United States
Environment,il Pruli" '
Agwncy
rial Environmental Rev v h F PA MX; ; /
Laboratory April T"t /M
Tnanglf Park NT 2/711
Fabric Filter Model
Sensitivity Analysis
Interagency
Energy/Environment
R&D Program Report
-------
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development. U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
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 Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects; assessments of, and development of, control technologies for energy
systems; and integrated assessments of a wide'range of energy-related environ-
mental issues.
EPA REVIEW NOTICE
This report has been reviewed by the participating Federal Agencies, and approved
for publication. Approval does not signify that the contents necessarily reflect
the views and policies of the Government, nor does mention of trade names or
commercial products constitute endorsement or recommendation for use.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
-------
EPA-600/7-79-043c
April 1979
Fabric Filter Model
Sensitivity Analysis
by
Richard Dennis, H.A. Klemm, and William Battye
GCA/Technology Division
Burlington Road
Bedford, Massachusetts 01730
Contract No. 68-02-2607
Task No. 7
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
-------
ABSTRACT
Preliminary testing of the GCA filtration model has shown good agreement
with field data. However, the apparent agreement between predicted and actual
values is based upon limited comparisons and the validation processes were
carried out without regard to optimization of the data inputs selected by the
filter users or manufactureres. As a precursor activity to further laboratory
and/or field tests, a series of sensitivity tests have been performed. The
procedure has been to introduce into the model several hypothetical data in-
puts that reflect the expected ranges in the principal filter system variables.
Such factors as air/cloth ratio, cleaning frequency, amount of cleaning, spe-
cific resistance coefficient (Kz) number of compartments and inlet concentra-
tion were examined in various permutations. A key objective of these tests
was to determine which variables would require the greatest accuracy in esti-
mation based upon their overall impact on model output. In the case of K£
variations, the system resistance and emission properties showed little change
but the cleaning requirement was drastically changed. On the other hand,
considerable difference in outlet dust concentration was indicated when the
degree of fabric cleaning was varied. To make the findings more useful to
those persons assessing the probable success of proposed or existing filter
systems, much of the data output has been presented in the form of graphs or
charts. This procedure enables control personnel, for example, to make rapid
decisions as to whether a given filter system can perform according to
specifications.
iii
-------
iv
-------
CONTENTS
Abstract iii
Figures vi
Tables xi
Acknowledgment xiii
1. Summary 1
2. Introduction 4
2.1 Program Scope 4
2.2 Background for Filtration Model 9
2.3 Dust Penetration With Woven Glass Fabrics 15
2.4 Model Applications 18
2.5 Summation 23
3. Critique of Major System Variables, Theory and Practice .... 26
3.1 Dust Dislodgement and Adhesion 26
3.2 Specific Resistance Coefficient 40
3.3 Effect of Filtration Velocity on K2 48
4. Sensitivity Analyses 53
4.1 Preliminary Screening Tests 53
4.2 Multivariable Sensitivity Tests 62
4.3 Use of the Sensitivity Test Data 107
References 120
Appendices
A. Equations for Estimating Dust Penetration 122
B. Results of Sensitivity Tests 123
C. Sensitivity Analysis Graphical Presentations for Multi-
variable Systems 133
D. Derivation of Relationships Between Average System Pressure
Drop and System Design Parameters 188
-------
FIGURES
Number Page
1 Typical drag versus loading curves for filters with different
degrees of cleaning and a maximum allowable level for terminal
drag, ST, and terminal fabric loading, WT ........... 11
2 Predicted and observed outlet concentrations for bench scale tests.
GCA fly ash and Sunbury fabric ................ 16
3 System breakdown for I bags and J areas per bag ......... 19
4 Nucla baghouse simulation, resistance versus time ........ 21
5 Estimated cleaned area fraction, ac, based upon dust removal by
(a) gravity and/or shaking acceleration forces or (b) aerodynamic
drag forces caused by reverse air flow. Coal fly ash and twill
weaves glass fabrics ..................... 28
6 Cleaned bag surface with inside illumination by fluorescent tube 29
7 Schematic, hoop stressing during reverse flow for depressed region,
collapsed bag with clean side (external) pressure exceeding
dirty side (internal) pressure, Pc > P^ ............ 39
8 Ratio of K2 values predicted by Happel and Kozeny-Carman equations
versus dust cake porosity ...... . ............ 42
9 Variations in porosity functions with porosity ......... 46
10 Variation in porosity function with bulk density and discrete
particle density ....................... 47
11 Drag versus fabric loading curves typifying abrupt cake collapse
and gradual cake and/or fabric compression .......... 50
12 K2 versus velocity for wet ground mica. From Spaite and Walsh . 52
13 Effect of face velocity and limiting pressure drop on average
pressure loss ......................... 65
14 Effect of face velocity and limiting pressure drop on average
pressure loss ....................... . . gg
15 Effect of face velocity and limiting pressure drop on average
pressure loss
16 Effect of face velocity and limiting pressure drop on average
pressure loss
17 Effect of face velocity and limiting pressure drop on average
pressure loss .......................
Vi
-------
FIGURES (continued)
Numbei
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
: I
Effect of face velocity and limiting pressure drop on average
pressure loss
Effect of face velocity and limiting pressure drop on average
pressure loss
Effect of face velocity and limiting pressure drop on average
penetration
Effect of face velocity and limiting pressure drop on average
penetration
Effect of face velocity and average pressure drop on average
penetration
Effect of face velocity and limiting pressure drop on average
penetration
Effect of face velocity and limiting pressure drop on average
penetration
Effect of face velocity and limiting pressure drop on average
penetration
Effect of face velocity and limiting pressure drop on average
penetration
Relationship between time between cleaning cycles, limiting
pressure loss and face velocity
Relationship between time between cleaning cycles, limiting
pressure loss and face velocity
Relationship between time between cleaning cycles, limiting
pressure loss and face velocity
Relationship between time between cleaning cycles, limiting
pressure loss and face velocity
Relationship between time between cleaning cycles, limiting
pressure loss and face velocity
Relationship between time between cleaning cycles, limiting
pressure loss and face velocity
Relationship between time between cleaning cycles, limiting
pressure loss and face velocity
Effect of velocity on average pressure loss for timed cleaning
cycle system
Effect of time between cleaning cycles, tf, on average penetration
Effect of variations in cleaning intensity on average pressure
drop
Effect of variations on inlet concentration on average pressure
Page
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
93
94
95
vii
-------
FIGURES (continued)
Number
38 Effect of cleaning intensity on average penetration ....... 96
39 Effect of inlet concentration on average penetration ...... 97
40 Effect of K2 and C± on average pressure loss .......... 100
41 Effect of K2 and C. on time between cleaning cycles ....... 101
42 Effect of K2 and C^ on average penetration ........... 102
43 P versus ac and PL ....................... 134
44 P versus ac and PL ....................... 135
45 P versus ac and PL ....................... 136
46 P versus ac and PL ...................... 137
47 P versus a and PL ....................... 138
48 ? versus ac and PL ....................... 139
49 P versus ac and PL ....................... 140
50 P versus ac and PL ....................... 141
51 P versus ac and P_ ....................... 142
52 P versus ac and PL ....................... 143
53 P versus C^ and P^ ....................... 144
54 P versus Ci and P ....................... 145
55 "P versus C^ and PL ....................... 146
56 P versus C. and PL ....................... 147
57 P versus C^ and PL ....................... 148
58 P versus C.^ and PL ....................... 149
59 P versus GJ and PT .................... ... 150
* JLi
60 P versus C^ and PL ....................... 151
61 P versus C^ and P ....................... 152
62 Pn versus ac and PT .... .................. 153
63 Pn versus ac and PL
64 Pn versus ac and P,
65 Pn versus ac and P.
66 Pn versus ac and P^
67 Pn versus ac and P^
68 Pn versus a_ and PT
t JL
viii
-------
FIGURES (continued)
Number Page
69 Pn versus ac and PT 160
70 Pn versus a and P, 161
71 Pn versus a and PT 162
C Li
72 Pn versus ac and P 163
Li
73 Pn versus ac and PL 164
74 Pn versus C. and PL 165
75 Pn versus C. and P, 166
76 Pn versus C. and P, 167
X lj
77 Pn versus C± and PL 168
78 Pn versus C^ and PL 169
79 Pn versus C* and PT 170
J_»
80 Pn versus C.^ and PL 171
81 Pn versus C± and P 172
82 Pn versus C. and PL 173
83 tf versus ac and PL 174
84 tf versus ac and PL 175
85 tf versus ac and PL 176
86 tf versus ac and PL 177
87 tf versus ac and PL 178
88 Pn versus ac and PL 179
89 tf versus a. and PT 180
I C Jj
90 tf versus Cj and P 181
91 tf versus C± and PL I82
92 tf versus C^ and PL 183
93 tf versus C^ and PL 184
94 tf versus C. and PL 185
95 tf versus C± and PL 186
96 tf versus C± and PL 187
97 Example of pressure-time trace for limiting pressure or time
controlled cleaning systems 189
98 Example of pressure-time trace for continuously cleaned systems . 189
ix
-------
FIGURES (continued)
Number Page
99 Estimation of average pressure drop by computer model and
simplified equations 194
100 Estimation of average pressure drop by computer model and
simplified equations 197
101 Estimation of average pressure drop by computer model and
simplified equations 198
-------
TABLES
Number Page
1 Required Data Inputs for Specific Model Application 6
2 Measured and Predicted Performance for Woven Glass Bags with
Coal Fly Ash 22
3 Variables Scheduled for Sensitivity Analysis Ik
4 Estimates of Maximum Aerodynamic Drag Forces During Reverse
Flow Cleaning 34
5 Instantaneous and Final Aerodynamic Drag During Reverse Flow
Cleaning, Fly Ash Filtration with Woven Glass Bags 37
6 Predicted and Measured K.2 Values for Various Dust/Fabric Combina-
tions, Size Properties and Operating Parameters 43
7 Input Parameters Selected for Baseline Tests 54
8 Effect of Variations in Input Parameters on System Performance . 56
9 Values of Key Parameters Used in Sensitivity Analyses 63
10 Data Inputs Required for Estimation of the Cleaning Parameters, ac 109
11 Figure Key for Estimating Major Filter Performance Parameters
Average Pressure Loss, (P~L) > Average Penetration (Pn), Time
Between Cleanings (tf) 112
12 Operating Data for Sample Field Problem 115
13 Corrected Input Parameters for Estimating Effect of K£ Variability
on Filter System Performance 117
14 Sensitivity Curve Selections for Estimating Effect of K2
Variability on Filter System Performance 118
15 Sensitivity Data Summary for Tables 16 through 22 124
16 Predicted System Performance with ac = 0.1 and C^ = 2.29 g/m3
as Fixed Inputs and V^ (m/min) and PL (N/m2) as Independent
Variables 125
17 Predicted System Performance with a = 0.1 and C^ = 6.87 g/m3
as Fixed Inputs and V^ (m/min) and PL (N/m2) as Independent
Variables 126
18 Predicted System Performance with ac = 0.1 and Ci = 2.29 g/m3
as Fixed Inputs and V± (m/min) and PL (N/m2) as Independent
Variables 127
xi
-------
TABLES (continued)
Number Page
19 Predicted System Performance with ac = 0.4 and C.^ = 2.29 g/m3
as Fixed Inputs and Vj (m/min) and PL (N/m2) as Independent
Variables 128
20 Predicted System Performance with ac = 0.4 and C± = 6.87 g/m3
as Fixed Inputs and V± (m/min) and PL (N/m2) as Independent
Variables 129
21 Predicted System Performance with ac = 0.4 and C± = 22.9 g/m3
as Fixed Inputs and Vt (m/min) and PL (N/m2) as Independent
Variables 130
22 Predicted System Performance with a = 1.0 and C^ = 6.87 g/m3
as Fixed Inputs and Vi (m/min) and PL (N/m2) as Independent
Variables 131
23 Predicted System Performance for Fixed and Variable Data Input
Combinations Not Specified in Tables 16 through 22 132
24 Values of Parameters Used to Generate Average Pressure Drop
Versus Velocity Curves 196
xii
-------
ACKNOWLEDGMENT
The authors express their most sincere appreciation to Dr. James H. Turner,
EPA Project Officer, for his advice, discerning technical reviews and encourage-
ment throughout the present and related modeling studies. We also wish to
acknowledge the capable support of Ms. Patrice A. Svetaka in the preparation of
the many graphs and tables developed for the sensitivity analyses.
xiii
-------
1.0 SUMMARY
Validation procedures for the original GCA filtration model have been
based mainly upon comparisons of resistance and emission levels predicted by
the model and the actual values measured at two field installations. The data
inputs for the model consisted of those parameters describing the collection
system operating parameters and certain properties of the dust and gas. In
the latter case, data indicating dust adhesion properties, specific resistance
coefficient for the dust, and unique relationships (and constants) for a
specified dust/fabric combination were determined in the field or laboratory
prior to testing the model.
Despite the apparent good agreement between predicted and actual values,
the data base for the model was still very limited. Many recognized variables
such as the number of individual compartments undergoing sequential cleaning,
the time intervals between successive cleaning cycles or the average collector
resistance could not be changed during the validation tests. Thus, there was
no opportunity to determine what impact the many possible permutations and
combinations of such variables might have had on filter performance. Therefore,
it is recommended that additional field and laboratory measurements be carried
out as soon as practicable to determine what variability must be expected in
field behavior or in the filtration properties of commercially available fabrics.
As a precursor activity, a sequence of sensitivity analyses were performed that
are intended to play a major role in defining the relative importance of many
-------
system variables and hence to provide useful guidelines for determining the
future direction of both field and laboratory investigations.
An immediate objective, however, was to generate supporting data for an
*
improved fabric filter model under development in a concurrent study.
The results of model sensitivity testing as presented in a series of
working tables and graphs are intended to assist the filtration model user
in several decision making processes. First, data inputs supplied by the filter
user and/or manufacturer can be screened to determine whether they are
compatible with practical field operations. Second, the degree of accuracy
(or margin of error) associated with variations in any data input can be
estimated beforehand. Third, in the event that an immediate (~ few hours)
estimate of a proposed filter system's performance is needed and computer
access is delayed by a day, the available sensitivity graphs and tables can
provide rough approximations.
In Section 2 of this report, the several mathematical relationships
among the variables defining overall filter system performance have been
reviewed. In addition, the capabilities of the former and revised models
and the unique treatment given fabric cleaning processes and their impact on
both particulate emissions and fabric pressure loss are also discussed.
Because of the critical roles played by dust dislodgement and adhesion
phenomena, several mechanisms involved in the separation of dust from woven
fabric were examined, Section 3, to determine their relative contributions.
It appeared that the magnitude of reverse flow velocities had minor impact on
*
Dennis, R. and H. A. Klemm. Fabric Filter Model, Format Change Vol I
Detailed Technical Report, Vol. II User's Guide. U.S. Environmental Protection
Agency, Industrial Environmental Research Laboratory, Research Triangle Park
North Carolina. EPA-600/7-79-043a, EPA-600/7-79-043b. February 1979.
-------
fabric cleaning insofar as aerodynamic drag effects or hoop stresses were
concerned. Modifications in the computation of the specific resistance
coefficient for the dust, K2, were also introduced by using a flow field concept
developed for higher porosity dust cakes; i.e., > 0.70.
The basic procedure for conducting the sensitivity tests described in
Section 4 was to first assume a set of input parameters satisfying the criteria
for proper filter model operation. Then the specific impact of different
data input combinations on performance (particulate emission rates and pressure
loss were noted for systems in which key variables were varied singly or in
pairs. Key parameters involved in these computer simulations were air-to-cloth
ratio, limiting pressure drop, inlet dust concentration, fabric cleaning para-
meter, number of compartments, time increment for iterations, compartment
cleaning time and reverse flow velocity. To keep the number of tests within
practical boundaries, provision was made for interpolations in many of the
model systems.
Because of the large number of graphs and tables involved, a special key
or index has been prepared so that premodeling assessments of estimated filter
system performance can be made. Given a fixed set of input parameters along
with the condition that one variable may undergo considerable change; e.g.,
filtration velocity, one can select the family of curves most closely bracketing
the input parameters and by appropriate interpolation (or extrapolation) make
rough estimates of system performance.
-------
2.0 INTRODUCTION
2.1 PROGRAM SCOPE
GCA/Technology Division has developed a mathematical model to describe
the performance of woven glass fabrics used for the filtration of fly ash
from coal burning combustion facilities.1"1* Because of the limited number of
such filter systems now used at major power plants, the preliminary validation
of modeling concepts was necessarily confined to a few systems. Therefore,
the Environmental Protection Agency requested that the model be tested under
many simulated field conditions to better assess its capabilities and, in
particular, to determine the overall strengths and weaknesses of the existing
model structure and methods of application.
The program discussed in this report describes the results of sensitivity
'"^
analyses whose major role has been to ascertain which variables have the
greatest impact upon model performance, and as a corollary, what degree of
precision and accuracy should be expected with presently available data and/or
field measurements. A given sensitivity test involves no more than allowing
a specified system variable to range within fixed percentiles of its estimated
average value when functioning as a basic data input to the model.
In Section 4, the results of the sensitivity tests are presented in
both graphical and tabular form. The model user is instructed as to how these
data can be used to assist him in assessing the importance of certain data
-------
inputs to the model and the degree of confidence to be placed in the model
output.
Supporting data to acquaint the reader with the basic operation of
the model and the unique relationships among the many variables entering into
the model are described in the following paragraphs. Typical field situations
are discussed where sensitivity analyses are expected to aid in the modelling
process.
At this time, the role of most variables constituting an input to the
fabric filter model can be identified with respect to how they affect the
performance of a single filter element; i.e., any part of the fabric surface
for which the approaching dust concentration, local drag, filtration velocity
and surface loading can be defined at a specified time.
These relationships, however, become very complex when the performance
of several filter elements operating in parallel and sequentially cleaned is
to be estimated. Although one can infer correctly that a higher K2 value will
lead to increased filter resistance unless the fabric is cleaned more frequently,
the precise effect of variations in K2 (the specific resistance coefficient
for the dust) can only be tested in the model. The same may be said with
respect to filtration velocity, number of compartments, duration and frequency
of cleaning, the adhesive characteristics of the dust, and other numerous
system variables.
Therefore, the insertion of several representative sets of trial
data into the model provides a very practical and inexpensive way (a) to
determine which variables exert the controlling influence and (b) to establish
permissible ranges for input data estimates. The required data inputs for a
specific model application are listed in Table 1.
-------
TABLE 1. REQUIRED DATA INPUTS FOR SPECIFIC MODEL APPLICATION
Item
Variable
Description
Comments
1 Number of compartments 6
2 Complete cleaning cycle 2i minutes
3 Cleaning time per compartment 4 minutes
4 Minimum time increment for 2 minutes
iterative computations^
5 Average face velocity (V) 0.824 m/min
6 Reverse flow velocity (V ) 0.0415 m/min
K
7 Inlet dust concentration (C^) 2.6 g/tn3
8 Temperature
412°K
Effective (clean) fabric drag 434 N'min/m2
(V
10 Specific resistance co- 0.76 N-mln/g-m
efficient (K2)
11 Residual dust loading (W.) 50 g/m2
K
12 Maximum allowable pressure 1160 N/tn'
13 Cleaned fabric area fraction 0.375
System design parameter
Time to sequentially clean six compartments
Indicates total compartment off-line time
Provides data points for maximum, minimum
and average resistance and penetration during
off-line period for on-line compartments
Based on total .flow and total fabric area
Weighted average velocity over total (4 min)
cleaning interval
Average baghouse temperature
Based on linear extrapolation of drag ver-
sus fabric loading measurements with
uniform dust deposit
Value determined at 0.61 m/min and 25°C
Refers to surface loading on freshly
cleaned area only
Fabric pressure loss at which cleaning
cycle is to be actuated
Fraction of cleaned surface exposed when
cleaning is initiated with a fabric load-
ing corresponding to a resistance of
1160 S/m2
Modeling of actual field performance of stoker-fired boilers at Nucla, Colorado, Colorado UTE
Electric Association.1-6
'Items 4 and 13 computed outside the program Co provide necessary data inputs. This
procedure used for original model (Reference 1) and also for sensitivity tests
described In this report.
-------
The sensitivity testing should make the model more versatile as well
as simplifying its use. From the point of view of state or federal control
personnel, the model should allow them to use the relevant system, fabric and
dust parameters to determine whether the filter system will provide acceptable
emissions at a resistance level within the working range of the induced or
forced draft fans or any supplemental gas moving capability.
If experienced filter design personnel are using the model, a detailed
series of sensitivity tests should enable the selection of operating and
cleaning parameters that afford the best compromise between allowable emission
levels and overall power requirements.
As stated previously, preliminary validations of the GCA filtration
model were based mainly upon comparisons of resistance and emission levels
predicted by the model and the actual values measured at two field installa-
tions. The data inputs for the model consisted of those parameters describing
the collection system operating parameters and certain properties of the dust
and gas. In the latter case, data indicating dust adhesion properties, specific
resistance coefficient for the dust, and unique relationships (and constants)
for a specified dust/fabric combination were determined in the field or lab-
oratory prior to testing the model.
Two important items were considered in developing the present program;
first, despite the apparent good agreement between predicted and actual values
for the Nucla, Colorado and Sunbury, Pennsylvania, filter installations, the
data bases for the model were still very limited. Second, the validation
process operates upon the specified input parameters without regard to whether
they represent optimum selections. For example, the number of individual
compartments undergoing sequential cleaning, the time intervals between
-------
successive cleaning cycles or the average collector resistance as specified
by the user or manufacturer may not have been optimum choices. Similarly,
by restricting average face velocities to less than 0.92 m/min it is usually
assumed by the designer that overall average system emissions will not exceed
permissible levels.
With respect to the first item, it is strongly recommended that
additional field and laboratory measurements be carried out as soon as
practicable to determine what variability must be expected in field behavior
or in the filtration properties of commercially available fabrics. The
sensitivity testing described in this report represents a logical precursor
activity to any formal laboratory or field experimentation for improving the
model in that many critical areas for future study can be readily identified.
If the input parameters for the filtration system are to be selected
for optimum performance in terms of minimum power requirements alone (excluding
emission values), Table 1, item 2, increased or more intense cleaning is
suggested as a solution provided that some estimate of bag service life versus
replacement cost is available. However, if strict adherence to emission
levels is to be maintained, the impact of oyercleaning on total emissions must
be ascertained. Here two possibilities may be examined as possible controlling
factors; the frequency and/or intensity of cleaning and the number of separate
compartments constituting the complete collection system.
Generally, increasing the number of compartments will reduce the
range between maximum and minimum effluent concentrations and, in many cases,
reduce the average effluent concentration. A similar reduction in the range
between maximum and minimum operating pressures will also take place.
-------
If the size and capital cost of fabric filters is reduced by
increasing the face velocity, one must ascertain whether the resultant increases
in operating costs due to higher resistance and more frequent fabric replace-
ment may override the capital cost advantage. Even when increased air-to-cloth
ratios appear to indicate an overall cost reduction, it is important to note
that effluent concentrations are strongly dependent on face velocity, increasing
approximately as the 2.2 power of velocity.
2.2 BACKGROUND FOR FILTRATION MODEL
2.2.1 Capabilities
The model that has been subjected to sensitivity testing is intended
for use with coal fly ash/glass fabric systems or with other dusts and fabrics
possessing similar physical properties. Within the above framework, the model
provides the following capabilities:
The model is adaptable to constant flow conditions.
The model can describe equally well a continuous or intermittent
cleaning regimen.
The present model can be used either with collapse and reverse
flow systems or mechanical shaking systems, but not in combina-
tion. It is not intended for use with pulse jet or high velocity
reverse jet cleaning systems.
The model can be used equally well with pressure or time-
controlled cleaning.
The model provides estimates of average and point values of
filter resistance for the selected set of operating conditions.
The model provides estimates of average and point values for
penetration and mass effluent concentration for the selected
set of operating conditions.
It is emphasized that in conjunction with the sensitivity analyses discussed
in this report, a separate study was conducted whose objective was to simplify
-------
the original model by performing supplementary calculations and data checking
routines within the program,7
2.2.2 Filter Drag Relationship
In this section, we have outlined briefly the basic structure and
development of the original GCA model and its preliminary trial runs. A very
detailed description of all aspects of the model is given in a recent EPA
report1 while various aspects of its design and applications appear in the
open literature.2 The central building block for the model is the classical
filter drag-fabric loading relationship that has been discussed extensively
in the literature.8
The equation:
S = SE + K2 W (1)
in which S is the total filter drag, S_ the effective residual drag, Ko the
b
specific resistance coefficient for the dust, and W the fabric dust loading
in mass per unit area describes the drag for any element of the filter for
which the dust loading is uniformly distributed and the local filtration ve-
locity is known.
Deposition of a uniformly distributed dust layer at a constant rate
upon an unused or completely cleaned fabric produces the characteristic
relationship shown in Curve 1, Figure 1. The origin for the curved section
of Curve 1 depicts the true residual drag, S_, at the minimal residual
K
loading, WR, which, for a cleaned glass fabric is approximately 50 grams/m2.
The effective residual drag, SE> which appears in Equation (1) is
usually employed to estimate filter drag or resistance properties. It is de-
termined by the linear extrapolation of Curve 1 to the zero fabric loading
level, Figure 1.
10
-------
oc
tU
Ul
O
DMCIIIPTHMi
MAXIMUM POSSIBLE CLEANING
HIGHLY EFFICIENT CLEANING
AVERAGE CLEANING RANGE
(MECHANICAL SHAKING)
AVERAGE CLEANING RANGE
COLLAPSE WITH REVERSE
FLOW
0 W,
Figure 1.
AVERAGE FABRIC LOADING, W
Typical drag versus Loading curves for filters with different degrees
of cleaning aad a maximum allowable level for terminal drag, Sj, and
terminal fabric loading, W .
-------
The slope of Curve 1; i.e., K2 = (S-S^/W, defines correctly the K2
value for the dust at the specified gas velocity and viscosity provided that
the dust is distributed uniformly over the filtration surface. In practice,
however, typical drag curves for steady-state field operation usually assume
the form of Curves 2 through 4 because (a) most fabric cleaning seldom reduces
the average filter loading by more than 50 percent and often as little as 10
percent and (b) dust is dislodged as slabs or flakes with the separation taking
place at the interface between the dust layer and the fabric surface. As a
result, unequal and changing flows take place through cleaned and uncleaned
o
regions so that a true K2 value cannot be determined directly.
The reason for this form of dust detachment is that there are far
fewer adhesive bonds between the dust surface and fabric yarns than there are
cohesive bonds within the dust cake itself. The result of this bonding pheno-
menon, which applies to the filters cleaned by reverse flow and/or mechanical
shaking, is that a cleaned fabric surface is always characterized by at least
two regions: (a) the actual cleaned area for which residual drag and dust
holdings are uniquely defined and (b) the uncleaned region from which no dust
is removed. Resumption of filtration upon filter surfaces such as described
above leads to the various curve forms shown in Figure 1.
The form of these curves is governed by several parallel flow paths
in which the approaching gas stream is apportioned according to the local
drag values at any specified time for cleaned and uncleaned surfaces:
(2)
\
12
-------
In Equation (2), S and A refer to overall drag and filter area,
respectively, a_ indicates any area fraction on the filter surface, J^ designates
the i1"" fractional area and its associated properties, _n is the total number of
filter areas making up the whole surface, and the subscripts £ and _u refer to
the cleaned and uncleaned filter areas, respectively.
The resultant pressure losses, P, at time t + At, for cleaned and un-
cleaned filter surfaces are equal and expressable by the following relationship:
P t+At = (SEV> t+At + t + At (3)
Equations (2) and (3) are the building blocks for the iteration
process from which local and average drag and resistance may be estimated for
any time and/or average filter dust loading during a filtration cycle. Two
important variables must be defined, however, before undertaking the computer
modeling, the cleaning parameter, a and the K2 value.
2.2.3 Fraction of Filter Surface Cleaned (a )
In the case of filter cleaning by bag collapse and reverse flow, the
amount of dust removed (expressed as fraction of the filter surface cleaned)
was related to the fabric dust loading immediately before cleaning (W ) by the
empirical equation:
a = 1.51 x 10~8 W2'52 (4)
c p
in which W is expressed in grams/tu2 . The term W has the special significance
P P
of identifying the fabric loading associated with the fabric pressure loss just
before initiating the cleaning action.
In the original modeling study,1 it was postulated that the gravity
field or artificially generated acceleration of the dust loading on the fabric
13
-------
surface produced tensile or shearing forces that constituted the principal
mechanism for dust dislodgement. When the magnitude of these forces exceeded
the local adhesion forces, it was expected that the cake would detach at the
dust/fabric interface. The net force in a gravity field is defined by Wg
whereas in a mechanically shaken system the force becomes Wa. In the latter
case, a is the acceleration of the dust and fabric produced by an essentially
horizontal motion of the driving shaker arms that can be calculated as:
a = 29.6f2 A (cm/sec2) (5)
In Equation (5), f refers to the shaking frequency (sec"1) and A to the
shaker arm amplitude (half stroke) in centimeters.
During the present study, further investigation was made of the
factors involved in estimating how much cleaning is achieved.
2.2.4 Specific Resistance Coefficient (K2)
The parameter 1^ has been shown to increase with the velocity of
dust deposition, presumably due to increased dust layer compaction and hence
lower cake porosity.1'8'9 For fly ash/glass fabric systems considered in the
original modeling study, Kg was adequately defined by the Equation:
K2 = l.SV1* (N-min/g-m) (6)
with V expressed in m/min. For broader applications, the general functional
form is applicable when it is desired to compute K£ for a different face
velocity and gas temperature (gas viscosity); i.e.,
K = [V actual \ /y actual \ (7)
2 \V measured} \v measured!
These relationships appeared satisfactory over the velocity range 0.3 to
1.5 m/min. The effect of velocity on K2 was also given further treatment in
the present study, along with a reappraisal of the possible merit of various
14
-------
theoretical procedures for calculating K2 from fundamental measurements.
2.3 DUST PENETRATION WITH WOVEN GLASS FABRICS
Laboratory and field measurements coupled with an analysis of the filtra-
tion process with twill-weave glass fabrics indicate that fly ash emissions
are due mainly to excessive gas flow through the low resistance paths presented
by unblocked pores, pinholes or damaged filter areas.
Furthermore, because few particles are removed from the gas fraction
passing through the pores (nearly 100 percent penetration for diameters
< 15 um) , the size distributions are nearly the same for upstream and down-
stream aerosols provided that size properties are measured in the immediate
vicinity of the dirty and cleaned filter faces.
The above findings suggest that mass emissions from glass fabrics should
depend upon both inlet concentration, C. and the unblocked pore area. The
latter variable, which is governed by the amount of dust deposited on the fil-
ter following resumption of filtration, may cease to be important once a
substantial dust layer has reaccumulated. In the absence of visible defects,
the relationships between outlet concentration, C , and fabric dust loading
and velocity appear as shown in Figure 2. The latter effect suggests
strongly that seeking to reduce collector size by increasing the face velocity
(air-to-cloth ratio) may lead to unacceptably high emission levels.
Another contributor to outlet loading is the low level, steady state,
slough-off agglomerated dust from the downstream region of the dust deposit
as the result of reentrainment augmented by mechanical vibrations. A safe
estimate of this residual concentration (CR) places it as not greater than a
0.5 mg/m3 contributor to the outlet concentration.
15
-------
10
r- 3-0
TEST
98
AVERAGE
96
INLET CONC. (o/m3) FACE VEJ.OCITYtm/min.1
8.09 0.39
7.01
5.37
0.61
1.52
4 D
97
4.60
3.35
NOTES-SOLID LINES ARE CURVES PREDICTED BY MODEL.
SYMBOLS REPRESENT ACTUAL DATA POINTS
K>
"20 40 so ~eo Too
FABRIC LOADING (W), g/m2
140
Figure 2. Predicted and observed outlet concentre Lions for
bench scale tests. GCA fly ash and Svm>ury fabric.1
16
-------
The curves shown in Figure 2 represent the best mathematical fits to
the experimental data. The outlet concentration, Co, is defined by the local
penetration level (Pn), the inlet dust concentration (C±), and the previously
cited resicual concentration, CR = 0.5 mg/m3:
C0 = Pn C± + CR (8)
The actual equations and their applications in the filtration model are
given in Appendix A. For present purposes, it suffices to indicate that
substitution of the necessary relationships into the general expression:
Pn or C0 = f (+, C± W, V,. CR) (9)
determines penetration or effluent concentration as a function of <}>> a param-
eter characterizing the dust/fabric combination of interest; constant inlet
and residual concentrations, C^ and CR, respectively; and the time and position
dependent variables; i.e., local face velocity, V, and local fabric dust load-
ing, W. It is again emphasized that because direct leakage is responsible for
nearly all of the particulate emissions, the size properties of typical coal
fly ashes do not enter directly into the estimation of dust penetration.
The total (and average) filter system penetration, Pn, at some time, t,
for a system consisting of I compartments and J areal subdivisions per bag is
determined by successive iterations in accordance with the general summation:
(10)
Coal fly ash MMD = 5 to 20 urn, ag = 2.5 to 3.5 depending upon the firing method.
17
-------
2.4 MODEL APPLICATIONS
The basic operations performed within the filtration model are indicated
schematically in Figure 3. The approaching aerosol is distributed among I
separate compartments and j; separate filtration regions on each bag. It is
assumed for simplification that the performance of each compartment is repre-
sented by any single bag within the compartment and that there are no concen-
tration gradients for C^ and W in the system. The model describes the overall
effect of many parallel flow paths through fabric surface elements bearing
different dust loadings. The local performance of each element is defined by
the working equations presented earlier in this paper.
The data inputs required to model the Nucla filtration process have been
given in Table 1. The actual numerical values for the filter system6 have
been listed in the "Description" column to show the approximate magnitude for
these variables in field applications.
Items 1 through 3 are based upon system design or operating data provided
by the manufacturer. The 2-minute minimal time interval, Item 4, was chosen
by the model user so that successive, stepwise iterations would always indicate
maximum, minimum, and average system resistance while any one compartment was
off-line for cleaning.
Average face and average reverse flow velocities, Items 5 and 6, respec-
tively, are operating parameters usually chosen by the filter manufacturer.
Inlet dust concentration and average filtration temperature, Items 6 and
7, are determined mainly by the combustion process and the type of fuel. The
estimates of So, K2 and WR, Items 9 through 11, respectively, are best deter-
mined by direct measurement if not already defined.
18
-------
VO
C|
C|2
W.,
w,
12
w,
'II
C2)
C22
C2J
W.
21
22
W.
2J
'2J
W
rIJ
'31
32* '
"IJ
Figure 3. System breakdown for I bags and J areas per bag.
-------
From the perspective of the model user, the only data inputs involving
decision-making (or supplementary calculations) are Items 4 and 13.
Item 4 is easily satisfied; i.e., data points for maximum, minimum and
average resistance and penetration for on-line compartments during fabric
cleaning, if the minimum time increment for output data points is half that
specified as the cleaning time per compartment. However, Item 4 will be
estimated by the program in the new model.
In the case of Item 13, the original model required an outside calculation
although it is planned that the revised model will incorporate the computa-
tion of ac within the model. The original process required that the uniformly
distributed fabric dust holding, W , corresponding to the assigned pressure
threshold at which cleaning is to be initiated (Column 12) be computed from
Items 5, 9, 10 and 12 as indicated below:
Wp = (PL/V - SE)K2 (11)
Then by means of Equation (2-8) the value of ac can be determined:
ac = 1.51 x 10-8 Wp2'52 (12)
In the case of the Nucla operation, the availability of performance data
allowed a preliminary evaluation of the model's capability. The superposition
of predicted and observed system resistance curves, Figure 4, shows fairly
good agreement although the model does predict a somewhat larger interval,
164 versus 126 minutes, between cleaning cycles. Table 2 shows that average
emissions during the cleaning cycles were about eight times those observed when
all Nucla compartments were on-line.
20
-------
2.0
hJ
O
UJ
oc
O
-------
TABLE 2. MEASURED AND PREDICTED PERFORMANCE FOR WOVEN GLASS
BAGS WITH COAL FLY ASH
Percent penetration
Measured
Predicted
Nucla, Colorado6
0.21
0.19
(1.52)f
Resistance-N/m2
Measured
Predicted
Nucla, Colorado6
Average, cleaning and filtering
During cleaning only
Maximum just before cleaning
Minimum just after cleaning
1030
1700
1160
850
972
1520
1160
760
Averaged over cleaning and filtering cycles.
During cleaning cycle only.
22
-------
2.5 SUMMATION
The preceding discussions have provided the relevant background on the
basic structure of the original filtration model and its intended application.
In the program results discussed in this report, a primary objective was to
establish an approximate ordering of what are considered to be the principal
variables in the filtration modeling process. The most important variables
are those for which a fixed error in estimation produces the greatest deviation
in the estimate of key output parameters such as dust penetration and filter
resistance.
A second objective was to ascertain whether the physical processes origi-
nally presumed to describe filtration and fabric cleaning phenomena are con-
sistent with experimental findings and if not, how to better define the filtra-
tion process.
A third objective was to reexamine certain parameters to determine which
might be evaluated from fundamental measurements, for example K£, and what
degree of accuracy (or error) might result if these parameters were calculated
rather than measured directly.
Table 3 provides a tentative listing without regard to priority of
those variables to be studied in the sensitivity analyses along with an indi-
cation of their expected impact areas. Although not stated explicitly in
Table 3, it is presumed that those variables that influence the cleaning
frequency may also affect the intensity of cleaning where the latter item
appears as an option; e.g., mechanical shaking with shaking frequency and
amplitude as the intensity factors.
It was planned that the description, method of calculation and/or method
of measurement of the varibles entering into the sensitivity analyses would
23
-------
TABLE 3. VARIABLES SCHEDULED FOR SENSITIVITY ANALYSIS
Variable
Expected impact areas
1. Filtration Velocity
2. Cleaning intensity and
frequency
3. Adhesion, dust cake
4. Specific Resistance
coefficient
5. Number of compartments
6. Length of filtration
cycle
7. Linear versus non-
linear model
8. Rear face slough off
9. Inlet concentration
10. To be identified
(if appropriate)
Emission levels
Cleaning frequency
Emission levels
Resistance
Cleaned area fraction, a
Emission level
Resistance
Cleaning frequency
Emission level
Emission level
Resistance range
Emission level
Resistance
Emission level
Resistance
Emission level
Emission level
Cleaning frequency
24
-------
be examined on an individual basis prior to assessing their roles in the fabric
filtration model. This step was intended to provide a rough estimate of the
trial ranges for system variables when tested in the model. The first section
of this report deals specifically with variables that are either difficult to
measure or perhaps are only partial descriptors of the true physical processes
taking place during filtration or fabric cleaning.
25
-------
3.0 CRITIQUE OF MAJOR SYSTEM VARIABLES, THEORY AND PRACTICE
3.1 DUST DISLODGEMENT AND ADHESION
3.1.1 Concepts Used in the Original Model
No practical forecast of filter system performance can be made until the
relationship between the method of fabric cleaning (which includes type,
frequency, and intensity) and the amount and location of dust removal has
been established. It was clearly demonstrated in recent studies1'10 that
the dust dislodgement process for woven glass fabrics cleaned either by mechan-
ical shaking or bag collapse with reverse air flow consisted of the detachment
of dust slabs or flakes with the separation occurring at the dust/fabric inter-
face. Furthermore, the cleaned fabric regions immediately below the dislodged
layers were shown to display nearly constant residual dust holdings and resis-
tance properties for many dust/fabric combinations.
Since the fabric loading and resistance properties are readily deter-
minable for both cleaned and uncleaned regions of a fabric, it is only required
that the fraction of cleaned area be known in order to compute the overall
filter performance. The above approach has been discussed in detail in prior
reports and in the open literature.1'2 At present, no reliable theoretical
approaches are available to determine how much cleaned fabric area, ac, is
exposed for various cleaning conditions with any dust/fabric combination.
Limited, semi-empirical solutions to this problem have been described which
26
-------
*
have proven effective for various fly ashes and woven glass fabrics. The
empirical formulas:
ac = 1.51 x 1CT8 W2'52 (13)
and
ac = 2.33 x l(T8 (f2 AW)2-52 (14)
deriving from Figure 5 appeared to provide reasonable estimates of ac in
terms of the average fabric loading, W, just before cleaning for a collapse
and reverse flow system, Equation (13), and a mechanically shaken system,
Equation (14). In the latter instance, the terms f and A, respectively,
refer to the frequency and amplitude (half stroke) of the shaking action.
Although dust separation from a fabric surface can be explained rationally
by several comparatively simple physical processes, more experimentation is
required to develop highly accurate cleaning descriptors. In prior reports,
it was indicated that a dust layer should detach from the fabric surface when
the tensile force exerted at the dust cake fabric interface exceeds the ad-
hesive force bonding the dust layer to the fabric. Because there are fewer
contacts between particles and fibers at the dust cake fabric interface than
there are particle-to-particle contacts within the cake per se, the interface
region with the weaker bonding constitutes the boundary for dust layer sepa-
ration. A graphic image of this separation phenomenon is shown in Figure 6,
where an interior light source within a real filter bag reveals the sharp line
of demarcation between the cleaned and uncleaned zones.
3/1 twill weave, 9.2 oz/yd2, Teflon coating - Menardi Southern
3/1 twill weave, 10.5 oz/yd2, graphite-silicone coating - W. W. Criswell.
27
-------
INTERFACIAL ADHESIVE FORCE, Ffl ,dyi*«/cm2
V , ^ K>2
" i
OINUCLA
tO 2 SUNBURY
03 BOW
. O.A.D
t-
o
Ul
a:
oo
o
Ul
Ul
u
10"
-6 W2-52
GCA SINGLE
BAG TESTS
i I
IOZ
u
a
Ul
_l
u
n O
D
A
DESCRIPTION
6CA LABORATORY
TESTS, SINGLE BAG
O I NUCLA, FIELD
<>2 SUNBURY, FIELD
1
10s
FABRIC LOADING ,W,Q/«|2
(a)
3 I03^ 2
AERODYNAMIC DRAG/FORCE,
(b)
Figure 5. Estimated cleaned area fraction, ac, based upon dust removal by (a) gravity
and/or shaking acceleration forces or (b) aerodynamic drag forces caused by
reverse air flow. Coal fly ash and twill weaves glass fabrics.
-------
Figure 6.
Cleaned bag
fluorescent
surface
tube.
with inside illumination bv
29
-------
Preliminary estimates of the intracake cohesive forces were determined
from the relationship:
Fa = 102 dp (dynes) (15)
where dp is the particle diameter in centimeters. For a monodisperse system
of 10 um particles, use of Equation (15) predicts a cohesive or tensile
strength of 105 dynes/cm2. If one assumes a typical polydisperse fly ash size
distribution; e.g., MMD = 6.4 ym and erg = 3.3, the number of particle-to
particle contacts increase significantly such that the computed cake strength
increases to about 106 dynes/cm2.
At the present time, only very rough estimates can be made of the adhesive
forces at the dust/fabric interface. In the case of collapse-reverse flow
systems, where tensile and shearing forces generated in a gravity field were
considered to be the major separating force, interfacial adhesive forces were
estimated to range from 50 to 100 dynes/cm2. The actual separating or tensile
force exerted by a 0.1 cm thick dust cake suspended from a horizontally aligned
fabric surface, for example, is roughly 100 dynes/cm2. If the interfacial
tensile stress is produced by mechanical shaking, the force field is now de-
fined by the local cake acceleration, usually in the range of 4 to 5 g's, and
calculable from the amplitude and frequency of the shaker arm. Since the
shaker and gravity acceleration vectors usually act perpendicularly to each
other, the absolute value for the resultant vector may be defined by the shaker
acceleration alone when a is > 4 g.
I*
The preceding discussion reflects the status of the dust removal aspects
of the modeling program at the beginning of the present study. Despite the
point scatter, Figure 5a indicated a significant correlation between
30
-------
cleaned area fraction, ac, and the fabric loading, W, at the inception of
cleaning. The same level of correlation was also observed with respect to the
cleaning force, Fc, associated with the fabric loading and its resultant
acceleration.
The fact that Point 3, which derives from tests on a mechanically shaken
system, falls on the curve appears to justify the concept that acceleration
forces, either artificially or gravity generated, are at least major factors
in causing dust dislodgement by some combination of tension and/or shearing
forces. It was assumed in the above analyses that tensile and shear forces of
equal magnitude would exert the same cleaning effect.
It is also pointed out in prior studies that the apparent adhesive force
levels suggested by Figure 5a reflect the interfacial bond strength after
the fabric has undergone several flexings (repeated cleanings). Therefore,
although the net bonding strength is difficult to predict, it appears reason-
able to assume that it might be appreciably lower than that exhibited prior to
initial flexure (at least 40 percent according to previous studies).1
It was also recognized that the rapidity of bag collapse (and hence rate
of flexure) and the ultimate radius of curvature of bag surface elements
might also be instrumental in the cake loosening process. The reverse air
velocity alone was not considered a major factor in cake dislodgement insofar
as aerodynamic drag was considered. For example, the reverse air velocities
of 0.15, 0.33, and 0.43 actual m/rain, respectively for GCA, Nucla, and Sunbury
tests, had no apparent effect on the amount of cleaning. The basis for the
above statement was the fact that data points from the above sources fell on
the regression line without any velocity adjustments.
31
-------
More recently, however, a significant improvement in reverse air cleaning
has been reported when the reverse flow rate was increased by a factor of
2.5.11 Therefore, the potential effects of both cleaning velocity and pressure
gradient across the fabric were reexamined to determine whether the original
relationships proposed for estimating the degree of fabric cleaning (a ); i.e.,
Equations (13) and (14), require modification.
3.1.2 Dust Dislodgement Factors - Reappraisal
As stated previously, gravity and/or artificially generated acceleration
forces were considered to be the main dust dislodging forces wherein tensile
or shear stresses exerted at the dust/fabric interface were assumed to over-
come the adhesive bonds. Without attempting to quantify the following factors,
it was also indicated that the rate and degree of fabric (and dust cake)
flexing or bending represented additional mechanisms that could lead to
severance of adhesive bonds. Electric charge and humidity were also presumed
to influence the strength of the dust cake itself via their effects on cohesive
bonds and the capability of the dust cake to detach itself from the fabric
surface. Although reverse flow velocity was expected to influence dust sepa-
ration, limited measurements appeared to place it as a secondary factor with
respect to the original data sources. In the foregoing discussion, the role
of reverse flow velocity has been reexamined for those filtration systems
evaluated in the design and development of the original filtration model.
3.1-3 Aerodynamic Drag
During the period of reverse air flow, the resulting aerodynamic drag
produces a tensile force that must be matched at the dust-fabric interface
if the dust layer is to be retained. Ordinarily, no provisions are made to
32
-------
measure the actual pressure drop across a filter during the reverse flow inter-
val. Its initial magnitude can be estimated, however, from the observed pres-
sure drop through the fabric as a function of the system face velocity and the
fabric dust loading immediately before cleaning. In terms of the system drag
parameter, the drag during reverse flow, Sr, is computed as:
Sr = SEf (Vr/Vf) + K2f (Vr/Vf)^ Wf (16)
where the subscripts r and f refer to the reverse flow and normal filtration
velocities, respectively. The resultant aerodynamic drag force per unit area
(or simply pressure drop) then becomes:
Fd = Ir Vr (17)
presuming that the reverse flow and filtration air temperature are the same.
Graphing of the data appearing in Table 4 gives a curve form very similar
to that reported earlier for the fractional cleaning, a , versus fabric loading
relationship, W (and the corresponding gravity separating force per unit area
W.g) Figure 5b. This is to be expected because with a constant reverse flow
velocity any calculated aerodynamic drag force must vary linearly with fabric
dust loading (or cake thickness). However, if the drag force is considered
to be the predominant dust separating mechanism, one should also assume that
any dust not dislodged from the filter is retained by an adhesive force at
least as strong as the opposing drag force. Additionally, it would appear
that dust losses via the avenues of gravity or mechanical shaking forces would
be relatively unimportant compared to the drag effects since the former forces
are calculated to be about 10 times smaller.
The above concepts, however, appear to be contradicted by the mechanical
shaking process. Although shaking systems are not accompanied by reverse
33
-------
TABLE 4. ESTIMATES OF MAXIMUM AERODYNAMIC DRAG FORCES DURING
REVERSE FLOW CLEANING
Run No.
P-2-1
P-2-2
P-2-3
P-2-4
P-3§
P-4-11"
P-4-2
P-4-3
P-4-4
P-4-5
P-5-1
P-5-2
P-5-3
P-5-4
P-5-5
P-5-6
Fabric Fabric
loading at loading
beginning of before
run cleaning
(g/m2) (g/m2)
113
327
387
498
-
85.9
274
382
476
549
550
501
537
554
553
559
937
422
545
723
735
696
429
536
631
704
705
656
692
709
708
714
Fabric
loading
after
cleaning
(g/m2)
345
387
498
5.98
.-
274
382
476
549
550
501
537
554
553
559
579
Cleaned
area
fraction
(ac)
0.67
0.09
0.09
0.19
0.19
0.65
0.12
0.12
0.14
0.23
0.32
0.20
0.21
0.24
0.23
0.20
Aerodynamic
dragt
(dynes /cm2)
1,040
530
640
820
830
790
550
630
720
800
800
750
790
810
810
815
Pilot scale tests on a 10 ft x 4 in. woven glass bag (Menardi-
Southem).
Run numbers appearing in Reference 1 (EPA-600/7-77-084).
TBased on reverse flow velocity of 0.15 m/min.
Average of 19 successive filtration cycles.
34
-------
flow, significant dust dislodgement is attainable even when the acceleration
forces are 10 times lower than the estimated aerodynamic drag forces. For
example, the removal of coal fly ash from sateen weave cotton bags indicated
ac values in the 50 percent range for an estimated acceleration force of only
250 dynes/cm2. It should be noted that a bag undergoes many shakes, 50 to
250, to accomplish the observed cleaning levels. However, after a finite
number of shakes (or repeated bag collapses in the case of reverse cleaning
systems), the dust removal appears to approach a limiting value based on the
acceleration imparted to the fabric and its dust holding.
A second inconsistency is noted when filter systems using different re-
verse flow velocities are compared on the basis of dust separation by aero-
dynamic drag.1'11 If one assumes that the reverse flow velocities reported
for Nucla and Sunbury tests were correct, the prior relationships between
laboratory pilot tests and real measurements, Figure 5a, appear to break
down. In the following discussion, possible reasons for the lack of corre-
lation are explored.
3.1.4 Instantaneous and Average Aerodynamic Drag
On the assumption that dust cake adhesive forces over the fabric surface
will follow some statistical distribution, the application of the aerodynamic
drag force calculated for the undisturbed dust cake is expected to dislodge
any surface element of dust for which the local adhesive force is exceeded.
In actual practice, the process of bag collapse itself invariably leads to
appreciable spalling off of dust as well as producing many cracks and defects
in the cake. At the same time, it must be presumed that a large fraction of
the underlying adhesive bonds are severed.
35
-------
Once a cleaned fabric area has been exposed, the flow now redistributes
itself such that a much larger fraction passes through the lower resistance
path. The result is an immediate reduction in overall air flow resistance
with a corresponding decrease in the drag force. How this phenomena affects
any subsequent cleaning action is summarized in Table 5. In the case of
Run No. P-2-1, the dust was uniformly distributed over the fabric prior to
cleaning with no flexing of the dust laden surface until the first bag collapse.
Upon resumption of filtration, Run No. P-2-2, most of the dust deposited on
the "just cleaned region" because of its low resistance to air flow. Therefore,
the filter drag, S, only increases about 7 percent for the original uncleaned
region, (695 to 740 N min/m3) wheras it is nearly doubled for the just
cleaned area (49.3 to 167 N min/m3). The key factor in this analysis is that
once a small fraction of dust has dislodged, the aerodynamic drag forces appear
to diminish to the general level of the tensile and shear forces attributed
to gravity and mechanical shake cleaning.
It is important to note that the estimated drag forces before cleaning,
Column 5, Table 5, were calculated on the assumption that the cake had not
been disturbed by the collapsing motion of the bag following compartment iso-
lation and preceding the initiation of reverse flow. Therefore, a high esti-
mate is suspected in Column 5, because no adjustment has been made for the
pressure reduction due to the increased permeability of the damaged cake. One
conclusion drawn from the above analysis is that the severance of adhesive
bonds by the flexing and related geometric perturbations of the cake induce
cake dislodgement due to gravity effects alone without the need for supporting
aerodynamic drag forces. In effect, any moderate "push" exerted by a fairly
36
-------
TABLE 5. INSTANTANEOUS AND FINAL AERODYNAMIC DRAG DURING REVERSE FLOW
CLEANING, FLY ASH FILTRATION WITH WOVEN GLASS BAGS
Aerodynamic drag force
Fabric loading Area (dynes/cm2)
-. Previous fabric before cleaning fraction
cleanings (g/m2) cleaned Before dust After dust
loss''' lossl-
P-2-1
P-2-2
P-2-3
0
1
2
937
422
545
0.61
0.09
0.10
1,040
530
640
106
240
325
Each flexing reduces adhesive bonding of any residual dust.
Dust cake assumed to be completely intact.
TCleaned area lowers overall filter resistance. Drag based upon new distri-
bution of fabric loading for Run Nos. P-2-2 and P-2-3.
37
-------
wide velocity range may result in essentially the same dust removal. As noted
in the next section, however, there are other velocity effects that may play
secondary roles in dust dislodgement.
3.1.5 Effect of Hoop Stresses on Cake Structure
In view of the several factors that may alter the contours of a collapsed
bag before and during the reverse flow phase; e.g., bag tension, fabric stiff-
ness, assymetry due to seam effects, anticollapse rings and pressure gradient,
it appears extremely difficult to make any rigid quantitative estimates of
their combined impact on dust cake loosening.
When a bag without support rings (and under 50 to 70 Ibs tension) reaches
the collapsed state, its external contour at some cross section as seen from
an axial perspective might appear as indicated schematically in Figure 7.
Tensioning of the bag can prevent total flattening under the influence of the
pressure gradient, PC - P^, from outside (clean) to inside (dirty) produced
by the reverse flow. As with a pressure vessel, the hoop stress, st, acting
over the wall cross section t x 1 where t is the dust cake thickness and 1
the bag length is computed as follows:
st = Pdfe/2t (16)
where P is the pressure gradient and dD is the diameter that characterizes the
local radius of curvature of the bag. To fit the convoluted depressed surfaces
shown in Figure 7, it would appear that the local "diameter" should be roughly
one-half that for the fully inflated bag; i.e., roughly db/2. Since the pres-
sure is a linear function of both cake thickness and reverse flow velocity, the
hoop stress also can be expressed in the form:
st = 6 Vrdb/2 (17)
38
-------
-A
SECTION A-A* x 4
T
INSIDE DUST
LAYER
A'
t
IELEMENT A
AIR
CAKE THICKNESS (t)
LOCAL RADIUS
OF CURVATURE
DUST CAKE
Figure 7. Schematic, hoop stressing during reverse flow for depressed
region, collapsed bag with clean side (external) pressure
exceeding dirty side (internal) pressure, Pc > Pd.
39
-------
which simply states that sfc depends only upon the reverse flow velocity, Vr,
the local radius of curvature, d£/2 and a constant, B, that is uniquely related
to the dust cake physical properties. For the fly ash used in the tests
summarized in Table 4, the numerical value for 6 is approximately 1.4 * 10 .
Thus, for a reverse flow velocity of 0.15 m/min and an assumed "diameter" of
curvature of 5 cm for the depressed region of the bag, the estimated hoop stress
would be 5.25 x 103 dynes/cm2. Because the latter value is considerably lower
than the estimated adhesive or tensile strength for the undisturbed dust cake
(~106 dynes/cm2), it does not appear that significant surface cracking or
checking should have arisen during the P-2 test series as a result of hoop
stress. Thus, the flexing of the cake prior to initiation of reverse flow is
suspected to be the major cause of surface "checking" or cracking, in which
either tensile or shear forces resulting from compression could be the failure
mechanism.
3.2 SPECIFIC RESISTANCE COEFFICIENT
It was emphasized in prior modeling studies that the specific resis-
tance coefficient, K2, should be determined by direct measurement, at least
until more dependable prediction methods become available. At the same
time, it was pointed out that if reliable sizing data were available for the
field aerosols (such as the mass median diameter and the geometric standard
deviation) in conjunction with good estimates of discrete particle density,
pp, and dust cake porosity, e, good (+50 percent) approximations of K2 should
be attainable. Although the above level of accuracy is not sufficient to
determine operating parameters for a filter system, it does alert the designer
to the probable degree of difficulty to be expected in filtering a given
dust. It is emphasized that a +50 percent precision level is attainable only
40
-------
when one computes the specific surface parameter, SQ, for the distribution of
sizes making up the dust cake. Then K2 for various fly ashes may be estimated
from the Carman-Kozeny relationship:
K2 = k'y S0 <19>
PP
where p is the bulk density of the cake and p the density of the discrete
particles.
In a recent paper by Rudnick and First,12 the authors indicated that use
of the Happel "free surface" flow field model provides a better estimate of dust
cake K£ values than the Kozeny-Carman equation when cake porosities exceed 0.7.
A graphical presentation of their calculations, Figure 8, shows that K2
values are actually much larger than those predicted by the Carmen-Kozeny
method when porosity values are greater than 0.8. Therefore, earlier data
showing measured and predicted K£ values were updated with respect to the
Happel concept13; as shown in Table 6. For those fly ash porosity values
within the 0.42 to 0.59 range, both predictive methods agree within 5 to 7
percent. In the case of granite dust with an estimated porosity of 0.68, the
Happel relationship predicts only a moderate, "20 percent, increase in K2.
However, a nearly 1.8 times increase in predicted K2 values results when the
porosity increases to 0.84. Although the Happel model has the broader appli-
cation, its predictive capabilities are still strongly dependent upon the
accuracy with which the porosity, bulk density and discrete particle density
41
-------
3.0 r
"T""""" i
2.5
M
oc
2.0
ui
hi
1.5
2 1.0 1
0.5 h
0.2
0.4
0.6
POROSITY,
0.8
i i i ii ii i
IX)
Figure 8. Ratio of Ka values predicted by Happel and Kozeny-Carman
equations versus dust cake porosity.
42
-------
TABLE 6. PREDICTED AND MEASURED K2 VALUES FOR VARIOUS DUST/FABRIC COMBINATIONS,
SIZE PROPERTIES AND OPERATING PARAMETERS
Dust parameters
Test dust
Coal fly ash
Public Service
Co., NH (GCA)
Coal fly ash
Public Service
Co., NH
Coal fly ash
Detroit Edison
(EPA)
Coal fly ash
Public Service
Co., NH (GCA)
Coal fly ash
Nucla, CO
Lignite fly ash
Texas Power
and Light
MMD*
(urn)
4.17(1)
5.0 (M)
6.38(1)
3.8 (I)
3.2 (M)
2.42(M)
11.3(1)
8.85(1)
8.85(1)
8.85(1)
og
2.44
2.13
3.28
3.28
1.8
1.77
3.55
2.5
2.5
2.78
Particle
density
(g/cm3)
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.4
2.4
2.4
(cm~
4.73 x
2.58 x
3.55 x
9.94 x
4.78 x
8.49 x
1.28 x
1.06 x
1.06 x
1.30 x
2)
108
108
108
108
10s
108
108
108
108
10*
Cake
porosity
(E)
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.46
0.42
0.46
Filtration
parameters nUer fabr±c
Velocity
(m/min)
0.915
0.915
0.605
0.823
0.915
0.915
0.851
0.605
0.605
0.605
Temp
21 Class,
3/1 twill
21 Napped cotton
sateen weave
21 Glass,
3/1 twill
138 Glass,
3/1 twill
21 Napped cotton,
sateen weave
21 Napped cotton,
sateen weave
124 Glass,
3/1 twill
21 Glass,
3/1 twill
21 Glass,
3/1 twill
21 Glass,
3/1 twill
Measured K-
ambient " ?«J^"{ K*
conditions @ 21 ^
oiO __^
21uc
(0.605 m/min) K/C
1.85 5.72
1.85 3.74
1.40 5.14
4.45 14.4
1.00 6.19
1.77 11.0
0.75 1.84
1.34 3.67
1.34t 5.16
1.34 4.49
H*
6.12
4.00
5.50
15.9
6.63
11.8
1.97
3.60
4.90*
4.40
Kp rat lo
predicted (H)
(measured)
3.31
2.14
3.93
3.46
6.63
6.66
2.63
2.69
3.66
3.28
(continued)
-------
TABLE 6 (continued)
Dust parameters
Test dust
Granite dust 9
9
9
8
9
9
1
Talc 2
2
2
vktn*
.21(1)
.21(1)
.21(1)
.1 (I)
.84(1)
.21(1)
.23(1)
.77(1)
.77 I)
.77(1)
ag
4.83
4.55
4.05
3.88
4.32
4.83
2.38
2.9
2.9
2.9
Particle g 2
density . °-j,
, , a( (cm O
(g/cm3)
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
5.05 *
4.13 x
2.88 x
3.24 x
3.44 x
5.05 x
5.10 x
1.51 x
1.51 x
1.51 *
10°
108
108
108
10e
10B
109
109
109
109
Cake
porosity
(E)
0.68
0.68
0.68
0.68
C.68
0.60
0.68
0.84
0.82
0.73
Filtration
parameters
Velocity
(m/min)
0.605
0.605
0.605
0.605
0.605
0.605
0.605
0.915
0.915
0.915
Temp
21
21
21
21
21
21
21
21
21
21
Measured K2
ambient
Filter fabric conditions
Predicted K2 Kj ratio
@ 21°C predicted (H)
210C
(0.605 m/min) K/Cf
Glass,
3/1 twill
Glass ,
3/1 twill
Glass,
3/1 twill
Glass ,
3/1 twill
Glass,
3/1 twill
Glass,
3/1 twill
Glass,
3/1 twill
Napped cotton,
sateen weave
Napped cotton,
sateen weave
Napped cotton,
sateen weave
1.38
1.38
1.38
1.38
1.38
1.38*
12.3
4.71*
4.71*
4.71*
2.64
2.15
1.50
1.70
1.69
5.28
26.7
2.35
2.72
5.78
4. (measured)
H
3.11
2.54
1.77
2.01
2.00
6.23*
31.5
4.00*
4.35*
7.40*
2.26
1.84
1.28
1.46
1.45
4.45
2.54
0.85
0.92
1.57
(I) refers to cascade impactor sizing; (M) refers to microscope
j.
K/C » Kozeny-Cannan equation; H » Happel equation.
^
fNot used for regression line statistics.
Note: Based on original data from Reference
sizing (light field, oil immersion).
-------
can be measured. In the following discussion, their accuracy levels are
examined with respect to their impact upon the final estimation of K2.
Given the situation where porosity is determined by an independent esti-
mate of void volume (in which no measurement of discrete particle density is
required), numerical values for the porosity function (1 -e )/e3 vary with
porosity e as shown in Figure 9. As indicated in a prior report,1 a 10
percent error in the estimation of e can lead to a 50 percent error in the
porosity factor and therefore a 50 percent error in the determination of K2
by the Kozeny-Carman equation.
When the porosity is calculated from bulk density, p, and discrete par-
ticle density, p , measurements, it is again shown that relatively small
errors in estimating either term may lead to large errors in K2 via the im-
pact of the porosity function, Figure 10. For example, if the true bulk
density were 1.1 rather than 1.0 g/cc, the error in K2 estimation would be
50 percent for a discrete particle density of 2.0 g/cc. A similar K2 error
results when a 10 percent error is made in the estimation of discrete particle
density. Since K2 also varies inversely with the square of the particle
diameter, dsp, characterizing specific surface; i.e., -^2" ~ f (so^2» ifc is
asp
also apparent that any error in size measurement will have a significant effect
on K2 estimation. Although the discussion so far has dealt with the Kozeny-
Carman equation, use of the Happel theory as discussed by Rudnick and First
will lead to essentially the same error ranges for K2. In the generalized
notation for calculating K2:
_ 18 u R R_
2 " P G " T c (20)
45
-------
100
0.2
0.4 0.6
POROSITY, C
0.8 LO
Figure 9. Variations in porosity functions with porosity.
46
-------
0.1 j
0.2
a 4 0.6 0.8
BULK DENSITY, f 9/cc
I Z
1.4
Figure 10. Variation in porosity function witn bis.!;, density
and discrete particle density.
47
-------
the term R is defined as:
R = 2 k (l-e)/e3 (21)
for use in the Kozeny-Carman equation and:
R = 3 + 2 (l-e)5/3
3 - 4.5 (1-e) 1/3 + 4.5 (l-e)5/3 - 3 (1-e)2
(22)
when the Happel model is selected. Both equations reflect.the fact that K2
becomes a complex exponential function of porosity in which a highly precise
determination of e is required to provide good working estimates for K2-
3.3 EFFECT OF FILTRATION VELOCITY ON K2
In a previous report, laboratory filtration of coal fly ash aerosols
showed that K2 was also dependent upon face velocity as well as upon the
variables called out in the Kozeny-Carman equation. For certain coal fly
ash/glass fabric systems1 K2 was observed to increase as the square root
of the velocity; i.e.:
K2 = 1.8 V0'5 N-min/g-m (23)
over the velocity range 0.39 to 1.53 m/min. It was postulated that the in-
creased particle momentum associated with higher velocities increased the dust
cake solidity and hence reduces its porosity. The former effect should not be
confused with porosity changes caused by the gradual compression of a dust
cake and/or underlying fabric substrate as the pressure drop across the
system increases. The change in cake porosity associated with gas stream and
particle velocity is readily identified since a linear relationship between
pressure loss and gas velocity will ensue when dust free air is passed through
the dust cakes formed at different face velocities. On the other hand, very
48
-------
loose dust deposits and heavily napped fabrics may display a curvilinear
relationship (concave up) between pressure loss (ordinate) and velocity(abscissa)
as the velocity of dust free air is increased, Figure 11.
In a recent communication,12 Rudnick has indicated that K2 values for
Arizona road dust in the submicrotneter size range showed only a weak dependency
on filtration velocity; i.e., K2 = f (V)0-19 Although confirming measurements
are lacking, it is postulated that two factors may contribute to the stability
of cake structure in the above instance. First, Rudnick's tests were performed
with a dust having a narrower size range than found for most coal fly ashes.
Hence, one expects the more uniformly sized particles to deposit in a denser
packing because the probability of random void space formation is reduced. In
the absence of significant voids, which may lead to an unstable cake structure,
any increase in face velocity would have little effect on porosity because the
initial deposit already has reached its maximum density.
A second explanation for the relatively constant K2 values may lie with
the fact that the smaller the particle diameters the greater the adhesive and
cohesive bonds in the system. Therefore, unless the gas stream lines change
radically with flow rate, there is a strong tendency for each approaching par-
ticle to remain where it first contacts the fabric or a previously deposited
particle. Conversely, larger particles may undergo a gradual migration and
assume a stabler and denser packing as the gas flow increases.
If the above concepts are correct, at least from the qualitative view-
point, it appears that considerable research is required in the cake structure
area before any generalized procedure can be established to related K2 to face
velocity. In addition, there are still no quantitative relationships to
describe the effects of electrical change, humidity, and particle shape on the
-------
DESCRIPTION
ABRUPT CAKE COLLAPSE
GRADUAL COMPRESSION,
DUST CAKE and/or FABRIC
0)
*
*
£
CAKE COLLAPSE ZONE
FABRIC LOADING, W
Figure 11. Drag versus fabric loading curves typifying abrupt cake
collapse and gradual cake and/or fabric compression.
50
-------
porosity of a deposited dust layer. For the above reasons, it is strongly
advised that direct measurements be made on the dust/fabric system of interest.
Earlier studies by Spaite and Walsh14 were reexamined to determine how
particle shape and velocity changes affected K2 values. A ground mica described
as nominal 5 to 10 urn flakes with 0.5 urn thickness appeared to behave very
much like fly ash when filtered through twill weave glass fabrics. Because of
uncertainties in interpreting the testing procedures, a regression line was
established for all data points regardless of fabric type, Figure 12. Despite
the differences in shape factor between fly ash and mica (roughly spherical and
platelets, respectively), both dusts appear to react the same to velocity
changes; i.e., K2 ~f (V)0'5. With respect to the mica particles, it is easy
to imagine a gradual collapsing of a card-like structure as the pressure gra-
dient increases across the dust layer. Thus, the apparent nonlinearity of the
data point array suggests that both momentum effects and compression may be
taking place. Reexamination of drag/loading curves reported by Borgwardt et al.
for the field filtration of fly ash suggests that the velocity exponent might
well be nearer to 0.75 than the reported 1.5 value.15 The current interpretation
is based upon analyses of recent tests1 coupled with the fact that the extra-
polation of long term, average measurements to define short-term changes
in any filtration system is a risky process. Despite the fact that the pro-
posed K2/velocity relationship for fly ash; i.e., K2 = f (V)0-5 appears
reasonable, it is recommended that the precise relationship be determined by
experiment whenever practicable.
51
-------
100
70
50
20
T 1 r
WoVIH «LA»« EAWiC
A £ 3/1 Crowfoot
O 3/1 Crowfoot
DC/ 3/1 Twill
0.52
K 2 =141VI
OMITTED FO* RCGKC3S10N
LINE ESTIMATE
FACE VELOCITY ,
10
Figure 12. ^ versus velocity for wet ground mica.
From Spaite and Walsh.
52
-------
4.0 SENSITIVITY ANALYSES
4.1 PRELIMINARY SCREENING TESTS
4.1.1 Objectives
In order to reduce the number of tests necessary for the sensitivity
analysis, several screening tests were performed to determine which input
parameters had the greatest effect on system performance. At present, the
model requires 10 input parameters as well as the fabric and dust properties
to completely describe a system. If each input parameter were assigned three
possible -values and all test combinations were investigated, over 1,000 tests
would be required. By varying a single input parameter over a typical range
of values with all other parameters held constant, the impact of that parameter
on system performance and the importance of the parameter relative to other
parameters can be determined for an "average'1 set of circumstances. A system
similar to that for the Nucla Station operation was chosen as a "baseline"
test to which subsequent tests could be compared. The operating parameters
for the baseline conditions are presented in Table 7. Although the system
described by the parameters in Table 7 is a pressure controlled cleaning
system, it may, in some instances, be forced into a continuous cleaning mode.
4.1.2 Variables Studied During Screening Tests
Each of the parameters shown in Table 7, with the exception of cleaning
cycle time, gas temperature and the fabric and dust properties, were varied
over typical field ranges and the results analyzed. A summary of the results
53
-------
TABLE 7. INPUT PARAMETERS SELECTED FOR BASELINE TESTS
Parameter Value
Number of compartments 10
Cleaning cycle time 30 min
Compartment cleaning time
(off-line time) 3 min
Reverse flow velocity 0 m/min
Limiting pressure drop 1000 N/m2 (4.0 in. w.c.)
System velocity 0.61 m/min (2 ft/min)
Gas temperature 150°C (300°F)
Inlet particulate concentration 6.87 g/m3 (3 grains/ft3)
Specific cake resistance, K2 1.0 N-min/g-m (6.0 in.w.c.-min-ft/lb)
Effective drag, Sg 400 N-min/m3 (0.49 in.w.c.-min/ft)
Residual fabric loading, % 50 g/m2 (0.0102 lb/ft2)
Residual drag, SR* 0
Initial slope, Kj^ 0
Time increment (for iterations) 1.0 min
Fractional area cleaned, ac 0.40
Measured at a face velocity of 0.61 m/min and a temperature of 25°C.
At 150°C K2 has a value of 1.322.
Measured at a temperature of 25°C. At 150°C SE has a value of 528.
'Zero values indicate no measurements available and automatic selection
of linear drag model.
54
-------
is presented in Table 8. Values shown under input parameter variations in
Table 8 indicate the value of the parameter in the baseline test and the
value used in the corresponding test. The reported maxima and minima are
those occuring at any time during a complete operating cycle.
4.1.3 Performance Parameters, Maximum and Minimum Values
Continuously cleaned systems exhibit a maximum resistance and a minimum
penetration just be initiation of cleaning of any compartment. Conversely,
the resistance is at a minimum and the penetration at a maximum immediately
following the cleaning process because of the reintroduction of freshly
cleaned fabric surface. The above effects are repeated cyclically as cleaning
continues such that pressure loss and penetration always oscillate between
the same fixed limits.
Pressure and time controlled systems also display maxima and minima except
that the values are not repetitive from compartment to compartment. In the
latter systems, the minimum penetration occurs prior to cleaning the first
compartment and the maximum pressure drop occurs just before the first
compartment is returned to service. Minimum pressure drop occurs after the
last compartment cleaned is put back on line.
The point at which penetration is at a maximum is less easily defined
since two opposing effects act concurrently during a cleaning cycle. As
cleaning progresses, the velocity gradients diminish thus favoring decreased
penetration while fabric loadings simultaneously decrease leading to increased
penetration. Maximum penetration appears to take place about halfway through
the cleaning cycle immediately after a cleaned compartment has been returned
to service.
55
-------
TABLE 8. EFFECT OF VARIATIONS IN INPUT PARAMETERS ON SYSTEM PERFORMANCE
Input imraart t-r
varlnt Ions*
B.pli'l i nr text
V, O.fcl O.I
11.61 » 1.22
().6I - 1.53
r , 1000 . son
inon isoo
... , 6.87 - 2.29
6.87 > 22.9
i . 0.4 » 0.1
' 0.4 » 1.0
Ni>. ruin|mrtnM*nl -i, 10 -» 5
10 - 2(1
Tlmr 1 nrrfinc-nt , 1 » 1
] O.h
1 * 0.3
At - 0.3, V - 1.53
At - 1.0, v - 1.53
Compartment cleaning
time, 3 2
3 1
3 0.1
Rrvcrac flow velocity
0 0.61
SK, 4UO 200
*
1 nil I en ted values 'in- (1)
₯or example, V, 0.61 » 1.
nil other base- I Ini- unluc
Penetration (percent)
Minimum
0.015
0.0078
0.35
0.81
O.OB9
0.015
0.029
0.013
0.028
0.013
0.015
0.015
U.015
0.015
0.015
0.86
0.81
0.015
0.015
0.015
0.015
Maximum
1.1
2.0
1.1
1.6
0.73
1.5
1.1
1.1
0.34
2.5
1.9
0.66
1.1
1.1
1.1
1.5
1.6
1.0
1.0
1.1
1.6
the bilMi- line levels of
3 mo.-infl ivifriri velocity
:o unclmnprH.
Average
0.13
0.037
0.57
1.06
0.36
0.09
-0.13
0.17
0.13
0.15
0.14
0.12
0.17
0.12
0.12
1.02
1.06
0.13
0.12
0.12
0.13
0.12
Tine
between
cleanings*
(nln)
81
672
0
0
0
160
-270
10
8
171
82
81
81
81
81
0
0
81
82
82
81
104
Pressure drop
Minimum
650
360
1,510
2,200
500
750
580
850
965
425
645
645
660
650
645
2,170
2,200
650
645
650
495
Table 4-1 or (2) modi ftc.it lona 1
of Table 4-1 decreased from n.fil
Maximum
1,165
1,165
1,745
2,700
565
1.755
1,160
1,210
1,170
1.170
1,385
1,080
1.180
1,165
1,160
2,645
2,700
1,170
1,165
1,325
1 ,176
n base I
to O.T
(N/m7)
Average
860
725
1,690
2,600
560
1,160
-810
1,050
1.130
715
880
840
885
860
850
2,550
2,600
855
845
830
895
776
Ine levels.
ra/mln with
Refrri to Lime Interval betveen the end of Che cleaning cycle and Che scare of the next.
56
-------
The performance characteristics of the system used to determine the impor-
tance of various input parameters are average penetration, average pressure
drop and the actual length of time between successive cleaning cycles. Pene-
tration will determine whether or not a particular system can meet a given
emission requirement. Pressure loss estimates will indicate whether the
existing fan capacity and the structural soundness of the baghouse are
adequate. Pressure loss and frequency of cleaning will also have a significant
bearing on system power requirements and fabric service life.
4.1.4 Identification of Key Variables
'According to the results of preliminary screening tests, the following
parameters appear to exert the greatest impacts on system performance.
System face velocity (air-to-cloth ratio), V
Limiting or maximum permissible pressure drop, P
Li
Inlet particulate concentration, C.
Specific resistance coefficient, Kj
Fractional area cleaned, a
4.1.4.1 Face Velocity (Air-to-Cloth Ratio)
Variations in system face velocity greatly affected average penetration
and pressure drop as well as the time between successive cleaning cycles.
The largest impact of velocity was on the average penetration, wherein a two-
fold velocity increase produced approximately a fourfold increase in pene-
tration. This result is not altogether surprising since laboratory tests on
filter panels1 yielded results which indicated that at fabric loadings of
100 g/m? and greater, penetration varied as velocity raised to the 2.2 power.
The effects of velocity on average pressure drop and the time between
cleanings are interrelated. First, K2 will increase as the velocity to the
57
-------
0.5 power as stated earlier. As a result, the dust cake drag will increase
in similar fashion. However, since the pressure drop is a linear function of
both drag and velocity, the pressure drop across a uniformly loaded filter
should increase as the velocity to the 1.5 power. Finally, velocity also
exerts a linear impact on the loading rate (mass of material deposited on the
filter per unit area per unit time. Thus for a single bag or compartment
system, the overall pressure drop would be expected to increase as the 2.5
power of velocity. When the number of bags is increased, however, and sequential
cleaning is initiated the velocity effects are less dramatic. An increase in
velocity from 0.3 to 0.61 m/min increased the average pressure drop by only
19 percent, as opposed to 400 or 500 percent which would have been predicted
based on the preceding analysis. The effect of velocity may have been de-
emphasized for the multicompartment systems either because of the number of
compartments or the frequency of cleaning. It should be noted, however, that
the time between cleaning cycles has been reduced from 672 to 81 minutes which
means that the bags are being cleaned five times as much (a matter of concern
with respect to service life.)
A further increase in velocity from 0.61 to 1.22 m/min forces the system
to clean continuously; i.e., the time between cleaning cycles reduces to zero
minutes. This situation arises because the cleaning process cannot keep up
with the fly ash deposition rate and still maintain a pressure drop of less
than 1000 N/m2, the preset limit. The increase in velocity from 0.61 to 1.22
m/min also produced a twofold change in the average pressure drop. A third
increase in velocity from 1.22 to 1.53 m/min caused an increase in average
pressure drop of about 50 percent, roughly equivalent to a velocity exponent
of 1.8. It appears that as the time between cleaning cycles decreases the
58
-------
effect of velocity becomes more important in regulating system performance.
Under the above conditions, the average performance is dictated mainly by
filter system behavior during the cleaning cycle.
4.1.4.2 Limiting Pressure Drop
Variations in the limiting pressure drop (P ) at which cleaning is ini-
LJ
tiated produced foreseeable results in the average pressure drop. An increase
in limiting pressure drop causes an increase in the average pressure drop.
Average penetration varies inversely with pressure changes. System penetration
is generally higher during the cleaning cycle than during the filtration period
between cycles. During cleaning, the flow from one compartment is diverted
to the remaining on-line compartments thereby increasing the average velocity.
Also, a cleaned compartment returned to service presents much less resistance
to air flow than an uncleaned compartment and the velocity through the cleaned
portions of the compartment is much higher than through the rest of the bag-
house. High velocity and low fabric loadings both serve to increase penetration.
During the period between cleaning cycles, the velocities in each compartment
tend to equalize as fabric loadings increase. Therefore, penetration will
decrease as time increases during the extended filtration period. Referring
to Table 8, as the limiting pressure drop increases, the time between clean-
ing cycles also increases. As this time increases, the high penetration levels
produced during cleaning become, in effect, diluted by the much lower levels
associated with extended filtration periods.
4.1.4.3 Inlet Dust Concentration
The greatest impact of variations in inlet particulate concentration is
on the time between cleaning cycles, due mainly to fabric loading rate changes.
The time between cleanings affects the importance of cleaning cycle penetration
59
-------
relative to the penetration during the extended filtration period and,
consequently, affects average penetration. An increase in inlet concentration,
C , from 2.29 to 22.9 g/m3 also produced a small increase, 30 percent, in
the average pressure drop.
4.1.4.4 Fabric Cleaning Parameter
Variations in the cleaning parameter, a , (the fractional area cleaned)
produced significant changes in the time between cleanings and, to a lesser
extent, changes in the average pressure drop. The time between cleaning
cycles would be expected to decrease as the amount of dust removed from the
bags is decreased, (i.e., smaller a ) since less dust must be added to the
bags to reestablish the previous loading conditions. With less dust removal
the system would operate at a larger average fabric loading and therefore,
a larger average pressure drop. Average penetration was not greatly affected
by changes in a . Although higher local velicities through the cleaned area
are expected when a is reduced (and thus higher local penetrations) the fact
that the fraction of air passing through the cleaned region is reduced minimizes
dust contributions from these areas. Hence, the impact on overall emission
rate is relatively small.
4.1.4.5 Number of Compartments
The number of compartments was varied between 5 and 20 with little effect
on performance. The maximum pressure drop and maximum penetration increased
as the number of compartments decreased. However, this effect is often
diminished when the extended filtration period and the cleaning cycle are
incorporated into an average value. The effect of changes in the number of
compartments should be more pronounced in continuously cleaned systems.
60
-------
4.1.4.6 Time Increment for Iterations
Due to the iterative nature of the model calculations, a time increment
must be determined before any calculations can be performed. The results of
the calculations performed at any time (t) in the cycle are also used as input
to the calculations for a time (t + At), the next iteration period. Further-
more, computed values for system parameters such as local drag and velocity are
held constant for the (t + At) interval. Therefore, in situations where local
velocity, drag or deposition rates undergo rapid changes, too large a value for
the time increment may reduce the accuracy of predictions. The results of
the tests performed to investigate the sensitivity of predicted performance
to time increment duration are presented in Table 8. In only one case was
penetration severely affected by changes in the time increment; i.e., At of
3 minutes. Little effect was observed with regard to pressure drop or time
between cleanings. For the compartment cleaning time of 3 minutes cited in
the "baseline" test data of Table 7, an iteration time of 3 minutes means
that all system variables are held constant from the time a cleaned compartment
is returned to service until the next compartment to be cleaned is returned
to service.
Since local face velocity and drag are likely to change more rapidly
during a cleaning cycle than during the extended filtration period, extended
averaging periods may conceal important transient changes in system performance.
Therefore, additional tests were performed for time increments of 0.3 and 1.0
minutes at a face velocity of 1.53 m/min. The above iteration times had little
effect on average penetration or pressure drop for the latter tests with respect
to a constant face velocity.
61
-------
4.1.4.7 Compartment Cleaning Time and Reverse Flow Velocity
Compartment cleaning time (off-line time) and reverse flow velocity had
little or no effect on system performance. The main effect of increasing
reverse flow velocity from 0 to 0.61 m/min was to increase the maximum pres-
sure drop from 1165 to 1325 m/m2- However, the average pressure drop increased
by only 4 percent. The effect of reverse flow velocity is expected to be more
evident in a continuously cleaned system. This follows from the fact that dust
penetration, which is highly velocity sensitive, is greatest during the clean-
ing intervals. With no dimunition of overall penetration by extended noncleaning
intervals, the maximum velocity impact is shown in the emissions.
Based on the results of the preliminary tests, a series of tests was
performed in which the four key parameters were varied independently with the
remaining parameters held constant. The results of these tests are discussed
in the next section.
4.2 MULTIVARIABLE SENSITIVITY TESTS
4.2.1 Introduction
The special tests described- in this section serve two purposes. First,
they indicate how accurately various input parameters should be measured to
estimate filter system performance within acceptable error boundaries. Second,
they show how various combinations of variable changes interact in determining
overall filter system performance.
Each of those parameters that were found to have a significant effect on
the predicted system performance were varied over the ranges listed in Table 9.
Different combinations of the values for the parameters listed in the table
were used as inputs to the model with all remaining parameters (see Table 7)
held constant.
62
-------
TABLE 9. VALUES OF KEY PARAMETERS USED IN SENSITIVITY ANALYSES
Velocity (V)
(m/mln)
0.3
0.61
(0.91)f
1.22
1.53
(1.75)f
Limiting
pressure
drop (PL)
(N/m2)
500
1,000
1,500
2,000
(2,500)f
Inlet
concentration (C-^)
(g/»3)
2.29
6.87
22.9
Fractional
area
cleaned (ac)
0.1
0.4
1.0
Not all combinations of all variables were tested.
Only used when results of other tests warranted further
Investigation.
63
-------
Certain variable combinations were excluded from the sensitivity testing
because they appeared to be well beyond the range of any practical field
conditions. For example, with a continuously cleaned system involving the
following input parameters; V = 1.75 m/min, C. = 22.9 g/m3, and a =1.0,
pressure drop and penetration values would have been unacceptable in any real
situations. In other cases, extrapolation from a partial test array was
sufficient to depict the entire range of variable combinations of interest.
The results of all tests are presented in Appendix B in tabular form and
in Figures 13 through 34. Average pressure drop and penetration (for an
entire cycle) have been plotted as functions of system velocity for various
pressure-drop-controlled and continously cleaned systems in Figures 13 through
26. The time between cleaning cycles is presented as a function of the
same variables in Figures 27 through 33. Each of the Figures 13 through
33 represents a system of constant inlet concentration, C^, and cleaning
intensity, a . From these figures, the variations in system performance due
to changes in operating conditions can be determined, estimates of the
performance characteristics for a given system can be made, or values for
system operating parameters to achieve a specific emission or pressure limita-
tion can be determined. Interpolation is necessary for any system not
operating at the inlet dust concentrations or cleaning levels for which the
curves were developed. To simplify the interpolation procedure and, also, to
present a broader description of the relationships between operating and
performance parameters, the results of the sensitivity tests have been replotted
in several alternate formats. The resultant curves are presented in Appendix
\
C. The data have been plotted for selected combinations of C., V and P and
X J_,
64
-------
sooo
4000
SOOO
UJ
I 2000
ui
3
1000 -
oc =0.1
C, «2.29
A « PL OF 2000
^ PL or isoo
El « PL OF looo
V PL * 80°
O CONTINUOUS
0.5 1.0
FACE VELOCITY, V, m/mln
1.5
Figure 13. Effect of face velocity and limiting pressure drop on
average pressure loss.
65
-------
9OOO
V PL OP ooo
O CONTINUOUS
FACE VELOCITY, V, m/min
«
Figure 14. Effect of face velocity and limiting pressure drop
on average pressure loss.
66
-------
5000
4000
30OO
I
u
E
Ul
§
5 2000
ui
IOOO
0
ac =0.1
<=o -22.9
O' CONTINUOUS
A A PL 1000
o-s
1.0
FACE VELOCITY, m/min
1.5
Figure 15. Effect of face velocity and limiting pressure
drop on average pressure loss.
67
-------
0000
4000
aooo
i 2000
IOOO
C, =2.29
OC * 0.4
A * PL OF 2000
^ > PL or IBOO
Q i»L or 1000
V ' *L OF BOO
O CONTINUOUS
0.5 1.0
FACE VELOCITY, V, m/min
1.9
Figure 16. Effect of face velocity and limiting pressure drop
on average pressure loss.
68
-------
OF 2500
of «ooo
OF ISOO
Q PL OP 1000
V« PL °*
0 COMTINUOU*
I.S
FACE VELOCITY, V, in/win
Figure 17. Effect of face velocity and limiting pressure drop
on average pressure loss.
69
-------
9000
A « P OF zooo
PL OF isoo
Q PL OF IOOO
V PL OF ooo
O CONTINUOUS
0-5 1.0
FACE VELOCITY, V, m/min
Figure 18. Effect of face velocity and limiting pressure drop
on average pressure loss.
70
-------
9000
= 1 =6*7
OC'I.O
4000
A
O PL OF IBOO
Q PL or looo
V PL of BO°
O CONTINUOUS
30OO
Ul
5
2000
1000
0.5 1.0
FACE VELOCITY, V, m/min
1.5
Figure 19.
Effect of face velocity and limiting pressure drop
on average pressure loss.
71
-------
10
1.0
8
*
ac
£ a
Ul
<9
O.I
O.OI
I I I I
oc =0-1
C| =2.29
O« CONTINUOUS
V»PLOF 500
Q PL OF 1000
A « PL OF 2000
JII' ' ' '
1
0.1. 0.2 0.5 1.0 2.0
FACE VELOCITY,V,m/min
J L
i i i
5.0
10
Figure 20. Effect of face velocity and limiting pressure drop
. on average penetration,
72
-------
10
1.0
Cj =6.87
O« CONTINUOUS
Vs PL OF BOO
Q PL OF 1000
A«PL OF IBOO
<£ » PL OF 2000
i 111 I I I I
0.« 0.2 0.5 1.0 2.0
FACE VELOCITY, V, m/min
5.0
10
Figure 21. Effect of face velocity and limiting pressure drop
on average penetration.
73
-------
1.0
0.7
O.5
0.2
w O.I
0.07
u>
O.O9
O.O2
O.O
0.1
oc =0.1
C0 »22.9
K2»I.O
O CONTINUOUS CLEANINO
D A PL «2000
A APL "000
0.2 0.3 O4 Q5 0.7 1.0
FACE VELOCITY, V, m/min
Figure 22. Effect of face velocity and average pressure
drop on average penetration.
74
-------
10
S 1.0
o
Z
O
ui
o
O.I
0.01
I f II
0C=0.4
C| =2.29
O* CONTINUOUS
V"PL OF 500
Q * PL OF IOOO
A'PL OF I5OO
^ « PL OF 2000
, . . .. .1
I I
O.I 0.2 0.3 1.0 2.0
FACE VELOCITY,V, m/min
5.0
10
Figure 23. Effect of face velocity and limiting pressure drop
on average penetration.
-------
10
S
I
1.0
-------
10
8
i
(L
O
UJ
UJ
ui
a
1.0
O.I
0.01
0C =0.4
Cj =22.9
G« CONTINUOUS
V«PL OF 900
Q PL OF IOOO
A'PL OF 1500
<> « PL OF 2000
O.f 0.2 0.5 1.0 2.0
FACE VELOCITY, V, m/min
5.0
10
Figure 25. Effect of face velocity and limiting pressure drop
on average penetration.
77
-------
10
110
o
tu
0.
o
<
or
O.I
0.01
oc =1.0
Cj =6.87
O'CONTINUOUS
V" PL OF 600
Q . PL OF 1000
A PL OF looo
^ PL OF zooo
1
0.1 0.2 O.S 1.0 2.0
FACE VELOCITY, V, m/min
5.0
10
Figure 26. Effect of face velocity and limiting pressure drop
on average penetration.
78
-------
2000
(00 -
1000 ~ 2000
LIMITING PRESSURE DROP, PL ,N/(i)2
3000
Figure 27. Relationship between time between cleaning cycles,
limiting pressure loss and face velocity.
79
-------
IOOO
9OO
800
C| « 6.87
0C> O.I
A*'0-3
Q V« 0.61
y V*0.9I
QV.I.ZS
V-l 33
TOO
600
til
d 500
400
300
ZOO
100
IOOO V2000
LIMITING PRESSURE DROP, P,_,N/in2
3000
Figure 28. Relationship between time between cleaning cycles,
limiting pressure loss and face velocity.
80
-------
4OO
oc =0.1
Co =229
n =v=o. 3
A =V=0.6I
3OO
zoo
100
I
1000
2000
3OOO
AP,
Figure 29. Relationship between time between cleaning cycles,
limiting pressure loss and face velocity.
81
-------
2000
i«ooh
LIMITING PRESSURE DROP,
3000
Figure 30.
Relationship between time between cleaning cycles,
limiting pressure loss and face velocity.
82
-------
1000
900
eoo
TOO
600
3
BOO
400
300
200
IOO
C| . B.tT
Oo« 0.4
Q V«0.6I
V v« o.»i
O V.I.M
1000 - 2000
LIMITIN0 PRESSURE DROP, PL ,
3000
Figure 31.
Relationship between time between cleaning cycles,
limiting pressure loss and face velocity.
83
-------
600
4QO -
300 -
Ui
o
200 -
IOO -
"000 - 2000
LIMITING PRESSURE OROP,PL,N/m2
3000
Figure 32. Relationship between time between cleaning cycles,
limiting pressure loss and face velocity.
84
-------
tooo
(00 -
«e.tT
Q
V
0vi.cc
^Vil.3S
0V. I. 79
2000
LIMITING PRESSURE DROP, PL ,IM/m2
3000
Figure 33. Relationship between tirae between cleaning cycles,
limiting pressure loss and face velocity.
85
-------
90OO
= "j = 30 rnin
*'f = SOmin
= 90min
,t( =120 mm
0.5 1.0
AVERAGE FACE VELOCITY, V, m/mln
1.5
Figure 34.
Effect of velocity on average pressure loss
for timed cleaning cycle systems.
86
-------
ac, V and PL. The use of figures shown in Appendix C and those presented here
will be discussed later in this section. Before discussing graph applications,
however, their development and interpretation will be reviewed in the following
paragraphs.
A.2.2 Description of Graphs Developed from Sensitivity Analyses
4.2.2.1 Average Pressure Drop
As stated previously, Figures 13 through 19 are graphs of average
system pressure drop versus velocity. The figures represent fabric filter
systems with fixed inlet concentrations (C-^) and cleaning parameters (ac).
In each figure, average system pressure drops for various combinations of
velocity and limiting pressure drop are presented. The value of other param-
eters, such as number of compartments and cleaning cycle times, which are the
same for all the tests, have been listed in Table 7.
The systems described in Figure 17 operate at an inlet concentration of
6.87 g/m3 (3 grain/ft3) and with a cleaning intensity such that 40 percent of
the dust is removed during cleaning (a = 0.4). The lowermost curve in
Figure 17 shows the relationship between average pressure drop and system face
velocity for a continuously cleaned system. The remaining curves depict
systems whose cleaning cycles are initiated at selected pressure drop levels.
A given limiting pressure drop curve intersects the continuous cleaning curve
when the minimum pressure drop (after the entire baghouse has been cleaned)
equals the limiting pressure drop. If the face velocity of a given system is
increased beyond this intersection point, the system must clean continuously
to keep up with the increased deposition rate and pressure drop. Although data
points are not shown at some intersections, the former can be determined by
plotting the minimum pressure drop after the cleaning cycle is complete versus
velocity for a given system. Velocities below 0.3 m/min were not used in the
87
-------
sensitivity analysis since the empirical relationship between penetration,
velocity and fabric loading was developed from field and laboratory tests
which were conducted at velocities greater than 0.3 m/rain.
4.2.2.2 Average Penetration
In Figure 24, the average penetration curves that correspond to the
systems described in Figure 17 are presented. Figure 24 also shows a con-
tinuous cleaning curve with which the curves for pressure drop limited systems
ultimately intersect. Note that the continuous cleaning curve appears to have
a minimum at a velocity of about 0.8 m/min. This minimum is attributed to the
fact that velocity changes produce opposing effects on dust penetration and
dust deposition, whereas penetration increases with velocity, it also
decreases with the quantity of dust deposited on the filter, the latter
factor being directly related to face velocity. Hence, the velocity/cake depth
interaction suggests that the concept of a minimum effluent for the continuous
cleaning system of Figure 24 is tenable. As the limiting pressure loss and/
or the face velocity is allowed to increase, however, the face velocity alone
dominates the penetration.
The graph of the time between cleaning cycles which corresponds to the
data inputs of Figures 17 and 24 is presented in Figure 31. Time has been
plotted versus limiting pressure drop for various face velocities to facilitate
use of the curves. Note that the intersections of the curves with the abcissa
indicate continuous cleaning systems (i.e., time between cleanings of zero).
4.2.3 Effect of Parameter Covariance on Predicted Performance
4.2.3.1 Simplified Single Equation Definition
Due to the complex interrelationships among the operating parameters, it
is difficult to describe accurately the impact of these parameters on system
88
-------
performance on the basis of a single variable change or a simple algebraic
expression. However, by means of some simplifying assumptions, relationships
between average pressure loss and key operating parameters were developed
(See Appendix D) . Although not intended to be accurate predictors of filter
system performance, these equations may be used to forecast general trends
in system pressure loss or to identify controlling variables among a specific
set of input parameters.
The average pressure loss estimator for a limiting pressure or timed cycle
system is :
p = * [! + (n-1) (1 + tf /tc)] [(2-ac)PL + acSEVi + (l-a^C^V^/ZJ (24)
and for a continuous system is:
_ _ tc _ 1
P = C*2 ln 1 + (l-a)/a \
- _ 2n-l _ _
(25)
The time between cleaning cycles or the limiting pressure drop can be
estimated from the following expression:
tf = (ac-l)tc/2 + ac(PL-SEV1)/(CiK2Vi2) (26)
By rearrangement of Equation (4-3) , PT is readily determined when t , is a
known quantity; i.e.,
n
PL = ?al (tf + d-acHc/2) + SEV. (27)
c
System face velocity and limiting pressure drop were found to exert the
greatest impact on system performance. The quantitative effects of these
parameters on average pressure drop, average penetration and the time between
cleanings are shown in Figures 13 to 19, 20 to 26, and 27 to 33,
respectively.
89
-------
4.2.3.2 Average Pressure Relationships
By comparing the continuous cleaning curves, or the lines of constant limit-
ing pressure, for selected values of inlet concentration and level of cleaning,
it can be seen that the effect of any one operating parameter on performance
is often a function of the magnitude of the other operating parameters. With
reference to Figures 13 and 14, changes in velocity at an inlet concentration
of 6.87 g/m3 produce greater changes in average system pressure drop than at
a concentration of 2.29 g/m3. This same effect can be seen in Figures 16
and 13, where the fractional area cleaned, a., decreases from 0.4 to 0.1
(40 to 10 percent). Average pressure drop increases with increasing velocity
more rapidly at low levels of cleaning and high inlet concentrations.
Although limiting pressure drop has a significant effect on average
pressure drop, the magnitude of the effect is not as dependent on other operating
parameters as is the effect of velocity. Changes in limiting pressure drop
produce roughly equivalent changes in average pressure drop, regardless of
inlet concentrations or level of cleaning (see Figures 13 and 14, and 13
and 16).
4.2.3.3 Average Penetration Relationships
The effects of velocity and limiting pressure drop on average penetration
are not as obvious as those on average pressure drop (see Figures 23, 24
and 25). The minimum average penetration on the continuous cleaning curve
occurs at lower velocities as the inlet concentration increases. -This is
consistent with the previous explanation for the appearance of a minimum.
It was postulated that at low fabric loadings the effect of reduced loadings
counteracts the effects of reduced velocity. At higher inlet concentrations
the minimum should then occur at a lower velocity.
90
-------
The effect of limiting pressure drop on penetration also appears to be a
complex function of several operating parameters. At a velocity of 0.61 m/min
limiting pressure drop has greater influence on penetration at a low concentra-
tion (Figure 23) than at a high concentration (Figure 25). Changes in
average penetration due to limiting pressure drop are also influenced by face
velocity. As velocity increases, such that the system is forced into continuous
operation, the effect of limiting pressure drop disappears since the system
must now operate on a continuous cleaning basis. For example, with reference
to Figure 24, at velocities greater than about 1.1 m/min, changing a limiting
pressure drop from 1000 to 500 N/m2 has no effect since if either of these is
chosen, the system is forced into continuous operation.
4.2.3.4 Time Between Cleaning Relationships
The effect of the time between cleaning cycles, tf, on performance is
described in Figures 34 and 35. These curves were developed by cross-
plotting data excerpted from Figures 17, 24 and 31. Time between cleaning
variations and limiting pressure variations exert similar effects on average
pressure loss; i.e., with fixed values assigned to velocity, concentration and
cleaning level, the change in average pressure loss will be roughly proportional
to the change in either t, or PT.
Since P and tf are linearly related (See Figures 27 to 33), the
proportionality should be expected. The effect of tf on average pressure loss
is also dependent on the face velocity, as shown in Figure 34. A change of
30 minutes in tf has a greater effect on average pressure loss when the face
velocity is increased from 0.6 m/min than at 0.9 m/min. Since both pressure
loss and dust deposition rate are linearly related to velocity and since there
exists no upper limit for pressure drop, average pressure loss would be expected
91
-------
to experience larger deviations at higher velocities. There is, of course,
a practical upper limit to pressure drop that is governed by draft fan capacity.
The effect of the time between cleaning cycles, tf, on average penetration
is generally similar to that for limiting pressure drop, PT. The effect is
LI
also more pronounced at low tf values than at high values (See Figure 35).
This same effect on penetration can be seen in Figure 24 with regard to
limiting pressure loss. Large excursions in average penetration result when
PT is varied from the indeterminate continuous cleaning level to 1000 N/m2
LI
(at a velocity of 0.91 m/min). The penetration changes are considerably less
for higher P values.
J_i
4.2.3.5 Fractional Area Cleaned and Inlet Concentration
The effects of the fractional area cleaned, a , and inlet concentration,
C., on system performance can be best demonstrated by inspection of Figures
36 through 39, the latter excerpted from the cross plots presented in
Appendix C. The two curves shown on each of the figures were chosen to represent
those conditions under which a and C. exert minor or major impacts on system
performance.
Varying the cleaning parameter, a , can produce significant changes in
average pressure loss when the system face velocity is high (See Figure 36).
At low a levels, variations or errors in a estimation produce much greater
effects than at high a levels.
The pressure loss response due to changes in inlet concentration show a
similar dependence on average face velocity. In the latter case, however,
the effect is not as pronounced.
The effects of C^ and a£ on average penetration are also influenced by
several operating parameters. As illustrated in Figure 38, a ten fold change
92
-------
0.5 -
Cj =6.87g/m3
V =0.9! m/min
1
S
0.2
O.I
0.07
0.09
0.02
O.OI
50 100 ISO 200 250
TIME BETWEEN CLEANING CYCLES,tf ,min
300
3 SO
Figure 35. Effect of time between cleaning cycles,
tf, on average penetration.
93
-------
5000
4000 -
3OOO
a
o
tt
a
UJ
flC
1
UJ
a:
a
&
K
UJ
5
2000
IOOO
CONTINUOUS CLEANINO
C( '6-BT
O V'O 5
L
_U
JL
O.I O.2 0.3 0.4 0.5 0.6 0.7
FRACTIONAL AREA CLEANED, 0C
0.8
0.9
Figure 36. Effect of variations in cleaning intensity on average
pressure drop.
94
-------
9000
4000
3000
a
o
K
of
8
111
8:
111
<
S 2000
1000
CONTINUOUS CLEANIN*
O v«o.s
A v»i.2z
'° INLET CONCENTRATION, C|, g/m3
25
30
Figure 37. Effect of variations on inlet concentration on average
pressure drop.
95
-------
10
S
i
X
H
Ul
kl
a
kl
<9
1.0
0.1
0.01
TI I I I
O V»0.6I
CONTINOUS CLEANING
C| =6.87
PL = 1000
C|=6.87
1
I
O.I
0.2 O.5 I.O
FRACTIONAL AREA CLEANED,Oc
Figure 38. Effect of cleaning intensity on average penetration.
1.5
96
-------
10
1.0
s
i
«
_i i i j i I
5 7 10 20 50
INLET CONCENTRATION, Cj|9/m3
100
Figure 39. Effect of inlet concentration on average penetration.
97
-------
in the fractional area cleaned produces only a 20 percent change in penetration
for a limiting pressure system at low velocity. On the other hand, for a
continuously cleaned system operating at a moderate face velocity (0.61 m/min),
the same a variation produces a four fold change in average penetration.
Two opposing effects are the likely reasons for the minimal penetration
variations for the limiting pressure system shown in Figure 38. As the
fractional area cleaned is increased, more areas of low resistance and low
loading are generated. However, more time is required for the system to
return to its limiting pressure of 1000 N/m2. During this intervening period
the system will operate at much lower penetration levels than those encountered
during the cleaning cycle. The net result is that penetration levels are
only weakly dependent on a for limiting pressure systems. In the continuously
cleaned system (top curve, Figure 38) there is no way to compensate for the
increased penetration during the cleaning cycle; i.e., extended periods of
filtration without cleaning. Thus, penetration continues to increase as the
level of cleaning increases.
The relationship between average penetration and inlet concentration is
presented for various operating conditions in Figure 39. The effect of inlet
concentration on penetration is also dependent on other system operating para-
meters. Penetration changes for limiting pressure systems are less responsive
to changes in C. than their counterparts in continuously cleaned systems.
Differences in velocity and the level of cleaning can also modify the effect
of concentration (lower curves on Figure 39).
4.2.3.6 Effect of K2 Variations-
Variations in the specific resistance coefficient, K2, can produce
significant changes in performance. The relationship between performance and
98
-------
K2 is presented in Figures 40 to 42. Performance variables have also
been plotted versus several parameters on the same graphs so that relationships
could be developed between K2 and other operating parameters whose effects
have been previously established. Average pressure loss has been plotted
versus K2 (the filled symbols) for a continuous and limiting pressure system
in Figure 40. As might be expected, an increase in K2 produces an increase
in average pressure loss and the effect is more pronounced for continuously
cleaned systems as indicated by the steeper slope.
4.2.3.7 Ka and Inlet Concentration
Average pressure loss has also been plotted against the relative or
dimensionless inlet concentration (C./C f). The data were graphed in this
manner so that coordinates at K2=l and C.=6.87 could be superimposed. By
using this approach it is demonstrated that the effect of K2 on average pressure
loss is approximately the same as that for inlet concentration. For example,
using the point K2 = 1 (or C^ = 6.87) as a reference point, increasing K2 by
a factor of 3 at a constant inlet concentration of 6.87 g/m3 produces roughly
the same change in average pressure loss as increasing C^ by a factor of 3 at
a constant K2 of 1. This means that average pressure loss can be described
equally well by the product K2 x C-^ as may be deduced from the classical
expression for pressure loss,
AP = K2VW = K2VCiVAt
Precise adherence to the above relationship should not be expected because in
real filter systems the average pressure loss is defined by a nonuniform
rather than uniform fabric loading. For continuously cleaned systems, a change
in K2 is expected to have little effect on penetration since the latter is
related mainly to fabric loading and face velocity. This follows from the
fact that for a continuously cleaned system, the fabric loadings will be
99
-------
3000
Kg
PL " 1000 N/»|2J
CONTINUOUS
PL =2000
CONTINUOUS
i -2.29
IQ PL =IOOON/m2)
Ci ) '
6.87
0 CONTINUOUS
2.29
PL=2OOO
CONTINUOUS
r
2000
1000
1.0
N-min/g-m
Z.O
Ci/
(DIMENSIONLESS)
3.0
Figure 40. Effect of K2 and C± on average pressure loss.
100
-------
(OIMENSIONLESS)
Figure 41.
Effect of K2 and
cleaning cycles.
on time between
101
-------
O.7
as
8 0.2
&
o
w O.I
If
£ O.O7
Ml
O.O9
0.02
0.01
Cj =6.87g/m3
oc »0.4
V 30.61 in/mi*
PL«IOOON/m2
CONTINUOUS
^
K2'3| CONTINUOUS, ac =0.4
K2S| I Cj =2.29, V«0.6I
0.1
o.z
0.3 a*
2
_l_
as 0.7 i.o
(1000 -0.611 529)
(PL -0.61x529)
N-min/g-m
Figure 42. Effect of K£ and C.^ on average penetration.
102
-------
controlled mainly by the data inputs a^, V^, C± and t , none of which are
affected by K2.
Minor variations may be observed, again for the reason that velocity and
drag usually differ from one location to another on fabric surfaces in real
filter systems. A typical case is illustrated by the upper curve of Figure
42 in which minimal penetration changes are indicated for K2 variations in
a continuously cleaned system. Actually, a tenfold increase in K2 led to only
a 16 percent increase in average penetration.
Limiting pressure controlled systems, on the other hand, exhibit a strong
dependence on K2 as shown in the lower curve of Figure 42. As K2 increases,
the average fabric loading must be less at any instant because of the limiting
pressure constraint. Hence, with a reduced dust cover, an increase in penetra-
tion is expected.
4.2.3.8 K2 and Limiting Pressure
The rationale for the projected interrelationship of K? and C with respect
to pressure drop can also be extended to limiting pressure, P , and K2 with
Li
respect to penetration. The same "K2 x C." relationship, however, does not
apply to penetration, because K2 and C. have no direct influence on penetration.
A similar correlation describing the combined impact of P and K2 on average
J_i
penetration can be developed, however, by examining their (PL, K2) effects
on those parameters that relate directly to penetration, such as fabric loading
and velocity. If K2 and PT are allowed to increase simultaneously by two
Li
independent paths but with the constraint that the final fabric loadings be
identical, then the resultant penetrations should be approximately the same,
regardless of the path. The following discussion presents the development
of this concept.
103
-------
First, for the two independent systems cited previously, the identical
fabric loadings prior to cleaning, Wi and W2, respectively, may be expressed
by the relationship in
w2 =
K2
K2
(28)
Now if the K2 value is fixed for the first system and the value of PL is
fixed for the second system (while V^ is maintained at the same level in both
systems to eliminate any velocity effects on penetration) a relationship can
be derived between P^ and K2 for the respective systems. Additionally, a
rearrangement of Equations (28), makes it possible to treat the effect of
PT variations on penetration for the first system as if they depicted the
effect of K2 variations in the second system. In other words, penetration
may be conveniently graphed as a function of PL as well as K2«
The curve passing through the open squares in Figure 42 is a graph
of average penetration versus the P^ function,
(29)
<*LHEF - SE Vi)/CPL - SE v±) x K2R£F
for a fixed K2 value of 1.0 N-min/g-m. Reference values of 1.0 N-min/gm
and 1,000 N/m2 were chosen for K2 and PL, respectively, which by forcing
curve superposition at an abscissa value of 1.0, permits ready comparison of
the relative impacts of K2 and/or PL on penetration.
Had the two curves coincided completely, a relationship between K2 and
PL could have been established over the entire abscissa scale such that the
effects of K2 variation could be described equally well by PL variations.
In fact, this situation is reflected in Figure 42 for all abscissa values
greater than 0.6. Over the K2 range of 0.3 to 0.6 N-min/g-m, which is
104
-------
equivalent to a PL range of 2,500 to 1,500 N/m2) curve superposition is no
longer indicated. A possible explanation for the deviation is that the
velocity distributions over the fabric surfaces are different for the two
systems.
For any specified abscissa value, the points on the two curves relate
to two systems for which all operating parameters except K2 and PL are the
same. For example, an abscissa value of 0.57 on the lower K2 curve (solid
square) depicts a system where PL is 1,000 N/m2 and K2 0.57 N-min/g-m. The
upper f(?L) curve (open square) relates to a system in which PL = 1,500 N/m2
and K£ = 1.0 N-min/g-m. These two systems, in accordance with the definition
of the PL function (Equation 28) operate at about the same average fabric
dust loadings. In addition, average face velocities, inlet concentrations
and cleaning parameters are the same for the two systems.
The time intervals between cleaning cycles are also approximately the
same for the two systems. Therefore, at any specified time during an operating
cycle, these two systems should be almost identical with respect to the
fabric loading and its distribution. It then follows that with the same average
face velocity, the penetrations should be similar for both systems. It should
by noted, however, that the velocity distributions are dependent upon local
drag values which are, in turn, are related to K2- Since the values of K2 are
different for the two systems, the velocity distribution may differ despite
the same average velocity. Hence, some difference in penetration might be
expected.
4.2.3.9 Summary of K2 Relationships
Although some differences exist between the K2 and f(PL) curves,
Figure 42, it appeared that the investigation of the effects of K2 variations
105
-------
on penetration was but pursued indirectly by investigating the effect of PL
on concentrations. The reason for this approach was that some 21 figures
and 50 related cross plots had already been developed to describe the relation-
ship between key operating parameters and system performance. To add another
degree of freedom; i.e. K2, would require approximately 42 additional figures.
Since the computer filtration model should be used in any final analysis
of system performance, and since the figures presented here are intended to
be used for preliminary assessments only the following procedure should be
used when investigating filter systems for which the K.2 value of the dust is
other than 1.0 N-min/g-m. For continuously cleaned systems K£ variations
exert only minor effects on penetration. There the sensitivity analysis curves
(Figures 13 to 33 and those in Appendix C) can be used without modification.
In the case of limiting pressure systems the present penetration curves
(Figures 20 and 62 to 82) can be used by generating a revised PL value
from the actual limiting pressure; i.e.,
^revised = ^ ((PL)actual ' S* Vi>)+ 529 Vi <30)
where
(Pi) , = the limiting pressure of the system under investigation,
actual ._ / o
N/m .
(PL) = the limiting pressure to be used in conjunction with the
sensitivity analysis curve, N/m^-
K2 = the value of the specific resistance coefficient of the
dust in question, reported at a velocity of 0.61 m/min
and the actual gas temperature, N-min/g-m.
Vj[ = the average system face velocity, m/min.
SE = effective residual drag for the fabric/dust combination
in question at the actual gas temperature.
106
-------
If an average pressure loss or the interval between cleaning cycles is
sought for either continuous or pressure controlled systems, then the inlet
concentration (rather than the limiting pressure) should be corrected to:
^revised = actual x (31)
(C-f )
1 actual = the inlet dust concentration of the system under
investigation, g/m3.
(Ci)rev:lge£j = the inlet concentration to be used in conjunction with
the sensitivity analysis curves, g/m3.
4.3 USE OF THE SENSITIVITY TEST DATA
4.3.1 Key Variables and Fixed Terms
There are three ways in which the results of the sensitivity tests
described in this report may be used to aid the solution of filtration problems.
The probable impact of uncertainties or errors in the key input
parameters upon predicted filter system performance can be estimated.
Preliminary estimates of filter system performance can be made based
upon specified input parameters.
Preliminary design parameters can be established for new filter
systems.
It is emphasized that the role of the sensitivity analyses is to aid, but
in no way substitute for, the formal computer modeling process. Of necessity,
several parameters were held constant during the sensitivity trials to keep the
graphical material and computer utilization within the program constraints.
Those parameters held constant were as follows: the number of compartments (10),
cleaning cycle time (30 min.), compartment cleaning time (3 min.), reverse
flow velocity (0 m/min) , gas temperature (150°C) and effective drag, SE,
(400 N-min/m3) . Thus, the use of the data for determining the performance of
a system whose operating parameters differ appreciably from those used in
developing the curves and tables will present some error.
107
-------
Use of the sensitivity analyses to investigate the effects of errors in
the operating parameters or to predict the performance of an existing fabric
i
filter system is a straightforward process. Provided that the approximate
value (s) for the principal input parameters are known in the above cases, the
performance of a filter system can be estimated directly from the appropriate
graphs with allowance for K£ variations taken into account. Since a measured
value for the cleaning parameter may not be readily available, an estimate of
ac must be made.
4.3.2 Estimation of a
Three relationships between ac and various operating parameters were
presented in Section 3 of this report for limiting pressure systems:
*- ?L " SE VjL + Cl Vi fcc
K2 V± 2 (32)
' 2-52
Collapse/Reverse Flow, ac, = 1.51 x 1CT8 (Wp) (33)
2.52
Mechanical Shaking, ac = 2.33 x l(T12 (f2AWp (34)
Two equations have been given for continuously cleaned or time cycle cleaning:
p , 0.716
Collapse/Reverse Flow, ac = 0.006 C^ (tf + tc) (35)
r J -.0.716
Mechanical Shaking, ac = 4.90 x 10~** f2 ACi Vi (tf + tc) (36)
The definitions of the terms and the appropriate units for their entry
into Equations (32) through (36) are given in Table 10 in the order of
their appearance.
Although the equation structure may appear inconvenient to manipulate,
it should be noted that only one equation, Equation (35) or (36), need be used
for continuous or time cycle cleaning. If a limiting pressure system applies,
Equation (32) in conjunction with either Equation (33) or Equation (34)
108
-------
TABLE 10. DATA INPUTS REQUIRED FOR ESTIMATION OF THE
CLEANING PARAMETER, a£
where
ac = fractional area cleaned, dimensionless
Wp = average dust loading on the fabric during cleaning, g/m2.
PL = limiting pressure loss, N/m2.
SE = effective drag at the actual gas temperature, N-min/m3
V = actual system face velocity, m/min, average value
C. = inlet dust concentration at actual conditions, g/m3.
tc = cleaning cycle time, min.
K£ = specific resistance coefficient corrected to actual gas
temperature and face velocity, see Equation (7), N-min/g-n.
f = shaker arm frequency, cycles/sec.
A = shaker arm half-stroke amplitude, cm.
te - filtration time between cleaning cycles for timed cycle
cleaning systems, min. Enter as zero for continuously
cleaned system.
L09
-------
must be used. Had ac been treated as a variable within the computer runs
used to generate the graphs, an unnecessarily large number of graphs and
computer simulations would have resulted.
Again, it is emphasized that aside from using the sensitivity analyses as
preprogramming guidelines, they can also provide rapid estimates (< 1 hour) of
filter system performance when delayed programming activities or lack of
computer access might readily entail a 24-hour delay.
The data inputs for the ac computations are those related to the actual
filter operating conditions. In the case of K£, a correction is required to
convert K£ by means of Equation (2-7) to the temperature and velocity condi-
tions of the filtration process. Having computed the ac value, the performance
of the fabric filter system of interest can be estimated from the appropriate
graphs with the aid of interpolation.
4.3.3 Guideline Table for Sensitivity Test Use
Table 4-4 has been prepared as a convenient guide to identify and locate
the various graphs used for preliminary estimates of fabric filter performance.
The information is presented in three groups for which the three indices of
filter system performance, average pressure loss, average penetration and time
between cleaning cycles are treated as the dependent variables (ordinates)
while inlet concentration, fractional area cleaned, and face velocity are
plotted as the independent variables (abscissas). Each group in turn is
represented by matrices (partially or nearly completed) in which the invariant
terms of each graph (ac, V-^) (C^, V^ and (C.^, ac), respectively, are represented
by families of curves. Thus by providing an interpolation capability, more
input parameters can be treated as system variables. Although not specified
110
-------
within the matrix structure itself, the limiting pressure, PL, is also treated
as a variable on several graphs by the construction of 4 to 5 constant PL curves
that embrace its expected range of field values.
If two of the three field values for ac, C^ and V-^ conform approximately
to those shown for the variable combinations on Table 11, it is then possible
to estimate the predicted field performance of the system in terms of average
pressure loss, P, average penetration, Pn, and time (interval) between cleaning
cycles. Variations in limiting pressure drop, PL, are evaluated by interpolation
between the constant P, lines shown on the appropriate graphs.
It is again pointed out that certain parameters listed in Table 7 were
held fixed in constructing the families of sensitivity curves; e.g., the number
of compartments, the compartment cleaning time, reverse flow velocity, effective
drag, residual fabric loading and the time increment for iteration. According
to the results of preliminary sensitivity testing summarized in Table 8,
except for the highly unusual situation, deviations from the base line values
shown in Table 8 should not cause any serious estimating errors.
A simple example of the use of Table 11 is given for an assumed set of
input parameters, C± = 6.87 g/m3, ac = 0.3, V = 0.9 m/min and PL = 1200 N/m2
that apply to a proposed filter system. If it is desired to estimate the
average pressure less, P, reference is made to Figure 49, which describes
precisely the P versus ac relationship for the indicated concentration and
velocity inputs. Interpolation between the lines of constant PL (1,000 and
1,500 N/m, respectively) then enables the location of the resultant P value,
roughly 1,450 N/m2. A similar procedure is used to estimate average penetra-
tion by now referring to Figure 68 and carrying out a similar P^ interpolation.
Ill
-------
TABLE 11. FIGURE KEY FOR ESTIMATING MAJOR, FILTER PERFORMANCE
PARAMETERS - AVERAGE PRESSURE LOSS (PL), AVERAGE
PENETRATION (Pn), TIME BETWEEN CLEANINGS (tf)
Ordinate \ 0.3 0.61 0.91 1.22
P
Pn
tf
P
Pn
tf
?
Pn
tf
*
0.1 C-ll
C-32
C-48
0.4 C-15
C-36
C-50
1.0
-
-
C-12
C-33
C-49
C-16
C-37
C-51
C-19
C-40
C-54
C-13
C-34
-
C-17
C-38
C-52
-
-
-
C-14
C-35
-
C-18
C-39
C-53
-
-
-
Note: Figure numbers for graphs of P, Pn, tf versus
inlet concentration, C^, at selected values of ac,
V and PL (PL also indicated as variable on several
graphs.) *
(continued)
112
-------
TABLE 11 (continued)
Ordinate N.
P 2.29
Pn
tf
P~ 6.87
Pn
tf
? 22.9
Pn
tf
0.3
C-l
C-20
C-41
C-5
C-24
C-43
C-9
C-28
C-46
0.61
C-2
C-21
C-42
C-6
C-25
C-44
C-10
C-29
C-47
0.91 1.28
C-3 C-4
C-22 C-23
-
C-7 C-8
C-26 C-27
C-45
-
C-30 C-31
-
Note: Figure numbers for graphs of P, Pn,
tf versus fractional area cleaned, ac at
selected values of C^, V-^ and P^.
\ ac
Ordinate \
ci \
P 2.79
Pn
tf
P 6.87
P~
n
tf
P~ 22.9
Pn
tf
0.1
4-1
4-8
4-15
4-2
4-9
4-16
4-3
4-10
4-17
0.4
4-4
4-11
4-18
4-5
4-12
4-19
4-6
4-13
4-20
1.0
-
-
-
4-7
4-14
4-21
-
-
-
JNote: Figure numbers for graphs of P,
Pn, tf versus velocity, V± at selected
values of C^, ac and PL.
*
C refers to Appendix C
113
-------
4.3.4 Predicting Filter Performance with Graphical Aids
In the following discussion, we have provided a specific example of how
the tabular and graphical descriptions of filter system performance generated
under the sensitivity analyses program can be used to make preliminary estimates
of filter system performance. There are three main reasons for conducting
premodeling analyses before engaging in a formal modeling study.
First, the tentative data inputs supplied by the filter user and/or
manufacturer can be screened to determine whether the predicted
system operation will fall within practical boundaries.
Second, one can estimate what degree of accuracy (or margin of
error) can be accepted for any one data input without seriously
impairing the model's predictive capability.
Third, in the event that computer availability will cause lengthy
delays in data retrieval (~ few days), the need for an immediate
assessment of a proposed filter system's capability can be made in
less than an hour with the aid of the graphical and tabular material
presented.
We wish to point out that the working ranges of some sensitivity curves
are limited because the primary role of the sensitivity analyses was to suggest
optimum procedures for improving the original fabric filter model.1 Hence,
certain computer runs were cancelled when a satisfactory guideline had been
established. Since the use of the curves for premodeling estimating purposes
was only a secondary objective and not intended to be more than a screening
process, it was not deemed advisable to extend the sensitivity testing beyond
the present range. In those cases where extrapolation beyond measured data
points has been required, dotted lines have been constructed on the appropriate
graphs.
4.3.5 Sample Field Problem
A Pollution Control Agency would like to determine whether or not Plant A's
proposed baghouse will achieve the level of performance necessary to meet a
ll/i
-------
specified emission level as well as operating at pressure losses within the
capacity range of the draft fans. The following operating data are available
for a baghouse utilizing woven glass bags and cleaned by collapse and reverse
flow air.
TABLE 12. OPERATING DATA FOR SAMPLE FIELD PROBLEM
Number of compartments (n) 15
Cleaning cycle time (tc) 22 min
Limiting pressure loss (P ) 1,250 N/m
Li
Inlet dust concentration (C^) 4.0 g/m
Average face velocity at operating temperature (V^) 0.9 m/min
Filtration temperature (T) 121°C
Effective residual drag at 25°C (SO 433 N-min/m3
K2 at 25°C and 1.1 m/min (K2 ) 0.83 to 1.44
m
N-min/g-m
With respect to the available values cited for K2 (K2m), it is uncertain
as to where in the 0.83 to 1.44 range the correct value for K2 should fall.
Therefore, before performing final computer simulations, the Agency would like
to determine the potential impact of the above K2 variations on performance.
The graphs and tables developed provide the means for this preliminary assessment.
The first step in investigating the effect of K2 variations is to correct
the measured values of K2 and SE to the gas viscosity corresponding to the
filtration temperature.
V 121°C'
= K2,
y 25°C
\ = v /O. 022 cp\
/ 2m \0.018 cp/
V 121°C\ - SB /°-022 CP
~ 25°C/ " SEm \ 0.018 cp
115
-------
With the above corrections, the K2^ range becomes 1.01 to 1.76 N-min/g-m
and Sgf is increased to 529 N-min/m3-
For use with the graphs listed in Table 4-4, K2m must also be corrected
to the reference velocity, 0.61 m/min, that was used in the generation of the
graphs.
0.61 m/min
1.1 m/min
Hence, when using the graphs listed in Table 11, the K2f r of 0.75 to
1.31 N-min/g-m is the proper data input for the K2 parameter.
A value for ac is also required prior to using the sensitivity graphs.
Since the filter system operation is to be governed by a limiting pressure,
PL, it is necessary to calculate ac by means of Equations (32) and (33).
PO T7 e~> TT x.
w- = L ~ bE vj + ci vi tc
ac = 1.51 x 10~8 W'2-51 (33)
noting that K2f)V is the proper value to use in Equation (32). Here, the
subscript v indicates that the K2 value has also been corrected from its
original measurement velocity of 1.1 m/min to the actual velocity at which
filtration takes place, 0.9 m/min.
»t _ . i u.vj m/min
-f,v "zf / -^ ~ K2f.
Vm ^ 1.1 m/min
The resulting K2f v range, 0.91 to 1.59 N-min/g-m, when used in conjunction
with Equations (32) and (33) leads to an ac input range of 0.89 to 0.22,
respectively.
116
-------
As a final step, additional adjustments must be applied to C^ and PT because
the graphs were generated on the basis of a constant K2 value of 1.0. This
requires that PL and Ci be revised in accordance with Equations (30) and (31),
respectively,
PL - SEf (vf) + 529 Vf
and
(31)
(C \ = r* v« /i T39
W-i / j. ^. K-2«r /J-.Jii
A adj. i r ,r
The values of K-2f,r to be used above are those calculated previously as
0.75 to 1.31 N-min/g-m. The corresponding range for revised PL values becomes
1,820 to 1,260 N/m2 while the revised concentrations increase from 2.3 to
3.96 g/m3.
The actual numerical value for Vi, ac, Ci and PL used with the sensitivity
curves to predict the differences in filter systems performance when K2 (as
measured) ranges from 0.83 to 1.44 N-min/g-m are listed in Table 13.
TABLE 13. CORRECTED INPUT PARAMETERS FOR ESTIMATING EFFECT
OF K2 VARIABILITY ON FILTER SYSTEM PERFORMANCE
Lower limit Upper limit
K2 = 0.83 N-min/g-m K2 = 1.44 N-min/g-m
Vi (m/min) 0.9 0.9
ac (fraction) 0.84 0.22
Ci (g/m3) 4.0* or 2.3"*" 4.0* or 3.96f
PL (N/m2) 1,820* or l,250f 1,260* or l,250f
*
Used for estimation of penetration
Used for estimation of pressure loss
117
-------
Note that two choices for PL and C-j^ are shown for each K2 value. When
penetration is to be estimated for the lower limit, the actual inlet concentra-
tion, 4.0 g/m^, and the revised limiting pressure, 1,820 N/m2, are used.
Conversely, if average pressure loss and time between cleanings are sought,
the revised concentration, 2.3 g/m3 and the actual limiting pressure, 1,250 N/m2
are to be used.
In conjunction with the input parameters listed in Table 13, the proper
working graphs for estimating pressure loss and penetration characteristics
can be selected from Table 11.
TABLE 14. SENSITIVITY CURVE SELECTIONS FOR ESTIMATING
EFFECT OF K2 VARIABILITY ON FILTER SYSTEM
PERFORMANCE.
Lower limit Upper limit
K2 = 0.83 N-min/g-m K2 = 1.44 N-min/g-m
P, N/m2 C-3 C-3, C-7
Pn, percent C-22, C-26 C-22, C-26
Based upon interpolation and/or extrapolation as needed, the following
estimates can be made for average pressure loss, P, and average penetration, Pn:
Lower Limit Upper limit
K2 = 0.83 N-min/g-m K2 = 1.44 N-min/g-m
P N/m2 -1,000 (1,250 to 1,625)1400
Pn percent (~0.15 to 0.18)0.16 (~0.27 to 0.29)0.28
The resulting analysis suggests that one should expect a pressure loss
increase of 400 N/m2 (1.6 in. w.c.) when K2 ranges from 0.83 to 1.44 N-min/g-m.
The corresponding range for penetration is 0.16 to 0.28 percent. The increase
in dust penetration is caused by the fact that less operating time is required
118
-------
to reach the preset limiting pressure. Thus, at a constant inlet loading less
dust is deposited on the fabric surface.
When Equations (24) and (26) were used to investigate the effect of
K2 changes on pressure loss, the predicted range was 860 to 1,200 N/m2 which
is in fair agreement with the value deduced from the sensitivity curves. It
is again emphasized that the above applications of the sensitivity analyses
are intended to establish whether rational performance levels will be attainable
with the given input parameters or whether any one input parameter is suspect.
119
-------
REFERENCES
j»
1. Dennis, R., et al. Filtration Model for Coal Fly Ash With Glass Fabrics.
Report No. EPA-600/7-77-084. August 1977. 455 p.
2. Dennis, R., R. W. Cass, and R. R. Hall. Dust Dislodgement From Woven
Fabrics Versus Filter Performance. J Air Pollut Control Assoc.
48 No. 1. 47:32, 1978.
3. Dennis, R. and H. A. Klemm. Modeling Coal Fly Ash Filtration With Glass
Fabrics. Third Symposium on Fabric Filters for Particulate Collection.
Report No. EPA-600/7-78-087. June 1978. p. 13-40.
4. Dennis, R. and H. A. Klemm. A Model for Coal Fly Ash Filtration.
(Presented at the 71st Annual Meeting of the Air Pollution Control
Association. Houston, Texas. June 22-30, 1978.)
5. Dennis, R. and H. A. Klemm. Verification of Projected Filter System
Design and Operation. (Presented at the Symposium on the Transfer and
Utilization of Particulate Control Technology Sponsored by the U.S. Environ-
mental Protection Agency. Denver, Colorado, July 24 to 28, 1978.
6. Bradway, R. M. and R. W. Cass. Fractional Efficiency of a Utility Boiler
Baghouse - Nucla Generating Plant. Report No. EPA-600/2-75-013a.
(NTIS No. PB240-641/AS.) August 1975. 148 p.
7. Dennis, R. and H. A. Klemm. Fabric Filter Model Format Change. Vol. I
Detailed Technical Report, Vol. II User's Guide. U.S. Environmental
Protection Agency, Industrial Environmental Research Laboratory, Research
Triangle Park, North Carolina. EPA-600/7-79-043a, EPA-600/7-79-043b.
February 1979.
8. Billings, C. E. and J. E. Wilder. Handbook of Fabric Filter Technology.
Volume I, Fabric Filter Systems Study. Environmental Protection Agency.
Publication Number APTD-0690 (NTIS No. PB-200-648). December 1970. 649 p.
9. Ensor, D. S., R. C. Hooper, and R. W. Scheck. Determination of the
Fractional Efficiency, Opacity Characteristics, and Engineering Aspects
of a Fabric Filter Operating on a Utility Boiler," Final Report.
EPRI-FP-297. November 1976.
10. Dennis, R. and J. E. Wilder, Fabric Filter Cleaning Studies. U.S. Environ-
mental Protection Agency, Control Systems Laboratory, Research Triangle
Park, North Carolina. EPA-650/2-75-009 (NTIS No. PB-240-372/3G1).
January 1975.
120
-------
11. Snyder, J. W. Mobile Fabric Filter Unit at Southwestern Public Service
Company, Harrington Station, Amarillo, Texas. Industrial Environmental
Research Laboratory, U.S. Environmental Protection Agency. EPA Contract
No. 68-02-1816, Technical Operations Report No. 5, November 1977.
12. Rudnick, S. N. and M. W. First. Specific Resistance (K2) of Filter
Dust Cakes: Comparison of Theory and Experiments. Third Symposium
on Fabric Filters for Particulate Collection. Report No. EPA-600/7-78-087.
June 1978. p. 251-288.
13. Happel, J. Viscous Flow in Multiparticle Systems: Slow Motion of Fluids
Relative to Beds of Spherical Particles. AIChE J. 4:197-201, 1958.
14. Spaite, P. W., G. W. Walsh. Effect of Fabric Structure on Filter
Performance. Amer Ind Hyg Assoc J. 24:357-365. 1963.
15. Borgwardt, R. H. and J. F. Durham. Factors Affecting the Performance
of Fabric Filters. (Presented at 60th Annual Meeting of the American
Institute of Chemical Engineers. New York. 1967).
121
-------
APPENDIX A
EQUATIONS FOR ESTIMATING DUST PENETRATION
The general form selected for the mathematical function defining penetra-
tion is:
Pn = Pn + (Pn - Pn ) exp (-aW) (37)
S OS
where Pn = penetration
Pn = penetration at steady state
S
Pn = initial penetration at W = WR
W = increase in fabric loading above the residual value, W^
a = concentration decay function
Equation (37) reflects both the rapid exponential decay observed for outlet
loadings as well as their ultimate leveling off at a fixed emission rate as
filtration progresses.
The constants Pn , Pn and a were evaluated for velocities of 0.39 to
s* o
3.35 m/min. A PnQ value of 0.1 was used for the initial penetration.
Pn = 1.5 x 10~7 exp I 12.7 | 1-exp (-1.03V) j (38)
S I L J (
a = 3'6 ;.10"3 + 0.094 (39)
where V is the local face velocity, m/min.
Equations (37) through (39) provide the means for predicting penetration
as a function of face velocity and fabric loading. The outlet concentration,
C , is found by multiplying the inlet concentration, C^, by the actual penetra-
tion followed by the addition of the residual outlet concentration, CR; i.e.,
C0 = Pn Ci + CR
122
-------
APPENDIX B
RESULTS OF SENSITIVITY TESTS
A complete summary of all sensitivity tests is presented in Tables 15
through 23. Because of the similarities in data content for Tables 16
through 22, a brief guideline table (Table 15) was prepared to facilitate
their use.
Insofar as predicted filter performance is concerned, maximum, minimum and
average values are indicated for system pressure drop and dust penetration. A
single value is given for the time between cleaning which provides an indirect
measure of potential fabric wear and an indication as to how well higher dust
loadings and/or higher air-to-cloth ratios might be tolerated without any
significant increase in system pressure drop. Many additional tests involving
variable combinations not specified in prior tables are shown in Table 23.
The data given in Tables 16 through 23 have been used to prepare the graphical
presentation of filter system performance.
123
-------
TABLE 15. SENSITIVITY DATA SUMMARY FOR
TABLES 16 THROUGH 22
Dependent^ Independent
variables variables Fixed inputs
Table
P(N/m2), tf(min) V^m/min), a<, Ci(g/m3)
and Pn (percent) PL(N/m2)
B-2
Pn
V±, PL 0.1 2.29
B-3
V
0.1 6.87
B-4
B-5
B-6
B-7
Pn
?
Pn
?
tf
Pn
P
_tf
Pn
V, PL 0.1 22.9
V, P, 0.4 2.29
V, PT 0.4 6.87
V, PT 0.4 22.9
B-8
Pn
V, PT 1.0 6.87
Maximum, average and minimum values given for P and Pn,
single value given for tf.
124
-------
TABLE 16. PREDICTED SYSTEM PERFORMANCE WITH ac = 0.1 AND C± = 2.29 g/m3
AS FIXED INPUTS AND V± (m/min) AND PL (N/m2) AS INDEPENDENT
VARIABLES
V
\
0.3 0.61 0.91 1.22
k _
1.53
Pressure drop, N/ra2
|
J
«
*
a
s
u
;>
5
|
_g
o
*
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
Time
C
500
1,000
1,500
2,000
607 1,164
576
1,162 1,155
-
2,053
601 1,149
466
877 976
-
1,690
532 1,010 -
412
660 860
-
978
between cleaning cycles, rain.
0 0
255 77
747
-
1,654
3,045
.
^
2,983
-
2,596
-
0
Penetration, percent
|
41
i
91
z
at
5
1
I
S
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
0.375 0.415 -.'
0.628
0.812 0.48
1.22
0.279 0.298 -
0.074
0.046 0.122
0.040
_
0.197 0.211
0.023 -
0.023 0.035
0.023 -
"...
1.21
1.05
-
-
0.864
-
C refers to continuous cleaning.
125
-------
TABLE 17. PREDICTED SYSTEM PERFORMANCE WITH a =0.1 AND C± = 6.87 g/m3
AS FIXED INPUTS AND V± (m/min) AND pL (N/m2) AS INDEPENDENT
VARIABLES
V
*\
0.3 0.45
0.61 0.91
1.22 1.53
Pressure drop, N/m2
§
1
01
00
a
M
01
<
B
2
*
c
500
1.000
1.500
2.000
C
500
1.000
1,500
2,000
C
500
1,000
1,500
2,000
Time
C
500
1,000
1,500
2,000
575
578
1,164
2,336
557
485
890
-
1,700
498
425
696
_
1,079
before cleaning
0
77.4
207
-
491
2,246
-
1,170
1,753
2,338
2,235
1,130
1,500
1,894
1,892
963
1,272
1,555
cycles, mln.
0
-
8
33.6
59.4
4,224 7,015
-
4,171 6,883
3,503 5,739
_
_
-
0 0
Penetration, percent
§
1
i
£
a
K
I
|
J|
5
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
0.033
0.356
0.566
1.04
0.126
0.056
0.036
-
0.033
_ _
0.008
0.0082 0.257
-
0.0081 -
0.586
-
0.34
0.486
0.646
0.344
-
0.13
0.117
0.13
0.246
_
0.028
0.027
0.026
1.06 1.55
-
-
: -
0.780 1.24
-
-
-
0.631 1.01
-
-
-
*
C refers to continuous cleaning.
126
-------
TABLE 18. PREDICTED SYSTEM PERFORMANCE WITH ac = 0.1 AND C± = 22.9 g/n
AS FIXED INPUTS AND V-^ (m/min) AND PL (N/m2) AS INDEPENDENT
VARIABLES
g
J
r^
1
01
ST
M
V
5
§
^
a
N. V
PL\
C*
500
1,000
1,500
2,000
C
500
1,000
1,500
2.000
C
500
1,000
1,500
2,000
Time between
C
500
1,000
1,500
2,000
0.3 0.61 0
531 2,421 4,
-
1,172
2,343
520 2,321 4,
947
1,740
454 1,987 3,
-
783
1,252
cleaning cycles,
0 0
49
-
134
.8
520
-
300
646
-
-
mln.
0
-
-
-
Penetration, percent
£
i
T-
1
4
C
500
1,000
1,500
2,000
C
500
« 1,000
«
5
E
i
r
C
1,500
2,000
C
500
1,000
1.500
* 2JOOO
*C refers to
0.29 0.618 0.
0.57
1.0
0.058 0.182 0.
-
0.035
-
0.038
0.004 0.081 0.
_
0.0032
_
0.0032
913
-
-
392
-
234
-
-
_
continuous cleaning.
127
-------
TABLE 19. PREDICTED SYSTEM PERFORMANCE WITH ac = 0.4 AND C± = 2.29 g/m3
AS FIXED INPUTS AND V± (m/tnin) AND PL (N/m2) AS INDEPENDENT
VARIABLES
V
*L
0.3
0.61 0.91 1.
22 1.53
1.75
Pressure drop, N/m2
1
t
a
*
C
500
1,000
1,500
_
577
1,163
* 2,000
ti
e
t-
a
3
i
J
St
C
500
> 1,000
1,500
2,000
C
500
1,000
1,500
2,000
400
714
281
337
-
-
457 - 1,
570
1,160 1,154
1,742 1,
2,328
457 1,
500
810 941
1,128 - 1,
1,445
453 - 1,
445
580 792
663 - 1,
720
Time between cleaning cycles,
C
500
1,000
1,500
2.000
0
809
1,798
-
0
46.8
270 59.4
520
759 - 43
156 1,621
739
- -
159 1.618
-
-
421
=
004 1,395
-
176
-
mln.
0 n
-
.2
1,961
_
-
-
2,350
1,834
2,038
1,904
-
-
1,815
0
10.8
Penetration, percent
§
J
S
o
a
2
1
§
J
5
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
_
1.96
2.4
_
0.076
0.0496
_
-
_
0.0224
0.0226
-
1.23 - 1.
0.997
1.1 1.17
1.76 - 1.
2.07
0.975 0.
0.574
0.13 0.322
0.096 - 0.
0.083
0.749 - 0.
0.0283
0.029 0.064
0.029
0.0295 - 0.
09 1.37
-
-
28
-
777 1.05
-
-
489
-
462 0.760
.
-!
191
1.67
-
1.77
1.36
-
-
-
1.27
1.16
-
0.767
C refers to continuous cleaning.
128
-------
TABLE 20. PREDICTED SYSTEM PERFORMANCE WITH ac = 0.4 AND C± = 6.87 g/m3
AS FIXED INPUTS AND Vt (m/min) AND PL (N/m2) AS INDEPENDENT
VARIABLES
E
i
!<
2
X
*
C
500
1,000
1,500
2,000
2,500
C
500
« 1,000
0.3
578
1,164
_
403
726
a 1,500
a
^
E
3
2,000
2,500
C
500
1,000
1,500
283
359
a 2,000
2 2,500
0.61 0.8
Pressure drop
566 860
-
1,166
1,756
2,335
2,922
560 855
860
1,160
1,480
1,793
500 737
-
649
750
819
873
Time between cleaning
C
500
1,000
1,500
2,000
2,500
_
286
672
0 0
80
160
236
318
0.91 1.22 1.53
, N/m2
1,746 2,700
1,175
-
2,346
2,969 3,030
1,690 2,600
1,097
-
1,679
2,291 2,750
1,510 2,200
935
1,456
1,762 2,282
cycles, mln.
0 0
6.6
63
28.2 4.8
1.75
3,500
3,358
-
2,819
-
0
-
-
-
Penetration, percent
[
J
k
|
A
C
500
1,000
1,500
2,000
2,500
C
500
a 1,000
1.22
2.0
0.06
0.037
1
2,000
< 2,500
f
I
f
C
500
1,000
1,500
2.000
0.008
0.0078
-
_
2J500
0.73 0.762
1.1
1.5
1.87
2.19
0.36 0.323
-
0.13
0.09
0.08
0.074
0.089 0.077
-
0.015
0.015
0.015
0.015
1.1 1.61
-
0.869
-
1.44
1.57 1.69
0.57 1.03
-
0.302
-
0.229
0.54 1.02
0.35 0.83
0.065
-
0.057
0.207 0.62
2.0
1.42
-
-
-
1.18
C refers to continuous cleaning.
129
-------
TABLE 21. PREDICTED SYSTEM PERFORMANCE WITH ac = 0.4 AND C± = 22.9 g/m3
AS FIXED INPUTS AND Vi (m/min) AND PL (N/m2) AS INDEPENDENT
VARIABLES
\
PL
. V
\
\
0.3 0.61 0.91
1.22
Pressure drop, N/m2
|
J
I
&
(8
w
0)
>
5
§
J
d
*
c
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
Time
C
500
1,000
1,500
2,000
280 915 2,111
582
1,169 1,210
1,756
2,342 2,373 2,389
276 887 1,995
428
739 1,050
1,053
1,368 1,073 2,156
272 862 1,850
321
406 850
458
494 1,604 1,741
between cleaning cycles
000
71.4
209 10
330
479 55.2 5.4
3,752
-
3,517
-
3.328
-
-
, min.
0
-
-
-
Penetration, percent
1
3
1
«>
CO
z
s
<
1
J
a
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
0.622 0.91 1.33
1.16
1.99 1.1
2,64
3.16 1.89 1.46
0.133 0.159 0.351
0.062
0.034 0.17
0.025
0.0219 0.114 0.352
0.0053 0.024 0.155
0.0027
0.0027 0.013
0.0027
0.0027 0.0104 0.102
1.8
"
0.768
0.534
-
-
-
C refers to continuous cleaning.
130
-------
TABLE 22. PREDICTED SYSTEM PERFORMANCE WITH a = 1.0 AND C± = 6.87 g/tn3
AS FIXED INPUTS AND V± (m/min) AND PL (N/ra2) AS INDEPENDENT
VARIABLES
§
$
s
K
a
ij
a
>
<
g
1
c
£
t>
c
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
Time
C
500
1,000
1,500
2,000
0.3 0.61 0.
Pressure drop,
475
578 576
1,164 1,163
1,750
2,336
475
314 492
591 713
957
1,203
413
183 415
184 421
425
427
between cleaning
0
553 25.2
1,431 170
317.4
464.4
91 1.22 1.53
N/m2
1,244 1,780
_
-
2,375 2,414
1,209 1,705
_
1,504 1,889
1,038 1,452
_
1,062 1,494
cycles, mln.
0 0
-
-
43 15
1.75
2,227
2,113
1,789
0
-
Penetration, percent
S
«"
«
b
01
4
a
J
e
£
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
C
500
1,000
1,500
2,000
1.57
2.62 1.69
4.04 2.5
3.24
3.83
0.805
0.054 0.459
0.029 0.143
0.0908
0.070
0.268
0.0077 0.013
0.013
0.013
0.0128
1.70 2.04
-
2.46 2.36
0.702 1.0
0.42 0.872
0.309 0.664
-
-
- 0.14 0.393
2.37
-
-
1.34
1.04
-
C refers to continuous cleaning.
131
-------
TABLE 23. PREDICTED SYSTEM PERFORMANCE FOR FIXED AND VARIABLE DATA INPUT
COMBINATIONS NOT SPECIFIED IN TABLES 16 THROUGH 22
*L '
1,000 0.61
1,000 0.61
1,000 0.61
1,000 0.61
1,000 0.61
1,000 0.61
continuous ,0.61
' 2,000 0.61
£J continuous 0.91
hO
continuous 0.61
2,000 0.61
continuous 0.91
continuous 0.91
1,000 0.61
1,000 0.61
continuous 0.61
continuous 0.61
ac
1.0
1.0
0.2
0.2
0.2
0.2
0.4
0.4
1.0
0.1
0.4
0.4
0.1
0.4
0.4
0.4
0.4
C-L Other parameters
2.29
22.9
6.87
2.29
22.9
22.9
2.29
2.29
6.87
22.9
2.29
6.87
6.87
6.87
6.87
6.87
6.87
-
-
-
-
-
-
K2 =
K2 =
nonlinear
nonlinear
nonlinear
K2 =
nonlinear
-
K2 = 0.
K2 = 3.
K2 = 0.
K2 = 3.
3
3
model
model
model
3
model
333
333
333
333
Pressure drop
min.
383
539
815
735
1,332
944
580
930
530
625
790
-
553
918
380
983
max.
1,156
1,196
1,166
1,155
1,436
1,211
670
2,340
770
2,330
1,053
-
1,156
1,197
430
1,030
avg. c
692
797
974
896
1,400
1,127
650
1,520
700
2,310
1,440
980
2,140
790
1,075
425
1,000
Time
between
: leanings
548
40
87
160
0
4
0
230
0
0
240
0
0
304
6
0
0
Penetration
; min.
0.0273
0.0079
0.018
0.031
0.041
0.021
0.40
0.029
0.093
0.029
0.12
-
0.014
0.030
0.15
0.12
max.
3.04
2.52
0.593
0.843
0.707
0.878
1.3
1.4
3.3
4.5
2.0
-
1.2
0.92
0.65
0.86
avg.
0.15
0.15
0.115
0.124
0.138
0.136
0.98
0.17
0.67
0.26
0.19
0.39
0.40
0.054
0.32
0.32
0.37
-------
APPENDIX C
SENSITIVITY ANALYSIS GRAPHICAL PRESENTATIONS
FOR MULTIVARIABLE SYSTEMS
133
-------
4000
3000
E
5
I
«
2000
1000
V «0.3 m/min
Cj *2.29
PL =1000
PL =500
O CONTINUOUS
FRACTIONAL AREA CLEANED,oc
Figure 43. ~p versus ac and PL.
134
-------
4000
V«0.61 m/mln
Cj =2.29 fl/m3
PL = 1500
PL =1000
PL =500
O CONTINUOUS
FRACTIONAL AREA CLEANED,oc
Figure 44. P versus ac and PL.
135
-------
4000
3000
CvJ
E
UJ
IT
1
E
3
2000
1000
t4H
II
Iti
Hi
-r~
mi
Bfirlj
^
11.'' i.:
MM 11
mm
III!
Mil
Vi-0.9! m/mln
Cj *2.2
A PL = 2000
O PL = 1500
B PL =1000
V PL =500
© CON TINUOUS
urn
0.9
FRACTIONAL ARIA CLEANED,«e
Figure 45. P versus ac and PL-
136
IN.
m
Uii
:jj;|ii i;
till!'!!
1.0
-------
4000
3000
M
O
ft
O
Ul
Ui
I
Ul
O
IT
U
2000
1000
FRACTIONAL AREA CLCAMCO,«e
Figure 46. P versus a and P..
137
-------
Ut
K
y,
s
FRACTIONAL AMU CLIAMEO,a0
Figure 47. P versus ac and
138
-------
4000
3000
(M
s
2000 -
1000 .
V«0.6I m/min
Cj =6.87 g/m3
FRACTIONAL AREA CLEANED, oc
Figure 48. P versus a and
139
-------
4000
3000
eg
I
I
UJ
2000 7
1000
V«0.9| m/min
C( =6.87 g/n>3
P|_ = 1500
D PL =1000
= 500
AND/OR
CONTINUOUS
FRACTIONAL AREA CLEANED,ac
Figure 49. P versus ac and P^.
140
-------
4000
3000
(M
5
I
2000
I
1000
3 PL =1000
O PL =500
AND/OR
CONTINUOUS
FRACTIONAL AREA CLEANEO,oc
Figure 50. P versus a and P .
Li
141
-------
m
h
3000
CJ
E
O
o
s
£
3
2000
1000
H*
IT
tri!
I ilji
;
.
njiTiT
. :
t
i'
N
i-J
--'- -
>
i II
tfl
s
; !'
trh
1-11' ' ' l ! : I , |; !
:
'urrtrri r!_La±i
m
V«0.3 tn/min
ci s 22.9 g/m3
^ PL = 2000
N/ 1 :
CD PL =1000
V PL =500
O CONTINUOUS
iiu
!
:
...
:|':
0.5
[
vm
FRACTIONAL AREA CLEANEO,ae
Figure 51. P versus a and PT
"
1.0
142
-------
4000
V=0.6I m/mlfi
C, *22.9
PL : 1500
D PL =1000
O CONTINUOUS
FRACTIONAL AREA CLEANEO,oe
Figure 52. P versus a and PT.
c L
-------
4000
3000
a
o
S
s
§
a:
UJ
2000
1000
O PL "500
CD PL «iooo
INLET CONCENTRATION, Cj
Figure 53. P versus C. and P .
1 J-j
144
-------
400*
3000
2000
-------
4009
3000
r
Tf'f
IT ,TE
V-0.91 m/mln
n^ =O I
0C =0.1
-
> 2000
1500
Q PL »iooo
n O PL =800,
AND/OR
CONTINUOUS
tt
m
n
0.
I
2000
3
cc
UJ
[tf:
ilil
-
1000
JffP
IflTr
Iffl
i i
H
;.;.
tttt
III
Ml
. i
:
10
20
INLET CONCfNTHATION.Ci (fl/m3»
Figure 55. P versus C. and P .
X Ij
146
-------
400»
3000
2000
I
I!
1000
INLET CONCENTRATION, C|
Figure 56. P versus C and PT.
147
-------
4009
3000
2000
1
u
1000 r
V-0.3 m/mtn
OC -0.4
«isoo
Q PL "iooo
PL =500
CONTINUOUS
INLET COMCBNTMATION.Ci
Figure 57. P versus C. and P .
1 I i
148
-------
4009
3000
at
a.
2000
i
UJ
1000
INLET CONCENTRATION, Ct
Figure 58. p" versus C. and P .
.1 l_i
149
-------
4009
3000
2000
«n
S
ui
1000
PL *iooo
O CONTINUOUS ;fi
INLET CONCENTRATION, C|
Figure 59. P versus C. and PT
1 Li
150
-------
4000
PL « 1500
O CONTINUOUS
INLET CONCENTRATION, C| (fl/m3)
Figure 60. p versus C. and P ,
i L
151
-------
4009
3000
a.
I
2000 r
1000 r
PL * isoo
B PL »looo
T V PL =500
CONTINUOUS
INLET CONCENTRATION, C|
Figure 61. P versus C. and P .
1 L
152
-------
i n
1.0
07
0 5
8*"
it
E
&
m O2
Z v-fc
0
C
u
5 o i
UJ - -^
O O.O7
at
> 005,
<
no?
0.01
G
IPPt
3.3 ut
.! !
< i 1
j."
: :.
.
i
r~i~r~
LH
i
L y
El
j ' :
-
i
r
;
:
B:
:
: i.
n! !
4 i
1]
-W i
" T^i ^
: ' ,
. :
;
ti
1-1 i
jlf ;
;
hi
' '
2
: :
, (
i
il ! |
;.|
iii!
I
i il
i 1
i
T[TH1
;; R
i j ;
!!" m
LLfi,:
IS
i !
Sit
1
.
: U
ik '1
fj 8
ii U
If
i
us
i:
It a
till
rn
: 1
I !
9 i
J It
i L
1
|! S
j|
ffit
> CM
! :'
M .> - > - -
\ :i
:.
iii
~
w ^tl
tTF
IB
% i i^
it |i| i i :
Iii
111
ijt j * .
.,
B
n tFf
.u ^..4.
, ,
i ^i
j i
i !!
j
lill i :;
till K
1 If '
t i » l» ..
ff If
Iii; %
TJJ j
-:
I 7
V«0.3 m/m
Cj «2.29 g/i«
vj/ PL s ISOO
n pi »iooo
*-" rL
^ PL =50O
1
1 |
I
S|
ill
i: h
.if !!
1
:
)
FRACTIONAL AREA CLEANED, oc
Figure 62. pn versus a and P_.
C L
153
-------
z~
o
E
UJ
o
or
UJ
V « 0.61 m/mln
C| »2.29 0/«>3
& PL s2000
O PL « 1500
Q PL »iooo
V PL =800
O CONTINUOUS
FRACTIONAL AREA
e 7 s e| |
CLEANED, ac
Figure 63. Pn versus a and PT.
c L
154
-------
If\
U
r\ 7
O.7
n i
$i
1
C
i
" f\ 9
2 O.Z
O
t-
ff
S
SA 1
U.I
u
u> 0.07
DC
U n0«
> u.uo
0 O2
o.o
Q
;, »
Ml
1
T
Jj h
r>TT
V '
> 1
>
1 ! > i
V
.1.1
£j~* -r T" ft" *"
f
; II
*l
2
5 i : ! i
I: ' :' :
. .1 i
SIT i ~t~ rtt T
"hi :^TT :^H
Gj": ttpl
! ! i i ;'
., : -I - - - -U
3rf 31
. u i; 4
: i ;HI i1
EEiH!
§
;:
n
ill -i ;
: |[ 8] flt Iff
:: :;::£;::
. -
. | |i|L MM i> ; ||
!ji.
11 '
!! ff! ilii ; i
i n; i i ;
11 1 ii: HI:
jitl !li: j (:: iJ : I'J;
iriiy
i;: U s u
:ia t Mi
1, jf
JH &i
II
; j, I i
33L
1 ; :: ill 3p*t I'll! T!
: i i i i! ! i i i i i i
1 i ! ; t it litt h
4 4. ! , . r |.
!i tf i H ;; i.: i IM
1 fllpisffl Puts
:; 1': [iii t : ' HitPi
:! ]l] IS 3TM|
I 1 U1E
||| I ISfP
;"::inf
^1:
':; :
"Wr
: if f
,,,: . ,.;. .
3 UW T~«7
v«0.9l m/mln
C| -2.29 fl/»3
-------
VI.22 m/mln
»2.29 fl/ms
* 2000
a.
Ul
3 04 » » 7 B »T )
FRACTIONAL AREA CLEANED, oc
Figure 65. Pn versus a and PT.
c L
156
-------
i-
UJ
tc
UJ
0.01
V«0.3 m/mln
Cj «6.87
^ PL a 2000
Q p|_ a 1000
V PU =500
0.1 3 6(4
FRACTIONAL AREA CLEANED, oc
Figure 66. pn versus a and P ,
c L
157
-------
£
s
tu
o
£C
UJ
1.0
0.7
0.9 -
V»0.6l m/mln
Cj »6.87 fl/ms
A PL "2000
O PL s' 50°
D PL *iooo
V PU =300
O CONTINUOUS
3 O4
FRACTIONAL AREA CLEANED, ac
Figure 67. Pn versus a and P,.
c L
158
-------
h
UJ
O
<
<£
ui
5
V=*0.9I m/min
C| «6.87 fl/m^
a £ PL s200°
b<> PL s ISO°
c D PL »iooo
d V f\. =500
e 0 CONTINUOUS
FRACTIONAL
3 Q4 " « 7 S B|jQ
AREA CLEANED, ae
Figure 68. Pn versus a and PT.
c L
159
-------
Ul
VM.22 m/mln
C| «6.87 0/m3
a A PL s 20°o
<> PL = 1500
c Q pL = 1000
dV PU =500
e O CONTINUOUS
a a 7 B «|
FRACTIONAL AREA CLEANED, ac
Figure 69. Pn versus a and PT .
c L
160
-------
1.0
0.7
0.5
o
>-
<
0.2
O.I
!S
0.3 m/mln
Ci *22.9 0* "*
a A PL 8 200°
b O PL 8190°
c Q PL *iooo
d V PL =500
e O CONTINUOUS
FRACTIONAL AREA CLEANED, Oe
Figure 70. pn versus a and P ,
c L
161
-------
a:
UJ
<3
ac
UJ
V«0.6I m/min
C| »22.9 0/">3
0 A PL "2000
PL B 1500
c D PL »iooo
PL s
e O CONTINUOUS
FRACTIONAL AREA CLEANED,oc
Figure 71. Pn versus a and P .
C L
162
-------
f
z"
o
H
o
a:
UJ
V « 0.91 m/mln
Cj »22.9 «/«3
a A PL « 2000
PL isoo
c Q PL "iooo
CONTINUOUS
0.0
FRACTIONAL AREA
8 e 7
CLEANED, ae
Figure 72. Pn versus a and P
c L
163
-------
u
s
<£
V* 1.22 m/mln
Cj «229 9/m'
0 A PL * 200°
b O PL s '500
c D PL »iooo
d V PU =500
e O CONTINUOUS
s a 7 (
FRACTIONAL AREA CLEANED, ae
Figure 73. Pn versus a and
16'.
-------
10
S 4 ft 6 7 69 10 20
INLET CONCENTRATION, Cj (g/m5)
SO « TO8 "100
Figure 74. Pn versus C. and P ,
i L
165
-------
V«0.6I m/min
g/m3
8 4 7 11 K> 20
INLET CONCENTRATION, C, (g/m3)
90 70- »IOO
Figure 75. Pn versus C. and P .
i L
166
-------
1.0
»2000
bO PL "500
PL «iooo
0.01
8 4 5 6 7 e 9 10 20
INLET CONCENTRATION, C,
9De TO8 100
Figure 76. pn versus C and P
J- i
167
-------
0.01
' 4 B 7 9 10 ZO
INLET CONCENTRATION, C( (g/«9)
* 50 ° 70» lOO
Figure 77. Pn versus C and P .
i Li
168
-------
PL «isoo
PL »iooo
500
© CONTINUOUS
5 4 86769 10 20
INLET CONCENTRATION, C| (g/m5)
50 e TO8 100
Figure 78. pn versus C. and P .
i L
169
-------
0.01
8 4
INLET
8 6 7 6 9 10 ZO
CONCENTRATION, C( (g/m3)
30 e 70s *IOO
Figure 79. pn versus C. and P .
1 1.
170
-------
V«0.9I m/mln
OC»0.4
(800
PL "iooo
»500
CONTINUOUS
§ .1
0,01
84867«»IO 20
INLET CONCENTRATION, C| (g/ms)
Figure 80. Pn versus C and PT.
i L
171
-------
V-1.22 ,/,,
°C»0.4
/WI T
» 10 20
INLET CONCENTRATION, C| (g/m9)
90 70- 100
Figure 81. Pn versus C. and P .
1 J_j
172
-------
0.01
ZO * 80 T0» 100
IMLET CONCINTWATIOH, C, lfl/m5)
Figure 82. Pn versus C. and P .
i L
173
-------
c
I
N
O)
o
V»0.3 m/mln
Cj «2 29 g/ir.3
:::8ttttti::ttttJtt ffl fflffl
FRACTIONAL AREA
0.4
CLEANED, ac
Figure 83. tc versus a and PT.
-------
CO
I
ijj
Ul
llllMIIIIIIIIMIIIIIIIIIimiiyil
V 0.61 m/min
Cj »2.29
FRACTIONAL AREA CLEANED, oc
Figure 84. t,. versus a and PT .
c L
175
-------
I 700
CO
UJ
V < 0.3 m/min
Cj »6.87
0 PL
V PL =500
10
O.I
0.4
FRACTIONAL AREA CLEANED, oe
Figure 85. t versus a and PT.
c L
176
-------
o
z
Ul
111
III
CD
w
V 10.61 m/mln
j »6.87 o/m3
FRACTIONAL AREA CLEANED, ae
Figure 86. tf versus a and P .
177
-------
f
-------
I
E
en
I
i
V =0.3 m/min
Ci «22.9
PL = 1500
CD PL =1000
V PL =500
FRACTIONAL AREA
0.4
CLEANED,ae
Figure 88. pn versus a and P .
c L
179
-------
-------
1000
-------
1000
900
800
i 700
UJ
-J
U
III
"'
t
UJ
CD
600
500
400
300
200
100
5 10
INLET CONCENTRATION, Ci (g/m3)
Figure 91. t,. versus C. and PT .
i LI
182
-------
'e
v
^"^-^
: ^'**N^^^_ .
'
: /
&
-
u
"""""V
:. t
.
1
i
I
5 10 20
INLET CONCENTRATION, Ci (g/m3>
Figure 92. tf versus C± and
183
-------
1000
900
800
700
UJ
_i
o
UJ
UJ
CD
600
500
400
= 300
200
100
V.Q.6I m/m,B
QC'0.4
5 10
INLET CONCENTRATION, Ci
Figure 93. tf versus C, and PT.
184
-------
n
c
c
E
10
<
UJ
900
8UU
600
500
400
200
100
0
! :' '
! :
.
:
i
3 : : i.
:-t-i '.
. 1
I ;
; : : :
-i ; : '
i > ' '
..: :. . .
r
B-
|
n
: ;
i ;
:
'!
- +--
.
- I
- : ;
i
.
Eta
Si
j.. . . .
:
: :
!' 1 i
i 1:
.; . .
H
hi;
-
-
j n |-
HTT
,.,.
.
::::
:H
. . ,
".:'
. . .
!
~~-
; ; ;
;;;
;
- -
. .
HI
n:
::;
i
: ::
:
. rr:
- :~
~7
trTrrrr
11
t-f -'ft
Eft «+
; 7 r r
Hi ill: ;
tt$ S
11
II
4-j-^ ^TT
. .
jj >. _.»» -
:^:r ::;; *
' L-, il' '
..^|-L 4_^_ ,
'-~i3:
In :*
: tta .: !
:::..
Hi
m :.,
-i 1,4 ,,4i
::;;;£ ±:
j*' +j> aj!
jji 4'r ^L
1 "I t T
i ^ rr
ni-^~
L l-P l-r
.
;
AV-
~-if
.
1
.
!
-t-
,
H
5
"'
...
"!*
i
!
I
1
r
-
1
iO.
'
1
i.
!
.
F
. . . . .
'
1
:
! :
-
. , .
V «0.9I m/min
QC *0.4 o/n»3
A PI s 2000
*
i
CD PL =1000
. :
-
.
. -
=--: . i -.--:.-
i
| : 1.
-
;
-
.
i '
'
... . -. ._
-
: '
- -
....
j -
i !
i
*
5 10
INLET CONCENTRATION, Ci
20
Figure 94. t versus C. and P_.
i L
185
-------
1000
900
800
5 700
3
c
£
o"
UJ
UJ
300
200
100
V-1.22 m/mln
OC-0.4
600
500
400
5 10
INLET CONCENTRATION, Ci (g/m3)
Figure 95. t versus C. and P .
1 Li
186
-------
1000
900
BOO
* ~rr\r\
fOO
»
a
c
E
uT 600
d 50°
* 400
g
V
i 30O
1-
200
100
0
Bffl
-HI :
- '
V;
I
! : .
'
1 ' ' 1-
v| : : !.
: i : :
.;:;;-
: ' . :
. i . . .
\
rfcEiEr:
: : ,
«-
£±
:
r4!
;
irr^
:
|
\ J-
: :
: r:
1
V
gi
:
.
. . -i
El ]
'
i :
!
rrr
:
1
, ;
.
H
t : : :
s
\
:
1
|
:iii
m
i
1 ; ; ;
i .1
.
i
: :
s
-
T-T
iif
itt
:
; |
M
-ii:
Hi
,::
:
n -
.
T 1-^
E^
:
:
S |
!
r-rtrrril
B±
£l; :-: i
1
11 '
S: S
apwt
Lin ". ' ', r
"! . L .
/;t ' +.
. .
~-',~t- nz^ -
1 ^E
EgE
ill
ill
it m m
II
T T,",u
: ,::! |
pr jtrrtjp
m i" Ht;
1 ' . j
ir ir*-1*-:
..-,... . _
|||
:; :;.T(!^
HI
E :: JJ:::
- W
-
'
1
i'1'
.
jn '
a. ,...
::: :::
:;; :::i
S .:::
| ::::
:::; ~
:~
1
_,
: i
t »
. -
m
" rr :ir.
-, ...1 .;>
- ;r. , «-
; :;;~
||
*c nr ~
*~H
.^
~; r_
i
U
^ .
1
.
,
. : ' :
: . . '
;-
. .
V « 0.61 m/mln
A P
L *2000
^J> PL = 1 3oo
CD PL =1000
V PL =500
..
- : : i
1
-
-
"~
^.^^^^
' : 1 .1
, , . .
, 1 i i
1
;
. i .
,
1 ~*^'J
5 10 20
INLET CONCENTRATION ,Ci (g/m^)
Figure 96. tf versus C and P .
18-
-------
APPENDIX D
DERIVATION OF RELATIONSHIPS BETWEEN AVERAGE SYSTEM
PRESSURE DROP AND SYSTEM DESIGN PARAMETERS
By examining the overall pressure drop characteristics of a fabric filter
system, equations can be developed to correlate the average system pressure drop
with the major operating and design parameters. Figures 97 and 98 represent
typical pressure versus time traces for limiting pressure or time controlled
systems and continuously cleaned systems, respectively. In order to simplify
the analysis, a four compartment system was chosen for illustration purposes.
The approach taken was to first resolve the total area under the curve for a
specified pressure-time trace into several readily definable secondary areas
such as deliniated by the bounding dotted lines. The area below the curve
divided by the appropriate time differential then represents the average system
operating pressure for the time range of interest. Since the two systems
described here behave differently with respect to the pressure-time relationship,
each one is analyzed separately.
LIMITING PRESSURE AND TIMED CYCLE SYSTEMS
The average pressure drop for the system conforming to Figure 97 can
be expressed as:
_ n = 8
P = £ a±/tc + tf (40)
noting that tc and tf refer to the cleaning cycle and the noncleaning time
intervals, respectively.
188
-------
Pmln
V)
V)
in
TIME
Figure 97. Example of pressure-time trace for limiting pressure
or time controlled cleaning systems.
max
tc/n
TIME
Figure 98. Example of pressure-time trace for
continuously cleaned systems.
189
-------
The area of sections 1 through 4
Z ai + a2 = Pinin (tf + tc) (41)
a.$ = -£. (?2 ~ Pmin) (42)
2
(*2 - Pmin)
If tf is large, >2 hours, the assumption of a linear path from Pmin to
PL will not cause a large error in the estimation of area 4 such that the Equa-
tion (43) approximation is acceptable. However, definition of areas 5 through 8
is more difficult since the dust loading distribution throughout the baghouse
changes with time during the cleaning cycle.
To simplify the integration process for areas 5 through 8 it was first
assumed that the area of each section could be approximated by a triangular
element. It has been further assumed that each section (5 through 8) could be
described by an average of the uppermost and lowermost areas; i.e., (35 + as)/2
in the present case. The base of the triangles (5 and 8) has been defined in
terms of the pressure increase that takes place when any compartment is taken
off line at any point during the cleaning cycle. The height of each triangle
is the time interval required to clean each compartment, tc/n.
For areas 5 and 8, respectively.
and
Thus the average area is estimated to be
190
-------
and the total area for elements 5 through 8 becomes
n = 8 to 8
V* Cc
f a . = ^" /p I p s
*~J i 4(n-l) ! rmin''
mm-'
" > ~~ *- f
i = 5
The combination of Equations (40) through (44) leads to the following
expression for average pressure drop, P
(45)
For any specified system design, the terms tc and either tf or PL represent
known quantities.
However, since a value for Pmin will not be available, Pmin must be defined
in terms of the other system parameters. If the value for the average fabric
dust loading in the baghouse is known at the point of minimum pressure loss,
^min» tnen ^min can ^e determined from:
Pmin = SEV + K2 WminV (46)
The average fabric loading just after cleaning, Wmin, can be estimated from
a material balance over the cleaning cycle.
Wmin = WP - ac Wp (47)
Since Wp is the average loading during the cleaning cycle and ac is the fractional
area cleaned, the product of ac and Wp describes the amount of dust removed
during the cleaning cycle. The average loading during cleaning can be estimated
from:
The first term on the right hand side of Equation (48) represents the
average fabric loading (W') corresponding to a pressure level of PL. The average
amount of dust added during cleaning is represented by the second term.
191
-------
Combining Equations (46) to (47) leads to the following equations for
Pmin = SEV± + (PL - SEVi + CiVi2K2tc/2) (l-ac) (49)
Depending upon the type of system (pressure or time controlled) either tf or
PL will appear as known quantities. Since both terms appear in Equations (45)
and (49), a relationship between P^ and tf is required. A material balance
over the filtration period results produces the following,
wmin + CiVitp = WP <50>
The term C±V±tf is the amount of dust added to the system over the filtra-
tion period. Thus the combination of Equations (47), (.48) and (5Q) results
in a relationship between tf and P^:
ac (PL - S V±)
tg te (ac-l)/2 + CE2 (51)
and rearranged:
PL = f + d-ac)tc/2
c
(52)
Since all critical parameters are now defined on the basis of known
quantities, the relationship b.etween average system pressure loss and the system's
operating parameters can be developed by combining Equations (45) and (49):
P = 1/2 L1 + 2(n-l)(l + tf/tc) J (53)
[pL(2-ac) + acSjjVi + (l-ac)C1K2Vi2tc/2]
The average pressure loss for limiting pressure systems can be estimated
from Equations (51) and (53).
Timed cycle systems can be analyzed with Equations (52) and (53).
Equation (51) can also serve to indicate whether or not a limiting pressure
system must be in fact clean continuously. If the time between cleanings, tf,
192
-------
reduces to zero then the system must clean continuously since the dust deposi-
tion rate is too high for pressure drops lower than PL to be achieved.
CONTINUOUSLY CLEANED SYSTEMS
The approach to the analysis of continuously cleaned systems is similar
to that used for limiting pressure systems. With reference to Figure 99 the
average pressure drop is:
p =
a2
tc/n
?min X tc/n + 1/2 (Pmax " Pmin)tc/n (54)
tc/n
p I "p
max min
2
The area of section 2 has been approximated by a triangular section. If
the Increase in pressure due to added dust can be neglected over the time
interval tc/n then Pm^n and Pmax can be related by:
11 (55)
*max (n-1)
Equation (55) describes the increase in pressure loss due to shifting the
flow of n compartments through n-1 compartments when a compartment is taken off
line for cleaning. A relationship for P ^ can be found if the fabric loading
distribution through the baghouse can be determined. The minimum and maximum
average compartment loadings are related by:
"max - *c Wmax = wmin (56)
and
wmin + civifcc = wmax
Equation (56) is basically a rearranged form of the relationship defining
the fractional area cleaned, ac.
193
-------
3000
2500
CM
E
2000
a
o
a:
a
ui
2; 1500
V)
-------
Equation (57) describes the material balance in which the term C.V.t
lie
is the amount of dust added to the system during the cleaning cycle. The
minimum and maximum loadings are therefore:
wmin = C±V±tc (l-ac)/ac (58)
Wmax = CiVitc/ac (59)
An expression for the minimum pressure loss can now be determined by inte-
grating the linear drag relationship over the loading distribution. If a linear
loading distribution is assumed then loading varies as:
W = C^itcd-a^/ac + C^tc n/NT (60)
Where n denotes an arbitrary bag area and NT is the total number of such
areas on the bag surfaces. The overall system minimum drag, Smin, is calculated
as:
Smin
n = 0
If the loading distribution is treated as a continuous function, Equation
(61) may be rewritten as,
NT
-!_ = J: [ 1 d
nin " NT J SE + K2 W
dn
SE + K2 W (62)
n=0
Upon substituting Equation (60) for W in Equation (62) and integrating
the following is obtained:
(63)
j1 + SE + K2CiVitc(l-ac)/ac
Since Pm^ = S . V^, an expression for the average pressure loss can be
obtained by combining Equations (54), (55) and (63) along with the rela-
tionship between pressure and drag.
195
-------
p =
In
i i
[ s^w^1-*^]
(2n-l)(2n-2)
(64)
Equations (51) and (40) and Equation (64) have been plotted in
Figures 99, 100 and 101 for selected combinations of filter operating param-
eters. Also shown in the figures are the curves developed by the baghouse
simulation program for the same operating parameters. The values of the para-
meters used in Equations (51), (53) and (64), other than those shown in
Figures 99 through 101 are listed in Table 24.
TABLE 24. VALUES OF PARAMETERS USED TO GENERATE AVERAGE
PRESSURE DROP VERSUS VELOCITY CURVES
Number of compartments, n =10
Cleaning cycle time, tc = 30 minutes
Specific resistance coefficient, K2 = 1.322 N-min/g-m at 0.61 m/rain, 150°c
Effective residual drag, SE = 529 N-min/m3 at 150°C
The specific resistance coefficient must also be corrected for velocity
before entry into the equations.
With reference to Figure 99, the system described as ac = 0.4 and C. = 2.29,
which is represented by the solid line, is the performance predicted by the bag-
house model computer program. The dashed curves, which follow roughly the path
of those predicted by the model were generated by Equations (51), (53) and
(64). The curve predicted by Equations (51) and (53) extends beyond the
lower continuous cleaning curve as indicated by the dotted line. The end point
of the dotted curve is the point at which Equation (51) predicts a time between
196
-------
3000
2500
OJ
2000
Q.
O
111
OC
3
CO
CO
U
1500
1000
500
CONSTANT PARAMETERS
"c "0.4
q «6.87 g/m3
SOLID LINE-RESULTS FROM FILTRATION
MODEL
DASHED LINE-RESULTS FROM SIMPLIFIED
EQUATIONS
0.5 1.0
AVERAGE FACE VELOCITY, m/min
1.5
Figure 100. Estimation of average pressure drop by computer
model and simplified equations.
197
-------
CONSTANT PARAMETERS
dc »
ci »6.87 (j/nv3
SOLID LINE-RESULTS FROM FILTRATION
MODEL
DASHED LINE-RESULTS FROM SIMPLIFIED
EQUATIONS
EQUATION D-25 »/
EQUATIONS 0-12. D-14
0.5 1.0
AVERAGE FACE VELOCITY, m/min
Figure 101. Estimation of average pressure drop by computer
model and simplified equations.
198
-------
cleanings, tf, of zero. The actual intersection of the limiting pressure
and continuous cleaning curves appears at a lower velocity, however. Performance
as predicted from Equations (51) and (53) is not dependable at very low
values of tj, even though the error in pressure drop is less than about 30 per-
cent. If the intersection of the limiting pressure and continuous cleaning
curves is taken as the point of actual transition to continuous cleaning, however,
then the differences in pressure drop as predicted by the model and the equations
presented in this section become smaller and perhaps more flexible. Inspection
of the remaining curves in Figures 99 through 101 suggests that the pressure
loss estimates for the two approaches are in fair agreement considering the
assumptions and simplifications used in the development of Equations (51),
(53) and (64).
The equations should be used mainly to investigate the interrelationships
between the various operating parameters and their combined effect on system
pressure loss. The basic equations are amenable to solution by conventional
pocket size calculators.
199
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO
EPA-600/7-79-043C
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
Fabric Filter Model Sensitivity Analysis
5. REPORT DATE
April 1979
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Richard Dennis, H.A.Klemm, and William Battye
8. PERFORMING ORGANIZATION REPORT NO.
GCA-TR-78-26-G
9. PERFORMING ORGANIZATION NAME AND ADDRESS
GCA/Technology Division
Burlington Road
Bedford, Massachusetts 01730
10. PROGRAM ELEMENT NO.
EHE624
11. CONTRACT/GRANT NO.
68-02-2607, Task 7
17. 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
Task Final; 6/78 - 2/79
14. SPONSORING AGENCY CODE
EPA/600/13
is. SUPPLEMENTARY NOTES
2925.
project officer is James H. Turner, MD-61, 919/541-
e. ABSTRACT
rep0rt gjves results of a series of sensitivity tests of a GCA fabric
filter model, as a precursor to further laboratory and/or field tests. Preliminary
:ests had shown good agreement with field data. However, the apparent agreement
between predicted and actual values was based on limited comparisons: validation
was carried out without regard to optimization of the data inputs selected by the fil-
ter users or manufacturers. The sensitivity tests involved introducing into the model
several hypothetical data inputs that reflect the expected ranges in the principal fil-
ter system variables. Such factors as air/cloth ratio, cleaning frequency, amount of
cleaning, specific resistence coefficient K2, the number of compartments, and inlet
concentration were examined in various permutations. A key objective of the tests
was to determine the variables that require the greatest accuracy in estimation based
on their overall impact on model output. For K2 variations , the system resistance
and emission properties showed little change; but the cleaning requirement changed
drastically. On the other hand, considerable difference in outlet dust concentration
was indicated when the degree of fabric cleaning was varied. To make the findings
more useful to persons assessing the probable success of proposed or existing fil-
ter systems , much of the data output is presented in graphs or charts.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATl Field/Group
Pollution
Filtration
Fabrics
Mathematical Models
Sensitivity
Analyzing
Pollution Control
Stationary Sources
Fabric Filters
Bag Houses
13B
07D
11E
12A
14B
8. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
213
20. SECURITY CLASS (This page/
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
200
------- |