A heat storage reactor for metal hydrides

Journal

of the Less-Common

A HEAT

STORAGE

S. WAKAO

and M. SEKINE

Tokai

University,

H. END0 National

Metals,

89 (1983)

REACTOR

Hiratsuka

Kanagawa

341

FOR METAL

259-l

341

- 350

HYDRIDES*

2 (Japan)

and T. IT0 Aerospace

Laboratory,

Chofu,

Tokyo

182

(Japan)

H. KANAZAWA Kawasaki

Heavy

(Received

May 24,1982)

Industries

Ltd.,

Noda

Chiba 278

(Japan)

Summary A reactor for a metal hydride heat storage system is required to have good heat transfer properties and as small a heat capacity as possible because the heat produced during the metal-hydrogen reaction is finite and its loss must be minimized. However, few theoretical studies of heat storage reactors that use finite quantities of heat have been made. The transfer of the heat of reaction in the reactor was studied theoretically and experimentally in this work and the results are summarized. The theoretical and experimental results agreed relatively well, so that the application of the fundamental concept proposed in this paper to the design of heat storage reactors using metal hydrides which produce finite quantities of heat is justified.

1. Introduction A heat storage reactor for metal hydrides is simultaneously a pressure vessel and a heat exchanger. However, its design is fundamentally different from that of an ordinary heat exchanger which is intended for an almost infinite quantity of heat because the amount of heat stored by the metal hydrides is finite depending on the heat lAIY,I of formation and the operating conditions of the heat storage reactor. One of the fundamental factors in the construction of a heat storage reactor is the selection of a metal hydride with characteristics appropriate for the operating conditions. A second important factor is a structural design which ensures low heat capacity and high heat transfer. A theoretical concept which could serve as a basis for the design of a heat storage reactor is proposed in this paper and representative experimental results are reported. *Paper presented at the International of Metal Hydrides, Toba, Japan, May 30 0022-5088/83/0000-0000/$02.75

Symposium

on the Properties

and Applications

- June 4, 1982. @ Elsevier Sequoia/Printed

in The Netherlands

342

2. Theory

The heat of the metal-hydrogen reaction, e.g. the heat of the exothermic reaction, is transferred to the heat exchange fluid and is also consumed in the temperature increase of the metal hydride itself, the hydrogen and the heat storage reactor. In addition to conduction losses, there will generally be heat losses by convection and radiation. Because the rate of the reaction of the metal hydride with hydrogen varies with temperature, it is possible that the reaction zone will start at a specific point in the metal hydride in the heat storage reactor and will move with time [ 11. Moreover, as is already known, the thermal conductivity of the metal hydride decreases as it absorbs hydrogen. 2.1. Constant heat transfer characteristics The first step in the derivation of a fundamental description is to consider the case where the overall heat transfer coefficient f between the metal hydride and the heat exchange fluid remains constant throughout the reaction in order to determine expressions for each physical quantity. If the calorific value of the metal hydride per unit time is q under reaction conditions where the flow rates of hydrogen and water are constant, the heat balance in the reactor can be approximately expressed by the following equations: q=wC,AT+MCRdt

dT,

q = wCp AT”

(2)

where q is the calorific value of the metal hydride per unit time, MCR is the sum of the heat capacities of all the substances (except water) that increase in temperature (mainly the metal hydride and the heat storage reactor), T, is the average temperature of all the substances (except water) that increase in temperature (mainly the metal hydride and heat storage reactor), w is the flow rate of the water, CP is the specific heat of water, AT is the difference between the outlet water temperature Tf, and the inlet water temperature Tt, and AT” is the difference between the outlet and iniet water temperatures when all q has been transferred to the water. If the logarithmic mean temperature difference between the metal hydride layer and the fluid is AT,,, AT=AT,-

fS

=

T, - $ (Tfl + Tf,)

WCP

where S is the area of the heating surface. Therefore Tm=Tf,+(;

+ $AT=TfI+iiaT

(3)

343

Since f is constant, the value of fl in eqn. (4) is also constant. following equation can be derived from eqns. (l), (2) and (4): wC~AT~=OC~AT+MC~~~--The solution

WT )

(5)

dt

(6)

St)/

AT” can be expressed in terms of the hydrogen enthalpy I AHfi of hydride formation:

flow rate

VH, and the

1AH,1 VH, (7)

22.4wCP

The reaction r=

the

of eqn. (5) gives

AT=ATO/l--exp(-

AT” =

Therefore

time r is given by

11.2 A([H] /[M])mn (8) % before where NW1 /WI) is the difference in the hydrogen concentrations and after the reaction expressed as the atomic ratio, m is the number of moles of the metal hydride and IZ is the number of atoms of the metal hydride in the composition formula. If the ratio of the total calorific value of the metal hydride to the quantity of heat acquired by the water, i.e. the thermal efficiency q of the reactor, is 7

JAT dt .n= O r AT”

(9)

It is clear from eqns. (6) and (9) that it is important to make the heat capacity MCR of the heat storage reactor including the metal hydride small and fS large. If hydrogen is applied to the metal hydride at a constant rate in actual operation, the initial response rate, i.e. the rate ATtitiai of temperature increase of the heat exchange fluid can be expressed as follows using eqn. (6): ATmithi = AT”-

WCP

(16)

MCRP Therefore

the ratio y of the time constant

to to the reaction

time r will be (11)

2.2. Variable heat transfer characteristics The overall heat transfer coefficient f generally changes reaction. The case where /3 changes linearly with time is expressed

during by

the

344

p =

po+ bt

(12)

where PO is the value of /3 at the start of the reaction and b is a constant coefficient. From eqns. (4) and (12),

d(AT)

dTm =bAT+p-

-

dt

(13)

dt

Therefore from eqns. (l), (2) and (13) d(AT) MCR (PO+ bt) dt

+ (oCp + M&b)

AT - wCp AT” = 0

(14)

Solution of eqn. (14) gives AT=

1

(15)

1 + M&b/w&

By approximation from eqn. (15) AT=

1

wCp + M&b

1 + hfCRb/WCp

= AToc

WCP

-

~

MCR&

AT’,

1

=

t

MCR&I

1 + MCR b/WCp

t)exP(-$ t)l

AT” = ;

(16)

AT”

(17)

If the coefficient b is small, ATo, = AT” and eqns. (16) and (6) agree. Equation (16) implies that AT will not reach AT” within a suitable reaction time but will gradually converge to AT’, (Fig. 1). From eqn. (16) the thermal efficiency vc is given by 1 ” = 1+ MCRb/wCp =

$

M&PO

lT(Wcp

+

MCRb)

(Wcp

+

MC,b)7

MCR@O

1-z\l-exp(-%I/] [

From eqn. (16) the initial response speed, i.e. the rate A!&,,, ture increase of the fluid will be

of tempera-

WCP

ATtitti, = AT’,-

(1%

MCRPO

which is the same result as obtained when fi is constant (eqn. (10)). The ratio yc of the time constant t”, to the reaction time r is G yc=-= 7

MCRPO

1

--=sy wcpr

6

1

(20)

345

t

7

Fig. 1. Theoretical

variation

of AT with time.

3. Experimental

results and discussion

We have conducted experiments using heat storage reactors with various structures and we report the results for a typical example here. Schematic drawings of the heat storage reactor (KHI type) and of the experimental arrangement are shown in Figs. 2 and 3 respectively. 5.46 kg of the metal hydride TiFe,,Mn,, ( IAHNfIab = 5.8 kcal (mol Hz)-‘) was used in the experiment. Its characteristic pressure-compositiontemperature curve is shown in Fig. 4. The hydrogen tank has a capacity of 380.6 1. In this experiment the mass flow of hydrogen and the flow of the heat exchange fluid (water) were constant and hydrogen was applied to the metal hydride for a specific time.

Filter Box

Fig. 2. Schematic

drawing

of the KHI reactor.

346 P Pressure T Temperature

I 0

filter

NI

02

04

06

Atom ratio

06

IO

wb$

Fig. 3. Schematic drawing of the flow diagram. Fig. 4. Isothermal pressure-composition the experiment.

relations for the TiFeo.9Mno.l hydride used in

Figure 5 shows an example of the time dependence of the pressure Pn in the heat storage reactor and the temperature difference AZ’ between the2 fluid outlet and the fluid inlet. The full curve in the diagram represents the pressure variation in the heat storage reactor and the broken line represents the variation in the equilibrium pressure obtained from the

Fig. 5. Variation in PH2 and AT with time.

347

relationship between the hydrogen content and the average temperature of the metal hydride for each period of time. The volume (VHJwp of hydrogen introduced into the heat storage reactor is the sum of the volume VH, of hydrogen that actually reacts with the metal hydride and the volume of hydrogen that is used to fill the dead space in the heat storage reactor. It is clear from the diagram that the temperature difference AT between the fluid outlet and the fluid inlet is constant in the middle of the reaction period because the linear increase in the pressure in the heat storage reactor makes the volume VH, of hydrogen reacting with the metal hydride constant, i.e. the quantity of heat produced in the reaction is constant. In the later part of the reaction period, however, the pressure in the heat storage reactor increases rapidly because both VH, and AT decrease. However, because the pressure again increases linearly later, AT again becomes constant at a decreased level. This is due to the effect of the dead space in the heat storage reactor. This effect decreases in direct proportion to the volume. The separation between the full and the broken curves in the diagram represents the pressure that must be applied to maintain a constant hydrogen flow reaction for each hydrogen composition. However, this pressure varies with the reaction conditions. The following equation for the initial stage of the reaction can be obtained from eqn. (16): ln[l---$$--=--St

(21)

The relationship between ln( 1 - AT”/AT”c) and t is linear, and MC&, can be obtained experimentally from its gradient. The result is shown in Fig. 6. MC&, is almost constant when the fluid flow w is below a specific value. The relationship between the overall heat transfer coefficient f. and the fluid flow rate w at the onset of the experiment obtained by substituting our experimental results in eqn. (3) is shown in Fig. 7. If the metal hydride layer and the heat exchange surface are represented by a plane plate model the variation in f can be expressed by _=

1

1 _+L

f

h

O

(22)

km

0.4

0.2 W

Fig. 6. Relationship

0.6

lKg/min)

between

MCRPo

and w.

Fig. 7. Relationship between fO and w at the onset of the experiment.

where h is the heat transfer coefficient in the film, r is the thickness of the metal hydride layer and k, is the thermal conductivity of the metal hydride layer. k, was found to have values of 3.4 - 3.7 kcal m-l h-i “C-l (an average value of 3.5 kcal rn-’ h-’ “C-‘). The value of MCa for the heat storage reactor used in the experiment was calculated from the value of &, obtained from MC&, and f0 (Fig. 8(a)) to be 0.89 - 1.38 kcal “C-l (Fig. 8(b)) and was dependent on w. The value of MCR calculated from the theory developed in Section 2 is approximately 0.8 kcal ‘C-l, i.e. the theoretical and experimental values agree well in the range where o is large. Figure 9 shows the experimental results for the performance of the heat storage reactor. The bold full curves in the diagram represent the range where a steady value of AT’, can be obtained, and the bold broken curves represent the range where AT varies during the time 7 when the metal hydride reacts with the hydrogen. It was also found that qc and l/ye increase at low values of AT” C9 thereby producing a steady heat with high thermal efficiency.

/k--_~ 0

qy,,;,

0.2 (,J

(6)

0.4

0.6

02

0.4 &J

(Kg/min) lb)

Fig. 8. Relationships between (a) DOand o and (b) MC, and w.

(Kglmin)

0.6

349

(hr) 2013 5

3

7

1.5

I

VHZ (NP/min Fig. 9. Experimental

results

0*75

1

1

for a KHI-type

reactor.

4. Conclusion The heat storage reactor used in the experiment had a structure which gave an excellent response with a very small ratio MCR/mn of the heat capacity of the equipment including the metal hydride to the weight of the metal hydride, i.e. about 0.2 kcal kg-’ “C-’ (0.01 kcal (kg atom hydride)-’ “C-‘). It was designed solely for experimental purposes and there is room for improvement regarding the values of fS and the dead space, A similar experiment was conducted on a structure in which the metal hydride was kept in a copper tube and the fluid flow was outside the tube. This heat storage reactor had a rather larger heat capacity and the rate of increase of the temperature of the fluid in the initial stage was slightly lower than that of the heat storage reactor discussed in detail in this paper but its AT”, value was higher because fS was larger. As stated above, the theoretical and experimental values agree relatively well so that the fundamental concept developed here can be applied to designing heat storage reactors using metal hydrides with finite quantites of heat. This concept indicates the route which should be followed in the development of a similar heat storage reactor.

350

The theory and experimental investigation have been discussed only briefly because of limitations on space and will be described in more detail elsewhere together with further consideration of the parameter 6.

Reference 1 S. Wakao, Kanazawa,

H. Endo, H. Takahashi, T. Ito, H. Sekine, H. Shimada, Tech. Rep. 11,1980, p. 55 (Tokai University, Tokyo).

M. Sekine

and H.