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ORNL-2677.txt
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MARTiH MARL
|
ORNL.2677
Reactors—Power
TiD-4500 (14th ed.)
Contract No, W-7405-eng-26
REACTOR PROJECTS DIVISION
ALUMINUM CHLORIDE AS A THERMODYNAMIC WORKING FLUID
AND HEAT TRANSFER MEDIUM
M. Blander, L. G. Epel, A. P. Fraas, and R. F. Newton
DATE ISSUED
SEP 911959
OAK RIDGE NATIONAL LABORATORY
Uak Ridge, Tennessece
- opesated b
UNION CARBIDE CORFORATION
for the
U.5. ATOMIC ENERGY COMMISSION
MARTIN MARIETTA ENERGY SYSTEMS LIBRARIES
R
3 4456 03LL3LY O
ALUMINUM CHLORIDE AS A THERMODYNAMIC WORKING FLUID AND HEAT TRANSFER MEDIUM
M. Blander L.. G. Epel A. P. Fraas R. F. Newton
ABSTRACT
The basic physical properties ond thermodynamic constants of aluminum chloride have been
calculated to obtain the data required for engineering calculations of thermodynamic cycles
employing aluminum chloride vapor. The possible corrosion problems invelved were evaluated
from the standpoint of basic chemical thermodynamics, and it was concluded that high-nickel-
content alfoys would contain aluminum chloride satisfactorily.
The advantages of gaseous aluminum chloride as an intermediate heat transfer medium in a
molten-salt-fueled reactor were evaluated. It was determined that the temperature range of the
molten-salt heat transfer system was too low to utilize aluminum chloride effectively. A gas.
turbine cycle employing aluminum chleride as the working fluid and a binary vapor cycle employing
water vapor for the lower temperature cycle were also considered. Meither of these studies showed
aluminum chloride to have outstanding advantages. It is believed, however, that special appli-
cations may be found in which it will be possible to exploit the unique characteristics of aluminum
chloride.
INTRODUCTION
Gaseous aluminum chloride appears to be attrac-
tive as a heat transfer medium and as a thermeo-
dynamic-cycle working fluid as a consequence of
the fact that it exists as the monomer AICI, at
high temperatures and as the dimer A|2C|6-ct fow
temperatures. The effective specific heat and
thermal conductivity of a gas that associates are
considerably enhanced because of the association
equilibrium at temperatures ot which there is an
appreciable fraction of both monomer and polymer,
and therefore aluminum chloride may be an excep-
tionally good heat transfer medium for some
applications. Its possibilities as the working
fluid in a thermodynamic cycle stem from the fact
that, in an idealized gas turbine with a negligible
pressure drop in the system, the pump compressor
will require work proportional to the compressor
inlet temperature times the specific gas constant
of the dimer for any given pressure ratio. In the
high-temperature region at the turbine, on the other
hand, if the gas is completely monomeric, this
same weight of gas will do work proportional to
the turbine inlet temperature times the monomer
gas constant for the same pressure ratio. Because
of the relatively large difference in the gas constant
between the monomer and dimer, the ratio of
turbine work to compressor work will be greater
than for a gos that does not dissociate. Further,
the energy losses due to the inefficiency of both
the compressor and the turbine will have relatively
smaller effects on the over-all thermal efficiency
with a dissociating gos as the working fluid.
BASIC PHYSICAL PROPERTIES OF
ALUMINUM CHLORIDE
The objective of this study was to investigate
the possible advantages of aluminum chloride
arising from its dissociation and the consequent
increase in effective specific heat and thermal
conductivity. Qualitatively the reason for these
increases is simple. Lowering the temperature of
the gas will yield not only the heat given off if
the composition of the gos were ‘‘frozen,”” but,
since the gas is more highly associated at lower
temperatures, it will also give off the chemical
heat due to the association of some of the monomer
molecules as a result of lowering the temperature.
The same phenomenon increases the thermal
conductivity. The thermal conductivity is the
amount of heat that would be transferred in unit
time across unit area from a temperature T + dT
to 1 divided by the temperature gradient, d7/dx.
The frozen thermal conductivity is that which
would occur if the composition were frozen at an
average weight fraction @ _ of the polymer and w,
of the monomer at both temperatures. Since w,
is higher at 7 + dT and w_ is higher at T than the
average, relatively more monomer would diffuse
from T +dT to T and more polymer from 1" to T +dT
than for a frozen composition. The composition
of the higher-temperature gas molecules diffusing
to the lower temperature would change with a
trend toward the lower equilibrium concentration
of monomer at the lower temperature and would
give off heat in the process. This chemical heat
contribution is part of the heat flux.
Quantitative expressions for these phenomena
have been given by Butler and Brokaw.! For a
substance which dimerizes,
AH2 w]wzfl + wl)
C, =C, + e (1
be v/ RT?2 4M]
AHZ (PP [y,
A, = A+ - : (2)
€ RT2A\RT /N 2
where
Cpe = effective specific heat in
cal.g™ .deg™ !,
Cpf = frozen specific heat,
AHl = heat change for the reaction
—_—
AlLCl = 2A1CH,,
R, R* = gas constants in proper units,
w, w, = weight fraction of monomer and dimer,
respectively,
A, = effective thermal conductivity in
caleem™ Vsec™ tideg™ !,
)\f = frozen thermal conductivity,
D12 = interdiffusion coefficients of monomer
and dimer,
P = total pressure,
M, = molecular weight of a monomer.
). N. Butler and R. S. Brokaw, J. Chem. Phys. 26,
1636 (1957).
The guantities of practical interest, the effective
specific heat, C, , the effective thermal conduc-
tivity, A, and the viscosity, have never been
These and other quantities of interest
must be estimated. It is fortunate that the theory
of gases is well developed and, for some calcu-
measured.
lations, is more reliable than measurements.
Effective Specific Heat
The effective specific heat was calculated by
use of Eq. (1). The frozen specific heat of Al Cl
C,, was estimated according to well-known
bl . 2
statistical mechanical methods* by use of the
infrared vibrational frequencies measured or esti-
mated by Klemperer.® The frequencies for AlCI,
were estimated by analogy with the compound
E’:C!3 (ref 4). The average value of the specific
heat in the temperature range 500 to 1000°K is
0.16 cal.g™.(°C)~' for ALCl, and is 0.14
cc:z]-g"]-(c(f)“1 for A|C|3. At each composition
of the gas, an average value was computed from
the composition-weighted average of these two
values for the monomer and the dimer.
The composition of the gas may be computed
from the equilibrium constant
, (3a)
where
AF® — All ~ TAS® = ~RT In K , (35)
in which AH is the heat of dissociation of the gos,
which was taken as 29.6 kcal/mole (ref 5), and
AS® is the entropy difference between 2 moles of
AICI; at 1 atm pressure and 1 mole of ALLCl, at
1 atm pressure, which was token as 34.6
cal.-mole™'.deg™! (ref 5). The values of )
calculated from Eqs. (3a) and (36) at pressures of
0.1, 1, and 10 atm, respectively, in the temperature
range 500 to 1200°K ore listed in column 2 of
Table 1. Column 3 of the same table lists the
2J. E. Mayer and M. G, Mayer, Statistical Mechanics,
Wiley, New York, 1940,
3W. Klemperer, J. Chem, Phys. 24, 353 (1956).
4G. Herzberg, Molecular Spectra and Molecular Struc-
ture, Yan Nostrand, New York, 1945,
SA. Shepp and S. H. Bauver, J. Am. Chem Soc. 76,
265 {1954}).
Table 1. Calculated Values of w,, cpe,if, and A for Aluminum Chloride
Temperature Weight Fraction Cpe Af Ae
(%) of Menomer, wy (1= Vdeg™ ) (caliem™ Lesec™ Lideg™ 1) (cabrem™Visec™ Vedeg™ )
For a Pressure of 0.1 atm
% 1078 x 1078
500 0.003 0.17 12 14
550 0.013 0.19 13 18
600 0.038 0.25 13 26
650 0.100 0.35 14 42
700 0.223 0.51 15 63
750 0.422 0.66 16 77
800 0.655 0.63 17 68
850 0.831 0.43 18 47
900 0.926 0.28 19 32
950 0.966 0.20 19 25
1000 0.984 0.17 20 23
1050 0.992 0.15 20+ 22
1100 0.996 0.15 21 22
1150 0.998 0.14 21 21+
1200 0.999 0.14 22 29—
For a Pressure of 1 atm
x 10~8 x 1078
500 0.001 0.16 12 13
550 ~ 0,004 0.17 13 15
600 0.012 0.19 13 17
650 0.032 0.22 14 24
700 0.072 0.28 15 34
750 0.145 0.36 15 46
800 0.264 0.47 16 60
850 0.428 0.55 17 68
900 0.612 0.54 18 63
950 0.766 0.44 19 50
1000 0.870 0.32 19 37
1050 0.929 0.24 20 30
1100 0.961 0.19 20 25
1150 0.978 0.17 21 24
1200 0.987 0.16 22 ’ 24
Table 1 {(continuved)
Temperature Weight Fraction Cpe ’\f ’\e
() of Monomer, 1 (cc[-g"l-deg"l) (cql-cm"']'sec'”]-deg"]) (cal-cm”]-sec“]-degwl)
For a Pressure of 10 atm
x 107° x 1076
500 0.000 0.16 12 12
550 0.001 0.16 13 14
600 0.004 0.17 13 14
650 0.010 0.18 14 17
700 0.023 0.20 14 20
750 0.047 0.23 15 26
800 0.087 0.27 16 34
850 0.148 0.32 16 42
%00 0.240 0.38 17 52
950 0.352 0.43 18 58
1000 0.4%90 0.46 18 59
1050 0.622 0.44 19 54
1100 0.740 0.38 20 47
1150 0.827 0.30 21 40
1200 0.888 0.25 21 33
values of € estimated by use of Eq. (1) for the
three pressures and the same temperature range.
A plot of Cpe and the average frozen specific heat
C f vs temperature at the three pressures is
presented in Fig. 1.
Effective Thermal Conductivities
The effective thermal conductivities were calcu-
lated using Eq. (2). The frozen thermal conduc-
tivities of monomer and of dimer were calculated
from the equation®
(1.9891 x 10~ (T/M )2 [, € 4
A - S e
f ’
where M is the molecular weight of o polymer,
o, is the average effective molecular diameter of
8J. 0. Hirschfelder, C. F. Curtiss, and R. B. Byrd,
Molecular Theory of Gases and Liquids, pp 14, 528,
534, Wiley, New York, 1954.
a polymer in angstroms, and {) is a factor which
corrects for intermolecular interactions and can
be calculated theoretically for simple potential
functions in terms of the parameters of the potential
function.”
A crude estimate of 02 was made for Al Cl. and
AlCI,. From electron diffraction data on A|2C|6
(ref g), structural estimates for A]Cl3 (ref 5), and
the van der Waals radii of chlorine atoms, the
dimensions of A|2C|6 and AICI; were estimated.
By comparison of the relative dimensions of
similar compounds to their effective collision
diameters,? the effective collision diameters of
Al,‘_)Cl‘5 and AICI; were estimated. For the
For a more accurate equation see J. O. Hirschfelder,
J. Chem. Pbhys. 26, 282 (1957). The use of the more
accurate equation leads to only a relatively small dif-
ference from the values calculated here.
BL. R. Maxwell, J. Opt. Soc. Am. 30, 374 (1940).
9Hirschfeic|er, Curtiss, and Byrd, op, cit., Table {-A,
pp 111112, 162.
Lennard-Jones 6-12 interaction potential, € has
been calculated as a function of the parameter
kT/€c, where € is the depth of the potential well,
The volue of ¢ is unknown for either AIZCié or
AICl,. We may, however, estimate € by analogy
with other halogen-containing compounds. Of
several halogen-containing compounds? the lowest
value of €/k is 324 for HI and the highest is 1550
for SnCl,. With these values as limits, the fol-
lowing values were obtained for (:
T {°K) €/k Q
500 324 1.3
1550 2.7
1000 324 1.0
1550 2.0
The range of values of O listed is 1,0 to 2.7, and
a value of & = 2 was arbitrarily chosen as being
reasonable. The value of D, P was estimated
from the equation !9
i ]/2
0.0026280 [ M1+ M,
12 Peoon — — | T ——o ’ (5)
sz % QMIMZ
where M, and M, are the molecular weights of
monomer and dimer, respectively, Tig= (a] + 02)/2,
and 7 is o correction for intermolecular inter-
actions. [t does not differ greatly from 0, and
therefore the value 2.0 was used. The calculated
values of I\, P in the temperature range 500 to
1200°K are listed in column 2 of Table 2. The
average frozen thermal conductivities, A, and the
effective thermal conductivity, A, calcu{afed' from
Fa. (2), ot pressures of 0.1, 1, and 10 atm were
listed in Table 1. Plots of —Xf and A_ vs tempera-
ture at the three pressures are presented in Fig. 2.
The constants and parameters used in these
calculations are summarized below:
R =1.9869 cal-mole™ T.deg™ !
R’ = 82.057 em®.atm-mole™ .deg™ !
AH = 29.6 keal for the reaction
AI2C|6 === 2A|C|3
AS®=34.6 e.u., entropy change for reaction
Al Cl, &= 2AICI, with both monomer and
dimer at their standard state of 1 atm
19pid., p 530.
UNCLASSIFIED
ORNL--LR-0OWG 35264R2
500 600 700 800 200 1000 1100 1200
TEMPERATURE [°K}
Fig. 1. The Calculated Effective Specific Heot of
Aluminum Chloride as a Function of Temperature at
Three Pressures.
UNCLASSIFIED
ORNL —~ LR DWG 397132
__ 8o [—~' T T T T
’g 70 L )_\9 ,,,,,,,,,,,,,,
g R
Tl BO bmevreemebeeeeeeee e AN L R
o I
S B0 e P N N N
T 40
5 3
- 30 ___________ 1
Q
< +
2
o 10 ............... Sreesmemmrssrmsesccsooseego
~< | )
O ——
500 600 700 800 200 1000 1100 1200
TEMPERATURE {°K)
Fig. 2. The Calculated Effective Thermol Conductivi-
ties of Aluminum Chloride as a Function of Temperature
at Three Pressuyres.
o2 = 40 A2
o2 - 65 A2
02, =51.7 A2
M, =M,/2=133.35 g/mole
Q=0 =20
Cv = Cp - R
Viscosity
The viscosity was estimated from the equation®
2.6693 x 105 (M _T) 1/2
N, = (6)
5 a2
n
Table 2. Valves of Dyy P, 74, and 175
T Dy, P Viscosity of Monomer, 17, Viscosity of Dimer, 7,
(°K) (cmz-atm-sec" } (g-cm“1-sec" ) (geem™ 'esec” )
x 10™3 x 107° x 1076
500 21.3 36 75
550 24.6 g0 79
600 28.0 94 82
650 31.6 98 86
700 35.3 102 89
750 39.2 106 92
8060 43.1 109 95
850 47,2 112 98
900 51.5 116 101
950 55.8 119 103
1000 60.3 122 106
1650 64.8 125 109
1100 69.6 128 111
1150 74.3 131 114
1200 79.2 134 116
for both monomer and dimer. The calculated values
are listed in columns 3 and 4 of Table 2.
mixture
For a
of monomer and dimer, a composition
weighted average would be an adequate approxi-
mation to the viscosity.
Vapor Pressure
The vapor pressure of solid aluminum chloride
in equilibrium with the gaseous phase may be
calculated from the equotion'!
| P(T)_~6360
og P (atm) = -
+3.77 log T —
~ 0.00612T7T + 6.78 . (7}
The vapor pressure is 1 atm at 180°C {453°K).
VYelocity of Sound in Aluminum Chleride
The velocity of sound, Cor in the working fluid
is needed for turbine design. At frequencies low
0. Kubaschewski and E. L. Evans, Metallurgical
Thermochemistry, Wiley, New York, 1956,
enough so that the velocity of association and
dissociation of the aluminum chloride is fast
enough to follow the compression and rarefaction
of the gas, the velocity of sound may be calcu-
lated from®
2
~1
co._ . 8
° (ov/oP), ' ®
where C is the velocity of sound in cm/sec, v is
the specific volume of the gas in cm>/g, P is the
pressure in dynes/cm2, and § is the entropy. The
value of (au/ap)s can be calculated from the
exact thermodynamic relation!?
; Ov ‘O \2
(@L) H(_é_) 4_1.(3__) (9)
or /. \op c, \oT /p
AT pe
12(3. N. Lewis and M. Randall, Thermodynamics and
the Free Energy of Chemical substances, p 164, McGraw-
Hill, New York, 1923.
and the equation
1 T
po=|— ') RT (10)
Mz
in which the reasonable assumption is made that
the gaseous monomer and dimer individually
behave as ideal gases and that all deviations from
an ideal gas are due to the association or dissoci-
ation of the goseous monemer or dimer. An evalu-
ation of (dv/dP) . and (du/3T), from Eq. (10) and
the thermodynamic relation
dlnk A dln [4w$1’/(] - w%)]
dT 2 aT
(1
leads to
/av v ZU.ILU2
) = (14
JP)p P 2
and
av> v( A11w1wz>
3T), T \ RT 2
]+w ) 5 14/
R i AH Y12
—_— 14+ — . (13)
P M2 RT 2
Substitution of Egs. (12) and (13) into Eq. (9}
leads to
L. RT (1 +wI> [ wyw,
-5
P /¢ p2 M, 2
R(1 +wl) < AH w‘wz)zl
- | T 4 e . (14)
M, Co RT 2 _
THERMODYNAMIC PROPERTIES
In the gaseous phase the state of an equilibriuvm
mixture of AlCl, and AICI, is determined by any
two independent properties, and knowledge of the
thermodynamic state makes it possible to determine
the thermodynamie properties. The two independent
defining properties
fraction of monomer, enthalpy, entropy, and specific
used to calculate weight
volume were temperotuwre and pressure. The
relations used in the computational procedure are
summarized below.
Determination of Weight Froction of Monomer,
wy. =~ It hos been shown by Newton, from free-
energy-change relationships, that
1 1 1/2
w] = (—5 +—2—tanh u) ' (]5)
where
1 P 13420
u=8.016 ~ —1In - ,
2 14.6%96 T
T is in °R, ond P is pressure in psia.
Determinction of Enthalpy, 5. — The enthalpy
of the mixture is the sum of the enthalpy the gas
would have if it were all in the dimer state plus
the enthalpy of dissociotion. Choosing absolute
zero temperature as the base for enthalpy and
0.1575 Btu.1b~ 1.(°R)~ ' as the frozen specific heat
averaged for the temperatures and pressures under
consideration, the ‘‘sensible” enthalpy, in Btu/lb,
is
b, = 0.1575T .
The enthalpy of dissociation is 199.7 Btu for each
pound of A|2CI6 monomerized. Therefore the total
enthalpy is
h=0,1575T + 199.71,0] . (16)
Determination of Entropy, s. — From the definition
of entropy in Btu.lb~ L(°R)™ 1,
erevarsible
ds = '
T
it can be shown'? that
du + P dv
ds =
T
Noting that
dh =du+ P dv +v dP
gives
dbh — v dP
ds = o
5
13568, for instance, J. H. Keenan, Thermodynamics,
p 85, Wiley, New York, 1941,
Then, for an isobaric process, that is, constant
pressure,
T
2 db Ab
,_\s]';‘zf — 17)
T T T
for small variations in T, where 1 and 2 are thermo-
dynamic states.
The entropy was considered equal to zero at
900°R and 150 psia, and the entropy ai other
temperatures at this pressure was approximated
by a stepwise, finite-difference procedure using
the approximation given above. To get the entropy
at 900°R and some other pressure, it is possible
to use one of Maxwell’s relations '4
s\ jo
(), = ~{3),
\ %
For a constant temperafure process, then
Py s
,\s]? = wf ? (—-L-> dP
o1,
Py NP
As shown below, tf I’ is expressed in pounds per
square foot (psf),
T
v =5.793(1 +u,)
=
Since (1 + u,) does not vary from unity by more
than about 0.3% at 900°R for the pressures under
consideration, it can be stated that
T 5.793
)
so that at constant temperature
\ P35.793
A\slt = ~ —dr
1 p
9
Pl
=5793 In— in ft-lb-lb~= 1.(°R) ™!
P2
P]
= 0.007444 In—— in Btu.lb™ LERY!
P2
14,04, p 342.
Determination of Specific Volume, v. —~ The
perfect gas law states that
RO -
Pv=—T, (18)
! m
where
R, = 1545 ff-lbf-mole”]e(oR)"“! ,
and M_ is the molecular weight of the mixture and
is 266??7/(1 + w]). Numerically this becomes
T
v=5793(01 4 w)) - inft3/lb
P ¥
where P is expressed in psf, or
T
v=0.00023(1 + w))— inft’/lb,
where P is in psia.
Example of Numerical Procedure. — As an example
of the calculational procedure employed, a compu-
tation of weight fraction of monomer, w,, enthalpy,
h, entropy, s, and specific volume, v, at a pressure
of 30 psia and a temperature of 1260°R follows:
1. For the weight fraction of monomer calcu-
lation,
/1 1 \N1/2
Wy = (——+—-fon'r| u) ,
2 2 ;
where | P 13420
©=8.016 ——in-——
2 14.696 T
] 30 13420
= 8.016 —— In -
2 14.696 1260
= —2.9923
ond therefore
11/2
1 1
_____ + —tanh (~2.9923)
2 2
Wy o=
1
= 0.05055
2. For the enthalpy calculation,
b= 0.15757 + 199.7u |
= (0.1575 x 1260) + (199.7 x 0.05055)
- 208.53 .
3. For the entropy calculation, at a constant
pressure,
AS]% 0y ——
T
__ 208.53 — 203.79
1260
A2 0.003792
und
s ~ 0.07298 .
4. For the specific volume calculation
T
v = 0.04023(1 + w1)—P-
1260
- 0.04023(1 + 0.05055) ——
= 1.7751
Data obtained for these functions at temperatures
from 900 to 2000°R and pressures of 1.5, 5, 15,
30, 60, 100, and 150 psia are listed in Table 3,
and an enthalpy-entropy chart is presented in
Fig. 3.
CORROSION BEHAVIOR
The corrosiveness of the gas is another important
consideration. The free energies of formation of
aluminum chloride and the chlorides of some
possible container materials at 500 and 1000°K
UNCLASSIFIED
ORNL-LR--DWG 39596
500 |——
450 [
400 |-
3150
300
ENTHALPY {Btu/Ib)
250