August 1951
NOMENCLATURE
drying area, sq. ft. heat capacity, B.t.u./(lb.) ( O F.) diffusivity,.sq. ft./hour mass velocity, Ib./(hr.)(sq. ft.) H = enthalpy, B.t.u./lb. L = length, feet hl = molecular weight P = total pressure, lb./sq. ft. W = weight,Ib. = heat transfer coefficient, B.t.u./(hr.) (sq. ft.) ( O F . ) h = factor defined by Equation 6 ( 3 ) j = mass transfer coefficient, Ib./(hr.) (sq. ft.) (atm.) k ka = thermal conductivity, B.t.u./(hr.) (sq. ft.) ( O F./ft.) p = partial pressure, atm. Q = heat transferred, B.t.u. = resistance t o heat transfer ( l / h ) r t = temperature, “ F . = absorptivity in radiant heat transfer 01 = emissivity in radiant heat transfer e p = density, lb./cu. ft. = viscosity, lb./(ft.) (hr ) p e = time, hours y = shape factor
A C, DO G
1837
INDUSTRIAL AND ENGINEERING CHEMISTRY
= = = =
LITERATURE CITED
(1) Broughton, D. B., IND.ENG.CHEM.,37, 1184 (1945). (2) Ceaglske, N. H., and Hougen, 0. A., Ibid., 29, 805 (1937). (3) Colburn, A. P., Trans. Am. I n s t . Chem. Engrs., 29, 174-210 (1933). (4) Gilliland, E. R., IND.ENG.CHEY., 30,506 (1938). (5) Govier, G. W., Sc.D. thesis, University of Michigan (1948). (6) Hausbrand, E., “Das Trocknen mit Luft und Dampf,” Berlin, Julius Springer, 1908. (7) Hottel, H. C., and Egbert, R. B., Trans. Am. Inst. Chem. Engrs., 38, 531 (1942). (8) Hougen, 0. A., McCauley, H. J., and Marshall, W. R., Jr., Ibid., 36, 183 (1940). (9) MoCready, D. W., and McCabe, W. L., Ibid., 29, 131 (1933). (10) Shepherd, C. B., Hadlock, C., and Brewer, R. C., IND.ENG. CHEM.,30,388 (1938). (11) Sherwood, T. K., Ibid., 21, 976 (1929). (12) Sherwood, T. K., and Comings, E. W., Ibid., 25, 311 (1933). (13) Ungewitter, C., “Science and Salvage,” London, Crosley Lockwood and Son, 1944. (14) Walker, W. H., Lewis, W. K., McAdams, W. H., and Gilliland, E. R., “Principles of Chemical Engineering,” New Yolk, McGraw-Hill Book Co., 1937. (15) Washington, L., and Marks, W. M., IND. ENG.CHEM.,29, 337 (1937). RECEIVED Septeiiiber 7, 1950.
Pressure Drop in Flow of Dense Coal-Air Mixtures
EngFnyring Process development
P. SIMONS, AND L. D. SCHMIDT BUREAU OF MINES, U. S. DEPARTMENT OF THE INTERIOR, AND ENGINEERING EXPERIMENT STATION, WEST VIRGINIA UNIVERSITY, MORGANTOWN, W. VA.
C. W. ALBRIGHT, J. H. HOLDEN, H.
T h i s investigation was undertaken to obtain a method of predicting the pressure drop in a pneumatic system used to feed pulverized coal to a generator in which the coal reacts with oxygen and steam to form synthesis gas (CO Hz). The feeding system operates by causing a partially settled mixture of coal and air to flow through a tube from a fluidized bed of pulverized coal. The results have been corrklated in the form of two empirical equations which give the pressure drop for the flow
of mixtures of air and coal (90% through 200-mesh) through horizontal tubes and in the ratio of approximately 200 pounds of coal per pound of air. So far as is known, these are the first pressuredrop measurements on mixtures using such a high solid-gas ratio, and the equations developed represent the best knowa method of determining the pressure drop for the flow of coal-air mixtures in the ratio of about 200 pounds of coal per pound of air.
A
pressure drop of the coal-air mixture flowing through the tube in terms of the weight rate of coal flow, the ratio of coal t o conveying air, and the tube diameter. Information in the literature on the flow of solid-gas mixtures is very limited, and no information has thus far been found concerning the flow of mixtures at the high solid-gas ratios utilized by the feeder. Therefore, measurements of the pressure drop have been undertaken for four tube diameters and for various coal-flow rates and coal-air ratios. The results of these measurements and an empirical correlation are presented.
+
S PART of the synthetic liquid fuels program, a feeder has been developed by the U. S. Bureau of Mines at Morgan-
town, W. Va., in cooperation with West Virginia University, t o deliver coal at a uniform rate to a pulverized coal gasifier for making synthesis gas. The feeder, which has been described previously ( 1 , Q), operates by forming a fluidized bed of coal in a vertical cylindrical container and by causing a mixture of coal and air t o flow through a tube to the gasifier, Part of the air used to fluidize the coal acts as the conveying gas, while the rest is vented from the top of the container. The entrance t o the coal-delivery tube is located near the bottom of the fluidized bed of coal and is protected from the direct action of the fluidizing gas by a shield that greatly improves the uniformity of the coal-air mixture. Tests (3)on the uniformity of the coal-air mixture flowing through the delivery tube have shown that the variation in the volumetric ratio of coal to air is small over time intervals of about 0.1 second. To predict the rate of coal delivery, it is necessary to know the
EXPERIMENTAL METHODS
Two different pieces of experimental apparatus were used to obtain the data. The first was a small scale model of the feeder ( I ) ; the test section was a horizontal 12-foot length of a/le-inch (0.0097-foot inside diameter) tubing equipped with pressure taps. The pressure measurements in this apparatus were inaccurate in spite of
INDUSTRIAL AND ENGINEERING CHEMISTRY
1838
attempts to develop a reliable method of measuring the pressure of the dense coal-air mixture flowing through the tube. To circumvent the difficulty of measuring the pressure in the line, the next set of pressure measurements were made in the feeder a t the level of the entrance to the delivery tube and in the collecting drum a t the exit of the delivery tube; and a long, horizontal section was used to minimize the effect of entrance and exit losses. Figure 1 shows a diagram of the second apparatus. Air enters a t the bottom of the column, fluidizing the coal. Part of the air is used t o convey the coal through the delivery tube, and
Vol. 43, No. 8
ments, the results for each pressure were averaged. Hence, the reported data for each run are averages of eight determinations, The results obtained on the second apparatus-those pertaining to the three larger tubes-were reproducible with an average deviation of 1%. These data are therefore assumed to be accurate. For the a/lo-inch tube the accuracy of the pressure measurements is doubtful; no entirely reliable method was found for measuring the pressure of the dense coal-air mixture while it was flowing through the tube. For the three larger tubes, the measured pressure drop inORIFICE
OR1 FlCE AIR
AIR
AERoTE
A E R O T E ~ ~
' I I I
61
a
T E S T SECTION
I
Figure 1.
I
__1
DIFFERENTIAL PRESSURE I N D IC A T 0 R
WET T E S T METER
I
I
k
Y
PRESSURE CONTROLLER
PLATFORM SCALES
AIR
Experimental Apparatus for Determination of Pressure Drop i n Flow of Dense Coal-Air Mixtures
the rest is vented from the top of the column. Coal is delivered from the batch feeder to the continuous feeder a t such a rat,e that the amount of coal in the continuous feeder is kept constant. The amount of coal in the feeders is measured by the differential pressure gage connected across the bed. The pressure in the feeder a t the level of the entrance t o the delivery tube is kept constant by a diaphragm control valve in the air inlet line. The pressure drop is measured between the column and the collecting drum in which coal is caught and weighed. The volumetric rate of f l o ~is measured by the wet-test meter and the fluidizing velocity by an orifice in the exit air line. Three tube sizes were used in the runs: b/16-inch (0.0205-foot inside diameter), 3/8-inch (0.0257-foot inside diameter), and 0.5-inch (0.0363-foot inside diameter). The length of t'he test section was in each case 58 feet. The coal used was 90% through aOO-mesh, as was used in the gasification experiments. I n making the measurements the desired pressure in the fluidizing column was set and the flow of coal through the test section started. The coal flow from the batch to the continuous feeder was set so t h a t the level in the continuous feeder was kept constant, The apparatus was then operated long enough to obtain steady conditions before the start of the run, as indicated by the cont,rol instruments. For t,he 0.5-inch tube 100 pounds of coal were collected per run; for the 3/8- and 6/16-inchtubes 50 pounds of coal were collected per run. Runs were made at four different fluidizing velocities, and duplicate but not consecutive runs n-ere made a t each pressure. RESULTS
The results are presented in Table I. As no consistent effect of fluidizing velocity could be found on the pressure-drop nieasure-
cludes ail). accaleration effects of the particles. An attempt was made to minimize this error by using a long t,est. section. I n malting the pressure drop measurements on the small tube, prcssure taps mvere used, but t'he accuracy of these measurements was doubtful. Reliable pressure measurements were preferred t o elimination of acceleration effects. The reported results may hence be consistently high by the amount of this error. Table I lists both the measured pressures and the corrected pressures. The inlet pressure was corrected for entrance loss by subtracting 0.5V2p,+ ,j2g ( 5 )and the outlet pressure by adding V2p,+,/2g (6). The specific pressure drop is the difference beti\-een the corrected pressures per unit length of test section. The average density of the coal-air mixture is the arithmetic average of the densities calculated at the corrected pressures. The average velocity is that comput,ed from the average density. The friction factor was calculated from the familiar Fanning equation, 1 = ApgD/2LV2p. From a mechanical energy balance it was found that the velocity t,erm was small enough to be neglected in calculating the friction factor. The ratio A p / A p , was obtained by first measuring t,he pressure drop of air alone and then calculating a pressure drop for air a t the same average velocity and pressure as that of the coal-air mixture. The Reynolds number for air \vas also calculated a t a velocity equal t o the average velocity of the coal-air mixture. Table I1 presents the averaged screen analysis of the coal used in the investigation.
August 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
1839
TABLE I. AVERAGED DATAA N D CALCULATED RESULTS
Tube 1.D Foo; 0.0363 0.0363 0.0363 0.0363 0.0363 0.0363 0.0363 0.0363 0.0363 0.0363 0.0257 0.0257 0.0257 0.0257 0.0257 0.0257 0.0257 0,0257 0.0257 0.0205 0.0205 0,0205 0.0205 0,0205 0,0205 0.0205 0.0205 0.0097 0,0097 0.0097 0.0097 0.0097 0,0097 0.0097 0.0097 0.0097 0,0097 0.0363 0,0363 0.0363 0.0257 0,0257 0.0257 0.0205 0.0205 0,0205
Coal Rate Lb./S&. 0.373 0.36 0.349 0.332 0.314 0.292 0.262 0,224 0.1842 0.1348 0.154 0.1483 0.1432 0.1348 0.1233 0.112. 0.0981 0.0815 0.0636 0.0895 0.0856 0.0809 0.0736 0.0686 0.0605 0.0508 0.0395 0.0266 0.0255 0.0223 0.0202 0.0192 0.0182 0.0154 0.0136 0.0113 0.0111 0 0 0 0 0 0 0 0 0
Air Rate Lb./S&. 0,00257 0.00238 0.00221 0.00201 0.001829 0.001578 0.001375 0.00109 0.000842 0.00057
0.00258 0.00176 0.00088 0,00126 0.000878 0.000673 0,000745 0.000632 0.000351
Coal-Air Ratio Lb./L6. 145 151 158 165 172 185 190 206 219 236 125 130 133 143 153 163 176 190 197 141 148 152 164 170 186 197 219 160 161 185 186 212 206 229 235 242 256
.o
0 0 0 0 0 0 0 0
SDecific Measured Corrected P'essure Pressures pressures, Lb./Sq. Ft. kbs. Lb./Ss. Ft. Abs. Ft./Ft. Inlet Outlet Inlet Outlet Length 4230 2374 4172 2562 27.7 4036 2526 4090 2355 26 24.3 3905 2495 3955 2339 22.8 3770 2446 3815 2309 3670 2280 21.2 3630 2400 3530 2256 19.67 3496 2354 3390 2231 18.15 3352 2308 16.77 3228 2254 3250 2200 3105' 2177 15.14 3092 2212 13.48 2965 2158 2958 2176 4186 2356 4230 2200 31.6 4049 2335 4090 2195 29.6 27.6 3916 2314 3955 2185 3815 2185 25.7 3782 2292 2161 24 3643 2247 3670 22.1 3508 2224 3530 2157 20.2 2154 3374 2202 3390 18.27 3239 2179 3250 2148 16.28 2135 3098 2154 3105 4196 2260 4230 2140 33.4 4060 2240 4090 2135 31.4 29.2 3928 2240 3955 2145 3793 2240 3815 2170 26.7 2133 3651 2193 25.1 3670 3530 2133 23.1 3516 2176 21 2163 3380 2135 3390 18.85 3244 2146 2130 3250 3690 2610 no correction 89.8 no correction 86 3635 2605 2460 68.3 no correction 3280 59.7 3095 no correction 2380 53.8 2970 no correction 2325 50.6 no correction 2925 2320 44.3 no correction 2765 2333 38.6 2685 2220 no correction 2625 36.4 2190 no correction 35 no correction 2500 2180 1.21 2223 2162 no correction 0.604 2170 2139 no correction 0.174 2133 2124 no correction 1.48 2219 2142 no correction 0.755 2169 2130 no correction 0.46 2149 2125 no correction 1.93 2132 2228 no correction 1.42 2127 2198 no correction 0.457 2121 no correction 2144
zfyg,i,
Av. Density Av. Mixture Velocity Lb./Cu. &t. Ft./Sec 14.41 25.2 14.6 23.9 14.86 22.8 15.04 21.4 15.18 20.1 15.69 18.1 15.64 16.2 16.26 13.37 16.65 10.71 17.21 7.57 24.1 12.39 12.55 22.9 12.55 22.1 13.06 19.97 13.48 17.72 13.89 15.6 14.48 13.1 15.05 10.47 15.16 8.11 13.54 20.1 13.83 18.83 13.89 17.7 14.56 15.4 14.61 14.27 15.39 11.96 15.73 9.81 16.85 7.12 14.86 24.4 14.83 23.4 15.51 19.5 14.97 18.32 16.23 16.03 15.72 15.7 12.68 16.49 11.15 16.62 16.74 9.16 17.13 8.8 0.0779 32 0.0766 22.2 0.0758 11.2 0.0773 31.5 22.2 0.0763 17.1 0.0757 29.2 0.0773 24.9 0.0768 14.1 0.0756
Fanning Friction Factor, No Units
0.0018 0.00185 0.00185 0.00203 0.00234 0.00269 0.00333 0.00465 0.00673 0.00201 0.0021 0.0022 0.00255 0.00277 0.00345 0.00456 0.00725
A p Mixture Re$:!ds b p Air a t for Air
Same Velocity, No Units 25.9 27.3 28.3 30.5 32.5 37.7 43.6 57.4 80 124.0 26.6 27.6 28.3 33 38.9 46 59 81 111 27.2 29.8 31.4 38.9 43.5 57.1 75.9 115
... ...
...
...
0.00885 0.00935 0.0107 0.008 0.0083 0.0086 0.0097 0,00985 0.01
... ... ... ... ... I
.
.
a t Same Velocity, NO Units 9080 8350 7770 7080 6450 5640 4920 3900 3020 2070 5950 5500 5200 4580 3940 3380 2760 2140 1610 3900 3570 3290 2800 2510 2050 1630 1150 2190 2080 1590 1430 1210 1180 920 780 630 585 7480 5100 2550 5170 3600 2750 3820 3240 1805
TABLE 11. AVERAGED SCREEN ANALYSIS Screen No.
Cumulative % ' Retained
50 100 150 200 Through 200
0.1 1.5 3.0 6.2 89.2
Vogt and White (6) plotted ( R e a / ~ ) ( p c / p o ) ( D c /against o)2 A p / A p a , obtaining a line with a negative slope of 1.0. The data
900
700
DISCUSSION O F RESULTS
Figure 2 shows ( A p / L ) p plotted against the mass velocity. The curves may be considered as consisting of two straight segments. Because the points of inflection lie on a straight line and the lines for the different diameters are parallel, an empirical equation has been developed that represents the results of the measurements within an accuracy of about 5%.
For G( A ~ P / L ) O>. ~1950, ~ App/L = 0.022 G1.12/Do.94 and for G( A ~ P / L ) O
