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Thermodynamics of M u l t i - S t e p
Water
Decomposition Processes
r
James
E.
Funk
\
i
College of Engineer ing
Un ive rsi ty of Kentucky
Le xin gto n, Kentucky 40506
Processes which con ve r t water i n t o hydrogen and oxygen are of i n t e r e s t
f o r many re as on s,
inc lud ing th e many advantages accru ing t o t he
t r a n s -
p o r t of en ergy a s hydrogen. Hydrogen may be used a s
a
sourc e of th er -
m a l or e l e c t r i c a l ene rgy , depending on w hethe r
it
i s burned or used i n
an e lec t roch emic al dev ic e such
as
a f u e l
c e l l .
Hydrogen i s a l s o a
key
raw
material
i n t h e c he m ic al pr o c e s s i n d u s t r i e s
and i n pe tr ol eum r e f in i ng . It i s e s ti m a te d t h a t by 1975 t h e t o t a l
consumption of hydrogen i n t h e
U . S . w i l l
b e
a t
t h e r a t e of f o u r
t r i l -
l i o n c u b i c
f e e t pe r yea r and growing. Gaseous and l i q u id hydrocarbons
are
now th e pr i nc ip a l r a w m a t e r i a l s f o r p ro du ci ng l a r g e q u a n t i t i e s o f
hydrogen by means of e i t h e r c a t a l y t i c steam reforming or p a r t i a l oxi-
d a t i o n .
a r t i f i c i a l n a t u ra l g as ,
w i l l
increase the demand for hydrogen even
more. I t would c l e a r l y b e i n t h e i n t e r e s t o f c o n s e r v a ti o n of n a t u r a l
reso urc es t o develop an economical proce ss t o produce hydrogen f rom
w a t e r .
A
comprehensive stud y of therm al pro ce sse s t o produce hydrogen from
water was performed and re p or te d by Gene ral Motors ( 1 , 2 ) . A t h r e e
s t e p p r oc e s s
i n v o l vi n g e i t h e r t a n ta lu m c h l o r i d e o r bi sm u th c h l o r i d e
and a f ou r s t e p p r oces s u s ing e i t h e r mercury ch l o r id e or vanadium
c h l o r i d e
w e r e
desc r ibed . A ge ne ra l d i sc us s io n of energy requirements
f o r th e decomposition of wa ter was pu bl ish ed by Funk and Reinstrom 3 )
and , more recen t ly , a f o u r s t e p t he rm a l p r o c e s s w a s descr ibed by
deBeni and Marchetti
4 ) . A
re vie w o f t h e c u r r e n t s t a t u s
of
e l e c t r o -
l y t i c hyd rogen as a f u e l has been pub li shed by G rego ry , e t . a l . ( 5 ) .
The p r e s s u r e f o r in e xp e ns iv e a nd p l e n t i f u l p i p e l i n e g a s ,
\
Second L aw L i m i t a t i o n s
I f one gram mole of wa ter of l i q u id wa te r
a t
25OC and 1 atm i s conver-
t e d i n t o one gram mole of hydrogen and one ha lf gram mole of oxygen
a t
25OC and
1
atm t h e g i b b s f u n c t i o n f o r t h e sys tem in cr ea se s by 56.7
kc al , th e en tha lpy inc rea ses by 68.3 kc a l and the en t ropy inc re as es by
39 cal/OK. I f t h e decom position i s done re ve rs ib ly a t 25OC an d1 atm--
4
s ay i n a n e l e c t r o l y s i s c e ll -- 56 .7 k c a l , t h e cha nge i n t h e g i b b s func-
t ion , mus t be supp l i ed
as
u s e fu l work and
11.6 k c a l
t h e d i f f e r e n c e
1
between t he ent hal py change and gibbs fu nc t i on change, m ust be sup-
p l i e d
as
h e a t .
The amount of us e fu l work re qu ir ed may be decreased by ope ra t in g the
si ng le s te p decomposit ion a t some hig her temp erature. The amount
of
energy requi red a s h e a t
w i l l
i n c r e a s e by t h e
same
amount th a t
the
work
r equ i r ed i s decreased under th e b e s t c ase assumpt ions of e qua l spec i -
f i c h e a t s a nd p e r f e c t t h er m al r e g e n e r a t i o n of p r o d u c ts a nd r e a c t a n t s .
\\
t
If the
pr oces s
i s
depicted on a temp erature e ntropy diagram, t h e work
r e d u c t i o n i s equa l t o t h e a r e a enc losed when t he p r oces s l oop i s
cl os ed by allowing t h e c oo le r hydrogen and oxygen
t o
form water
,
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The total work and heat requirements
4) over the I reactions to obtain
I
1
\
i=I
w
=
AG, -
AS(^)
i=l
are obtainedby summing
3)
and
[T i)
-
To] 5 )
Another important feature becomes apparent if the process is divided
into J reactions which have positive entropy changes and L reactions
which have negative entropy changes.
To
minimize the required work,
the first group of reactions
should be operated at some high tempera-
ture,
TH,
and the second group operated at To.
In this case,
j=
As is evident from Eqn. (-71, the required
-
To]
work is zero when
There is no reason why
( 8 ) cannot be satisfied along with
7 )
i=I i=J
l=L
This result cannot be obtained for a single step process, in which
case the zero work requirement must be accomplished by a temperature
manipulation rather than the selection
of
a suitable sequence
of
reactions.
Work of Separation
The theoretical work of separation, AGs, required to separate a mix-
ture of ideal gases into its components is given by
AGs
= -
R T . ~k In Xk 10)
is the number of moles of the kth component and xk is the
whereole fr ction of that camponent.
Fig. 1 shows a reaction process which accomplishes the reaction
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82
The amount of
material
e n t e r i n g t h e s e p a r a t o r dep end s o n
E ,
t h e f r a c -
t i o n a l mola r c onve r s i on o f R1, w hich i n t u rn de pe nds on t h e s t a nda rd
f r e e ene rgy change fo r
t h e reaction,
AGR.
t h e s t a n da r d f r e e e n e rg y ch an ge f o r a r e a c t i n g m i x tu r e
of
i d e a l g a s e s
with Eqn. (10) y i e l d s
Combining t h e de f i n i t i o n of
A G ~ A G ~ - R T [ ~
-1 I n
s1 r2
In
s2 --- - C p - C r )
In p*]
(12)
where
and p* i s t h e o p e r a t i n g p r e s s u r e
4 x 1 .
(12)
shows t h a t t h e t h e o r e t i c a l work of s e p a r a t i o n
i s
g r e a t e r
t h a n s t a n d ar d f r e e e ne r gy ch an ge f o r t h e r e a c t i o n . I
An example of th e t h e o re t i c a l work of se pa ra t io n f o r the vanadium
c h l o r i d e p r o c e s s i s shown i n F igs . 2 and 3. Fig. 2 i s
a
schematic of
t h e f i r s t s t a g e i n which t h e r e
i s
a g a s ph as e r e a c t i o n o f c h l o r i n e
w i t h w a t e r
a t
1000K a t
1
atm. P ig . 3 shows th e th eo re t i ca l w o r k of
s e pa ra t i on a nd it may b e noted t h a t th e sep ara t io n work
i s
i nc re a s e d
i f the mi x t u re l e a ve s the r e a c t i o n cham ber a t less t ha n e qu i l i b r i um
c ond i t i ons . F i g. 3 i s
f o r t h e s e p a r a t i o n of a l l four components and
the minimum work requirement i s 9.2 k c a l pe r gram mole of hydrogen
produced.
A
s imilar
c a l c u l a t i o n f o r t h e s e p a r a t i o n of o n ly t h e
HC1
and O 2 y i e l d s a work requirement
of
7.1 kca l .
i
The Vanadium Chloride Process
I
Thi s p roc e s s
w a s
s t u d ie d i n c o n si d er a bl e d e t a i l . A p l a n t l a you t was /
The en t i r e vanadium c hl or id e process
i s
shown i n F ig . 4. The
sums
of
t he e n t ha lpy , e n t ropy ,
and f r e e energy changes o n o t e x a c t l y equal
t h o s e f o r w a t e r com pos it ion becau se of q ue st io na bl e thermochemical-data.
made assuming a h el iu m c o o l e d n u c l e a r r e a c t o r a s t h e h e a t s ou rc e.
Estimates
w e r e
made f o r pumping, he a t re gen era t ion , etc. The r e s u l t s
are shown
i n T ab le 1 and, as can b e s e e n , t h i s p r o c e ss
i s
no t as
e f f i c i e n t
as
a
w a t e r
e l e c t r o l y s i s p l an t .
The ob je c t he re i s n o t to d e s c r i b e a n i n e f f i c i e n t p r o ce s s - any number
of such proce sses can be e a s i l y d e v i s e d . It is, ra ther
an a t t e m p t t o
qu i c k l y l o s e t h e i r a ppe a l when subjected t o sa ne what more p ra c t i c a l
co ns ide ra t ion s of work of sep ara t io n , the rmal reg ene ra t io n , pumping
F e r
etc .
Such
a
r e s u l t i s n o t e s p e c i a l l y s u r p r is i n g i n v i e w of the
ob l e c t i ve , w hich , i n i t s most fundamental
t e r m s ,
i s
an a t t em pt t o con-
v e r t h e a t t o u s e f u l work more e f f i c i e n t l y t h a n i n a s ta te of t h e a r t
power plant .
Refe rences
1.
r
i n d i c a t e t h a t p r o c es s e s which may be i n i t i a l l y a t t r a c t i v e
can
q u i t e
F i n a l
Technica l Repor t - Ammonia P rod uct i on F e a s ib i l i t y Study ,
Al l i so n Div i s ion of Genera l Motors ,
EDR
4200, November,
1965.
f
2.
System Study of Hydrogen Gen era tio n by Thermal Energy, A ll is o n
Div i s io n of Genera l Motors EDR 3714, vol . 11, Supplement A, 1964.
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3.
Funk, J.
E. ,
and Reinstrom,
R . M . ,
Energy Requi rements i n t h e
Product ion
of
Hydrogen From Water ,
I
EC Proc. D e s .
D e v . ,
v o l . 5, N o . 3, pp 366-342, Ju ly 1966 .
4 .
deBeni,
G .
and Marchet t i ,
C . ,
Hydrogen, Key
t o
t h e Energy Market ,
Eur o Spe c t r a , 9 ,
46-50,
June, 1970.
Parameter
Maximum helium t em -
p e r a t u r e
Minimum helium t em -
p e r a t u r e
H e l i u m
system pres-
sure
P r o c e s s h e a t i n p u t
T o t a l h e a t re-
5. Gregory, D. P., Ng D.Y.C. , and Long, G .
M.,
t o be pu bl is he d i n The
Elect rochemis t ry of Cleaner Environments, J . O ' M . Bockr is , Ed.,
New York, Plenum P re s s ,
1971.
U n it s Systems Remarks
F
2000
2000 1500 1500
F 37 37
67 67
atm
1 0
1
10
1 H e
p r e s s u r e
drop
e q u a l s
1 0
p s i i n
a l l c a s e s
k c a l 1 5 5
155
475 475
Adknowledgment
This work
w a s
done a t t h e A l l i s o n D i v is i on
of
General
Motors
and was
p a r t i a l l y s u pp o rt ed by
U.S.
Army Engineer
Reac to r s
Group,
F o r t B e l -
v o i r , V i r g i n i a . P e rm i ss io n
t o
p u b l i s h t h e s e
r e s u l t s
i s g r a t e f u l l y
acknowledged.
Tab le
1
Vanadium Chloride
Process
D a t a Tabu la t ion
I
j e c t e d
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L
l
n
c
0
L
0
s z
Z
.e,
u
0
Z
a
2
a
. .
m
a,
Lc
a
:
a,
a
Lc
d
JZ
U
4
.
a .
E
m
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8
100
-
0
2
0
N
.L
Temperature
=
IOOOOK
Pressure
=
atm
al l components separated)
0 . 2
0.4 0.6 0.8
1.0
Extent
of
reaction -e
F i g .
3
Th e o re ti c a l Work of Separat ion
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112 Q l)
Stage I
g]+Cl, g) -2HCl g )
+
1/2
O, g) a t
1340OF
+
-
77OF
Stage
III
4VCt3 s)+2VCl4
9 )
+OVCC 8 ) a t 1340OF
Stage
Ip:
@
c
2VCI4
I)e
V C J ,
(E) C12 s )
a t
77OF
Enthalpy, entropy, and f ree energy tab ulat ion
values in kilocalories)
. .
Fig Vanadi- Chloride Process
9
O r
-26.71 73.4
-46.0 48.3'
5 3 9
59.9