On the chemical heat pump system and its second-law efficiency

Energy Convers. Mgmt Vol. 28, No. 2, pp. 123-127, 1988 Printed in Great Britain. All rights reserved

0196-8904/88 $3.00 +0.00 Copyright © 1988 Pergamon Press plc

ON THE CHEMICAL HEAT PUMP SYSTEM A N D ITS SECOND-LAW EFFICIENCY K. S. CHEN and W. C. H W A N G Department of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan 800, Republic of China (Received 20 August 1986; in revisedform 28 July 1987; receivedfor publication 5 August 1987) Abstract--This paper is concerned with the description of a chemical heat pump for the recovery or upgrading of low-level thermal energy. A four-tank configuration of a chemical heat pump is presented that has potential applications for heating and cooling of thermal energy storage. An analysis of the second-law efficiency of the chemical heat pump system, operated in the heating or cooling mode, is made. Effects of the temperatures of the heat source, surrounding and desired task on the second-law efficiency are also discussed. Chemical heating pump

Second-law efficiency

NOMENCLATURE Cp = Ex = H = Hfg = P = Q = R = S = T= A= r/=

Specific heat Exergy Total enthalpy or energy Latent heat of evaporation Pressure Amount of heat Gas constant Total entropy Temperature Difference Efficiency of chemical heat pump

Superscripts H = Denotes high temperature tank L = Denotes low temperature tank

Subscripts avail = cooling = g= H= heating = L= 1= loss = M= out = s= 0= 1= 2=

Available quantity For cooling purpose Gas state Heat-source state For heating purpose Surrounding state for the heating mode; also task state for the cooling mode Liquid state Lost quantity Task state for the heating mode; also surrounding state for the heating mode Output quantity Solid state Reference state First law Second law 1. INTRODUCTION

It has been recognized t h a t efficient utilization o f c o n v e n t i o n a l energy sources should be seriously considered in parallel with the d e v e l o p m e n t of new energy sources. In particular, industrial processes exhaust a large a m o u n t o f thermal energy in water or gas when its t e m p e r a t u e is low ( ~ 2 0 0 ° C ) . A n o t h e r practical source o f low-level energy is the solar energy o b t a i n e d from fiat plate or c o n c e n t r a t i n g collectors.

Waste heat recovery

For the purpose of recovering such a low-level energy, a F r e o n - t u r b i n e a n d a n a b s o r p t i o n heat p u m p , for example, have been p r o p o s e d a n d developed so far. However, they are economically n o n - a t t r a c t i v e either due to high cost or sensitivity to e n v i r o n m e n t a l conditions, a n d their uses are still not widespread. New devices or systems are still being sought. A m o n g them, the C H P (chemical heat p u m p ) is a n attractive one that can recover low-level thermal energy for heating, cooling or storage purposes [1, 2]. The C H P utilizes the chemical reaction of inorganic substances, such as Ca(OH)2 a n d SO3 to store the energy in the chemical b o n d , and releases it when needed. Because the energy is in the form of the chemical bond, it can easily be stored w i t h o u t heavy insulation. In addition, due to the large a m o u n t o f reaction enthalpy involved, it can be stored in a relatively small volume o f tank, which is very i m p o r t a n t when spacing or t r a n s p o r t a t i o n problems have to be considered. W e n t w o r t h a n d C h e n [3] a n d Prengle a n d Sun [4] discussed the selection a n d testing o f the reaction material for the CHP. Descriptions a n d first-law analysis of the C H P system based on a t w o - t a n k configuration were given by R a l d o w a n d W e n t w o r t h [5], R a l d o w [6] a n d Fujii [7]. Recently, K a n z a w a a n d Aria [8] a n d Fujii a n d Tsuchiya [9] discussed practical system operations. In this paper, a f o u r - t a n k configuration of the C H P is presented t h a t gives a better description o f the system o p e r a t i o n for the purposes o f heating, cooling a n d energy storage. In addition, its second-law analysis based on the available energy are given. 2. CHEMICAL HEAT PUMP The simplest form o f a C H P consists o f two vessels linked together, as s h o w n in Fig. 1, within which a volatile c o m p o n e n t (the working fluid) volatizes or 123

CHEN and HWANG: CHEMICAL HEAT PUMP SYSTEM

124

(a)

IJ

il

- o:0:l H

tonk

L tonk

QHin

fQLout

I i

OHout

l/r.

OL.I.

P -

AH

RT

-4

AS

R

(1)

where AH and AS are, respectively, the reaction enthalpy and reaction entropy, and R is the gas constant. Because a phase change occurs in the L-tank, P and T also obeys the Clapeyron equation [2]: d P _ Hfg d r P R T2

AH t = AH~.

(3)

(2) Temperatures of A s and Be drops to T M due to the release of sensible heat AH2; that is,

- A H 2 = (Co,,, + Cp%) (TH -- TM).

(4)

(3) A~ and Be recompose to form AB~ at T M and release heat AH3, i.e. - AH3 = - AHHM.

(b)

(5)

(4) The temperature of AB~ increases from TM to TH, by absorbing sensible heat AH4 from heat source

2

I I i

r~

r,

I L I

TH

T Fig. 2. (a) Pressure and temperature diagrams for an absorption heating or cooling cycle; (b) enthalpy and temperature diagrams for a heating or cooling cycle. at TH; that is,

AH, = CpABs(Tn- TM).

(6)

(5) Bg condenses to B l at TM and releases latent heat AHs; that is, - AH5 = - A H L.

(7)

(5) Temperature of B I drops from T M to T L due to the release of sensible heat, AH6, to the heat sink at temperature TL; that is,

(2)

where Hfg is the latent heat of evaporation of the working fluid. Referring to Figs 2a and 2b, the operation of a CHP can be adequately described at three temperature levels, Trt, TM and T L (T L < T M < TH) as below. (1) ABs absorbs heat AHI from heat sources at temperature T H and decomposes to A S and Be, that is,

1/rL

I/T

Fig. 1. A two-tank configuration of chemical heat pump system.

distills. This volatile compound is bound differently in both tanks. If heat is absorbed at the hightemperature tank, H, the compound AB s will decompose into A S and Bg. Due to a pressure difference, B s flows into the low-temperature tank, L, where it releases heat and condenses into liquid, Bt; this is the so-called generation process. On the other hand, if heat is absorbed by the L tank, B~ can be evaporized to form gas Be and flow into the H tank. At the H tank, Bg is recomposed with A s to form ABs, and releases heat there. This is the so-called working process. A cycle is completed when these two processes have taken place in series. If the pressure difference between the two tanks is infinitessimal, the pressure P and temperature T in the tank are given by [5, 6]

i

1/r.

- - A H 6 = Cps, (T M -- TL).

(8)

(7) BI absorbs latent heat, Hfg, to evaporate to Bg at TL; that is, AH7 = Hfe = AH~

(9)

(8) Bg absorbs sensible heat from medium at TM; that is, AH 8 = Cp,, (T M - To).

(10)

Notice that for heating purposes, - A H 2 , - A H 3 and - A H 5 are supplied to the heated space at temperature T M, and TL is the surrounding temperature. For cooling purposes, AH7 was extracted from the cooled space at temperature To, and TM is the surrounding temperature. According to Raldow and Wentworth [5], the CHP can operate in three modes: absorption storage between two temperatures levels; absorption heating or cooling cycle, and absorption upgrade cycle, all among three temperature levels.

CHEN and HWANG: CHEMICAL HEAT PUMP SYSTEM

125

Table I. Operation modes of a chemical heat pump Valve I Valve 2 Mode Open Closed Storage mode in generationprocess Closed Open Storage mode in working process Open Open Absorption heatingor coolingcycle

VaLve I

8~

,M

and Wentworth [5], they are operated among three temperature levels, instead of only two.

8t

3. SECOND-LAW ANALYSIS

Fig. 3. A four-tank configuration of chemical heat pump system. The first mode of operation is impractical due to the fact that absorption of heat in the generation process is at the same temperature at which the release of heat in the working process takes place. It is very difficult to find a substance to release and absorb heat at the same temperature. The third mode of operation described by Raldow and Wentworth [5] involves heat release at a temperature higher than that at which heat is absorbed. Such a mode of operation is also impractical if the heat absorption and heat release rely on the same chemical reaction. Fujii [7] presented a practical CHP system for recovering and upgrading low-level energy by utilizing three different chemical reactions. The second mode of CHP has potential applications for heating or cooling purposes. Raldow and Wentworth [5] discussed such a system with a twotank configuration. In what follows, a four-tank configuration operated at three temperature levels is presented. It is shown that by suitable control of the valves, a CHP can work in the heating, cooling or storage mode within three temperature levels. Referring to Fig. 3, the heat source at temperature TH provides heat AH~ to decompose ABs in tank H, into As and Bg. Then, As flows to tank H2, while Bg flows to tank L~ if valve 1 is open. Bg in tank L~ releases latent heat AHr~ to form liquid BI, and B 1 flows to tank L2. B~ in L2, at temperature TL, absorbs latent heat AH~ to evaporate to form Bg. If valve 2 is open, Bg flows to H2 to compose with As into ABe. AB~ then releases sensible heat AHr~ and returns to tank H to complete the cycle. We can see from Fig. 3 that different operation mode can be achieved by the suitable control of valves 1 and 2. As seen from Table 1, if only one valve is open, the CHP can be used for energy storage purposes. However, if both are open, an absorption heating or cooling cycle can be accomplished. Notice that, although the two storage modes shown in Table 1 are similar to the ones described by Raldow

The second-law (exergy) analysis adopts the concepts of available energy and irreversibility to measure the performance of energy conversion/recovery systems. As described by Ahern [1], exergy or available energy, Ex, for the working fluid at any state is given by E x = ( H - Ho) -- T o ( S - So)

(11)

if the potential energy, kinetic energy and radiation can be neglected. In the above, H and S are total enthalpy and entropy, respectively and the subscript 0 denotes the ambient condition. We can see from the above equation that a change of exergy between any two states in a process is determined by AEx=(H2-

H~)-

T o ( S 2 - SI).

(12)

The efficiency of a system based on the exergy concept is defined by [1] Ex . . . . Ex...J, - Ex .... q2 = Ex ..... Ex ..... ,

(13)

where Exava~, is the total available exergy for the system, and Ex,o~' is the total loss of available exergy due to the irreversibility in the process. For a heat pump receiving heat AH at Try, the available exergy is given by [1] Ex,va~,= A H ( I -

TT~°n).

(14)

The irreversibility, L in the process is determined by [10] l=T0

AS-

.

(15)

In what follows we will use the above concept of second-law (exergy) efficiency to discuss a CHP under the absorption heating and absorption cooling cycles. Referring to Fig. 2b, the available exergy comes from the heat input in processes 1 and 4. From equation (14), we have E'va" = (AH' + A H 4 ) ( 1 - T ~ ) " The irreversibility for each process is

i1 : T0(AS,-AH' r . / '

(16)

CHEMICAL HEAT PUMP SYSTEM

CHEN and HWANG:

126

(a)

90

(b)

92

94

96

J,

(‘Cl

98

100

0

2

4

6

8

10 25

27

29

31

r,

rL (T)

33

35

(‘Cl

Fig. 4. Dependencies of q, and o2 on (a) r,, (b) TL and (c) r,.

**=

To(As2+$y,

I,=

.(*s,+$y,

14=

T,(Ax+),

I,=

To(As,+~),

&=

+,+~),

I,=

T(As,-g,

Notice that for the heating cycle, heated space is at temperature TM, and To = T,_. For the same cycle but for cooling purposes, cooled space is at temperature TL and T, = TM. Following similar procedures, its second-law efficiency can be obtained as

Wf:: + c,l,’ (TN - TM)}(1 -

T&-H)}

(21)

[(-AH!,)

i=l

We can see from equations (20H22) that the following relations hold: (1 -?)I(1

Ex,oss= f: I,= -TL($+z+z I=,

(2-

+F+F+$!!

-AH6-AH,.

M>

[(-AH,)+(-AH,)+(-AH,)-AH,1 x (1 -Sj] \ ‘M/J ,

T

\l

-$)

for heating;

l),/( 1-2)

for cooling.

(23)

(19)

It follows from equation (13) that the second-law efficiency for an absorption heating cycle is given by

I-

+ CC,,. + C,,_)

G’2b)

From equations (17), total irreversibility of 1he cycle is

=

+ (-A%,)

(17)

Heat absorption or release for each process has been given in equations (3)-(10). For a cycle, it requires i AH,=O, 2 AS,=O. (18) I=1

M

-- 1))

The first-law efficiencies for the above heating and cooling modes are given by Rallow [6] as

r,= ++).

M

{[AHb - Co_.(TM - T,,)l U’,lr, Qcoohng =

4. EXAMPLE It is apparent that the second-law efficiency is influenced by the temperatures of heat source, surrounding and desired task; but this is not so for the first-law efficiency. To see this, consider the heating mode of a CHP with CaCl,. 8NH3 as the working medium. The chemical reaction of CaCl,. 8NH, is CaCl,

.8NH,(,,+ CaCl, .4NH,,,, + 4NH,(,, ,

with the reaction Wentworth [5]

enthalpy

given by Raldaw and

AH; x - AH; = 41.2 kJ/mol NH,; AHL x AH: = 23 kJ/mol NH,.

If variation of the reaction enthalpy with temperature can be neglected, and the sensible heat is negligible as compared with the reaction enthalpy,

CHEN and HWANG: CHEMICAL HEAT PLrMP SYSTEM equation (22a) can be simplified as

(--AHHM)+(--AH L) qa...... ~ ~

AH~

(24)

Dependencies of r/1 and r/z shown in equations (23) and (24) on Te, TM and TH are presented in Fig. 4a--c. It can be seen from Fig. 4a--c that q~, unlike r/2, remains unchanged with the variation of Tn, TM or Tt. Figure 4a shows that r/z decreases with increasing heat-source temperature TH under fixed TM and T,. That is, if the quality of the heat-source energy is raised but the task temperature TM remains the same, the system efficiency becomes lower. Similarly, r/2 decreases with increasing surrounding temperature TL under fixed TM and TH as shown in Fig. 4b. However, q2 increases with increasing task temperature TM under fixed TH and TL as shown in Fig. 4c. That is, if the task temperature TM is raised, but the heat source and surrounding temperatures remain the same, the available energy and the system efficiency are also raised. As can be seen from equation (23b), the temperatures of heat source, surrounding and desired task effect the second-law efficiency of a CHP operating in a cooling mode in a similar manner.

5. CONCLUSION The chemical heat pump is an attractive system for storage and recovery of low-level energy. In this paper, a description of the CHP system based on a four-tank configuration and analyses of its secondlaw efficiency are presented.

127

The following conclusions can be drawn from this study: (1) By suitable control of the valves shown in Fig. 3, a CHP can work as an energy storage device or a heating and cooling heat pump at three temperature levels. (2) The second-law efficiency of a CHP decreases with increasing heat-source temperature under fixed surrounding and task temperatures both in the heating and cooling modes. (3) The second-law efficiency of a CHP decreases (or increases) with increasing surrounding temperature under fixed heat source and task temperatures in the heating (or cooling) mode. (4) The second-law efficiency of a CHP increases (or decreases) with increasing task temperature under fixed heat source and surrounding temperatures in the heating (or cooling) mode. REFERENCES

1. J. E. Ahern, The Exergy Method of Energy Systems Analysis. Wiley, New York (1980). 2. K. Frank, Principles of Solar Engineering. McGrawHill, New York (1978). 3. W. E. Wentworth and E. Chen, Sol. Energy 18, 205 (1976). 4. H. W. Prengle Jr and C. H. Sun, Sol. Energy 18, 561 (1976). 5. W. M. Raldow and W. E. Wentworth, Sol. Energy 23, 75 (1976). 6. W. M. Raldow, Sol. Energy 27, 307 (1981). 7. S. Fujii, J. chem. Engng Japan 10, 224 (1977). 8. A. Kanzawa and Y. Aria, Sol. Energy 27, 367 (1981). 9. I. Fujii and K. Tsuchiya, Sol. Energy 34, 367 (1985). 10. G. A. Hawkins, Engineering Thermodynamics. Wiley, New York (1960).