Energy & Fuels 1989, 3, 595-603
595
Physical Transformations during Cas(s) Oxidation Rowena J. Torres-Ordoiiez,**tJohn P. Longwell, and Adel F. Sarofim Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received August 8, 1988. Revised Manuscript Received May 23, 1989
In the oxidation of CaS(s) to CaO(s), the molar volume of the solid product is smaller than that of the solid reactant. This can result in the development of porosity or particle shrinkage, or a combination of both, as conversion proceeds. This paper studies the physical transformations that occur during the oxidation of dense CaS(s) crystals to CaO(s). The effective diffusivity Dd through the CaO(s) product layer during the oxidation of CaS(s) crystals was calculated from the experimentally determined structural properties of the oxidation products by using pore and grain models. The calculated Deffof cm2/s compared favorably with the Deffinferred from application of the shrinking unreacted core model to the conversion-time data at 0.10 atm of 02(g)and 1400-1750 K, in a parallel study. The SEM pictures indicate a grain rather than a pore structure. The structural changes accompanying oxidation to CaO(s) consisted of surface area increase with conversion throughout the conversion range and particle shrinkage with constant porosity up to a critical conversion x * , beyond which the porosity increases at constant volume. Beyond x * , the formation of cracks is also observed. These structural changes are consistent with a shrinking unreacted core of CaS(s) surrounded by a product layer of uniform CaO(s) grains. The CaO(s) shell shrinks with conversion until the circumferential tensile stress at the reaction interface exceeds the material yield point, after which cracks form at the interface and propagate to the particle surface as conversion proceeds to completion. This material failure is consistent with the results of a stress analysis for a shrinking spherical shell subjected to a uniform internal pressure.
Introduction The oxidation of CaS(s) crystals at 1400-1750 K in 0-0.20 atm of 02(g)for 0-0.25 s was studied in a laboratory laminar flow oxidation furnace. In a parallel study,' the shrinking unreacted core model, which assumes constant product layer diffusivity D e f f ,was then applied to the conversion (x)-time ( t ) data to determine the intrinsic reaction rate constant for the oxidation of CaS(s) to CaO(s). Results of the model application inferred that the product layer was porous, with Deff= cm2/s. This diffusivity value corresponds to estimates from experimentally measured structural properties, such as porosity or grain sizes, as will be shown in this paper. The oxidation of CaS(s) to CaO(s) belongs to the class of gas-olid reactions where the solid product has a smaller molar volume than that of the solid reactant. This can result in the development of porosity or particle shrinkage, or a combination of both, as conversion proceeds. This paper studies the physical transformations that occur during the oxidation of dense CaS(s) crystals to CaO(s). A structural model for the CaO(s) product layer that will account for the effects of the competition between pore evolution and particle shrinkage as conversion proceeds is also proposed. Experimental Section The structure of the surfaces of CaS(s) and CaS(s) oxidation products was studied by using scanning electron microscopy. An Amray AMR lOOOA microscope with a resolution of 70 8, (for a tungsten gun) was used. The samples, which were mounted on aluminum stubs, were coated with carbon followed by gold of a Present address: Center for Catalytic Science and Technology, Department of Chemical Engineering, Colburn Laboratory 307, University of Delaware, Newark, DE 19716. 0887-0624/89/2503-0595$01.50/0
few angstroms thickness in order to minimize the charging on the samp 1es The CaS(s) and oxidation products were characterized structurally in terms of surface area; porosity, particle volume, and pore size distributions; and grain sizes. Nz(g) adsorption data, in conjunction with the BET method, were used to determine the surface areas of the CaS(s) oxidation products. The measurements were performed on a Quantachrome Corporation Quantasorb sorption system using Nz(g)as the adsorbate and He(g) as carrier gas. The sensitivity of the instrument was 0.10 m2. The samples were outgassed either in 1 atm of N2(g)at 423 K for at least 20 h or in vacuum at 423 K for at least 30 min. N,(g) adsorption was conducted at 77 K with a liquid nitrogen bath for at least 20 min (equilibrium adsorption was reached after 10 min) and Nz(g) desorption was conducted at 393-413 K in a glycerol bath. The desorption volume was used to calculate the sample area. The results of multipoint BET analyses on (1) unreacted CaS(s) crystals, and (2) 87% reacted CaS(s) crystals compared favorably with the results from the corresponding single-point analyses. Hence, all reported areas were calculated by using the single-point BET method. The porosity and pore size distributions of the oxidation samples were determined by mercury porosimetry using an AMINCO Model 7121 porosimeter with a maximum operating pressure of 15000 psi, which corresponds to a minimum cylindrical pore diameter Dmi, of 120 A. Measurements on an AMINCO Model 7192 porosimeter with a maximum pressure of 60 000 psi (or D- = 30 A) were performed on the CaS(s) feed crystals and reacted CaS(s) a t the following levels of conversion: 80,87, and 95%. The intrusion measurements indicated that pores in the range 30-120 A were not present in appreciable amounts. The analyses were performed by using a breakthrough pressure of 550 psi or a maximum cylindrical pore diameter D , of about 3200
.
A. The grain size D, was determined by using X-ray diffraction with finer 20 step scans (0.01-0.02°/min) for 10-min counting (1) Torres-Ordoiiez,R. J.; Longwell, J. P.; Sarofm,A. F.Energy Fuels 1989,3,506-515.
0 1989 American Chemical Society
596 Energy & Fuels, Vol. 3, No. 5, 1989
Torres-Ordoiiez et a1.
c
Figure 2. SEM pictures of a partially reacted CaS(s) crystal oxidized a t 1650 K with x = 0.80. Magnification factors: (a, top); 1952X; (b, bottom) 7360X. (determined from the diffraction spectra of a silicon standard whose crystal strain is zero),E is the crystal strain, c is a geometric constant assumed to be equal to 0.9, and X is the wavelength of the K q radiation (1.54054 A). Linear plots of (B: - B t ) cos2 8 vs sin2 8 yield Dgand E.
Figure 1. SEM pictures of (a, top) an unreacted CaS(s) crystal and (b, middle; c, bottom) a partially reacted CaS(s) crystal oxidized a t 1650 K with x = 0.40. Magnification factors: (a) 1856X; (b) 2080X; (c) 3296X. about several Bragg angles 28. Combination of the modified Warren equation and Scherrer’s equation2 yields
where Bt is the total peak breadth, BI is the instrument breadth (2) Cullity, B. D.Elements of X-ray Diffraction; Addison-Wesley Publishing Co., Inc.: Reading, MA,1978; pp 281-284.
Results SEM Results. Scanning electron micrographs of CaS(s) crystals at various stages of oxidation show that the product layer is definitely porous, especially at high conversions. Figure l a shows an unreacted CaS(s) crystal; it is seen that the crystals are cubic, with relatively smooth surfaces. The CaS(s) feed had a thin outer layer of CaO(s) (corresponding to 1.25% conversion) due to oxidation by atmospheric m0isture.l In Figure lb,c, which shows a particle that is 40% converted, it is seen that the particle has retained its cubic shape but has had some change in surface structure. As oxidation progresses, pits form on the surface, producing a granular structure. There is, however, no dramatic change in appearance of the partially reacted crystals until about 60% conversion where cracks are observed. Figure 2a shows a particle that is 80% converted; the higher magnification picture in Figure 2b shows these cracks to be about 0.2-0.5 pm wide. Moreover, these cracks seem to extend from the surface to some position within the particle. An SEM picture of an 87% converted particle in Figure 3a shows that this may be the case. At high conversions, i.e., x = 0.95, as in Figure 3b, some particles have developed very open structures.
Energy & Fuels, Vol. 3, No. 5, 1989 597
CaS(s) Oxidation
un
6.32
0 12
10
Cas Crystals (Lot 11 0 . 2 0 atm 0,
-
I
0 1400 K 0 1500 K 0 1650 K A 1750 K
I
A
A A \ en N
A
E
d
A
A
e
0
Ll
o
0
m 0
E
A
o A
n
o
0 0
6
cn 0 c( + ."
0
E 4
m t-W
O
2
0
0
A 0
I
1
I
I
20
40
60
eo
X
0
Conversion to CaO
Figure 4. BET specific surface area vs x for oxidation of lot 1 CaS(s) crystals in 0-0.20 atm of Ot(g) for 0-0.25 s at 1400-1750 K. Values are per gram of total sample. un CaS
6.32
0
0 1500 K
-
Crystals. (Lot 11
0.20 a t n 0,
A 1750 K
0.35
:!
0.30
0
Figure 3. SEM pictures of highly reacted CaS(s) crystals (a, top) oxidized at 1650 K with x = 0.87 (b, bottom) oxidized at 1750 K with x = 0.95. Both pictures are at 2080X magnification.
BET Surface Areas. Because the CaS(s) crystals are essentially nonporous and the molar volume of CaO(s) (ucao) is less than that of CaS(s) (uta), an increase in porosity and, therefore, an increase in surface area are expected with conversion of CaS(s) to CaO(s). Figure 4 shows the specific surface area S vs x for the oxidation of lot 1CaS(s) crystals in 0-0.20 atm of 02(g)for 0-0.25 s at 1400-1750 K. The area increases with conversion throughout the whole conversion range. Within the scatter in the data, which may be due to possible hydration of the CaO(s) during short periods of atmospheric exposure (samples were stored and handled, whenever possible, under N2(g) in a glovebox), the variation of S with x appears to have no dependence on reaction conditions (i.e., T and Po ). Particfe Volume, Porosity, and Pore Size Distribution. If the particle volume V remains constant, the conversion of CaS(s) to CaO(s) wih result in the development of porosity E. Figure 5 shows the variation of e vs x for the oxidation of lot 1CaS(s) crystals in 0-0.20 atm of 02(g)for 0 . 2 5 s at 1400-1750 K. The porosity remains virtually unchanged up to about x = 0.50 and then increases thereafter as x increases. Also shown in the figure is the expected porosity, assuming no change in particle size (Vp = Vo = initial particle volume), i.e. e
= 1- (1- eo)[l + (2- l)x]
(2)
where e,, and Voare the porosity and volume of the reactant
A
A
0
40
20
X
60
eo
Conversion to CaO
Figure 5. Porosity vs x for oxidation of lot 1 CaS(s) crystals in 0-0.20 atm of Oz(g) for 0-0.25 s at 1400-1750 K.
CaS(s) (which has an initial degree of conversion xo = 0.0125),l and 2 = U C ~ O / U C=~0.60. The corresponding variation of Vp vs x is shown in Figure 6; also included in the figure is Vp/Vo = 2, the molar volume change expected a t complete conversion, assuming a dense product layer. The results indicate that there is particle shrinkage with conversion. By assuming a structural model for the pores, we can calculate the pore sizes and areas from the pressure-volume (p-V) intrusion data. If a cylindrical pore model is used to interpret the p-V data, the intrusion pressure is inversely proportional to the pore diameter DPe accessed at that pressure. Figure 7a shows the specific cumulative pore volume vs log D ,, for selected samples from the oxidation of lot 1 crystals a t 1650 and 1750 K. For x I 0.50, the specific volume is approximately constant (i.e., the porosity is essentially unchanged). Differentiation of
Torres-Ordoiiez et al.
598 Energy & Fuels, Vol. 3, No. 5, 1989 6.32
un 0
/
(
I
"
CaS C r y s t a l s [ L o t 11 - 0.20 atm 0,
'
I
'
0.12-
,
-
0X
"
0 1400 K 0 1500 K 0 1650 K A 1750 K
1.10
0.10-
1.00
::
-.
0.90
t
-
-- 0.80, 0.48.
1650 K
0
X-0.55,
1650 K 1750 K
0.00-
01
oc0
\
A
Q O
E
n
I
A
p
0
0
0.06-
3
O
I
> 0
O.EOt
0.60
0 X
A X * 0.07, 1550 K
0
I
-Vclo
Ai
L D
g 0.04-
0.02-
1
V,/,
0.000
20
40
80
60
% Conversion t o
100
CaO
Figure 6. Particle volume vs x for oxidation of lot 1 CaS(s) crystals in 0-0.20 atm of O,(g) for 0-0.25 s at 1400-1750 K.
this pore volume with respect to log Dporegives the pore size distributions in Figure 7b. For x I0.50, porosity is small and pore size distributions are approximately identical, with pores of 550 A appearing to be the mean size. At much higher conversions, porosity increases markedly in the pore size range 120-1000 A. Pore surface areas may also be calculated from the p-V data by assuming a symmetrical (not necessarily cylindrical) pore s t r u ~ t u r e . ~Figure 7c shows these areas for the samples whose pore volumes and pore size distributions were shown in parts a and b of Figure 7, respectively. It is seen that pore area increases with conversion, as expected if the samples did not undergo sintering. The CaS(s) crystals used had a porosity of 0.030-0.062 (pore surface of 0.6-0.8 m2/g) and a total specific surface area of 0.9-1.2 m2/g. The difference (0.40 m2/g) between the total and pore area corresponds to the external surface of spheres having a diameter of 5.8 pm, in satisfactory agreement with the average particle size of 6.32 pm for the CaS(s) crystals used. Since the external area of the particles (-0.40 m2/g) is generally negligible compared to the pore area at high conversions, the areas inferred from the mercury porosimetry data should be equal to those obtained from the single-point BET measurements at these high conversions. The BET areas (SBET) and the areas from porosimetry (SH,) for selected samples from the oxidation of lots 1 and 2 CaS(s) crystals are compared in Figure 8. The agreement is within the error and scatter of the measurements. Grain Sizes. Estimates of the grain sizes D, of CaS(s) and CaO(s) in selected samples were obtained from X-ray diffraction line broadening. For CaS(s), D, 1 2000 A, the diffractometer detection limit. For a sample reacted at 1650 K in 0.20 atm of 02(g)for 0.22 s with x = 0.87, the intensity functions for four CaO(s) Bragg angles are shown in Figure 9a-d. The dotted curves are the Gaussian fits to the intensity functions for the dichromatic (Kal and Ka2) Cu K a radiation source. The solid curves are the intensity functions due to the Kal radiation, reconstructed by using the method of R a ~ h i n g e r . Application ~~ of eq (3) Rootare, H. M.; Prenzlow, C. F. J . Phys. Chem. 1967, 71, 2734-2136.
i 0 X
-
0.48, 1650 K
0 X - 0 . 8 0 . 1650 K A X - 0 . 5 7 . 1650K 0 X 0.95. 1750 K
-
1
1
I 0.001
1
1
2.0
Log,,
12.0,
10.0
,
3.0
2.5
I
I
1
3.5
Dport [Angstroms)
0X
-0.40,
1650 K 0 X -0.80. 1850 K
--
A X 0.87. 1860 K
0
Log,,
Door.
X
0.95. 1750 K
IAngstromsI
Figure 7. (a, top) Integral pore volume, (b, middle) pore size distributions, and (c, bottom) pore surface area for selected lot 1 CaS(s) crystals oxidized at 1650 and 1750 K. Pore volumes and surface areas are per gram of total sample.
Energy & Fuels, Vol. 3, No. 5, 1989 599
CaS(s) Oxidation 6.32 m CaS C r y s t a l s (Lots 1 and 21
o-
12.0
Table I. Comparison between Calculated Den and Den from Model Fits effective product layer diffusivity (Dd,cm2/s from shrinking from structural properties core model temp, K fits" pore modelb grain modelc 1400 4.77 X (0.8-1.5)X lo-' (2.5-3.6)X 10" 1500 1.11 lo-' (0.7-1.5)X 10" (2.0-3.2)X 10" (1.0-5.0) X lo-' (0.4-1.2)X lo-' 1650 2.47 X lo-' 1750 2.60 X lo-' (1.0-6.4)X (0.4-2.5)X lo-'
arm o2
0.20
I
0 1400 K 10.0-
0 1500 K D 1550 K 0 1650 K A 1750 K
m
\
E
-+.
8.0-
m
E
Model applied to conversion-time data from the oxidation of CaS(s) crystals at 0.10 atm of 02.'*Calculated from the pore size distributions determined from mercury porosimetry. Calculated from experimentally determined porosities from mercury porosimetry, a CaO(s) grain size of 425 A, and a tortuosity of 1.5.
t. 6.0k m L nl m 0
P
4.0-
L
3
0.ov 0.0
X lo' erg/(mol K) if D, is in cm and DU,effis in cm2/s). If all the pores in a solid of volume V, run parallel to the macroscopic gradient, then 7, = 1, and integration over the pore size distribution will yield I
I
2.0
4.0
I
6.0
6.0
10.0
12.0
S u r f a c e a r e a ( f r o m p o r o s ~ m e t r y l , m'/g
Figure 8. BET specific surface areas vs pore surface areas determined from porosimetry data for selected oxidized lot l and lot 2 CaS(s) crystals.
1 gives a straight line with r2 = 0.97, D, = 850 A, and E = 8.5 X lo4.
Discussion Product Layer Diffusivity. The effective product layer diffusivity Deffcan be estimated from the experimentally measured structural properties of the CaS(s) oxidation products, as follows' 1
1
-E-
DA,eff
+-
1
DKA,eff
DAB,eff
(3)
where DA,d = effective diffusivity of gas A (cm2/s) = Deff, DABeff= effective binary diffusivity for gases A and B (cmS/s),and D ,, = effective Knudsen diffusivity for gas A (cm2/s). Under the oxidation conditions used, Knudsen diffusion dominates over molecular diffusion so that Ddf DKA,eff, which is approximated by
-
t
k , e f f
=
-&A
(4)
7,
where c and 7, are the porosity and tortuosity of the solid, respectively. Two structural models are used to calculate Deff: cylindrical pores and spherical grains. For a single cylindrical pore of diameter DWre,the effective Knudsen diffusivity is given by8
where T i s the gas temperature (K), MA is the molecular weight of gas A (g/mol) and R is the gas constant (8.317 (4)Rachinger, W.A. J. Sci. Znatrum. 1948,25,254. (5) Doerr, W. W. The Effects of the Magnesium Constituent on Removal of Sulfur Dioxide by Fully Calcined Dolomitic Limestone. Ph.D. Thesis, MIT, 1979. (6)Snow, M. J. H. The Sulfation of Limestone and Calcium Oxide: Direct and Series Reaction. Ph.D. Thesis, MIT, 1985. (7) Froment, G.F.; Bischoff, K. B. Chemical Reactor Analysis and Design; John Wiley and Sons: New York, 1979;p 169. (8)Satterfield,C. N. Heterogeneous Catalysis in Practice; McGrawHill Book Company: New York, 1980; pp 336-337.
where VD= volume of pores of diameter D (cm3)and Dand D, = minimum and maximum pore diameters (cm) = 1.2 X lo4 and 3.2 X lo+, respectively, for pore diameters accessed in the mercury intrusion measurements. If the product layer is assumed to be a solid matrix composed of uniformly sized spherical grains of radius r,, the effective Knudsen diffusivity is9
The tortuosity factor was assumed to be equal to 1.51° and the CaO(s) grain radius was assumed to be uniform with conversion and equal to the experimentally determined 425
A.
Figure 10a,b shows the values of DKA,eff vs conversion for lot 1CaS(s) crystals oxidized at 1400-1750 K in 0-0.20 atm of 02(g)for 0-0.25 s, assuming (a) parallel cylindrical pores and (b) spherical grains. It is seen that whether a pore or grain model is used, Deff cm2/s and did not vary significantly with conversion, except at high conversions, i.e., at x 1 0.80. This value compares favorably with the D, inferred from the application of the shrinking unreacted core model to the x-t data at 0.10 atm of 02(g),l as seen in Table I. Proposed Structural Model for the CaO(s) Layer. Although the calculated Dd values based on either a pore or a grain model are not appreciably different, the SEM observations indicate a grain rather than a pore structure. The CaS(s)-CaO(s)solid matrix is envisioned as composed of a dense core of CaS(s) surrounded by a product layer made up of uniformly sized CaO(s) grains, as shown in Figure 11. Hence, the total specific area (m2/g) of the solid matrix can be written in terms of the area due to CaS(s) and that due to CaO(s) as follows:
-
ST = S C a S W C d + SCaOWCaO
(8)
where SCdand Sca0 = surface areas (m2)of CaS(s) and (9)Mason, E.A.; Malinauskas, A. P.; Evans, R. B. J . Chem. Phys. 1967,46,3199-3216. (10)Torres-Ordofiez,R. J. The Oxidation of CaS(s) Crystals During Simulated Coal Combustion. Ph.D. Thesis, MIT, 1986.
600 Energy & Fuels, Vol. 3, No. 5, 1989
Torres-Ordoiiez et al.
-
Lot 1 C I S 181, 1850 K 0.20 at. 0,. 0.22 sec. I 0.87
--
Lot 1 CSSISI.
--
201Kall
2 8 1 ~ a i 1 37 36s u 0.1044
U
-
1650 K
0.20 atm 02, 0.22 sec. x
0.87
32.210
0,0985
r
10-
.=
0 E-
1 0 -
. . .
1
0 E-
*
z
.L1
Y
VI
C VI
2
.
-
0.6-
$ 06r-
CI
0
0
N D
2 0
-
4-
0
N
2
0 4 -
E 0
L
P
z
.
.e+._.
36 9
37 3
37 7
31 7
-
--
U
u
10-
L .
0 8-
CaO(s) per gram of CaS(s) and CaO(s) and wc& and wcao = weight fractions of CaS(s) and CaO(s). The weight fractions can be related to the fractional conversion (or the mole fraction of CaO(s)) as follows: =
-
53.880 0,1195
.
0 8-
Weas
--
201KalI
64.182 0.1276
1 0 1
32 5
32 1
L o t 1 CSSISI. 1850 K 0.20 at. O 1 . 0.22 sec, x 0.87
L o t 1 C a S ( S 1 . 1650 K 0.20 atm D e , 0.22 S C C . x 0 87
281Kall
,
MCas(1 - x ) - X ) + Mcaox
(94
where M c and ~ Mca0 = molecular weights of CaS(s) and CaO(s) = 56 and 7 2 . Moreover
(11)
where rc = radius of the essentially nonporous CaS(s) core,
r = CaO(s) grain radius, and peas and pca0 = densities of C!aS(s) and CaO(s) = 2.58 and 3.35 X los g/m3. If the change in rc with conversion is modeled as that of a shrinking core, then
r, = ro[Z + ( 1 - z)(1 - x ) ] ' / ~
(12) Substitution of eq 9-12 into eq 8 will yield an expression for ST in terms of ro, r , and x . Estimates of re may be obtained from either ( l fthe X-ray diffraction line-broadening analysis (which gave 425 A) or ( 2 ) the BET surface area data. From eq 11, using scao = 10.5 m2/g, which is estimated from the ST vs conversion plot (Figure 4 ) at 100% conversion, gives rg = 850 A. Figure 12 shows the total specific surface area obtained from single-point BET measurements as a function of conversion x for lot 1 CaS(s) crystals oxidized at 1400-1750 K for 0-0.25 s in 0-0.20 atm of O,(g). The curves are predictions for ro = 3.16 pm and for rg = 425 and 850 A. It is seen that using the experimentally obtained value of 425 A from the XRD analysis predicts surface areas about
CaS(s) Oxidation
Energy & Fuels, Vol. 3, No. 5, 1989 601 XO
8 0
4 1400 K 0 1500 K
Cas
EO
CaO
SO
0 1650 K A 1750 K
VO
i
A
. ..
0.061
.
0.05-
y1
0 E
-.
0.04-
d 0.03-
o.olb4
X*
v/vo * =
0.02-
s"
;4
20
0
AAo
40
60
80
*
(V/VJ
E
= E,
s*
> SI
100
X Conversion t o CaO 6.32 L Cas C r y s t a l s (Lot 11 0 - 0.20 atm O2
4 1400 K 0 1500 K
0 1650 K A 1750 K
0.05
.
0.04
m
0 E
zi N
0 1400
K
0 1500 K
-
O'Or
A
A
A
0 0
0
0.02
0
20
40
60
60
X Conversion to CaO
Figure 10. Dma vs conversion for oxidation of.lot 1 CaS(s) in 0-0.20 atm of Oz&)for 0-0.25 s at 14QO-1750 K (a, top) cylindrical pore model; (b, bottom) spherical grain model.
O.OL-0
' 20
__.
40
60
80
0
X Conversion t o CaO
twice as great that obtained from the BET measurements. The XRD grain size determination method used is valid for grain radii less than 1000 A (because of the diffractometer detection limits). The use of rg = 850 A in the calculation of Deffby assuming a grain model for the product layer, doubles the Deffvalues shown in Figure lob, and makes them closer in value to the Deffcalculated by assuming a pore model for the product layer. However, the D&'s calculated by either method are within an order of magnitude cmz/s). The experimental V, vs x relationship shows that the particle shrinks with x . Figure 13 shows the experimental data along with the theoretical relationship, assuming the volume variation is due to a change in molar volume from reactant to product, i.e. VP _ - 2 + (1- z)(1 - x )
VO
(13)
Figure 12. Specific surface area vs conversion for lot 1 CaS(s) oxidized at 1400-1750 K for 0-0.25 s in 0-0.20 atm of O,(g). Curves are predictions of grain model for ro = 3.16 pm and for rg = 425 and 850 A. I t is seen that the particles follow this relationship up to some critical conversion x* after which the particle volume remains approximately constant. Figure 14 shows the experimental and theoretical variation of E with x , assuming x* = 0.50. In the initial region x Ix*, the relationship in eq 13 results in the formation of no additional porosity in the product layer, i.e., E = 6.In the region x 2 x * , where V, is constant, the theoretical E-x relationship is
The experimentally observed volume shrinkage, porosity, and surface area behavior are consistent with a structural model equivalent to a shrinking unreacted core
Torres-Ordofiez et al.
602 Energy & Fuels, Vol. 3, No. 5, 1989 6.32 m Cas C r y s t a l s (Lot 11 0 - 0.20 atm 0,
0
1400 K
0 1500 K 0 1650 K
A 1750 K
Steel
Concrete \ >
>
s m a 111.
0.0 I
I
20
0
I
I
I
I
60
40
I
100
80
0.2
0.4
[i
0 6
- (rc/r0)' I
-
-
P1"l"S
after x
EOn.tMt
0.50
0.8
1.0
x
Figure 15. Circumferential tensile stress at reaction front (00)-
X Conversion to CaO
Figure 13. Experimental and theoretical particle volume vs conversion relationship for oxidation of lot 1 CaS(s) in 0 . 2 0 atm of Oz(g) for 0-0.25 s at 1400-1750 K. 6.32 ya Cas Crystals (Lot iI 0 - 0.20 atm 0,
vs x for concrete and steel.
timately exceed some yield point characteristic of the material. This formation and propagation of cracks can be predicted from consideration of the strength of materials. The problem may be viewed as that of the CaO(s) product layer (of outer radius rp and inner radius rc) subjected to a uniform internal pressure pl. This pressure is exerted by the CaS(s) core due to retreat of the reaction interface because of particle shrinkage. At low conversions, when the product layer is a thin shell, cracks can develop, but because the particle also shrinks, these cracks do not propagate. At high conversions, when the product layer is a thick shell, the formation and propagation of cracks may not be as easily prevented. The solution to the above problem of the shrinking spherical shell subjected to a uniform internal pressure is"
0'3
0.00 0
I
I
20
I
I
40
I
I
60
I
I
SO
I
100
X Conversion t o CaO
where d(r) is the total radial displacement of a point at position r, X is L a m B ' s constant, and G is the shear modulus or modulus of rigidity of the material. The radial and circumferential stresses in the CaO(s) shell, u, and u.g (respectively) are given by
Figure 14. Experimental and theoretical porosity vs conversion relationshipfor oxidation of lot 1 CaS(s) in 0-0.20 atm Oz(g) for 0-0.25 s at 1400-1750 K.
of CaS(s) surrounded by a product layer of spherical CaO(s) grains (Figure 11). The CaO(s) product shell shrinks with conversion, causing the grain packing to be tighter 90 that porosity can remain constant. This decrease in volume and constancy of porosity continues until x* reaches a value beyond which further particle shrinkage is not possible, probably because the grains are at their tightest packing. As x increases further, the particle size remains constant and the porosity increases as the grains can now be more loosely packed. Moreover, cracks develop and extend from the reaction front to the particle surface. The sharp transition in porosity and volume change with x at x = x* may be related to this formation of cracks in the particles that occurs around this conversion. One possible cause of crack formation is the development of stresses within the shrinking outer CaO(s) shell that ul-
Hence, the shell undergoes compression, and the maximum circumferential tensile stress, which occurs at the reaction front r = r,, is given by
The pressure p1is solved by equating the total deformation (11) Volterra, E.; Gaines, J. H. Aduanced Strength of Materials; Prentice-Hall: Englewood Cliffs, NJ,1971;pp 205-212.
Energy & Fuels 1989,3,603-612
experienced by the shell, $(rJ + $(rp), to the shrinkage experienced by the particle, ro - rp, where ro is the original particle radius and
which is obeyed by the Cas-CaO particles up to about x = 0.50 for lot 1, as seen in Figure 6. Figure 15, which shows (ne), vs x for concrete and steel, shows that (ne),,, does increase dramatically with x . The material properties of the CaO(s) crystals are not known, but its behavior may be reasonably assumed to be intermediate between that of concrete and steel. Also shown in the figure is the tensile strength of A1203(s)crystals, ( ~ g ) ~ 2 0 8which , illustrates the high values attainable for small crystal dimensions where the effect of flaws is min-
603
imized. The tensile strength of the CaO(s) crystals is possibly less than that of A1203(s),but greater than that of concrete. It is seen that failure at 2 0.50 for CaO(s) can occur at a point intermediate between the curves for concrete and steel and at a tensile stress lower than the tensile strength of A1203(s).Hence, this failure (i.e., crack formation and propagation) is expected on the basis of strength of materials consideration. Figure 15 also shows that if the particle size remains constant after x = 0.50 (dashed curve for concrete), lower stresses do develop in the shell.
-
Acknowledgment. This research was funded by the MIT-Exxon Combustion Research Program. Assistance with the analytical techniques from Prisca Chen and Linda Sheehan are gratefully acknowledged. Registry No. Cas, 20548-54-3; CaO, 1305-78-8.
Molecular Transformations in Hydrotreating and Hydrocracking Richard F. Sullivan,* Mieczyslaw M. Boduszynski, and John C. Fetzer Chevron Research Company, 576 Standard Avenue, Richmond, California 94802 Received December 13, 1988. Revised Manuscript Received June 2, 1989
This study involved three hydroprocessing steps. The first step simulated a commercial residuum desulfurization (RDS) process. The second step, in which the residuum-derived vacuum gas oil (RDS-VGO) was hydrotreated, simulated the first stage in a two-stage hydrocracking process. The third step simulated the second stage of a two-stage hydrocracker, operating in an extinction-recycle mode. The study was made by using pilot plants that simulate state of the art refinery units. The focus of this paper is on compositional changes that occurred during hydrocracking of a RDS-VGO to make jet fuel as the primary product. Molecular transformations leading to the buildup of polycyclic aromatic hydrocarbons (PAHs) in the second-stage hydrocracker recycle stream were of particular interest. A combination of high-performanceliquid chromatography (HPLC) with UV/vis diode-array detection and field-ionization mass spectrometry (FIMS) was used to follow changes in composition of VGO through a series of hydroprocessing steps. Detailed compositional data helped unravel some of the complex chemistry of the reactions involved. The results explain why VGO produced in a high-severity RDS process is much harder to hydrocrack than that produced at lower severity. The difference is due to the presence of high-ring-numberPAHs in the high-severity product. These PAHs involve only a small portion of the total process stream. Specific PAHs produced in hydrocrackers have been identified. The PAHs have a unique distribution pattern involving only the most stable PAH isomers of a given ring number. These findings suggest a reaction pathway referred to as the “naphthalene zigzag” to account for the buildup of PAHs in the hydrocracker recycle streams.
Introduction
usually petroleum oils that are very complex mixtures of hydrocarbons and heteroatom-containingcompocds. The The reaction chemistry of pure hydrocarbons over hyreaction chemistry can be quite different from that which drotreating and hydrocracking catalysts has been studied occurs with individual pure compounds. Hydrocracking extensively as discussed in a number of review arti~les.l-~ (HCR) catalysts are usually dual functional-that is, they However, feeds to commercial hydroprocessing units are contain both an acidic cracking component and a hydrogenation component. The relationship between these catalytic components can be altered by the preferential (1) Bolton, A. P. Hydrocracking,Isomerization, and Other Industrial Processes. In Zeolite Chemistry and Catalysis; &bo, J. A., Ed.; ACS adsorption of reactant hydrocarbons and heteroatomMonograph 171; American Chemical Society: Washington, DC, 1976; pp containing compounds on catalytic sites. Furthermore, 714-779. bimolecular reactions such as disproportionation and al(2) Choudhary, N.; Saraf,D. N. Hydrocracking: A Review. Ind. Eng. kylation make the reaction chemistry exceedingly comChem. Prod. Res. Deu. 1976,14(2), pp 74-83. (3) Langlois, G.E.;Sullivan, R. F. Chemistry of Hydrocracking. In plicated. Refining Petroleum for Chemicals; L. J. Spillane, L. J., Leftin, H. P., Even with modern analytical techniques, it is impossible Eds.; Advances in Chemistry 97; American Chemical Society: Washingto identify all of the individual compounds present in ton, DC, 1970, pp 38-67. 0887-062418912503-0603$01.50/0 0 1989 American Chemical Society
