EPA
United States
Environmental Protection
Agency
Office of
Reseach and
Development
EPA-600/7-77 022
Industrial Environmental Research EPA-60Q/7-1
Laboratory
Research Triangle Park. North Carolina 27711 March 1977
FILTER CAKE
REDEPOSITION IN A
PULSE-JET FILTER
Interagency
Energy-Environment
Research and Development
Program Report
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S.
Environmental Protection Agency, have been grouped into seven series.
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2. Environmental Protection Technology
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4. Environmental Monitoring
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6. Scientific and Technical Assessment Reports (STAR)
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This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from
the effort funded under the 17-agency Federal Energy/Environment
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mission to protect the public health and welfare from adverse effects
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is to assure the rapid development of domestic energy supplies in an
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environmental data and control technology. Investigations include
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EPA-600/7-77-022
March 1977
FILTER CAKE
REDEPOSITION
IN A PULSE-JET FILTER
by
David Leith and Melvin W. First
Harvard School of Public Health
665 Huntington Avenue
Boston, Massachusetts 02115
Grant No. R801399
Program Element No. EHE624
EPA Project Officer: James H. Turner
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
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ABSTRACT
To the extent that collected dust redeposits rather than
falls to the hopper, pulse-jet filter cleaning is ineffective.
dust tracer techniques were used to measure the amount of re-
deposition in a pilot scale pulse-Jet filter. A mathematical
model based on experimental results was developed to describe
dust transfer from bag to bag, redeposition on the pulsed bag
itself, and migration to the dust hopper.
At conventional filtration velocities, most of the dust
freed from the bag by a cleaning pulse was found to redeposit
rather than fall to the dust hopper. At high filtration veloci-
ties, redeposition became more pronounced. At a sufficiently
high filtration velocity, redeposition may become total. As a
result, no dust will fall to the hopper, the dust cake will con-
tinue to increase in thickness, and pressure drop will Increase
without limit as long as constant filtration velocity can be
maintained.
At a filtration velocity of 5 cm/s, 38? of the dust freed
from a bag by a cleaning pulse was found to redeposit on the
pulsed bag, 25$ redeposited upon each neighboring bag, and 125?
fell to the dust hopper. At a filtration velocity of 15 cm/s,
83% of freed dust redeposited on the pulsed bag, 1158 on each
neighboring bag, and only 1% fell to the hopper.
As a result of this work, it is clear that reasonable pres-
sure drop can be achieved at high velocity only when there is a
reduction in filter cake redeposition. Although filter perfor-
mance depends upon more parameters than were examined here, the
trend of increasing redeposition with increasing velocity may
persist regardless of the dust, fabric, or filter configuration
used. The internal components of a pulse-jet fabric filter as
well as the characteristics of the cleaning pulse can be adjusted
or arranged to minimize redeposition. Work on these and other
ideas is proceeding.
This report was submitted in fulfillment of Grant No.
R801399 by the President and Fellows of Harvard University under
the sponsorship of the U.S. Environmental Protection Agency.
This report covers the period from February 1, 1Q76 through
July 31, 1976.
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CONTENTS
Abstract ii
Figures and Tables iv
List of Symbols v
Acknowledgement vi
1. Introduction 1
2. Conclusions 2
3- Recommendations 3
^. Experimental Procedures .... ^
Background *J
Equipment 7
Procedure 12
5. Mathematical Modeling Procedures 13
Form of the Model 13
6. Results and Discussion 18
?. Discussion 23
8. Current Program 25
References . 27
Appendix 28
References for Appendix 32
iii
-------
FIGURES AND TABLES
Figure
6
7
Pressure drop vs. filtration velocity from Bakke(l)
for 15 oz wool felt, talc dust at 23 g/m3. . . .
Pressure drop vs. filtration velocity, from present
experiments
Schematic representation of fabric filter equip-
ment
Cumulative size distributions by count, untagged
and tagged fly ash
Photograph of turntable-pneumatic dust feeder, show-
ing dust storage can atop vibrating trough feeder,
turntable with scraper blade, aspirator with pres-
sure gauge and regulator, and gas inlet duct.
Location of tagged dust feeder ring.
10
Schematic of pathways followed by freed dust after
pulsation of (a) bag 1, (b) bag 2, (c) bag 3-
Tag concentration vs. number of pulses following
application of tagged dust. Velocity, 5 cm/s. .
/ '
Tag concentration vs. number of pulses following
application of tagged dust. Velocity, 10 cm/s.
Tag concentration vs. number of pulses following
application of tagged dust. Velocity, 15 cm/s.
Page
5
6
8
9
10
11
15
19
20
21
Table
Transfer Parameters,
Page
17
IV
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LIST OF SYMBOLS
C, — matrix defined by Equation 5
C2 — matrix defined by Equation 9
Co — matrix defined by Equation 10
D — vector defined by Equation A4
h(t) — tagged dust falling to the hopper between time
t-1 and time t
K, — fraction of dust freed by a cleaning pulse which
redeposits on the pulsed bag itself
K2 — fraction of dust freed by a cleaning pulse which
redeposits on each of two neighboring bags
K_ — fraction of dust freed by a cleaning pulse which
J falls to the hopper
m.(t) — mass of tagged dust in bag i at time t
M(t) — matrix defining amount of dust on each bag at time t
p — parameter
p* — estimated value of a parameter
SS — residual error
t — time
v — variable
v — observed value of a variable
v* — estimated value of a variable
n — random multiplicative factor, see Equation A2
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ACKNOWLEDGEMENT
Buffalo Forge Co., Buffalo, New York kindly supplied the
Venturis, bag support cages, bags, pulse valves, and timer used
in this project. Their assistance is gratefully acknowledged.
VI
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SECTION 1
INTRODUCTION
Fabric filters are the most efficient industrial dust collec-
tors for fine particle emissions and yet their operation is poorly
understood. Knowledge of the means by which particles pass
through, collect in, and are cleaned from a fabric filter is
essential if high velocity filtration technology is to proceed
rationally and if successful models for predicting filter per-
formance at high as well as conventional velocity are to be
developed.
Pulse-jet fabric filters have been used frequently in recent
years, in part because they operate at higher superficial filtra-
tion velocities (air to cloth ratios) than do filters cleaned by
other methods. Because the required size and first cost of fil-
ters decrease as velocity increases, it is tempting to increase
filtration velocity still further. The objective is to increase
filtration velocity while keeping the pressure drop reasonably
low, maintaining collection efficiency, and sustaining bag life.
In this report, the relationship between high filtration velocity
and filter cake redeposition is discussed. Redeposition, which
is aggravated at high velocities, must be minimized if reasonable
pressure drop is to be maintained.
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SECTION 2
CONCLUSIONS
This study, utilizing a pulse-jet fabric filter containing
three 11.4 cm diameter by 244 cm long polyester needled felt
bags, has determined the extent and effect of filter cake re-
deposition. At conventional filtration velocities such as 5
cm/s, over 80 per cent of the dust freed by a cleaning pulse
redeposited on the pulsed bag itself or on a neighboring bag.
At higher filtration velocities, such as 15 cm/s, redeposition
became more of a problem as 99 per cent of the freed dust re-
deposited.
At conventional velocities, most of the redeposition occured
upon bags near the pulsed bag. At high velocity, most of the
redeposition occured on the pulsed bag itself.
At high filtration velocities, a small rise in velocity has
been found by us and by others to cause an increas'e in pressure
drop which is much larger than expected. As velocity is increased
beyond this point, pressure drop appears to increase without
limit. Such increases in pressure drop at high velocity may be
caused by increased redeposition of the filter cake. As velocity
increases, gas flowing toward the bags drags agglomerates freed
by the cleaning pulses toward the bags and does not allow them
to fall to the dust collection hopper. At a sufficiently high
velocity, no dust may be able to escape from the bag surface
and redeposition may become total. At this point, pressure drop
increases without limit as the filter cake becomes thicker and
thicker.
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SECTION 3
RECOMMENDATIONS
Filter cake redeposition must be overcome for high velocity
fabric filtration to become feasible and a continuing effort
should be made in this direction.
The tests reported here reflect filter construction and
cleaning procedures typical of those currently used in industry.
Innovative modifications are needed to minimize the filter cake
redeposition problem.
A gas inlet near the top of the filter housing (rather than
from below) is thought to be helpful for sweeping the dust
cleaned from the bags toward the hopper rather than holding it
the filter bag section where redeposition occurs. Increased
spacing between the bags should help prevent redeposition on
the pulsed bag. Shorter bags may reduce redeposition although
the industry trend is toward larger bags. Modification of the
magnitude and form of the cleaning pulses may minimize redeposi-
tion without using additional compressed air. Finally, modifica-
tions to the Interior of the filter such as downward directed
compressed air jets, baffles between the bags, or other devices
may help alleviate the redeposition problem although they would
make the filter more complex to fabricate or operate.
The effect of these modifications must be considered in terms
of their potential to minimize redeposition and pressure drop as
well as their effects on collection efficiency, bag life, opera-
ting cost, filter size, and first cost.
A solution to the redeposition problem will provide divi-
dends both by reducing the pressure drop across pulse-jet fil-
ters operated at conventional filtration velocities and by making
more feasible the application of low cost, high velocity pulse-
jet filters in the future. These matters should form the basis
for a continuing research effort.
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SECTION 4
EXPERIMENTAL PROCEDURES
BACKGROUND
Evidence suggests that pressure drop Increases ever more
rapidly with filtration velocity until a limiting value is
reached, beyond which velocity cannot be increased regardless of
the pressure drop employed. Figure 1, a plot of pressure drop
against filtration velocity from Bakke(l) illustrates this point
as for all operating conditions pressure drop increased dramati-
cally with increased filtration velocity until a limiting value
was reached asymptotically. Figure 2 is a plot of pressure drop
against filtration velocity taken from data obtained in the pre-
sent study. For these data, the amount of dust fed between pulses
was kept constant by pulsing the filters proportionately more often
as the velocity was increased. Again, pressure drop was found to
increase rapidly. Before pulse-jet filters can be adapted to
operation at higher filtration velocities, it is necessary to iden-
tify and overcome those factors which cause excessive pressure drop,
Dennis and Wilder(2) have stated that during cleaning, the
filter cake separates from a pulse-jet-cleaned felt as agglom-
erates of about 100 ym diameter. Ideally, the filter cake will
fall into the dust collection hopper en masse. Actually, some
of the cake may redeposit upon the same.bag from which it came,
or upon neighboring bags. To the extent that filter cake rede-
position takes place, pulse-jet cleaning is ineffective.
Cinephotographic observations of the dust cloud produced
during pulse-jet cleaning indicate that 100 ym agglomerates are
blown from the fabric surface with an initial velocity of about
200 cm/s, which is sufficient to project" them from 4 to 8 cm in
a quiescent gas(3). Although the gas within the filter housing
is not quiescent, the distance the agglomerates might be pro-
jected is comparable to the distance between bags hung side by
side. A 100 ym particle has a terminal settling velocity of
about 50 cm/s and so would take several seconds to fall under
gravity to the dust collection hopper from a point of removal at
the top or middle of a bag 244 cm tall. During this time, it
seems reasonable that the agglomerate could redeposit.
There is reason to suspect that redeposition becomes greater
-------
40
(T
LJ
<30
u.
O
o
or
o
oe
o
UJ
o:
CO
CO
20
10
a:
0.
(a)
(b)
(c)
(d)'
T
T
T
T
hopper Inlet, 1.9 cm valve,
100 ms on time, 1 mln cycle time
same, top inlet
same, 2.5^ cm valve
same, 38 ms on time,
1:1*3 min cycle time
0 2 4 6
FILTRATION VELOCITY, CM/S
Figure 1. Pressure drop vs. filtration velocity from Bakke
for 15 oz wool felt, talc dust at 23 g/m3.
-------
60
a:
ui
i
40
or
o
o
UI
20
CO
CO
UJ
8:
FILTRATION
10 20
VELOCITY, CM/S
Figure 2. Pressure drop vs. filtration velocity
for present experiments.
-------
as filtration velocity increases. Higher gas velocity toward a
bag should help drag dust cake agglomerates back toward the bag
and not allow them to fall unhindered into the hopper. Some
fabric filters have gas inlets located near the bottom of the
filter housing to allow coarse particles to fall directly into
the dust hopper, and in these, the direction of bulk gas flow is
upward. Unless the filter bags are spaced further apart as fil-
tration velocity increases, the upward gas velocity thr.ough the
housing increases and tends to hold up the cake agglomerates for
redeposition rather than allowing them to fall freely to the dust
hopper.
When redeposition occurs, the thickness of the dust deposit
on the filter bags increases and pressure drop rises. If re-
deposition is extensive, pressure drop increases substantially.
As velocity increases, a point is reached where the filter cake
can no longer fall to the hopper. When this occurs, pressure
drop does not stabilize, but continues to increase without limit.
The present work was undertaken to determine the extent to
which filter cake redeposition occurs and its dependence on super-
ficial filtration velocity. The ultimate goal is to make higher
velocity fabric filtration feasible by developing methods for
minimizing redeposition.
EQUIPMENT
A three bag pulse-jet fabric filter was designed and fab-
ricated for use in this study. The filter contained three needled
felt polyester bags of industrial size arranged in a row; each
bag was 11.4 cm in diameter and 244 cm tall. The bags were sup-
plied by Summit Filter Co., Summit, N.J., had a permiability of
15 cm/s (30 cfm/ft2) at 1 cm (1/2 inch) of water pressure drop,
and had no surface treatment. The ratio of bag cross sectional
area to housing cross sectional area was about 1 to 5, a some-
what smaller ratio than is found in industrial units where bags
are usually packed as closely as possible. The gas entered
through a 20 cm diameter duct with centerline 25 cm below the
top of the housing. A pyrimidal hopper, with walls inclined 40°
from the vertical, funneled collected dust into a dust collection
vial. The front of the filter housing was 0.64 cm thick safety
glass covered with 0.95 cm thick clear acrylic plastic, to permit
observation of the filtration and cleaning processes. A drawing
of the apparatus is given in Figure 3. For all experiments, pulse
pressure was fixed at 7 atmospheres (100 psig), pulse frequency
was one pulse per bag per minute, with pulse valve electrical on
time of 75 milliseconds.
Fly ash, collected from a coal burning utility boiler by
electrostatic precipitation, was used as a test dust for all
experiments; its size distribution is shown in Figure 4. Figure
-------
00
PULSE
VALVE
MANOMETER
FOR
FILTER
PRESSURE
DROP
TO COMPRESSED
AIR RESERVOIR
STAIRMAND DISC
BLOWER
DUST FEEDER
FILTER
BAG
MANOMETER
FOR VOLUMETRIC
AIR FLOWRATE
Figure 3. Schematic representation
of fabric filter equipment.
HOPPER
-------
CO
(ft
QC
10
ui
cr
UJ
UJ
I
0.8
^ 0.6
QC
$
I I I I I I I I
O UNTAGGED FLY ASH
Q TAGGED FLY ASH
I
1
• lilt I
i
2 10 30 50 70 90 98
PER CENT BY COUNT LESS THAN
STATED SIZE
Figure 4. Cumulative size distributions by count, untagged and tagged fly ash.
-------
5 is a photograph which shows the dust feeder and its relation-
ship to the gas inlet duct. The aerosol passed a Stairmand disc(6)
to mix the particles thoroughly with the gas stream, past an inlet
baffle, and into the fabric filter. The pressure drop across
the Stairmand disc was monitored and used to measure the volu-
metric flow rate of gas. From the filter, cleaned gas passed a
flow regulator, through a radial blade fan, acoustic muffler, and
into a waste air system.
Figure 5. Photograph of turntable-pneumatic dust feeder,
showing dust storage can atop vibrating trough
feeder, turntable with scraper blade, aspirator
with pressure gauge and regulator, and gas inlet
duct.
The experimental method to be described required a chemi-
cally tagged dust as well as untagged dust. Fly ash was tagged
by dissolving uranine in water, adding fly ash, and evaporating
the water to produce a dust tagged 0.5% by weight with the dye.
The size distribution of the tagged dust is also shown in Figure
4.
Tagged dust was aerosolized by an NBS dust feeder-(5) and
fed to a 0.6*4 cm OD tube formed into a closed ring, which passed
around the center bag 60 cm from its top as shown in Figure 6.
The ring had perforations at interior, radial positions to allow
the tagged fly ash to flow toward that band on the center bag
which was within the ring. The NBS dust feeder could be turned
10
-------
I I
11.9 cm
19 cm
so cm
Figure 6. Location of tagged dust feeder ring,
-------
on and off independently of the pneumatic aspirator which fed
untagged fly ash to all three bags.
PROCEDURE
Experiments were performed at superficial filtration veloci-
ties of 5, 10, and 15 cm/s through the filter bags. For each
experiment, the system was brought to a pressure drop equilibrium
while operating at a fixed filtration velocity and while feeding
untagged fly ash to the inlet air stream at a fixed rate.
The center bag was conditioned with uranine tagged fly ash
by feeding this dust through the ring for a one minute interval
between pulses of the center bag. Meanwhile, and throughout the
rest of each experiment, untagged fly ash was fed into the inlet
gas stream for collection on all three bags.
Dust freed from a bag by a cleaning pulse is representative
of the dust on the bag at that time. Freed dust falling into the
hopper was collected in a plastic vial which was replaced follow-
ing each cleaning pulse, and labeled to identify the time it was
collected and the bag from which the dust in it came. In this
way, samples of the dust on each of the three bags were obtained
from the time the tagged dust was fed.
The filter cake at a-particular site on a bag may be thought
of as composed of "primary" particles collected at that site by
the filtration of dirty gas passing through the bag and "secondary",
filter cake particles, previously deposited at that site or else-
where. The primary and secondary particles make up the filter
cake which is dislodged during the next cleaning pulse and it can,
in turn, fall to the hopper, migrate to an adjacent bag, or re-
deposit at the same or a different site on the same bag.
To the extent that uranine tagged "secondary" fly ash par-
ticles are replaced by untagged "primary" particles, the filter is
"washed clean". By monitoring the uranine concentration in the
dust which falls to the hopper following each pulse, the degree
to which fly ash migrates to adjacent bags and to the hopper can
be determined using an appropriate mathematical model. The dust
freed from a well conditioned fabric during cleaning is thought
to have little interaction with the residual dust locked within
the fabric structure.(2)
Dust samples collected from the hopper were analyzed for
uranine by mixing with 15 ml of water, centrifuging to remove
suspended fly ash, and measuring fluorescence with a Photovolt
Multiplier Fluorescence Unit (Model 5*O . With care, uranine con-
centrations as low as 10-10 g/ml of water can be measured using
this technique(7)•
12
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SECTION 5
MATHEMATICAL MODELING PROCEDURES(10)
FORM OP THE MODEL
A mathematical model was developed to relate to uranine con-
centration in the collected dust to fly ash migration between bags,
to redeposition on the pulsed bag itself, and to migration to the
dust hopper from where it is removed from the system. The assump-
tion was made that a cleaning pulse blows all the dust deposit
from the bag into the air within the filter housing.
The fraction of dust freed from the pulsed bag which re-
deposits upon the pulsed bag itself was assumed constant from bag
to bag and was called K]_. The fraction of freed dust which migrates
to and redeposits upon each neighboring bag was assumed constant
and called K2, and the fraction falling to the hopper was called
K3. Prom the housing air, most dust will redeposit on the pulsed
bag itself, migrate to and redeposit upon a neighboring bag, or
fall to the dust hopper and be removed from the system. However,
some of the dust in the housing air penetrates through the filter
cloth and leaves in the cleaned air stream, and some could deposit
upon the chamber walls. The fraction of freed dust which pene-
trates through the filter was called Kjj, and the fraction which
deposits upon the chamber walls was called 1(5.
Because all freed dust must redeposit, fall to the hopper,
penetrate through the filter, or deposit on the chamber walls.
the sum of the fractions of total freed dust which follow each
path must equal unity.
KX + 2K2 + K + Kjj + K5 = 1 (1)
The factor 2 appears before K2 because dust can redeposit upon two
neighboring bags in the three bag system.
Little dust penetrates in a normal fabric filter; efficiency
is close to 100?. The fraction of freed dust which penetrates the
filter, K/j, can be assumed to be zero without introducing a sub-
stantial error. Observation of the interior walls of the filter
housing through its transparent front indicated that little dust
was sticking to the smooth sheet metal walls. For the purpose of
analysis, the fraction of freed dust which deposited on the
housing walls, 1(5, was also assumed to be zero. Rearrangement of
13
-------
Equation 1, after deletion of factors Kij and 1(5, yields an expres-
sion for K3 (the fraction of freed dust which falls to the hop-
per) as a function of KI and K2 (the fractions which redeposit on
the pulsed and neighboring bags).
K3 = 1 - KI - 2K2
This process is shown schematically in Figure 7-
(2)
In the mathematical model, time zero was taken as the instant
at which the tagged dust feed to a section of the central bag was
discontinued. After the first pulse:
m1(0)
m2(l) = m2(0)
m1(0)
(3a)
(3b)
(3c)
J J <=- J-
Here, m-j^(t) is the mass of tagged dust on bag i at time t, and the
interval between pulses is arbitrarily set at 1 unit. Bag 1 is
the center bag, to which tagged fly ash was applied. Bags 2 and 3
are the adjacent bags to the left and right of the center bag. In
matrix form,
M(D =
M(0)
(1)
where
KI
K2
K2
0
1
0
0
0
1
(5)
m1(t)
m2(t)
H(t) =
Similar equations express the transfer of mass after pulses in
bags 2 and 3-
M(2) = C2 M(D
M(3) = C3 M(2)
(6)
(7)
(8)
14
-------
BAG BAG BAG
f*2 HKI
HOUSING
J|K,
HOUSING
JK2 fK2
HOUSING
Figure 7.
HOPPER
Schematic of pathways followed by freed dust
after pulsation of (a) bag 1, (b) bag 2, (c) hap 3,
15
-------
where
C2 =
C3 =
" K2
0 K-j^
0 K2
1 0
0 1
0 0
0
0
^^
K2
K2
Kl
(9)
(10)
The tagged fly ash collected in the hopper after time t is h(t).
For the first three pulses the appropriate values of h(t) are:
h(2) =
h(3) =
m1(0)
m2(l)
m3(2)
(11)
(12)
(13)
After the third bag was cleaned, the cycle of pulses was
repeated without addition of more uranine so that: '
M(4) = G! M(3)
M(5) = C2 M(*0
M(6) = C3 M(5)
M(7) = G! M(6)
(15)
(16)
(17)
and
m]L(3)
h(5) =
h(6) =
h(7) =
(15)
(16)
The data consisted of the time series h(l), h(2), ... , to
which it was necessary to fit values of K^, K2, and a mass scaling
parameter, mj(0). This was done independently for filtration velo-
cities of 5, 10, and 15 cm/s so that the effect of velocity on the
16
-------
parameters K]_, K2, and K3 could be observed.
The Gauss-Newton procedure was used for fitting the para-
meters. It is a least squares method for non-linear models, des-
cribed in the Appendix. Logarithms of the data were taken before
fitting. A computer program was written in FORTRAN which calcu-
lated best fit values for the transfer parameters K^ and K2-
Table 1 lists the values of these parameters.
TABLE 1. TRANSFER PARAMETERS*
Filtration
Velocity,
cm/s
5
10
15
Kn
1
0.38±0.16
0.75±0.03
0.83±0.03
K0
2
0.25+0.09
0.0?±0.02
0.08±0.02
K,
3
0.12±0.21
0.11±0.04
0.0110.04
K, = Fraction of dust freed by a cleaning pulse which redeposits
on the pulsed bag itself.
Kp = Fraction of dust freed by a cleaning pulse which redeposits
on each of two neighboring bags.
K_ = Fraction of dust freed by a cleaning pulse which falls to
J the hopper (K_ = 1 - ^ - 2K2>.
* Listed uncertainties are one standard error of the estimate.
17
-------
SECTION 6
RESULTS AND DISCUSSION
Figure 8 is a plot of the uranine tag concentration in the
fly ash falling to the hopper against pulses since the application
of tagged dust at a filtration velocity of 5 cm/s. Figures 9 and
10 are similar plots for filtration velocities of 10 and 15 cm/s.
The solid lines in all three plots are the mathematical model's
predictions using the transfer parameters listed in Table 1.
Figure 8, the concentration vs. pulses plot for filtration
velocity of 5 cm/s, shows that the uranine tagged dust concentra-
tion on the bags decreases rapidly after the tagged dust feed is
discontinued. Even at this moderate filtration velocity, however,
the data in Table 1 show that redeposition is substantial. Trans-
fer parameter K]_, the fraction of dust freed from the pulsed bag
which redeposits ,on the pulsed bag itself, was found to be 0.38.
The fraction of freed dust which redeposits on each of the two
neighboring bags, K2, was found to be 0.25 or a total of 0.50 for
the two neighboring bags together. Adding the fraction of the
freed dust which redeposited on the pulsed bag itself to the frac-
tion which redeposited on" each of the two other bags gives a total
fractional redeposition of 0.88. Even at this modest filtration
velocity, the majority of the dust freed from the bag by a clean-
ing pulse was found to redeposit somewhere within the filter sys-
tem. At the 5 cm/s velocity, the fraction of dust freed from the
bags which fell to the hopper, KQ, was found by difference to be
0.12.
At a filtration velocity of 10 cm/s, tagged dust reaches the
dust hopper from the filter bags more slowly, as can be seen in
Figure 9, the plot of tag concentration vs. pulses after tagged
dust feed has ceased. Table 1 shows significant differences in
the values of transfer parameters from those found at 5 cm/s. At
10 cm/s, the fractional redeposition on the pulsed bag itself, K]_,
was 0.75, a substantial increase, whereas fractional redeposition
on each of the two neighboring bags, K2, decreased to 0.0?. The
fraction of freed dust which fell to the dust hopper with each
pulse, K3, decreased slightly, to 0.11.
At the 15 cm/s filtration velocity, established trends con-
tinued. The fraction of freed dust which redeposited on the pulsed
bag, KI, was found to be 0.83, and fractional redeposition on each
of the neighboring bags, K2, was 0.08. The total fractional re-
deposition at this high filtration velocity was found to be 0.99,
18
-------
CC
UJ
o.
a.
o
g I03
e>
en
CO
u.
o
£
1
0
PULSES
MODEL
1
40 80
TAGGED DUST FEED
Figure 8. Tag concentration vs. number of pulses followlnR
application of tagged dust. Velocity, 5 em/s.
19
-------
CL
0.
O
O
OT .4
2I04
o:
e
or
CO
b. _R
10 5
UJ
<
o:
o
O
MODEL
40
80
PULSES SINCE TAGGED DUST FEED
Figure 9. Tag concentration vs. number of pulses following
application of tagged dust. Velocity,16 cm/s.
20
-------
IT
Ul
O.
e>
Bid3
CD
o
a:
o
u.
o
s
10
4
(0
UJ
o o
MODEL
0 40 80
PULSES SINCE TAGGED DUST FEED
Figure 10. Tag concentration vs. number of pulses following
application of tagged dust. Velocity, 15 cm/s.
21
-------
leaving only 0.01 to fall into the dust hopper. The slow rate at
which tagged dust washed from the filter can be seen in Figure 10,
the plot of tagged dust concentration vs. pulses since the appli-
cation of tagged dust at this velocity. Tag concentration de-
creases very gradually with cleaning pulses, which reflects the
high amount of redeposition and the slow rate at which dust fell
to the hopper.
The computer simulation model predicts oscillating values
for the tag concentration in the dust falling to the hopper. The
peaks of the oscillations are concentration of tagged dust from
the bag to which the uranine tagged dust was fed initially. The
lower values of the oscillations are tag concentrations on each
of the two other bags.
At all filtration velocities, the oscillations which the
model predicts center around straight lines on the semi-log plots
of tagged dust concentration vs. pulses since tagged dust feed.
A straight line on such a plot would correspond to a uniform con-
centration of uranine tag; on all filter bags(ll). The magnitude
-and persistence of the oscillations indicate the degree to which
complete mixing of the dust within the system fails to occur due
to low transfer of dust from bag to bag as quantified by K2, the
fraction of freed dust which redeposits upon each of the neigh-
boring bags with each cleaning pulse.
At the 5 cm/s filtration velocity, the value of K2, was
found to be relatively high. As a result, the tag concentration
on the three bags evened out rapidly, because of the substantial
interchange of dust from .bag to bag in the filter system as the
bags were cleaned. Figure 8, the plot of tag concentration vs.
number of pulses following application of tagged dust since tagged
dust feed for the 5 cm/s filtration velocity, shows that the oscil-
lations in the model prediction damp out rapidly as the tagged
dust distributed itself rapidly throughout the system. Figure 8
also shows that the tag concentration declined quickly with clean-
ing pulses, as is reflected in the large value for 1(3, the frac-
tion of freed dust which falls to the hopper with each cleaning
pulse.
By comparison, the model predicts substantially different
behavior for the system at the 15 cm/s filtration velocity. Here,
oscillations are greater, persist for a longer time, and result
from a smaller value for K2, the fraction of freed dust which re-'
deposits on neighboring bags. The exchange of dust from bag to
bag with cleaning pulses is less pronounced at the higher filtra-
tion velocity. Also, at the higher velocity, the rate at which
tagged dust concentration decreased over time and cleaning pulses
is low. This reflects the slow rate at which the tagged dust is
"washed" from the filter bags, as a comparatively small fraction,
K3, of the freed dust fell to the hopper with each cleaning pulse.
22
-------
SECTION 7
DISCUSSION
The effect of high filtration velocity on the performance of
the pulse-jet filter is now clearer. Even at a conventional fil-
tration velocity such as 5 cm/s, the data shown in Table 1 indi-
cate that most of the dust freed from the bag by a cleaning pulse
redeposits rather than falls to the dust hopper. Minimizing re-
deposition, therefore, is important even when operating the filter
at conventional velocities.
As filtration velocity increases, the redeposition problem
becomes even more important. The fraction of freed dust which re-
deposits on the pulsed bag itself increases from 0.38 to 0.83 as
filtration velocity increases from 5 to 15 cm/s. At the same
time, the fraction of dust which redeposits on neighboring bags
decreases from 0.25 to 0.08. What is more important, from the
standpoint of cleaning the bags adequately, is that the total
fractional redeposition increases from 0.88 to 0.99 as filtration
velocity increases from 5 to 15 cm/s. The fraction which falls
to the dust hopper, the complement of the fraction which redeposits,
decreases from 0.12 to 0.01. Increasing velocity leads to less
effective cleaning of the bags.
At conventional velocities, dust cake agglomerates may be
projected far into the dirty gas stream. However, at high filtra-
tion velocities, the agglomerates may have difficulty in traveling
far from the filter bag surface, as the high velocity of the fil-
tering gas sweeps dust back onto the bag. As filtration velocity
increases, redeposition is primarily upon the pulsed bag itself,
rather than on neighboring bags. As redeposition increases, the
filter cake becomes thicker, a smaller fraction of the dust cake
falls to the hopper, and pressure drop increases. At a suffi-
ciently high filtration velocity, redeposition may become total,
and no dust may fall to the hopper. At this point, the dust cake
will continue to increase in thickness, and pressure drop will
increase without limit, at least as long as constant filtration
velocity can be maintained. In this way, redeposition may account
for the exceptionally rapid increases in pressure drop with filtra-
tion velocity shown in Figures 1 and 2.
The results described here must be taken in the context of
the experimental apparatus used. Although commercial pulse-jet
components were employed throughout, the three bag unit tested
here was smaller than a commercial unit and had a different geo-
23
-------
metry. Additionally, the three bags used here were pulsed-cleaned
one by one causing 33% of the total bags to be pulsed at a time.
Larce industrial units with many bags have a lower ratio, cleaning
from 5% to 2Q% of the bags at one time. As a result, each un-
pulsed bag in the three bag experimental unit had to handle 50%
more air during cleaning than it would handle during the time be-
tween pulses. For an industrial unit, each filtering bag handles
only 5% to 25% more air. For this reason, dust migration to
neighboring bags may have been exaggerated in the experiments.
The experimental filter had a minimum fabric to fabric dis-
tance of about twelve centimenters, whereas the spacing between
bags in an industrial pulse-jet filter is minimized to conserve
filter floor space, and may be as little as five centimeters.
Because migration to neighboring bags should increase if the bags
are close together, the experiments may have underestimated the
amount of dust migration to neighboring bags which occurs in a
full scale filter.
The net effect of a higher pulsed bag ratio and greater bag
spacing in the experimental filter is unknown. However, the en-
hanced redeposition upon neighboring bags caused by increased
pulse ratio, and the decreased redeposition upon neighboring bags
caused by increased bag spacing in the experimental filter should
balance somewhat.
Because the experimental filter had only three bags, most
of the fabric faced housing walls rather than addit'ional bag sur-
faces as would be the case in an industrial filter. The walls may
reflect dust onto the pulsed bag, rather than allow it to migrate
to a neighboring bag or to the dust hopper. These experiments may,
therefore, have overestimated self-redeposition.
Effects of scale in pilot plant experiments such as these
can never be entirely overcome, although they can be minimized by
careful experimental design. As this program continues, it may
become necessary to conduct experiments on apparatus with more
bags if potential scale up problem bias experimental results and
cannot be overcome in other ways. This may require experiments
with operating filters in the field. The results reported here
should be interpreted with caution; quantitative results should
not be applied to pulse-jet filters different from the one tested.
However, the trends reported here should be useful in interpreting
pulse jet behavior in full scale units and assist in optimizing
filter performance.
24
-------
SECTION 8
CURRENT PROGRAM
The performance of a pulse-jet filter will depend upon more
parameters than those discussed here. Dust characteristics includ-
ing particle dize, fabric material and construction, gas properties
including humidity and temperature, bag length, and spacing, and
other variables may all influence redeposition and filter behavior.
Pulse pressure, duration, and form should have a strong
effect on redeposition and cleaning effectiveness. Pressure in-
fluences bag acceleration(2), which may affect the distance which
dust cake agglomerates travel from the fabric surface. Pulse
duration may affect redeposition in that a longer pulse allows a
longer time for freed dust to fall toward the dust hopper before
filtration air sweeps back through the fabric and pulse form may
affect redeposition as well. A rapid increase in pressure at the
beginning of the cleaning pulse may be important to maximize out-
ward bag acceleration, and for this reason quick opening valves
are used in a pulse-jet filter- However, a gradual reduction in
pressure at the end of the cleaning pulse should prolong pulse
duration without the consuming of excessive amounts of compressed
air, and may ease the fabric back to its supporting cage gently.
This should also tend to prolong bag life. Quick opening valves
also close quickly, and do not provide these benefits. Modifica-
tions to standard pulse valves to combine quick opening with
gradual closing may help minimize redeposition while maximizing
cleaning effectiveness.
The current experiments were conducted with a filter designed
to replicate current industrial practice, although current filters
are not designed for operation at the high velocities intended in
this program. One goal of this program is to identify modifica-
tions to current filter designs which permit effective high velo-
city operation. On the basis of the experiments reported here,
appropriate modifications can begin to be identified. A gas inlet
near the top of the filter housing should help sweep dust cleaned
from the bags toward the hopper rather than hold it up for redeposi-
tion upon neighboring bags, whereas shorter bags should reduce the
opportunities for redeposition upon the pulsed bag itself. Changes
in the size and form of the cleaning pulse may have an important
effect on bag cleanaility and redeposition at high velocity as
discussed above.
Modification such as these, to the filter housing, to bag
25
-------
length and spacing, and to the nature of the cleaning pulse, hold
promise for the reduction of redeposition and should be effective
whatever fabric and dust are used. In addition, some fabrics may
have advantage over others for particular applications. Identi-
fication of the most effective fabric for each pulse-jet applica-
tion will multiply the benefits of structure and operational modi-
fications.
These ideas and others form the basis for a program currently
underway to investigate redeposition further and eliminate it as
a problem in high velocity filtration. It is anticipated that
additional reports will be issued in which current progress will
be reported.
26
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REFERENCES
1. E. Bakke, "Optimizing Filtration Parameters," J. Air Poll.
Control Assoc., 24:1150 (197*0.
2. R. Dennis and J. Wilder, Fabric Filter Cleaning Studies,
EPA Report EPA-650/2-75-009, Research Triangle Park, N.C.,
1975.
3. N. A. Fuchs, The Mechanics of Aerosols, Pergamon, New York,
p. 78, 1964.
4. M. W. First, L. Silverman, R. Dennis, G. A. Johnson, A. T.
Rossano, Jr., R. Moschella, C. E. Billings, E. Berly, S.
Friedlander, and P. Drinker, Air Cleaning Studies Progress
Report for Feb. 1, 1950 - Jan. 31, 1951, AEC Report No.
NYO-1581, April, 1952.
5. L. Silverman and C. E. Billings, "Methods of Generating
Solid Aerosols," J. Air Poll. Control Assoc. 6:76 (1956).
6. C. J. Stairmand, "Sampling Gas-Borne Particles," Engineering,
p. 41 (August 22, 1941).
7. W. A. Burgess, L. Silverman, and F. Stein, "A New Technique
for Evaluating Respirator Performance," Am. Ind. Hyg. Assoc.
J., 22:422 (1961).
8. D. G. Stephan, G. W. Walsh, and R. A. Herrick, "Concepts in
Fabric Air Filtration," Am. Ind. Hyg. Assoc. J., 21:1 (I960).
9. C. E. Billings and J. Wilder, Handbook of Fabric Filter Tech-
nology, N.T.I.S. Report PB-200 648, 5285 Port Royal Rd.,
Springfield, Va., 1970.
10. H. Feldman, Harvard School of Public Health, assisted with
the formulation of the mathematical model and with program-
ing described in this section and in the Appendix.
11. D. Leith and M. W. First, "Filter Cake Redeposition in a
Pulse-Jet Fabric Filter," paper 76-31.4 presented at the
69th Annual Meeting of the Air Pollution Control Associa-
tion, Portland (1976).
27
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APPENDIX
The Gauss-Newton fitting procedure takes a known functional
relationship among variables (v) , parameters (p) , and time (t),
and fits it to a set of observed variables (vo) by adjustment of
the parameters. In the present case the variable is the tagged
dust collected, h(t), and the parameters are KI, K2, and mi(0).
Their functional relationship is given in detail at the end of
this section.
The procedure is begun by making an estimate, p*, for each
parameter, p. These estimates give rise, via the known functional
relationship, to estimated variables, v* , which ideally will coin-
cide with the observations, vo. At this point partial derivatives,
(8v/3p)*, can also be calculated by the functional relationship;
the role of these quantities will be made clear momentarily.
Usually, the agreement of v* with vo is unsatisfactory and
the estimates for parameters KI, K2 and m^CO) must be adjusted
to produce a better fit. The Gauss-Newton method does this by
local linerization of the functional relationship, as expressed
by a first-order, multidimensional Taylor series expansion:
log v - log v. + lirffS)'*' (A1)
where Ap = p - p*, and the summation runs over the set of para-
meters p. By this equation the difference between the "true" v
and its current estimate v* is "blamed" on errors in the various
parameters, in proportion to their effect on v.
The reason for expanding log v instead of v will now be
explained. The best simple model of measurement error in tracer
studies is that the observed activity VQ differs from its "true"
value by an unknown, random multiplicative factor n:
VQ = nv. (A2)
Thus log v can be rewritten as log VQ - log n and Equation Al can
be rewritten so that the only unknown quantities are the random
errors n and the parameter errors Ap:
log • I() " (A3)
Letting v and n range over each observation, a matrix equation can
be written:
D = D CAp] + [log n]. (Ail)
28
-------
Thus D is a vector of length equal to the number of data points,
with elements vo/v«, while D is a matrix of breadth equal to the
number of parameters and length equal to the number of data points,
with elements (l/v«)(8v/3p)».
Our goal now is to "eliminate" the unknown random error n,
and we accomplish this by a minimization step, as follows. The
residual error arising from the choice of p* is
SS* = D'D- (A5)
if the parameter estimates were perfect, Ap would be zero and SS*
would reach its minimum value, the unknown error of measurement:
SS* = [log n]'[log n]. (A6)
Applying the least-squares criterion, the values of p which mini-
mize SS are sought as a "best" model. It follows directly from
Equation A3 that the appropriate choice of Ap is
[AP] = (D'D) "•'•D'D. (A7)
These Ap values are used to correct the current estimates p*,
ostensibly obtaining least-squares values for the "true" p. How-
ever, because of the truncation of the Taylor series, these results
are not exact. The farther p* lies from p, the more the truncated
Taylor series is in error. Therefore, the new parameter values
must be taken merely as improved estimates, and the procedure re-
peated until all Ap are near zero. At that point SS* has pre-
sumably reached SS, and the procedure ends.
Under the assumption that the measurement error n is log-
normally distributed, the statistical properties of the parameter
estimates can be approximated as follows. After convergence, the
matrix (D'D)-1 is multiplied by SS (the final SS*) and divided by
the degrees of freedom, df (number of observations minus the num-
ber of fitted parameters). The diagonal elements of the result-
ing matrix are approximate variances of the parameters, and the
off-diagonal elements are the covariances(l). These quantities
indicate the range the parameters would cover if the experiment
and fit were repeated with different sets of random error, taken
from the same distribution (log n of mean zero, variance SS/df).
Note that since the matrix D'D is positive-definite, and
symmetric, its inversion, Equation A7» can be accomplished with
high efficiency by the Cholesky decomposition(2).
Marquardt(3) suggested enhancing the diagonal of D'D before
inversion, by a variable factor 1+e. The larger e is, the more
the method behaves like the method of steepest descent(3), and the
less susceptible it is to the erratic behavior sometimes seen in
the early stages of Gauss-Newton fitting. Powers of 10 are used
29
-------
here for e, starting at 10~2. At each iteration, if SS decreases
with the corrected parameters, e is divided by 10. If SS in-
creases, the parameter corrections are rejected and recalculated
with e multiplied by 10. An optimal e is not sought at each
iteration, as suggested by Fletcher and Shrager(4), for as
Marquardt has stated(3) "such a strategy would inherit many of
the properties of steepest descent; e.g., rapid initial progress
followed by progressively slower progress."
Numerical differentiation might be used to calculate (3v/3p)*;
one could apply the calculation of v* iteratively, perturbing each
unknown parameter in turn. The analytical method is far more
efficient in this application, however, since the partial deriva-
tives can be computed in parallel with the variables, without
iterating, as shown below.
The functional relationship between h(t) and the parameters
KI, K2, and mi(0) can be written recursively, with m(t) as inter-
mediary :
m(0) =
m(t) =
. 0
(A8)
(A9)
where t = 1,2,3,4,..., and i = remainder when t is divided by 3.
h(t) = (l-K1-2K2)m1(t-l) . (A10)
The derivatives are then defined recursively by differentiation
of the above:
3m(0) _
3m(t) _
J
3h(t)
3lT
0
0
P
3C
, andf^
(All)
:-l)
J
and
3m(t) _ c 3m(t-l)
(A12)
3m.(t-1)
3lT a
J
3m.. (t-1)
2)35Tor- (A13)
30
-------
where j = 1,2,
example,
The terms
so that
3C4
IF
are simple constant matrices; for
C2 -
IT/"
P
o KI
0 K2
0
o
i.
(A14)
010
000
010
(A15)
The other derivatives appearing on the right sides of these equa-
tions are the results of earlier calculations; i.e., left sides
of the same equations for smaller t.
31
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REFERENCES FOR APPENDIX
1. M. Herman, E. Shahn, and M. F. Weiss, "The Routine Fitting
of Kinetic Data to Models: A Mathematical Formalism for
Digital Computers," Biophys. J. 2:275 (1962).
2. G. E. Forsythe, and C. B. Moler, Computer Solution of Linear
Algebraic Systems, Prentice-Hall, Englewood Cliffs, N.J.,
(1967).
3- D. W. Marquardt, "An Algorithm for Least Squares Estimation
of Non-Linear Parameters," J. Soc. Indust. Appl. Math. 11:
K31 (1963).
4. J. E. Fletcher and R. I. Shrager, A User's Guide to Least-
Squares Model Fitting, Division of Computer Research and
Technology, National Institutes of Health, Bethesda, M.D.
(1968).
32
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/7-77-022
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
Filter Cake Rede posit ion in a Pulse-Jet Filter
5. REPORT DATE
March 1977
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
David Leith and Melvin W. First
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Harvard School of Public Health
665 Huntingdon Avenue
Boston, Massachusetts 02115
10. PROGRAM ELEMENT NO.
E HE 62 4
11. CONTRACT/GRANT NO.
Grant R801399
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final: 2/76-1/77
14. SPONSORING AGENCY CODE
EPA/600/13
15.SUPPLEMENTARY NOTES r£RL_RTp prOject officer for this report is J.H. Turner, Mail
Drop 61, 919/549-8411 Ext 2925:
16. ABSTRACT Tne reporj. gives results of Si pilot-scale study of pulse-jet filter cleaning,
a process that is ineffective to the extent that collected dust redeposits, rather than
falling to the hopper. Dust tracer techniques were used to measure the amount of
redeposition. A mathematical model based on experimental results was developed to
describe dust transfer from bag to bag, redeposition on the pulsed bag, and migration
to the hopper. At conventional filtration velocities (5 cm/s), most of the dust freed
from the bag by the cleaning pulse was found to redeposit (38% on the cleaned bag and
50% on the two neighboring bags) rather than fall to the hopper. At high velocities
(15 cm/s), redeposition was more pronounced, 83% on the cleaned bag and 16% on the
neighboring bags. At a sufficiently high velocity, redeposition may become total: no
dust will fall into the hopper, the dust cake will continue increasing in thickness, and
the pressure drop will increase without limit as long as constant velocity is main-
tained. The study indicates that reasonable pressure drop can be achieved at high
velocity only when there is a reduction in filter cake redeposition. Although filter
performance depends on more parameters than were examined, the trend of increa-
sing redeposition with increasing velocity may persist regardless of the dust, fabric,
or filter configuration.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air Pollution
Dust Filters
Dust
Pulsation
Jets
Cleaning
Caking
Fabrics
Filtration
Air Pollution Control
Stationary Sources
Particulate
Pulse-Jet Cleaning
Redeposition
Fabric Filters
muses
13B
13K
11G
20D
13H
07A
HE
07D
18. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS (Thispage)
Unclassified
21. NO. OF PAGES
39
22. PRICE
EPA Form 2220-1 (9-73)
33
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