Ind. Eng. Chem. Process Des. Dev. 1081, 20, 19-26
R = gas constant, Btu/lb-mo1.R RED = COD reduction, % S = unit entropy of gases on dry basis, Btu/lb S = entropy of gases, Btu T = temperature, R W = unit work consumed or generated, Btu/lb w = mass of components, lb/lb Greek Letters p = density of waste water, g/cm3 TJ = efficiency, % Subscripts 0 = initial conditions or feed a = air c = compressor dg = dry gases g = gas phase 1 = liquid phase P = Pump r = reactor s = saturated gas Literature Cited
10
icai Engineering, Universlty of Kansas, 1977.
Can. Chem. Process. Nov 1977, 20. Chowdhucy, A. K.; Ross, L. W. AIChE Sy.mp. Ser. No. 151 1976, 71, 46. Farha, F. E.: Box, E. 0.;Dunn, R. 0.. Jr.; Kuerston, R. D., "Uquld Phase Catalytic Oxidetlon of Waste Water", General Paper presented betore the Divlslon of Petroleum Chemistry, 175th Natlonal Meeting of the American Chemical Society, Anahelm, Calf., Mar 12-17, 1978. Flynn, E. L. Chem. Eng. Bog. 1979, 75(4), 66. Hamilton, C. E.: Teal, J. L.. Kelly, J. A. US. Patent 3442802, May 6, 1969. Herding, J. C.; Griffin, G. E. WPCF J . 1965, 37, 1134. HeMemann, R. A.; Prausnitz, J. M. Ind. Eng. Chem. Process Des. Dev. 1977, 16,375. Hurwitz, E.: Dundas, W. A. WPCE J. 1960, 32, 918. Hurwh, E.; Teletzke, G. H.; Gitchel, W. 8. Wafer Sewage Works 1965, 112, 298. Jagow, R. E. et ai. NASA-CR-112151 (1972). JagOW, R. B. ASME 72-ENAV-3 (1973). Katzer, J. R.; Ficke, H. H.; Sadana, A. WPCF J . 1976. 48,920. Pradt, L. A. Chem. Eng. Prog. 1972, 66(12), 72. Rosson. H. F., private communlcatlon, 1977. Teletzke, 0. H. Chem. Eng. Prog. 1964, 60, 33. Weitzman, A. L. et ai., NASA-CR-151324 (1977). Wheaton, R. B.; Cailoway Brown, J. R.; Ramlrez, R. V.; Roth, N. 0. NASA Contract No. NAS.1-6295, 1967. Yunis, S. M. W.D. Dlssertation, Illinds Institute of Technology, 1967. Zlmmermann, F. J. Chem. Eng. Aug 25, 1958, 65, 117. Zimmermann, F. J. Tappll960, 43, 710.
Received for reuiew June 1, 1979 Accepted September 15, 1980
Bishop, K. A,; Rosson, H. F., Ramanathan. V. "Wet Oxidation of Waste Siurdes wlth Net Energy Recovecy", Department of C h e m b i and Petrochem
Pulsed Transport of Bulk Solids between Adjacent Fluidized Beds Dennls M. Bachovchln,'
P. Richard Mullk, Rlchard A. Newby, and Dale L. Kealrns
Westinghouse Research and Development Center, Pittsburgh, Pennsytvania 75235
A cold model test facility capable of transporting up to 6.3kg/s bulk solids between adjacent fluidlzed beds was operated, with solids flow controlled by pulsed air input. This technique is applicable when a continuous gas seal is impossible due to an unfavorable pressure balance. The effects of pulse on- and off-times, air rate, and fluidizing velocity on solids flow capacity and efficiency were examined. A theoretical model was developed and used to project the effects of these and other key variables.
Introduction The transport of high-temperature particulate solids between fluidized-bed reactors is required in several processes, including the important energy technologies of fluid-bed combustion and gasification (Keairns et al., 1973, 1975;Newby et al., 1978). Desirable conceptions of these processes feature sulfur capture by a lime-based sorbent which is continuously removed for regeneration and recycled. Economics, space limitations, or heat conservation may require that material be transported betwen two beds in close contact at the same level. In such instances the difficulty of providing simultaneous seals in both directions requires innovative and careful design. The Chemically Active Fluid Bed Process was conceived by the Esso Petroleum Company and is now being developed for the gasification of lignite under EPA sponsorship (Rakes, 1978). A technique was suggested by &so (Craig et al., 1971)for transport of solids between gasifier and regenerator vessels by pulses of transport gas introduced at the elbows of transport ducts connectiqg the vessels. The short vertical legs between relatively dense fluidized vessels cannot provide a seal against gas interchange by the vessels with continuous aeration. Westinghouse built and operated a large cold test unit and developed a mathematical model of the transport 0196-4305/81/1120-0019$01 .OO/O
process as part of a broad CAFB engineering support program sponsored by EPA. The purpose of the program was to gain an understanding of this transport technique to permit analysis of scale-up and optimization. Transport system optimization must deal with the following desirable features: high solids capacity, minimum air requirement, controllability, a seal against reactor gas exchange, and freedom from plugging or other malfunction.
Test Program Equipment and Procedures. A schematic of the test facility is shown in Figure 1. Solids were transported between two identical semicylindrical vessels (0.7m radius by 3 m height) via transport legs (Figure 2) connecting them. m i d operating conditions were a pressure of 115 kPa and a temperature of 340 K, with a bed height of 1.0 to 1.5 m. View porta were installed in vessels and legs to allow observation of solids fluidization and flow characteristics. A pulsation control vessel (Figure 1)in the pulse air line to each leg isolated the orifice meter from the pulsation and permitted the steady state measurement of the overall (time averaged) pulse air rate. Pulsation waveforms for each leg were set by an electrically controlled solenoid valve near the nine pulse injection nozzles (Figure 2) a t the back of each leg. 0 1980 American Chemical Society
20
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
rh 2.5
--4
2.0
I
t
\
i
Slope at This h i n t
i
1 5
least Squares line AP = 1. 713 t 0. 03161 -0.
A,r
o-..
MI?
Quadratic Fit
,' .I, Tranrprt
~
4
1
~
PliIidtlO" contrc1
Alr
Pressure Trace
ierre1
Blower
Figure 1. Test facility flow diagram.
10
20
30
40
M
bo
70
80
Time, I
i
Figure 3. Typical solids transport rate determination.
,
Supplying Vessel
s, a differential pressure transmitter covering the surface of the deeper bed would be used to record t3e be+ depths vs. time. The solids flow rate was then given by
G, = -(ABgc/g) d(&J/dt
,Top View Ports I
t
Receiving Vessel 1
Equally Spaced 5 08 cm Center to Center Each Coverrd By 325Mesh Screen.
?
cm
v L H = 0.42 mNote: Width: W =O. 457m
Figure 2. Test facility transport leg. Table I. Particle Size Distribution start of av size, test series, U.S. mesh pm wt %
~
~
-~
+8 -8 t12 -12+16 -16 +20 -20 +30 -30 +40 -40
0.1 41.0 35.8 11.2 6.0 2.8 3.0 99.9 1274pm
2605 2030 1435 1016 718 508 350
surface mean size ( xi/&) 1
end of test series, wt %
2.1 12.9 26.0 21.2 14.2 8.0
15.0 99.9 794pm
The bed material was activated alumina, chosen on the basis of its bulk density ( 1g/cm3 as expected for CAFB material). The size distribution is given in Table I and varied during the test series because of attrition. Direct measurement of solids flow was not possible because of its pulsing, turbulent character. We therefore measured solids flow by noting bed level changes. Material was shifted so that one bed was about 0.3 m deeper than the other. Then pulsation was started in that leg transferring solids from the deeper bed to the shallow bed until the relative depths were reversed, at which time flow was turned off. During this test, which typically took 20 to 30 N
The rate of change of bed pressure drop varied with relative bed depth because system pressure gradients wouid depend on fluidized bed depths. The pressure drop vs. time curve was therefore mathematically smoothed by least-square fit to a quadratic and its slope taken at the point of equal bed depth as determined by averaging the pressure drops across the two beds. Each m was repeated in the opposite direction. Figure 3 is an example calculation.
Results A total of 272 formal tests were made. An extensive matrix of pulse durations of from 0.05 to 4.0s and off-times of from 0.5to 3.1 s was tested. These were chosen on the basis of the results of preliminary tests not discussed in this paper. Overall pulse air rates of from 0.015 to 0.13 kg/s were used. The fluidizing velocity was about 1.0 m/s for most runs. This value was selected as a compromise between the desires for maximum bed expansion and for limited attrition and entrainment. Fluidizing velocities as low as 0.37 m/s were tested later. Detailed results are given by Bachovchin et al. (1978). With proper selection of the pulse pattern, average solids transfer rates in excess of 4.0 kg/s were often obtained. Several runs had rates greater than 5.0 kg/s. On a flow per unit area basis, our time-averaged rates were optimally 80 to 110 kg/s m2. Transfer efficiencies (mass of solids/mass of gas) varied considerably, but values in excess of 100 were frequently obtained. We observed that the solids above the pulse jet became fluidized with each pulse. Transport gas was divided into a fast-moving dilute phase a t the top of the horizontal section (SeeFigure 6) and upward moving slugs or bubbles near the upper vertical face, moving more slowly. Some recirculation seemed to occur near the base of the vertical section. After a short time all gas would apparently rise upward and blow the leg completely. The time required for this to occur was about 0.4 s. Before this rise solids transport occurred; after it, transport stopped and gas escaped upward. No transfer was possible with continuous (non-pulsed) aeration. For on-times in excess of about 0.4 s, at least 1.2 s was needed for complete defluidization of the vertical leg prior to the next pulse. For shorter ontimes proportionately less defluidizing time was needed. Off-times only slightly longer than the minimum defluid-
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981 21 400
I
I
I
I
t
on
e
3% 0
VI
0
e g
g
2%
0
o tS=t
off toff=2.05
A
'off =2.05
Runs48-67 Runs48-67 Runsld5 Runs 1-45
eoo e
200
vs3
v3
Solids out
Gas out
=3
=3
'RH
8
Gas o u t
e o
al
L
"0"0
c I-
=l. 05
Section
e
0
EB
off
t
P4 at Top of Vertical
Solids in
I
0
E n
E
t '=LO5
$=t,
A t =t s .on
0
300
I
I
varies depentently with W p
1x
0
s2*
1M: A
51
Control Volume Boundary
A
Figure 6. Solids transport model flow profile and nomenclature. 51
A
0
e e* I
a-a
I
I
I
I
s
W =Gas Flow Rate During Pulse, kgls
Figure 4. Effect of pulse air rate on modified transfer ratio.
125
I
I
1 AA
25
i
A
1 I
0
I
6 m A ' 0. 5 1.0
I
I
1.5 Off-lime,
2.0
1
2.5
3.0
s
Figure 5. Effect of off-time on modified transfer ratio.
izing time would not allow a complete repacking, resulting in more gas flowing upward and reduced efficiency. The optimum configuration, therefore, would have an on-time of just less than 0.4 s and an off-time of about 1.6 to 2.0 s. Within these bounds higher pulse air rate will give higher transfer rate. A shorter on-time or a longer off-time would result in a lower fraction of transfer time. This would result in a lower overall transfer rate. Longer ontimes or shorter off-times resulted in an unacceptable loss of gas upward, reduced efficiency or negligible solids flow, respectively. Typical data are shown in Figure 4 and 5, in which the modified transfer ratio mass solids transfer solids flow time
-. mass gas I"fer
pulse on-time
is compared to the pulse gas instantaneous flow rate. Note that on-time is not constant on this graph but is related to the gas flow rate and hence the graphs cannot be used to calculate transfer rates. The striking feature is that efficiency increases sharply with decreasing gas input rate a t the low values of airflow. The two presumed interrelated reasons for this are that (1)high solids mass flow is required to compensate for decreased velocity in the mo-
mentum balance, and (2) horizontal transport occurs in a denser phase (i.e., the jets are more persistent). Although the ratios are large here, the low flows result in solids transfer rates not being correspondingly large. Also the low velocity runs generally correspond to long pulse ontimes, so true transfer ratios suffer, as actual solids flow time is less than gas input time. In Figure 4 the 1.0 s off-time curve is displaced substantially lower than the 2.0 s off-time curve because with the 1.0 s off-time complete defluidization does not occur, and great efficiency loss occurs as gas flows upward. The exceptions are the cases where fluidization is not completed (A in the 1.0 s case). Here the modified transfer ratio is similar to those of the other off-times. Figure 5 shows the importance of allowing sufficient time between pulses. Theoretically, the curve should level off with increased off-time. This is evident in the cases of the low instantaneous air flow rates. Fluidizing velocity (equal for the two beds) had no noticeable effect on the system performance for the range tested. Solids Transport Model Description. A mathematical model was developed using a macroscopic momentum balance corrected for the major unsteady aspects of the flow behavior. Figure 2 defines geometric variables and Figure 6 hydrodynamic variables. Time Sequence. With no transport gas input the overall pressure drop (P3- P4),which is determined by the bed pressure balance, is easily sealed by the packed solids in the horizontal and vertical sections. Gas flows between vessels at a low rate estimated from the Ergun equation for packed-bed pressure drop (expressed in terms of relative interstitial gas-solids velocity)
Assuming the fluid-bed vessels to be operating at approximately equal fluidizing velocities, the imposed pressure drop will be p3 - p4
= PFBgLv/gc
(2)
With the introduction of pulse air, solids flow begins, and the pressure Pl jumps to a level larger than P3. The pressure drop now imposed upon the vertical leg section will now be
(3)
If the imposed pressure gradient is greater than the density of the vertical leg solids, in other words
22
Ind. Eng. Chem. Process Des. Dev., Vol. 20,No. 1, 1981
(1 - tp)g P1 - P4 P P g C (4) L, then the state is unstable and the leg will fluidize to relieve the excess pressure, liberating pulse gas in the upward direction and causing loss (or reversal) of solids flow. In practice the fluidization of the downcomer is inevitable unless pm is rather low. Solids flow can occur only before fluidization is complete. Steady State Assumptions. We assumed a steadystate flow pattern during the effective portion of each pulse-in other words, before fluidization was completed. Several unsteady aspects of the momentum exchange process had to be neglected. (a) A finite time is required for jet formation and decay. Much greater model complexity would be required by unsteady mass and momentum balances. Jet formation did appear rapid in the experiments. (b) The velocity of gas issuing from the pulse nozzles may not be constant during a pulse. In this study an average flow duting the pulse was derived and used in the analysis. The results suggest that the relationship between solids and gas flow is not a strong function of gas velocity except at low values where the assumption is most likely valid. ( c ) We assumed that the vertical solids voidage was constant during the entire effective pulse time. Relaxation of this assumption would require more knowledge of the unsteady behavior of fluidized systems than is now available. Mass Balances. The control volume is shown in Figure 6. Gas enters the system at the nozzle, generating a jet which entrains and carries solids to the receiving vessel in dilute phase transport above a region of stagnant solids. The mass balance for the pulse gas is then U&PZ + UliJISipi=u g e S 3 ~ 3+ U R H (~S~ - S3)Pl (5) A d In the above equation the terms represent: A, gas in at nozzle; B, gas in from above with solids (for the present application u1 will usually be negative); C, gas out in dilute phase; D, gas out through the stagnant solids. For solids the mass balance is (u1 + uR)(1 - 61)Sl = b 3 ( 1 - c 3 ) s 3 (6) where the left-hand term represents the solids entering from above, and the right-hand term is the efflux of solids in the lean phase. Momentum Balance. A momentum-force balance for the horizontal direction was developed. Note that because of the angle of the vertical section, solids enter the control volume with a finite, though small, horizontal momentum. The overall balance is
'
where the various terms are A, force of gas on projected area to rear of leg; B, gas momentum in at nozzle; C, gas momentum out in dilute phase to receiving vessel; D, solids momentout in dilute phase to receiving vessel; E, pressure of outlet stream (assumed constant over the entire cross section); F, pressure of gas in at nozzle (note that the control surface crossed by the gas in the vertical section has no vertical component); G , gas momentum out via vertical section; if the net flow of gas in the vertical section is downward, the sign of this term is reversed; H, solids
momentum in from above. In this balance the viscous fluid-wall effect and the momentum of the gas leaking through the stagnant solids have been neglected. Horizontal Pressure Drop. The vertical and horizontal relative velocities can be estimated from the Ergun equation (eq 1) using pressure gradients of (Pl - P4)/Ls and (P1 - P3)/LH,respectively. The jet pressure, P2, is assumed equal to P,.P3 and P4must be estimated from system pressure balances. The pressure drop (P1- P3)in the horizontal dilute phase was modeled by the correlation of Wen and Simons (1959)
By definition PDS
= Pp
2 0 - '3)S3
+ (1 - d(S1 - 8 3 ) S1
where the average dilute phase density is approximated as twice the final density due to acceleration. Then
us =
ku3S3(1 2s1PDS
dPp
(10)
Dilute Phase Flow Area. Referring to Figure 6, the areas S1 and S2will be known in any application, but S3 must be estimated. For this model we estimate this dilute phase flow area by assuming that the similarity of jet expansion is valid for the heterogeneous system. The final flow area will therefore be a function of leg geometry only. The individual gas jet a t each nozzle expands as a circular jet until interference from neighboring jets is encountered. Beyond this point expansion is as a plane jet. No further jet expansion is assumed to occur once the jet passes beneath the lip of the horizontal section. From this point dilute phase horizontal transport occurs to the exit of the transfer leg. In practice, the dilute phase exists at the top of the horizontal section because of buoyancy. The vertical position of the dilute phase has no influence in the model. The distance from the nozzle outlet to the transition from circular jets to a plane jet is Xn - do X1 = 2 tan 6 If x1 L Xh, the find area s3is given by
In the model p was taken as 7.64' and B as 6.35'. Derivations and developments of the half-angle estimates are given by Bachovchin et al. (1978) based upon the work of Merry (1971) and Rajaratnam (1976). Fluidizing Time. The time required to blow a leg when a pressure drop in exceas of the bulk density of the material in the leg is imposed is approximated by
The derivation of eq 14 is given in the original report (Bachovchin et al., 1978). For
Ind Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
23
Table 11. Comparison of FWEC Final Design Dataa and Model hedictions
and Ls = Lv, eq 14 reduces to tM =
(
:)'2
In the model solids flow was assumed to stop completely during a pulse at t M given by eq 14. Vertical Section Voidage. The vertical void fraction, cl, was assumed to be constant during any given pulse. The value of el can, however, be significantly greater than the normal packed density if sufficient defluidizing time is not allowed. Experimentally, we observed that at least 1.5 s defluidizing time is required for complete repacking (Le., insensitivity of transfer efficiency to off-time) when the pulse on-time exceeded t M . Proportionately less time is needed for shorter on-times because only partial expansion of the vertical leg section solids occurs. The voidage el will thus be a function of the pulse on-off times. Its importance is in determining the optimum on-time, t M (requiring an iterative procedure), and the amount of pulse gas that escapes vertically upward during each pulse. As the offtime is reduced, el will approach unity, and bypassing of pulse gas will be complete. In the model, semiempirical relationships were used to reflect this behavior. The rationale behind these is discussed in the original report (Bachovchin et al., 1978). For tON
tM
actual solids FWrun onoff- av airflow rate, no. time, s time, s rate, kg/s kg/s
pred solids rate, kg/s
LS-1 -2 -3 -4 -4R
1.26 1.33 0.98 2.17 2.15 1.78 1.76 1.34
-5 -5R -6 a
0.5 0.7 0.5 0.5 0.5 0.5 0.5 0.5
7.5 9.2 12.0 2.6 2.6 4.0 4.0 7.0
0.0120 0.0110 0.0086 0.0300 0.0277 0.0221 0.0207 0.0149
1.34 1.21 0.86 2.38 2.47 2.03 1.99 1.64
See Bazan (1977).
Table 111. Total Gas Flow Rate
GA,kg/s
T.R., k d k g
0.007 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.050 0.070 0.100 0.200
193 135 91 70 58 50 45 41 36 30 27 23
1.35 1.35 1.37 1.40 1.45 1.51 1.57 1.64 1.79 2.13 2.66 4.50
and k, ul,and u3 are found by simultaneous solution of eq 5, 6, and 7. Also us3
=
k ~ 3
(21)
and
In either case el cannot be less than E? or greater than unity. Dilute Phase Voidage. An empirical relationship was derived to estimate the dilute phase voidage, e3. The ratio of dispersed density to initial settled density was presumed to be dependent upon the particle Reynolds number at the nozzle and the on-, off-, and fluidizing times. The dependence on periodicity is presumably needed to account for the development and degeneration of the jet and dilute phase during the pulse cycle. For toN 2 t M
(2) (z)'u (T) = 0.0376
(18)
As might be expected from jet similarity criteria, voidage is not strongly dependent on nozzle velocity. The voidage does vary strongly with the shape of the pulse waveform around a median of about 0.85. Given SI,S2,P3, P4,cp, GA, system geometry, particle properties, and the pulse on- and off-times, the equations may be solved by the procedure outlined in Figure 7. Note P1is assumed equal to P2, u2 is calculated by u2
=
GA P2S2
(
ON + OFF toN
)
Model Performance. The model predicted the test data with an average error of 0.67 kg/s, which was about the preproducibility of the data at the highest flow rates. Figure 8 illustrates. Worst performance occurs for short off-time runs, which are characterized by incomplete defluidization between pulses, and for runs with toN = 0.4 where the highest flow rates occur. Apparently t M is slightly greater than 0.4 rather than slightly lower as from eq 14. To further test the model, we applied it to the conditions of testa conducted by Foster Wheeler Energy Corporation (FW) on the CAFB prototype transport slot selected for the demonstration plant, as detailed by Bazan (1977). Table I1 compares FW's test resulta with the predictions of the model for a single leg. The experimental results and model predictions support one another well. The surmised relative freedom of the FW testa from downcomer fluidization or voidage variation allow these data points to fall into the range of conditions that is most easily and accurately modeled. The FW testa were conducted at high (1.9 to 2.3 m/s) gas velocities at which the beds must have been highly expanded and therefore causing low pressure gradients across the legs and hence high t M (eq 14). In our own tests, the bed was never highly expanded, and therefore the lack of dependence on fluidizing velocity. Effects of Operating Parameters. In the experimental work we were often unable to change only one variable at a time. The model permits exploration of the effects of individual variables. The model was applied to a particular design, and effects of variables are shown in
24
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
@
Eq 12 or 13
i
Measured Solids Flow k g l s
Figure 8. Comparison of experimental data and model predictions. Table VI. Pressure Gradient AP", kPa
T.R., kg/kg
0 2 3 6 8 10 20
61 61 51 50 50 50 50
,Yes
Gs, kg/s 1.82 1.83 1.52 1.51 1.51 1.49 1.49
Table VII. Particle Size ,
4, m
v 2 < v 53
500 750 1000 1500 2000 2500
Figure 7. Transfer leg model flow sheet. Table IV. On- and Off-Times
0.1 0.2 0.3 0.4 0.5 1.0 1.5 0.3 0.3 0.3 0.3 0.3
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.0 1.5 2.0 2.5 3.0
1.39 1.61 1.51 1.36 1.26 0.98 0.81 0.78 1.51 1.63 1.72 1.73
46 54 50 45 42 33 27 26 50 54 57 58
Table V. On. and Off-Times at Constant Wp
0.1 0.2 0.3 0.4 0.5 1.0 1.5 0.3 0.3 0.3 0.3 0.3
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.0 1.5 2.0 2.5 3.0
0.0156 0.0294 0.0417 0.0526 0.0625 0.1000 0.1250 0.0577 0.0417 0.0326 0.0268 0.0227
69 54 40 30 24 12 8 18 40 51 62 73
1.08 1.60 1.67 1.57 1.50 1.20 1.00 1.03 1.67 1.67 1.67 1.66
Tables 111 through XI. The following are base conditions, constant except as noted in the tables. Leg geometry: LH = 0.503 m,L, = 0.564 m, Hh = 0.089 m; W = 0.152 m; CY
T.R., k g / k 54 47 48 50 52 53
Gs, kg/s 1.62 1.4 2 1.45 1.51 1.55 1.58
Table VIII. Particle Density k/m3 1500 1800 2000 2500 3000
Pp,
T.R., kg/kg 43 50 55 80 94
Gs, kg/s 1.28 1.51 1.64 2.40 2.82
Table IX. Horizontal Section Height Hh, m 0.1530 0.1274 0.1020 0.0892 0.0764
T.R., k/kg 60 58 54 52 50
Gs/S,,
kgls m 2 78 89 105 116 130
GS
9
kg/s 1.81 1.73 1.63 1.57 1.51
Table X. Vertical Height at Constant (P,- P,)/L, 0.800 0.700 0.600 0.564 0.500 0.400
63 63 53 52 52 52
1.88 1.88 1.58 1.57 1.55 1.55
= 0. Pulse gas: toN = 0.3 s; t o F F = 1.5 s; GA = 0.03 kg/s; Particle size, 1500 p m ; packed bed voidage, 0.45; particle density, 1800 kg/m3; gas, air at 500 K; pressure at leg
Ind. Eng. Chem. Process Des. Dev., Vol. 20,No. 1, 1981 25
Table XI. Horizontal Length
LH,m
T.R., k / k g
G s , kg/s
0.100 0.200
36 43 48
1.29
0.400
0.503 0.600 0.800
52 57 66
1.08 1.43
1.57 1.70 1.98
discharge, 128 kPa abs; imposed P on leg (P3- P4),4 kPa. Table I11 shows that increasing the transport gas rate while holding all other parameters constant will result in increased solids transfer but lower efficiency (T.R.). Table IV shows that as the on-time is increased beyond t M both transfer rate and efficiency fall. Both flow rate and efficiency increase regularly with off-time because more time is allowed for repacking between pulses. Table V lists the expected flows at the same on- and off-times as Table IV but at constant transport gas flow rate during the pulse. The trends are similar to those in Table IV with efficiencies varying more and solids flow rates less. The effect of the imposed pressure difference is illustrated in Table VI. At no pressure gradient, P2- P4 = P2- P3,and no tendency to fluidize occurs. At P3 - P4= 2 kPa fluidization is now possible but takes more time than the pulse (at this ontime). A sharp drop in both flow rate and efficiency occurs with a further increase in P .Thus the imposed pressure drop simply determines in which of two regimes the system will operate, fluidizing or nonfluidizing. Within either category operation is nearly independent of the pressure drop. System pressure level variation (from 100 to 180 kPa) and temperature (400-1500 K) have little effect on transfer performance. As particle size increases, upward gas loss will increase, according to the Ergun equation. In addition, the horizontal pressure loss will increase (according to the Wen and Simons (1959) correlation used in the model, (P2- P3) 0: ~i,0.~~), A look at the momentum balance shows the factors have opposite effects on solids flow rate. Table VI1 shows that the transfer rate and efficiency do have shallow minima as particle size increases. On the other hand, one can see that particle density (Table VIII) is of paramount importance. Higher particle density results in a higher horizontal pressure drop (eq 8 to 10) and, hence, higher PI and Pz. One would also expect the particles to be less completely accelerated so Ku, is lower. A look at the momentum balance (eq 7) shows that
all of which factors are increased. In Table IX the horizontal channel height is varied from ita normal 0.089 m, with all other leg dimensions remaining constant. This variation essentially allows variation in the stagnant solids inventory in the horizontal line. Solid flows are given both on an absolute and per unit area basis for comparison. Shallower channels are both less efficient (T.R. column) and of lower capacity. As expected, they permit more flow on a per unit area basis simply because proportionately less area is devoted to stagnant solids. At some point one might wish to operate the transport leg between deeper fluid beds. The vertical height could thus be greater, but the imposed pressure drop would be correspondingly larger, APIL remaining about the same. Table X shows that a deeper packed vertical bed will require more time to fluidize and, in this case, the transition from fluidizing to nonfluidizing flow occurs, with a
corresponding increase in solids flows and efficiency. Horizontal length is important because it affects the pressure at the transport slot elbow as shown in Table XI. The model suggests that an increase in the angle of tilt of the downcomer from the vertical will yield slightly improved performance at low angles. Part of the improvement will be due to the additional solids horizontal momentum existing when the jet entrainment area is entered. The main effect, however, is in allowing the use of a longer downcomer at equivalent vertical spacing of leg hopper and discharge.
Summary and Conclusions The pulsed transport system was found to be capable of high capacity operation at reasonable air requirements. Using a recessed pulse gas nozzle system similar to that being used in the CAFB demonstration plant, solids flows of 80 to 110 kg/s m2were obtained. Transfer ratios (mass of solids to mass of air) in excess of 100 were frequently obtained. The transport technique was shown to involve the transient behavior of fluid beds. Each pulse of transport gas imposes a pressure drop upon the vertical section of a transport leg that is in excess of that needed to fluidize the leg. The nonequilibrium state existing during the short time required to fluidize the leg is a vertical seal during which transfer of solids can occur. This time is about 0.3 to 0.4 s. Longer on-times only waste transport gas. If a pulse is long enough to complete fluidization, a minimum time is required to complete defluidization and repacking of solids prior to the next pulse. This time is about 1.5 s. Proportionately less time is needed at shorter on-times. Excessive off-time may result in overpacking and resistance to new pulse jets. Adequate solids flow is not possible under continuous (i.e., not pulsed) aeration conditions unless there is a low pressure drop imposed across the leg by virtue of highly expanded beds or the receiving bed being at a lower pressure than the feeding bed. In the latter case simultaneous transport in the opposite direction would be extremely difficult. A model was developed that allows the projection of transport system performance under different conditions and sets of variables. The model is essentially a momentum balance with appropriate assumptions. The following points are model predicted trends. Other conditions being constant, a higher gas input rate will yield increased solids flow and reduced transport efficiency. The pressure gradient across a leg is important in that it determines whether a leg will fluidize or not during a pulse. Within either of these regimes the imposed pressure gradient does not seem to have a major effect. Both solids flow rate and transport ratio (mass of solids to gas) are sensitive to particle density. Heavier particles are more rapidly moved than lighter ones. The model predicts that increasing any of several leg dimensions (vertical height, horizontal length, horizontal depth) will improve capacity and efficiency. Acknowledgment This work was funded by the U.S. Environmental Protection Agency. We are grateful to our EPA project officer, Mr. S. L. Rakes, for his support and guidance. Mr. P. P. Turner and Mr. R. P. Hangebrauck, of the Industrial Environmental Research Laboratory, EPA, have made continuing contributions to the support of this program. Important contributions to the design, construction, and
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
26
operation of t h e test facility were made by W. J. Havener and E. J. Vidt of Westinghouse.
terference, m = distance from nozzle plane to plane of horizontal ceiling lip, m xn = center-to-center nozzle separation, m
xh
Nomenclature AB = fluidized bed cross-sectional area, m2 do = nozzle diameter, m d = average particle dimension, m $t = four times mean hydraulic radius, m g = gravitational acceleration, m/sz g, = conversion constant, 1 kg m/(N s2) GA = overall average pulse gas input rate, kg/s Gs = solids flow rate, kg/s Hh = horizontal section height, m
k
x1 = distance from nozzle plane to plane of mutual jet in-
E v83/v3
LH = length of horizontal leg section, m Ls = length of vertical leg section, m Lv = vertical component of Ls, m N = number of nozzles per leg Pl = pressure at leg bend, N/m2 Pz = transport gas pressure issuing from nozzles, N/m2 P3 = pressure at leg discharge, N m2 P4 = pressure a t to of leg, N / m AP PI - P4,N/mF APo = P3- P4,N/m2 APB pressure drop across upper portion of fluidized bed, N/m2 S1 = cross-sectional area of leg, m2 Sz = inside area of N nozzles, m2 S3 = area of dilute phase horizontal flow, m2 t M = fluidizing time in response to imposed hp, s t o F F = pulse off-time, s toN = pulse on-time, s ts = time during which solids may flow: minimum of t M , toN,
4
S
T.R. = transport ratio = mass of solids moved per mass of transport gas required U f = fluidizing velocity (superficial), m/s U, = interstitial gas velocity relative to solids with no transport gas injection, m/s Us = superficial horizontal solids velocity, m/s v1 = downward velocity of gas in leg vertical section, m/s v 2 = pulse gas nozzle exit velocity, m/s v3 = velocity of gas exiting leg in dilute phase, m / s U R I uS1 - V I , m/s uRH = interstiaitl gas velocity in stagnant solid area of horizontal leg section, m/s vsl = downward solids velocity in leg vertical discharge, m/s vS3= velocity of solids in dilute phase at leg discharge, m/s W = leg width, m Wp = transport air rate during pulse, kg/s
Greek Letters a = angle of leg downcomer from vertical, deg
@ = plane jet half-angle, deg e1 = vertical section voidage e3 = dilute phase discharge voidage tp = packed bed voidage 6 = circular jet half-angle, deg p = gas viscosity, kg/m s p1 = gas density at transfer leg bend, kg/m3 pz = gas density issuing from nozzles, kg/m3 p3 = gas density a t transfer leg discharge, kg/m3 PDS = su erficial bulk density of horizontal section material, kg/m PFB = fluid-bed density, kg/m3 pg = gas density, kg/m3 pp = particle density, kg/m3
B
Literature Cited Bachovchln, D. M.; Mulik, P. R.; Newby. R. A.; Keaims, D. L. Solids Transport between AdJacent Fluidhed Beds, Experimental Support for CAFB Demonstration Plant. Report to EPA, Westinghouse Research and Development Center, Plttsburgh, PA, Aug 1978, EPA 80017-74-021. Bazan, J. A.; Chemically Active Fluid Bed (CAFB) Process Solids-Transport Studies. Report to EPA, Foster Wheeler Energy Corporation, Llvingston, NJ, OCt 1977, EPA-60017-77-114, Craig, J. W. T.; Johnes, G. L.; Moss, G.; Taybr, J. H. Study of Chemically Active Fluid Bed Gasifier for Reduction of Sulfur Oxide Emission. Report to EPA, Esso Research Centre, Abingdon, UK, APCO Contract CPA 7048, Feb 1971. Keairns, D. L.; Archer, D. H.; Newby, R. A.; O’Nelll, E. P.; Vldt, E. J. Evaluation of the FluMued-Bed Combustion Process, Vol. IV, Fluidized-Bed Oil GasMcationlDesulfurizatlon. Report to EPA, Westinghouse Research Lab oratories, Pittsburgh, PA, Dec 1973, EPA-650/2-73-048d, NTIS PB 233101. Keairns, D. L.; Newby, R. A.; Vidt, E. J.; O’Nelll, E. P.; Peterson, C. H.; Sun, C. C.; Buscagli, C. D.; Archer, D. H. Fluidized Bed Combustloo Process Evaluatlon-Fiesklual 011GasificationlDesulfurizatkm Demonstration at Atmospheric Pressure. Report to EPA, Westinghouse Research Laboratorles, Plttsburgh, PA, Mar 1975, EPA-65012-75-027a&b, NTIS PB 241 834 241 835. Merry, J. M. D. Trans. Inst. Chem. Eng. 1971, 49, 189-195. Newby, R. A.; Katta. S.; Keairns, D. L. Calcium-Based Sorbent Regeneration for Fluidized-Bed Combustion: Engineering Evaluation. Report to EPA, Westlnghouse Research Laboratories, Pittsburgh, PA, Mar 1978, EPA60017-7a039. Rajaratnam, N. “Turbulent Jets”, Eisevler: New York, 1976; Chapters 1 and 2. Rakes, S. L. Energ. Spectrum 1978, 2(5),:130-133. Wen, C. Y.; H. P. Simons AIChE J . 1959, 5(2), 263-267. June 1959.
Received for review August 8, 1979 Accepted August 6, 1980
