Thermodynamic analysis of two-stage ternary metal hydride heat pumps

0360-3199/92 $5.00+ 0.00 Pergamon Press LRI. © 1992InternationalAssociationfor HydrogenEnergy.

Int. J. Hydrogen Energy, Vol. 17, No. 9, pp. 731-735, 1992. Printed in Great Britain.

THERMODYNAMIC ANALYSIS OF TWO-STAGE TERNARY METAL HYDRIDE HEAT PUMPS S. SRINIVASAMURTHY and M. V. C. SASTRI Refrigeration and Air-Conditioning Laboratory, Indian Institute of Technology, Madras 600 036, India (Received for publication 29 April 1992)

Abstract--This paper presents a thermodynamic analysis of two-stage metal hydride heat pumps (MHHP) employing three alloys. Results are obtained for five different combinations involving eight alloys. The operating temperatures and pressures are chosen so that the MHHP operates in the dual-effect mode, i.e. delivers both heating and refrigeration effects. Overall coefficient of performance (COP) values in the range 2.0-3.2 and second law efficiencies in the range 0.5-0.8 are obtained.

NOMENCLATURE A, B C COP H/M h m p Q R T x X/M

Van't Hoff's equation coefficients Specific heat capacity (kJ kg -t K -~) Coefficient of performance Hydrogen to metal alloy mass ratio Heat of formation/dissociation (kJ kg ~ mol) Mass (kg) Pressure (bar) Heat quantity (kJ) Gas constant Temperature (K) Number of atoms of hydrogen absorbed per Molecule of the metal alloy Heat exchanger to metal alloy mass ratio

Greek letters Exergetic efficiency tSp Pressure differen~ze (bar) Subscripts 1, 2, 3 Components of heat quantities a, b, c Metal alloy designation H Hydrogen h High temperature i Input 1 Low temperature m Intermediate temperature o Output r Reference temperature s Sensible heat component v Container vessel and heat exchanger Note: double subscripts are also used, e.g. Q .... is heat output at intermediate temperature

INTRODUCTION Multistaging of metal hydride heat pumps (MHHPs) has been suggested by many investigators [ 1 - 3 ] to improve both performance and operating ranges. Various possibilities of multistaging together with a comparison with single stage MHHP are given by Orgaz and Dantzer [2]. Srinivasa Murthy et al. [3] have presented a thermodynamic study of two-stage heat transformers employing four alloys. These systems function as two single-stage systems operating in cascade. Double staging can also be achieved with three alloys. An analysis of such systems is given in this paper. SYSTEM DESCRIPTION The ternary heat pump system analysed here is shown schematically in Fig. 1. The system operates with two lowtemperature alloys M, and Mb, and one high-temperature alloy Me. Process I involves desorption of hydrogen from alloy M~. at high temperature Th and absorption by alloy M~ where heat is released at intermediate temperature Tm. In Process II, hydrogen is released by M,H in absorbing heat at low temperature T~, thus providing the refrigerating effect. Simultaneously, heat of hydride formation is released by alloy Mb at Tin. The cycle is completed by Process III, where low-temperature heat is taken in to release hydrogen from MbH. Simultaneous formation of McH delivers heat at Tin. It may be observed that heat addition at high temperature (Q,) occurs once in a cycle, whereas low-temperature heat absorption, i.e. the cooling effect (QH, Q~.2) occurs twice. Intermediate-temperature heat rejection (Qm,~, Qm.2 and Qn,.3) takes place three times in a cycle. 731

732

S. SRINIVASA MURTHY and M. V. C. SASTRI

QI,2

Qm,2 Process l

Process I l l

P r o c e s s II

l

.I

T

I

I

I

P P2

p 3

l

h

m

I

I

lIT Fig. 1. Schematic of the two-stage ternary metal hydride heat pump.

ASSUMPTIONS To make the analysis tractable for solution the following assumptions are made. (a) The heat exchangers are 100% effective. (b) The heat conducted through the insulated walls of the heat and mass exchanger to or from the surroundings is negligible. (c) Hydrogen absorption and desorption processes are perfect. (d) The plateau pressures for hydrogen desorption are valid for absorption also. The hysteresis effect is negligible. (e) The performance factors are defined as the ratio of heat outputs to the heat inputs in one cycle, as these heat exchanges are intermittent in a single element of the system. (f) The mass ratio of the heat and mass exchanger to the metal alloy (X/M) is taken to be 0.5. (g) The heat and mass exchanger is assumed to be made of stainless steel and aluminium. The specific heat value of the heat and mass exchanger is derived by assuming 1:1 proportion by weight of stainless steel and aluminium. (h) The pressure drop of hydrogen gas in flowing from one container to the other is 0.1 bar.

We also assume that the following temperature ranges are valid for the definition of performance factors: Temperatures below 25°C. Heat absorption by the system is considered as a useful refrigerating effect, while heat rejection is accomplished by external refrigeration and hence becomes an input into the system. Temperatures between 25°C and 45°C. Heat rejection is to the ambient sink and is considered as useless. Heat absorption is from the ambient source and hence is taken to be freely available. Temperatures above 45 °C. Heat absorption is considered as input energy expended. Heat rejection is sought as the useful output.

ANALYSIS The various heat quantities are written as follows: Qh = mahc = Qm,a

(1)

Ql,l

(2)

Qm,2 = muhb = Qi,2.

(3)

Qm,I = mnha =

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ANALYSIS OF METAL HYDRIDE HEAT PUMPS The sensible heat exchanges for bringing out a change in temperature of the heat and mass exchanger are: Qs,, = ( m , . , C v + m . C , ) (Tin - Tj)

(4)

Qs,b = (m,,bCv + mbCb) (Tin - Z)

(5)

Qs., = (mv.cC, + m¢C¢) (Th - Tin).

(6)

C a s e (ii) t m - 45°C. In addition to Qo,i, Qo.mbecomes another useful output of the system in this range of temperature. Therefore, C O P = (Qo.i = =

(7)

Q.,2 = m n C .

(8)

(Th -- Tin)

Qrt.3 = an, i.

Qi,, = Qh =

(16)

(9)

Energy input from the high temperature heat source is given by: (10)

Q~x.

Energy outputs, i.e. cooling and heating effects are calculated from: Qo., = Ql,I + QI.2 - (Qs.a + Os,b)

(11)

ao,m = Qm.I + Qm,2 + Qm.3 + Qn.I + Q~x - (Qs.a + Q~,b - Qn,2 - QH,3). (12) For calculation of performance factors, T~ is taken to be always below 298 K (25°C) and therefore Qo.~ will be a useful cooling effect. However, the two following cases can occur for the heating effect: C a s e (i) 25°C
(13)

e = Qo., (TdT~ - 1)/Q~,h (1 - TdTh).

(14)

1)

+ Qo.m (1 - T, ITm)]IQ~.h (1 - T / T , ) .

Heat quantities spent in sensible cooling/heating of hydrogen gas are: Qn.J = m n C n (Tin - Ti)

[ Q o , , ( T , IT~ -

(15)

Qo.m)/ai,h

RESULTS AND DISCUSSION Table 1 lists the properties of the eight metal alloys considered in this study. Table 2 gives the designation of the five alloy combinations studied in this paper. The intermediate temperature Tin, which is the heat delivery temperature, is taken as the independent variable. The upper limit of T,, was curtailed when the value of TI exceeded 25°C. The temperatures T~ and T, are fixed by the Van't Hoff relations for the metal alloys. The reference temperature for calculating the exergetic efficiency is taken to be 35°C. The results of the analysis are shown in Fig. 2. Combination (3) yields high performance, but cannot provide low temperature refrigeration. It consumes and also delivers heat at lower temperature levels than other systems. Combination (5) covers a wide dual-effect range, although at the expense of high source temperatures. Figure 2 can also be used as a nomogram to predict the performance of the system. For the example shown, in order to deliver heat at 50°C, combination (2) requires a heat source at about 185°C. It also provides refrigeration at - 2 ° C . The overall C O P and second law efficiencies are about 2.4 and 0.53, respectively. Table 3 reveals that, under similar heat delivery and refrigeration temperatures, two-stage ternary heat pumps yield higher C O P values compared to single-stage systems, but demand higher heat source temperatures. However, there is no visible difference in second law efficiency between the two systems.

Table 1. Properties of selected metal hydrides

Number

Nominal composition

1 2 3 4 5 6 7 8

MNi5 MNi4.sFeo 85 MNi45AI05 FeTi Feo.9Mno.~Ti LaNi5 LaNi4.TAl0.3 CaNi5

Heat of formation (kJ mol- ~ of H2)

Van't Hoff's coefficients

Hydrogen capacity

A(K)

B

H/M

wt%

Specific heat capacity (kJ kg -I K -I)

20.93 25.12 28.05 28.05 29.31 30.98 33.91 31.82

-2539 -3041 - 3366 -3383 - 3545 -3712 -4090 -3838

11.64 12.60 12.61 12.76 12.87 12.96 12.84 12.17

1.01 0.82 0.83 0.90 0.92 1.02 0.95 0.71

1.41 1.15 1.20 1.75 1.79 1.43 1.36 1.39

0.419 0.419 0.419 0.544 0.544 0.419 0.419 0.540

734

S. SRINIVASA MUKTHY and M. V. C. SASTRI Table 2. Designation of alloy combinations studied Alloy combination (low temperature - low temperature - high temperature)

Designation

MNi4.15Feo.85 - Feo.9Mno. iTi - LaNi4,TAlo.3 Mni5 - FeTi - CaNi5 MNi5 - MNi4 15Feo.85- MNi4.sA10.5 MNi4 15Feo.85- Feo.9Mno. iTi - CaNi5 MNi5 - LaNi5 - Feo.aMn0.2Ti

Table 3. Comparison of performances of single- and two-stage systems

Parameter 1. 2. 3. 4. 5.

COP Second law efficiency (0 Cooling temperature (TI), °C Heat source temperature (Th), °C Heat supply temperature (Tin), °C

Single -stage (two-alloy system)

Two-stage (ternary system)

1.6-2.3 0.6-0.85 - 10-25 70-130 45 - 65

2-3.2 0.5-0,8 - 10-25 100-200 45 - 80

5

24( - J

,/

5

f

oU

..~20( -

--" 1 6 0 u L.. -1 0

in 1 2 0 -

/3

3/

I

I

80

I

I

I --1.0 --3

3 -

--4

I

-0.8

3 ~"

£ CL o 2 (J

-0.6

2" -0.4

0

! 0 0 Refrigeration

I I 10 20 t e m p . , t t (°C)

I

I

30 50 70 90 Heat delivery temp.,t m (°C)

Fig. 2. Performance of the two-stage ternary metal hydride heat pump.

ANALYSIS OF METAL HYDRIDE HEAT PUMPS CONCLUSIONS

735

the project on the development of metal hydride heat pumps and heat transformers, under which this work was carried out.

Two-stage ternary metal hydride heat pumps yield better

COPs than single-stage systems operating between similar temperature levels. Combination (3) yields the best performance, but it provides only limited operating range and temperature lifts. Even though combination (5) needs a high temperature heat source, it offers a wide range of heat output temperature, with additional possibilities of refrigeration output.

Acknowledgements--Thanks are due to the Department of Nonconventional Energy Sources, Government of India, for funding

REFERENCES 1. S. Suda, Recent development of hydride energy systems in Japan. Hydrogen Energy Progress V, Vol. 4, pp. 1201-1211 (1984). 2. E. Orgaz and P. Dantzer, Thermodynamics of the hydride chemical heat pump: III. Consideration for multistage operation. J. Less-Common Metals 131, 385-398 (1987). 3. S. Srinivasa Murthy, M. V. Krishna Murthy and M. V. C. Sastri, Two-stage metal hydride heat transformers: a thermodynamic study. Hydrogen Energy Progress VII, Vol. 2, pp. 1253-1265 (1988).