Hydrogen separation and the direct high-temperature splitting of water

0360-3199/86 $3.09 + 0.00 Pergamon Press Ltd, © 1986 International Association for Hydrogen Energy.

Int. J. Hydrogen Energy, Vol. 11. No. 2, pp. 91-100, 1986. Printed in Great Britain.

H Y D R O G E N SEPARATION A N D THE DIRECT H I G H - T E M P E R A T U R E SPLITTING OF W A T E R J. W. WARNER and R. STEPHEN BERRY Department of Chemistry and the James Franck Institute, The University of Chicago, Chicago, IL 60637, U.S.A. (Received for publication 15 July 1985)

Abstract--The thermodynamics of several approaches to generating and separating hydrogen by direct thermal splitting of water is examined, and the major energy consuming step for each is evaluated. In all, 11 cases are studied, including gas quenching, injection quenching, high-temperature separation and catalytic reaction. It is shown that some of these processes will not break even with respect to energy consumption. The most effective separation st;ategies have overall process efficiencies in the range 0.1-6%.

1.

Some reactor configurations might not break even in terms of fuel energy generated per unit of energy consumed. The purpose of the present work is to examine strategies for the least understood part of the direct-splitting process, the quenching of the effluent from the reactor, and then integrate favorable strategies into complete hydrogen generating systems. In a sense, this work is a natural extension of the engineering analyses of Bilgen [4] and of its predecessors [7-11]. Section 2 gives expressions for efficiency and work consumption that we have employed, and also provides the description of the water kinetics that we have used. Gas quenching is examined in Section 3. It is shown that, due to the large quantity of coolant required, several strategies will not break even, or will have only marginal efficiency. Injection quenching is examined in Section 4. This approach is potentially very effective, because most of the separation work is done by gravity. In Section 5, we briefly reexamine high-temperature separation within the context of the present formulation. It is not always appreciated that if the separation work is done with electricity, the device cannot break even. In Section 6, we examine the catalytic directsplitting reactor, which can be operated at lower temperatures than the uncatalyzed processors. The catalytic reactor has a number of appealing features, including the possibility of membrane separation of the hydrogen. Its main drawback is the low degree of conversion to hydrogen inherent in the operation of the reactor.

INTRODUCTION

Several research groups have built small-scale solar reactors for hydrogen production by direct high-temperature water splitting. Led6 et al. [1] quenched the hot effluent with streams of argon gas and steam and verified hydrogen production by gas chromatography. Diver et al. [2] verified hydrogen production by igniting the effluent. Bilgen et al. [3] employed mass spectrometry to show the presence of hydrogen in the effluent from their reactor. The work of these groups demonstrates that solar direct splitting of water can be accomplished in a reactor constructed with currently available materials. However generation of hydrogen is only one component of a system that can supply Hz. A major problem remains in separating the hydrogen. Bilgen [4] has shown that high-temperature separation may be efficient, but no currently known materials are available for this process. Ihara [5] has discussed the materials problem for membrane separations. Membranes decompose rapidly at high temperature in the presence of water. Another approach is to perform the separation at low temperatures with known materials, after cooling the effluent so rapidly that recombination of products is prevented. Led6 et al. [1] employed a cooling rate of 106-107 degrees s -1, and recovered hydrogen from the mixture. This quenching rate is very high in comparison with most industrial processes. (One exception is the fast quenching employed in the production of some metallic glasses [6], but for metallic glasses energy efficiency is not so important a consideration as it is for fuel production.) In a conventional quenching process, most of all of the thermal energy of the effluent is lost. At 2500K, hydrogen constitutes only 4% mole fraction of the equilibrated reaction mixture produced from pure water. Hence heating water and quenching the hot reacted mixture is inevitably an inefficient process. Besides the cyclic heating and cooling of the 96% of the mixture that is only ballast, other losses may be associated with handling and recycling the coolant.

2. 2.1

FORMULATION

Criteria o f performance

When reporting the efficiency of a fuel-producing solar device, it is important to maintain a separation between two types of energy input. Heat delivered to the reactor as solar energy may be considered almost free, apart from capital costs. On the other hand, energy for driving pumps and compressors for, say, membrane 91

92

J. W. WARNER AND R. STEPHEN BERRY

separation, would probably be delivered as electricity. If the energy consumption of the nonsolar components of a fuel-supplying system exceeds the energy of the fuel produced, the process is a net energy loser and is very unlikely to be worth pursuing. As a suitable definition of the process efficiency which accounts for this, we take AH(H2)-eex el

Es

-

AH(Hz) (lb)

where e, and e,x are the efficiencies of delivery of solar heat and the electric power source, respectively. We will always take E,~ to be the mechanical work done on the system. The efficiency with which solar energy is delivered to the reactor will be incorporated in the expressions discussed in the conclusion. In Sections 35, the reported results correspond to 100% efficiency for the solar energy delivery. Our method throughout will be to identify major contributions to E~x and Es, in an attempt to identify satisfactory reactor configurations. Among the contributions to Eex, we will be concerned with only a few types of work: Separation work w =

nRT

Yxi In xi.

(2)

Isothermal compression work w=

nRT V2 In - - . r/ V1

(3)

Adiabatic compression work w = nCv (T2 - T1).

7/

(4)

Gravitational work mgh w =

r/

H+H+M H+O+M H+OH H+OH+M H+H20 H+O2 H2 + O 2 20+M O + HzO

(la)

In equation (la), AH(H2) is the enthalpy of combustion of hydrogen, 57.8 kcal mo1-1. Eex is the energy input for nonsolar devices, per mole of hydrogen produced and Es is the solar energy input. The numerator of equation (la) is the net energy delivered by the process, so that the definition of e reduces to the net fuel energy delivered divided by the solar energy required. It can be negative if the process consumes more nonsolar energy than it delivers. One other measure of performance will be used in the concluding discussion. This is

e2 = Es/e, +Eex/eex

Table 1. Chemical reactions for the kinetic simulations. M is any species

(5)

In equations (2)-(5) the factor r/ accounts for the efficiency when the process is carried out irreversibly. We follow previous approaches [4] and assume that all

~ ~ ~ ~ ~.~ ~ ~.~ ~

H2+M OH+M H2+O H20+M Hz+OH O+OH 2OH O2+M 2OH

work is done at 50% of reversible efficiency, so that r/= 0.5. 2.2

Kinetic model

The kinetics of the water-splitting reaction may be very thoroughly described with a compilation of data by Oran et al. [13] for 43 half-reactions involving eight species. Analysis of the equilibrium composition at high temperatures shows that the concentrations of HO2 and 1-1202are always many orders of magnitude smaller than those of the other species. We have, therefore, excluded these two species from the kinetics. Table 1 gives the list of chemical reactions, involving six species, that have been employed in the kinetic simulations. It should be noted that the equilibrium results from the kinetic data differ by up to 5% from the values obtained with purely thermodynamic data [12, 14] so this 5% is the measure of inconsistency in the data, and is not a large amount compared with other uncertainties in this work, such as the uncertainty of the efficiency of mechanical work. We assume that the reactor operates at 2500 K, which is probably close to the current material limitation [4]. At this temperature, hydrogen makes up 4% mole fraction of the reaction mixture. Higher temperature reactors will be discussed in Section 7. We further assume that the effluent is delivered at 1 atm pressure, with no carrier gas. Although an inert carrier gas can increase the degree of splitting [14], it will be seen in the next section the additional separation work that would be required would be expected to prevent a reactant-plus-inert-carrier system from breaking even. At i atm and 2500 K the heat of reaction is 81 kcal mol -x Hz [12], and exceeds the 57.8 kcal mo1-1 H2 enthalpy of combustion of H2 because some of the molecular species are split to atomic form. The total heat needed to raise water from room temperature to 2500 K and react is 912 kcal mo1-1 [12]. 3.

GAS Q U E N C H I N G

In this section we examine several strategies for gas quenching of the effluent, assuming the coolant is either steam or argon [1]. We begin with an elementary heat recovery configuration, and develop from this a

H Y D R O G E N SEPARATION AND THE DIRECT HIGH-TEMPERATURE SPLITTING OF WATER

93

Table 2. Thermodynamic and kinetic data for gas quenching to several final temperatures. Columns (2) and (3) give the amounts of steam and argon, respectively, needed to bring the effluent to the final temperature of column (1). The injection temperature of the steam is 375 K, and of argon is 225 K. Column (4) gives the percent of H2 that is recovered after 30 s, and column (5) gives the depletion rate of the hydrogen, averaged over the first 10 s at the quench temperature

Final Temperature (K)

Moles steam per mole H2

Moles argon per mole H E

Percent of H2 recovered at 30 s (steam)

2654 527 278 182 131 99

652 400 282 213 168 136

100 100 52 5.9 1.7 0.86

400 500 600 700 800 900

Depletion rate 1 A[H:] [H2] At (steam) (s -1) 1.0 6.9 2.3 8.9 9.7 9.9

Section 6). T a b l e 3 indicates t h a t , for a q u e n c h e d t e m p e r a t u r e of 600 K or higher, at least half of t h e h y d r o g e n is lost within 30s. H o w e v e r , q u e n c h e d to 500 K t h e p r o d u c t s are m o r e dilute a n d c o m p l e t e hydrogen r e c o v e r y is possible. T h e h y d r o g e n d e p l e t i o n rate at 500 K is a few p e r c e n t every 100 s. In this section, t h e n , we assume t h a t t h e effluent is b r o u g h t to 500 K by the c o o l a n t gas, a n d t h a t all t h e h y d r o g e n in t h e q u e n c h e d gas is r e c o v e r e d . F o r s t e a m q u e n c h i n g , t h e h e a t b a l a n c e indicates t h a t 527 moles of s t e a m m u s t b e c o m b i n e d with 25 moles of effluent in o r d e r to p r o d u c e 1 mole of h y d r o g e n . F o r argon, 400 moles m u s t b e used for each mole of hydrogen. T h e mixing m u s t b e fast, so t h a t t h e effluent is cooled in 1 ms or less [1]. In o r d e r to achieve this rapid 4 0 : 1 mixing of the c o o l a n t a n d t h e r e a c t i o n mixture, we assume t h a t t h e c o o l a n t is i n j e c t e d t h r o u g h a conv e r g e n t , critical nozzle, sonic at t h e t h r o a t . This gives

Table 3. Bubble composition vs time: initial radius is 0.7 cm; composition in moles a~oH= 1

0 1 2 3 4 5 10 20 30 40 50 60 70

10 -5 10 -5 10 -2 10 2 10 -2 10 -2

infra,

s e q u e n c e of r e a c t o r configurations, each of which a t t e m p t s to r e d u c e or e l i m i n a t e some energy intensive step t h a t has previously b e e n identified. It is first n e c e s s a r y to decide t h e final t e m p e r a t u r e of the q u e n c h e d mixture. Cooling a n d dilution are the two principal effects i m p o r t a n t to p r e v e n t i n g r e c o m b i n a t i o n of products. T a b l e 2 gives the q u a n t i t y of coolant r e q u i r e d to r e a c h several final t e m p e r a t u r e s , as well as t h e results of kinetic analyses o n t h e a m o u n t s of recovery a n d d e p l e t i o n r a t e s of t h e h y d r o g e n at each temp e r a t u r e . T h e i n j e c t i o n t e m p e r a t u r e for the a r g o n will be e x p l a i n e d below. In p r e p a r i n g T a b l e 2, we h a v e a s s u m e d t h a t gas q u e n c h i n g r e q u i r e s of t h e o r d e r of 30 s to m o v e the m i x t u r e f r o m t h e q u e n c h i n g c h a m b e r to a h e a t e x c h a n g e r a n d achieve final cooling. F o r e x a m p l e , a 600 K m i x t u r e will b e cooled to 4 0 0 K in a h e a t e x c h a n g e with boiling w a t e r in 30 s, if t h e e x c h a n g e r has a surface a r e a of a b o u t 5 m 2 p e r mole of fluid (vide

Time

× × x x × ×

x 109;

time in s × 1(I6 and

H

H2

O

02

OH

H20

radius (cm)

(K)

36.3 52.7 76.7 80.8 66.4 46.4 3.52 4.26 x 10 -1 1.84 × 10-1 1.11 × 10 -1 7.78 x 10 -2 5.93 x 10-2 4.77 x 10 -5

279 249 208 184 183 191 211 213 213 213 213 213 213

12.3 12.1 10.0 5.37 1.86 3.58 × 10 -1 6.15 × 10-5 5.55 × 10 -7 1.14 × 10 -7 4.76 × 10-8 2.69 x 10 -8 1.81 x 10 -8 1.36 × 10-8

102 91.2 82.1 76.4 74.4 74.1 74.0 74.0 74.0 74.0 74.0 74.0 74.0

161 78.9 24.7 4.29 5.57 x 10-~ 6.85 x 10 -2 4.98 x 10 _6 3.12 x 10-8 5.58 × 10 _9 2.15 × 10-9 1.17 × 10-9 7.65 x 10 -~° 5.61 x 10 -1°

6410 4170 3030 2180 1520 1030 166 38 23 17.9 15.5 14.1 13.2

0.7 0.564 0.457 0.373 0.309 0.259 0.153 0.129 0.125 0.123 0.122 0.121 0.121

2500 1970 1419 1049 812 660 405 337 319 310 306 303 301

T

94

J.W. WARNER AND R. STEPHEN BERRY

the most rapid coolant flow. The critical pressure is given by [15]

Pc=

( 2_~_._]vl'-I

Pl

\V+ 17

(6)

where 7 is the heat capacity ratio, and pl is the backup pressure. The temperature drop due to expansion of the coolant is [15]

T! = (Pc] V-Vr T1

\P-7/

y+l

(7)

where T~ is the temperature in the nozzle and T2 is the temperature of the coolant when it meets the effluent, at the face of the nozzle. For steam, 7"2 can be no less than 375 K, without danger of wetting the nozzle. Argon may have T 1 at room temperature, which gives T2 = 225 K. We assume that the mixing occurs at 1 atm, so that no pumping work is needed after mixing. There are two ways to achieve the backup pressure in the nozzle: (1) compress the coolant, which contributes to E~x, or (2) vaporize the steam in a restricted volume cavity with heat, contribution only to Es. Our first quenching strategy employs the former approach.

Case (1) The separation for the first case is done as follows: (a) The effluent is quenched with steam to 500 K. (b) H2 and 02 are separated at this temperature. (c) A portion of the steam (23.3 moles/mole H2) is then split off and heated to 2500 K to feed the reaction mixture. One mole of water at 300 K is added to this to make up the portion reacted. (d) The steam is then recompressed adiabatically for recombination. From equation (2) the separation work of step (b) is 21.1 kcal tool -1 H2 for the 552 mole mixture. The heat required for step (c) is 625 kcal mo1-1 Hz. The compression work for step (d), from equations (4) and (6) is 645 kcal mo1-1 Ha. In terms of the variables in equation (1), step (c) is the only contribution to E,. The work Eex is that for steps (b) and (d). The efficiency is then -0.97. It is negative, indicating that the process does not break even, due to the large work input for step (d). For the present, negative efficiencies are acceptable because, as mentioned above, they become positive if the electricity is supplied with solar energy, as will be treated in Section 7. However, with the understanding that photovoltaic electricity may be expensive, it is desirable to construct a separation strategy which avoids a large work input. Case (2) circumvents the work input of step (d) above by pressurizing the steam in the phase transition with heat.

Case (2) Steps (a), (b) and (c) are the same as for case (1). Step (d) is modified as follows. The steam remaining

after step (c) is heat exchanged with a new working fluid at 375 K. Additional heat is added to vaporize the new coolant in a fixed volume, so that pressurization occurs simultaneously. The old coolant is condensed and held at 375 K to become the input for this step. About 1 kcal mo1-1 H 2 0 is recovered in the heat exchanger. The enthalpy of vaporization of water is nearly independent of pressure at 9.7 × 103 cal tool < H20, so that 8.7 x 103cal tool -1 H 2 0 or 4.59 × 103 kcal mo1-1 H2 of heat is required for step (d). The efficiency is then 7.0 × 10 -3. The reactor breaks even, but the efficiency is low, due in part to the large work of separation. In the next strategy this term is reduced by condensing the steam prior to separation.

Case (3) This case begins with step (a) of case (1), but then is followed by step (c); 4% of the hydrogen is lost when the unseparated steam is fed back into the reactor. Then the heat exchange of case (2), step (d) is carried out. When the old coolant is condensed, the hydrogen and oxygen bubble out. Since gravity separates the water, the separation work is greatly reduced, to 1.1 kcal mol -l He, needed to separate the hydrogen from the oxygen. The efficiency is then 1.0 x 10 -2. Case (3) is the most efficient steam quenching strategy we will consider. The major loss arises from the large amount of heat needed to produce the steam coolant. Argon coolant avoids the limitation of case (3) because no preheating of the coolant is necessary. Case (4) examines this approach. Because the coolant must be recycled, this is similar to case (1).

Case (4) Conditions for case (4) are as follows: (a) The coolant is argon; the temperature of the argon is 225K after adiabatic expansion from room temperature. (b) The mixture is separated at 500 K, and the steam is fed back into the reactor. (c) The argon is cooled to room temperature and compressed isothermally for recycling. Again, 625 kcal mo1-1 H2 are required for heating to 2500 K. The separation work of step (b) is large, 209 kcal mo1-1 H2, because the steam as well as the hydrogen and oxygen must be separated from the argon. The compression work for the argon is 345 kcal tool -l H2. The efficiency is -0.79. The approach of case (5) reduces the work.

Case (5) (a) The first step is the same as for case (4). (b) The mixture is cooled to room temperature in a heat exchanger which heats more water. (c) The water in the quenched mixture condenses. The hydrogen and oxygen are separated from the argon.

HYDROGEN SEPARATION AND THE DIRECT HIGH-TEMPERATURE SPLITTING OF WATER (d) The argon is compressed isothermally. For efficient multipass flow, about 220 kcal mo1-1 H2 can be recovered in the heat exchanger. This is to be subtracted from the 912 kcal mo1-1 H2 required to produce the reaction mixture at 2500 K. The separation work for step (c) is 124 kcal mol -~ H2. The compression work is again 345 kcal mo1-1 H2. The efficiency is -0.59. The energy utilized in handling a large quantity of coolant can be eliminated, with the coolant, by cooling the gas adiabatically with a supersonic nozzle [16, 17]. The next case examines this approach. Case (6)

(a) The reaction mixture is expanded rapidly and adiabatically to about room temperature. (b) The expansion chamber is purged by first compressing the mixture to 1 atm, during which the water vapor condenses, and then pumping out the chamber. (c) The hydrogen and oxygen are separated. The pressure drop required in step (a) is P2/Pl = 1.1 x 105 . The pumping work for step (b) is then 348 kcal mo1-1 H2. This value could be reduced by about a factor of two if the mixture is cooled only to about 900 K. The reaction would stop because of dilution. However the water vapor would not condense on compression and the reaction would start again. The separation work of step (c) is 1.1 kcal mo1-1 H2 and the efficiency is -0.32. Many other approaches to gas quenching are possible. Bilgen [4] discusses a liquid water aspiration system for the coolant. We have not examined this approach because the mixing is so difficult to describe that we have not been able to obtain a satisfactory quenching model that can indicate, through the kinetics, how much hydrogen may be recovered. Another approach is to remove water from the quenched mixture by passing it through beds of some hygroscopic material like calcium chloride. The advantage is that the beds can be sundried, so that the large separation work for the water is included in E, rather than Eex. We do not report on this approach because due to the high binding energy of water to most hygroscopic materials (usually about 70 kcal mol -I H20) [18], the efficiency is very low.

4.

most of the water is removed by condensation. The work of handling the coolant consists of lifting the water into the tube, and is about 0.1 kcal mo1-1 H2. Hydrogen is only sparingly soluble in water, to the extent of about 1 cm3/100 ml [18], and in any case, the coolant can be recycled, so that once it is saturated there is no further solubility loss. Bubble heat transfer coefficients are very large [19, 20] due to the absence of a resistant thermal boundary layer for the new, clean surface so that high cooling rates can be achieved. In order to describe injection quenching, we develop in the Appendix a model for bubble collapse. The model incorporates coupled heat transfer, mass transfer and reaction kinetics. The high temperature of the bubble on injection from the direct-splitting reactor actually enhances cooling. Consider for example two bubbles with the same pressure and initial volume, one at 2500 K and the other at 400 K. The heat that must be removed to cool the bubbles to 300 K is: q = n [ ( T h - 3 0 0 ) C p + AHvap]

(8)

where n = P V / R T h , and Th is the initial temperature. As Th increases, q decreases, and for water it is necessary to remove twice as much heat from the 400 K bubble as from the 2500 K bubble with the same initial size, in order to cool to 300 K. It is apparent from the volume dependence of q that the cooling time can be made as small as desired, simply by making the initial bubble size very small. However too small an initial size is undesirable because it would require forcing the material through a porous material. The backup pressure in the reactor would then deplete the hydrogen. Results of the bubble collapse model are given in Tables 3 and 4. Table 3 follows the composition and temperature of a 0.7 cm bubble to terminal collapse. Table 4 gives the hydrogen recovery and cooling time for several bubble sizes. The quantity OloHis the accommodation coefficient for the O H radical, which appears to be an important parameter of the model for reaction and collapse. When Olon is one, all OH that strikes the bubble wall is depleted and removed from the bubble. When ~on is zero, OH rebounds from the bubble wall. The reaction between OH and the coolant is slow; OloH is more a measure of solubility than reactivity. Because Table 4. Hydrogen recovery and bubble cooling time for injection quenched direct-splitting reactor Hydrogen recovery (%)

INJECTION Q U E N C H I N G

The results of the preceding section indicate two important sources of energy consumption for gas quenching: the separation work and the energy needed for coolant handling. Injection quenching can reduce both. In this process, the hot effluent is injected directly into the base of a vertical tube, through which there is a steady flow of liquid water. Bubbles form, cool and are removed at the top as a mixture of hydrogen and oxygen, with a small amount of water. The separation work is small, on the order of 1 kcal mo1-1 H2 because

95

Initial bubble radius (cm)

assuming Oro~ = 1

assuming OloH= 0

0.01 0.05 0.1 0.5 1.0 3.0 5.0

97 81 76 76 77 78 76

82 68 66 73 76 78 75

Cooling time 2500-370 K (s) 6.0 x 10-7 2.3 × 10 -6 4.2 × 10 -6 1.2 × 10-5 2.8 x 10 -5

8.5 x 10-5 1.3 × ] 0 . 4

J. W. WARNER AND R. STEPHEN BERRY

96

it is not possible to calculate a~OH,we simply carried out the calculations for both extremes. The results for the two limits are not far apart. Further discussion of the accommodation coefficient is given in the Appendix. The results of Table 4 indicate that, even though the cooling times are very short, about one quarter of the hydrogen is lost during injection quenching. We were surprised to find that some of the hydrogen depletion reactions increase in rate as the bubble cools. The explanation is this: the rate of a half-reaction from Table 1 may be written R =

Ae-°/rC 1C2

(9)

where 0 is the activation temperature, Ea/R, and C1 and (:?2 are the concentrations of the two species involved. During cooling, the size of the bubble decreases. In a constant pressure model, the volume of the bubble is proportional to the temperature, so that C1 and C2 vary inversely with temperature. Then the rate takes on a temperature dependence of

keO/r R = T---T-

(10)

where k incorporates all other numbers that do not depend on T. Equation (10) has a maximum at T = 0/2. If the activation temperature is large compared with T, the rates decrease during cooling. However if 0 is less than 2T, the rate increases during cooling until T drops below 0/2. This is what we found to occur in the kinetic simulations. It is the free radical reactions that have low activation temperatures and increase in rate during cooling. The principal hydrogen depletion reaction is Ha + OH---~ H20 + H.

(11)

The activation temperature for this reaction is 2590 K [13], so that the rate does not begin to decrease until the temperature drops below 1295 K. At 700 K, the temperature factor of equation (10) is still greater than at 2500 K. The equilibrium ratio of OH to H2 at 2500 K is 0.57. If reaction (11) goes to completion and the atomic hydrogen combines to give H2, about 28% of the H2 is lost. Additionally, the equilibrium ratio of H to H2 at 2500 K is 0.12. When this source of atomic hydrogen combines, the amount of H2 increases by 6%. Considering only reaction (11), one expects about a 22% loss of H2 during cooling. This is close to the 24% loss reported in Table 4. The minimum hydrogen recovery occurs for bubbles of about 0.1 cm radius. For bubbles of this size, there seems to be a tendency for the atomic oxygen and hydrogen to combine to produce more OH, which further depletes the hydrogen. A small recovery of heat might be made in the injection cooling process because the water is heated. Suppose the coolant is heated to 80°C. Then about 25 kcal mo1-1 H2 can be used to help heat the reaction mixture. The separation work, computed for the terminal bubble of Table 3, is 0.7 kcal mol -~ H2. The work of lifting the coolant to 1 m is about 0.1 kcal mol -~ H2. With a 76%

recovery and a heat input of 912-25 kcal tool -1 H2 for 355-2500 K, respectively, the efficiency is 0.049. 5.

HIGH-TEMPERATURE SEPARATION

As pointed out in the Introduction, this extended discussion of separation arises because, while materials limitations prevent high-temperature separation of the products of direct thermal splitting, the potential advantages are considerable. Consequently it is of interest to examine the efficiency of a hypothetical high-temperature separation process, within the context of the Present formulation. We assume that all six species of Table 1 are separated and the water is returned to the reactor, with no heat leak. Since both atomic and molecular hydrogen are recovered, the units in this section will be per total mole of H2, i.e. per mole of (H2 + ½H). We assume the hydroxide and atomic oxygen are rejected after separation with no attempt at heat recovery. The hydrogen is cooled to room temperature with recombination of the atomic hydrogen in an efficient heat-exchanger with a small temperature drop while more water is heated. Another heat exchanger recovers heat from the molecular oxygen. The heat recovered in the exchangers is about 29.1kcal mo1-1 H2. It is necessary to heat 1.26mol H20 mo1-1 H2 from room temperature to 2500 K to make up the reaction mixture with a heat input of 43.0 kcal mol -~ H2. Thus a net heat of 13.9 kcal mo1-1 Hz must be added to bring the water to 2500 K. The heat of reaction is 76.8kcalmo1-1 H: (not 81 because both Hz and H are recovered in this model). The separation work at 2500 K is large, 88 kcal mo1-1 H2, due to the several dilute species. Because the separation work exceeds the enthalpy of combustion of H2, the device cannot break even unless the separation is done with solar energy. Assuming this can be done at 50% efficiency and neglecting heat leaks, the efficiency is 0.32.

6. CATALYTIC REACTOR Recently Jellinek and Kachi [21] have discussed a catalytic direct-splitting reactor, which operates in the range 1500-1700K. The equilibrium degree of dissociation is low at these temperatures; the mole fraction of H2 is 2 . 1 4 × 1 0 -4 at 1500K, and 9 . 9 6 x 1 0 -4 at 1700 K. However rapid hydrogen evolution occurs at the platinum catalyst. The reactor has several appealing features including a simpler technology than the 2500 K reactor and the possibility of membrane separation at the lower operating temperature. We examine three approaches to hydrogen separation for this reactor.

6.1 High-temperature membrane separation Due to the low degree of dissociation, the separation work is large. At 1500 K, it is 87 kcal mo1-1 H2, and at 1700 K it is 83 kcal mo1-1 H2. Again this exceeds the enthalpy of combustion of H2 and the reactor will only

HYDROGEN SEPARATION AND THE DIRECT HIGH-TEMPERATURE SPLrIq'ING OF WATER break even if the separation is accomplished with solar energy. Assuming this can be done at 50% efficiency, with no heat leak, the efficiency at 1500 K is 0.39 and only slightly larger, 0.40, at 1700 K. 6.2

Table 6. Percent hydrogen recovery for catalytic reactor with heat exchange, as a function of linear cooling rate from 1500 K to 500 K Hydrogen recovery (%)

Cooling rate (K s-1)

70 78 85 93 100 100

200 300 500 1000 5000 10,000

Injection quenching

The hydrogen recovery and cooling times for the injection quenched catalytic reactor at 1500 K are given in Table 5. Nearly complete recovery is achieved due to the low O H composition. A t 1500 K, the equilibrium ratio of O H to H2 is about 12% and 6% of the hydrogen is lost when the O H rebounds from the bubble wall. At 1700 K, the ratio of O H to H2 is 0.27, so a 13% loss of H2 is expected. We have not repeated the simulations at 1700 K, but assume a 13% loss. As in Section 4, we assume that the coolant is brought to 80°C by quenching and that the heat is recovered. The heat needed to raise the reactant from 353 K to 1500K is 9.75 × 104kcal mo1-1 H2. For the 1700 K case, 2.40 × 104 kcal mo1-1 H2 is needed. The separation work is 1.1 kcal mol -~ Hz. If the coolant is lifted to a height of 1 m, the required work is about 8kcal mol -x H e. The efficiency is 4.7 x 10 -4 at 1500 K and 1.8 x 10 -3 at 1700 K. 6.3

97

Heat exchange and low temperature separation

Once the reaction mixture is removed from the catalyst, the reaction is slowed. This suggests that one could cool the mixture in a heat exchanger, recover most of the heat and separate the hydrogen at low temperature. In order to test this possibility we have investigated the kinetics for several linear cooling rates. The results given in Table 6 indicate that good hydrogen recovery requires the mixture be cooled to 500 K in 2 s or less. This suggests that a fast, single-pass counterflow heat exchanger be employed. The heat available on cooling to 375 K is 10.9 kcal mo1-1 H20. As this exceeds the 9.7 kcal mol -~ H20 enthalpy of vaporization, the following approach is possible. The mixture is heat exchanged with water at 373 K, vaporizing the water. The new vapor is heated to 1500 K in the reactor. The old vapor is condensed to remove the water and the

Table 5. Hydrogen recovery and bubble cooling time for injection quenched catalytic reactor Hydrogen recovery (%) Initial bubble radius (cm)

assuming OloH = 1

assuming O~OH= 0

0.01 0.05 0.1 0.5 1.0 3.0 5.0

100 100 100 100 100 99 98

94 94 95 95 94 94 94

Cooling time 1500-370K (s) 2.1 X 9.0 × 1.6 × 1.1 x 1.7 x 6.0 x 9.3 ×

1 0 -7

10-7 10-6 10-5 10-5 10-5 10-5

hydrogen and oxygen are separated. We can determine the characteristics of the heat exchanger as follows. Assuming Newton's Law cooling, one has dT

- n C p --d-ft = ~ = h A ( T - Tw).

(12)

Here n is the moles of fluid and A is the surface area of the exchanger. Since T~ is constant at 373 K, equation (12) may be integrated:

/T-Tw\

A h

- l n l Th---'/-~ ) = n~-~p t.

(13)

The heat transfer coefficient for steam is about 1.8 x 10 -5 cal cm 2 s -1 K -1 [22], and the heat capacity is 11 cal mo1-1 K -1. In order to cool the mixture from 1500 K to 500 K in 2 s, the heat exchanger will need a surface area of 67 m 2 per mole of steam. This is surely very large, but possible. The heat input per cycle is reduced to 5.09 x 104kcal mo1-1 H2 at 1500K and 1.36 x 104kcal mo1-1 Ha at 1700K. The separation work, after the water condenses, is again 1.1 kcal molH2. The efficiency is then 1.1 x 10 -3 at 1500K and 4.2 x 10 -3 at 1700 K. These values are competitive with some of the high-temperature steam quenching strategies. 7.

CONCLUSIONS

The results of Sections 3--6 are summarized in Table 7. In preparing this table we have incorporated the 30% loss in the solar collectors and reactor given in ref. [4]. This value is based on a,, optimization of the collectors described in ref. [23]. The first column of Table 7 gives the efficiency if the compression and separation work are included in Eex of equation (1). For the second column we have assumed that electricity is delivered to the work devices with photocells at 11% efficiency [24]. The efficiency is then given by equation (lb), where E, and Ee~ are the values calculated above, e~ is the efficiency of the electric power source (11%), and es is the efficiency of heat delivery (70%). For the first column of Table 7, the most effective approach is injection quenching. This is no accident, as the process was designed to minimize the work of

98

J. W. WARNER AND R. STEPHEN BERRY

Table 7. Overall process efficiencies. The el values are com- Table 8. Efficiency of injection quenched direct splitting reacputed from equation (1) and include a 30% loss in the collec- tor as a function of the operating temperature. Bubble model tors. The e2 efficiencies assume that electricity is delivered to is for a radius of 1 cm, with O~oH= 1 the process with solar photogalvanic cells at 11% efficiency [equation (14)] Equilibrium Hydrogen Temperature hydrogen recovery Efficiency (K) (mole fraction) (%) el Gas quenching el e2 Case (1) Case (2) Case (3) Case (4) Case (5) Case (6) Injection quenching High-temperature separation Catalytic reactor (1700 K) High-temperature separation Injection quenched Heat exchanged

-6.8 × 10-2 4.9 × 10-3 7.0 × 10-3 -5.5 x 10-1 -4.1 × 10-1 -2.2 x 10-1 3.4 x 10-2 -2.3 × 10-1

8.3 × 7.6 × 7.4 × 2.7 x 1.1 x 1.3 x 3.4 × 6.2 ×

10-3 10-3 10-3 10-2 10-2 10-: 10-2 10-2

-3.4 x 10-1 1.3 x 10-3 2.9 × 10 -3

6.6 x 10-2 1.7 × 10-3 4.2 × 10 -3

separation and coolant handling. For the second column, with electricity delivered by solar cells, the catalytic reactor with membrane separation appears to be most efficient. The 6.6% efficiency for this process, however, may be optimistic. The sample is very dilute in hydrogen. To achieve a one-stage separation, the pressure on the hydrogen-rich side of the membrane must be less than 2.14 x 10 -4 atm. To achieve the separation in a reasonable time, the pressure would have to be much less than this and a large membrane surface area would be required. It could turn out that the separation is so slow that the catalyst is unnecessary. Alternatively, a multistage separation might be required, with further losses at each stage. The large surface area of the membranes could be the source of considerable heat leakage. The same can be said of the other processes in Table 7 that require separation of a dilute species. We do not presently have a method for determining realistic efficiencies for dilute separations carried out at practical rates, but the 50% efficiency assumed for Table 7 is probably far too high. An example illustrates the difficulties. The SEPAREX Butamer hydrogen recovery system [25] purifies hydrogen from a composition of 70-96%. In order to achieve rapid separation a pressure gradient across the membrane of almost 18 : 1 is employed. The operation is far from the reversible limit. The dilute separations of Sections 3 and 6 would require an even larger pressure gradient in order to proceed at a reasonable rate. Excluding the dilute separations, the most appealing e2 efficiency is again for injection quenching, for which the reported efficiency is believed to be very realistic. Furthermore the performance of this process improves as the peak temperature is raised. Because of this, we have examined the improvement in the efficiency for the injection quenched process carried out at higher temperatures. The initial choice of 2500 K is close to the current material limit, but one can imagine the possibility of a higher reactor temperature achieved

2600 2800 3000 3200 3400

0.051 0.088 0.130 0.168 0.188

72 59 49 42 39

0.039 0.047 0.050 0.047 0.042

by development of new refractory materials, or, more likely, by a nonequilibrium steady-state technique whereby the reaction mixture is significantly hotter than the reactor walls. Such an advance could permit a more efficient process with a greater degree of water splitting. The results of the higher-temperature injection quenched process are reported in Table 8. An optimum efficiency of 5% occurs near 3000K. This could be raised further if a free radical (OH) scavenger could be introduced. A n interesting competitor for injection quenching is case (6) of Section 3, cooling by rapid adiabatic expansion, with an e2 efficiency of 1.3 × 10 -2. This value could almost surely be improved, as we have made no attempt to find the optimum temperature after expansion. In summary, we believe the prospects for any case involving ultradilute gas phase separation of the hydrogen are poor. This includes cases (1), (4) and (5) of the gas quenching strategies and high-temperature separation for the catalytic reactor. The hygroscopic-bed water-separation strategy mentioned at the end of Section 3 could, however, change this conclusion. Cases (2) and (3) of the gas quenching strategies utilize very large amounts of heat in order to supply the steam coolant. This limitation is overcome by injection quenching. The adiabatic expansion strategy of case (6) requires much of the energy to be delivered as electricity, but probably deserves more detailed evaluation than we have given it. The heat exchanged catalytic reactor requires a very large surface area exchanger, but could be more efficient than injection quenching of the same temperature reaction mixture. The injection quenched high temperature process wastes a large amount of heat on ballast but is free of the defects of dilute separation and coolant recycle work.

Acknowledgements--This work was supported by Contract No. 5083-260-0834with the Gas Research Institute, Chicago, Illinois. The authors thank Martin Carrera and Bengt Mhnsson for many helpful discussions. REFERENCES 1. J. Led6, F. Lapicque and J. Villermaux, Int. J. Hydrogen Energy 8, 675 (1983).

HYDROGEN SEPARATION AND THE DIRECT HIGH-TEMPERATURE SPLITTING OF WATER 2. R. B. Diver, S. Pederson, T. Kappauf and E. A. Fletcher, Energy 8, 12, 947 (1983). 3. E. Bilgen, M. Ducarrioer, M. Foex, F. Sibleude and F. Trombe, Int. J. Hydrogen Energy 2, 25 (1977). 4. E. Bilgen, Int. J. Hydrogen Energy 9, 1, 53 (1984). 5. S, Ihara, Int. J. Hydrogen Energy 3, 287 (1978). 6. J. Gilman, Science 205, 856 (1980). 7. J. E. Funk and R. M. Reinstrom, I. & E.C. Proc. Des. Deol. 5, 336 (1966). 8. J. E. Funk, Int. J. Hydrogen Energy 1, 33 (1976). 9. W. L. Conger, J. E. Funk, R. H. Carty, M. A. Saliman and K. E. Cox, Int. J. Hydrogen Energy 1,245 (1976). 10. J. E. Funk and W. Eisermann, In Alternative Energy Sources II, Vol. 8 Hydrogen Energy, T. Nejat Veziroglu (Ed). Hemisphere, New York (1981). 11. R. Shinnar, D. Shapira and S. Zakal, I & E.C. Proc. Des. Devl. 20, 581 (1981). 12. D. R. Stull and H. Prophet, JANAF Thermochemical Tables, 2nd edn, p. 37. NSRDD-NBS (1971). 13. E. Oran, T. Young and J. Boris, 17th Int. Symposium on Combustion, p. 47. The Combustion Institute, Pittsburgh (1979). 14. S. Ihara, In Solar Energy Systems, T. Ohta (Ed.), p. 59. Pergamon Press, New York (1979). 15. T. D. Eastop and A. McConkey, Applied Thermodynamics for Engineering Technologists. Longman, New York (1978). 16. E. Becker, Gas Dynamics. Academic Press, New York (1978). 17. R. Smalley, L. Wharton and D. Levy, Acc. chem. Res. 10, 139 (1977). 18. R. C. Weast (Ed.), CRC Handbook of Chemistry and Physics, 58th edn. CRC Press, Cleveland (1977). 19. S. G. Bankoff and J. P. Mason, A.LCh.E. Jl. 8, 30 (1962). 20. N. W. Snyder and T. T. Robin, J. Heat Transfer 91C, 404 (1969). 21. H. H. G. Jellinek and H. Kachi, Int. J. Hydrogen Energy 9, 8, 667 (1984). 22. R. C. Lord, P. E. Minton and R. P. Slusser, Chem. Engng Jan. 26, 96 (1970). 23. J. Galindo, Etude et optimisation du captage du rayonnement solaire concentre en vue de la realisation d'un reacteur pour la production d'hydrogene. Doctoral Dissertation, Ecole Polytechnique, Montreal (1982). 24. E. Berman, personal communication; C. Carpetis, Int. J. Hydrogen Energy 9,969 (1984). 25. W. C. Shell and D. Houston, Industrial Gas Separations, T. E. White, Jr. (Ed.), p. 142. ACS Symposium Series 223, Washington 26. E. H. Kennard, Kinetic Theory of Gases, p. 69. McGrawHill, New York (1938). 27. T. T. Robin and N. W. Snyder, Int. J. Heat Mass Transfer 13, 523 (1970). 28. M. S. Plesset and S. A. Zwick, J. appl. Phys. 23, 1, 95 (1952). 29. E. R. G. Eckert and R. M. Davis, Heat and Mass Transfer. McGraw-Hill, New York (1959), 30. M. Jakob, Heat Transfer. John Wiley, New York (1949). APPENDIX: BUBBLE COOLING AND COLLAPSE The bubble collapse model incorporates the following features: (1) Condensation occurs at the bubble wall, causing heat and matter to leave the bubble.

99

(2) Evaporation at the bubble wall injects cool matter into the bubble, lowering the temperature. (3) Heat flux into the liquid carries heat away from the bubble. (4) The bubble volume and temperature, as a function of time, are inserted into the water kinetics, to determine the bubble composition. In order to couple the bubble collapse to the reaction kinetics, it is convenient to have a uniform temperature within the bubble. It is assumed, then, that mixing within the bubble is rapid, so that an average bubble temperature Th, is a valid approximation. The pressure is assumed constant, and equal to 1 atm. There is no need to account for hydrostatic pressure, as the bubble is quenched before it has moved 1 cm. In practice a small increase in pressure is required to achieve injection. Solution of the equilibrium problem indicates that a tenfold increase in pressure depletes about half of the hydrogen [14]. The pressure dependence of the equilibrium hydrogen composition is so small that the pressure increase for injection has little effect. The volume of the bubble is given by

4 ntotRTh V = g Jrr 3 P

(A1)

where ntot is the number of moles of gas within the bubble. The rate of condensation at the bubble wall is given by [26] dnout 4~r2 ocP dt - (2;rRTh) ~/2"

(A2)

In this expression, the accommodation coefficient o¢ is the fraction of molecules that condense upon striking the bubble wall. Robin and Snyder [27] first suggested that equation (A2) be used in connection with bubble collapse. We assume, like Robin and Snyder, that for the new, clean bubble surface the accommodation coefficient for water is unity [26]. The accommodation coefficients for the insoluble, nonpolar species are taken to be zero. The hydroxide radical is polar, so it may be soluble in the liquid, but the accommodation coefficient would probably be less than unity. To account for this, we have analyzed the bubble at both extremes, ~-or~= 0 and CroH= 1. Equation (A2) then becomes dnout dt

4YIr2pH2O (2~tRTh) 1/2

dno~t 4azr2(PH2o + POll) dt = (2srRTh) 1/2

(A3)

(A4)

where P~ is the partial pressure of species i. Equation (16) is for 0:oH = 0, and equation (17) is for troll = 1. The rate of evaporation at the bubble wall is given by [26] dnin 4.r/'r2Pvap dt - (2:rRTw) 1/2

(A5)

where Tw is the temperature of the bubble wall, and Pv~pis the vapor pressure at T~ [15]: [AHvap/ 1 1 \q Pwp = P 0 e x p [ - - - ~ ~ T ~ ) ].

(A6)

The temperature within the bubble is taken to be the number-weighted average temperature of the material in the bubble

100

J. W. WARNER AND R. STEPHEN BERRY

at Th, and the material added to the bubble at Tw. This gives d Th

(Tw - Th)

dt

ntot

dni, dt "

(A7)

There remains one more variable, the temperature of the bubble wall, Tw which is determined by the heat flux into and out of the wall. It would be best to employ the Plesset-Zwick temperature integral for T~ [28]:

where k is the thermal conductivity and the skin depth dt grows according to 6 = N/4at (A10) with tr the thermal diffusivity. The temperature at the bubble wall is determined by equating the heat flux into and out of the wall:

dn°ut [ AHvap + C" dni,

~-,r2(x) (OT/Ot)r=rdt

dt AHv.p +

(A8)

We have found, however, that due to the weak singularity in the integrand, equation (A8) is very inconvenient for numerical integration. We have employed a different approach, based on the Schmidt graphical method [29]. The heat flux into the liquid is taken to be

q=

4~rr2k(T~ - To) 6

(A9)

4zr2 k( Tw - T¢ )

(All) = For large bubbles, this expression tends to give unstable values for Tw. However, it is unlikely in practice that bubbles much larger than I cm in radius would occur. We have included calculations for larger bubbles only to show that the H2 composition is stable. The bubble collapse model does not include any effects due to flow of coolant past the surface. The transitional velocity of the bubble through the liquid due to buoyancy is on the order of 25-50 cm s -1 [30] so that on the millisecond timescale for quenching the motion of the bubble can be neglected.