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Hydrogen and oxygen from water—II
HYDROGEN AND OXYGEN FROM WATER-II SOME CONSIDERATIONS IN THE REDUCTION OF THE IDEA TO PRACTICE RICHARD Department
of Mechanical
B. DIVERand &m
Engineering,
A. FLETCHER~
University of Minnesota. MN 554% U.S.A. (Receiwd
I I I Church !%ree.t S. E.. Minneapolis,
9 April 1979)
Abstract-An analytical model of an archetypai device for using solar energy in a one-step thermochemical process for producing hydrogen and oxygen from water is presented. It is used to help us anticipate and evaluate sources of irreversibiitks associated with the operation of various components of such a device and to suggest alternatives which should be considered. INTRODUCTION Production of hydrogen and oxygen from water by the use of solar energy is a subject of current interest. In a previous paper,’ we suggested that a high-temperature, one-step thermochemical process which makes use of effusional separation in the Knudsen flow regime is a tantalizing possibility. In that paper, we considered ideal systems. Irreversibilities were given only superficial consideration. The objective of that study was to explore the possibilities offered by a new idea. The results were idealized so that the process could be compared with others that had seen similarly presented. The process is essentially an application of what follows: When water is heated to sufficiently high temperature, an equilibrium mixture of H, HZ, H20, OH, 0, and 02 is produced. The extent of water decomposition increases with increased temperature and reduced pressure. If such a mixture is fractionated through a barrier in the Knudsen flow regime, the lighter components will have become enriched in the effusate; the heavier components will have become enriched in the uneffused fraction?’ Thus, it is possible to effect the partial separation of the H and Hz from the other components of equilibrium mixtures of water. Application of the technique has been made in the separation of uranium isotopes3 The maximum thermal efficiency of a thermochemical process can be related to the Camot efficiency of a heat engine, (TH - TJTH, where TH and TL are, respectively, the upper and lower temperatures between which the device operates. Thus, from a thermodynamic standpoint, high temperature processes are good. From an operational standpoint, however, the thermal efficiency of real devices is limited by irreversibilities associated with the various internal processes needed to make them work. The principal objective of the present study was to pinpoint likely sources of inefficiency and to observe how these inefficiencies depend on operating variables and system con&nation. Sources of irreversibilities in the separator and other components of a postulated device were evaluated. Our approach was to calculate the entropy produced as a consequence of the operation of each of the major components and to relate this entropy production, which is ultimately manifested as a system ineIIkiency, to the operating variables. In this paper, we present the results of an investigation which makes use of an archetypal construct which has many features of a real device. Irreversibilities and losses which may be encountered in the principal components of real devices which use effusional separation are sought and evaluated so that they can be anticipated and perhaps avoided in succeeding models. THE MODEL
The specification of a model for such an arcktypal study is somewhat arbitrary. Different configurations are possible. Merences arise, for example, in the arrangement of pumps and heat exchangers and in the mechanisms selected for ekcting heat transfer. We constructed a +To whom correspondence
on this paper should be addressed. 1139
1140
R. B.
DIVER
and
E. A.
fiETCHER
model which we felt would be general enough to reveal the merits and shortcomings of the basic concept, and specik enough to identify the problem areas of real devices. Fiie 1 is a schematic diagram of our model. Its notable features are: (1) it is feasible, and each component can, at least in principle, be constructed and made to operate; (2) any real device will be likely to contain components similar to those which are considered in this model; (3) ail of the heat addition occurs at the high temperature and all rejection at the low temperature. The third feature serves a useful purpose insofar as the introduction of a certain thermodynamic formalism into our presentation is concerned, but it is not a necessary attribute of a practical device. As we shall see, this feature makes it judicious for us to introduce, later, an elaborate mechanism for heat transfer to the cold water to evaporate it. In practice, such heat transfer might easily be effected by the introduction of low-grade, low-temperature, flat solar collectors and by the rejection of more heat to the surroundings. The formal effect of this fix would be to reduce substantially the thermal efficiency of the device, but it might give us much cheaper hydrogen and oxygen from water. The operation of the device is described in the caption of Fig. 1. The individual components are discussed in the paragraphs which follow.
Solar collector
The solar collector concentrates the incident solar radiation. The eficiency of the collection process, r),, depends on the characteristics of the collector and the absorber. It is defined as
REACTORSElwtARm
LKXJIO SEPARAT!DRS Fig. 1. Schematic diagram of a system for producing hydrogen and oxygen from water. Water enters the system through an inkt valve which reduces its pressure from atmospheric to P, With neghgiik friction losses, P, will be the pressure everywbae of tbe uneffused material. It is heated to its saturation temperature and vaporixed in the low-temperature heat exchanger. The heat of vaporization is provided by heat exchange from the condenser of a heat pump and by the hot products emerging from the hiitemperature heat excw. The vapor is then butted to the hi& temperature, Tu, in the counter current high-temperature heat exchanger. The reactor-separator is in a Ma&body cavity equipped with a transparent window. Concentrated sunlight is iatroduced through the window to provide the heat necessary to maintain the high temperature of the reactor-separator. The interior of the cavity contains pipes whose might not be unlihe that of a tube-in-shell heat walls constitute the effusion membmne. Its ve exchanger. The effusate, eariched in Ii&r components, and the uneBused material are the sources of heat which is used to heat incomkg water to the high temperahue in Ure high- and low-temperature heat exchangers. The low-temtkratum beat exchanger ako serves as the heat source for the heat pump. The descendii streams are cookd to ambknt tempmature in the coder. They are then separately pumped, isothermally, to a useful pressure. Water that condenses in the low-temperature heat exchanger, cooler. and pumps is separated from the permanent gases in the liquid separators and may be returned to the system through the inlet valve. The numbers on the figure refer to stations referred to in the analysis.
Hydrogenand oxygenfrom water-11
&,JlA
1141
and is given by
t)h
aIAq* - acuT;, IA
rl,=-=IA
(1)
where &,, is the net energy thrx into the reactor-separator, I is the incident ambient solar energy flux, A is the collector area normal to the incident solar radiation, a is the effective reradiation area of the reactor-separator (the window area), I)~ is the optical efficiency of the collector, a and c are the effective absorptance and emittance of the reactor-separator, respectively, and u is the Stefan-Boltmann constant. The collector concentration ratio, C, is
Ala. Reactor-separator The reactor-separator
functions as the solar absorber, and it separates the components of the quihbrium mixture. It is assumed to be well stirred and in equilibrium. It operates isothenmdly; internal heat transfer is assumed to be very fast.t Fme 2 shows a possible separator configuration. The total membrane area, A, can be made indeperxlent of the reradiating area, a, in contradistincnon to the presumption of Ref. 1 that these areas must be coupled. Mass conservation requires that the mass flow rates, rit, be related as follows: fit* =
rirg,
tif,=lit3+rit,.
(2) (3)
Molar flow rates, ri, of hydrogen and oxygen atoms, in whatever molecules they may be found, must satisfy the conservation equations: fi0X.l
=
riox.4 + iox.
fiox.2= riox.3. nHY.1
= fiHY.4 + dHY.3r
dHY2
WINDOW
= dHY.3,
(4) (5) (6) (7)
1142
R. B. DIVERand E. A. FLETCHER
where
(8) (9) Also, since Hz0 is fed to the reactor, hHY.1 = 2dOX.l
Each of the six species effuses through the membrane at a rate given by4 h,2 = 44*63(J’ti- J’iy)&$ I. (MGrP2 ’
(11)
where Pi, and Piy are the pressures of the it/r species on the x and y sides of the membrane (atm), A,,, is the membrane area (cm’>, f is the fractional open area, and Mi is the molecular weight of the ith component. In this analysis, the Knudsen number is assumed high; ideal effusional separation is assumed. In practice, some viscous flow and some diffusion through the solid part of the membrane might be encountered. Additionally, the gas composition on each side of the membrane must satisfy. simultaneously, each of four independent equilibrium constants K(Tn) (eight equations in all), viz. KH*( TH) = k,Ip2w
WI
KH~o( TH) = ~H,O/pH*~O KoH(TH)
Ko,( TH)
= POH/POPH,
(13) (14) (15)
= ~,~~o*.
From Daltons law, 8P, = P,,
(16)
SPi, = Py3
(17)
and
Finally, an energy balance about the reactor-separator
gives
&,,ar= &hj+ k,h4- ti,h,,
(20)
where the tih are the enthalpy flows through the appropriate stations. The set of equations was reduced to give equations in five unknowns, which were solved by the use of NONLIN, a nonlinear equation system root-finder computer program? Heat-recovery systems The high and low temperature heat exchangers are assumed to operate without pressure loss. Their analysis is complicated by the chemical reactions and phase changes which occur in them. There are sometimes mismatches between the availability of the latent heat of a phase change or the heat of a reaction and the temperatures at which the transformations occur in the three streams. A sketch of the variation of the enthalpies of the streams with temperature, shown in Fig. 3(a), helps point this out. Figure 3(b), which shows the first derivative, C,,, is also helpful. These figures have no numbers on the coordinates because each operating condition is
Hydrogen and oxygen from water-11
1143
b
9+10)(‘+6’ ,Y.---
I (5*6)
0
-;I
TL
.’ Y
Descending Streams,/ / ,’
(3+4) /
Ascendmg Streams
TVAP
TH
Fig. 3. Schematic representation of the thermal characteristics of the working fluid as they vary with temperature in the heat exchangers and the cooler; a. enthalpy; b, heat capacity. The numbers on the figures refer to stations identified in Fig. 1. different;
however, the salient features are the same for all operating conditions. In the high temperature heat exchanger, the heat capacity of the descending (cooled) streams will be greater than that of the ascending (heated) stream because the combined heat capacity of hydrogen and oxygen is always greater than that of an equivalent amount of water and because the descending streams, being at a lower pressure than the ascending streams, are always more dissociated. Thus, the descending streams will always have a greater than needed capability for transferring heat to the ascending stream in the high temperature heat exchanger. The heat capacity spike at Tvap,the saturation temperature of HZ0 at P,, represents the latent heat of vaporization of the ascending (heated) stream. Since the descending stream is at a lower pressure than the ascending stream, its latent heat becomes available at a temperature which is lower than that needed to vaporize the ascending stream. In our construct, we use a reversible heat pump to transfer this heat and accept as a penalty the work required to operate the pump. An alternative might be to eliminate the heat pump and supply the heat necessary for vaporization from an additional source, as we have previously noted. The high temperature section of the exchanger energy balance is nighs+ ti.,hd + ti,h, - riz,h, - n&h5- tilghc,= 0,
(21)
where h is the specific enthalpy of the fluids. If it is assumed that the two descending streams emerge at the same temperature, hs, h6, and T5 = T6 can be determined. The energy balance for the low temperature heat exchanger is
The power supplied to the idealized heat pump, wr,,, is
*HP= &p( Tvap- TJ/ Tvapr
(23)
where &, is the rate at which heat is supplied to vaporize the feedwater minus the heat lost by the descending streams as they cool from T5 to T_, We required the two descending streams to have the same exit temperature; the unknowns he, h7, and W,, can be determined from the appropriate energy balance. Cooler and pumps The temperature of the descending streams is reduced to ambient by heat rejection to the
R. 3. DIVERand E. A. FLETCHER
1144
surroundings. Then the hydrogen and oxygen are pumped reversibly and isothermally to one atmosphere. The pump power required for the two-component, two-phase, hydrogen-enriched mixture is fit0
,
(24)
I
where R is the gas constant, P is the pressure to which the mixture is to be pumped (in this analysis, 1 atm plus the vapor pressure of water), Py is the pressure at the pump inlet, Pvapis the vapor pressure of water at TL, and PC is the pressure at which condensation begins. A similar equation applies to the oxygen pump. The first term in the brackets gives the work required to compress the steam to the saturation point and the second gives the work of compressing the steam as water is condensing in it; PY cannot be greater than PC. Since the work equivalent of the hydrogen produced is -AGH20(,j,m.16,the pump work is taken as a debt on our hydrogen production in this construct. Eficiencies
The system efficiency, defined as the work equivalent of the net hydrogen production rate divided by the solar power intercepted, is given by the product of the collector efficiency and the thermal efficiency, viz 7s = %
x
(25)
7th.
The collector efficiency has already been discussed. The thermal efficiency is given by
%et -
77th =
7
~H,,AGH,wI,,~.,~
=
-
%P -
%mm,,
&lar
QH
(26)
This approach to calculating thermal efficiency is straightforward but tells us nothing about where, in a particular operating configuration, losses occur and how efficiency might be improved. For the purpose of learning the sources of thermal inefficiencies, we invoke the use of entropy production as a measure. The irreversibilities and the lost power in each component can be calculated from the rate of entropy production associated with its operation. The rate of entropy production associated with the reactor-separator, for example, is
3 = t&s3 + nh--
ni,s,- (&,,JT,d.
(27)
The lost power associated with the operation of each component is equal to the product of the rate of entropy production associated with its operation and the ambient temperature. The thermal efficiency can therefore be calculated by the alternative relationship Available Power-ELost Power 7th
(28)
= Qwlar
where the available power is the product of the Camot efficiency and &,rar, while ZLost Power is the sum of the lost power in all of the components. ANALYSIS
Variable selection
To provide a realistic scale for our analysis, we used a collector system patterned after the French CNRS solar furnace at Ode&-Font Romeu.6 The effective collector area, A,, is 2800 m*. The intensity of solar radiation, I, is 0.1 W per square centimeter. The concentration ratio is 10,000. The collector efficiency, absorptance, and emittance are all taken to be one; it is a blackbody cavity. Thus, &,, is a function of TH only. Once &rar and the ambient
Hydrogenand oxygen fromwater-11
1145
temperature have been specified, the problem has four remaining degrees of freedom. In this analysis, we selected TH, P,, the membrane open area, A,, = fA,, and the gross hydrogen production rate, riH2c.The dependent operating variables are thus P,, the mass flow rates, the component power requirements, the heat-rejection rates and irreversibilities, the fluid properties in the various parts of the system, the efficiencies, and the net power equivalent of hydrogen produced. The inputs chosen were chosen because they facilitate solution of the reactor-separator problem and permit sequential solution of the equations that pertain to the remaining components. Although we have used the Odeillo furnace as a prototype, the results of this analysis for any given Tn and P, can be applied to any other collector system by scaling A ,_,,, tiHzO,and the resultant, dimensionally-dependent variables, in proportion to the net solar heat rate, &,I,. RESULTS
In the interest of economy of presentation, we first discuss the effects of varying the extensive variables tinzc and Aopenat a representative combination of Tu and PI. Our observations are then extended to other temperatures and pressures. Figures 4-11 give results for the example condition: TH = 2800°K; P, = 0.2atm. Figure 4 shows that PJP, and fi3 depend only slightly on the gross hydrogen production demand, ri,,. This surprising result is a consequence of the fact that an increased demand for hydrogen production is met by this system as follows: the mass flow rate to the reactor, ml, increases, as is shown in Fig. 5. The hydrogen content of the x-side gas is then less depleted than it would have been at a lower flow rate. The demand for additional hydrogen production is thus met primarily by the changing composition of the effusate rather than its quantity; it does not, therefore, affect strongly the irreversibility. Figures 4 and 5 also show that smaller membranes require larger pressure drops to achieve a given gross hydrogen production rate. They also require smaller effusate flow rates because the higher pressure drop increases the separation efficiency. Because larger pressure drops entail compensating smaller effusate flow rates, the irreversibilities associated with the smaller membranes are less than those associated with the larger membranes. The effusate fraction or cut, tiJk(, is the dependent variable in Fig. 6. The hydrogen production rates corresponding to points where these lines cross the horizontal axis are the TH i 2600 IO
4
e
px
.6 .4
PK zO.2
0
K otm
A own
#0.5 ’ 0.3 -
T,, = 2800 K
dl
PX=0.20tm
0.1
2
q 9
1.4 1.2 -
f
1.0 -
z -0 L
.6 -
b
I 0.5 8 0.3 A own
Cm21
.6 -
2 5:
.4 -
g.=
2-
-
0.1 I
I
0
2
1
4
1
6
2
GrossH,
I
6
GrossH2 ProductionRate,moles/s
3
Production
4
5
6
Rate, moles/s
Fig. 5.
Fii. 4. Fig. 4. Variationof pressureratio (a) and mass effusion rate (b) across the membranewith the hydrogen demand. The membrane’sopen area is the parameter.The pressure ratio, and hence, the mass flow rate throughthe membrane,are both virtuallyindependentof the hydrogendemandbecause increaseddemand is achieved by modificationof the compositionof the feedstreamby increasingthe water feed rate (Fig.5). Fii. 5.
Variation of water feed rate to the reactor-separatorwith hydrogendemand.The effusionmass flow rate, MI,,is also shown for comparison.
7
R. B. DIVERand E. A.
1146
FLETCHER
TH = 2600 K Px=0.2atm
e Gross
H,
Production
Rate,
Effusate
moles/s
Cut,
$/+I,
Fig. 7.
Fig. 6.
Fig. 6. Variation of the effusatecut (rirJk,) with hydrogendemand. Fig. 7. Variation of &,/dHzwith cut (&/rir,) at variousopen
areas.
limiting hydrogen production rates. Since rir3cannot be zero, the tir, required to maintain steady operation at these points approaches infinity. Hydrogen demand rates higher than those at the intercepts cannot be achieved by any feed rate, no matter how high. The figure also shows that larger membranes can produce more hydrogen. The next two figures show the importance of effusate fraction (cut) as an operating variable. Figure 7 shows the amount of water which must be circulated to collect each mole of hydrogen as a function of effusate fraction for three membrane sizes. An optimum operating condition here is indicated at an effusate fraction of about 0.5 for all of the open areas. This result is in qualitative agreement with experimental results obtained with two component, non-reacting mixtures.’ From the standpoint of separation, smaller membranes are better than larger ones because they involve larger pressure drops and consequently less back effusion of the lighter components. In Fig. 8, the thermal efficiency of the device is plotted as a function of effusate fraction for the various open areas. For each Aown,an optimum &/rir, and, therefore, fiiH2cand ti,, exists. Up to a point, smaller open areas provide better thermal efficiencies and require lower effusate fractions for optimum operation. In Fig. 9, the component losses are plotted as functions tiHsc for a single open area. These losses were calculated from the rates of entropy production in each of the components. For this temperature and pressure, the separator irreversibilities are relatively small and insensitive to tin2c because irreversibility is proportional to the logarithm of pressure ratio and tijtg,both of 7” = 2800 R * 0.2ohn
5 2 s
E w 2 I
.35 L a.1
k
,629_------__-----~)o__ bc&
Px = 0.2
a5
_____
IWO-
6.67 -6
z 9%
125o-
.20-
A opsn(m21
2
.g 4
.I5 .I0 -
,
$“,
z
Aow. s 0.3m2
TH = 2600
.m.25 -
.05 .2
.4
Effusate
.6 Cut,
Fig. 8.
.6
1.0
d IOCOg 750a
Hqh Temp. Heal Each. LOSS
Net
Low Temp. Heal Ev.ch. LOSS
4
500-
ri~,/riq
:
FzeOCtor - Separotw 1015 Co& 0
2.0 Gross
4.0 H,
6.0
Production moles/s
loss 0.0
Rate,
Fig. 9. Fig. 8. Variation of thermal efficiencywith cut at various open areas. Fig. 9. Summary which showshow the performanceof the device and the sourcesof irreversibility losses at the operatingcondition:2tWPK, P, = 0.2 atm, A.,, = 0.3 m3, dependon the hydrogendemand.
1147
Hydrogen and oxygen from water-11
which are insensitive to rlr.i2c.Irreversibilities in the other components are associated with heat transfer across larger temperature differences imposed by the constraints under which this model operates. The high temperature heat exchanger losses are highest at low hydrogen production rates because the heat absorbed in the separator and not used directly for separation provides much more energy than is necessary to preheat the ascending stream. The temperature of the descending stream is thus much higher than it has to be. Its temperature at the exit of the high temperature heat exchanger is high. Losses in the low temperature heat exchanger pass through a minimum. Losses to the left of the minimum result primarily because of the increasing temperature difference between the streams coming out of the high temperature heat exchanger and vaporizer. Losses to the right of the minimum result primarily from greater mass flows. Figure 10 shows the burdens imposed by the various components which require work inputs for the same set of operating conditions as those of Fig. 9. The ordinate is power; the abscissa is gross hydrogen production rate. The uppermost line is the power equivalent of the hydrogen produced by the reactor-separator. However, some of the hydrogen must be used to operate the heat pump and the fluid pumps. The heat pump power burden and the pump power burden are also shown in the figure. If these requirements are met by the use of hydrogen in a reversible fuel cell to produce electric power and subtracted from the gross power output drive, the result is the net power output equivalent curve. This gives the net amount of hydrogen produced in the process. Thus, the system efficiency, even at a given operating temperature, pressure, and open area, depends on the hydrogen demand and has a maximum value at demands somewhat lower than that corresponding to the highest gross production rates achievable. Figure 11 shows how these maximum thermal and system efficiencies depend on TH, P,, and A _,. They both increase with temperature and, at a given temperature, increase as the T” = 28cm P~*o.*mn
A..pn’03td ,6*g-__-__--
____
‘Icornal XQro1.r _____ ____
_--6.87
1500 1250 -
2.0
4.0
Gross
8.0
6.0
Hz Productton KlOkS/S
Role,
Fig. IO. Summary which shows variation of pump power consumption and the net power equivalent of the hydrogen produced with the hydrogen demand.
b
Aopcn = 0.1 tn2 ---
ql
300
I 2400
I 2500
I 2600
T,,K
I 2700
I 28W
I 2900
1 3000
I
2300
Thermal System
I 2400
,,
I 2500
I 26co
I 2700
I 28X1
I 2900
T,,K
Fii. 11. Variation, with temperature of the maximum thermal and system efficiencies corresponding to a given pressure, P,, with a membrane having an open area of (a), 0.5 m* and (b) 0.1 n#. WY Vd. 4. No. 61
I Yxcl
R. B. DIVER
1148
and E. A.
FLETCHER
pressure is reduced. These results reflect the advantage of having to circulate smaller amounts of water. They also suggest that the use of smaller membranes increases the system efficiency, provided that the membrane is not made so small that the requisite amount of hydrogen cannot be produced. Figure 12 shows how the minimum riO/riH,cdepends on the same variables. In general, thermal efficiency and ease of separation improve with increased temperature and reduced pressure because of increased dissociation. However, as Fig. 13 shows, collector efficiency and &,,_ decrease with temperature in the temperature range of our interest. Thus, temperature has opposite effects on the two components of system efficiency. Figure 14, which shows the variation of the pressure ratio across the membrane with temperature, membrane area, and P,, illustrates the fact that higher temperatures in general entail less irreversibility by requiring higher pressure ratios and, concurrently, lower mass flow rates. The lost work of the separator, presented in Fig. 15, illustrates the point further.
-
Aopen = 0.5
rn2
0.1 0 2300
I 2400
I 2500
I 2600
I 2700
I 2.900
I 2900
I 3000
T, K
Fig. 12. Variation, with temperature, of the minimum molar water flow rate per mole of hydrogen demand corresponding to a given pressure, P, with membranes having open areas of 0.5 m* and 0.1 m*.
T,.,,K Fig. 13. Variation of collector efficiency with temperature. C = 10,000;qA = (I = l = 1, in Eu. (I).
T,,,K
T,,,K
_ Fig. 15. Fig. 14. Fig. 14. Variation of pressure ratio, PJP,, with temperature, at various upstream pressures at maximum overall efficiency at two membrane open areas. Fig. IS. Variation of irreversibility losses associated with the separation process with temperature at various upstream pressures at maximum overall efficiency when membrane open area is 0.5 m*.
Hydrogen and oxygen from water--II
1149
DISCUSSION
In principle, a reversible thermochemical procedure for producing hydrogen and oxygen from water can have, as a limiting efficiency, the Camot efficiency. In practice, two kinds of losses are encountered: (1) Those which are inherent in the process itself, such as those which result from pressure discontinuities. (2) Those which result from the fact that, in real processes, compromises must be made in order to make the process work within reasonable constraints, usually temporal or economic. The magnitudes of the former, in the present process, depend on the operating conditions of the reactor-separator component and can be made quite small at sufficiently high temperatures. The magnitudes of the latter depend on the nature and arrangement of auxiliary components and hardware, which are quite arbitrary. In this study we have used an archetypal device, a construct which can be improved as we learn about the intricacies of its operation. We have proposed an u priori reasonable arrangement of auxiliary components to serve as a starting point from which the operation of the process can be improved. Our construct points out where losses are likely to be encountered, demonstrates that some fears we had about irreversibilities we would encounter in the reactor-separator are not so serious as we feared they might be, and suggests where and what kinds of alternative components should be considered. Our approach to the problem is thus not as general as some others: but it has the advantage for us of being easily understood and of telling us how to go about improving our process. For example, we can illustrate some general conclusions with reference to Fig. 9. Fire 9 shows that, if we choose to operate the reactor-separator at a temperature of 2800°K with an upstream pressure of 0.2 atm using a membrane with an open area of 0.3 m*, a perfectly reversible process should permit us to produce hydrogen at a net production rate of about 6.9 mol per set at any gross hydrogen production rate. This result corresponds to an overall thermal efficiency of 0.89, the Camot efficiency. The system efficiency, 0.58, is lower because of reradiation losses. What this means is that a reversible device can produce 6.9 mol of hydrogen per second (net). However, if its inner workings require the use of pumps or other power-using components, the reactorseparator will have to process enough material so that it produces more than 6.9mol of hydrogen per second. The excess will be exactly what is required by the power-consuming components to make the process work. In other words, if the reactor-separator is operated in such a way that its gross hydrogen production is 7.9mol/sec, it will take the power generated by the use of 1 mol/sec of hydrogen, reversibly, to make it work. If the gross hydrogen demand is less than 6.9mol/sec, even though the device is internally reversible, energy will be wasted by transfer to the surroundings at the cold interface. In a real process, however, there are irreversibilities, and their magnitude will depend on the gross hydrogen demand. The more hydrogen we require the reactor-separator to produce, the more material we are required to handle, and the greater will be the losses within the machine. Thus, in practice, because of losses in the various components, the net hydrogen production rate will be reduced by an excessive hydrogen demand. Figure 9 shows how these losses depend on the hydrogen demand, i.e. the gross amount that we require from the reactorseparator. (1) A surprising result is that the power lost in the reactor-separator is small and virtually independent of the hydrogen demand. Irreversibility in the reactor-separator is associated with the pressure drop across the membrane. It is approximately proportional to fi9 In (PJP,). However, increased hydrogen demand is met in this system be an increase in the recirculation rate of the water. Both ti3 and In (P,lP,) remain about the same (Fig. 4), regardless of the hydrogen demand, and so, at 28OVK, losses in the reactor-separator are not great and virtually independent of the hydrogen demand. (2) The greatest losses occur in components in which the losses are not intrinsic to the process itself, the heat exchangers. At low hydrogen demands, the high temperature heat exchanger losses predominate. The losses are manifested as an unnecessarily high temperature of the emergent product stream, i.e. not all of the available energy of this stream has been effectively used. If some of this stream were used as the source for a heat engine to operate pumps, for example, the efficiency of the process might be substantially improved.
1150
R. B. DIVERand E. A. FLETCHER
(3) At high hydrogen demands, the heat pump power burden and the irreversibilities incurred in the low temperature heat exchanger are both high, The need for this component stems from our requirement that all process heat must come from the solar collector. This is an unnecessarily circumscribing restriction. Actually, a very substantial fraction of the heat required for the process could be relatively inexpensive heat furnished at low temperatures by flat plate solar collectors, since it would have to be furnished at temperatures in the range 300-350°K. If this incoming solar energy were figured as part of the input, it would have the (pointless) effect of decreasing the system efficiency, but it would most likely substantially reduce the cost of the hydrogen produced. From a practical standpoint, the cost of the hydrogen produced is of greater concern that an arbitrarily defined system efficiency. The present work has thus provided us with a gross picture of what such a device might look like, and it has suggested to us where tradeoffs should be sought to reduce the size and cost of hardware. For example, at high hydrogen demands, the burden on the high temperature heat exchanger and on the heat pump are both high, suggesting that the use of heat from the high temperature heat exchanger to drive a heat engine for operating pumps, coupled with the replacement of the heat pump by a low temperature solar collector, might provide important contributions to the economy of the process. Acknowledgements-Part of the support of this work came from the UnitedStates Department of Energy, Office of Basic Energy Sciences, Division of Advanced Energy Projects, Contract Number ER-78-S-02-4737.We are grateful for this support. REFERENCES 1. E. A. Fletcher and R. L. Moen, Science 197, IO50(1977).
J. D. Henry, Jr., Chemical Engineers HandbooR, pp. 17-44. McGraw-Hill, New York (1973). Techniques of Chemistry, Vol. VII: Membranes in Separation, pp. 31-33. Wiley, New York (1975). L. Lomb, The Kinetic Theory of Gases, p. 302. McGraw-Hill, New York (1934). K. M. Brown, Numerical Solution of Systems of Nonlinear Algebmic Equations, pp. 281-348. Academic Press,New York (1973). 6. F. Trombe, A. Le Phat Vinh, and C. Royere, Large-Scale Energy Test Facilities, Proceedings of the NSF International Seminor, p. 139. New Mexico State University, Las Cruces (1974). 7. R. C. Yu and E. A. Fletcher, Energy 4, (1979). A. Broggi, R. Joels, M. Morbello, and B. Spelta, Hydmgen Energy 2.23 (1977). ! R. B. Diver and E. A. Fletcher, Am. Ceramic Sot. Bull. 56, 1019(1977). 10: Private communication from B. Hill, Zircan Products, Inc., 110N. Main Street, Florida, NY 10921. 2. 3. 4. 5.
of Mechanical
B. DIVERand &m
Engineering,
A. FLETCHER~
University of Minnesota. MN 554% U.S.A. (Receiwd
I I I Church !%ree.t S. E.. Minneapolis,
9 April 1979)
Abstract-An analytical model of an archetypai device for using solar energy in a one-step thermochemical process for producing hydrogen and oxygen from water is presented. It is used to help us anticipate and evaluate sources of irreversibiitks associated with the operation of various components of such a device and to suggest alternatives which should be considered. INTRODUCTION Production of hydrogen and oxygen from water by the use of solar energy is a subject of current interest. In a previous paper,’ we suggested that a high-temperature, one-step thermochemical process which makes use of effusional separation in the Knudsen flow regime is a tantalizing possibility. In that paper, we considered ideal systems. Irreversibilities were given only superficial consideration. The objective of that study was to explore the possibilities offered by a new idea. The results were idealized so that the process could be compared with others that had seen similarly presented. The process is essentially an application of what follows: When water is heated to sufficiently high temperature, an equilibrium mixture of H, HZ, H20, OH, 0, and 02 is produced. The extent of water decomposition increases with increased temperature and reduced pressure. If such a mixture is fractionated through a barrier in the Knudsen flow regime, the lighter components will have become enriched in the effusate; the heavier components will have become enriched in the uneffused fraction?’ Thus, it is possible to effect the partial separation of the H and Hz from the other components of equilibrium mixtures of water. Application of the technique has been made in the separation of uranium isotopes3 The maximum thermal efficiency of a thermochemical process can be related to the Camot efficiency of a heat engine, (TH - TJTH, where TH and TL are, respectively, the upper and lower temperatures between which the device operates. Thus, from a thermodynamic standpoint, high temperature processes are good. From an operational standpoint, however, the thermal efficiency of real devices is limited by irreversibilities associated with the various internal processes needed to make them work. The principal objective of the present study was to pinpoint likely sources of inefficiency and to observe how these inefficiencies depend on operating variables and system con&nation. Sources of irreversibilities in the separator and other components of a postulated device were evaluated. Our approach was to calculate the entropy produced as a consequence of the operation of each of the major components and to relate this entropy production, which is ultimately manifested as a system ineIIkiency, to the operating variables. In this paper, we present the results of an investigation which makes use of an archetypal construct which has many features of a real device. Irreversibilities and losses which may be encountered in the principal components of real devices which use effusional separation are sought and evaluated so that they can be anticipated and perhaps avoided in succeeding models. THE MODEL
The specification of a model for such an arcktypal study is somewhat arbitrary. Different configurations are possible. Merences arise, for example, in the arrangement of pumps and heat exchangers and in the mechanisms selected for ekcting heat transfer. We constructed a +To whom correspondence
on this paper should be addressed. 1139
1140
R. B.
DIVER
and
E. A.
fiETCHER
model which we felt would be general enough to reveal the merits and shortcomings of the basic concept, and specik enough to identify the problem areas of real devices. Fiie 1 is a schematic diagram of our model. Its notable features are: (1) it is feasible, and each component can, at least in principle, be constructed and made to operate; (2) any real device will be likely to contain components similar to those which are considered in this model; (3) ail of the heat addition occurs at the high temperature and all rejection at the low temperature. The third feature serves a useful purpose insofar as the introduction of a certain thermodynamic formalism into our presentation is concerned, but it is not a necessary attribute of a practical device. As we shall see, this feature makes it judicious for us to introduce, later, an elaborate mechanism for heat transfer to the cold water to evaporate it. In practice, such heat transfer might easily be effected by the introduction of low-grade, low-temperature, flat solar collectors and by the rejection of more heat to the surroundings. The formal effect of this fix would be to reduce substantially the thermal efficiency of the device, but it might give us much cheaper hydrogen and oxygen from water. The operation of the device is described in the caption of Fig. 1. The individual components are discussed in the paragraphs which follow.
Solar collector
The solar collector concentrates the incident solar radiation. The eficiency of the collection process, r),, depends on the characteristics of the collector and the absorber. It is defined as
REACTORSElwtARm
LKXJIO SEPARAT!DRS Fig. 1. Schematic diagram of a system for producing hydrogen and oxygen from water. Water enters the system through an inkt valve which reduces its pressure from atmospheric to P, With neghgiik friction losses, P, will be the pressure everywbae of tbe uneffused material. It is heated to its saturation temperature and vaporixed in the low-temperature heat exchanger. The heat of vaporization is provided by heat exchange from the condenser of a heat pump and by the hot products emerging from the hiitemperature heat excw. The vapor is then butted to the hi& temperature, Tu, in the counter current high-temperature heat exchanger. The reactor-separator is in a Ma&body cavity equipped with a transparent window. Concentrated sunlight is iatroduced through the window to provide the heat necessary to maintain the high temperature of the reactor-separator. The interior of the cavity contains pipes whose might not be unlihe that of a tube-in-shell heat walls constitute the effusion membmne. Its ve exchanger. The effusate, eariched in Ii&r components, and the uneBused material are the sources of heat which is used to heat incomkg water to the high temperahue in Ure high- and low-temperature heat exchangers. The low-temtkratum beat exchanger ako serves as the heat source for the heat pump. The descendii streams are cookd to ambknt tempmature in the coder. They are then separately pumped, isothermally, to a useful pressure. Water that condenses in the low-temperature heat exchanger, cooler. and pumps is separated from the permanent gases in the liquid separators and may be returned to the system through the inlet valve. The numbers on the figure refer to stations referred to in the analysis.
Hydrogenand oxygenfrom water-11
&,JlA
1141
and is given by
t)h
aIAq* - acuT;, IA
rl,=-=IA
(1)
where &,, is the net energy thrx into the reactor-separator, I is the incident ambient solar energy flux, A is the collector area normal to the incident solar radiation, a is the effective reradiation area of the reactor-separator (the window area), I)~ is the optical efficiency of the collector, a and c are the effective absorptance and emittance of the reactor-separator, respectively, and u is the Stefan-Boltmann constant. The collector concentration ratio, C, is
Ala. Reactor-separator The reactor-separator
functions as the solar absorber, and it separates the components of the quihbrium mixture. It is assumed to be well stirred and in equilibrium. It operates isothenmdly; internal heat transfer is assumed to be very fast.t Fme 2 shows a possible separator configuration. The total membrane area, A, can be made indeperxlent of the reradiating area, a, in contradistincnon to the presumption of Ref. 1 that these areas must be coupled. Mass conservation requires that the mass flow rates, rit, be related as follows: fit* =
rirg,
tif,=lit3+rit,.
(2) (3)
Molar flow rates, ri, of hydrogen and oxygen atoms, in whatever molecules they may be found, must satisfy the conservation equations: fi0X.l
=
riox.4 + iox.
fiox.2= riox.3. nHY.1
= fiHY.4 + dHY.3r
dHY2
WINDOW
= dHY.3,
(4) (5) (6) (7)
1142
R. B. DIVERand E. A. FLETCHER
where
(8) (9) Also, since Hz0 is fed to the reactor, hHY.1 = 2dOX.l
Each of the six species effuses through the membrane at a rate given by4 h,2 = 44*63(J’ti- J’iy)&$ I. (MGrP2 ’
(11)
where Pi, and Piy are the pressures of the it/r species on the x and y sides of the membrane (atm), A,,, is the membrane area (cm’>, f is the fractional open area, and Mi is the molecular weight of the ith component. In this analysis, the Knudsen number is assumed high; ideal effusional separation is assumed. In practice, some viscous flow and some diffusion through the solid part of the membrane might be encountered. Additionally, the gas composition on each side of the membrane must satisfy. simultaneously, each of four independent equilibrium constants K(Tn) (eight equations in all), viz. KH*( TH) = k,Ip2w
WI
KH~o( TH) = ~H,O/pH*~O KoH(TH)
Ko,( TH)
= POH/POPH,
(13) (14) (15)
= ~,~~o*.
From Daltons law, 8P, = P,,
(16)
SPi, = Py3
(17)
and
Finally, an energy balance about the reactor-separator
gives
&,,ar= &hj+ k,h4- ti,h,,
(20)
where the tih are the enthalpy flows through the appropriate stations. The set of equations was reduced to give equations in five unknowns, which were solved by the use of NONLIN, a nonlinear equation system root-finder computer program? Heat-recovery systems The high and low temperature heat exchangers are assumed to operate without pressure loss. Their analysis is complicated by the chemical reactions and phase changes which occur in them. There are sometimes mismatches between the availability of the latent heat of a phase change or the heat of a reaction and the temperatures at which the transformations occur in the three streams. A sketch of the variation of the enthalpies of the streams with temperature, shown in Fig. 3(a), helps point this out. Figure 3(b), which shows the first derivative, C,,, is also helpful. These figures have no numbers on the coordinates because each operating condition is
Hydrogen and oxygen from water-11
1143
b
9+10)(‘+6’ ,Y.---
I (5*6)
0
-;I
TL
.’ Y
Descending Streams,/ / ,’
(3+4) /
Ascendmg Streams
TVAP
TH
Fig. 3. Schematic representation of the thermal characteristics of the working fluid as they vary with temperature in the heat exchangers and the cooler; a. enthalpy; b, heat capacity. The numbers on the figures refer to stations identified in Fig. 1. different;
however, the salient features are the same for all operating conditions. In the high temperature heat exchanger, the heat capacity of the descending (cooled) streams will be greater than that of the ascending (heated) stream because the combined heat capacity of hydrogen and oxygen is always greater than that of an equivalent amount of water and because the descending streams, being at a lower pressure than the ascending streams, are always more dissociated. Thus, the descending streams will always have a greater than needed capability for transferring heat to the ascending stream in the high temperature heat exchanger. The heat capacity spike at Tvap,the saturation temperature of HZ0 at P,, represents the latent heat of vaporization of the ascending (heated) stream. Since the descending stream is at a lower pressure than the ascending stream, its latent heat becomes available at a temperature which is lower than that needed to vaporize the ascending stream. In our construct, we use a reversible heat pump to transfer this heat and accept as a penalty the work required to operate the pump. An alternative might be to eliminate the heat pump and supply the heat necessary for vaporization from an additional source, as we have previously noted. The high temperature section of the exchanger energy balance is nighs+ ti.,hd + ti,h, - riz,h, - n&h5- tilghc,= 0,
(21)
where h is the specific enthalpy of the fluids. If it is assumed that the two descending streams emerge at the same temperature, hs, h6, and T5 = T6 can be determined. The energy balance for the low temperature heat exchanger is
The power supplied to the idealized heat pump, wr,,, is
*HP= &p( Tvap- TJ/ Tvapr
(23)
where &, is the rate at which heat is supplied to vaporize the feedwater minus the heat lost by the descending streams as they cool from T5 to T_, We required the two descending streams to have the same exit temperature; the unknowns he, h7, and W,, can be determined from the appropriate energy balance. Cooler and pumps The temperature of the descending streams is reduced to ambient by heat rejection to the
R. 3. DIVERand E. A. FLETCHER
1144
surroundings. Then the hydrogen and oxygen are pumped reversibly and isothermally to one atmosphere. The pump power required for the two-component, two-phase, hydrogen-enriched mixture is fit0
,
(24)
I
where R is the gas constant, P is the pressure to which the mixture is to be pumped (in this analysis, 1 atm plus the vapor pressure of water), Py is the pressure at the pump inlet, Pvapis the vapor pressure of water at TL, and PC is the pressure at which condensation begins. A similar equation applies to the oxygen pump. The first term in the brackets gives the work required to compress the steam to the saturation point and the second gives the work of compressing the steam as water is condensing in it; PY cannot be greater than PC. Since the work equivalent of the hydrogen produced is -AGH20(,j,m.16,the pump work is taken as a debt on our hydrogen production in this construct. Eficiencies
The system efficiency, defined as the work equivalent of the net hydrogen production rate divided by the solar power intercepted, is given by the product of the collector efficiency and the thermal efficiency, viz 7s = %
x
(25)
7th.
The collector efficiency has already been discussed. The thermal efficiency is given by
%et -
77th =
7
~H,,AGH,wI,,~.,~
=
-
%P -
%mm,,
&lar
QH
(26)
This approach to calculating thermal efficiency is straightforward but tells us nothing about where, in a particular operating configuration, losses occur and how efficiency might be improved. For the purpose of learning the sources of thermal inefficiencies, we invoke the use of entropy production as a measure. The irreversibilities and the lost power in each component can be calculated from the rate of entropy production associated with its operation. The rate of entropy production associated with the reactor-separator, for example, is
3 = t&s3 + nh--
ni,s,- (&,,JT,d.
(27)
The lost power associated with the operation of each component is equal to the product of the rate of entropy production associated with its operation and the ambient temperature. The thermal efficiency can therefore be calculated by the alternative relationship Available Power-ELost Power 7th
(28)
= Qwlar
where the available power is the product of the Camot efficiency and &,rar, while ZLost Power is the sum of the lost power in all of the components. ANALYSIS
Variable selection
To provide a realistic scale for our analysis, we used a collector system patterned after the French CNRS solar furnace at Ode&-Font Romeu.6 The effective collector area, A,, is 2800 m*. The intensity of solar radiation, I, is 0.1 W per square centimeter. The concentration ratio is 10,000. The collector efficiency, absorptance, and emittance are all taken to be one; it is a blackbody cavity. Thus, &,, is a function of TH only. Once &rar and the ambient
Hydrogenand oxygen fromwater-11
1145
temperature have been specified, the problem has four remaining degrees of freedom. In this analysis, we selected TH, P,, the membrane open area, A,, = fA,, and the gross hydrogen production rate, riH2c.The dependent operating variables are thus P,, the mass flow rates, the component power requirements, the heat-rejection rates and irreversibilities, the fluid properties in the various parts of the system, the efficiencies, and the net power equivalent of hydrogen produced. The inputs chosen were chosen because they facilitate solution of the reactor-separator problem and permit sequential solution of the equations that pertain to the remaining components. Although we have used the Odeillo furnace as a prototype, the results of this analysis for any given Tn and P, can be applied to any other collector system by scaling A ,_,,, tiHzO,and the resultant, dimensionally-dependent variables, in proportion to the net solar heat rate, &,I,. RESULTS
In the interest of economy of presentation, we first discuss the effects of varying the extensive variables tinzc and Aopenat a representative combination of Tu and PI. Our observations are then extended to other temperatures and pressures. Figures 4-11 give results for the example condition: TH = 2800°K; P, = 0.2atm. Figure 4 shows that PJP, and fi3 depend only slightly on the gross hydrogen production demand, ri,,. This surprising result is a consequence of the fact that an increased demand for hydrogen production is met by this system as follows: the mass flow rate to the reactor, ml, increases, as is shown in Fig. 5. The hydrogen content of the x-side gas is then less depleted than it would have been at a lower flow rate. The demand for additional hydrogen production is thus met primarily by the changing composition of the effusate rather than its quantity; it does not, therefore, affect strongly the irreversibility. Figures 4 and 5 also show that smaller membranes require larger pressure drops to achieve a given gross hydrogen production rate. They also require smaller effusate flow rates because the higher pressure drop increases the separation efficiency. Because larger pressure drops entail compensating smaller effusate flow rates, the irreversibilities associated with the smaller membranes are less than those associated with the larger membranes. The effusate fraction or cut, tiJk(, is the dependent variable in Fig. 6. The hydrogen production rates corresponding to points where these lines cross the horizontal axis are the TH i 2600 IO
4
e
px
.6 .4
PK zO.2
0
K otm
A own
#0.5 ’ 0.3 -
T,, = 2800 K
dl
PX=0.20tm
0.1
2
q 9
1.4 1.2 -
f
1.0 -
z -0 L
.6 -
b
I 0.5 8 0.3 A own
Cm21
.6 -
2 5:
.4 -
g.=
2-
-
0.1 I
I
0
2
1
4
1
6
2
GrossH,
I
6
GrossH2 ProductionRate,moles/s
3
Production
4
5
6
Rate, moles/s
Fig. 5.
Fii. 4. Fig. 4. Variationof pressureratio (a) and mass effusion rate (b) across the membranewith the hydrogen demand. The membrane’sopen area is the parameter.The pressure ratio, and hence, the mass flow rate throughthe membrane,are both virtuallyindependentof the hydrogendemandbecause increaseddemand is achieved by modificationof the compositionof the feedstreamby increasingthe water feed rate (Fig.5). Fii. 5.
Variation of water feed rate to the reactor-separatorwith hydrogendemand.The effusionmass flow rate, MI,,is also shown for comparison.
7
R. B. DIVERand E. A.
1146
FLETCHER
TH = 2600 K Px=0.2atm
e Gross
H,
Production
Rate,
Effusate
moles/s
Cut,
$/+I,
Fig. 7.
Fig. 6.
Fig. 6. Variation of the effusatecut (rirJk,) with hydrogendemand. Fig. 7. Variation of &,/dHzwith cut (&/rir,) at variousopen
areas.
limiting hydrogen production rates. Since rir3cannot be zero, the tir, required to maintain steady operation at these points approaches infinity. Hydrogen demand rates higher than those at the intercepts cannot be achieved by any feed rate, no matter how high. The figure also shows that larger membranes can produce more hydrogen. The next two figures show the importance of effusate fraction (cut) as an operating variable. Figure 7 shows the amount of water which must be circulated to collect each mole of hydrogen as a function of effusate fraction for three membrane sizes. An optimum operating condition here is indicated at an effusate fraction of about 0.5 for all of the open areas. This result is in qualitative agreement with experimental results obtained with two component, non-reacting mixtures.’ From the standpoint of separation, smaller membranes are better than larger ones because they involve larger pressure drops and consequently less back effusion of the lighter components. In Fig. 8, the thermal efficiency of the device is plotted as a function of effusate fraction for the various open areas. For each Aown,an optimum &/rir, and, therefore, fiiH2cand ti,, exists. Up to a point, smaller open areas provide better thermal efficiencies and require lower effusate fractions for optimum operation. In Fig. 9, the component losses are plotted as functions tiHsc for a single open area. These losses were calculated from the rates of entropy production in each of the components. For this temperature and pressure, the separator irreversibilities are relatively small and insensitive to tin2c because irreversibility is proportional to the logarithm of pressure ratio and tijtg,both of 7” = 2800 R * 0.2ohn
5 2 s
E w 2 I
.35 L a.1
k
,629_------__-----~)o__ bc&
Px = 0.2
a5
_____
IWO-
6.67 -6
z 9%
125o-
.20-
A opsn(m21
2
.g 4
.I5 .I0 -
,
$“,
z
Aow. s 0.3m2
TH = 2600
.m.25 -
.05 .2
.4
Effusate
.6 Cut,
Fig. 8.
.6
1.0
d IOCOg 750a
Hqh Temp. Heal Each. LOSS
Net
Low Temp. Heal Ev.ch. LOSS
4
500-
ri~,/riq
:
FzeOCtor - Separotw 1015 Co& 0
2.0 Gross
4.0 H,
6.0
Production moles/s
loss 0.0
Rate,
Fig. 9. Fig. 8. Variation of thermal efficiencywith cut at various open areas. Fig. 9. Summary which showshow the performanceof the device and the sourcesof irreversibility losses at the operatingcondition:2tWPK, P, = 0.2 atm, A.,, = 0.3 m3, dependon the hydrogendemand.
1147
Hydrogen and oxygen from water-11
which are insensitive to rlr.i2c.Irreversibilities in the other components are associated with heat transfer across larger temperature differences imposed by the constraints under which this model operates. The high temperature heat exchanger losses are highest at low hydrogen production rates because the heat absorbed in the separator and not used directly for separation provides much more energy than is necessary to preheat the ascending stream. The temperature of the descending stream is thus much higher than it has to be. Its temperature at the exit of the high temperature heat exchanger is high. Losses in the low temperature heat exchanger pass through a minimum. Losses to the left of the minimum result primarily because of the increasing temperature difference between the streams coming out of the high temperature heat exchanger and vaporizer. Losses to the right of the minimum result primarily from greater mass flows. Figure 10 shows the burdens imposed by the various components which require work inputs for the same set of operating conditions as those of Fig. 9. The ordinate is power; the abscissa is gross hydrogen production rate. The uppermost line is the power equivalent of the hydrogen produced by the reactor-separator. However, some of the hydrogen must be used to operate the heat pump and the fluid pumps. The heat pump power burden and the pump power burden are also shown in the figure. If these requirements are met by the use of hydrogen in a reversible fuel cell to produce electric power and subtracted from the gross power output drive, the result is the net power output equivalent curve. This gives the net amount of hydrogen produced in the process. Thus, the system efficiency, even at a given operating temperature, pressure, and open area, depends on the hydrogen demand and has a maximum value at demands somewhat lower than that corresponding to the highest gross production rates achievable. Figure 11 shows how these maximum thermal and system efficiencies depend on TH, P,, and A _,. They both increase with temperature and, at a given temperature, increase as the T” = 28cm P~*o.*mn
A..pn’03td ,6*g-__-__--
____
‘Icornal XQro1.r _____ ____
_--6.87
1500 1250 -
2.0
4.0
Gross
8.0
6.0
Hz Productton KlOkS/S
Role,
Fig. IO. Summary which shows variation of pump power consumption and the net power equivalent of the hydrogen produced with the hydrogen demand.
b
Aopcn = 0.1 tn2 ---
ql
300
I 2400
I 2500
I 2600
T,,K
I 2700
I 28W
I 2900
1 3000
I
2300
Thermal System
I 2400
,,
I 2500
I 26co
I 2700
I 28X1
I 2900
T,,K
Fii. 11. Variation, with temperature of the maximum thermal and system efficiencies corresponding to a given pressure, P,, with a membrane having an open area of (a), 0.5 m* and (b) 0.1 n#. WY Vd. 4. No. 61
I Yxcl
R. B. DIVER
1148
and E. A.
FLETCHER
pressure is reduced. These results reflect the advantage of having to circulate smaller amounts of water. They also suggest that the use of smaller membranes increases the system efficiency, provided that the membrane is not made so small that the requisite amount of hydrogen cannot be produced. Figure 12 shows how the minimum riO/riH,cdepends on the same variables. In general, thermal efficiency and ease of separation improve with increased temperature and reduced pressure because of increased dissociation. However, as Fig. 13 shows, collector efficiency and &,,_ decrease with temperature in the temperature range of our interest. Thus, temperature has opposite effects on the two components of system efficiency. Figure 14, which shows the variation of the pressure ratio across the membrane with temperature, membrane area, and P,, illustrates the fact that higher temperatures in general entail less irreversibility by requiring higher pressure ratios and, concurrently, lower mass flow rates. The lost work of the separator, presented in Fig. 15, illustrates the point further.
-
Aopen = 0.5
rn2
0.1 0 2300
I 2400
I 2500
I 2600
I 2700
I 2.900
I 2900
I 3000
T, K
Fig. 12. Variation, with temperature, of the minimum molar water flow rate per mole of hydrogen demand corresponding to a given pressure, P, with membranes having open areas of 0.5 m* and 0.1 m*.
T,.,,K Fig. 13. Variation of collector efficiency with temperature. C = 10,000;qA = (I = l = 1, in Eu. (I).
T,,,K
T,,,K
_ Fig. 15. Fig. 14. Fig. 14. Variation of pressure ratio, PJP,, with temperature, at various upstream pressures at maximum overall efficiency at two membrane open areas. Fig. IS. Variation of irreversibility losses associated with the separation process with temperature at various upstream pressures at maximum overall efficiency when membrane open area is 0.5 m*.
Hydrogen and oxygen from water--II
1149
DISCUSSION
In principle, a reversible thermochemical procedure for producing hydrogen and oxygen from water can have, as a limiting efficiency, the Camot efficiency. In practice, two kinds of losses are encountered: (1) Those which are inherent in the process itself, such as those which result from pressure discontinuities. (2) Those which result from the fact that, in real processes, compromises must be made in order to make the process work within reasonable constraints, usually temporal or economic. The magnitudes of the former, in the present process, depend on the operating conditions of the reactor-separator component and can be made quite small at sufficiently high temperatures. The magnitudes of the latter depend on the nature and arrangement of auxiliary components and hardware, which are quite arbitrary. In this study we have used an archetypal device, a construct which can be improved as we learn about the intricacies of its operation. We have proposed an u priori reasonable arrangement of auxiliary components to serve as a starting point from which the operation of the process can be improved. Our construct points out where losses are likely to be encountered, demonstrates that some fears we had about irreversibilities we would encounter in the reactor-separator are not so serious as we feared they might be, and suggests where and what kinds of alternative components should be considered. Our approach to the problem is thus not as general as some others: but it has the advantage for us of being easily understood and of telling us how to go about improving our process. For example, we can illustrate some general conclusions with reference to Fig. 9. Fire 9 shows that, if we choose to operate the reactor-separator at a temperature of 2800°K with an upstream pressure of 0.2 atm using a membrane with an open area of 0.3 m*, a perfectly reversible process should permit us to produce hydrogen at a net production rate of about 6.9 mol per set at any gross hydrogen production rate. This result corresponds to an overall thermal efficiency of 0.89, the Camot efficiency. The system efficiency, 0.58, is lower because of reradiation losses. What this means is that a reversible device can produce 6.9 mol of hydrogen per second (net). However, if its inner workings require the use of pumps or other power-using components, the reactorseparator will have to process enough material so that it produces more than 6.9mol of hydrogen per second. The excess will be exactly what is required by the power-consuming components to make the process work. In other words, if the reactor-separator is operated in such a way that its gross hydrogen production is 7.9mol/sec, it will take the power generated by the use of 1 mol/sec of hydrogen, reversibly, to make it work. If the gross hydrogen demand is less than 6.9mol/sec, even though the device is internally reversible, energy will be wasted by transfer to the surroundings at the cold interface. In a real process, however, there are irreversibilities, and their magnitude will depend on the gross hydrogen demand. The more hydrogen we require the reactor-separator to produce, the more material we are required to handle, and the greater will be the losses within the machine. Thus, in practice, because of losses in the various components, the net hydrogen production rate will be reduced by an excessive hydrogen demand. Figure 9 shows how these losses depend on the hydrogen demand, i.e. the gross amount that we require from the reactorseparator. (1) A surprising result is that the power lost in the reactor-separator is small and virtually independent of the hydrogen demand. Irreversibility in the reactor-separator is associated with the pressure drop across the membrane. It is approximately proportional to fi9 In (PJP,). However, increased hydrogen demand is met in this system be an increase in the recirculation rate of the water. Both ti3 and In (P,lP,) remain about the same (Fig. 4), regardless of the hydrogen demand, and so, at 28OVK, losses in the reactor-separator are not great and virtually independent of the hydrogen demand. (2) The greatest losses occur in components in which the losses are not intrinsic to the process itself, the heat exchangers. At low hydrogen demands, the high temperature heat exchanger losses predominate. The losses are manifested as an unnecessarily high temperature of the emergent product stream, i.e. not all of the available energy of this stream has been effectively used. If some of this stream were used as the source for a heat engine to operate pumps, for example, the efficiency of the process might be substantially improved.
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R. B. DIVERand E. A. FLETCHER
(3) At high hydrogen demands, the heat pump power burden and the irreversibilities incurred in the low temperature heat exchanger are both high, The need for this component stems from our requirement that all process heat must come from the solar collector. This is an unnecessarily circumscribing restriction. Actually, a very substantial fraction of the heat required for the process could be relatively inexpensive heat furnished at low temperatures by flat plate solar collectors, since it would have to be furnished at temperatures in the range 300-350°K. If this incoming solar energy were figured as part of the input, it would have the (pointless) effect of decreasing the system efficiency, but it would most likely substantially reduce the cost of the hydrogen produced. From a practical standpoint, the cost of the hydrogen produced is of greater concern that an arbitrarily defined system efficiency. The present work has thus provided us with a gross picture of what such a device might look like, and it has suggested to us where tradeoffs should be sought to reduce the size and cost of hardware. For example, at high hydrogen demands, the burden on the high temperature heat exchanger and on the heat pump are both high, suggesting that the use of heat from the high temperature heat exchanger to drive a heat engine for operating pumps, coupled with the replacement of the heat pump by a low temperature solar collector, might provide important contributions to the economy of the process. Acknowledgements-Part of the support of this work came from the UnitedStates Department of Energy, Office of Basic Energy Sciences, Division of Advanced Energy Projects, Contract Number ER-78-S-02-4737.We are grateful for this support. REFERENCES 1. E. A. Fletcher and R. L. Moen, Science 197, IO50(1977).
J. D. Henry, Jr., Chemical Engineers HandbooR, pp. 17-44. McGraw-Hill, New York (1973). Techniques of Chemistry, Vol. VII: Membranes in Separation, pp. 31-33. Wiley, New York (1975). L. Lomb, The Kinetic Theory of Gases, p. 302. McGraw-Hill, New York (1934). K. M. Brown, Numerical Solution of Systems of Nonlinear Algebmic Equations, pp. 281-348. Academic Press,New York (1973). 6. F. Trombe, A. Le Phat Vinh, and C. Royere, Large-Scale Energy Test Facilities, Proceedings of the NSF International Seminor, p. 139. New Mexico State University, Las Cruces (1974). 7. R. C. Yu and E. A. Fletcher, Energy 4, (1979). A. Broggi, R. Joels, M. Morbello, and B. Spelta, Hydmgen Energy 2.23 (1977). ! R. B. Diver and E. A. Fletcher, Am. Ceramic Sot. Bull. 56, 1019(1977). 10: Private communication from B. Hill, Zircan Products, Inc., 110N. Main Street, Florida, NY 10921. 2. 3. 4. 5.