservoir to a hot reservoir. Therefore, using a type of machine called heat

Table 6.1: Ground Source Heat Pumps in Selected Countries.

Country Capacity Energy Use Number of

(MWt) (GWh/year) Units Installed

Austria 275 370 23,000

Canada 435 600 36,000

Germany 640 930 46,400

Sweden 2,300 9,200 230,000

Switzerland 525 780 30,000

Uunited States 6,300 6,300 600,000

Source: Geothermal (Ground-Source) Heat Pumps:

A World Overview, GHC Bulletin, September 2004 [53].

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134  Thermodynamics of Solar Energy

Figure 6.5 Ground source heat pump. The temperature in the ground about 10-m deep, T

,is

basically constant over the year. (a) In the winter, by applying a mechanical work W , a heat pump

P transfers heat Q

from the ground heat reservoir at temperature T

to a radiator in the house at

temperature T

. The total heat discharged into the radiator is the sum of the heat extracted from the

ground and the work, Q

= Q

+ W . (b) In the summer, the heat pump P reverses its function: it

transfers heat from the rooms at temperature T

into the ground heat reservoir at temperature T

pump, it is possible to extract heat from within the ground at 15

◦

C to a ﬂoor heat-

ing system in the house at T

=50

◦

C. In the ideal case, if the machine is reversible,

according to Eq. 6.19, the eﬃciency is

=1−

273 + 15

273 + 50

≈ 0.108. (6.61)

According to the deﬁnition of eﬃciency (Eq. 6.15), the mechanical work required to

transfer heat from the ground at T

to the radiator at T

to become Q

W = ηQ

=0.108 × Q

. (6.62)

In other words, mechanical energy equal to a fraction of the heat is needed to transfer

heat from the ground to the radiator.

In the summer, assuming that heat Q is extracted from an air-conditioning system

at T

= −10

◦

C into the ground at T

=15

◦

C using a reversible Carnot engine. The

machine is in fact a refrigerator. The Carnot eﬃciency is

=1−

273 − 10

273 + 15

≈ 0.087. (6.63)

Because the heat extracted from the air conditioning system is Q

in Eq. 6.15, the

mechanical work required is

W =

1 − η

=0.095 × Q

. (6.64)

Theoretically, if the refrigerator as a Carnot engine is reversable, the work needed to

cool the space is less than one tenth of the amount of heat taken. Practically, no

machine is perfect. The actual work needed is more than that from the theoretical

limit.

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6.6 Ground Source Heat Pump and Air Conditioning  135

6.6.2 Coeﬃcient of Performance

In the industry, a dimensionless number called the coeﬃcient of performance (COP) is

used to characterize the performance of the heat pump and refrigerator. For the heat

pump, it is deﬁned as

COP =

, (6.65)

and for the refrigerator, it is

COP =

. (6.66)

The theoretical limit looks extremely attractive: The conversion ratio from mechanical

work to heat can be as high as 10. Practically, a conventional vapor-compression

heat pump or refrigerator can achieve a COP of 3–4. Nevertheless, this is still highly

desirable. Replacing an electrical heating system with a ground-source heat pump can

achieve an energy saving up to 70%.

6.6.3 Vapor-Compression Heat Pump and Refrigerator

The commercial geothermal systems use the vapor compression cycle for both heat

pumping and refrigeration. Most are reversible, which can be used for room heating

and cooling by using a reversing valve. Figure 6.6 shows the cooling cycle. It is

very similar to an ordinary central air-conditioning system based on the principle of

the vapor compression cycle. A liquid with a low boiling point serves as the working

medium, called the refrigerant. Since the early twentieth century, ammonia (NH

also called R12, was the favorite refrigerant. Because of its toxicity, in air-conditioning

systems, it was replaced by chlorodiﬂuoromethane (CHClF

), or R22. In spite of its

ﬂammability, propane (C

), or R290, is recently used in place of R22 because of its

zero ozone depletion potential .

The central piece of a vapor compression refrigeration system is the compressor,(1

in Fig. 6.6). This is the point at which mechanical power is input. The compression

process is approximately adiabatic. If the initial pressure is P

and the ﬁnal pressure

is P

, according to Eq. 6.54,

= P

, (6.67)

where γ is the ratio of speciﬁc heats (see Eq. 6.50), and the γ value of a typical

refrigerant, R-22, is 1.26,

γ ≡

=1+

. (6.68)

Combining with the equation of state of an ideal gas, we ﬁnd that the temperature is

changed according to





γ−1





0.2857

. (6.69)

If the gas is initially at room temperature (273 K), compressing it by a factor of 3, the

temperature is raised to 3

0.2857

× 273 = 1.3687 × 273 = 373 K, which is about 100

◦

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136  Thermodynamics of Solar Energy

Figure 6.6 Ground-source heat pump: cooling mode. The refrigerant is compressed by a

compressor (1) to become superheated. Through the heat exchanger (2), it ﬁrst heats the domestic

water. Then the still-hot refrigerant goes to the heat exchanger (4) to be cooled to underground

temperature and condenses into liquid. Through an expansion valve (5) it becomes vapor. The

evaporation process absorbs large quantity of heat from the space through the heat exchanger (6).

The space is thus cooled. After Ref. [53].

Therefore, the refrigerant is a superheated gas. The heat thus generated is ﬁrst utilized

to heat the domestic water through the heat exchanger (2). Then, through reversing

valve (3), the still hot refrigerant comes through the heat exchanger to contact with

the water from the ground and is cooled to the underground temperature, for example,

=15

◦

C, or 288 K. Because of the high pressure, the refrigerant condenses into liquid.

Therefore, such a heat exchanger is called a condenser. The liquid refrigerant at T

and still under high pressure is letting through an expansion valve (5) to become vapor.

The evaporation process absorbs large quantities of heat and the vapor temperature

becomes very low, typically many degrees below 0

◦

C. The cold vapor goes int the heat

exchanger (6), a cold radiator. A fan blows warm air from the room onto the zigzag

tubes and ﬁns of the cold radiator (6). The cooled air then ﬂows into the space to be

conditioned. The warmed-up vapor of refrigerant is again sucked into the compressor

(1) through the reversing valve (3). And the process goes on.

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6.6 Ground Source Heat Pump and Air Conditioning  137

Figure 6.7 Ground source heat pump: heating mode. The refrigerant is compressed by a

compressor (1) to become superheated. Through the heat exchanger (2), it ﬁrst heats the domestic

water. Then the still-hot pressurized gas-phase refrigerant goes to the radiator (4) to warm the space

and become liquid. The liquid refrigerant goes through an expansion valve (5) to become supercooled

vapor. The evaporation process absorbs large quantities of heat from the groundwater through the

heat exchanger (6). After Ref. [53].

If domestic water heating is not required, the heat exchanger (2) can be eliminated.

However, the fringe beneﬁt of having this unit is obvious.

By turning the reversing valve (3) to another position, the system becomes a heat

pump to be used in the winter; see Fig 6.7. Again, the compressor (1) squeezes the

refrigerant into a superheated gas and transfers part of the heat to domestic water via

the heat exchanger (2). Then, through the reversing valve (3), it goes into the heat

exchanger (4), which is a heat radiator and refrigerant condenser. A fan (4) forces

warm air into the space to be conditioned. At that time, the refrigerant is liqueﬁed by

the cool air. The liquid refrigerant goes through the expansion valve (6) and becomes

supercooled vapor, often below the freezing point of water. By going through the heat

exchanger (7) to contact the water at ground temperature, the refrigerant vapor picks

up heat from the ground and the temperature recovers to T

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138  Thermodynamics of Solar Energy

6.6.4 Ground Heat Exchanger

A ground heat exchanger can have many diﬀerent conﬁgurations. Fig. 6.8 shows several

of them. The requirement for a good ground heat exchanger is to access a large volume

of soil, groundwater, or bedrock. Figs. 6.8(a), (b) show closed-loop heat exchangers.

The vertical well does not require a large area, and so can be used in highly populated

area. It is no surprise that most of the geothermal systems in New York City are

vertical-well systems. However, drilling even a 100-m well is costly. For suburban or

rural buildings, it is suﬃcient to bury a few hundred meters of copper coil in the ground

a few meters deep. In places where groundwater is easily accessible, an open-loop

system is even less expensive. By drilling two wells into the groundwater (Fig. 6.8(c))

or to access a pond (Fig. 6.8(d)), eﬀective heat exchange could be established. In the

United States, 46% are vertical closed-loop systems, 38% are horizontal closed-loop

systems and 15% are open-loop systems.

Figure 6.9 shows the details of a vertical well at the Headquarters of the American

Institute of Architects (AIA), Greenwich Village, New york City. It is a 1250-ft deep,

Figure 6.8 Heat-exchange conﬁgurations for ground-source heat pumps. The ground heat

exchanger can have many diﬀerent conﬁgurations. (a) and (b) are closed-loop heat exchangers. The

vertical well in (a) does not require a large area, which means it can be used in a highly populated

area. For suburban or rural buildings, the horizontal heat exchanger in (b) is much less expensive that

the deep well. In places where groundwater is easily accessible, the open-loop system in (c) and (d)

are even less expensive.

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6.6 Ground Source Heat Pump and Air Conditioning  139

6-in-diameter well drilled into the sidewalk in front of the building. The underground

water level is 40–50 ft down from the ground. A metal casing is placed to protect

the well from collapsing due to the pressure of the soil. The lower part of the well is

in the bedrock, which is strong enough to maintain the shape for probably hundreds

of years. A 6-in-diameter polyvinyl chloride (PVC) tube, the so-called shroud straw,

extends almost to the bottom of the well. Near the bottom, the shroud straw has 120

1-in-diameter holes. The water from the deep well is extracted by a submersible pump

to the heat exchange unit; see Fig. 6.7. The water from the heat exchanger returns

to the well through a return pipe and runs outside the shroud straw. Therefore, the

water runs all the way through the full depth of the vertical well and thus reaches

thermal equilibrium with the ground bedrock, where the temperature is always 12

◦

Figure 6.10 is a photo of the ground connection to the geothermal well in the basement

of the AIA.

Figure 6.9 Vertical well in a heat pump system. Detail of the vertical well of a heat pump

system at AIA. The depth is 1250 ft. About 20 ft below the underground water level, a submersible

pump extracts water to the heat exchange unit. A 6-in-diameter PVC tube, the so-called shroud

straw, extends almost to the bottom of the well. The water from the heat exchanger returns to the

well through a return pipe and runs outside the shroud straw. Courtesy of American Institute of

Architects.

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140  Thermodynamics of Solar Energy

Figure 6.10 Ground connection of geothermal well. Both incoming and outgoing pipes are

shown. Photo taken by the author. Courtesy of American Institute of Architects.

The AIA ground source geothermal system was the ﬁrst in New York City, but now

there are many other systems in the City. One of the largest is the Knox Hall system

at Columbia University; see Fig. 6.11. A 50,000-ft

oﬃce space, seminar rooms, and

Figure 6.11 Knox Hall of Columbia University. Knox Hall of Columbia University, a century-

old historical building, is located at 606 West 122nd Street, Manhattan. During a 16-month-long

renovation, ended on Februay 2010, one of the largest shallow geothermal energy facilities in New

York City was installed. It has four 1800-ft (547 m) geothermal wells and heat pumps for both heating

and cooling. The only visible marks of the project on the exterior of this historical building are four

covered manholes on the sidewalk. Courtesy of Columbia University.

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6.6 Ground Source Heat Pump and Air Conditioning  141

Figure 6.12 Heat pumps in the basement of Knox Hall. A photo taken by the author in

the basement of Knox Hall, Columbia University. An array of heat pumps are shown on the left-hand

side. The right-hand side is ground-well connections. Deep in the ground, the temperature is always at

◦

F(14

◦

C). In the winter, the heat pumps extract heat from the ground to warm the rooms. In the

summer, the heat pumps extract heat from the rooms and dump it into the ground. The investment

can be recovered in about 7 years from saving electricity. Courtesy of Columbia University.

classrooms for several departments of Columbia University, it has four 1800-ft (547-

m) deep wells for both heating and cooling of the building for a 95-ton heating and

cooling load. Their use contributes to a 23% reduction in energy consumption (over

a conventional system). The four wells were drilled on the sidewalk, which has no

interference with the entire building. After installation, the only visible marks are the

four manhole covers on the sidewalk. Figure 6.12 shows the heat pumps inside the

basement of Knox Hall.

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142  Thermodynamics of Solar Energy

Problems

6.1. The COP for heat pumps and refrigerators achieved in the industry is about 50%

of the Carnot limit. Make estimates for the following cases:

1. For refrigerator to achieve −10

◦

C in the freezer area with an external temperature

of 25

◦

2. For the same refrigerator to achieve -10

◦

C in the freezer area but using the

geothermal heat reservoir as the external source, at 10

◦

6.2. A solar heat collector of 2 m

using the running water through underground pipes

at 15

◦

C to generate hot water at 55

◦

C. If the eﬃciency of the solar collector is 80%,

on average, how much hot water can this system generate per day?

1. In a region of 5 h of daily insolation

2. In a region of 3 h of daily insolation

Hint: The standard insolation is 1 kW/m