Download Chapter 11 Absorption Air Conditioners

Chapter SM 8 Absorption Air-conditioning Systems
SM 8.1 Introduction
Although most of the air conditioning systems in buildings are conventional in that an
electrically driven compressor is used to circulate the refrigerant, there are other approaches to
air conditioning. One option is absorption air conditioning. These machines were developed
over a century ago and are in use today. The central difference between the absorption and
conventional machine is that the compressor is replaced by a set of components in which the
refrigerant vapor is absorbed into solution with another fluid, a pump is used to increase the
solution pressure, and then heat is used to boil the refrigerant and separate it from the other fluid.
The electrical work requirement for the pump is small compared to that for a compressor, but the
heat required to produce the refrigerant vapor is large. As a consequence, absorption machines
are often termed heat driven air conditioning systems.
Early absorption machines were made in relatively small sizes and used for household
refrigeration. The heat source was typically a natural gas burner. Pumping was accomplished by
thermal means (like the percolator in a coffee maker) and electricity was not required. Large
machines using steam as the heat source, with cooling capacities in the range of hundreds of tons,
were eventually developed for commercial applications. These machines had a limited market in
office buildings because a steam supply was required and electricity was readily available. In
those commercial applications where a boiler was used to supply heat to the building in winter, it
could be used to provide steam for the absorption machine in summer. Industrial applications
were more feasible. High temperature steam could be produced for high temperature heating and
then the low temperature “waste steam” at a lower temperature could be used to drive the
absorption machine. These units were physically large with a relatively low energy performance.
There has been renewed interest in absorption air conditioners. One contributing factor is
that gas utilities have become more active in marketing gas for use in cooling. Gas sales are
naturally low in summer, and gas cooling provides an opportunity for year-round sales. Active
oil and gas field exploration has also increased natural gas supplies. As electrical use has grown,
utilities have increased the price of the peak electricity demand, which has driven a need to seek
alternative methods of cooling during peak periods. Commercial establishments need to provide
an economic and reliable means of maintaining building comfort and the absorption chiller
industry has responded to this opportunity with technical developments that significantly
increase the performance of the units. Because absorption systems use refrigerants that are
environmentally benign, they provide an acceptable alternative to the potentially detrimental
halocarbons used in conventional refrigeration systems.
Absorption air conditioners use a pair of fluids that circulate, compared to the single fluid
used in a conventional refrigeration system. One of the fluids is the refrigerant and the other is
the carrier, or absorbent. Lithium bromide and water comprise a commonly used pair of
substances, with water as the refrigerant and the lithium bromide salt as the absorbent. The two
compounds form a liquid solution for salt concentrations of less than about 70 % and can
8.1
therefore be pumped around a system. Lithium bromide has an extremely low vapor pressure
and does not exist as a vapor at the typical operating conditions for absorption, which makes it
suitable as a carrier.
Chillers based on lithium bromide and water are generally quite large (100 to 3000 tons) and
are mainly used in commercial applications. The use of water as the refrigerant limits the lowest
cooling temperature to above freezing and thus these machines are only suitable for air
conditioning. The pressure of the water vapor in the evaporator is low, and the construction of
the equipment requires care to eliminate air leakage into the system. A cooling tower is also
required to maintain the solution within a temperature range that does not allow the lithium
bromide to crystallize at low temperatures.
The other common pair of fluids used in absorption machines is ammonia and water.
Ammonia is flammable and toxic and so safety requirements limit the amount of ammonia that
can be contained in a building. As a result these machines are limited to a relatively small
maximum capacity of about five tons of cooling. With ammonia as the refrigerant, temperatures
below freezing can be obtained and these units are suitable as residential refrigerators. They are
often air-cooled which makes them suitable for domestic applications.
An absorption refrigeration machine is shown schematically in Figure 8.1. The refrigeration
components on the left side of the dotted line are those of a conventional mechanical
refrigeration machine and the components on the right hand side are specific to an absorption
machine.
Water, which is the refrigerant leaves the condenser at state 2, passes through the expansion
valve, and enters the evaporator as a mixed phase (state 3). The water evaporates in the
evaporator and the vapor enters the absorber at state 4. The cooling effect of the cycle is the heat
transfer to the evaporator.

Q
gen

Q
c
2
1
Condenser
Generator
8
7
HX
Expansion
valve
6
9
Throttling
valve 10
3
Evaporator
Pump
5
W
Absorber
4

Q
e

Q
abs
Figure 8.1 Schematic diagram of an absorption machine
The compressor of the conventional refrigeration system, which would compress the vapor
from the pressure at state 4 to that at state 1, is replaced by the components on the right side of
8.2
the figure. Water vapor coming from the evaporator (state 4) is absorbed in the absorber, which
is cooled to remove the heat of sorption. The cool dilute liquid solution (state 5) is then pumped
to a higher pressure and sent to the generator (state 6). A heat recovery heat exchanger is usually
installed to increase the temperature of the flow to the generator and reduce the temperature of
the solution entering the absorber. Heat is added in the generator to desorb the entering solution
to state 7. The temperature of the solution in the generator is high enough so that the vapor
pressure of the solution is higher than the saturation pressure of water at the condenser
temperature, allowing water vapor to transfer out of the solution. The concentrated lithium
bromide solution from the generator (state 8), sometimes termed the strong solution, is cooled in
the heat recovery heat exchanger (state 9) and enters the absorber at state 10.
The main advantage of the absorption cycle over a vapor compression system is that the
liquid solution, rather than a refrigerant vapor, is pumped from the evaporator pressure to the
condenser pressure. The work required to pump the liquid is much less than that to compress the
refrigerant vapor as in a conventional refrigeration system. The work input of the conventional
system is then replaced by the significant heat requirement for the generator. The absorption
system is a heat operated refrigeration system, and the limit on performance can be determined
from thermodynamic considerations.
An ideal absorption system is thermodynamically equivalent to Carnot heat engine with a
power output that is the input to a Carnot refrigeration machine. The heat engine, which is on
the right hand side of Figure 8.1, operates between the temperatures of the generator and the
absorber. The Carnot thermal efficiency of this heat engine can be expressed in terms of the
temperatures as:
Weng
Qgen  Qabs
Tgen  Tabs
eng 


(8.1)
Tgen
Qgen
Qgen
The refrigeration system operates between the temperatures of the evaporator and the
condenser. The refrigeration coefficient of performance is the evaporator heat transfer divided
by the power input. For an ideal refrigeration system, the coefficient of performance can be
expressed in terms of the temperatures as.
Qe
Te
COPr 

(8.2)
Qc  Qe Tc  Te
The coefficient of performance of an absorption system is the refrigeration effect divided by
the heat input. The ratio of the evaporator and generator heat flows can be put in terms of the
ratios of the power inputs, which are related to the thermal efficiency and COP.
Qe
Q Weng
1
COPabs 
 e

(8.3)

W
Qgen
eng COPr
eng Qgen
The maximum COP for the absorption system can then be put in terms of the temperatures of the
absorption system using equations 8.1 and 8.2 as:
T  Tgen  Tabs 
COPideal  e 
(8.4)

Tgen  Tc  Te 
8.3
The maximum COP relation is useful to show the importance of the different temperature
levels on performance. As with a vapor compression machine, a small difference in temperature
between the condenser and the evaporator leads to a high COP and the performance is better at
higher evaporator temperatures. The highest COP is obtained with a high generator temperature
and low absorber temperature. The lower limit on the absorber temperature is a practical one due
to the potential of crystallization of the high concentration solution at low temperatures.
Example 8.1 illustrates the evaluation of the maximum COP of an absorption system.
Example 8.1 Determine the maximum COP of an absorption machine. The unit operates with a
source temperatures of 40 F for the evaporator and 180 F for the generator, and sink temperatures
of 90 F for the absorber and 100 F for the condenser.
The maximum, ideal COP is determined using equation 8.4.
 40  460 (R) 180  90 (F)
COPideal 
*
 1.17
180  460 (R) 100  40 (F)
The maximum COP is about double that of an actual machine, in which a number of processes
are not thermodynamically reversible. The sorption process is irreversible. Heat transfer to and
from the solution is over a temperature range in the generator and absorber. The absorption and
desorption processes require a finite vapor pressure difference for the water to enter and leave
the solution. There are temperature differences in each component for the heat transfer into and
out of the system. The pressure drops for the water flow through the expansion valve from the
condenser to the evaporator and for the solution flow from the generator to the absorber are
irreversible.
The inherent irreversibilities prevent the cycle from reaching the
thermodynamically maximum value.
The COP of an absorption machine based on the energy flows is significantly less than that
of a conventional vapor compression machine. This is due to the fact that the heat energy
supplied to the generator is much greater than the electrical energy supplied to the compressor of
a vapor compression machine. However, if the efficiency of the power plant used to generate
electricity for the vapor compression machine is considered then the overall primary energy
usage is similar. On a Second Law basis the absorption machine is as efficient as a vapor
compression machine.
SM 8.2 Fundamentals of Absorption
The basic principle behind the operation of an absorption machine is that refrigerant vapor
can be absorbed into another fluid at a low temperature and pressure and will remain in solution
until the temperature is raised sufficiently. The absorption process is analogous to condensation,
with the absorbed, low temperature refrigerant in a liquid state as opposed to the vapor state in a
conventional system. The low pressure liquid solution can then be pumped to the higher pressure
of the condenser using a pump that requires much less power than a vapor compression system
compressor.
8.4
The principles of the absorption refrigeration cycle will be illustrated using the lithium
bromide and water pair since these are the common compounds for commercial air conditioning
systems. The solution undergoes a series of temperature and pressure changes and the properties
of the solution are needed over the range of operation. The equilibrium saturation condition for a
lithium bromide salt and water solution depends on three variables: temperature, pressure, and
concentration. The concentration is defined on a mass basis, and is the mass of lithium bromide
per unit mass of the mixture:
X
m LiBr
m mix
(8.5)
where X is the mass concentration, mLiBr is the mass of lithium bromide and mmix is the mass of
the mixture.
Figure 8.2 shows the equilibrium vapor pressure for a lithium bromide and water solution as
a function of temperature for different levels of salt concentration. The vapor pressure is shown
on a logarithmic scale. Pure water is a solution with a zero concentration of lithium bromide.
The property relations show that at any concentration level, the vapor pressure increases as the
temperature increases. At a given temperature the equilibrium vapor pressure decreases as the
concentration increases. These property characteristics provide the basis for the operation of an
absorption machine.
D
C
A
B
Figure 8.2a Saturation properties of Lithium bromide and water (English units)
8.5
Figure 8.2b Saturation properties of Lithium bromide and water (SI units)
The mechanisms by which the absorption processes lead to refrigeration can be illustrated
using Figure 8.2a. An absorption refrigeration system could be designed to use water as the
refrigerant and to operate between an evaporator temperature of 40 F and a condensing
temperature of 120 F. As indicated in Figure 8.2a, the vapor pressure of pure water at 40 F is
0.122 psia (State A), and this state is the temperature and pressure at which water vapor is in
equilibrium with liquid water. At 40 F the vapor pressure of water over a solution with a
concentration of 0.50 (50 % lithium bromide) is only 0.031 psia (State B), which is much less
than the vapor pressure of pure water. Thus, if water vapor at 40 F and 0.122 psia (State A) were
to leave an evaporator and be brought into contact with a 0.50 concentration solution of lithium
bromide and water at 40 F (State B), the vapor would be absorbed by the salt and go into
solution. This is analogous to the condensation process in a conventional system.
Also as indicated in Figure 8.2a, if the 0.50 concentration solution were heated to 165 F
(State C) the vapor pressure of the vapor over the solution would increase to 1.8 psia, which is
also the vapor pressure of pure water at 120 F (State D). Increasing the solution temperature
above 165 F causes water to desorb and leave the solution as water vapor. The water vapor
could then be condensed and then sent through the expansion valve to the evaporator. Increasing
the pressure of the solution and then heating it to produce high pressure water vapor is analogous
to the compression process in a vapor compression system.
The high pressure water vapor could then be condensed in a conventional condenser using a
heat rejection source such as water from a cooling tower. The liquid water, which is the
refrigerant, would then flow through the expansion valve and drop to a pressure of 0.122 psia,
8.6
corresponding to a saturation temperature of 40 F. The low pressure water vapor-liquid mixture
could then evaporate in the evaporator and provide cooling. The processes of absorption,
pressure increase, and desorption replace the vapor compression process of a conventional
refrigeration system.
The crystallization limit shown in Figures 8.2a and 8.2b represents the condition for which
the lithium bromide solution is too highly concentrated to remain liquid. For the high
concentrations and low temperatures that are below this limit, crystals of lithium bromide would
form in the liquid solution and grow, making it difficult to pump the solution. The critical
conditions for an absorption refrigeration system are at low temperature. The concentration
needs to be relatively low to prevent crystallization. When solid lithium bromide salts form in a
machine the operation stops. Although the salts can be dissolved with the addition of water, the
machine is inoperative until the condition is remedied. Absorption machines need to be designed
to operate above the limit.
Figure 8.2 presents the equilibrium relationship between saturation temperature, pressure,
and concentration, but does not contain any information about the energy content of the solution.
The relation between these properties and the enthalpy of the mixture are important to the design
of the absorption system. The saturation enthalpy of a lithium bromide and water mixture in
liquid phase as a function of the concentration and temperature is given in Figure 8.3. Although
the graph is for saturation conditions, they are also valid for the subcooled conditions as the
enthalpy of the liquid phase, which is an incompressible liquid, is independent of pressure. At a
given concentration, the enthalpy increases almost directly proportional to temperature, as
expected for liquids. The enthalpy is not a strong function of the concentration at any one
temperature. The crystallization limit is shown at the right side of the figure. It is not necessary
to show saturated vapor lines for the mixture enthalpy because the vapor pressure of lithium
bromide is so low that essentially no lithium bromide vapor exists within the typical range of
operating temperatures for absorption. Thus, all vapor states within an absorption cycle are
assumed to be pure water.
8.7
Figure 8.3a Enthalpy of a lithium bromide solution (English units)
Figure 8.3b Enthalpy of a lithium bromide solution (SI units)
The property relations presented in Figures 8.2 and 8.3 are needed to design the components
of an absorption unit and evaluate its performance. One component is the absorber, in which the
water as a vapor is absorbed by the liquid lithium bromide solution. In an absorber, two streams
8.8
enter and one leaves as depicted in Figure 8.4. The states are numbered according to Figure 8.1.
One of the entering streams is water vapor with zero concentration of lithium-bromide (State 4)
and the other is a concentrated solution of lithium bromide and water (State 10). The stream
leaving is a dilute solution of lithium bromide (State 5). The absorption process is similar to
condensation in that heat is released when the vapor is absorbed. The absorber thus needs to be
cooled and maintained at a low enough temperature so that the water vapor is absorbed.
Concentrated solution
State 10
Water
State 4
Dilute solution
State 5
Absorber
Heat flow
Qabs
Figure 8.4 Mass and energy flows for an absorber
Water and lithium bromide are the two components of the flow, and the mass of each is
conserved as well as the mass of the mixture. Thus there are three conservation of mass
relations, although only two are independent. It is conventional to apply the conservation of
mass relations to the mixture flow and to the lithium bromide flow. For the total mass of the
mixture, the flow of the outlet stream equals the sum of the two entering streams:
m 4  m10  m5
(8.6)
For the conservation of mass relation for the lithium bromide, it is common to express the mass
flow rates of lithium bromide in terms of the concentrations using equation 8.5. The flow rates
of lithium bromide are given as:
X 4 m 4  X10 m10  X5 m5
(8.7)
In a typical situation the inlet states would be known. By using the overall conservation of
mass relation (equation 8.6) to find the total flow rate, the leaving concentration can be found
using equation 8.7. The concentration of lithium bromide in the incoming water flow is zero and
the outlet solution concentration for the absorber is given directly by:
X m
(8.8)
X5  10 10
m5
The energy balance relation, which brings in the enthalpies of the three streams and the heat
transfer from the absorber, is expressed as:
m 4 h 4  m10 h10  m5 h 5  Qabs
(8.9)
The heat that must be removed from the absorber is evaluated by rearranging equation 8.9 as:
(8.10)
Qabs  m4 h 4  m10 h10  m5 h5
where the enthalpies are evaluated at the temperature and concentration of each of the flow
streams.
8.9
In an absorption machine, the lithium bromide-water solution entering the absorber comes
from a generator where it is saturated at the generator temperature and pressure. The generator
pressure is considerably higher than that of the absorber and a throttling valve is used to drop the
pressure. The reduction in solution pressure causes some of the water in the solution to leave the
solution, similar to the throttling process for a refrigerant, and the solution enters the absorber as
a two phase mixture. The properties of lithium bromide are such that lithium bromide vapor is
not produced. The concentration of the solution phase increases due to the reduced water in
solution but the overall concentration remains the same. Example 8.2 illustrates the process of
solving for the states and heat flow in an absorber of an absorption cycle that employs lithium
bromide and water. The property values are those of the absorption refrigeration cycle of
Example 8.4.
"Example 8.2 In an absorber, 1000 lb/hr of water vapor enter an evaporator at 40 F and mix with a 9000
lb/hr flow of lithium bromide solution that enters at a temperature of 116.6 F, a pressure of 0.122 psia, a
concentration of 0.6, and an enthalpy of 85.8 Btu/lbm. Determine the concentration and temperature of the
outlet stream and the heat transfer rate."
"Problem Specifications"
T_4 = 40 "F"
m_dot_4 = 1000 "lbm/hr"
T_10 = 116.4 "F"
m_dot_10 = 9000 "lbm/hr"
X_10 = 0.60
"Water vapor temp"
"Water flow rate"
"Solution inlet temp"
"Solution inlet flow rate"
"Solution concentration"
"The pressure in absorber is the saturation pressure of water at the inlet temperature of 40 F."
p_4 = Pressure(Water,T=T_4,x=1)
"Water vapor pressure"
"Determine the properties of the water vapor entering the absorber. The concentration of the water is zero
and the enthalpy is that of saturated water vapor."
X_4 = 0
h_4 = Enthalpy(Water,T=T_4,x=1) "Btu/lbm"
"Water vapor enthalpy"
"Determine the enthalpy and pressure entering the absorber "
h_10=H_LiBrH2O(T_10,X_10)
"Inlet solution enthalpy"
p_10=P_LiBrH2O( T_10, X_10)
"Solution vapor pressure"
"Determine the total flow rate using equation 8.6 and outlet stream concentration using equation 8.7"
m_dot_4 + m_dot_10 = m_dot_5 "lbm/hr"
"Total mass balance"
m_dot_4*x_4 + m_dot_10*X_10 = m_dot_5*X_5
"LiBr mass balance"
"The heat flow is determined using the energy balance, equation 8.10. The solution leaving the absorber is
saturated at the absorber pressure and outlet concentration."
T_5=T_LiBrH2O(p_4,X_5)
h_5 = H_LiBrH2O(T_5,x_5) "Btu/lbm"
"Outlet enthalpy"
Q_abs = m_dot_4*h_4 + m_dot_10*h_10 - m_dot_5*h_5 "Btu/hr" "Absorber heat flow"
Results and Discussion
In order for water vapor to transfer into the solution, the vapor pressure of the solution must
be lower than the pressure of the incoming water flow. This requirement links the temperature of
the incoming water stream to the temperatures of the incoming and exiting solution streams.
8.10
The properties of the lithium bromide solution are determined using the built-in EES
functions (from a library of external functions). For example, the enthalpy of a solution is
determined from the thermodynamic function H_LiBrH2O(Temperature, Composition)
The property values are given in the table below. Liquid concentration is denoted X and the
quality of the water vapor is denoted x. It is assumed that pressure drops in the absorber are
negligible.
Stream
 (lb/hr)
m
T (F)
X
h (Btu/lb)
p (psia)
4
1,000
40
0.00
1079.0
0.122
10
9,000
116.4
0.6
85.5
0.122
5
10,000
89.5
0.54
32.1
0.122
Using the absorber energy balance equation (8.9) the heat flow required to cool the solution
is 1,530,000 Btu/hr. The amount of heat that must be rejected is a little greater than that to
condense 1000 lb/hr of water vapor in a conventional condenser. This shows that from the point
of view of energy, the absorption process is very similar to that for condensation. A relatively
low solution temperature is required to obtain a vapor pressure low enough to absorb the water
vapor from the evaporator. Without heat removal, the temperature of the exiting solution would
rise and water could not be absorbed. A relatively low temperature sink for the heat rejection
must be utilized.
The generator is the other unique component of an absorption machine and the processes
inside the generator are the reverse of those for the absorber. As indicated in Figure 8.5, a dilute
solution enters and flows of a concentrated solution and water vapor leave.
Heat flow
Water
State 1
Qgen
Generator
Concentrated solution
State 8
Dilute solution
State 7
Figure 8.5 Mass and energy flows for a generator
As with the absorber, the conservation of mass principle applies both to the mixture and to
the lithium bromide flows through the generator. The mass balance for the total flow is:
m7  m1  m8
(8.11)
The conservation of mass for the lithium bromide is written using concentrations as:
X7 m7  X1 m1  X8 m8
(8.12)
where the concentration in the leaving water stream, X 1, is zero. The leaving concentration of
the concentrated lithium bromide stream is determined from equation 8.11 and 8.12 as
8.11
X8 
X 7 m7
m8
(8.13)
The heat that must be added in the generator is determined from an energy balance for the
generator as
Qgen  m7 h7  m1 h1  m8 h8
(8.14)
Example 8.3 illustrates the calculations of the outlet states and the heat transfer for a generator.
"Example 8.3 Determine the heat required and the water flow produced for the generator of a lithium
bromide unit. A solution flow rate of 10,000 lb/hr leaves an absorber at a temperature of 90 F and a
concentration of 0.54. The pump increases the vapor pressure of the entering solution to that of the water
vapor, and the solution leaves the generator at a concentration of 0.60. The saturation temperature for the
water vapor in the condenser is 100 F and the temperature of the vapor leaving the generator is 140 F."
"Problem specifications"
T_1= 140 "F"
T_sat = 100 "F"
T_7 = 90 "F"
m_dot_7 = 10000 "lbm/hr"
X_7 = 54
X_8 = 60
"Water vapor temp"
"Saturation vapor temp"
"Solution inlet temp"
"Solution inlet flow rate"
"Inlet concentration"
"Outlet concentration"
"Determine the water vapor pressure and enthalpy. The concentration of the water vapor stream is zero."
p_1 = Pressure(Water,T=T_sat,x=1) "psia"
"Water vapor pressure"
h_1 = Enthalpy(Water,T=T_1,p=p_1) "Btu/lbm"
"Water vapor enthalpy"
X_1 = 0
"Determine the enthalpy of the lithium bromide mixture and the vapor pressure of the mixture entering the
generator"
p_7 = P_LIBR('ENG',T_7,x_7) "psia"
"Inlet vapor pressure"
h_7 = H_LIBR('ENG',T_7,X_7) "Btu/lbm"
"Inlet solution enthalpy"
"Determine the total flow rate using equation 8.11 and outlet stream concentration using equation 8.12"
m_dot_7 = m_dot_8 + m_dot_1 "lbm/hr"
"Total mass balance"
X_7*m_dot_7 = X_8*m_dot_8+ X_1*m_dot_1
"Solution mass balance"
"The outlet flow of the solution is at saturation conditions. The vapor pressure is the saturation pressure
and equal to the saturation pressure of the water leaving the generator. The temperature is the saturation
temperature of the solution."
p_8 = p_1 "psia"
"Outlet vapor pressure"
T_8 = T_LIBR('ENG',p_8,x_8) "F"
"Outlet temperature"
h_8 = H_LIBR('ENG',T_8,x_8) "Btu/lbm"
"Outlet enthalpy"
"The heat flow is determined using the energy balance, equation 8.14."
Q_gen + m_dot_7*h_7 = m_dot_8*h_8 + m_dot_1*h_1"Btu/hr" "Absorber heat flow"
Results and Discussion
As with the absorption process, the temperature of the solution leaving the generator is
linked to the vapor pressure of the water that leaves as vapor and enters the condenser. The
vapor pressure corresponding to a condensing temperature of 100 F is 0.950 psia. However, the
vapor leaving the solution in the generator is superheated to a higher temperature by contact with
8.12
the high temperature solution and heat exchanger surfaces, but not to the same temperature as
that of the exiting concentrated solution.
At a concentration of 0.60, the saturation temperature for the lithium bromide solution
corresponding to a vapor pressure of 0.950 psia is 180.7 F. This is the minimum temperature for
the lithium bromide solution leaving the generator, and it will be assumed that the solution is at
this temperature. The properties at the different states are given in the table below. It is assumed
that any pressure drops in the absorber are negligible.
 (lb/hr)
m
T (F)
X
h (Btu/lb)
p (psia)
Stream
1
1,000
140
0.0
1123.0
0.950
7
10,000
90
0.54
32.4
0.950
8
9,000
180.7
0.60
85.8
0.950
The generator heat transfer is 1,571,000 Btu/hr. The total heat flow is slightly larger than that
necessary to boil 1,000 lb/hr of water, which shows that in terms of energy, the desorption
process is similar to boiling.
SM 8.3 Performance of a Single Effect Absorption Refrigeration Cycle
In a single effect absorption refrigeration system, the set of conventional processes that the
refrigerant goes through are coupled to the absorption and desorption processes for the solution
described in Section 8.2. The term "single effect" refers to the fact that there is only one
generator as more sophisticated machines have more than one generator. The schematic of an
actual single effect absorption system, which is shown in Figure 8.7 of Section 8.4, shows that
the components are physically close to each other and tightly inter-connected. In analyzing an
absorption machine, it is convenient to think of each component as distinct. The idealization of
an absorption system is shown in Figure 8.1 and the determination of performance will be based
on that model.
It is conventional to show the states of the lithium bromide and water inside an absorption
refrigerator on the pressure-temperature coordinates of Figure 8.2 even though not all of the
states are at saturation conditions. The pressure drops in the absorber, generator, condenser, and
evaporator are assumed to be negligible, with the only pressure changes due to the pump,
throttling valve, and expansion valve. The states and processes for the system of Figure 8.1 are
shown in Figure 8.6. The pure water states in the condenser and evaporator are as shown at the
left along a line for a concentration of zero, which is the saturation line for water. The
condensing process occurs at constant pressure and the condensate leaves as saturated liquid
(state 2). State 1 is superheated vapor and cannot be shown on the saturation plot. The
evaporator process that occurs from state 3 to 4 is a constant pressure and temperature process.
In the absorber, water vapor at state 4 mixes with the concentrated solution at state 8 to
produce an intermediate concentration at state 5. The pressure of the dilute solution is increased
as it is pumped into the generator. Heat is added to the solution in the generator, as represented
8.13
by the process from 5 to 6 to 7. Desorption occurs in the generation and the concentration
increases, as represented by the process from 7 to 8. States 6 is a compressed liquid state and
state 9 is in the two phase region, and because these are not saturation states they cannot be
shown on the pressure-temperature coordinates.
X=0
X = 0.54
Condenser
2
0.60
7
8
Generator
Pressure
Evaporator
3, 4
5
10
Absorber
Temperature
Figure 8.6 Process representation for an absorption system
The heat flows in the evaporator and the condenser are given in terms of the mass flow rates
of the water and the corresponding enthalpy values. Since the concentration is zero, the
enthalpies values are for pure water, either as liquid, vapor, or a mixture, as appropriate. For the
condensing process from 1 to 2, the condenser heat flow is given by
 m
 1 h1  h 2 
(8.15)
Q
c
For the process through the expansion value, there is no heat transfer, and the enthalpy
change is zero. The energy balance reduces to:
(8.16)
h2  h3
The energy balance for the evaporation process from state 3 to 4 is given by
 m
Q
e  3 h 4  h 3 
(8.17)
where the flow rate through the evaporator is the same as that through the condenser.
The heat transfer in the heat exchanger between the absorber and the generator is internal to
the refrigeration system. The energy balance for the heat exchanger relates the temperature rise
of the solution going to the generator to that returning to the absorber. The flow rates on the two
sides of the heat exchanger are not equal due to the differences in water content. The energy
balance for the heat exchanger is given by:
 7 h 7  h 8   m
 5 h 6  h 5 
m
(8.18)
The temperature changes of the solution flowing through the heat exchanger are given in terms of
a heat exchanger effectiveness (Chapter 14). The concentrated solution is the minimum
capacitance rate and the effectiveness of the heat recovery heat exchanger can be expressed in
terms of temperatures as
8.14

T8  T9
T8  T6
(8.19)
A throttling valve is needed to reduce the pressure of the solution leaving the generator before it
enters the absorber. As the pressure is reduced, some of the water in the lithium-bromide
solution flashes into water vapor, and the evaporation of this water vapor lowers the temperature
of the solution. A function in EES is used to determine the equilibrium properties after the
expansion valve.
These relations allow the cooling capacity of the absorption system to be determined. As
with a conventional system, a measure of the performance of an absorption cycle is the
coefficient of performance, or COP. This is the refrigeration effect, which is the heat transferred
in the evaporator, divided by the high temperature energy supplied, which is the heat input to the
generator. The COP is given as
Qe
COP 
(8.20)
Qgen
The set of assumptions conventionally made in determining the performance of an absorption
system are listed below:
There are no temperature differences for heat transfer between the working fluids and the
heat sources and sinks.
The only pressure changes occur as the fluid passes through the throttling valve, expansion
valve, and pump.
The pressures of the solution in the absorber and generator equal the saturation pressures of
the water vapor in the evaporator and condenser, respectively.
The lithium bromide-water solution leaving the absorber and the generator is saturated.
The water vapor enters the condenser as superheated vapor.
The water vapor leaves the condenser as saturated liquid.
The water vapor leaves the evaporator as saturated vapor.
The pump is isentropic and the temperature rise is zero.
Example 8.4 illustrates the use of the thermodynamic relations to evaluate the performance of an
absorption refrigeration system.
" Example 8.4 Determine the heat flows, COP, and pumping power of an absorption system operating with
an evaporator at a temperature of 40 F and a condenser at a temperature of 100 F. The solution entering the
generator has a flow rate of 10,000 lb/hr and a concentration of 0.54, and the solution leaving the generator
has a concentration of 0.60. The saturation temperature for the water vapor in the condenser is 100 F and
the temperature of the vapor leaving the generator is 140 F The heat recovery heat exchanger has an
effectiveness of 0.75."
"Problem specifications"
T[1] = 140 "F"
T_sat = 100 "F"
T[4] = 40 "F"
m_dot[7] = 10000 "lbm/hr"
X[7] = 54
X[8] =60
"Water vapor temp"
"Saturation vapor temp"
"Evaporator temp"
"Gen inlet flow rate"
"Gen inlet conc"
"Gen outlet conc"
8.15
Eff = 0.8
"Heat recovery HX eff"
"GENERATOR"
"The states are indicated in the diagram window. Determine the water and outlet solution flow rates and
concentration from mass balances. The concentration in the water flow is zero "
m_dot[7] = m_dot[1] + m_dot[8] "lbm/hr"
"Total mass balance"
X[7]*m_dot[7] = X[1]*m_dot[1]+ X[8]*m_dot[8]
"Solution mass balance"
X[1] = 0
"Water concentration"
"The pressure in the generator equals the saturation pressure of the water vapor flowing to the condenser.
Determine the properties of the water vapor."
p[1] = Pressure(Water,T=T[1],x=1) "psia"
"Water vapor pressure"
h[1] = Enthalpy(Water,T=T[1],p=p[1]) "Btu/lbm"
"Water vapor enthalpy"
"Determine the properties of the lithium bromide-water solution entering and leaving the generator. The
inlet temperature is not known but is a result of the heat transfer in the heat recovery heat exchanger."
p[7] = p[1] "psia"
"Generator pressure"
h[7] = H_LIBR('ENG',T[7],X[7]) "Btu/lbm"
"Inlet solution enthalpy"
p[8] = p[1]"psia"
"Outlet vapor pressure"
T[8] = T_LIBR('ENG',p[8],x[8]) "F"
"Outlet temperature"
h[8]= H_LIBR('ENG',T[8],x[8]) "Btu/lbm"
"Outlet enthalpy"
"Determine the heat transfer to the generator"
Q_gen + m_dot[7]*h[7] = m_dot[1]*h[1] + m_dot[8]*h[8]"Btu/hr"
"Generator EB"
"HEAT RECOVERY HEAT EXCHANGER
The flow rate of the solution from the generator is less than that to the generator and is the minimum
capacitance fluid. The effectiveness, written in terms of temperatures, yields the temperatures entering the
absorber and generator given the temperatures leaving the two units."
Eff = (T[8] - T[9])/(T[8] - T[6])
"Effectiveness"
"The temperature of the solution entering the generator is determined from an energy balance performed on
the heat exchanger."
m_dot[6]*h[6] + m_dot[8]*h[8] = m_dot[7]*h[7] +m_dot[9]*h[9] "Btu/hr"
"HX Energy balance"
"The mass flow rates, concentrations, and pressures entering and leaving the exchanger are equal"
m_dot[6] = m_dot[7] "lbm/hr"
"Mass flow rate"
X[6] = X[7]
"Concentration"
p[6] = p[7] "psia"
"Pressure"
m_dot[9] = m_dot[8] "lbm/hr"
"Mass flow rate"
X[9] = X[8]
"Concentration"
p[9] = p[8] "psia"
"Pressure"
"The enthalpies of the solution are determined from the temperatures and concentrations"
{h[6] = H_LIBR('ENG',T[6],x[6]) "Btu/lbm"
"Solution enthalpy"}
h[9] = H_LIBR('ENG',T[9],x[9]) "Btu/lbm"
"Outlet enthalpy"
"PUMP
Determine the pump work and the increase in enthalpy across the pump. "
v[5] =V_LIBR('ENG',T[5],X[5]) "ft3/lbm"
X[5] = X[6]
m_dot[5] = m_dot[6]
W_p = v[5]*(p[6]--p[5])*convert(ft3-psia/lbm,Btu/lbm) "Btu/lbm"
W_dot_p=W_p*m_dot[5] "Btu/hr"
h[6] = h[5] +W_p "Btu/lbm"
T[6] = T[5] "F"
"Specific volume"
"Concentration"
"Specific pump work"
"Pump work"
"Pump outlet enthalpy"
"Pump outlet temp"
"THROTTLING VALVE
Determine the state of the lithium bromide after the throttling valve. The pressure of the solution decreases
from p[9] to p[1] and the enthalpy and overall concentration remain the same. The concentration of the
solution increases due to water vapor formation as the pressure is reduced. The procedure Q_LiBr(h, P, z :
Q, T, x) returns the quality (Q), temperature (T) and liquid composition (X) of a 2-phase mixture of liquid
8.16
lithium bromide-water and water vapor at specific enthalpy (h), pressure (P), and overall composition (z).
State 9 is the known inlet condition entering the valve and state 10 is the outlet state.
Call Q_LiBr('Eng', h[9], p[10], X[9]: Q[10], T[10], Z[10])
"Solution quality"
h[10] = h[9] "Btu/lbm"
"Enthalpy"
X[10] = X[9]
"Concentration"
m_dot[10] = m_dot[9] "lbm/hr"
"Mass flow rate"
"ABSORBER
The pressure in absorber is the saturation pressure of water at the inlet temperature of 40 F. The entering
solution is at this pressure"
p[4] = Pressure(Water,T=T[4],x=1) "psia"
"Water vapor pressure"
p[10] = p[4] "psia"
"Pressure"
"Determine the properties of the water vapor entering the absorber. The concentration of the water is zero
and the enthalpy is that of saturated water vapor."
X[4] = 0
"Concentration"
h[4] = Enthalpy(Water,T=T[4],x=1) "Btu/lbm"
"Water vapor enthalpy"
m_dot[4] = m_dot[1] "lbm/hr"
"Mass flow rate"
"Determine the properties of the solution leaving the absorber. The solution is saturated at the absorber
pressure and outlet concentration."
p[5] = p[4] "psia"
"Pressure"
T[5]=T_LIBR('ENG',p[5],X[5]) "F"
"Outlet temperature"
h[5]= H_LIBR('ENG',T[5],x[5]) "Btu/lbm"
"Outlet enthalpy"
"Determine the heat flow is determined using an energy balance on the absorber."
m_dot[4]*h[4]+m_dot[10]*h[10] = m_dot[5]*h[5] + Q_abs "Btu/hr"
"Absorber heat flow"
"CONDENSER
Determine the properties of the water leaving the condenser and the condenser heat transfer"
m_dot[2] = m_dot[1] "lbm/hr"
"Water flow rate"
p[2] = p[1] "psia"
"Water pressure"
x[2] =0
"Water quality"
T[2] = Temperature(Water,p=p[2],x=x[2])
"Water temperature"
h[2] = Enthalpy(Water,P=p[2],x=x[2]) "Btu/lbm"
"Water enthalpy"
m_dot[1]*h[1] = m_dot[2]*h[2] + Q_cond "Btu/hr"
"Condenser EB"
"EVAPORATOR
Determine the properties of the water vapor entering and leaving the evaporator and the heat transfer to the
evaporating fluid. The fluid entering the evaporator after the expansion valve is in the two-phase region
with the same enthalpy as that leaving the condenser and with a pressure equal to the saturation pressure at
the evaporator temperature."
m_dot[3] = m_dot[2] "lbm/hr"
"Mixture in flow rate"
p[3] = p[4] "psia"
"Mixture pressure"
h[3] = h[2] "Btu/lbm"
"Mixture enthalpy"
T[3] = T[4] "F"
"Mixture temperature"
Q_evap + m_dot[3]*h[3] = m_dot[4]*h[4] "Btu/hr"
"Evaporator EB"
"SYSTEM PERFORMANCE"
Q_tons = Q_evap*convert(Btu/hr,tons) "tons"
COP = Q_evap/Q_Gen
"Cooling capacity"
"System COP"
Results and Discussion
The properties of the water in the refrigerant side of the system are determined using the
same relations as for a vapor compression system. The vapor leaves as superheated vapor at a
pressure of 0.950 psia, corresponding to the condenser temperature of 100 F, and a temperature
of 140 F due to heat transfer from the hot solution. Saturated liquid leaves the condenser and
8.17
flows through the expansion valve and enters the evaporator in the mixed phase state at the
evaporator pressure, which is 0.122 psia, corresponding to a saturation temperature of 40 F.
The properties of the lithium bromide-water solution in the generator and absorber are
determined following the procedures illustrated in Examples 8.2 and 8.3. The heat transfer,
solution temperatures, and enthalpy changes for the heat recovery heat exchanger use the
effective relation 8.19. The pump work and the solution enthalpy change follow the relations in
Example 8.3. The properties of the water and solution at the different state points are given in
the table below. States 1 to 4 are for pure water and states 5 to 10 are for the solution
State

m
(lbm/hr)
p
(psia)
T
(F)
x
quality
X
conc.
h
(Btu/lbm)
1
1000
0.950
140.0
1.00
0
1122.8
2
1000
0.950
100.0
0.00
0
68.0
3
1000
0.122
40.0
0.06
0
68.0
4
1000
0.122
40.0
1.00
0
1078.5
5
10000
0.122
88.3
0
54
31.0
6
10000
0.950
88.3
0
54
31.0
7
10000
0.950
144.4
0
54
59.1
8
9000
0.950
178.6
0
60
84.1
9
9000
0.950
110.8
0
60
52.9
10
9000
0.122
109.0
0.07
60.1
52.9
The states are plotted on pressure-temperature coordinates below; these are not saturation states
and so the lines of constant concentration are not process lines. A critical state is the outlet of
the flow through the generator after it passes through the heat recovery heat exchanger and the
then the throttled. The concentration of the fluid at this point is 61.5 and the temperature is
108.7. As shown in Figure 8.2a the state is still above the crystallization limit. The need to
avoid crystallization limits both the concentration and the pressure in the absorber.
8.18
The four heat flows for the cycle are given in the table below. All of the flows are of the
same magnitude since they are related to the evaporation, desorption, condensation, and
absorption of the same amount of water vapor. The generator and absorber heat flows are greater
than the condenser and evaporator heat flows because of the sensible heating and cooling of the
solution.
Component
Heat flow
(Btu/hr)
Generator
1,288,000
Absorber
1,244,000
Condenser
1,055,000
Evaporator
1,010,000
The capacity of the unit corresponds to 84 tons of cooling. This is, then, a relatively large
machine and would be suitable for commercial application. The pump work is 20 Btu/hr, or
about 5 watts. The pump work is so small because the pressure difference across the pump is
only about 0.8 psia. Even accounting for pump and electric motor efficiencies and additional
fluid friction losses the pumping power is small.
Four heat exchangers are needed to operate the absorption system and there is the additional
heat recovery heat exchanger. Only two exchangers are needed in a conventional refrigeration
system, and there is then significantly more heat transfer in an absorption machine than in a
conventional refrigeration machine with the same cooling capacity. Further, since the heat
transfers occur at the very low pressures of the water vapor or lithium bromide solution, the heat
exchangers are quite large compared to those in conventional refrigeration units. The heat
8.19
exchangers dominate the machine, and thus absorption systems tend to be much larger than the
mechanical vapor compression units.
The COP of the system, evaluated as the cooling heat flow into the evaporator divided by the
heat input into the generator 0.784. The COP appears to be low compared to that of a vapor
compression unit, which is typically in the range of three to six. However, an absorption
machine uses heat rather than electricity to drive the system, and heat has a lower
thermodynamic availability than electrical work. On a second law basis, the COP of 0.807 is
comparable to COP of an electrically drive unit of about 2.5.
As shown in the property table, the absolute pressure levels in the system are below
atmospheric. Air leakage into the system would significantly reduce performance and could
cause the system not to operate. Absorption systems need to be hermetically sealed. The low
level of pressure also means that hydrostatic pressure changes are important. The difference
between the pressure in the condenser and the evaporator is about 0.8 psia, which corresponds to
a difference in height of the lithium bromide solution of about two feet. In the designing a unit,
the level of the fluid in the different locations is an important consideration.
The heat recovery heat exchanger is essential to high performance. Without the exchanger
the COP would be 0.651, or 20 % lower. In addition to improving the performance the
exchanger reduces the load on the cooling tower.
A final aspect of the operation of the absorption machine is that to allow the evaporator to
operate at 40 F, the solution in the absorber must be cooled to 88.2 F. In the air conditioning
season, ambient air would not be sufficiently cold to achieve this temperature in most locations.
A cooling tower that produces water with a temperature near that of the ambient wet bulb would
be required. In hot humid conditions it might not even be possible to reach the necessary low
absorber temperature, and the temperature of the evaporator might be higher than desired.
SM 8.4 Absorption Machine Configurations
In actual absorption machines, the components are closely coupled and not as distinctly
identifiable as shown in the schematic of Figure 8. 4. An example of a commercially made
single effect absorption machine using lithium bromide and water is shown in cross-section in
Figure 8.7.
8.20
Figure 8.7 Single effect absorption machine (courtesy of Trane, a business of Ingersoll Rand)
The major components (generator, absorber, condenser, and evaporator) are contained in a
single steel shell that is designed for the sub-atmospheric pressures at which the system operates.
The pumps and the heat recovery heat exchanger are located outside the shell. The generator is
located at the upper left of the container where the heat source, a flow of steam or hot water,
enters. The generator is also termed a concentrator because the solution becomes more
concentrated as the water is boiled off. The water vapor that is desorbed from the solution flows
over the wall to the right and into the condenser where it then becomes liquid.
The liquid water leaving the condenser is throttled to the lower pressure in the evaporator by
the openings in the plate that separate the condenser from the evaporator. The liquid drains onto
the evaporator tubes, through which the chilled water flow from the building circulates. Some of
8.21
the liquid evaporates directly from the chilled water tubes and the remainder is collected in a pan
directly under the tubes. This liquid is recirculated by the middle pump at the bottom left and
sprayed back over the evaporator tubes to further the evaporation of water.
The low-pressure water vapor migrates from the top of the evaporator down into the absorber
where it is absorbed into solution. The diluted solution drains from the absorber at the bottom,
where it is mixed with concentrated solution returning from the generator. This mixture is recirculated by the pump on the right and sprayed over the absorber tubes. The spray both
improves the heat transfer to the cooling water tubes and promotes contact between the liquid
solution and the water vapor, increasing absorption.
The mixture of the dilute and concentrated solutions is pumped back to the generator through
the pump on the left. The dilute and concentrated solutions flow through the counter-flow heat
exchanger, which precools the fluid entering the absorber and heats the fluid entering the
generator. Finally, there is an open tube that connects from the bottom of the absorber to the top
of the concentrator. This is an overflow tube that controls the level of the liquid in the unit.
Although there are three liquid pumps for this machine, the power is less than 1 % of the total
cooling capacity of the unit.
As shown in example 8.4, the absorber temperature needs to be relatively low to allow the
evaporator to produce the chilled water temperatures required for air conditioning. As the
absorber temperature increases, both the COP and capacity decrease significantly. A low
absorber temperature is more critical to the overall performance than a low condenser
temperature. Thus the cooling water returning from the cooling tower flows first through the
absorber and then through the condenser. The COP of the unit illustrated in Figure 8.7 is about
0.63
The performance of a single effect refrigeration system is low, which has led to designs with
improved performance. One such design is the double effect system, which consists of two
absorption systems. One has a generator that operates at a high temperature and in the other the
generator operates at a low temperature. The heat source for the generator of the low
temperature cycle is the heat rejection from the condenser of the high temperature cycle. Using
the condenser heat transfer in this manner reduces the total heat input, although the heat needs to
be supplied at a higher temperature than that for single effect machine. The combination of the
higher generator temperature and second low-temperature generator results in a COP that is
almost twice that of the single effect cycle. A double effect machine is shown schematically in
Figure 8.8. The process representation is shown in Figure 8.9 on pressure-temperature
coordinates.. Only the saturation states are labeled. As shown in Example 8.4, the actual process
diagram becomes quite involved when the effects of the pumps, throttling valves, and heat
recovery heat exchanger are included.
8.22
Qgen,high
Hi T Generator
1
12
2
11
Hi T HX
Hi T Condenser
10
Pump
9
13
Expansion
valve

Q
c , low

Q
c, high
14
Lo T Generator
3
Lo T Condenser
8
Lo T HX
Expansion
valve
7
15
Pump
6
16
Evaporator
4
Absorber
5
Qabs
Qe
Figure 8.8 Schematic of a double effect absorption machine
Lines of constant concentration
1, 2
12
Pressure
9
3
15
4, 5
6
Temperature
Figure 8.9 Process diagram for a double effect absorption machine.
As with the single effect machine, the components of an actual double effect machine are
tightly integrated, with a single evaporator and a single absorber. A schematic of a commercial
double effect absorption chiller is shown in Figure 8.10. The high temperature generator is fired
by natural gas as shown on the right side of the diagram. The water vapor produced in this
8.23
generator (upper right of the diagram) is condensed in the low temperature generator, which is
the right side of the condenser at the upper left of the diagram. The water vapor produced in the
low temperature generator migrates to the left side of the condenser, where it is condensed by the
cooling water flow. The condensate from the high temperature cycle mixes with the condensate
from the low temperature cycle at the bottom of the condenser.
All of the condensate flows through the orifice plate to the single evaporator located at the
middle left of the figure. All of the vapor produced by evaporation is absorbed in the single
absorber to the right of the evaporator. The dilute solution from the absorber is then recirculated back through the low temperature generator. The concentrated solution leaving the
high temperature generator flows through two heat recovery heat exchangers and then to the
absorber. The dilute solution is then pumped to the low temperature concentrator and then back
to the high temperature concentrator.
Figure 8.10 Schematic of a double effect absorption machine
(courtesy of Trane, a business of Ingersoll Rand)
The COP of a double effect machine is about twice that of a single effect machine and about
1.2. As indicated on Figure 8.9, the generator temperature is over 300 F. Double effect
machines require considerably higher temperatures than do single effect machines, and for that
8.24
reason gas-fired units are more common than steam heated units. Although high temperature
steam could be used to run the machine, it would probably be more valuable to use the steam for
a process other than space cooling. Additionally, in most commercial applications boilers used
to supply space heat are not designed to produce steam at high temperature.
The COP and capacity of absorption machines are relatively constant over a wide range of
chilled water temperatures. This is in contrast to the performance of a vapor compression unit
for which the capacity and COP decrease significantly as the chilled water temperature is
lowered. The COP over a wide range of part load operation is essentially the same as at full
load. Thus, an absorption system has desirable characteristics for air conditioning.
A disadvantage of an absorption unit is that the thermal capacity associated with the large
amount of metal is very large. Starting up and shutting down a machine takes considerable time.
Capacity modulation to meet varying cooling demands is obtained by modulating the heat supply
rather than by cycling the unit on and off.
The parasitic power consumption to operate the electric pump motors is relatively small. For
a large absorption machine the electric power required is about 0.02 kW per ton of cooling. This
compares to a value of about 0.6 kW per ton for an electrically driven machine. Thus the electric
consumption is only about 3 % of that for the electrically driven chiller, which enhances its value
in reducing electrical demand. Example 8.5 illustrates the economics of an absorption machine
compared to those of a conventional air conditioner.
Example 8.5 Compare the operating and purchase costs for a double effect absorption machine in
a commercial operation to that for a conventional vapor compression system. The absorption
machine has an initial cost of $ 1500 per ton of cooling capacity, a COP of 1.2 and is fired with
natural gas that costs $ 8/106 Btu. The vapor compression unit has an initial cost of $ 500 per ton
of installed capacity and a COP of 5. The rate schedule for electricity is an energy use charge of
$ 0.10/kWh and a monthly demand charge of $ 9/kW. The building load is uniform at 1000 tons
for 2000 hours per year.
For the vapor compression system, the cost for electricity includes both the demand and
energy charges. The annual electrical energy use is estimated as
Load * Hours 1000 ( tons ) * 2000 (hr ) * 12,000(Btu / ton  hr )
Electricity Use 

COPac
5 * 3413(Btu / kWh )
 1.41x10 6 kWh / yr
The cost of electrical energy is
VC Energy Cost  1.41x106 (kWh / yr) * 0.10($ / kWh)  $ 141,000 / yr
The demand charge is based on the electrical for the peak load, assumed to be 1000 tons. The
peak demand is
PeakLoad 1000 (tons ) *12,000(Btu / ton  hr )
Electrical Demand 

 703 kW
COP
5 * 3413(Btu / kWh )
The annual demand cost is the sum of the monthly demand cost for the 12 months, or
Demand Cost  703 (kW) *9 ($ / kW) *12  months   $76,000 / yr
8.25
The annual electricity cost for the vapor compression machine is the sum of demand and energy
costs, or $ 217,000.
The annual natural gas energy for the absorption machine is estimated from the load, hours
of operation, and COP as
Load * Hours 1000(tons) * 2000(hr) *12,000(Btu / ton  hr)
Absorption Energy 

COPabs
1.2
 20x109 Btu / yr
The annual cost of the natural gas fuel is the use times the fuel price
Abs Energy Cost  Fuel Use * Pr ice  20x109 (Btu / yr) *8x106 ($ / Btu)  $160,000 / yr
There is also a small power consumption for the absorption system pumps of 0.02 kW/ton of
cooling. The total power draw is 20 kW. Following the procedure for the electrical consumption
of the vapor compression machine, the total electrical cost is $ 6,000 per year. The total annual
cost to operate the absorption machine is $ 166,000. The absorption unit costs $ 63,000 less for
fuel than the vapor compression machine.
The initial cost of the vapor compression machine is the unit cost times the installed
capacity, or
Vapor Compression Cost  500($ / ton) *1000(ton)  $ 500,000
and that of the absorption machine is
Absorption Cost  1500($ / ton) *1000(ton)  $ 1,500,000
The absorption machine costs $ 1,000,000 more to purchase and install than the vapor
compression machine. With cost savings of about $ 63,000 per year, the absorption machine
would need to operate about 15 years for the energy savings to pay for the greater initial cost.
This is a very long time for an investment to pay off in operating cost savings. In the current
situation of uncertain energy prices the larger investment for an absorption machine would
probably not be made. However, if absorption machines were to increase their market
penetration, the costs could be expected to decrease and the cost effectiveness improve.
Example 8.5 illustrates the fundamental tradeoff between conventional and non-conventional
methods of refrigeration and air conditioning. Conventional vapor compression machines have
been developed over the years by a number of manufacturers and the field is very competitive.
The costs of the equipment are relatively low and improvements in technology have resulted in
relatively high efficiency. The market for absorption machines has been very limited and so
manufacturing and development costs make the price of the units relatively high. Even though
these machines have significantly lower operating costs, the high initial costs have been a barrier
to wide-spread to adoption in the commercial cooling area
SM 8.5 Summary
Absorption air-conditioning machines are heat driven cooling devices. The condenser,
expansion valve, and evaporator are the same as in a conventional refrigeration system. The
compressor is replaced by a series of processes in which the refrigerant vapor is absorbed into a
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solution and pumped to a generator where heat is added, and then heated to desorb the solution
and produce refrigerant vapor. Lithium bromide as the absorbent and water as the refrigerant is
commonly used in large commercial units. Units that employ ammonia as the refrigerant and
water as the absorbent are available for small domestic-sized applications.
The use of water as a refrigerant limits the lithium bromide-water units to air-conditioning
applications. Ammonia-water units operate at the lower temperatures required for applications
below freezing. However, ammonia-water units have not been developed with the capacities
required for industrial applications.
The Coefficient of Performance is based on the refrigeration effect and the thermal input of
the absorption machine. For single effect units, the COP is about 0.6, and for double effect units
it is about 1.2. In comparison, vapor compression systems typically have COP values in the
range of 3 to 6. However, the cost of the energy to operate an absorption machine may be
significantly less since the price of electricity is three to four times that of the natural gas or
similar fuel used to provide heat. Further, the fuel cost of absorptions machines that utilize
"waste heat" would be even less.
Currently, absorption chillers are significantly more costly per ton of installed cooling
capacity than vapor compression units. The price can be expected to decrease if absorption air
conditioners become more widely used. Absorption cooling is an alternative to vapor
compression cooling in many applications where waste heat is available or electricity costs are
very high.
SM 8.6 Nomenclature

eng
COPabs COP of absorption system
COPr COP of refrigeration system
COPideal COP of an ideal absorption system
h
specific enthalpy
m
mass
mass flow rate
m
p
pressure
heat flow rate
Q
T
temperature
power
W
x
quality
X
mass concentration
effectiveness
thermal efficiency
Subscripts
abs
absorber
c
condenser
e
evaporator
eng
heat engine
gen
generator
ideal ideal
LiBr lithium bromide
mix
mixture
SM 8.7 References
ASHRAE, Chapter 2, "2009 ASHRAE Handbook - Fundamentals," ASHRAE, Atlanta, GA,
2009
ASHRAE, Chapter 41, "2010 ASHRAE Handbook - Refrigeration," ASHRAE, Atlanta, GA,
2010
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Herold, K. E., R. Radermacher, and S. A. Klein, "Absorption Chillers and Heat Pumps," CRC
Press, 1996.
TRANE, a business of Ingersoll Rand, LaCrosse, WI
SM 8.8 Problems
Problems in English Units
8.1 In the absorber of a lithium bromide refrigeration system, 50 lb/hr of water vapor from the
evaporator at 45 F mixes with a flow of 500 lb/hr of lithium bromide that has a temperature
of 85 F and a concentration of 65 %. Determine the concentration and temperature of the
outlet stream and the heat that must be transferred from the absorber.
8.2 In the absorber of a lithium bromide refrigeration system, 50 lb/hr of water vapor from the
evaporator mixes with a flow of 500 lb/hr of lithium bromide that has a concentration of 65
%. Determine the concentration and temperature of the outlet stream and the heat that
must be transferred from the absorber as a function of the evaporator temperature between
35 and 50 F and the lithium-bromide temperature between 70 and 100 F. Draw some
conclusions from your analysis.
8.3 A flow of 4000 lb/hr of lithium bromide at 120 F and a concentration of 60 % enters the
generator of an absorption unit. The heat flow into the generator is 400,000 Btu/hr. The
saturation temperature for the water vapor in the condenser is 90 F and the temperature of
the vapor leaving the generator is 110 F. Determine the amount of water vapor produced,
the operating temperature of the generator, and the concentration of the outlet stream.
8.4 A flow of 4000 lb/hr of lithium bromide at 120 F enters the generator of an absorption unit.
The heat flow into the generator is 400,000 Btu/hr. The saturation temperature for the
water vapor in the condenser is 90 F and the temperature of the vapor leaving the generator
is 110 F. Determine and plot the amount of water vapor produced, the operating
temperature of the generator, and the concentration of the outlet stream as a function of
inlet concentration over the range of 50 to 65 %. Draw some conclusions from your
analysis.
8.5 A simple lithium bromide absorption cycle without a heat recovery heat exchanger
operates with an evaporator temperature of 45 F and a condensing temperature of 120 F.
The water vapor leaves the generator at 140 F. The cooling capacity of the evaporator is
400 tons. In the absorber the lithium bromide operates between concentrations of 65 %
and 55 %. Determine the COP of the cycle and the amount of heat addition required.
Show the cycle on pressure-temperature coordinates. Draw some conclusions from your
analysis.
8.6 A lithium bromide absorption cycle operates with an evaporator temperature of 45 F and a
condensing temperature of 120 F. The cooling capacity of the evaporator is 400 tons. In
the absorber the lithium bromide operates between concentrations of 65 % and 55 %. The
water vapor leaves the generator at 140 F. A heat exchanger is added to recover heat for
the lithium bromide flows to and from the generator. Determine the COP of the cycle and
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the amount of heat addition required as the heat exchanger effectiveness is varied from 0 to
1.0. Draw some conclusions from your analysis.
8.7 A lithium bromide absorption cycle operates with a condensing temperature of 120 F. The
cooling capacity of the evaporator is 400 tons. In the absorber the lithium bromide
operates between concentrations of 65 % and 55 %. The water vapor leaves the generator
at 140 F. A heat exchanger with effectiveness of 0.7 is added to recover heat for the
lithium bromide flows to and from the generator. Determine the COP of the cycle and the
amount of heat addition required as the evaporator temperature is varied between 35 and
55 F. Draw some conclusions from your analysis.
8.8 A lithium bromide absorption cycle operates with an evaporator temperature of 45 F. The
cooling capacity of the evaporator is 400 tons. In the absorber the lithium bromide
operates between concentrations of 65 % and 55 %. The water vapor leaves the generator
at 140 F. A heat exchanger with effectiveness of 0.7 is added to recover heat for the
lithium bromide flows to and from the generator. Determine the COP of the cycle and the
amount of heat addition required as the condensing temperature is varied between 90 and
130 F. Draw some conclusions from your analysis.
8.9 A lithium bromide absorption cycle is to be designed for 400 tons of cooling capacity and
operate with a condensing temperature of 120 F and an evaporator temperature of 45F.
The water vapor leaves the generator at 140 F. A heat exchanger with an effectiveness of
0.7 will be used to recover heat for the lithium bromide flows to and from the generator.
Determine the optimal concentration values for the lithium bromide in the circuit. Discuss
the implications of the different choices for the concentration.
8.10 Determine the breakeven number of annual hours of operation for single and double-effect
absorption machines to compete with vapor compressor systems. For comparison
purposes, take a vapor compression unit that has an initial cost of $ 500 per ton of installed
capacity and a COP of 5, a single effect absorption machine that has an initial cost of $ 900
per ton of installed capacity with a COP of 0.6, and a double effect absorption machine
that has an initial cost of $ 1500 per ton of cooling capacity and a COP of 1.2. The
absorption machines are fired with natural gas at a costs $ 7/106 Btu. The electric rate
schedule is an energy use charge of $ 0.15/kWh and an annual demand charge of $
120/kW. Use a building load of 1000 tons and a 5 year life span. Consider the economic
parameters and draw some conclusions from your results.
Problems in SI Units
8.11 In the absorber of a lithium bromide refrigeration system, 0.01 kg/s of water vapor from the
evaporator at 7 C mixes with a flow of 0.1 kg/s of lithium bromide that has a temperature
of 30 C and a concentration of 65 %. Determine the concentration and temperature of the
outlet stream and the heat that must be transferred from the absorber.
8.12 In the absorber of a lithium bromide refrigeration system, 0.01 kg/s of water vapor from the
evaporator mixes with a flow of 0.1 kg/s of lithium bromide that has a concentration of 65
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8.13
8.14
8.15
8.16
8.17
8.18
%. Determine the concentration and temperature of the outlet stream and the heat that
must be transferred from the absorber as a function of the evaporator temperature between
1 and 10 C and the lithium-bromide temperature between 20 and 30 C. Draw some
conclusions from your analysis.
A flow of 0.5 kg/s of lithium bromide at 40 C and a concentration of 60 % enters the
generator of an absorption unit. The heat flow into the generator is 120 kW. The
saturation temperature for the water vapor in the condenser is 28 C and the temperature of
the vapor leaving the generator is 37 C. Determine the amount of water vapor produced,
the operating temperature of the generator, and the concentration of the outlet stream.
A flow of 0.5 kg/s of lithium bromide at 40 C enters the generator of an absorption unit.
The heat flow into the generator is 120 kW. The saturation temperature for the water
vapor in the condenser is 28 C and the temperature of the vapor leaving the generator is 37
C. Determine and plot the amount of water vapor produced, the operating temperature of
the generator, and the concentration of the outlet stream as a function of outlet
concentration over the range of 50 to 65 %. Draw some conclusions from your analysis.
A simple lithium bromide absorption cycle without a heat recovery heat exchanger
operates with an evaporator temperature of 7 C and a condensing temperature of 50 C. The
water vapor leaves the generator at 55 C. The cooling capacity of the evaporator is 1500
kW. In the absorber the lithium bromide operates between concentrations of 65 % and 55
%. The water vapor leaves the generator at 55 C. Determine the COP of the cycle and the
amount of heat addition required. Show the cycle on pressure-temperature coordinates.
Draw some conclusions from your analysis.
A lithium bromide absorption cycle operates with an evaporator temperature of 7 C and a
condensing temperature of 50 C. The cooling capacity of the evaporator is 1500 kW. In
the absorber the lithium bromide operates between concentrations of 65 % and 55 %. The
water vapor leaves the generator at 55 C A heat exchanger is added to recover heat for the
lithium bromide flows to and from the generator. Determine the COP of the cycle and the
amount of heat addition required as the heat exchanger effectiveness is varied from 0 to
1.0. Draw some conclusions from your analysis.
A lithium bromide absorption cycle operates with a condensing temperature of 50 C. The
cooling capacity of the evaporator is 1500 kW. In the absorber the lithium bromide
operates between concentrations of 65 % and 55 %. The water vapor leaves the generator
at 55 C A heat exchanger with effectiveness of 0.7 is added to recover heat for the lithium
bromide flows to and from the generator. Determine the COP of the cycle and the amount
of heat addition required as the evaporator temperature is varied between 2 and 15 C.
Draw some conclusions from your analysis.
A lithium bromide absorption cycle operates with an evaporator temperature of 7 C. The
cooling capacity of the evaporator is 1500 kW. In the absorber the lithium bromide
operates between concentrations of 65 % and 55 %. The water vapor leaves the generator
at 55 C A heat exchanger with effectiveness of 0.7 is added to recover heat for the lithium
8.30
bromide flows to and from the generator. Determine the COP of the cycle and the amount
of heat addition required as the condensing temperature is varied between 30 and 50 C.
Draw some conclusions from your analysis.
8.19 A lithium bromide absorption cycle is to be designed for 1500 kW of cooling capacity and
operate with a condensing temperature of 50 C and an evaporator temperature of 7 C. The
water vapor leaves the generator at 55 C. A heat exchanger with an effectiveness of 0.7
will be used to recover heat for the lithium bromide flows to and from the generator.
Determine the optimal concentration values for the lithium bromide in the circuit. Discuss
the implications of the different choices for the concentration.
8.20 Determine the breakeven number of annual hours of operation for single and double-effect
absorption machines to compete with vapor compressor systems. For comparison
purposes, take a vapor compression unit that has an initial cost of $ 150 per kW of installed
capacity and a COP of 5, a single effect absorption machine that has an initial cost of $ 250
per kW of installed capacity with a COP of 0.6, and a double effect absorption machine
that has an initial cost of $ 450 per kW of cooling capacity and a COP of 1.2. The
absorption machines are fired with natural gas at a costs $ 7/106 kJ. The electric rate
schedule is an energy use charge of $ 0.15/kWh and an annual demand charge of $
120/kW. Use a building load of 3000 kW and a 5 year life span. Consider the economic
parameters and draw some conclusions from your results.
8.31