- Email: [email protected]
Pneumatic transport in a 10-cm pipe horizontal loop
Powder
Technology,
49 (1987)
207
207
- 216
Pneumatic Transport in a lo-cm Pipe Horizontal Loop WEN-CHING
Research
YANG
and Development
and T. C. ANESTIS,
KR W Energy Systems (Received
February
Center,
R. E. GIZZIE,
Westinghouse
Electric
Pittsburgh,
PA (U.S.A.)
G. B. HALDIPUR
Inc., Madison, PA (U.S.A.) 21,1986)
SUMMARY
Pneumatic transport studies were performed in a 1 O-cm pipe diameter horizontal loop about 80 m in length, at gas velocities ranging from 12 to 31 m/s, and solid/gas mass ratios up to 8, using three different elbows and a dead-end tee. Preliminary data on line pressure losses using crushed acrylic particles are reported.
INTRODUCTION
Pneumatic transport technology, otherwise known as pneumatic conveying, is the art of transporting particulate solid materials through a pipeline by a gas medium. Transport phenomena occurring in the pipeline are very complex depending on the gas velocity, characteristics of the solid particles (size, distribution, density and shape), relative weight ratio of gas and solids, pipeline size and configuration, solids feeding device, and transport direction (vertical, horizontal, or inclined). Though pneumatic transport technology has been practised for many years in various industries, principally for loading and unloading dry bulk materials, the design of a pneumatic conveying system remains empirical. It is safe to say that any dry particulate materials of reasonable particle sizes can be transported pneumatically if the gas velocity is sufficiently high. However, it is important to understand that the optimal design can only be achieved through understanding the phenomena to guarantee not only the reliability of the operation but also to minimize the gas usage, the attrition of the 0032-5910/87/!$3.50
Corporation,
solids, the erosion of the pipes, and the power consumption. Pneumatic transport technology is particularly feasible and expedient in feeding solids into, and removing solids from, a fluidized bed. In fact, most of the fluidized bed coal combustors and coal gasifiers employ the technology. Chemical reactions can also be performed in pneumatic transport reactors [ 1,2]. Actually, the so-called entrained-bed reactors are essentially vertical pneumatic transport reactors with a relatively dilute solid loading. The much-publicized ‘fast fluidized bed’ is not really a fluidized bed where the solid particles remain predominantly in the bed. The particles in a ‘fast fluidized bed’ are transported as in a pneumatic transport line [3]. It can be more aptly classified as a vertical dense-phase pneumatic transport reactor without slugging [ 41. In fact, similar phenomena observed in a ‘fast fluidized bed’ have been observed in vertical pneumatic transport lines with fine particles [ 51. There is no lack of studies on pneumatic transport technology in the literature. However, most of the studies are restricted to pipes less than 7.5 cm in diameter using particles of relatively narrow distribution and emphasize primarily the pressure drop along a pipeline usually less than 15 m in length [ 61. Because of different phenomena occurring in the line which are not well understood, the data obtained are often inconsistent. Thus, the selection of a set of design equations for scale-up is difficult. Operational data of actual industrial plants with large, long transport lines and with particles of wide size distribution are generally not available. In addition, most of the studies are carried out under ambient temperature and atmospheric pres@ Elsevier
Sequoia/Printed
in The Netherlands
208
sure. The effect of temperature and pressure on the transport line performance is not well known. Critical phenomena such as saltation in horizontal lines, choking in vertical lines, acceleration length and acceleration pressure drop, and pressure drop around the bends require further studies.
EXPERIMENTAL
APPARATUS AND
EXPERIMENTAL
CONDITIONS
069m
064m
0 89m
1 63m
@ Rotarv Feeders
The representative particle size distribution is presented in Fig. 1. The particle shape was determined to be 0.9 employing a packed bed and correlating the pressure drop with the Ergun equation. The mean particle size was determined to be 1100 pm at 50 wt.% using Fig. 1. These two parameters were used in the subsequent analysis. Experiments were conducted at a horizontal pneumatic transport loop approximately 80 m in length. A schematic of the transport loop with all pressure taps is shown in Fig. 2. The transport line was constructed of lo-cm (4-in) Schedule 40 carbon steel pipe with six sections of transparent acrylic pipe located at various points along the loop to allow visual observation of flow patterns. Altogether 23 pressure taps were scattered along the length of the transport loop to measure the differential pressure drops along the line. All pressure taps led into a common manifold. Selected pressure taps at the common manifold were connected to the differential pressure transmitter during operation and the measured differential pressure was recorded with a high-speed strip-chart recorder. The elbow between the 104 \_
E I d %
dp = 1100 vm
103
; k
i,,,
102 001
,,,.:;,,
,,
5
50
Percentage of Pam&s
90 Fmer Than, 56
Fig. 1. Particle size distribution - FR-002.
99
99 99
b----I
Transparent SectIons
All Unmarked Taps Are 2 29m Apart
1 14m
Fig. 2. Flow schematic of pneumatic transport loop - FR-002.
pressure taps P20 and P21 (see Fig. 2 for details) was designed to allow easy modification to accommodate different elbow configurations. Four elbow configurations including a 122-cm (4%in), a 91-cm (36-in), a 61cm (24-in) radius elbow, and a dead-end tee were tested. The transport air supply and the solids feeders were essentially the same equipment used for operation of a large cold-flow fluidized bed. Air flow rate was measured with an orifice plate, and the solids feed rate was measured by load cells. With the two solids rotary feeders operating at full capacity, a solids feeding rate up to 4550 kg/h could be achieved. Both the gas flow rate, solids feeding rate, and other system operating parameters were continuously logged in a minicomputer, a Digital MINC II System. Three nominal line velocities of 15.2, 22.9, and 30.5 m/s were employed at three nominal solid feed rates of 1364, 2727, and 4091 kg/h. The baseline data where only the gas was flowing were also obtained for comparison. The experimental conditions are tabulated in the Table.
209
TABLE Experimental conditions for 61cm dead-end tee Set point No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
61-cm (24-in) elbow
Deadend tee
Transport air (m3/min)a
Transport air (m3/min)a
-
6.0 7.1 7.9 7.4 8.5 9.2
Solids feed rate (kg/b)
6.1 7.1 7.7 7.6 8.4 9.3 9.8 12.0 12.8 13.8 15.2 16.8 18.2 18.6 20.9
0
1322 2832 0 1405 2839 -
11.6 12.6 13.4 -
0 1279 2811 -
14.8 17.9
0 3340
(2)
(24-in) elbow and
Solids feed rate (kg/h) 0
1495 2795 0 1334 2733 3547 0 1341 2532 4144 0 1422 2788 3780
aEvaluated at 101 kPa and 20 “C.
Altogether 57 out of 72 planned set points were completed. The 15 planned set points which were not completed were mostly due to extensive erosion and degradation of the elbow and to problems experienced with the solid rotary feeders. Experimental results and their comparison with available correlations are detailed in the following sections.
Rate of acceleration for the particles in section dL depends on the net force exerted on the particles, as shown in eqn. (3) for horizontal conveying in an acceleration region.
dull _ - dF,
dJG--
dt
- dF,
Beyond the acceleration region, where the solid particles travel essentially at a constant velocity, eqn. (3) becomes dF, = dFf
(4)
The total drag force on dN particles in dL is the sum of the drag force on each individual particle as shown in the following: 3 4.7 Pf(Uf - w2 dF, = -4 Co&(PP -
Pi&l
(5)
cw
where ee4*’ is correcting for the drag coefficient in a relatively dense fluid-solids mixture [ 81. The solid frictional loss is defined following the familiar Fanning equation with a particle friction coefficient fp. dFf=
f”u”zdM,
(6)
W
Substituting eqns. (5) and (6) into eqn. (4), we have (7)
CORRELATIONS PARTICLE
FOR PRESSURE
ACCELERATION
DROP AND
LENGTH
The theoretical analysis for pressure drop and particle acceleration length employed here follows essentially the unified theory for dilute-phase pneumatic transport developed by Yang [7]. The approach starts with the material and force balances in a differential section of pipe length dL. W, is the solid flow rate in kg/s, and dM, is the effective weight of solid particles in the pipe length dL. The total number of solid particles in dL is (assuming spherical particles) dN=
cm (PP- PW,~/~
Voidage e in section dL is given by
For particle shapes other than spherical, correction factors can be applied following Pettyjohn and Christiansen [ 91. To solve for solid particle velocity from eqn. (7), a knowledge of solid friction factor fp is necessary. Yang [lo] proposed an empirical equation for the horizontal pneumatic conveying as follows: 1-e
fp = 0.117 -
e3
(Re)t 1(I-e)(Re),
Uf
-‘*r’
fl -1
(8) Since the variables U, and fp are interrelated, a trial and error solution is required to solve eqns. (2), (7), and (8).
210
To estimate the particle acceleration length, substitute eqns. (4) and (5) into eqn. (3) and note that dL = U,dt. This yields UP2
AL=J
UPI
UPdUP
3 4 cDSe-
4.7 Pf(Uf -
UPj2
(Pp-PfWP
fPUP2 -
20
(9) The lower limit of integration Up, is derived from eqn. (2) with an assumed voidage of 0.45. The upper limit Up2 is the equilibrium particle velocity at steady state and can be calculated from trial and error solution among eqns. (2), (7), and (8), as discussed earlier. Once the acceleration length is known, the acceleration pressure drop can be calculated from the following equation : AP,=
’ 2f,PfUf2 dl + I fpPp(l - @Up2 dl s D 20 0 0 s
+ [PpU
-
wp21at
I
(10)
If the pipe is short enough such that the particles are still being accelerated, AL in eqn. (9) is the pipe length. If the pipe length is larger than the particle acceleration length, the acceleration length can be calculated from eqn. (9) in conjunction with eqns. (7) and (8). Total pressure drop in the conveying lines is usually divided into the following individual contributions: AP,=ap,+APs+AP,
(12)
2fsPpU
-
Wp2L
(14)
D
Here the solid friction factor fp defined in eqn. (8) is used throughout. By definition, fp is equal to 4f,. Beyond the particle acceleration region, the total pressure drop in a horizontal conveying line becomes 2f,PfUf2L D
A.&=.
+ fpP,U
-
dUp2L
20
(15)
The only unknowns in eqn. (15) are usually fp, and E. They can be obtained by simultaneously solving eqns. (2), (7), and (8). Up,
EXPERIMENTAL
RESULTS
The measured differential pressure between different pressure taps along the transport loop can be plotted as cumulative pressure drop profiles. Typical examples are shown in Figs. 3 to 10 for the cumulative pressure drop profiles along the loop starting from the pressure tap P5 and extending through pressure tap P23 for the 61-cm (24-in) elbow and the dead-end tee. The baseline data where only the gas flow was on were also obtained for comparison. From the cumulative pressure drop profiles, the acceleration pressure drop, 75 70
r 12 2 mlsec A Set Point 1 lBase Case1
60
(11)
Calculation of the acceleration pressure losses AF, is presented in eqn. (10). For horizontal conveying, the static head term is Ms = 0. The frictional term APF is often separated into two terms due separately to gas alone and to the effect of solid particles. ap, = A&g + A&s
es =
55
L
.
Set Pant
2
0 SetPoint 3
50 0, I
45
g d 0e
40 35
s D 30 $
25
Friction due to conveying fluid alone is defined following the Fanning equation as f&g
=
2fgPfUf2L D
4
(13)
Friction due to solid particles A.PFs is defined similarly but is based on solid particle velocity and the dispersed solid density.
-I 0 2 4 6 6
10121416182022242626303234363640 Line Length From Tap P5, meters
Fig. 3. Cumulative pressure drop profiles (24-in) elbow.
61-cm
211
30 5 misec JO
JO 15.2 mlsec 65
d set Pant 4 (Base Case)
65
60
.
60
Set Pore
o Set Pant
55 k-
5
.
Set Pant
.
Set Potnt 126
12A
0
Set Pant
1 340 cm H2Oim 13
.’
55
6
50 0, I L Ii 0 0
e
0
?! Ci z h
35
0 520 cm HpOim
? a i? &
30 0 462 cm HpOim 25
45 40 35 30 25 20 15
1 0
2
4
6
5 0 0
810121416162022242628303234363840
2
4
6
6
10121416162022242626303234363640 Lone Length From Tap P5. meters
Lane Length From Tap P5, meters
Fig. 4. Cumulative (24~in) elbow.
pressure
drop
profiles
-
61cm
Fig. 6. Cumulative (24-in) elbow.
pressure
drop
profiles
-
61-cm
75 JO
12 2 mlsec
65
0 Set PoMlt 1 (Base Case)
60
.
55
0 Set Point 3
Set Powlt 2
50 0, I
0 907 cm H20im
i d b S
35
I z
30
0 781
cm HpOim
&
0 467 cm H2Oim
40
% E
35
: 2
30
i
25
45
25 20 15 10 5 0
0
2
4
6
6
10121416162022242628303234363840
0
2
4
6
8
Fig. 5. Cumulative (24-in) elbow.
pressure
drop
profiles
10121416162022242626303234363840 Line Length From Tap P5. meters
Lme Length From Tap P5, meters
-
61-cm
the particle acceleration length, the steady state pressure drop per linear pipe length, and the elbow pressure drop can be obtained as shown in Fig. 11. In the present experiments, however, only the steady state pressure drop per linear pipe length will be extracted for comparison with the theoretical model. The pressure drop
Fig. 7. Cumulative tee.
pressure
drop profiles
-
dead-end
around the elbow obtained following that illustrated in Fig. 11 could not be determined accurately, unfortunately, because the distance required to reaccelerate the particles beyond the elbow was substantially greater than that originally envisioned. Except for the dead-end tee, the pressure drop around the elbow occurred primarily beyond the
212 75 ,
145
I
F
140 70
15 2 misec
65 60
I
0 Set Pant 4 (Base
130
.
Set Pant 5
125
0 Set Pant 6
120 115
A Set Point 14
110
.
a Set Pant 7
55
0,
135
0 604 cm H20im
13
Set Pant
Set Pant
100
0 473 cm H2O/m
40 35
$
30
.
15
0 559 cm H2Oim-,
25 20
1 776 cm I
95 0
i ?
h
12
.
105
50 45
k &
0 Set Pant
90
I”
85
5 &
80 75
g
70
C
65
I 2
60
&
55
1 273 cm H20lm
50 15
45 40
10
35 30
5
25
0 0
2
4
6
8 1012
1416
1820222426
28303234363840
Line Length From Tap P5. meters
Fig. 8. Cumulative pressure drop profiles - dead-end tee.
20 15 10 5 0 0
4
8
12 16 20
24
28
32
36 40
Lone Length From Tap P5. meters
Fig. 10. Cumulative pressure drop profiles - dead-end
75 15 Pmlsec
70
0 Set Point
8 (Base Case1
.
3
Set Potnt
60 A Set Point 10 .
Set Pant
036
11
cm H20im
._
7
F ; 35 $ Ii
30 25 20 15
’ Length
10
L,ne Length, L
5
I I
0 0
2
4
6
I I I
I
I I I I I I I 1 I I I_
Fig. 11. Extraction drop profiles.
of data from cumulative pressure
8 10121416182022242628303234363840 Line Length From Tap P5. meters
Fig. 9. Cumulative pressure drop profiles - dead-end tee.
elbow rather than at the elbow as commonly expected. The elbow pressure loss also depends strongly on the solid loading and apparently is expended for redispersing the solid particles, which are gathered into dense ribbons, beyond the elbow. The physical restraint of the existing solids feeding devices precluded an ideal loop arrangement such that the acceleration pres-
sure drop could not be obtained as shown in Fig. 11. The particle acceleration length is more difficult to determine accurately because the equilibrium pressure drop profile is approached asymptotically and thus, theoretically, the particle acceleration length should be infinite. In actual practice, however, the experimental error and the instrument sensitivity will prevent the detection of this small asymptotical change of pressure drop. Determination of the acceleration length can thus be obtained simply from that
213
0 0
05
10
15
20
25
30
Calculated Line Pressure Drop, cm H2Oim
Fig. 12. Comparison steady state pressure
of experimental and predicted drop per linear line length.
shown in Fig. 11. Since the pressure tap P5 is located 0.91 m from the tee, 0.91 m should be added to the particle acceleration lengths determined from Figs. 3 to 10 following the procedure outlined in Fig. 11. Particle acceleration length obtained here is thus not the true acceleration length commonly referred to in the pneumatic transport as derived in eqn. (9). It is actually a length required for recovery after a dead-end tee. The particle acceleration length calculated from eqn. (9) gave a value ranging from 12 to 17 m. This is in reasonable agreement with that found experimentally, despite all the uncertainties involved. Pressure drop per linear length at steady state under different operating conditions can be obtained from the slope of the straight line portion of the cumulative pressure drop profiles shown in Figs. 3 to 10, as illustrated in Fig. 11. The comparison between the experimental and the calculated steady state pressure drop per linear pipe length is summarized in Fig. 12 for elbows of 122cm (4% in), 91cm (36-in), and 61-cm (24-in) radius and for the dead-end tee. It is seen that the theoretical correlation presented earlier predicts reasonably well, within f 30%.
EROSION AROUND
AND
SOLIDS
FLOW
velocities. These included 122~cm (48~in), 91cm (36-in), and 61-cm (24-in) radius clear PVC elbows as well as a steel dead-end tee. The transport line was constructed of lo-cm (4-in) Schedule 40 carbon steel pipe and lo-cm (4-in) diameter clear acrylic pipe with the replaceable elbows located at the end of a straight section approximately 33.5 m (110 ft) long as shown in Fig. 2. All set points using the steel tee were completed with no problems; however, all three PVC elbows were destroyed due to wall erosion when transport velocities of 30.5 m/s (100 ft/s) were used with feed rates of 1364 kg/h (3000 lb/h) or higher. The failures were all approximately the same in appearance and occurred at the point where the stream of acrylic particles first hit the elbows. This erosion, once it started, occurred in the short period of approximately 5 min and was due to the PVC pipe melting. This was fast enough that an observer could actually see the hole being formed and pieces of plastic breaking off inside the pipe. Figures 13 and 14 show
PATTERN
THE ELBOW
Four elbow configurations were used during experiments to investigate erosion and solids flow patterns at various feed rates and
Fig. 13. elbow.
Pipe wall erosion
-
61-cm
(24-in)
radius
214
4 in. Plastic
Elbow
Worn Area and Bubble Approximately 3 in Long by 1 in Wide
View
A
I
4 in.
I Flow = Material
and Air Flow Through
the Line View “A” Cross-Section
View “A” Front
Fig. 14. Pipe wall erosion
-
61cm
(24-in)
radius elbow.
examples of this erosion. To further illustrate the problem, photographs of the transport elbows during test operations are shown in Figs. 15 through 17. From these it can be seen that, at a feed rate of 2727 kg/h (6000 lb/h) and a velocity of 10.7 m/s (35 ft/s), the material is transported through the line in a large ‘bundle’. As the velocity is increased, the band narrows and is not only moving faster but is concentrated on a smaller area of the piping elbow. This resulted in more heat due to friction and the pipe wall eroded rapidly. The results confirmed the general recommendation that dead-end tees instead of elbows be employed in pneumatic transport lines to prevent erosion failure.
CONCLUSIONS
Fig. 15. Acrylic flow -91-cm (36-in) Gas velocity 10 - 12 m/s; solids 2700
radius elbow. kg/h.
Experiments were conducted at a horizontal pneumatic transport loop constructed of lo-cm (4-in) Schedule 40 carbon steel pipe with transparent PVC pipe sections. The total loop length is approximately 80 m. Four elbow configurations were also tested.
215
(2) The acceleration lengths can be estimated by the existing correlation with reasonable confidence. (3) Except for the dead-end tee, the pressure drop around the elbow occurs primarily beyond the elbow rather than at the elbow as commonly expected. The elbow pressure loss is apparently expended for redispersing the solid particles, which are gathered into dense ribbons, beyond the elbow. (4) Erosion mechanism on elbows during pneumatic transport was elucidated by observing through transparent PVC elbows of different radii. The results confirm the general recommendation that the dead-end tees, instead of elbows, be used in pneumatic transport lines to prevent erosion failure.
LIST OF SYMBOLS cDS
dFc_i Fig. 16. Acrylic flow - 91-cm (364n) radius elbow. Gas velocity 15 - 23 m/s; solids 2700 kg/h.
dFf
dFs dL
dN d,
D
ff3
t (W,
drag coefficient for a single particle drag force on the particles in the pipe section dL solid frictional force of the particle in the pipe section dL net gravitational force on particles in the pipe section dL differential length of a conveying pipe total weight of solid particles contained in the pipe section dL total solid particles contained in the pipe section dL average particle diameter inside diameter of a conveying line gas friction factor as defined in eqn. (13) solid friction factor, fp = 4f, solid friction factor as defined in eqn. (14) gravitational acceleration length of pipe Reynolds number defined as dp( Uf WPflP
VW, Fig. 17. Acrylic flow - 91-cm (36-in) radius elbow. Gas velocity 31 m/s; solids 2700 kg/h.
The preliminary data indicate that (1) The experimental pressure drops can be correlated to within k30% by the existing correlation.
Reynolds number defined as d,U,p,l~ interstitial gas velocity actual particle velocity terminal velocity of a single particle solid flow rate particle acceleration length acceleration pressure drop total frictional pressure drop
216 A&
A&s MS
apT
E
Pf PP
frictional pressure drop due to gas frictional pressure drop due to solid particles pressure drop due to static head total pressure drop in a line voidage gas density solid particle density
REFERENCES
1 L. A. B&et, An Engineering Assessment of Entrainment Gasification, Morgantown Energy
Research Center, Morgantown, WV, 1978; NTISMERC/R1/78/2. 2 L. S. Fan and S. J. Hwang, Chem. Eng. Sci., 36 (1981) 1736. ‘2 J. Yerushalmi and N. T. Cankurt, Powder Technol., 24 (1979) 187. W. C. Yang, AIChE J., 30 (1984) 1025. Y. Yousfi and G. Gau, Chem. Eng. Sci., 29 (1974) 1939. Institute of Gas Technology, Preparation of a Coal Conversion Systems Technical Data Book, 1977, NTIS-FE-2286-16. 7 W. C. Yang, J. Powder Bulk Solids Tech., I (1977) 89. 8 W. C. Yang, I&EC Fundamentals, 12 (1973) 349. 9 E. S. Pettyjohn and E. B. Christiansen, Chem. Eng. Prog., 44 (1948) 157. 10 W. C. Yang, AZChE J., 20 (1974) 605.
Technology,
49 (1987)
207
207
- 216
Pneumatic Transport in a lo-cm Pipe Horizontal Loop WEN-CHING
Research
YANG
and Development
and T. C. ANESTIS,
KR W Energy Systems (Received
February
Center,
R. E. GIZZIE,
Westinghouse
Electric
Pittsburgh,
PA (U.S.A.)
G. B. HALDIPUR
Inc., Madison, PA (U.S.A.) 21,1986)
SUMMARY
Pneumatic transport studies were performed in a 1 O-cm pipe diameter horizontal loop about 80 m in length, at gas velocities ranging from 12 to 31 m/s, and solid/gas mass ratios up to 8, using three different elbows and a dead-end tee. Preliminary data on line pressure losses using crushed acrylic particles are reported.
INTRODUCTION
Pneumatic transport technology, otherwise known as pneumatic conveying, is the art of transporting particulate solid materials through a pipeline by a gas medium. Transport phenomena occurring in the pipeline are very complex depending on the gas velocity, characteristics of the solid particles (size, distribution, density and shape), relative weight ratio of gas and solids, pipeline size and configuration, solids feeding device, and transport direction (vertical, horizontal, or inclined). Though pneumatic transport technology has been practised for many years in various industries, principally for loading and unloading dry bulk materials, the design of a pneumatic conveying system remains empirical. It is safe to say that any dry particulate materials of reasonable particle sizes can be transported pneumatically if the gas velocity is sufficiently high. However, it is important to understand that the optimal design can only be achieved through understanding the phenomena to guarantee not only the reliability of the operation but also to minimize the gas usage, the attrition of the 0032-5910/87/!$3.50
Corporation,
solids, the erosion of the pipes, and the power consumption. Pneumatic transport technology is particularly feasible and expedient in feeding solids into, and removing solids from, a fluidized bed. In fact, most of the fluidized bed coal combustors and coal gasifiers employ the technology. Chemical reactions can also be performed in pneumatic transport reactors [ 1,2]. Actually, the so-called entrained-bed reactors are essentially vertical pneumatic transport reactors with a relatively dilute solid loading. The much-publicized ‘fast fluidized bed’ is not really a fluidized bed where the solid particles remain predominantly in the bed. The particles in a ‘fast fluidized bed’ are transported as in a pneumatic transport line [3]. It can be more aptly classified as a vertical dense-phase pneumatic transport reactor without slugging [ 41. In fact, similar phenomena observed in a ‘fast fluidized bed’ have been observed in vertical pneumatic transport lines with fine particles [ 51. There is no lack of studies on pneumatic transport technology in the literature. However, most of the studies are restricted to pipes less than 7.5 cm in diameter using particles of relatively narrow distribution and emphasize primarily the pressure drop along a pipeline usually less than 15 m in length [ 61. Because of different phenomena occurring in the line which are not well understood, the data obtained are often inconsistent. Thus, the selection of a set of design equations for scale-up is difficult. Operational data of actual industrial plants with large, long transport lines and with particles of wide size distribution are generally not available. In addition, most of the studies are carried out under ambient temperature and atmospheric pres@ Elsevier
Sequoia/Printed
in The Netherlands
208
sure. The effect of temperature and pressure on the transport line performance is not well known. Critical phenomena such as saltation in horizontal lines, choking in vertical lines, acceleration length and acceleration pressure drop, and pressure drop around the bends require further studies.
EXPERIMENTAL
APPARATUS AND
EXPERIMENTAL
CONDITIONS
069m
064m
0 89m
1 63m
@ Rotarv Feeders
The representative particle size distribution is presented in Fig. 1. The particle shape was determined to be 0.9 employing a packed bed and correlating the pressure drop with the Ergun equation. The mean particle size was determined to be 1100 pm at 50 wt.% using Fig. 1. These two parameters were used in the subsequent analysis. Experiments were conducted at a horizontal pneumatic transport loop approximately 80 m in length. A schematic of the transport loop with all pressure taps is shown in Fig. 2. The transport line was constructed of lo-cm (4-in) Schedule 40 carbon steel pipe with six sections of transparent acrylic pipe located at various points along the loop to allow visual observation of flow patterns. Altogether 23 pressure taps were scattered along the length of the transport loop to measure the differential pressure drops along the line. All pressure taps led into a common manifold. Selected pressure taps at the common manifold were connected to the differential pressure transmitter during operation and the measured differential pressure was recorded with a high-speed strip-chart recorder. The elbow between the 104 \_
E I d %
dp = 1100 vm
103
; k
i,,,
102 001
,,,.:;,,
,,
5
50
Percentage of Pam&s
90 Fmer Than, 56
Fig. 1. Particle size distribution - FR-002.
99
99 99
b----I
Transparent SectIons
All Unmarked Taps Are 2 29m Apart
1 14m
Fig. 2. Flow schematic of pneumatic transport loop - FR-002.
pressure taps P20 and P21 (see Fig. 2 for details) was designed to allow easy modification to accommodate different elbow configurations. Four elbow configurations including a 122-cm (4%in), a 91-cm (36-in), a 61cm (24-in) radius elbow, and a dead-end tee were tested. The transport air supply and the solids feeders were essentially the same equipment used for operation of a large cold-flow fluidized bed. Air flow rate was measured with an orifice plate, and the solids feed rate was measured by load cells. With the two solids rotary feeders operating at full capacity, a solids feeding rate up to 4550 kg/h could be achieved. Both the gas flow rate, solids feeding rate, and other system operating parameters were continuously logged in a minicomputer, a Digital MINC II System. Three nominal line velocities of 15.2, 22.9, and 30.5 m/s were employed at three nominal solid feed rates of 1364, 2727, and 4091 kg/h. The baseline data where only the gas was flowing were also obtained for comparison. The experimental conditions are tabulated in the Table.
209
TABLE Experimental conditions for 61cm dead-end tee Set point No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
61-cm (24-in) elbow
Deadend tee
Transport air (m3/min)a
Transport air (m3/min)a
-
6.0 7.1 7.9 7.4 8.5 9.2
Solids feed rate (kg/b)
6.1 7.1 7.7 7.6 8.4 9.3 9.8 12.0 12.8 13.8 15.2 16.8 18.2 18.6 20.9
0
1322 2832 0 1405 2839 -
11.6 12.6 13.4 -
0 1279 2811 -
14.8 17.9
0 3340
(2)
(24-in) elbow and
Solids feed rate (kg/h) 0
1495 2795 0 1334 2733 3547 0 1341 2532 4144 0 1422 2788 3780
aEvaluated at 101 kPa and 20 “C.
Altogether 57 out of 72 planned set points were completed. The 15 planned set points which were not completed were mostly due to extensive erosion and degradation of the elbow and to problems experienced with the solid rotary feeders. Experimental results and their comparison with available correlations are detailed in the following sections.
Rate of acceleration for the particles in section dL depends on the net force exerted on the particles, as shown in eqn. (3) for horizontal conveying in an acceleration region.
dull _ - dF,
dJG--
dt
- dF,
Beyond the acceleration region, where the solid particles travel essentially at a constant velocity, eqn. (3) becomes dF, = dFf
(4)
The total drag force on dN particles in dL is the sum of the drag force on each individual particle as shown in the following: 3 4.7 Pf(Uf - w2 dF, = -4 Co&(PP -
Pi&l
(5)
cw
where ee4*’ is correcting for the drag coefficient in a relatively dense fluid-solids mixture [ 81. The solid frictional loss is defined following the familiar Fanning equation with a particle friction coefficient fp. dFf=
f”u”zdM,
(6)
W
Substituting eqns. (5) and (6) into eqn. (4), we have (7)
CORRELATIONS PARTICLE
FOR PRESSURE
ACCELERATION
DROP AND
LENGTH
The theoretical analysis for pressure drop and particle acceleration length employed here follows essentially the unified theory for dilute-phase pneumatic transport developed by Yang [7]. The approach starts with the material and force balances in a differential section of pipe length dL. W, is the solid flow rate in kg/s, and dM, is the effective weight of solid particles in the pipe length dL. The total number of solid particles in dL is (assuming spherical particles) dN=
cm (PP- PW,~/~
Voidage e in section dL is given by
For particle shapes other than spherical, correction factors can be applied following Pettyjohn and Christiansen [ 91. To solve for solid particle velocity from eqn. (7), a knowledge of solid friction factor fp is necessary. Yang [lo] proposed an empirical equation for the horizontal pneumatic conveying as follows: 1-e
fp = 0.117 -
e3
(Re)t 1(I-e)(Re),
Uf
-‘*r’
fl -1
(8) Since the variables U, and fp are interrelated, a trial and error solution is required to solve eqns. (2), (7), and (8).
210
To estimate the particle acceleration length, substitute eqns. (4) and (5) into eqn. (3) and note that dL = U,dt. This yields UP2
AL=J
UPI
UPdUP
3 4 cDSe-
4.7 Pf(Uf -
UPj2
(Pp-PfWP
fPUP2 -
20
(9) The lower limit of integration Up, is derived from eqn. (2) with an assumed voidage of 0.45. The upper limit Up2 is the equilibrium particle velocity at steady state and can be calculated from trial and error solution among eqns. (2), (7), and (8), as discussed earlier. Once the acceleration length is known, the acceleration pressure drop can be calculated from the following equation : AP,=
’ 2f,PfUf2 dl + I fpPp(l - @Up2 dl s D 20 0 0 s
+ [PpU
-
wp21at
I
(10)
If the pipe is short enough such that the particles are still being accelerated, AL in eqn. (9) is the pipe length. If the pipe length is larger than the particle acceleration length, the acceleration length can be calculated from eqn. (9) in conjunction with eqns. (7) and (8). Total pressure drop in the conveying lines is usually divided into the following individual contributions: AP,=ap,+APs+AP,
(12)
2fsPpU
-
Wp2L
(14)
D
Here the solid friction factor fp defined in eqn. (8) is used throughout. By definition, fp is equal to 4f,. Beyond the particle acceleration region, the total pressure drop in a horizontal conveying line becomes 2f,PfUf2L D
A.&=.
+ fpP,U
-
dUp2L
20
(15)
The only unknowns in eqn. (15) are usually fp, and E. They can be obtained by simultaneously solving eqns. (2), (7), and (8). Up,
EXPERIMENTAL
RESULTS
The measured differential pressure between different pressure taps along the transport loop can be plotted as cumulative pressure drop profiles. Typical examples are shown in Figs. 3 to 10 for the cumulative pressure drop profiles along the loop starting from the pressure tap P5 and extending through pressure tap P23 for the 61-cm (24-in) elbow and the dead-end tee. The baseline data where only the gas flow was on were also obtained for comparison. From the cumulative pressure drop profiles, the acceleration pressure drop, 75 70
r 12 2 mlsec A Set Point 1 lBase Case1
60
(11)
Calculation of the acceleration pressure losses AF, is presented in eqn. (10). For horizontal conveying, the static head term is Ms = 0. The frictional term APF is often separated into two terms due separately to gas alone and to the effect of solid particles. ap, = A&g + A&s
es =
55
L
.
Set Pant
2
0 SetPoint 3
50 0, I
45
g d 0e
40 35
s D 30 $
25
Friction due to conveying fluid alone is defined following the Fanning equation as f&g
=
2fgPfUf2L D
4
(13)
Friction due to solid particles A.PFs is defined similarly but is based on solid particle velocity and the dispersed solid density.
-I 0 2 4 6 6
10121416182022242626303234363640 Line Length From Tap P5, meters
Fig. 3. Cumulative pressure drop profiles (24-in) elbow.
61-cm
211
30 5 misec JO
JO 15.2 mlsec 65
d set Pant 4 (Base Case)
65
60
.
60
Set Pore
o Set Pant
55 k-
5
.
Set Pant
.
Set Potnt 126
12A
0
Set Pant
1 340 cm H2Oim 13
.’
55
6
50 0, I L Ii 0 0
e
0
?! Ci z h
35
0 520 cm HpOim
? a i? &
30 0 462 cm HpOim 25
45 40 35 30 25 20 15
1 0
2
4
6
5 0 0
810121416162022242628303234363840
2
4
6
6
10121416162022242626303234363640 Lone Length From Tap P5. meters
Lane Length From Tap P5, meters
Fig. 4. Cumulative (24~in) elbow.
pressure
drop
profiles
-
61cm
Fig. 6. Cumulative (24-in) elbow.
pressure
drop
profiles
-
61-cm
75 JO
12 2 mlsec
65
0 Set PoMlt 1 (Base Case)
60
.
55
0 Set Point 3
Set Powlt 2
50 0, I
0 907 cm H20im
i d b S
35
I z
30
0 781
cm HpOim
&
0 467 cm H2Oim
40
% E
35
: 2
30
i
25
45
25 20 15 10 5 0
0
2
4
6
6
10121416162022242628303234363840
0
2
4
6
8
Fig. 5. Cumulative (24-in) elbow.
pressure
drop
profiles
10121416162022242626303234363840 Line Length From Tap P5. meters
Lme Length From Tap P5, meters
-
61-cm
the particle acceleration length, the steady state pressure drop per linear pipe length, and the elbow pressure drop can be obtained as shown in Fig. 11. In the present experiments, however, only the steady state pressure drop per linear pipe length will be extracted for comparison with the theoretical model. The pressure drop
Fig. 7. Cumulative tee.
pressure
drop profiles
-
dead-end
around the elbow obtained following that illustrated in Fig. 11 could not be determined accurately, unfortunately, because the distance required to reaccelerate the particles beyond the elbow was substantially greater than that originally envisioned. Except for the dead-end tee, the pressure drop around the elbow occurred primarily beyond the
212 75 ,
145
I
F
140 70
15 2 misec
65 60
I
0 Set Pant 4 (Base
130
.
Set Pant 5
125
0 Set Pant 6
120 115
A Set Point 14
110
.
a Set Pant 7
55
0,
135
0 604 cm H20im
13
Set Pant
Set Pant
100
0 473 cm H2O/m
40 35
$
30
.
15
0 559 cm H2Oim-,
25 20
1 776 cm I
95 0
i ?
h
12
.
105
50 45
k &
0 Set Pant
90
I”
85
5 &
80 75
g
70
C
65
I 2
60
&
55
1 273 cm H20lm
50 15
45 40
10
35 30
5
25
0 0
2
4
6
8 1012
1416
1820222426
28303234363840
Line Length From Tap P5. meters
Fig. 8. Cumulative pressure drop profiles - dead-end tee.
20 15 10 5 0 0
4
8
12 16 20
24
28
32
36 40
Lone Length From Tap P5. meters
Fig. 10. Cumulative pressure drop profiles - dead-end
75 15 Pmlsec
70
0 Set Point
8 (Base Case1
.
3
Set Potnt
60 A Set Point 10 .
Set Pant
036
11
cm H20im
._
7
F ; 35 $ Ii
30 25 20 15
’ Length
10
L,ne Length, L
5
I I
0 0
2
4
6
I I I
I
I I I I I I I 1 I I I_
Fig. 11. Extraction drop profiles.
of data from cumulative pressure
8 10121416182022242628303234363840 Line Length From Tap P5. meters
Fig. 9. Cumulative pressure drop profiles - dead-end tee.
elbow rather than at the elbow as commonly expected. The elbow pressure loss also depends strongly on the solid loading and apparently is expended for redispersing the solid particles, which are gathered into dense ribbons, beyond the elbow. The physical restraint of the existing solids feeding devices precluded an ideal loop arrangement such that the acceleration pres-
sure drop could not be obtained as shown in Fig. 11. The particle acceleration length is more difficult to determine accurately because the equilibrium pressure drop profile is approached asymptotically and thus, theoretically, the particle acceleration length should be infinite. In actual practice, however, the experimental error and the instrument sensitivity will prevent the detection of this small asymptotical change of pressure drop. Determination of the acceleration length can thus be obtained simply from that
213
0 0
05
10
15
20
25
30
Calculated Line Pressure Drop, cm H2Oim
Fig. 12. Comparison steady state pressure
of experimental and predicted drop per linear line length.
shown in Fig. 11. Since the pressure tap P5 is located 0.91 m from the tee, 0.91 m should be added to the particle acceleration lengths determined from Figs. 3 to 10 following the procedure outlined in Fig. 11. Particle acceleration length obtained here is thus not the true acceleration length commonly referred to in the pneumatic transport as derived in eqn. (9). It is actually a length required for recovery after a dead-end tee. The particle acceleration length calculated from eqn. (9) gave a value ranging from 12 to 17 m. This is in reasonable agreement with that found experimentally, despite all the uncertainties involved. Pressure drop per linear length at steady state under different operating conditions can be obtained from the slope of the straight line portion of the cumulative pressure drop profiles shown in Figs. 3 to 10, as illustrated in Fig. 11. The comparison between the experimental and the calculated steady state pressure drop per linear pipe length is summarized in Fig. 12 for elbows of 122cm (4% in), 91cm (36-in), and 61-cm (24-in) radius and for the dead-end tee. It is seen that the theoretical correlation presented earlier predicts reasonably well, within f 30%.
EROSION AROUND
AND
SOLIDS
FLOW
velocities. These included 122~cm (48~in), 91cm (36-in), and 61-cm (24-in) radius clear PVC elbows as well as a steel dead-end tee. The transport line was constructed of lo-cm (4-in) Schedule 40 carbon steel pipe and lo-cm (4-in) diameter clear acrylic pipe with the replaceable elbows located at the end of a straight section approximately 33.5 m (110 ft) long as shown in Fig. 2. All set points using the steel tee were completed with no problems; however, all three PVC elbows were destroyed due to wall erosion when transport velocities of 30.5 m/s (100 ft/s) were used with feed rates of 1364 kg/h (3000 lb/h) or higher. The failures were all approximately the same in appearance and occurred at the point where the stream of acrylic particles first hit the elbows. This erosion, once it started, occurred in the short period of approximately 5 min and was due to the PVC pipe melting. This was fast enough that an observer could actually see the hole being formed and pieces of plastic breaking off inside the pipe. Figures 13 and 14 show
PATTERN
THE ELBOW
Four elbow configurations were used during experiments to investigate erosion and solids flow patterns at various feed rates and
Fig. 13. elbow.
Pipe wall erosion
-
61-cm
(24-in)
radius
214
4 in. Plastic
Elbow
Worn Area and Bubble Approximately 3 in Long by 1 in Wide
View
A
I
4 in.
I Flow = Material
and Air Flow Through
the Line View “A” Cross-Section
View “A” Front
Fig. 14. Pipe wall erosion
-
61cm
(24-in)
radius elbow.
examples of this erosion. To further illustrate the problem, photographs of the transport elbows during test operations are shown in Figs. 15 through 17. From these it can be seen that, at a feed rate of 2727 kg/h (6000 lb/h) and a velocity of 10.7 m/s (35 ft/s), the material is transported through the line in a large ‘bundle’. As the velocity is increased, the band narrows and is not only moving faster but is concentrated on a smaller area of the piping elbow. This resulted in more heat due to friction and the pipe wall eroded rapidly. The results confirmed the general recommendation that dead-end tees instead of elbows be employed in pneumatic transport lines to prevent erosion failure.
CONCLUSIONS
Fig. 15. Acrylic flow -91-cm (36-in) Gas velocity 10 - 12 m/s; solids 2700
radius elbow. kg/h.
Experiments were conducted at a horizontal pneumatic transport loop constructed of lo-cm (4-in) Schedule 40 carbon steel pipe with transparent PVC pipe sections. The total loop length is approximately 80 m. Four elbow configurations were also tested.
215
(2) The acceleration lengths can be estimated by the existing correlation with reasonable confidence. (3) Except for the dead-end tee, the pressure drop around the elbow occurs primarily beyond the elbow rather than at the elbow as commonly expected. The elbow pressure loss is apparently expended for redispersing the solid particles, which are gathered into dense ribbons, beyond the elbow. (4) Erosion mechanism on elbows during pneumatic transport was elucidated by observing through transparent PVC elbows of different radii. The results confirm the general recommendation that the dead-end tees, instead of elbows, be used in pneumatic transport lines to prevent erosion failure.
LIST OF SYMBOLS cDS
dFc_i Fig. 16. Acrylic flow - 91-cm (364n) radius elbow. Gas velocity 15 - 23 m/s; solids 2700 kg/h.
dFf
dFs dL
dN d,
D
ff3
t (W,
drag coefficient for a single particle drag force on the particles in the pipe section dL solid frictional force of the particle in the pipe section dL net gravitational force on particles in the pipe section dL differential length of a conveying pipe total weight of solid particles contained in the pipe section dL total solid particles contained in the pipe section dL average particle diameter inside diameter of a conveying line gas friction factor as defined in eqn. (13) solid friction factor, fp = 4f, solid friction factor as defined in eqn. (14) gravitational acceleration length of pipe Reynolds number defined as dp( Uf WPflP
VW, Fig. 17. Acrylic flow - 91-cm (36-in) radius elbow. Gas velocity 31 m/s; solids 2700 kg/h.
The preliminary data indicate that (1) The experimental pressure drops can be correlated to within k30% by the existing correlation.
Reynolds number defined as d,U,p,l~ interstitial gas velocity actual particle velocity terminal velocity of a single particle solid flow rate particle acceleration length acceleration pressure drop total frictional pressure drop
216 A&
A&s MS
apT
E
Pf PP
frictional pressure drop due to gas frictional pressure drop due to solid particles pressure drop due to static head total pressure drop in a line voidage gas density solid particle density
REFERENCES
1 L. A. B&et, An Engineering Assessment of Entrainment Gasification, Morgantown Energy
Research Center, Morgantown, WV, 1978; NTISMERC/R1/78/2. 2 L. S. Fan and S. J. Hwang, Chem. Eng. Sci., 36 (1981) 1736. ‘2 J. Yerushalmi and N. T. Cankurt, Powder Technol., 24 (1979) 187. W. C. Yang, AIChE J., 30 (1984) 1025. Y. Yousfi and G. Gau, Chem. Eng. Sci., 29 (1974) 1939. Institute of Gas Technology, Preparation of a Coal Conversion Systems Technical Data Book, 1977, NTIS-FE-2286-16. 7 W. C. Yang, J. Powder Bulk Solids Tech., I (1977) 89. 8 W. C. Yang, I&EC Fundamentals, 12 (1973) 349. 9 E. S. Pettyjohn and E. B. Christiansen, Chem. Eng. Prog., 44 (1948) 157. 10 W. C. Yang, AZChE J., 20 (1974) 605.