I
L. G. AUSTIN Fuel Technology Department, The Pennsylvania State University, University Park, Pa.
Reducing Tungsten Oxides A kinetic model of reduction with hydrogen explains experimental data
E X P E R I M E N T A L DATA on the reduction of pellets of tungsten oxides with dry hydrogen have been published by Hougen, Reeves, and Mannella (2). An examination of their results indicates that the over-all rate of reduction is controlled by the areas of the phase boundaries present, which move into the interior of a pellet as reduction procedes. Assuming that the pellets initially have a density corresponding to that of WOB, the rate constants for 1 atm. of dry hydrogen are
WOs * WaOll; kl = 8.35 exp( -20.4/RT) g. 0 cm.-2 sec. WaOli
w o , ; kz = 4.49 exp( -21.2/RT) g. 0 cm.-Z set.-' ---f
WOz* W ; ks = 0.75 exp( -15.5/RT) g. 0 cm.-2 set.-' T h e activation energies are in kilocalories per gram mole.
Experimental Procedures and Results
As reported by Hougen and others (2), cylindrical pellets of compressed yellow W 0 3 and of brown WOz were reacted with a stream of dry hydrogen a t 1-atm. pressure under known tempera-
ture conditions. Pellets were reacted for different lengths of time, withdrawn, cooled in nitrogen, and weighed. They were also fractured so that the color changes within the pellet could be observed. The reaction rate curves, in the form of plots of per cent oxide removed against time, are reproduced here in Figures 1 and 2. On the basis of color changes, gravimetric analysis, and x-ray analysi3 the following conclusions were drawn : 1. The reduction proceeds stepwise and concurrently by the reactions
+ Hz WaOll + H 2 0 + 3Hz 4W02 + 3H20 WOz (brown) + 2H2 +.
4WOs (yellow)
-+
w4011 (blue-purple)
--f
Examination of Results Hougen and others ( 2 ) made a kinetic analysis using specific reaction rates expressed as per cent oxygen removed per c m e 3 Since percentage rates are automatically in terms of unit volume, they were in effect using rates proportional to grams oxygen per second per cm.6 This factor obscured the significance of the results. Initial rates of reduction of W 0 3 were obtained by extrapolation of the rate curves to zero time. Using the results in the units of per cent oxygen removed per second and assuming that the pellets are roughly spherical in shape, the initial rate is
+ 2H-D
k~ = (1/3)(Rpa/lOO)(dP/dt)g. 0 cm.-2 set.-' (1)
2. The reduction begins with the rapid formation of W4011 throughout the pellet. 3. As this reduction nears completion a thin layer of WOa appears on the surface of this pellet and further reduction results in a n inward movement of this color boundary. 4. A tungsten layer finally appears and grows inward in a similar manner to that of the WOZ, but a t a slower rate.
where R is the radius of the sphere, p is the initial density of the pellet, b is the ratio of weight of oxygen to total weight in WO,, and dP/dt is the initial rate in per cent oxygen removed per second. Figure 3 is a plot of R.dP/dt against 1000/T"K. Equation 1 appears to be applicable for the three pellet sizes. T h e slope of the line gives a n activation energy of 20.4 kcal. per mole. Assuming that p is the density of WOa (7.16 g.
W (grey)
80
70
3 60 z 050 n W
i2 w
301 0
1
200
I
400
600
I
800
I 1000
40
a 5 30
REACTION TIME, SECONDS
A Figure 1. Per cent reduction of l/A-inch pellets of WOr, as a function of reaction time and temperature. Reduced in 1 atm. of dry hydrogen
b
Figure 2. Per cent reduction of '/r-inch pellets of wo3, as a function of reaction time and temperature. Reduced in 1 atm. of dry hydrogen
0
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200 400 REACTION TIME. SECONDS
NO. 8
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600
659
~ m . - ~ )kl, = 8.35 exp(-20.4/RT) g. 0 c m . ? set.? for the reaction CVO3 + w4011.
Let us now consider the data for the reaction WOZ + W. If the reaction rate (at a fixed partial pressure of hydrogen) is proportional to the phase boundary area of M i 0 2 present, then (dW/dt)/A =
kj
(2)
where A is the spherical area a t a penetration of tungsten into the pellet corresponding to r . Also d Wldt =
- 41rr2pb dr/dt
(3)
Eliminating d W / d t ka = pb dr/dt
(4)
Integrating from t = 0, r = R to t = t , r = r R
0.gl
I
I
I
I
-r
kat/bp
(5)
Total oxygen is proportional to R3 while the amount left to react when the phase boundary is a t r is proportional to r3, therefore the fraction, F, left to react, is F = r3/Ra
and Equation 5 goes to 1
- F113 =
(kd)/(bPR)
(6)
When the fractional reactions are expressed from W 0 3 instead of WOn (as in Figure 1) 0.875 - F''3
0
400 6 00 REACTION TIME, SECONDS
200
I xlo-
800
1000
A
I
Figure 4.
Plot of fraction remaining to be reduced to the ' / 3 power as a function of reaction time and temperature, for the reduction of '/i-inch pellets of woz
8X 106x10-
'0. 4x10W 0)
'Z 0 "
2 x 10-
" :
Y
I-'
z
20 z 0
1x10-
t 8x16
Figure 5. Arrhenius plots of specific rates of reduction of W02 to W and
Q:
6x16
w4011 to
4 4x16
088
0.92
0.96 IOOO/T,
660
1.00
I04
OK'
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
1.08
woz
(7)
Figure 4 is a plot of F113 against t . It can be seen that the data fit Equation 7 very well, even to reductions of over 90y0. As predicted, the lines extrapolate to 0.875 a t zero time (except for the 805' C. case where it appears that the starting pellets may have been slightly overreduced in their preparation from W03). The slope of the lines is --k3/0.764bpR; therefore k~ can be calculated. Figure 5 is a n Arrhenius plot of the values of ka, From this plot the specific rate constant W is ks = 4.49 for the reaction WOz exp (-21.2/RT) g. 0 cm.? set.-'. Consider now the mixed system W4011 + WOS -+ W. A reaction scheme which explains the over-all rate curve is as follows. Initially, the supply of oxygen from the rearrangement of W 4 0 1 1 to WO 2 is sufficient to supply the oxygen being removed by hydrogen from the outer surface. Consequently, tungsten is not formed. The rate is controlled by this rearrangement and -+
dW/dt
0
k s t / O 764bpR
k24 r r i 2
(8)
where T I is the radius of the phase boundary WOZ - W 4 0 1 1 . As r1 decreases with increasing reaction this rate cventually becomes too slow to supply enough oxygen to keep the external WOZ oxidized and the WOS +- W rate takes over. However, the radius, r , of the WOz - W boundary does not move in as fast as if 110 W4011 were present,
REDUCING TUNGSTEN OXIDES since part of the oxygen being removed is being supplied by the W4011 + WOZ reaction proceeding in the interior. The differential equation for the progress of phase boundaries is now k3r2 = pbr2 dr/dt
+ (pb/4)(r1)~(dri/dt) (9)
Since the reaction W4011 -+ is faster than WOZ W it proceeds to completion fairly rapidly, T I becomes zero, and Equation 9 becomes -f
ka = pb dr/dt
(10)
This, of course, is the same as Equation 4. Consequently, it should be possible to superimpose the later parts of the reaction curves of Figure 1 onto these cf Figure 2, with the zero time points or Figure 1 placed a t times on Figure 2 corresponding to somewhere near 33l/s% reduction. Superposition is almost perfect escept for the 770’ C. rate data. Figure 5 shows that the rate a t this temperature deviates widely from the Arihenius plot and may be somewhat inaccurate. It is readily shown that k2
E
p
(11)
bR/‘lbt‘
Comments o n
where t’ is the time from 8.4% total reduction to 22.8% total reduction. I t is difficult to get accurate values of t1 from Figure 2 due to the steep slope of the reaction curves. Figure 5 gives estimated rate constants as a function of inverse temperature. The specific rate constant for the reaction W4011 + WO? is thus estimated as kz = 0.75 exp (-15.5/RT) g. 0 cm.-* set.-'
Discussion of Results Although this type of experimental technique cannot be expected to be very precise, carefully performed experimental work by Hougen, Reeves, and Mannella (2) has produced data which form a consistent pattern of results. I t seems likely that the over-all rate is controlled by the moving phase boundary areas since this gives a mathematical model which explains the data quite well. Application of internal diffusion control concepts, either for diffusion of gas in pores or diffusion of ions within the solid, does not give the correct form of rate equations. Diffusion of oxygen. probably as ions, appears to occur so fast
as to have no control on the rate. Large oxygen diffusion gradients can occur in these materials without phase change because of the relative stability of nonstoichiometric tungsten oxides (7). T h e frequency factor term in the rate equations may be considerably in error due to the assumption made concerning the density of WOs in the pellet. The values of the activation energies for kl and ks are probably accurate to =t1 kcal. per g. mole. No information is available on the order of the reaction with respect to hydrogen but the suggested model implies that a t 1 atm. of hydrogen, the slow step in the process is the rearrangement of oxide t o a more reduced phase. Consequently, the reaction would be expected to be zero order with respect to hydrogen a t this pressure.
literature Cited (1) Anderson, J. S., Ann. Repts. on Progr. Chem. (Chem. Soc. London) 43, 115 (1946). (2) Hougen, J. O., Reeves, R. R., Mannella, G. G., IND.ENG. CHEM.48, 318 (19 56).
RECEIVED for review August 16, 1960 ACCEPTED February 20, 1961
...
Reducing Tungsten Oxides SIR:
M r . Austin refers to discrepancies in the reduction data “for the 805”C. case where it appears that the starting pellets had been overreduced in their preparation from W03” and in his conclusion says “Although the experimental technique cannot be expected to be very precise.. . .” Several years were devoted to developing the experimental technique and the work was done by some very skilled and talented personnel. The technique was found to give reproducible data and much of the information reported represents results from duplicate, triplicate, and more observations. M r . Austin can find a detailed discussion of
the experimental procedure in the original theses upon which the published data were based. Because we used the technique of starting each reduction with a new pellet and permitted the reactions to proceed progressively farther each time, experimental data for a given reduction curve is based on the reaction of many pellets. This helps to eliminate erroneous data as well as to “average out” the differences in individual pellets. Of course, we would have preferred to use the differential technique of investigation rather than, or in addition to, the integral method. We were very limited in capital and equipment and under the conditions of the experimenta-
tion, differential techniques may have been even more time consuming to develop. In view of the fact that the esperimenters are confident that all data are equally reliable, care should be taken not to reject summarily those which d o not fit a n assumed model. Perusal of the original theses might help to elucidate certain facets of the work and clarify somc of the discrepancies.
JOEL0. HOUGEX Research & Engineering Division Engineering Department Monsanto Chemical Co. St. Louis 66, Mo.
VOL. 53, NO. 8
AUGUST 7961
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