Exergetic efficiency of high-temperature-lift chemical heat pump (CHP) based on CaO-CO2 and CaO-H2O working pairs, ...
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INTERNATIONAL JOURNAL OF ENERGY RESEARCH
Int. J. Energy Res. (2012)
Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.2918
TECHNICAL NOTE
Exergetic ef
ciency of high-temperature-lift chemical
heat pump (CHP) based on CaO/CO
2
and CaO/H
2
O
working pairs
Mehdi Arjmand
1,2,
*
,
â€
, Longcheng Liu
1
and Ivars Neretnieks
1
1
Division of Chemical Engineering, Department of Chemical Engineering and Technology, Royal Institute of Technology (KTH),
Stockholm SE-100 44, Sweden
2
Division of Environmental Inorganic Chemistry, Department of Chemical and Biological Engineering, Chalmers University of
Technology, Göteborg SE-412 96, Sweden
SUMMARY
The use of reversible chemical reactions in recuperation of heat has gained signicant interest due to higher magnitude of
reaction heat compared to that of the latent or sensible heat. To implement chemical reactions for upgrading heat, a
chemical heat pump (CHP) may be used. A CHP uses a reversible chemical reaction where the forward and the reverse
reactions take place at two different temperatures, thus allowing heat to be upgraded or degraded depending on the mode
of operation. In this work, an exergetic efciency model for a CHP operating in the temperature-level amplication mode
has been developed. The rst law and the exergetic efciencies are compared for two working pairs, namely, CaO/CO
2
and
CaO/H
2
O for high-temperature high-lift CHPs. The exergetic efciency increases for both working pairs with increase in
task,
T
H
, decrease in heat source,
T
M
, and increase in condenser,
T
L
, temperatures. It is also observed that the difference in
reaction enthalpies and specic heats of the involving reactants affects the extent of increase or decrease in the exergetic
efciency of the CHP operating for temperature-level amplication. Copyright © 2012 John Wiley & Sons, Ltd.
KEY WORDS
chemical heat pump (CHP);
rst law ef
ciency; second law (exergetic) ef
ciency; temperature ampli
cation; heat transformer; CaO/
CO
2
; CaO/H
2
O
Correspondence
*Mehdi Arjmand, Division of Chemical Engineering, Department of Chemical Engineering and Technology, Royal Institute of Technology
(KTH), Stockholm SE-100 44, Sweden.
â€
E-mail: arjmand@kth.se
Received 25 September 2011; Revised 18 February 2012; Accepted 1 March 2012
1. INTRODUCTION
engaging reversible chemical reactions for recuperation
of heat has gained signi
cant interest because of the higher
magnitude of reaction heat compared with that of the latent
or sensible heat as retrieved in physical recovery techni-
ques or vapor compression and sorption heat pumps [11].
To use chemical reactions for upgrading low-grade waste
heat, a chemical heat pump (CHP) may be used which
offers a wider range of operating temperature and versatil-
ity in comparison with the conventional vapor compression
or (de)sorption heat pump. In practice, temperatures as low
as 230 K in refrigeration or freezing systems, and up to 870
K in heat generation systems can be supplied using CHPs
[12
Depending on the type of the process, waste heat may be
released at any temperature in the range of chilled cooling
water to high-temperature gases from an industrial furnace
[1]. High-temperature waste heat provides a higher recov-
ery rate and thus can be often effectively recovered using
conventional and physical recovery solutions (e.g. using
a series of heat exchangers). However, most waste heat
streams in the industry have a low temperature (
400 K)
and therefore are called low-grade waste heat [2]. In this
case, physical recovery may not be effective in retrieving
the lost energy.
A low-temperature waste heat may be upgraded using a
vapor compression heat pump, which requires electricity,
and/or sorption heat pumps, which uses the heat of (de)
sorption of a medium [3
–
10]. In recent years, however,
<
20].
In theory, a CHP operates in either of three different
modes: (a) heat generation, (b) refrigeration, or (c)
temperature-level amplication; also known as chemical
heat
–
transformer (CHT) [21
–
23]. First and/or second
Copyright © 2012 John Wiley & Sons, Ltd.
M. Arjmand, L. Liu and I. Neretnieks
Exergetic efficiency of high-temperature high-lift chemical heat pump
law (exergetic) efciency analyses of a range of CHPs
with different working pairs (working uid or medium)
operating mainly for heat generation and refrigeration,
that is, modes a and b, have been carried out
[12,20,24
–
31]. The kinetic aspects of some of the work-
ing pairs have also been investigated [14,17,20,32
–
34].
However, the work on exergetic efciency analysis of
a CHP operating in the temperature-level amplication
mode, that is, mode c, is still limited [27,35].
The temperature-level amplication mode may be used
to upgrade low-grade waste heat. It also shapes the basis
for high-temperature lift CHPs particularly for power gen-
eration or other industrial applications [36], an area where
progress is to be seen [23,34,37
–
40]. It is well known that
the conventional heat balance for evaluation of losses and
system efciency does not fully represent the effectiveness
of a system. On the other hand, an estimation of available
energy (exergy) is advantageous for a closer measurement
of losses and thus effective conservation of energy during
design and operation of such systems. In addition, the eval-
uation of the exergetic efciency for this mode of operation
offers a criterion to discern heat transformers that are ther-
modynamically effective from those that are not. More-
over, exergetic efciency can be used to identify systems
that have potential for improvements. A signicant differ-
ence between the exergetic and the practical efciency sug-
gests that there may be room for possible performance
enhancements [41].
Thus, an exergetic efciency model for a CHP operating
in the temperature-level amplication mode has been devel-
oped. The model is then used to compare the efciencies of
two working pairs, namely, CaO/CO
2
and CaO/H
2
Ofor
high-temperature-lift CHPs.
operation (i.e. refrigeration, heat generation, or tempera-
ture-level amplication) [19]. By absorbing heat through
the reverse endothermic reaction in Equation (1),
C
is
decomposed to
A
(a nonvolatile compound) and
B
(a vola-
tile compound). On the other hand, the forward reaction in
Equation (1) is exothermic, during which
C
is formed
again. Thus, in the simplest form, a CHP comprises a
decomposition reactor, a condenser, an evaporator, and a
synthesis reactor [18]. The evaporator is the source of the
volatile compound
B
for later formation of
C
in the synthe-
sis reactor.
B
is eventually condensed in the condenser
after
C
is decomposed into
A
and
B
in the decomposition
reactor. Because the chemical compound
C
and the con-
densate are pure phases, the pressure of the volatile com-
pound
B
in the reactors and the evaporator depend only
on the temperature. Thus, the operation is monovariant,
that is by specifying the pressure, the temperature will also
be determined [42,43].
The modes of heat generation or refrigeration have sim-
ilar fundamentals in using the low temperature heat from
the environment or surrounding to achieve the output
effect, that is, producing heat or cold, respectively. How-
ever, they differ in the de
nition of the user as demanding
cold (refrigerating) or hot (heat generating) streams. Such
CHPs have been thoroughly studied, and the evaluation
of both thermal efciencies has been reported in several
publications [12,20,24,27
–
31].
The temperature-level amplication mode on the
other hand operates on a somewhat different basis that
uses an intermediate-level heat source to generate a
high-temperature-level heat [9,43]. In order for this to
occur, the forward and the reverse directions of the
reversible reaction (Equation (1)) must both take place
at temperatures higher than that of the environment. To
further distinguish between the heat amplication and
the heat generation and cooling modes, consider
T
M
and
T
L
representing different media as outlined in Figure 1.
In the case of a CHP for heat generation,
T
M
represents
the temperature of the synthesis reaction that releases
the
useful
heat to the user, which is generated with the
help of heat from the endothermic reaction at the higher
temperature,
T
H
, (e.g. using surplus heat) and heat from
the environment at the lower temperature,
T
L
.By
contrast, in the case of a CHP operating for temperature
amplication,
T
L
represents the condenser, which releases
nonuseful heat to the environment (from part of the sup-
plied heat) while offering the upgraded heat at the higher
temperature,
T
H
, with the help of the medium-temperature
heat source,
T
M
, (e.g. from surplus heat).
Figure 2 shows the schematic of a CHP operating in the
temperature-level amplication mode. Here, an intermediate-
level heat (e.g. waste heat) at
T
M
is supplied to both the
decomposition reactor to breakup
C
into its constituents and
later to the evaporator to vaporize the working uid,
B
.The
vapor
B
generated from the decomposition reactor condenses
in the condenser during the charging phase. During the dis-
charging phase, the working uid
B
is admitted to the evap-
orator, where it is vaporized and allowed to react with
A
in
2. CHEMICAL HEAT PUMP
In contrast to the heat engine dened by Carnot where
work is delivered between a high-temperature heat source
and a low-temperature heat sink, the CHP uses three (or
four) temperature levels of high, medium, and low to con-
sume or produce thermochemical energy. Thus, for a CHP,
a closed cycle in which the forward reaction is endothermic
and the reverse reaction is exothermic may be considered.
The endothermic reaction occurs at a lower temperature,
whereas the exothermic reaction is carried out at a higher
temperature. As a result, a low-temperature heat may be
absorbed by the endothermic reaction and released at a
higher temperature by the exothermic reaction.
In principal, the general reaction in a CHP may be
assumed as follows:
A þ B
↔
C
(1)
It should be noted that the reaction is reversible and that
the forward and the reverse reactions are assumed to take
place at two different temperatures, thus allowing heat to
be upgraded or degraded depending on the mode of
Int. J. Energy Res.
(2012) © 2012 John Wiley & Sons, Ltd.
DOI: 10.1002/er
Exergetic efficiency of high-temperature high-lift chemical heat pump
M. Arjmand, L. Liu and I. Neretnieks
Figure 1. Operation principle of a CHP operating in heat generation mode (left) and temperature-level ampli
cation mode (right).
Figure 2. Schematic of a CHP operating in the temperature-level ampli
cation mode.
the synthesis reactor. Thus, compound
C
is formed at a
higher temperature-level,
T
H
, and with a higher quality than
that of the original source supplied to the system. The con-
denser is used to partly remove the low-temperature heat at
ambient,
T
L
, and to complete the cycle. The result is that a
medium-temperature heat,
T
M
(e.g. from waste heat), is
absorbed by the system through the reverse endothermic re-
action and evaporation of the working uid and is upgraded
to a high-temperature heat,
T
H
, by the exothermic heat of
the forward reaction. Figure3showstheenergyowsofa
CHP operating in the temperature-level amplication mode.
It can be noticed that the intermediate temperature-level heat,
T
M
, is required during both charging and discharging
modes, that is, decomposition of
C
and evaporation of
B
. If this source is not always available, two CHPs may
be integrated [43].
3. THERMAL EFFICIENCIES
Figure 3. Energy
ow of a CHP operating in the temperature-
level ampli
cation mode.
3.1. First law ef
ciency
T
M
T
L
T
M
max
HE
¼
(2)
The maximum efciency of any heat engine, heat pump, or
refrigerator can be derived for cyclic reversible processes
using the well-known Carnot efciency. To derive the
Carnot efciency of a CHP, two cycles consisting of one heat
pump (operating in the higher temperature interval) and one
heat engine (operating in the lower temperature interval) may
be considered [9,42]. The maximum (or Carnot) efciency of
the heat engine may then be expressed as
and the maximum efciency of the heat pump may be
written as
T
H
T
H
T
M
max
HP
¼
(3)
The overall maximum efciency of the CHP is dened as
the ratio of the heat obtained to the heat supplied. Thus, the
Int. J. Energy Res.
(2012) © 2012 John Wiley & Sons, Ltd.
DOI: 10.1002/er
M. Arjmand, L. Liu and I. Neretnieks
Exergetic efficiency of high-temperature high-lift chemical heat pump
maximum efciency of a CHP operating as a temperature
amplier is as follows
Utilized heat at higher temperature
Supplied heat
max
CHP
¼
T
H
T
M
T
M
T
L
T
H
T
L
¼
(4)
Equation (4) shows that the ideal performance of a CHP
depends only on the cycle temperature boundaries [19]. An
investigation of different working pairs and optimum operat-
ing temperatures has also been reported. An overview of the
working pairs used for CHPs can be found in the reviews by
Wongsuwan
et al
. [18] and Aristov
et al
.[19].
However, the actual efciency of a CHP is not depen-
dent on the temperature levels but on the enthalpy changes
in the high and low temperature cycle. Thus, assuming
negligible variation in reaction enthalpy with temperature
and neglecting sensible heat, the actual efciency of a CHP
in operation for temperature-level amplication is [43]
Figure 4. Process con
guration of a CHP operating in the
temperature-level ampli
cation mode.
Δ
H
H
þ
Δ
H
M
CHP
;
I
¼
(5)
Δ
H
M
In Equation (5), the superscripts refer to either the high- or
the low-temperature reaction (or reactor) and the subscripts
indicate the temperature level. It should be mentioned that
the temperatures of the CHP cycle are not independent of
each other, and with the determination of one, the other
two temperatures are also set. Consequently, the actual ef-
ciency of the CHP (Equation (5)) can theoretically reach
the Carnot efciency (Equation (4)), irrespective of the
chemical nature of the working pair [19].
3.2. Second law (exergetic) ef
ciency
In contrast to the rst law, the second law analysis uses the
concept of available energy (exergy) and irreversibility
[44]. Exergy analysis provides the means for evaluation
of the degree of thermodynamic perfection of a process.
On the basis of the exergy function, the efciency of a heat
pump can be expressed as [45]
Figure 5. Cycle path of a CHP operating in the temperature-
level ampli
cation mode.
path of such CHP. It can be observed in Figure 5 that the
available exergy is provided as heat input during processes
1, 2, 5 and 8; thus,
E
X
out
E
X
avail
:
¼
E
X
avail
:
E
X
loss
E
X
avail
:
CHP
;
II
¼
(6)
For a heat pump receiving heat at
T
i
, the available
exergy is given as per the following equation [45]:
T
L
T
M
E
X
avail
:
¼
Δ
H
1
þ
Δ
H
5
þ
Δ
H
8
ð
Þ
1
(7)
T
L
T
H
T
0
T
i
þ
Δ
H
2
ð
Þ
1
(8)
E
X
avail
:
¼
Δ
H
i
1
where
T
0
represents the reference (or ambient) temperature
in Equation (7).
Figure 4 shows the scheme of the processes congura-
tion for a CHP operating in the temperature amplication
mode, and Figure 5 represents the corresponding cycle
To account for the exergy losses, the irreversibilities of
the process should also be determined. For this, irrevers-
ibility can be expressed in terms of entropy and enthalpy
change with respect to the reference temperature (
T
0
) for
each cycle path as [46]
Int. J. Energy Res.
(2012) © 2012 John Wiley & Sons, Ltd.
DOI: 10.1002/er
 Exergetic efficiency of high-temperature high-lift chemical heat pump
M. Arjmand, L. Liu and I. Neretnieks
Δ
H
i
T
sink
=
source
Δ
H
6
¼ C
P
B
T
M
T
L
ð
Þ
(20)
I ¼ T
0
Δ
S
i
(9)
and
In Equation (9),
i
refers to the
i
th cycle path and
T
sink/source
is the temperature at the end of the cycle path of the process,
which can either be a sink or a source depending on the cycle
path.
Considering Equation (1) for the CHP, the cycle paths
in the processes involved can be described as follows:
Δ
S
6
Δ
H
6
T
L
I
6
¼ T
0
(21)
(7)
B
condenses at
T
L
, releasing latent heat
Δ
H
7
is supplied
Δ
H
7
¼
Δ
H
L
(22)
(1) Dissociation of compound
C
at
T
M
,
Δ
H
M
Δ
H
1
¼
Δ
H
M
(10)
and
Δ
S
1
Δ
H
1
T
M
Δ
S
7
Δ
H
7
T
L
I
1
¼ T
0
(11)
I
7
¼ T
0
(23)
(2) Temperature of the constituting compounds
A
and
B
increases to
T
H
, absorbing sensible heat
Δ
H
2
(8)
B
absorbs sensible heat from the medium at
T
M
Δ
H
8
¼ C
P
B
T
M
T
L
ð
Þ
(24)
Δ
H
2
¼ C
P
A
þ C
P
B
ð
Þ T
H
T
M
ð
Þ
(12)
and
and
Δ
S
2
Δ
H
2
T
H
Δ
S
8
Δ
H
8
T
M
I
2
¼ T
0
(13)
I
8
¼ T
0
(25)
is released
(3) Formation of compound
C
at
T
H
,
Δ
H
H
because for the entire process, it is known that
X
X
Δ
H
3
¼
Δ
H
H
(14)
Δ
H
i
¼
0
;
Δ
S
i
¼
0
(26)
and
the total irreversibility of the process can be written as
Δ
S
3
Δ
H
3
T
H
I
3
¼ T
0
(15)
E
X
loss
¼
X
I
i
¼T
L
Δ
H
1
T
M
þ
Δ
H
2
T
H
þ
Δ
H
3
T
H
þ
Δ
H
4
T
M
þ
Δ
H
5
T
M
þ
Δ
H
8
(4) Temperature of compound
C
decreases to
T
M
, releasing
sensible heat
Δ
H
4
T
M
Δ
H
6
Δ
H
7
(27)
Δ
H
4
¼ C
P
C
T
H
T
M
ð
Þ
(16)
Considering that the overall enthalpy change of a cycle is
zero, that is,
and
Δ
S
4
Δ
H
4
T
M
I
4
¼ T
0
(17)
Δ
H
1
þ
Δ
H
2
¼
Δ
H
3
ð
Þþ
Δ
H
4
ð
Þ
(28)
(5)
B
evaporates at
T
M
, absorbing latent heat
Δ
H
5
using Equations (8) and (27), Equation (6) can be written as
Δ
H
5
¼
Δ
H
M
(18)
T
L
T
H
T
L
T
M
ð
Δ
H
3
Þ
1
þ
Δ
H
4
ð
Þ
1
and
CHP
;
II
¼
Δ
S
5
Δ
H
5
T
M
T
L
T
M
T
L
T
H
ð
Δ
H
1
þ
Δ
H
5
þ
Δ
H
8
Þ
1
þ
Δ
H
2
ð
Þ
1
I
5
¼ T
0
(19)
(29)
(6) Temperature of
B
decreases from
T
M
to
T
L
,releasing
sensible heat
Δ
H
6
which by substituting
Δ
H
i
,the
CHP,II
is obtained as
Int. J. Energy Res.
(2012) © 2012 John Wiley & Sons, Ltd.
DOI: 10.1002/er
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