September 1949
.*
*r
INDUSTRIAL AND ENGINEERING CHEMISTRY
1977
alone. Also, the rate is not dependent on the amount of sulfur present and not contacting the steel, as in the case of the excess sulfur i n the experiment first discussed. To show this more definitely, the following experiments were carried out:
corrosion found in the field was the same as those found in these laboratory experiments,
Coupons were exposed to sulfur alone and water alone, and sulfur-covered coupons to water. I n the first case, a 3-hour exposure caused only a slight discoloration. Coupons exposed in water alone showed some attack (slight rusting). Weight losses were about 0.2 mg., just within the limit of experimental error. The relationship between the extent of attack and sulfur-covered areas of the coupon with constant weight of sulfur in each case is shown in Figure 7. I n this experiment, coupons were immersed t o different levels in liquid sulfur for 2 hours, so that adherent coatings covering a variety of areas on the coupons were obtained. Approximately 1.75 grams of sulfur were found to adhere t o the totally covered coupons. I n order t o maintain a constant quantity of sulfur in each bomb, sulfur was added to the amount needed to bring the weight present as a coating t o 1.75 rams. The results shown in Figure 7 indicate that the total wei Et loss after 2 hours at 130" C. bears a linear relationship to t i e area covered by the sulfur. The rate of attack with no sulfur coating was considerably higher than the rate in water alone with no sulfur present. These losses were 3.0 mg. (shown in Figure 7 a s the value at 0 area) for water and sulfur and 0.2 mg. for water alone.
ments, t h a t much of the corrosion experienced in the producing tubing and air line could be cut appreciably by decreasing t h e water contact time. This means decreasing the periods of boost and blow. The highest corrosion rates are apparently experienced when liquid sulfur as well as liquid water and air is in good contack with steel. The rate a t which steel is attacked by sulfur and air under normal pumping conditions is negligible compared t n the rates during the boost and blow periods. The use of a multiple coupon container in the field was effective in studying the variation in corrosion during the sulfur production cycle. Evaluation of alloys in these recognized corrosive conditions can be made in the field by the same means. A laboratory method has been described which appears useful in studying and evaluating the highly corrosive conditions found during certain periods of sulfur well operation.
These data suggest t h a t the severely corrosive condition in sulfur-producing wells is due to the effect of water and sulfur together when the latter is in intimate contact with the steel. Confirmatory evidence is offered by an experiment in which the lower end of a n uncoated steel coupon, which was exposed to water under the usual conditions, touched a 1.75-gram sulfur button. The extent of attack was again low, b u t most of t h a t which took place was in the area of contact with the sulfur. Furthermore, the visible effects were clearly decreased as the distance along the coupon increased. The corrosion product and type of attack of the totally covered coupon resembled t h a t on the coupons from the field taken during the boosting period. The order of magnitude of the types of
SCMRZARY
It is evident, on the basis of the field and laboratory experi-
ACKNOWLEDGMENT
The authors wish to acknowledge the financial support of the Freeport Sulphur Company in carrying on this work. They also wish to thank the field and production personnel for their cooperation. LITERATURE CITED
(1) Fanelli, Rocoo, IND.ENG.CHEW,38,39-43 (1946).
(2) Hackermsn, Norman, and Shock, D. A.,Zbid., 39,863-7 (1947). (3) West, James R., Chem. Eng.,53,No. 10,225-34 (1946). RECEIVED November 4, 1948. Presented before the Division of Industrial and Engineering Chemistry at the 114th Meeting of the AMERIUAN CEEMICAL SOCIETY, St. Louis, Mo.
Effective Thermal Conductivities in Gas-Solid Systems J
D.G.BUNNELL, €3. B. IRVIN, R. W. OLSON, AND J. M. SMITH, b
*
Purdue University, Lafayette, Ind.
Point to point temperatures have been measured for both the solid and gas in a %inch reactor, packed with 0.125-inch alumina cylinders, and through which hot air was passed at mass velocities from 150 to 500 lb./(hr.) (sq. ft.). The entering air temperature was maintained at $00' C. and the reactor wall held at about 100" C. by a boiling water jacket. Measurements were made at seven points across the diameter of the reactor and at packed bed depths of 0, 2, 4, 6, and 8 inches. While significant temperature gradients were observed, even near the center of the tube, the solid and gas temperatures were identical
within the accuracy of the measurements. This combined with the fact that the temperature varied considerably with mass velocity indicated that the radial heat transfer in a packed bed, under the conditions of this work, depended primarily on the characteristics of the gas rather than the solid pellets. Effective thermal conductivities computed from the temperature measurements ranged from about 0.1 to 0.4 B.t.u./(hr.)(ft.)(' F.). The increase in effective thermal conductivities over the value at static conditions was directly proportional to the mass velocity of gas flow.
T
This paper reports experimentally measured temperature gradients, both in the direction of gas flow (longitudinally) and perpendicular t o i t (radially), in a 2-inch inside diameter tube packed with 0.125-inch cylindrical alumina pellets. From these data effective thermal conductivities, K values, were computed assuming t h a t a heat transfer mechanism based upon conduction could be used to interpret the temperature data. Actually, the heat transfer rates within the gas-solid bed are
HE design of equipment for gas-solid catalytic reactions is complicated by the fact that the reaction rate may change rapidly with temperature and gas composition. This is especially important when the reactor is jacketed for heating or cooling because of the existence of radial temperature gradients within the reactor bed. Therefore, a knowledge of temperature from point t o point in the gas-solid system is necessary in order t o understand what takes place in a reactor.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1978
probably more influenced by heat transfer coefficients between the flowing gas and the solid pellets than by the true thermal conductivity of either the solid or gas. Hence, t'he effective thermal conductivity niay be likened to a heat transfer coefficient and would be expected to be a function of such variables as mass velocity of the gas, its physical properties, such as thernial conductivit'y and viscosity, and solid particle size and shape. The advantage of t,he effective thermal conductivity concept is that, once the K values are available, temperature gradients within the reactor can be predicted at any operating conditions without additional thermal data.
AIR IN
1%-
Figure 1.
J
Schematic Drawing of Equipment
Apparently, there is no published information concerning the effective thermal coriductivities in fixed bed systems except the few results of Hall and Smith (3)at a single mass velocity of 350 lb./(hr.) (sq. ft,.) and with 0.125-inch alumina pellets in a 2inch inside diameter tube. Considerable data are available for the condition of zero gas flow (static beds) and these have been summarized by Wilhelm, Johnson, Wynkoop: and Collier ( 6 ) . Also Brinn et al. ( 1 )have determined K values for the case of solid particles flowing through a slationary gas mass under the action of gravity. The work reported in this paper is a continuation of that of Hall and Smith (3) and covers range of mass velocities from 150 to 5001b./(hr.) (sq. f t . ) .
Fiberglas insulation and protect,ing tubes extended t o within 0.125inch of the bare junction. EXPERPhIENTAL PROCEDURE
The largest single source of error in the results is probably due to errors in measuring the posit,iorl of the thermocouples in the> bed. This information was obtained as accurately as possible i n t'he following way: The thermocouple tubes were threaded through three stainless steel scrcens at different loc,zt,ionsin the reactor. The lowest was placed about 1 inch above the tip of the tubes, the highest' 16 inches above the top of the solid packing, and the third screen midway beixveen the other two. The thermocouple tubes xere fastened securely to the screens to prevent movement radially and longitudinally by st,ainlesssteel wire. The effect o f packing depth upon t'he t,emperature \vas determined by placing the thermocouple assembly (Figure 3) at different dspt,hs (0, 2, 4, 6) and 8 inches) from the bottom of the packing. The procedure for filling the reactor and measuring thermocouple positions!for any one bed depth mas as follows: The react,or head to which the thermocouples were attached was partially inserted into the reactor and the space between the lower two screens filled wit.h the cylindrical pellets. The head was then Drogressivelv lowered as thc reactor was filled to the ton screen, n-hicK was alkays adjusted to give a total packed beb. deDth of 16 inches. The reactor was inverted and the longitudinal and radial locations of the therniocouples were deternnued by obtaining thermocouple junction impressions on a cardboard disk cut t o the size of the reactor tube. This disk was inserted into the bottom of the reactor and tapped with a rod to obtain a sufficient impre3sion. The distance of each thermocouple from the center of the tube, T , was then measured with a rule. The thermocouple junctions for measuring solid temperatures were inserted into the center of solid pellets and sealed with water glass. Finally, with the reactor still invei ted, sufficient additional pellets were added to fill the space between the lowest screen and
PLES S
APPARATUS
The s,pparatus was designed to measure both gas and solid temperatures at enough points in the reactor to evaluate radial and longitudinal temperature gradients. A schematic flow diagram of the equipment as a whole is shown in Figure 1. Air was filtered and dried with silica gel I,measured through rotameter 2, heated in gas-fired furnace 3, and passed into preheat,er 4 immersed in constant temperature bath 5. The air then entered the integral reactor 6, which consist,ed of 2-inch inside diameter st,ainless steel pipe, 38 inches long, connected vertically to the tube extending outside the bath, 5. The temperature measurements were made within this piece of, equipment. To obtain significant' radial temperature gradients the temperat.ure at the center of the gas stream entering the reactor was maintained a t 400" C. in all the runs, while the outside wall surface was held at approximately 100' C. by a jacket, 7, containing boiling water. The details of the integral reactor, 6, are shown in Figure 2. Fourteen calibrated Chromel-Alumel thermocouples, insulated with Fiberglas, were placcd in 0.125-inch inside diameter stainless st,eel tubes and insert,ed down through the top of the reactor. The method of insertion is illustrated in Figure 2 where four of the thermocouples are shown. Seven bare junctions were used to measure gas temperatures and seven for the solid temperatures. Both sets of junctions were in a single horizontal plane across the diameter of the reactor as shown in Figure 3. The
Vol. 41, No. 9
STEAM OUTLET
1
1 / / /
Figure 2.
Integral Reactor
Scale, 0.25 inch = 0.50 inoh
EXIT
)
INDUSTRIAL AND ENGINEERING CHEMISTRY
September 1949
the thermocouples and to provide the required bed depth. Then a retaining screen was placed above this material and held in osition by a stainless steel ring threaded into the reactor. T l i s furnished support for the desired depth of packed bed when the reactor was turned upright and Inserted into the system. A reference thermocouple was placed just below the retaining screen, so that the center temperature of the air a t the entrance of the bed could be maintained a t the constant value of 400" C.
GAS STREAM ' THERMOCOUPLES
Figure 3. THERMOCOUPLES EMBEDDED IN SOLID PELLETS
t,'C. 308 315 313 303 291 269 280 267 251 241 238 210 191 176 172
0,078 0.091* 0.121 0.167 0.174 0.200
230 237
0.341 0.349* 0.355* 0.364 0.384* 0.384 0.386 0.400 0.409* 0.569* 0,560* 0,600 0.645 0.652 0.652 0.667* 0.714* 0.743: 0.729 0.800 0.835 0.850 0.091* 0.151 0.197 0,200 0.212* 0.348* 0,364 0.394* 0,400 0,440 0.545* 0,600 0.652 0.665:
0.729 0.800 0.804
7 Mass Velocity, Lb./Hr./Sq. Ft. 351 511 244 K t,'C. K t,OC. K t,OC. K Bed Depth, 2 Inches 304 . . . 357 ... 374 373 . . . 382 . . . 358 371 358 . . . 382 o'.'is 355 0 . 1 8 370 0.24 380 O:i8 ... 335 . . . 351 . . . 367 346 335 ... . . . 362 . . . 363 351 0.26 0.33 0.21 o'..lb 330 349 333 . . . 315 ... ,.. 333 317 295 ... 326 0:24 311 0.24 0:38 0'.20 288 312 ... . . . 272 . . . 245 ... 296 ... 258 . . . 278 0.12 267 245 0.21 o.'is 228 0.25 244 228 ... ... . . . 210 ... . . . 228 210 . . . 209 Bed Depth, 4 Inches . . . 315 . . . 343 ... 300 . . . 323 . . . 347 . 293 . . . . . . . . . . . ... 318 . . . 344 ... ... ...
Reactor Thermocouples Scale, 0.50 inch 0.50 inch
=
147
0,114 0.160* 0.176 0 I200 0,359* 0.397 0.400 0.466 0,687* 0.600 0.670 0.725 0.800 0.848* 0.864
0.212*
"
c
Posi-
tion of Integral
TABLEI. EXPERIMENTAL TEMPERATURE DATAA N D CALCULATED K VALUES Radial Positiona, r/ro
1979
... ...
232
229 229 219
...
219
...
211 211
... ... 195 ..*
213
186
...
.
I
.
I
169
176 168 171 166 153 152 149 140 137 129 130
.
...
I
:
d.'ig
.
.
...
zii
292
......
... . . . 277' . . . . . . ... 272 ...... . . . . . . 270 o'.iii 268
...
266
0.'12
237 229 210
...... ... . . . . . ... ... 2ii ,,. . . . 190'
... ...
0.23
... ...
...
...
... ...
. . . . . . . . . . . . 0.34 338 0.39 ... 335 ... ... 319 ... . . . . . . . . . . . . 328 ... . . . . . . . . . 283 . . . 307 ...
315 312 295 304
289
...
364
...
0.17
291
0.27
315
0.31
...
267
I
.
,
I
.
. . . . . . . . . . . .
.
.,. 0.17
'
183 183 179 180 178
.
I . .
... ... 178 ... ... ... 162 ... 160 ... ... 195 ... 150 O ' . ' l O 174 0 . 13 143 . . . . . . . . . . . . . . . 160 ... 176
... ...
...
245 245 230 209 213
::: ... ...
... ...
264 255 22s 231
::: ... :. :. :.
iii o : i i iia 0:3+ 183 . . . 203 ... . . . . . . . . . . .
Bed Depth, 6 Inohes ... . . . 237 265 . . . 239 ... 268 233 . . . 259 260 0 , ' l 233 0.21 . . . 228 ... 258 . . . 215 ... 238 . . . 226 250 212 ... 238 o.'ib 216 0.18 241 . . . 211 . . . 234 188 . . . 205 O.'i3 188 0.17 206 . . . 184 204 . . . 165 ... 181 163 176 O'.'fl 148 0.10 159 . . . 148 . . . . 158 Bed Depth, 8 Inches 203 . . . 228 . . . 203 . . . 236
...
. . . . . . . . . 290 ... 0.26 iio o:i8 ... ...
... ... ... 0.26 ...
...
...
...
0.23
...
...
...
0.20
...
...
... ...
0.u
...
293 294 282 286
285 264 269 261 262 257 224 225 223 194 192 174 173
...
...
...
0.31
... ...
... ... ...
0.31
... ...
... 0.18
...
0.100* 155 . . . 252 155 ... 257 ... 0.150 0.187 ... ... ... ... ... 0.200 154 0.12 0.13 22s 0.14 252 0.14 155 0.203* 250 ... . . . 227 ... 150 0.339 214 ... ... ... 238 149 0.354* 215 ... . . . 238 ... 0.384* 146 210 ... . . . 231 146 0.400 209 0.12 o:ii 228 0.20 o:ii 0.421 205 145 ... 225 ... 0.535* 138 188 . . . 206 0.587 134 178 196 ... 134 180 0.18 0,600 O.'i3 0: 196 0.41 130 184 173 0.655* ... . . . ... 129 169 0.655 188 ... 125 0.729* .., . . . 162 . . . 177 121 0.784 149 ... 161 120 0 . 1 2 149 0.800 0 083 0:023 160 0'066 a Radial positions marked with an asterisk indicate the location of a thermocouple in a solid partiole. Other locations are in the gas phase.
...
...
...
...
...
... ii ...
...
-
CALCULATION O F EFFECTIVE THERMAL CONDUCTIVITIES
The derivations of the differential equations relating the temperature and position in the bed have been summarized by Hall and Smith (3). If the gas and solid temperatures are identical, the final form of the equation is:
...
... .
...
The temperature data for t h e complete range of mass velocities, radial positions, r/ro, and bed depths are reported in Table I. The results a t r/ro values of 0.200, 0.400, 0.600, and 0.800 were read from smoothed curves, while the other temperatures are observed values (9). In Figures 4 t o 6 , inclusive, temperatures of both gas and solid are plotted versus r/ro for different mass velocities. Perhaps the most important conclusion to be drawn from these figures is that, in general, the temperatures of both gas and solid fall on a single curve, indicating that there is no significant difference between the gas and pellet temperatures. It is also observed that the temperature gradients are quite large, showing that complete mixing of the gas in the packed bed is not obtained. This would suggest that the gas flows through the void space in the bed in the form of channels or bundles and t h a t any one bundle does not intermix rapidly with adjacent bundles. The significant and identical effect of mass velocity on both the gas and solid temperatures points to the conclusion that the rate of heat transfer radially through the bed is primarily dependent upon the characteristics-turbulence, physical properties, etc.of the aas surroundina- the *Dellets rather than the thermal conductivity of the pellets themselves. Experimental measurements with solid materials of different thermal conductivitie~should be obtained t o investigate this problem fully. The considerable variation of temperature with mass .velocity is evidence that the effective thermal conductivity of gas-solid packed beds is more analogous t o a heat transfer coefficient than the true thermal conductivity of either the solid or gas.
...
0.27
.... ...
...
RESULTS
.
I
... ...
All the quantities in Equation 1 are known or obtainable from the data except the effective thermal conductivity, K . The temperature derivatives with respect to T and x were obtained geometrically by measuring the slopes of curves of t versus r , t versus x, at @ versus T , and - versus x. The K values were then evaluated dT
bX
from Equation 1 at even increments of radial position. These results are also shown in Table I. Effective thermal condiictivities were not computed at zero bed depth, because it was felt t h a t the close proximity of the retaining screen t o the thermocouple junctions might affect the temperatures.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1980
400
40 0
Vol. 41, No. 9 G,ib/hr-ft! - -G A S
CATALYST
147
0
X
244
A
V
37 5
350
I
Y
a 3
+
2
325
n w
z
w
30 0
275
2 50 400
100
I
I
I
~
I
350
9
300
I w
a a c
a
250
W
:
Y
t
200
I50
i; j
; 51I
IO0
02
06
0 4
oa
LO
r/ r. Figure 4.
Plot of Temperature 2)s. Radial Position Above. 0-inch bed depth Below. 2-inch bed depth
0
0 2
04
06
r/ CORRELATIOK OF K VALUES
The effective thermal conductivity values in Table I range from about 0.1 to 0.4 B.t.u./(hr.)(ft.) ( " F.) and, in g:neral, increase with increase in mass velocity. Also there are variations with respect to location in the bed. The possible effects of radial position and bed depth are not clear from the data as presented in the table because of the accompanying changes in temperature. I n an attempt t o remove the influence of temperature it was assumed t h a t the effective thermal conductivity was related to the physical properties of the system by the following equation:
This equation is analogous to the empirical expression used to correlate heat transfer coefficients. The static effective thermal conductivity, k,, can be estimated from the correlation of Wilhelm (6) but this requires a knowledge of the true thermal conductivity of the solid phase as a function of temperature. Because this information was not available for alumina pellets, Equation 2 was modified to the approximate form
Figure 5 .
08
10
r,
Plot of Temperature c s . Radial Position Above. Below.
K E -o
4-inch bed depth 6-inch bed depth
=
a
d,G b (7)
(3)
The quantity e (equal to k,/k,) was assumed to be constant. If the change in IC, and k , with temperature is about the same, this assumption would not introduce significant error. Figure 7 is a plot of the results as - versus @ in accordance ka ( P > Kith the form of Equation 3. The individual points on the chart are the average of the values a t all bed depthsfor theparticular radial position and mass velocity. This procedure was followed despite the considerable variation of K / k a with bed depth, because this variation was not consistent. Presumably the changes due to bed depth were due to nonuniformities in the packed bed.
INDUSTRIAL AND ENGINEERING CHEMISTRY
September 1949 2?5
increase in K appears to be directly proportional to the Reynolds’ number. There is a sizable but inconsistent variation of K / k , with packed bed depth which suggests nonuniformitiesin packing. This makes an entirely accurat,ecorrelation of the results impossible. There is no appreciable change in K / k a with radial position until the tube wall is approached.
G,lWhrrfte G A S - 0-CATALYST X 147
i?
250
51 I
-
A
a
0
b
COMPARISON WITH HEAT TRANSFER COEFFICIENTS
22 5
The type of correlation shown in Figure 7 for treating thermal conductivities may be compared with Leva’s (4)recent esperimental measurenients of heat transfer coefficientsfor gases flowing in packed tubes. At the inside surface of the tube, the heat transfer rate per unit area is given by the two espressions:
$200
I a
W
a
.
1981
I-
* 175
5=h
U
L x w
-
=
t,)
-K
(3w
Leva found that h was directly proportional to the true thermal conductivity of air, k,, and proportional to the 0.9 power of the Reynolds’ number. From Equation 5 it would be expected that K , would vary with k , and the Reynolds’ number in the same
c I50
*
way, provided (t, - t,) and
125
100
(1,
I
I
I
I
I
I
0
02
0 4
06
08
10
(E),
are also affected in the
same way. In other words, the results of Leva mould suggest that the effective thermal conductivity should be proportional to k , and to
r:)”’”.
Figure 7 is in reasonably good agreement with
this conclusion, since it indicates that K is proportional to k , and the 1.0power of the Reynolds’ number.
r/ r. Figure 6 . Plot of Temperature us. Radial Position 8-inch bed depth
NOMENCLATURE
a, b = constants, dimensionless
Figure 7 indicates that there is no significant variation of K l k , with respect to radial position, except near the tube wall (for an r/ro of 0.8). The lower values of K / k , a t any average Reynolds’ number may be due to channeling caused by larger void spaces near the tube wall. The straight lines drawn through the points in Figure 7 correspond to a value of b equal to 1.0 in Equation 3. The final form of the expression for the central portion of the tube 1s
K k,
E
5.0
+ 0.061
(4)
The results may be summarized as follows: Effective thermal conductivities in a 2-inch tube packed with 0.125-inch alumina cylinders varied from 0.1 to 0.4 B.t.u./ (hr.) (it.) ( ” F.) within the mass velocity interval 150 to 500 Ib./(hr.) (sq. ft.). When the effect of temperature is considered, the
l 3 H CORRELATION OF EFFECTIVE THERMAL 12 CONDUCTIVITIES
c
d,
= specific heat of the gas (air), B.t.u./(lb.)( O F.) = diameter of the solid pellets, ft. Calculated on the basis of
equivalent area spherical particles = heat transfer coefficient for gases in packed tubes, B.t.u./ (hr.)(sq. ft.)( F.) G = mass velocity of gas flow, lb./(hr.)(sq. ft.) K = effective thermal conductivity, B.t.u./(hr.)(ft.)( F.) IC, = true thermal conductivity of air, B.t.u./(hr.)(ft.)( ’ F.) k , = thermal conductivity of the solid-gas system under static conditions, B.t.u./(hr.)(ft.)( F.). K , = effective thermal conductivity at tube wall, B.t.u./(hr.) (ft.)( F.) PIA = heat transfer rate per unit area a t the tube wall, B.t.u./ (hr.)(sq. ft.) r = radial distance measured from center of the reactor tube, ft. ro = radius of the yactor tube, Et. t = temperature, F. tw = bulk mean temperature of gas, F. te = temperature of the gas, F., a t the wall z = longitudinal position measured from bottom of packing in the direction of gas flow, ft. 6 = ratio k,/L., dimensionless p = gas (air) viscosity, lb./(hr.)(ft.) w = subscript indicating conditions a t the tube wall
h
O
O
LITERATURE CITED
(1) Brinn, M.S.,Friedman, S.J., Gluckert, F. and ENG.CHEM.,40,1050(1948). Pigford, R. L., IND. (2) Bunnell, D.G., M.S. thesis, “Temperature Distri-
bution in Catalytic Reactors,” Purdue University, June 1948. (3) Hall, R. E., and Smith, J. M., presented at Regional Meeting, American Institute of Chemical Engineers, French Lick, Ind., September 1948. (4) Leva, Max, IND. ENQ.CHEM.,39,857 (1947). ( 5 ) Wilhelm, R. H., Johnson, W. C., Wynkoop, R., and Collier, D. W., Chem. Eng. Progress, 44, 105 (1948). Reynolds’ Number,
Figure 7
dPG -
R E C E I V ~September D 23, 1948. Presented before the Division of Industrial and Engineering Chemistry a t the 116th Meeting of the AMERICANCHEIIICIL S O C I ~ T Y ,San Francisco, Calif.
