&EPA
                 IncJi          EPA •
        Environmental Pr< '    Lilt
                         /1 1
Filtration Parameters
for Dust Cleaning Fabrics

Interagency
Energy/Environment
R&D Program Report

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                  RESEARCH REPORTING SERIES


Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into 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
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    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
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essary environmental data and control technology. Investigations include analy-
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                       EPA REVIEW NOTICE
This report has been reviewed by the participating Federal Agencies, and approved
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This document is available to the public through the National Technical Informa-
tion Service. Springfield, Virginia 22161.

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                                     EPA-600/7-79-031

                                           January 1979
     Filtration  Parameters
for  Dust Cleaning  Fabrics
                       by

            J.R. Koscianowski, Lidia Koscianowska,
              and Eugeniusz Szczepankiewicz

         Institute of Industry of Cement Building Materials
                    45-641 Opole
                Oswiecimska Str. 21, Poland
             Public Law 480 (Project P-5-533-3)
               Program Element No. EHE624
             EPA Project Officer: James H. Turner

          Industrial Environmental Research Laboratory
            Office of Energy) Minerals, and Industry
              Research Triangle Park, NC 27711
                    Prepared for

          U.S. ENVIRONMENTAL PROTECTION AGENCY
             Office of Research and Development
                 Washington, DC 20460

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                                 ABSTRACT


   This report describes laboratory and pilot scale testing of bag filter
fabrics.  Filtration performance data and mathematical modeling para-
meters are given for four Polish fabrics tested with cement dust, coal
dust, flyash and talc.

   The following conclusions were reached:

       The process  of clean air flow, as  well as the dust fil-
       tration process,  are stochastic processes of the nor-
       mal type.
       For filtration Type I (laboratory scale - as defined in
       the report), dust collection efficiency is an exponen-
       tial function depending on air-to-cloth ratio, dust cov-
       ering, and type of filtration structure.

       For filtration Type I, resistance increases with time
       or dust covering  in a parabolic fashion. Outlet concen-
       tration as a function of dust covering is also a para-
       bolic relationship. Structurally, the fabrics are heter-
       ogeneous , anisotropic media.

       Free area is presently the best structural parameter
       for characterizing structure of staple fiber fabrics.
       Electrostatic properties of dusts depend on their his-
       tory; charge  decays with time. Dust cake formation
       can be influenced by specific electrostatic properties
       of the fabric  and  dust.
                                  11

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                                  CONTENTS

                                                                      Page

Figures	       iv

Tables  	        x

Acknowledgement 	      xii

     Section I.  Conclusions  	        1

     Section II.  Recommendations 	        2

     Section III.   Introduction 	        3

          Research Objectives 	        4
          General  Program 	        4
          Detailed Program for the Second Phase 	        6
          Fabric and Dust Selection 	        9

     Section IV.  Theory of Dust Filtration 	       10

     Section V.  Laboratory Testing 	       26

          Equipment and Procedures  	       26
          Results	       26
          Discussion of Results 	       44
          Conclusions	       56

     Section VI.  Preliminary Mathematical Model of Dust
       Filtration	       57

     Section VII.   Study of Filter Medium Parameters  	       69

          Introduction  	       69
          Clean Air Flow Through Filtration Structures  	       72
          Estimation and Comparison of Some Fabric Parameters .  .       87
          Testing of Fabric Geometry  	       91
          Conclusions	       91

     Section VIII.  Study of Dust Parameters  	       92

          Introduction  	       92
          Equipment and Procedures  	       93
          Results and Discussion  	       93
          Conclusions	       99

     Section IX.  Electrostatic Properties of Dusts and
       Fabrics	      100

          Introduction  	      100
          Equipment and Proceduress 	      101
          Results and Discussion  	      109
          Conclusions	      131

     Section X.  Additional Work  	      132

Appendix A	      133
Appendix B	      207
Appendix C	      211


                                     111

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                                  FIGURES
No.
 1      Filtration Process Schematic 	     11
 2      Types of Dust Filtration	     14
 3      Efficiency as a Function of Dust Covering	     20
 4      Schematic Representation of Basic Performance Parameters
        for Fabric Filters   	     23
 4a     Geometrical Considerations Attributed to Fabric
        Structures	     71
 5      Particle Size Distribution for Cement Dust ........     95
 6      Particle Size Distribution for Coal Dust	     96
 7      Dependence of Kinetic Specific Surface On Degree of
        Dispersion Measurement M	     97
 8      Dependence of Kinetic Specif-ic Surface On Degree of
        Dispersion Measurement MMD 	     98
 9      Diagram of Dust Charge Measurement 	    102
10      Electrodes for Measurement of Fabric Resistivity 	    104
11      Measurement Schematics for Fabric Electrical  Properties   .    106
12      Measurement of Charge Decay Time 	    108
    «                                             . •
13      Particle Charge Dependence on Diameter (Non-
        fractionated Cement Dust)	;	    Ill
14      Particle Charga Dependence on Diameter (Fractionated
        Cement Dust	'.	    HZ
15      Particle Charge vs. Diameter for Non-fractionated
        Cement Dust Passed Through an Electrical Discharge ....    112f
16      Particle Charge Dependence on Diameter (Non-fractionated
        Coal Dust) .  . i	    115
17      Particle Charge Dependence on Diameter (Fractionated
        Coal Dust)	    116
18 ° *   Particle Charge vs. Diameter for Non-fractionated
        Coal Dust Passed Through an Electrical Discharge 	    117
19      Dependence of Bulk Resistivity on Pressure	'    122
                                                                  •»
20      The Effect of Humidity Upon Cement Dust Resistivity  ...    125
21      Dependence of Dust Resistivity Upon Temperature
        (K=10X)	    126
22      Function U(t) for Fabric ET-4	    127
23      Function U(t) for Fabric ET-30	    128

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                               FIGURES (con.)
 No.                                                                  Page
 24      Function U(t) for Fabric F-tor 5	     129
 25      Function U(t) for Fabric PT-15	     130
A-l      Particle Size Distribution for Cement Dust 	     134
A-2      Particle Size Distribution for Coal Dust	     135
A-3      Particle Size Distribution for Talc Dust 	     136
A-4      Particle Size Distribution for Fly Ash Dust	     137
A-5      Pressure Difference vs. Dust Cover for Cement Dust
         and Fabric ET-4 (separated dust) 	     138
A-6      Pressure Difference vs. Dust Cover for Cement Dust
         and Fabric ET-4 (unseparated dust) 	     139
A-7      Pressure Difference vs. Dust Cover for Coal Dust and
         Fabric ET-4 (separated dust) 	     140
A-8      Pressure Difference vs. Dust Cover for Coal Dust and
         and Fabric ET-4 (unseparated dust) 	     141
A-9      Pressure Difference vs. Dust Cover for Talc Dust
         and Fabric ET-4 (separated dust) 	     142
A-10     Pressure Difference vs. Dust Cover for Fly Ash and
         Fabric ET-4 (separated dust) 	     143
A-11     Pressure Difference vs. Dust Cover for Cement Dust and
         Fabric ET-30 (separated dust)  	     144
A-12     Pressure Difference vs. Dust Cover for Cement Dust and
         Fabric ET-30 (unseparated dust)  	     145
A-13     Pressure Difference vs. Dust Cover for Coal Dust and
         Fabric ET-30 (separated dust)  	     146
A-14     Pressure Difference vs. Dust Cover for Coal Dust and
         Fabric ET-30 (unseparated dust)  	     147
A-15     Pressure Difference vs. Dust Cover for Talc Dust and
         Fabric ET-30 (separated dust)  	     148
A-16     Pressure Difference vs. Dust Cover for Fly Ash Dust
         and Fabric ET-30 (separated dust)  	     149
A-17     Pressure Difference vs. Dust Cover for Cement Dust
         and Fabric F-tor 5 (separated dust)  	     150
A-18     Pressure Difference vs. Dust Cover for Cement Dust
         and Fabric F-tor 5 (unseparated dust)  	     151
A-19     Pressure Difference vs. Dust Cover for Coal Dust and
         Fabric F-tor 5 (separated dust)  	     152

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                               FIGURES  (con.)

 No.                                                                  £§fl§

A-20     Pressure Difference vs. Dust Cover for Coal Dust and
         Fabric F-tor 5 (unseparated dust)  	     153

A-21     Pressure Difference vs. Dust Cover for Coal Dust and
         Fabric F-tor 5 (unseparated dust)  	     154
A-22     Pressure Difference vs. Dust Cover for Fly Ash Dust and
         Fabric F-tor 5 (separated dust)  	     155

A-23     Pressure Difference vs. Dust Cover for Cement Dust and
         Fabric PT-15 (separated dust)  	     156

A-24     Pressure Difference vs. Dust Cover for Cement Dust and
         Fabric PT-15 (unseparated dust)  	     157

A-25     Pressure Difference vs. Dust Cover for Coal Dust and
         Fabric PT-15 (separated dust)  	     158

A-26     Pressure Difference vs. Dust Cover for Coal Dust and
         Fabric PT-15 (unseparated dust)  	     159

A-27     Pressure Difference vs. Dust Cover for Talc Dust and
         Fabric PT-15 (separated dust)  	     160

A-28     Pressure Difference vs. Dust Cover for Fly Ash Dust and
         Fabric PT-15 (separated dust)  	     161

A-29     Theoretical Laboratory Efficiency for Cement Dust and
         Fabric ET-4 (separated dust) 	     162

A-30     Theoretical Laboratory Efficiency for Cement Dust and
         Fabric ET-4 (unseparated dust)   	     163

A-31     Theoretical Laboratory Efficiency for Coal Dust and
         Fabric ET-4 (separated dust)  	      164

A-32     Theoretical Laboratory Efficiency for Coal Dust and
         Fabric ET-4 (separated dust)  	      165

A-33     Theoretical Laboratory Efficiency for Talc Dust and
         Fabric ET-4 (separated dust)  	      166

A-34     Theoretical Laboratory Efficiency for Fly Ash Dust
         and Fabric ET-4 (separated dust)  	      167

A-35     Theoretical Laboratory Efficiency for Cement Dust and
         Fabric ET-30 (separated dust) 	      168

A-36     Theoretical Laboratory Efficiency for Cement Dust and
         Fabric ET-30 (unseparated dust) 	      169

A-37     Theoretical Laboratory Efficiency for Coal Dust and
         Fabric ET-30 (separated dust) 	      170

A-38     Theoretical Laboratory Efficiency for Coal Dust and
         Fabric ET-30 (unseparated dust) 	      171
                                     v1

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                               FIGURES (con.)
 No.                                                                  Page
A-39     Theoretical Laboratory Efficiency for Talc Dust and
         Fabric ET-30 (separated dust) 	     172
A-40     Theoretical Laboratory Efficiency for Fly Ash Dust and
         and Fabric ET-30 (separated dust) 	     173
A-41     Theoretical Laboratory Efficiency for Cement Dust and
         Fabric F-tor 5 (separated dust) 	     174
A-42     Theoretical Laboratory Efficiency for Cement Dust and
         Fabric F-tor 5 (unseparated dust) 	     175
A-43     Theoretical Laboratory Efficiency for Coal Dust and
         Fabric F-tor 5 (separated dust) 	     176
A-44     Theoretical Laboratory Efficiency for Coal Dust and
         Fabric F-tor 5 (unseparated dust) 	     177
A-45     Theoretical Laboratory Efficiency for Talc Dust and
         Fabric F-tor 5 (separated dust) 	     178
A-46     Theoretical Laboratory Efficiency for Fly Ash Dust and
         Fabric F-tor 5 (separated dust) 	     179
A-47     Theoretical Laboratory Efficiency for Cement Dust and
         Fabric PT-15 (separated dust) 	     180
A-48     Theoretical Laboratory Efficiency for Cement Dust and
         Fabric PT-15 (unseparated dust) 	     181
A-49     Theoretical Laboratory Efficiency for Coal Dust and
         Fabric PT-15 (separated dust) 	     182
A-50     Theoretical Laboratory Efficiency for Coal Dust and Fabric
         PT-15 (unseparated dust)  	     183
A-51     Theoretical Laboratory Efficiency for Talc Dust and
         Fabric PT-15 (separated dust) 	     184
A-52     Theoretical Laboratory Efficiency for Fly Ash Dust and
         Fabric PT-15 (separated dust) 	     185
A-53     Dependence of Function F, and F« On the Air-to-Cloth
         Ratio, q .
         a.  Fabric ET-4 and Unseparated Cement Dust
         b.  Fabric ET-4 and Unseparated Coal Dust	     186
A-54     Dependence of Function FI and F? On the Air-to-Cloth Ratio
         V
         a.  Fabric ET-4 and Separated Fly Ash Dust
         b.  Fabric ET-30 and Separated Cement Dust  	     187
A-55     Dependence of Function F, and F. On the Air-to-Cloth
         Ratio, qg.
                                     vii

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                               FIGURES  (con.)
 No.                                                                  fafl§
         a.  Fabric ET-30 and Unseparated Cement Dust
         b.  Fabric ET-30 and Separated Coal Dust	     188
A-56     Dependence of Function F, and  F? On the Air-to-Cloth
         Ratio, q  .               '      *
         a.  Fabric ET-30 and Unseparated Coal Dust
         b.  Fabric £T-30 and Separated Talc Dust	     189
A-57     Dependence of Function F, and  f9 On the Air-to-Cloth
         Ratio q .                '      *
         a.  Fabric ET-30 and Separated Fly Ash Dust
         b.  Fabric F-tor 5 and Separated Cement Dust	     190
A-58     Dependence of Function F, and  fy On the Air-to-Cloth
         Ratio, q  .               i      *           .
         a.  Fabric F-tor 5 and Unseparated Cement Dust
         b.  Fabric F-tor 5 and Unseparated Coal Dust	     191
A-59     Dependence of Function F, and  F9 On the Air-to-Cloth
         Ratio, q  .               '      *
         a.  Fabric F-tor 5 and Separated Talc Dust
         b.  Fabric F-tor 5 and separated Fly Ash Dust 	     192
A-60     Dependence of Function F, and  F9 On the Air-to-Cloth
         Ratio, V
         a.  Fabric PT-15 and Separated Cement Dust
         b.  Fabric PT-15 and Unseparated Cement Dust  	     193
A-61     Dependence of Function F, and  F, On the Air-to-Cloth
         Ratio, q  .               '      *
         a.  Fabric PT-0.5 and Separated Coal Dust
         b.  Fabric PT-15 and Unseparated Coal Dust  	     194
A-62     Dependence of Function F, and  F« On the A1r-to-Cloth
         Ratio, qg               '      z
         a.  Fabric PT-15 and Separated Talc Dust
         b.  Fabric PT-15 and separated Fly Ash Dust 	     195
A-63     Variation of Final Concentration for Fabric ET-4
         and Separated Cement Dust 	     196
A-64     Variation of Final Concentration for Fabric ET-4
         and Separated Coal Dust	     197
A-65     Variation of Final Concentration for Fabric ET-30 and
         Separated Cement Dust 	     198
A-66     Variation of Final Concentration for Fabric ET-30 and
         Separated Coal Dust	     199

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                               FIGURES (con.)
 No.                                                                  Page
A-67     Variation of Final Concentration for Fabric F-tor 5 and
         Separated Cement Dust	      200
A-68     Variation of Final Concentration for Fabric F-tor 5 and
         Separated Cement Dust	      201
A-69     Variation of Final Concentration for Fabric PT-15 and
         Separated Cement Dust	      202
A-70     Variation of Final Concentration for Fabric PT-15 and
         Separated Coal Dust	      203
A-71     Diagram of the Laboratory Test Stand  	      204
A-72     Loss of Charge for Fabric F-tor 5	      205
                                      ix

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                                  TABLES
No.                                                                  Page
 1      Fabric Parameters  ....................       7
 2      Particle Size Distribution of Test Dusts  ........       8
 3      Permeability of Filtration Fabrics  ...........      27
 4      Laboratory Efficiency of Polyester Style ET-4 ......      28
 5      Laboratory Efficiency of Polyester Style ET-30  .....      29
 6      Laboratory Efficiency of Polyester Style F-tor 5  ....      30
 7      Laboratory Efficiency of Polyamide Style PT-15  .....      31
 8      Laboratory Efficiency of Polyester Style ET-4
        (unseparated dust)  ......... . ..........      32
 9      Laboratory Efficiency of Polyester Style ET-30
        (unseparated dust)  ...................      33
10      Laboratory Efficiency of Polyester Style F-tor 5
        (unseparated dust) ....................      34
11      Laboratory Efficiency of Polyamide Style PT-15
        (unseparated dust)  .....                                  35
12      Final Pressure Drop in Laboratory Testing for
        Polyester Style ET-4  ..................      36
13      Final Pressure Drop in Laboratory Testing for
        Polyester Style ET-30 ..................      37
14      Final Pressure Drop in Laboratory Testing for
        Polyester Style F-tor 5 .................      38
15      Final Pressure Drop in Laboratory Testing for
        Polyamide Style PT-15 ..................      39
16      Final Pressure Drop in Laboratory Testing for
        Polyester Style ET-4 (unseparated dust) .... .....      40
17      Final Pressure Drop in Laboratory Testing for
        Polyester Style ET-30 (unseparated dust)  ........      41
18      Final Pressure Drop in Laboratory Testing for
        Polyester Style F-tor 5 (unseparated dust)  .......      42
19      Final Pressure Drop in Laboratory Testing for
        Polyamide Style PT-15 (unseparated dust)  ........      43
20      E  as a Function of q   .................      46
21      Coefficient n as a Function of q  ............      47
22      Coefficients of Parabolic Equation:  FI = a-|(qQ)  +
        bl1g * cl .................... ' ' •  •      «
23      Coefficients of Parabolic Equation F  = n =         *
               C2 ........................      50
24      Extremal Alr-to-Cloth Ratios qg ext  ...........      51

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                               TABLES (con.)
No.                                                                  Page
                                       o
25      Outlet Concentration, CQ in q/m ,  in Laboratory
        Testing of Cement Dust	      53
                                      3
26      Outlet Concentration c  in g/m , in Laboratory
        Testing of Coal Dust	      54
27      Clean Air Flow Through Fabrics   	      73
28      Standard Deviation in the Air-to-Cloth Ratio
        (in m3/m2/min)   	      76
29      Results of a Kolmogorov Test   	      80
30      Similarity of Tested Fabrics   	      83
31      Clean Air Flow Through Fabrics at Low Values
        of Pressure Drop   	      84
32      Values of Coefficient a and b for Equation 88	      86
33      Comparison of Dust Parameters	      94
34      Charges on Non-fractionated Cement Dust  	     109
35      Charges on Fractionated Cement Dust	     110
36      Charges on Non-fractionated Cement After Passing
        Through an Electrical Discharge  	     114
37      Charges on Non-fractionated Coal Dust	     114
38      Charges on Fractionated Coal Dust	     114
39      Charges on Non-fractionated Coal Dust Passed
        Through an Electrical Discharge  	     114
40      Values of Slope K	     118
41      Charges on Fresh Industrial Dusts  	     120
42      Resistivity of Fabrics   	     123
                                    xi

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                               ACKNOWLEDGMENT

     For their contribution and help, the authors thank each employee of the
United States Environmental Protection Agency who participated in this
endeavor.  Special thanks for help and support throughout the program are
extended to our Project Officer, Dr. James H. Turner.

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                                  SECTION I
                                 CONCLUSIONS

     The analysis and research of phase II of this project lead to
the following conclusions:
          The process of clean air flow as well as the dust filtration
          process are stochastic processes of the normal type.
          According to Filtration Type I (laboratory scale), dust
          collection efficiency is an exponential function depending
          on the air-to-cloth ratio, the dust covering, and the type
          of filtration structure.
          The increase of filtration resistance with time or dust
          covering shows a parabolic relation on the laboratory scale.
          The variation of outlet dust concentration as a function of
          dust covering L  is, on the laboratory scale, a parabolic
          relationship.  From a structural viewpoint, the fabrics
          are regarded as heterogeneous anisotropic media.
          At present Free Area is the best structural parameter
          characterizing the structure of fabrics made of staple
          fibers.
          Electrostatic properties of dusts depend on their history.
          Dust charges are higher for fresh dusts than stored dusts.
          Specific electrostatic properties of fabrics and highly
          charged dusts can influence the formation of dust cake.

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                                 SECTION II
                               RECOMMENDATIONS
     To obtain more representative statistical material  for the definition
of relations between large scale dust collection efficiency and filtration
resistances, changes in the program for phase III (the final  phase)  were
made.  The experiments will be conducted for:
          Five levels of air-to-cloth ratio—i.e., 60, 80,  100, 120, and  160
           3  2
          m /m /hr, and
          Six levels of dust covering—i.e.,  LNK + 100,  LNK + 200,  LNK +
          300, LNK + 400, LNK + 600, and LN|( + 800 g/m2.
This large-scale testing will be conducted according to the conditions set
forth in the original detailed program statement.
     Because of the enlarged experimental program, testing  will be  accom-
plished on at least two types of fabrics and one kind of dust.   Similar
additional experiments have been planned for the laboratory scale in order
to establish correlations between Dust Filtration Type I and Type III.
     The above changes in the program were discussed with and accepted by
the Project Officer, Dr. J. H. Turner, during the April  1976 meeting.

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                                 SECTION III
                                INTRODUCTION
     This report Includes the results of research conducted in phase II of
Project No. 5-533-3, a contract between the United States Environmental
Protection Agency and IPWMB, Opole, Poland.  Also, for continuity with phase
I, laboratory testing of selected filtration fabrics, this report recapit-
ulates work concerning the efficiency of Filtration Type I (characteristic
of laboratory-scale filtration) conducted during the first 2 years of the
project.
     These results were the subject of discussions between the Project
Officer, Dr. J. H. Turner, and representatives of IPWMB during their visit
to the United States in April 1976.  During that meeting the authors pro-
posed modifying the detailed program and performing auxiliary work on both
the laboratory scale and large scale.  The proposal was accepted by the
Project Officer.
     The changes in the detailed program concern enlargement of some ele-
ments of the basic testing in order to obtain more empirical data and permit
verification of complex empirical relations.  The original fabric test plan
prbvided a maximum of three levels of parameter variations, which is not
satisfactory for adequate mathematical interpretation.  Laboratory testing
carried out by IPWMB before 1973 cannot be regarded as valid auxiliary
statistical material because of the differences in degree of dispersion and
dust concentration.
     The theoretical interpretation of the conducted experiments is based on
the dust filtration process rather than other filtration processes.  This
Interpretation avoids comparisons of the dust filtration process to the air
filtration process over the range of the results.
     The results of phase II are very promising.  Some difficulties in the
correct description of the physical structure of woven materials are recog-
nized.  The structural parameters used at present do not give the specifics
of the filtration structure.  By considering the hydraulic properties of the
fabrics, 1t 1s possible to classify the woven materials with a definite

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quantitative measurement.  But this measurement does not indicate the dif-
ferences in the filtration properties of the fabric or its method of produc-
tion.  The description of the structure of a woven filtration medium will be
the basic problem of phase III of the project.
RESEARCH OBJECTIVES
     The basic objectives of the program financed by EPA and conducted by
the Institute of Cement Building Materials in Opole were established as:
          A viable description of the effects of fabric structural parameters
          on the pressure drop of gas flow through a clean fabric.
          A viable description of the effects of fabric structural parameters
          and of the dust cake on pressure drops during the filtration
          process.
          A viable description of the relationship between dust collection
          efficiencies and the variables of the dust filtration process.
          Testing, by mathematical modeling, of those fabric structures with
          the best filtration properties.
Total program research will include laboratory testing, including that of
the dust and the fabrics, large-scale testing, auxiliary studies, and appli-
cation of mathematical methods including modeling.
GENERAL PROGRAM
Laboratory Testing
     Laboratory testing was accomplished on four kinds of filtration fabrics
and four types of dust.  The following conditions existed at the time of
measurement.
          Dust concentration in the air at the inlet of the test chamber:
                3
          10 g/m  + 10 percent.
                                              22             9
          Dust covering of the filter: 100 g/m , 400 g/m , and 700 g/m
          with AP < 250 mm of water.
          Air-to-cloth ratios: 60 n»3/m2/hr, 80 m3/m2/hr, and 120 m3/m2/hr.
          Humidity of the dispersion medium (not adjustable): RH = 40 percent
          + 10.
          Temperature of the dispersion medium:  20° to 30° C.

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          Dispersion medium:  atmospheric air.
          Pressure:  atmospheric pressure.
Large-Scale Testing
     Large-scale tests were scheduled using filtration bags with an operating
length of 3,000 mm and the same dusts used in the laboratory testing.   Test
conditions were identical to those of laboratory testing except for dust
covering on the filter being tested only at 400 and 700 g/m2 (excluding the
       O
100 g/m  condition of laboratory testing) and air-to-cloth ratios of only 60
        32                        32
and 80 m /m /hr (excluding the 120 m /m /hr condition used in laboratory
testing).
Definition of the Structural Parameters of a Fabric
     Research leading to the identification and definition of significant
structural parameters of a fabric involved analyses, measurements, and
experiments.
     Measurements and analyses, specifically, concerned and included the
geometry of the spatial structures of fabrics, the technological parameters
and production variables of fabrics and fabric structures, the technological
parameters and production variables of threads and filaments, microscopic
tests, etc.
     The parameters defined by analyses and measurements under atmospheric
air flows were then evaluated experimentally.  Four types of filtration
fabrics, all manufactured in Poland and each differing as to raw material,
filament diameter, weave, etc., were studied.  A literature search was
included in this program.
Definition of the Structural Parameters of Dust Layers
     Industrial polydispersed dust layers in the testing program were charac-
terized by particular physical and chemical properties.  The research program
for dust layers was conducted in the same manner as that for fabrics using
analyses, measurements, and experiments.
Testing of Electrostatic Properties of Dusts and Fabrics
     Determination of the electrostatic properties of dusts and fabrics was
accomplished using the same materials for both laboratory and large-scale
testing.

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     Testing included measurement of dust charge by the Kunkel-Hansen method;
and determinations of the influence of the gas medium on dust charge; the
electrical resistance of the dust layers; the kinetics of the fabric charging
process during both clean and dusty air flows; the electrical resistance of
the fabrics (surface, bulk); and other electrostatic effects during the dust
filtration process.
DETAILED PROGRAM FOR THE SECOND PHASE
Laboratory Tests
     During laboratory tests, the following tasks were accomplished:
          Completion of the entire testing program and compilation and
          analysis of the results.
          Completion of the fabric auxiliary tests for definition of basic
          technological and production parameters.
          Completion of auxiliary tests on dusts for determination of physical
          and chemical properties.
          Determination of empirical relations between dust collection
          efficiency and air-to-cloth ratio.
          Preliminary determination of a mathematical model of dust filtra-
          tion through fabrics.
Definition of the Structural Parameters of Fabrics
     Defining the structural parameters of fabrics entailed examination of
fabric geometry (taking under consideration the definition of the structural
parameters of woven materials) and preliminary analysis of the results.
Definition of the Structural Parameters of Dust Layers
     In defining the structural parameters of dust layers, determination of
the influence of dust dispersion degree on the hydraulic properties of dust
layers and analysis of the results (considering the definition of parameters
characteristic of a dust layer) were Included.
Definition of Characteristic Properties of Dusts and Fabrics
     Characteristic properties of dust and fabrics were defined by  determina-
tion of dust charges by the Kunkel-Hansen method and elaboration of results,

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                                                    Table 1.  FABRIC PARAMETERS
PARAMETER
1
Width of fabric
Kind of yam: warp
fill
hread count 1n
0 cm: warp
fill
Fabric weight
'Mckness ?
pressure lOOg/cm )
Tensile strength,
less than: warp
fill
Elongation during
tension ,• no more
than: warp
fill
Permeability
Weave
Finishing

UNIT

2
cm


g / mz
nin
KG/5cm width
KG/5cm width
X
X
3 2
m /m mln
at 20 mm H20
-

FABRICS
ET-4 ET-30 F-tor 5 PT-15
PS*
3
as required
SOTexZ x 2S
IBOTex Z
IBOrS
126-5
450-31
_
220
260
70
50
18-24
1 z
steaming
Measured
4
36
45,21Tex x 2
178.25 Tex
180
126
428,1
0.92
240
310
51
35
20.73
1 ;
Steaming
PS*
5
140-4
21TexZ x 2S
21TexZ x 25
477j10
276-6
365^25
.
250
130
6
50
12-18
2 z
thermal
stabiliza-
tion,
washing
Measured
6
135
22,15Tex x 2
21.99Tex x 2
488
274
361.6
0.74
323
182
60
48
7.54
2 z
thermal
stabiliza-
tion,
washing
PS*
7
140-4
Td 125/2
Td 2SO/1
540,12
376-12
271-13
-
346
276
20
30
-
2-j-z
crude
Measured
8
140
Td 136,37
Td 253,52
528
360
307.5
0.50
310
225
37
15
14.6
v>
crude
• PS*
9
85tl
Td 210/1
Td 210/1
564 jl 2
360-1 1
272-14
-
300
200
60
40
-
3 	
stabilized
Measured
10
85
Td 228,43
Td 233,77
545
363
247
0.39
336
233
43
28
3.65
3 	
stabilized
•Polish standards

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Table 2.  PARTICLE SIZE DISTRIBUTION OF TEST DUSTS
                a.  Before separation
Range of
Particle size
in jam
1
5
5-10
10-20
20 - JO
30 - 40
40 - 50
50 - 60
60
Percent by weight

Cement
2
12.0
12.0
16.0
9.5
10.0
10.0
7.5
23.0

Coal
3
9.0
16.0
24-5
13.0
7-5
6-5
4.5
19.0

Talc
4
23-0
33-0
30-0
8-5
2-5
1 .2
0.5
1 -3

Fly Ash
5
19-0
45-5
15-0
5-0
3-0
2.0
1 -5
9-0
                b.  After separation
Range of
Particle size
in jMin
1
5
5-10
10-20
20
Percent by weight

Cement
2
26 .0
36.5
33 .0
4.5

Coal
3
24. 0
40.0
34-5
1.5

Talc
4
32.5
37 .5
25 0
5 -0

Fly Ash
5
40 .0
50 .0
9-7
0-3
                         8

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determination of the electrostatic properties of fabrics, and recapitulation
and analysis of results.
FABRIC AND DUST SELECTION
     Four types of filtration fabrics, differing in spatial structure,  were
selected for testing under Project No. 5-533-3.  These selected fabrics are
produced from the following raw materials:
          Polyester (staple fiber)
               Fabric ET-30
               Fabric ET-4
          Polyester (continuous filament)
               Fabric F-tor 5
          Polyamide (continuous filament)
               Fabric PT-15.
Technical characteristics of these fabrics are shown in table 1.
     Also, four types of dust—cement, coal, talc, and fly ash—were tested.
These industrial dusts were selected because of their chemical composition
and their uniform particle size.  Samples for testing were taken from appro-
priate points in the production processing line.
     The selection of dust samples is dependent on various physical and
chemical properties.  Instead of testing material as sampled, testing under
this project, in accordance with suggestions from Dr. James H. Turner,  EPA
Project Officer, was of only those dust samples containing no more than 10
percent by weight of particles with diameters greater than 20 pm.  For
laboratory testing, this separation was done by use of the ALPINE separator.
For the large-scale tests, the dusts were preseparated and prepared by
subcontractors.  The characteristics of the test dusts before and after
separation are shown in table 2 and figures A-l through A-4.

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                               SECTION IV
                       THEORY OF DUST FILTRATION
     In the most general sense, filtration is a process for the removal of
dispersed solid particles from a fluid stream (dispersion medium) by flow
through a porous medium.  Depending on the kind of dispersion medium and the
kind of porous medium, several characteristic filtration processes differing
in quantity and quality can be described.  This program considers industrial
aerosol filtration through woven filter fabrics.
     In this program, aerosols are regarded as a two-phase system composed
of a gas-dispersed phase and a solid-dispersed phase, which, under certain
conditions, can be treated as quasi-stable.  This definition implies a
secondary classification of aerosols:  atmospheric and industrial.  Size
distribution and concentration vary between these two types of aerosols.
For both atmospheric and industrial aerosols, fractional composition depends
on the absolute velocity of the gas and on thermodynamic parameters.  It is
a result of the terrestrial gravitational field in which the aerosol is
regarded as a quasi-stable dispersion system.
     This definition of an aerosol as a two-phase system is appropriate only
for dry filtration.  Including the third phase, fluid, of an aerosol would
completely change the physics of dry filtration.
     From a physical point of view, the filtration process is described by
state parameters (SP), filtration parameters (FP), and structural parameters
of the filtration medium (SPFM).  The process is shown schematically in
figure 1.
     State parameters characterizing the aerosol before and after filtration
are the thermodynamic and physico-chemical parameters of the gas medium, and
the physico-chemical parameters of the dispersed medium (the dust).
The basic state parameters are:
          The thermodynamic parameters of the dispersion medium:
               Temperature
               Humidity
                                  10

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                                             SPFM 1
           FP  1
    STATE 1
    SP 1
SP 1, SP 2             = State  Parameters,
FP 1, FP 2, FP 3       = Filtration Parameters,
SPFM 1, SPFM 2, SPFM 3 = Structural Parameters of the Filtration Medium.
SP 1 ? SP 2
FP 1 + SPFM 1  ^ FP 2 + SPFM 2 f  FP 3 + SPFM 3
E (efficiency) = constant.
              Figure 1.  Filtration process schematic.
                                  11

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               Pressure, etc.
          The chemical properties of the dispersion medium:
               Chemical constitution.
          The physical parameters of the dust:
               Weight density
               Degree of pulverization
               Concentration
               Electrification, etc.
          The chemical parameters of the dust:
               Chemical constitution
               Chemical activity, etc.
     Filtration parameters are the independent variables of the process:
flow rate, dust loading, cleaning time, and energy, etc.  The basic filtra-
                                               3  2
tion parameters are the air-to-cloth ratio in m /m /hr, the normalized dust
                p
feed rate in g/m /hr, and pressure drop (filter resistivity) in mm of water.
     Structural parameters of the filtration medium describe, from a physical
viewpoint, the filter structure as characterized by its production, and also
the physico-chemical properties of its raw materials.
     For woven materials, the basic structural parameters of the filtration
medium are porosity, mean pore diameter, specific surface, free area, and
fiber diameter, etc.
     The effectiveness of the filtration process is estimated by the filter
efficiency, which is functionally correlated with the state parameters
before and after filtering according to:
                    E =  (l - CQ/C.) x 100                            (1)
where  E  = filter efficiency,
       C.. = initial aerosol concentration (before filtering),
       CQ = final aerosol concentration (after filtering).
     As shown in figure 1, the transformation from a definite state 1 to a
state 2 of an aerosol, at a given filter efficiency, does not depend on the
path of transformation, but only on the initial and final concentrations
(the state parameters).  There are an infinite number of structural and
filtration parameters by which a given filtration process effectiveness
(efficiency) can be achieved.
                                  12

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     Analyzing the above relation in equation 1, the conclusion is made that
filter efficiency can be the qualitative parameter used to describe the
filter structure (at a specific initial concentration, determining the
physical properties of the process).  And because of this, three main types
of filtration processes can be selected:
     1.   High efficiency air filtration at an initial aerosol concentration
          C. < 1 mg/m3;
                                                                    o
     2.   Air filtration at an initial aerosol concentration, 1 mg/m  < C. <
                 3                                                       1
          50 mg/m ; and
     3.   Dust filtration at an initial concentration, C. > 50 mg/m .
     High efficiency air filtration, as well as air filtration in general
(filtration processes 1 and 2,) have their theoretical base in classical
filtration theory and satisfy the assumptions required by those physical and
mathematical models.  In contradistinction to air filtrations, dust filtration,
characteristic of industrial fabric filters, has become the subject of
research only during the last few years—inspired by increased air pollution
emissions from industrial plants.   It has no theoretical base as yet.
     Initial attempts to apply the  classical filtration theory to the dust
filtration process showed the wrong way to point out the differences between
dust filtration and other processes of dry filtration.
     Large initial concentrations of solid particles in the aerosol and
regeneration phases of the filtration medium are characteristic of the dust
filtration process.  So, practically, the presence of a clean filtration
structure and its interaction with  aerosol particulates is reduced to a very
short  initial period, not having a  major influence on the filtration process
under  actual industrial conditions.  Figure 2 shows the actual variation of
filtration resistances with time.   It is clear that the state of the filtra-
tion medium can be described by definite pressure drops at a constant air-to-
cloth  ratio (q  in m3/m2/hr) from which its degree of structural filling can
be deduced.
     The filtration medium exists in one of the following states:
          Pure filtration (a dust-free filter),
                                  13

-------
„  DUST FILTRATION ^ /_
                          REGENERATION
   DUST
FILTRATION
                           REGENERATION
  DUST    /   DUST
ILTRATI01L /FILTRATIQJ
                                                      \STABILIZED VALUE

                                                       OF PRESSURE DROP
                            INCREASE PRESSURE DROP
                              AFTER REGENERATION
                             a_ = const. - nr/m /hi
                             ^5               j
                             a  = const. - g/m /hr
                                  TIME
                  Figure 2.  Types  of  Dust  Filtration.

-------
          Partly filled with dust,
          Filled up with dust (fully filled),
          Covered with dust (fully filled plus dust cake).
     A pure (clean) filtration structure is characterized by:
               AP  at q  = constant, q  =0, and L = 0,
where APQ is the pressure drop at a constant air-to-cloth ratio, q  ; for a
zero dust feed rate, (q  = 0); and with no dust load in or on the fabric
(L=0).
     A filter partly filled with dust for a specific regeneration system is
characterized by the successive values APW tending towards AP,...., at  q  =
                                         n                   Nl\     p
constant.  During this time period the fabric is filling with dust  as described
by L=Li (where i = Nl ... NK).  A filter fully filled with dust for a" specific
regeneration system is characterized by APW1, at q,, = constant, q^ = constant,
                                          NI\     g              p
and L = LNK, meaning a certain amount of dust is present  in  the fabric
structure after the regeneration cycle.  A structure covered with dust is a
filter fully filled with dust and with a dust cake on its working surface.
This is characterized by AP., at q  = constant, q  = constant, and L = L  -
                2          N     g              p                      o
LUI/ * LD  in 9/m  where L  is the areal mass density of the  dust cake and
 Nl\    r                 P
LNK = the areal mass density of dust filling a fabric for a  specific regenera-
tion system after the equilibrium state is reached, in g/m .
     The concept of "fabric filling" (with dust) is set forth as:

                         "i • L1/LNK                                  (2)
where L. = the areal mass density of dust filling a fabric after the
             th
           "i  " regeneration cycle but before the equilibrium state
                             2
           is reached, in g/m , and
      Pj = the fabric filling factor for cycle "i" (dimensionless).
To estimate the fabric filling from hydraulic pressure data, a fabric fill-
Ing factor can be described as:

                         Pr. = APNi/APNK
                                  15

-------
where APNi =  the pressure drop for the filled fabric after the "i  "
              regeneration cycle, but before equilibrium is reached, in
              mm of water,
      APM1/, =  the pressure drop for the filled fabric for a specific
        Nlv
              regeneration cycle after the equilibrium point is reached,
              in mm of water,
       ^r  = relative fabric filling factor, for cycle "i."

     The following conclusions are based on previous and present research.
     1.   Dust filtration processes display cyclical filtration resistiv-
          ities in time.
     2.   Each of the basic cycles prior to equilibrium is qualitatively
          different because each begins at a different fabric filling factor.
     3.   A stabilized presence of residual dust particles in the filtration
          structure (as in classical filtration theory) is impossible because
          the process is cyclic; particle penetration through the filter can
          occur.
     4.   Basic filtration mechanisms (interception, inertial impaction and
          diffusion) determine the efficiency of the process; however, their
          interaction with a fully filled structure is difficult to model,
          both physically and mathematically.
     5.   Dust cake formation is accompanied by compression effects related
          to the increase of pressure differences, and structural defects
          depending on the fabric structural composition and the physico-
          chemical properties of the dust.
Based on these conclusions, three main types of dust filtration were identi-
fied for true dry dust filtration.   They were defined as Filtration Types I,
II, and III (see figure 2).
     Dust Filtration Type I is the initial phase of the complete process,
when the fabric first begins to operate as a filtration medium.  This phase
ends when the pressure drop reaches a predetermined level.  This phase
includes:
          Stationary filtration during the initial capture of dust
          particles (corresponding to classical filtration theory),
                                  16

-------
          Nonstationary filtration as the fabric structure  fills  with  dust,
          and
          "Ductive" (canal) filtration as the dust cake forms and filters
          successively impinging dust particles.
     Dust Filtration Type II is characteristic of the next  filtration  cycles
or until the fabric is fully filled with dust, i.e., a stabilized quantity
of residual dust remains in the fabric structure after its  regeneration.
Characteristics of this phase are p. <1 and p  <1.  Dust cake formation

depends on the properties of both the dust and the fabric,  and also on the
intensity of regeneration.   This phase includes:
          Nonstationary filtration, and
          "Ductive" filtration.
     Dust Filtration Type III occurs when the equilibrium point of filling
the fabric by dust has been reached and when the pressure drop measured
after regeneration is a stable value during successive regeneration cycles.
As for Dust Filtration Type II, this phase includes:
          Nonstationary filtration, and
          "Ductive" filtration.
For this phase p. = 1 and Pr  =1.

     Specific types and phases of the dust filtration process, occurring at
definite conditions (q  = constant and q  = constant), correspond to prede-
termined values of pressure drop, AP, quantity of dust, L,  and describe the
momentary states of the filtration structure.
     The three types of filtration specified above describe all possible
variants of dust filtration occurring in fabric filters.  The differences in
filling the filtration structure by dust, characterized by definite values
of L in g/m2, lead to the conclusion that individual types of dust filtra-
tion represent noncomparative physical processes.  Therefore, the efficien-
cies of Dust Filtration Type I and Dust Filtration Type III (for the same
initial state parameters, filtration parameters, and filtration medium) are
not the same:

                         Ei " Eni     •
                                 17

-------
A correlation function, RE, is defined as:
                         Ei-Vm   •
Nonequi valence of efficiency of types I and III dust filtration, according
to equation 4, shows that there is no base by which filtration efficiency in
the laboratory can be compared with industrial scale filtration efficiency.
Similar relations can be written for pressure drops, which also depend on
the state of the filtration structure.
     In spite of much experimental work,  the form of the correlation func-
tion RE has not yet been worked out, because there is no mathematical model
of the filtration process itself.
     F. H. H. Valentin, testing the filtration efficiency of 24 kinds of
fabrics, has given the general form of the functional dependence of the
laboratory filtration efficiency as follows:

                    E = 100 x exp  (-blj)                               (6)
where E = filtration efficiency in percent,
     L  = the areal  mass density of the dust in or on a dust covered
          filter, and
     b,n = constants.
     Equation 6 plotted on Rosin-Rammler  Paper (log log reciprocal  efficiency
vs.  log weight of dust on the fabric)  yields a straight line from the equation:
               log log -r-  = n log LQ + c                          (7)

 where c = log b + log log e.
     Determining the coefficients b and n from such a plot (figure 3) enables
one to compare different kinds of fabrics.  However, the relationship between
the above dependencies and the structural properties of the fabrics and the
properties of the dust have not been determined.
     By analyzing the Valentin dependence, the following conclusions are
made:
     1.   Filtration efficiency increases with increasing thickness of dust
          cake.
                                  18

-------
     2.   The coefficient n, being the slope of the E-L  line on Rosin-Rammler
          Paper, is different for different kinds of fabrics.  It depends on
          the mechanism of dust cake formation, and hence on the structural
          parameters of the fabrics, the dust properties, and the filtration
          parameters.
     3.   For fixed process parameters, the value of the coefficient b is
          constant.
     4.   If the value of L  approaches zero, the filtration efficiency
          reaches its minimum and is the initial efficiency, depending
          mainly on the structural parameters of the filtration medium and
          on the filtration parameters.
     5.   The value of initial filtration efficiency can be extrapolated
          from the Rosin-Rammler equation (eq. 7):
Consequently:
                    n log L  = 0, i.e., L  = 1 (see figure 3).
                              100
                     log log -=!— = c = log e + log b
so                   100 _ £b
                       o
and                  EQ = 100 exp(-b).                                (8)
From the above, the following relations can be hypothesized:
          The initial efficiency E  depends mainly on the structural parameters
          of the filtration medium and on the filtration parameters, but
          also on the air-to-cloth ratio, q .  Because q  is a function of
                                           9            y
          the structural parameters:
                    EQ = 100F1
= f |qg (SPFM) ....   .                 (9)
          The slope, n, in the Rosin-Rammler equation is also a function of
          the air-to-cloth ratio and the structural parameters of the filtra-
          tion medium, so:
                         n = F2 = f|qg (SPFM) ....  .                 (io)
Using the above relations and equation 8, the Valentin formula can be re-
written:
                                  19

-------
                                                               1000
            DUST COVERING , IQ  ,
Figure 3.  Efficiency as a function of dust covering.

-------
                          - 100
or                      E = 100  (F^  °    .                          (lla)
     The dependence given in equation 11 is valid only on the laboratory
scale (and for L  > 0 because equation 11 is of the functional form, y =
a'").
     In the case of Dust Filtration Type III (characteristic of industrial
scale operations), where regeneration of the filtration medium occurs,
filtration efficiency is greater than for Dust Filtration Type I.   Higher
efficiency results because of the filling dust remaining between the elemen-
tal fibers after regeneration.  This value is constant for specific filter
structures, types of dust, and parameters of filtration and regeneration.
Based on studies conducted by M. W. First, it can be presumed that dust does
penetrate the structure of the fabric; however, this does not negate the
specific properties of the fabric manifested by the state-filling constant,
L., for a definite set of operating conditions.
     Introducing to the Valentin formula the additional function:
                    F3 = f |>K(SPFM)....J                          C2)
where LNK = the areal mass density of the filtration structure filled with
dust for specific process conditions, g/m , we obtain an equation for Dust
Filtration Type III:

                                          /  x  -L   F4
                            EIII = 100F3  (Fl/          '              (13)
     The above equation is also a straight line on Rosin-Rammler Paper, but
its position depends on the degree of structure filled with dust, L^.   The
initial efficiency, being a hypothetical value calculated from an extrapola-
tion of equation 13, is higher than the initial efficiency calculated for
type I filtration.   Introduced as an exponent for the dust-covered structure,
F. is not equivalent to the function F--  F. represents another mechanism of
dust cake formation on the filled structure:
                                     21

-------
                    % = f [q
     The process of filtration is accompanied by an increase in static
pressure drop proportional to the increase in dust cake thickness.  Accord-
ing to Stephan, Walsh, and Berrick, filtration drag Is the ratio of pressure
drop to the air-to-cloth ratio:
                    S = AP/q,,.                                        (15)
                            9
     Assuming a linear dependence of drag with time (or a linear dependence
of S with L ), it is possible to express equation 15 as:
                    S = L0/K                                          (16)
where L  = the areal mass density of the dust on a filter covered
                           2
           with dust in g/m , and

      K  = dust cake permeability in

     The above dependence was regarded as suitable for the filtration range,
including dust cake formation on a fabric surface.  When dust cake forms,
the depedence S = F(L ) is actually curvilinear.   Assuming a linear dependence
for this range, and calculating the Initial drag from extrapolation of
equation 16, a practical formula for filtration drag is:

                         S = SR'  * L0/K                               (17)
where K is designated from empirical data according to:
                         K = LQ/S, and
                         SR = projected residual  drag.
This dependence 1s shown in figure 4.   To make filtration drag depend upon
time, the following simplified relation is used:

                         dLo/dt = Vo

                         L0 =

     and                 S = SR + qg-cQ-t/k.                           (18)
                                  22

-------
     fi
     a
         INITIAL
         CAKE
                         TOTAL CYCLE
INTERVAL OF
CAKE RF.PATB

PROJECTED

RESIDUAL DRAG
DEPOSITION OP
HOMOGENEOUS

DUST MASS
                    RESIDUAL DRAG,  SR
                     DRAG POR A NEW FABRIC,
                                                    TERMINAL

                                                    DRAG, ST
                         FILTERED DUST MASS, g/m2
Figure 4.  Schematic representation of basic performance

           parameters  for fabric filters.
                         23

-------
 In reality, in many cases the dust concentration after the -filter is too
 high for the above relation to be right.  Accordingly:
Based on our own research and on that published by R. De.i is the cutlet con-
centration varies with dust cake during type I, as veil as during type III
dust filtration.  Dennis, examining the effect of different filtration
parameters on Dust Filtration Type III (industrial scale), found the follow-
ing dependence for fly ash at LQ = 50-500 gr/ft2 (35-348 g/m ) and qg = 3
ft/mi n (55 m/hr):
                         CQ = 0.65 exp(- 0.0476L0J .                   (.20)
Substituting the above dependence into equation 19 we obtain:
                         LQ =  c. - 0.65 exp(-0.0476LQ)   q At.       (21)
Our own research indicates a parabolic dependence of outlet concentration
upon LQ.
     Not discussing at this time the form of the functional  dependence c  =
f(L ),  it is sure that the assumption of a linear dependence of drag increas-
ing with time needs revision.   The development of the right relationship
seems to be essential, especially for submicron particle penetration in the
dust filtration process.
     Because of the empirical  character of the dependencies occurring in the
dust filtration process,  their verification is possible only by collecting a
large amount of statistical  data.
     The problem directly connected with the previous deliberations is that
of defining the necessary physical parameters of the fabric and of the dust
cake formed during the filtration process.
     The fabric, because of its very complicated geometrical composition, is
very difficult to describe physically using only one parameter.  Periodicity
of structure does not resolve this problem because of the many variations in
fibers and weave, making it impossible to model elemental surfaces or volumes.
The extra condition accounting for the structural pareaieters of the filtration
medium is its functional connection with its technological parameters of
production.  The present use of  the parameter Free Area (FA) gives a connec-
tion to the technological parameters, but it seems too "weak" because it
                                  24

-------
does not take several fabric properties into consideration.   Over the range
of values FA = 0 (or negative values, where FA is regarded as FA = 0), it
does not describe the structure.  The problem of finding a good structural
parameter has been the subject of much prior research.
     The physical parameters of a porous layer composed of elemental particles
are comparatively well studied.  However, according to dust cake formation
on the filtration fabric, the hydraulic and qualitative effects resulting
from its structural parameters cannot be predicted from knowledge of the
aerosol state parameters before filtration  alone.  Dust cake structure does
not depend only on degree of pulverization, geometry of grains, and surface
properties of grains; but also on conditions of dust cake formation and on
the structural properties of the fabric.  However, observation of the external
effects of dust cake formation is comparatively easy and leads to practical
dependencies being applied in dust control technology, e.g., dust cake
permeability, K = f (type of dust, kind of fabric, filtration parameters).
Not enough such dependencies are yet known to be able to optimize research
and take specific measures towards improvement of dust filtration process
efficiency.
                                  25

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                               SECTION V
                          LABORATORY TESTING

EQUIPMENT AND PROCEDURES
     Laboratory testing was conducted on a test stand,  as illustrated in
figure A-71.   This apparatus was specially designed by  the IPWMB and adopted
for the testing of flat fabric specimens at unregulated temperature and
humidity of the dispersion medium.   A detailed description of the laboratory
stand was included in the report on the first phase the work conducted in
this project.
     Average dust collection efficiency was determined  by the weighing
method.  This method requires weighing the dust covered fabric and the
control filter, and then applying the following relation:
                     100
where G  = weight (grams) of dust collected on the fabric,
      G  = weight (grams) of dust collected on the control filter, and
      GC = weight (grams) of dust fed into the test chamber.
     Using criteria given in the assumptions of the detailed program
(Section III), laboratory testing was conducted on four kinds of Polish
fabrics and four types of separated dusts.  Previous test results by the
IPWMB on unseparated cement and coal dusts were also added to the empirical
data base.
RESULTS
     Laboratory testing consisted of the following:
          A determination of the permeability of the filtration fabrics,
          A determination of the average laboratory dust collection efficiency
          of the tested fabrics, and
                                  26

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          A determination of the Increase of filtration resistances as a
          function of time with the dust cover in or on the filter.
     This section of the report includes the results of all testing carried
out during both the first and the second phase of the project.  Relevant
test results previously obtained by the IPWMB on unseparated dusts are also
included in this section.
     In table 3, the results of permeability testing (a very important
technological parameter) are shown.  These values of permeability are based
on averages of 20 to 50 measurements made on the same fabric but in different
places.  The complete set of measurements will be enclosed in the final
report.
              Table 3.  PERMEABILITY OF FILTRATION FABRICS
                      3  2
                 (in m/m/min at AP = 20 mm of water)
ET - 4
20.70
ET - 30
7.54
F-tor 5
14.60
PT - 15
3.65
     Tables 4-7 show the results of testing certain filter fabrics with
separated dusts of cement, coal, talc, and fly ash.   The tables include the
means from five measurements carried out over the range of test variables
previously agreed upon.  All data will be enclosed in the final report.
     In tables 8-11, the archival results, obtained previously for the same
kinds of fabrics but for unseparated cement and coal dusts, are shown.
These data also represent the means of five measurements conducted under
specific test conditions.
     Tables 12-15 and 16-19 include the results of recording the final
resistances (means from five measurements) obtained for different values of
a1r-to-cloth ratio q  and dust covering LQ.  These results are from the
testing of this program and from the archival data obtained from the testing
of filtration fabrics with unseparated dusts.
     The Increase of resistances during filtration and as a function of dust
covering L  1s shown 1n figures A-5 through A-28.  Source materials (measure-
ment reports) will be enclosed in the final report.
                                  27

-------
             Table 4.  LABORATORY EFFICIENCY ( in percent ) OF POLYESTER STYLE ET-4 (ci = 10 g/m3)
ro
00
Air-to-Cloth
Ratio q , in
m /m /h

1
60


80


120


'Dust covering
in/on the filter
L0, in 2

2
100
400
700
100
400
700
100
400
700
Kind of dust
Separated
Cement
Dust
3
99.72
99.93
99.97
99,86
99.96
99.94
99.12
99-44x
99-17x
Separated
Coal
Dust
4
99.63
99.85
98.62
98.45
97.66
96.47
96.01
96.03
87-53
Separated
Talc
Dust
5
99.71
99.95
99.975
99.48
99.66
99.80
97-94x
96-98x
97-34x
Separated
Fly Ash
Dust
6
99-48
99-82
99-91
99-62
99-91
99-94
99-23
99-82
99-79x
              x  Ducts/Canals  present

-------
            Table 5.  LABORATORY EFFICIENCY (in percent) OF POLYESTER STYLE ET-30 ( c = 10g/m5)
ro
UD
Air- to- Cloth
Ratio a, in
o p9
mW/h

1
60


80-


120
•

Dust covering
in L , in
-5
g/nr

i
2
100
400
700
100
400
700
100
400
700
Kind of dust
Separated
Cement
Dust
3
99.78
99.92
99.96
99.81
99-96
99-98
99.89
99.95
99.97
Separated
Coal
Dust
4
99-82
99.96
99.96
99-74
99.96
99-97
99.50
99.95
99.97
Separated
Talc
Dust
5
99.93
99.97
99.98
99.71
99.89
99-95
99.82
99.92
99.95
Separated
Fly. Ash
• Dust
6
99.54
99.91
99.98
99.74
99.90
99.95
99-66
99.90
99-94

-------
             Table 6.  LABORATORY EFFICIENCY  (in percent) OF POLYESTER STYLE F-tor 5 (c =10g/m3)
u>
o
Air-to-Cloth
Ratio q, in
m3/m2/h
1
60


80


120
x Ducts/Canal
Dust Covering
in/on the filter
Lo> '" 2
g/mz
2
100
400
700
100
400
700
100
400
700
Kind of dust
Separated
Cement
Dust
3
99.65
99.90
99-93
97.72
99.48
99.65
93.18
99.47
99.38X
Separated
Coal
Dust
4
98.41
99.65
99.93
94.50
99.81
99.91
98.46
98.15
98.64
Separated
Talc
Dust
5
99.53
99.47
99.81
98.80
99.70
99.80
94.51*
98.82X
96.94X
Separated
Ply Ash
Dust
6
99.62
99.91
99.94
99.55
99,85
99.90
99.18
•99.74
99.79
s present

-------
Table 7.' 'LABORATORY EFFICIENCY (in percent)  OF POLYAMIDE STYLE PT-1 5 ( c^l
Air-to-Cloth
Ratio qn, in
3 ?=>
nr/ur/h
1
60 -
,

80


120


Dust covering .
in/on the filter
Lo> in ,
g/nr
2
100
400
700
100
400
700
100
400
700
1 ' T
Kind of dust
Separated
Cement
Dust
3
99,80
99.96
99.98
99.84
99.98
99.98
99.90
99.98
99.98
Separated
Coal
Dust
4
99.85
99.96
99,98
99.89
99,98
99.99
99.94
99.96
99.98
Separated
Talc
Dust
5
99.91
99.986
99.946
99.80
99.98
99.98
99.82
99,92
99.95
Separated
Fly Ash
Dust
6
99,95
99.97
99.97
99.70
99.93
99.96
99,83
99,94
99.96

-------
Table 8.  LABORATORY EFFICIENCY (in percent) OF POLYESTER
        STYLE ET-4 (unseparated dust) (c. = 30 g/m3).
Air- to- Cloth
Ratio a, in
o o 9
nr/mVh
L
1
60


80


120

•
Dust Covering
in/on the
filter Ln, in
2
g/rrr
2
100
400
700
100
400
700
100
400
700
Kind o'f dust
Non-separated
Cement
Dust
J>
99.84
99.96
99.95
99.27
99.88
99,94
99.28
99.82
99.88
Non-separated
Coal
Dust
4
99.65
99,84
99.93
99.58
99.91
99.94
99.54
99.73
99.76
                             32

-------
Table 9.   LABORATORY EFFICIENCY (ir percent) OF POLYESTER
       STYLc Ei  30 (unseparated dust) (c. = 30 g/m3)
I
Air-to-Cloch
i
Patio qg, in
m3/m2/h
A
Dust Covering
in/on the
filter L , in
9 °
g/nr
2
1
I
i
60

i
80
-

120
i
i
,

100
400
700
100
400
700
100
400
700
Kind of' dust
Non-separated
Cement
Dust
3


99.79
99.97
99.98
99.63
99.91
99.95
99.82
99.93
99.93
Non-separated
Coal
Dust
4


99.88
99.97
99.98
99.88
99.96
99.98
99,72
99.91
99.94
                             33

-------
Table 10.   LABORATORY EFFICIENCY (in percent) OF POLYESTER
      STYLE F-tor 5 (unseparated dust) (c. = 30 g/m3)
Air-to-Cloth
Ratio q_, in
•3 0 9
mW/h
1
60


80


120


Dust Covering
in/on the filter
Lo> 1n 2
g/nr
2
100
400
700
100
400
700
100
400
700
Kind of dust
Non-separated
Cement
Dust
3
99.82
99.87
99.95
98.49
99.88
99.95
96.23
99.89
99.70
Non-separated
Coal
Dust
4
99.85
99.95
99,90
96.56
98.68
99.67
94.49
98.47
99.73
                            34

-------
Table 11.  LABORATORY EFFICIENCY (in percent) OF POLYAMIDE
         STYLE PT-15 (unseparated dust) (c. = 30 g/m3)
Air-to-Cloth
Ratio q , 1n
m3/m?/h

1
60
•

80


120


Dust Covering
in/on the
filter LQ,
g/m
2
100
400
700.
100
400
700
100
400
700
Kind of dust
Non- separated
Cement
Dust
3
99.88
99.99
99.99
98.59
99.90
99.99
99.89
99.93
99,95
Non-separated
Coal
Dust
4
99.92
99.96
99.97
99.77
99.92
98.99
99,93
99.94
99.97
                            35

-------
00
01
                Table  12.  FINAL PRESSURE DROP  IN  LABORATORY TESTING ( in mm of water ) FOR

                           POLYESTER STYLE ET-4 ( C1  =10
Air-to-Cloth
Ratio q_, in
q o 9
mW/h
1
60


80


t
120


i
Dust Covering
in/on the
f i 1 ter L. , in'
•a °
g/m3
2
100
400
700
100
400
700

100
400
700
Kind of 'dust
Separated
Cement
Dust
3
8,06
28.50
63.50
13,60
• 48,50
99.50

28.50
118.30
212.80
Separated
Coal
Dust
4
6.10
39.10
81,40
14.60
67.30
128.00

27,80
122.20
190.00
Separated
Talc
Dust
5
5,89
32.71
65.09
10.71
55.30
132.25

22.04
119.59
221.80
Separated
Fly Ash
Dust
6
5.55
14.20
28.09
9.86
29,36
60.12

19.84
69.76
125.45

-------
OJ
              Table 13.  FINAL PRESSURE DROP IN LABORATORY TESTING (in mm of water ) J?OR
                         POLYESTER STYLE ET-JO .(GI =  10 g/m5)
Air- to- Cloth
Ratio q , in
32"
nT/irr/h
1
60


80-


120


Dust Covering
in/on the filter
Lo* in2
g/nT
2
100
400
700
100
400
700
100
400
700
Kind of dust
Separated
Cement
Dust
3
16.88
46.25
77.13
28.24
67.90
123.06
54.80
130.00
229.00
Separated
Coal
Dust
4
15.30
48.10
87.20
27,00
80,20
149,20
55.50
174,70
340.30
Separated
Talc
Dust
5
10.24
45.11
85.64
20,03
71.41
115.81
44.95
156.58
281.80
Separated
Ply Ash
Dust
6
9.10
17.41
30.18
19.05
41.16
68.45
41.06
89.82
159.53

-------
               Table 14.  FINAL PRESSURE DROP IN LABORATORY TESTING  (in mm of water) JPOR

                          POLYESTER STYLE P-tor 5  ( C1 = 10 g/m5 )
co
oo
A1r-to-Cloth
Ration q_, in
o o 9
irr/nr/h
1
60


80


120


Dust Covering
in/on the
filter Lrt, in
9 °
g/irr
2
100
400
700
100
400
700
100
400
700
Kind of dust
Separated
Cement
Dust
3
18.64
41.23
70,00
25.59
73.71
122.40
60.7.2
163.00
269.00
Separated
Coal
Dust
4
19.10
49.90
102.40
27.06
94.60
166.00
76.60
199.70
331.00
Separated
Talc
Dust
5
14.41
45.82
89.90
25.40
77.88
134.81
46,57
173.74
319,00
Separated
Ply Ash
Dust
6
11,50
22,50
39.34
23.00
43.53
67.78
42.34
88,32
150.42

-------
oo
10
               Table  15.  FINAL PRESSURE DROP IN LABORATORY TESTING (in mm of water) FOR

                          POLYAMIDE STYLE PT-1 5  (c.  =10
Air-to-Cloth
Ratio qn, in
o p 9
rr.W/h
•
1
60


80


120


Dust Covering
in/on the filter
g/m2

2
100
400
700
100
400
700
100
400
700
Kind of dust
Separated
Cement
Dust
3
32.20
53.40
79.50
48.40
79.30
150.40
110.70
219.80
290.00
Separated
Coal
Dust
4
28.40
67.10
110.30
53.50
111.40
183.20
111.40
256.20
408.00
Separated
Talc
Dust
5
19.24
45.98
85.16
53.00
87.22
155.95
79.47
192.60
312.20
Separated
Ply Ash
Dust
6
16.65
27.21
42.24
33.34
51 .27
83.27
77.73
128,45
206,80

-------
       Table 16.   FINAL PRESSURE DROP IN LABORATORY  TESTING  (in mm
of water) FOR POLYESTER STYLE ET-4 (unseparated dust)  (^ =  30 g/m3)

Air- to- Cloth
Ratio q. in
•3 ?9
nr/nr/h

1
60


80


120



Dust Covering
in/on the filter
Lo* 1n2
9/r/
2
100
400
700
100
400
700
100
400
700
Kind of dust


Non- separated
Cement
Dust
1>
5.40
15.20
25.30
8,60
33,12
49.50
17,20
57.50
92.30
Non- separated
Coal
Dust
4
4.15
16.80
20.40
7.20
27,04
41,90
14.30
47.80
68,40
                                  40

-------
    Table 17.  FINAL PRESSURE DROP IN LABORATORY TESTING (in mm
of water) FOR POLYESTER STYLE ET-30 (unseparated dust) (c. = 30 g/m3)
A1r- to- Cloth
Ratio q , in
m3/m2/h
1
60


80.


120


Dust Covering
in/on the filter
Lo« in ,
g/iir
2
100
400
700
100
400
700
100
400
700
Kind of
Non- separated
Cement
Dust
3
13.60
23.70
38,80
23.40
51.00
71.70
50.30
104.00
121.00
dust
lion— separated
Coal
Dust
4
6.20
21.00
24.50
12.40
34.20
51-40
37.20
84.40
94.00
                                 41

-------
      Table 18.   FINAL PRESSURE DROP IN LABORATORY TESTING (in mm
of water) FOR POLYESTER STYLE F-tor 5 (unseparated dust) (c.  = 30 g/m3)
Air-to-Cloth
Ratio q , in
o o 9
nr/nr/h
1
60


80


120


Dust Covering
in/on the
filter L_, in
2°
g/nr
2
100
400
700
100
400
700
100
400
700
i
Kind of dust
Non-separated
Cement
Dust
3
11,80
24.85
36,60
21.80
47.70
72,00
44.20
93.50
128.00
Non-separated
Coal
Dust
4
12,45
29.20
33.10
19.49
47,30
64.06
41.08
99.54
135-88
                                    42

-------
     Table 19.  FINAL PRESSURE DROP IN LABORATORY TESTING (in mm
of water) FOR POLYAMIDE STYLE PT-15 (unseparated dust) (c. = 30 g/m3)
Air-to-Cloth
Ratio q , in
m3/m2/h
1
60


80


120


Dust Covering
in/on the
filter Ln, in
9 °
g/irr
2
100
400
700
100
400
700
100
400
700
Kind of dust
Non-separated
Cement
Dust
3
17.80
29.80
46.30
32.80
62.20
86,10
68.80
117.00
156.70
Non-separat ed
Coal
"Dust
4
10.90
22.70
30.90
35.63
67.86
96,54
57.50
89.20
124.00
                                  43

-------
     The laboratory testing was conducted according to conditions previously
defined in the detailed program description.
DISCUSSION OF RESULTS
     In contradistinction to the discussion of results conducted in phase I
of this project (based on comparative analyses rather than theoretical
analysis), this phase (phase II) analyzes Dust Filtration Type I (laboratory
scale) beginning with the modified Valentin relation for dust collection
efficiency (eq. lla, section IV):
                                                                      (23)
where E, = laboratory dust collection efficiency in percent,
      LQ = the areal mass density of the dust in or on the dusty filter
           (the dust load), g/m ,
                    F  -A
                    rl   100
                              = f |qa(SPFM),   ...1  and
                               f              1  J
                    F2 = n = f  qg(SPFM),  ....
According to equation  23, L  and E, should plot as  straight lines on Rosin-
Rammler Paper (at constant q ).  Most of the empirical  data confirm this
assumption.  However, for some kinds of fabrics, discrepancies characterized
by a large dispersion of points exist.
     To fit a linear relation to a specific set of empirical data, regression
lines were determined, after eliminating outlying data points—those that
deviated widely from the average or were not consistent with the theoretical
predictions.
     The calculation was conducted for:
               y = a * bx
         where y = log log =^-                                        (24)
               x = log LQ at q  = constant.
     The coefficients of the regression equation (a and b) are empirically
determined and are calculated from the following relations:
                                  44

-------
          a = log log     =                   .
                       fco        n(Zx^) - (Zxr                       (25)
and          b = n = "(Ixy) - (Zx) (Zy)                               (26)
                       n(ZxZ) - (Zx)Z
where n in the numerator and denominator of the right hand side of the
equation is the number of points through which the regression line was
fitted.
     The plots of the empirical data and the corresponding regression lines
on Rosin-Rammler Paper are shown in figures A- 29 through A-52.
     Calculated values of a = log log 100  = f(q_) and b = n = f(q ) are
                                       c        y                 y
                                        0
shown in tables 20 and 21.  Values of n and EQ as a function of air-to-cloth
ratio q  are shown in figures A-53 through A-62.
     The data collected  in tables 20 and 21 show that for individual groups
of dusts of the same kind and for specific faorics, F.^ and F2 are not linear:
and        F2 =  n =  f(qg).                                             (28)

     The  hypothesis was  presented  that the  relations  in  equations 27 and 28
would be  at least quadratic,  so  the  empirical  data  should  be  better approxi-
mated by  a parabola.   Applying the least squares  method  to determine the
coefficients a, b,  and c of the  parabolic equation:
           y = ax2 + bx + c,                                          (29)
the  following sets  of equations  should be solved:
                         2
           en +  bZx  +  aZx  = Zy
          cZx +  bZx2 + aZx3 = Zxy                                     (3°)
            9       3       A     2
          cZx* + bZx"5  + aZxH = Zx*y

where x = qg] ,  qg2, ...
      y = EQl ,  Eo2, ...  and y =  n1 ,  n2, ....
and  n in  the first  equation is the number of  data points being fitted.
                                  45

-------
Table 20.   INITIAL EFFICIENCY EQ AS A FUNCTION OF qg.
Type
of filtration
fabric
1
BT-4


ET-30


F-tor 5


PT-15


*«
in
m3/m2/hr
2
60
80
120
60
80
120
60
80
120
60
80
120
Kind of dust
Sep.
cement
3
56.75
85.43
-
88,97
68.68
97,74
83.96
12.27
0
58.89
0.077
82,71
Non-sep.
cement
4
87.64
12.72
64.89
48,85
57.01
98.06
96.99
0
0
19.23
0
99,34
Sep.
coal
5
92,30
—
-
80.32'
58.14
9.61
1.71
0
98.14
77.52
62.46
99,07
Non-sep.
coal
6
88.89
64.47
97.97
90.25
89.21
90.42
93-63
76.75
0
99,25
0.075
99,75
Sep
talc
7
37.44
95.24
-
98.55
79.94
96,25
97,18
69.11
0
91.16
39.86
31.66
Sep.
fly ash
8
72,99
70.72
41.58
0.11
85.47
83-33
76.69
83.68
80.06
99,45
71.28
94.97

-------
Table 21.   COEFFICIENT n AS A FUNCTION OF q  .
Type
of filtration
fabric
1
ET-4


ET-30


F-tor 5


PT-15


*g
in
m5/m2/hr
2
60
80
120
60
80
120
60
80
120
60
80
120

Sep.
cement
3
-1.14
-0.96
-
-0.86
-1.15
-0.66
-0.85
-0.99
-1.77
-1.21
-1.77
-1,15
Non-sep.
cement
4
-0.77
-1.24
-0.90
-1.28
-1.05
-0.53
-0.60
-1.90
-2.45
-1.57
-2.39
-0.39
Kind of dust
Sep.
coal
5
-0.66
-
-
-1.06
-1.17
-1.36
-1.49
-2,17
-0.03
-1.09
-1.30
-0.57
Non-sep.
coal
6
-0,78
-1.02
-0.33
-0.97
-0.97
-0.78
-0,82
-0.60
-1.43
-0.49
-1,66
-0,29
Sep.
talc
7
-1.27
-0.47
-
-0,66
-0.92
-0.66
-0.36
-0.91
-1.13
-0,55
-1.34
-1.35
Sep.
fly ash
8
-0,88
-0.98
-1.03
-1.56
-0.87
-0.87
-0.94
-0.79
-0.72
-0.46
-1.02
-0.74

-------
Consequently the coefficients a, b, and c were calculated according to
relations E  = f(q ) and n = f(q ).  The results are shown in tables 22 and
23.
     The determination of the true values of the coefficients a,  b, and c
enable one to write the explicit modified form of the Valentin relation as
follows:
                                          [ao(O  + b?(O + C9
                                           2  g      2  g     2J       (31)

where a1, a2, b1, b2, c.j, c2 = constants depending on the kind of dust and
the structural parameters of the fabric.
     The first part of equation 31 corresponds to the function F^:

          F, = Ui(O  + bi^a) * ci •                                ^^
     It is easy to notice that equation 32 has its extreme at an  air-to-to
cloth ratio of q    «.:
                g ext
                     b,
           9 ext = ' 2^                                              (33)
The sign of the second derivative of equation 32 decides whether  the extreme
is a maximum or a minimum.  The calculated values of q    .  for specific
                                                      g ext
initial dust collection efficiency are shown in table 24.
     In most cases, the extreme corresponds to a minimal initial  efficiency.
The filtration of fly ash is an exception—in three of four cases a maximum
of initial efficiency was observed.
     It is very interesting that the extreme values of the function F, occur
                                                               3   2
over a  relatively narrow range of air-to-cloth ratios, 70-100 m /m/h.  The
above regularity was also observed in other testing conducted by the IPWMB
for 16  kinds of fabrics and unseparated dusts.
     The parabolic dependence of initial dust collection efficiency on the
air-to-cloth ratio has a very important consequence because it leads to the
hypothesis that there are two separate dust penetration processes—one for
low q   values and another for high q  values.  The value of q    .  is probably
     9                              9                        9 °xt
that air-to-cloth ratio at which the transition from one mechanism to the
other occurs.  This hypothesis applies also to the function F2 = f(q ),
                                  48

-------
Table 22.  COEFFICIENTS OF THE PARABOLIC EQUATION:  FI = a (3
}   +
Type of
filtration
fabric
1
ET-4
ET-30
F-tor 5
PT.-15
Parabola
coe-
fficient
2
a1
C1
a1
C1
a1
b1
C1
a1
C1
Kind of dust
Sep.
cement
3
-
0.029016
-5,07683
289,12
0.054629
-11,23258
561.25
0,083441
-14,6~242
635,85
Kon-sep.
cement
4
0,082545
-15.20491
700,82
0,000262
0,37125
25,63
0,080825
-16.165
775.92
0,057416
-8.99966
352.52
Sep.
coal
5
—
0,001737
-0.86575
300.14
—
0.027804
-4.64558
256.16
l\on-sep
coal
6
0.034308
-6,02416
326.83
0.001370
-0.24391
99,95
0,017912
1.66375
58.29
0.124177
-22.34354
992.825
Sep.
talc
7
—
0.022304
-4.05308
261.44
-0.005404
-0,64691
155.45
0.039333
-8.07166
433.06
Sep.
fly ash
b
-0.010250
1,32150
30.60
-0.069208
13.95716
-588.17
-0.007345
1,37616
20.43
0,033345
-6.07841
344.02

-------
                     Table 23.  COEFFICIENTS OF THE  PARABOLIC  EQUATION:   F£  =  n  =  a2(q )Z + b2q  +
tn
o
Type of
filtration
fabric
1
ET-4


ET-30


P-tor 5


PT-15


Parabola
coeffici-
ent
2
a2
b2
C2
a2
b2
C2
a2
b2
C2
a2
b2
C2
Kind of dust
Sep.
cement
3
^
—
—
0,000445
-0.07691
2.15
-0.000208
0,02216
-1.43
0.000725
0.12950
3.95
Non-sep.
cement
4
0.000567
-0.105
3.52
0,000108
-0,03
-2.49
-0.000045
-0.02258
0,92
0.001516
0,25333
8.17
Sep.
coal
5
_
—
—
0,000012
-0.00725
-0,67
-
-
».
0.000479
-0.07758
1.84
Non-sep.
coal
6
0.000488
-0,08025
2.28 '
0,000079
-0.01108
-0.59
-0.000529
0.08508
-4.02
0,001545
-0.27491
10,44
Sep.
talc
7
^ .
—
—
0,000325
-0.05850
1.68
0.000366
-0.07883
3.05
0.000654
-0.13108
4.96
Sep.
fly ash
8
0,000063
-0.01375
-0.30
-0,00056
0.115
-6.39
-0.000095
0,02091
-0,85
0.000583
-0.10966
4.02

-------
                     Table 24.  EXTREMAL AIR-TO-CLOTH RATIOS, q
Type of
filtration
fabric
1
ET-4

ET-30


F-tor 5

PT-15


Initial
effi-
ciency*
2
o min
o max
0 roi n
Ert mo
o max
OWl"? VI
/% ma Y
o min
E
o max
Kind of dust
Sep.
cement
3
-
-
87,48


102,81
^^
87.62


Non-sep.
cement
4
92.10
—
-708,49


100.00
^
78.37


Sep.
coal
5
_
—
249.21



—
83.54


Non-sep.
coal
6
87.80
—
89.02


-46.44
—
89.97


Sep.
talc
7
—
-
90.86


.
-59.85
102.61


Sep.
fly ash
8
—
64.46
.
100.83

mm
93.68
91.14
^

*Listing q    .  as corresponding to E     or E     depends on the sign of
          a                           min      max
the coefficient at (Table 22); i.e.  positive ax implies a minimum value
of E ;  negative at, a maximum.

-------
which mainly describes the filtration properties of the dust cake, taking
under consideration the conditions of its formation.  F« functions for
various dust-fabric combinations are shown in figures A-53 through A-62.
     Considering the fact that the analyses of the dust filtration process
include only a comparatively narrow statistical range, it is necessary to
verify them, based on data obtained from additional individual tests conducted
both in the laboratory and on large scale.
     The  increase of pressure drops accompanying dust filtration results
from thickening of the dust cake formed on the fabric surface.  The analysis
of results obtained at laboratory scale for separated cement and coal dusts
was carried out according to the previously presented theoretical aspects of
the dust  filtration process (section IV), where nonlinear behavior of filtra-
tion resistance as a function of time (or as a function of dust load, L )
was confirmed.
     For  specific dust-fabric combinations and values of air-to-cloth
ratio, q  , the outlet dust concentrations (C ) corresponding to definite
dust loadings L , were calculated consecutively.  The results of these calcula-
tions are shown in tables 25 and 26 and figures A-63 through A-70.
     Applying the least squares method, the forms of the functions CQ =
f(LQ) were determined, assuming a parabolic relationship as the first approxi-
mation.   The following equations were developed:
     For  separated cement dust and fabrics as indicated:
                                  ET-4
     qg = 60;  CQ = 1.0 x 106 (LQ)2  12.3 x 10~4 (LQ) + 0.403
     qg = 80; CQ = 0.066 x 10"6(L0)2 - 0.66 x 10~4(L0) + 0.01994
     qg = 120; CQ = 0.338 x 10~6(LQ)2 - 2.76 x 10"4(LQ) + 0.11422
                                   ET-30
     qg = 60; CQ = 0.627 x 10"7(LQ)2 - 0.796 x 10"4(LQ) + 0.02934
     qg = 80; CQ = 0.7 x 10"7(LQ)2 - 0.8472 x 10"4(LQ) + 0.0265
     q  = 120; CQ = 0.33 x 10"7(LQ)2 - 0.412 x 10"4(LQ) + 0.015734
                                  52

-------
                     Table  25.   OUTLET CONCENTRATION,  CQ in g/m° ,  IN LABORATORY TESTING OF CEMENT DUST.
01
CO
Type of
filtration
fabric
1
ET-4


ET-30


J?-tor 5


PT-15


Air-to-Cloth
Ratio in
m3/m2/h
2
60
80
120
60
80
120
60
80
120
60
80
120
2
Dust loading, g/n
LQ = 100
3
0.29
0.014
0.09
0.022
0,01875
0.012
0,035
0,22782
0,73
0,021
0.01594
0.01
LQ = 400
4
0,07
0,0041
0,058
0,0075
0,00388
0,00475
0.009
0.05129
0.0555
0.00425
0.001935
0.00225
LQ = 700
5
0.03
0,0061
0.087
0.00429
0.001667
0,003428
0.007
0.03417
0.06129
0.001857
0.001667
0.001714

-------
Table 26.  OUTLET CONCENTRATION CQ IN g/ro3, IN LABORATORY TESTING OF COAL DUST
Type of
filtration
fabric
1
ET-4


BT-30


P-tor 5


PT-15


Alr-to-Cloth
Ratio in
m3/m2/h
2
60
80
120
60
80
120
60
80
120
60
80
120
2
Dust Loading, g/m
L a 100
0
3
0.037
(0,1528)
(0.375 )
0.016
0.02438
0.046
0,16
0,5653
(0,165)
0.016
0,01125
0.006
LQ « 400
4
0.0145
(0.2327)
(0.401)
0,0035
0,003629
0.006
0.03375
0.01839
(0.18075)
0.00475
0.001694
0.004
Lo=700
5
0.117
(0,3622)
(1.3753)
0.003571
0.0025
0.003
0.007
0.0094
(0.1324)
0.001857
0,0011
0.002714

-------
                                  F-tor 5
    q  = 60; CQ = 0.133 x 10"6(LQ)2 - 0.78 x 10"3(LQ) + 0.06766   •
    qg = 80; CQ = 2.405 x 10"6(LQ)2 - 1.037 x 10~3(L0) + 0.32207
    qg = 120; CQ = 3.676 x 10"6(LQ)2 - 4.138 x 10"3(LQ) + 1.1060
                                  PT-15
    qg = 60; CQ = 7.976 x 10"8(LQ)2 - 9.57 x 10"5(LQ) + 0.02977
    q  = 80; CQ = 7.63 x 10"8(L0)2 - 8.48 x 10~5(L0) + 0.023435
    q  = 120; CQ = 4.0 x 10"8(LQ)2 - 4.58 x 10~5(L0) + 0.014864.
         For separated coal  dust  and fabrics as Indicated:
                                  ET-4
    q  = 60; CQ = 9.361 x 10"7(LQ)2 - 4.22 x 10"4(LQ) - 0.04613
                                  ET-30
    q  = 60; CQ = 6.983 x 10"8(LQ)2 - 7.6583 x  10"5(LQ) + 0.023198
    q  = 80; CQ =  10.9 x  10"8(L0)2 -  12.36 x 10"5(LQ) + 0.034547
    q  =  120;  CQ =  20.55 x  10"8(LQ)2  - 23.611 x 10"5(LQ) + 0.0676
                                  F-tor  5
    q  =  60; CQ =  5.527 x 10"7(LQ)2 - 6.922 x 10~4(L0) + 0.224194
    q  =  80; CQ =  21.838  x  10"7(LQ)2  + 8.206 x  10"4(LQ) + 0.5055
                              PT-15
    q  =  60; CQ =  4.652 x  10"8(LQ)2 - 6.076 x 10"5(LQ) + 0.021611
    q  =  80; CQ =  5.0288  x  10"8(LQ)2  - 5.6744 x 10"5(LQ) + 0.016426
    q  =  120;  CQ = 0.4  x  10"8(LQ)2 -  0.8655 x 10"5(LQ) + 0.006825.
The time and Initial concentration (cp dependence of the dust covering
                         n:
                         Lo = (ci - eo> V*                     (34)
L  is described by the equation:
                                 55

-------
where c  corresponds to the functions of L  just presented.
     Based on the dust cake equation:
                              S = LQ/K                                (35)
which, according to experimental data given by many authors, describes a
straight line in the S-L  coordinate system (with slope 1/K, where K is the
permeability of the dust cake and fabric).   The obtained results show that
the coefficient K cannot be a constant dependent only on the specific dust
and fabric.  Intuitively, the above statement is also ascertained.
     The permeability coefficient of a porous layer in the Darcy Formula
assumes a stationary spatial system of layered elements, while in a dust
filtration process displacement and compression effects appear.   First's
experiments, conducted using trace elements, confirm this statement.
     During our testing, a nonlinear dependence of filtration resistivities
upon dust cover was recorded.   The complete analysis of the empirical data
will be included in the final  report.
CONCLUSIONS
     Based on the results of fabric testing on a laboratory scale,  a modified
form of the Valetin equation for dust collection efficiency as a function of
dust cover L  and air-to-cloth ratio q  was developed.   Also, the experiments
performed confirmed the appearance of defects in the dust cake structure, in
the form of canals (ducts), considerably reducing the dust collection effi-
ciency.   And finally, nonlinear variation of filtration resistances with
time (dust cover), which results from differences between the theoretical
and the real models of dust cake formation, were found.
                                  56

-------
                               SECTION VI
           PRELIMINARY MATHEMATICAL MODEL OF DUST FILTRATION*
     The problem of inferring fabric properties has all the characteristics
needed for applying the methods of statistical inference.   The characteris-
tics of a population are inferred from the behavior of a sample.  Thus, a
specific fabric can be considered a population whose characteristics we wish
to describe.  The sample is a piece of that fabric on which measurements are
made of certain specific characteristics, either in the laboratory or on a
large scale.  The parameter examined most often is fabric permeability to
the flow of air or clean or dirty gas.  The basic problem from a statistical
point of view is that of the existence and interpretation of a random vari-
able representing a specific characteristic.  The random variable can be
introduced in many ways depending on the questions to be answered.
     Fibers from which a fabric is built are not heterogeneous but they do
differ in shape and in such properties as elasticity or thickness.  This
element of heterogeneity comes about because of random variations in the
production process.  In the case of fabric production from synthetic mate-
rials, just a little temperature variation causes the fibers to vary in
thickness and other properties.  With natural fabrics, variations in the
fiber properties cause the fabric to be heterogeneous.  The variables in-
fluencing the above processes have random character.  So each of the examined
fabric parameters related to the above heterogeneity is a random variable.
Thus we have, by the nature of the manufacturing processes, a probability
space in which random variables are situated.
     More practical is the random variable introduced in another way. Let
the probability space (E, A, P) be given.  As random variables, we consider
the univariate real functions making up a set of elementary events E (a
Borel.field of sets) in IRn (a Borel field of sets in IRn).  As an elemen-
*Section VI was written by Dr. Eugeniusz Szczepankiewicz, Institute of
Mathematics of WSP, Opole.
                                  57

-------
tary event in the set IRn, we consider an arbitrary open rectangle.  As an
elementary event on the fabric, we consider an arbitrary rectangle cut out
from the fabric bale.  As a set of elementary events we consider all the.
rectangles covering the fabric bale.   Circles can be used as easily as
rectangles.  This definition of a random variable is very useful in applying
statistics to fabrics and especially in studying those fabric characteris-
tics related to filtration.
     It is important to notice that fabric properties related to filtration
are random variables having finite expected values and variances.  Since the
filtration process acts in time, it is a stochastic process.  If we want to
make this process dependent upon geometrical parameters (which is advisable
in many cases) we develop a random field.   This random field has finite
expected value and variance.   Thus it is a stationary random field in the
broad sense, but if it depends on the distance between points, it is an
isotropic random field.
     Let f(p) be the examined characteristic of the fabric filtration
process—a stationary random field in the broad sense.   The properties of
the random field can be described as
               E  [f (p)]   = m = const,  at    E   ff(p)l    <»           (36)
               D2  [f(p)J   = o2  <».                                   (37)

 The correlation function depends only on the distance between points p and
,  f(q)]  =
                                                                      (38)
     Since the fabric filtration process involves many characteristics of
the fabric, many parameters of this process can be examined.  Each charac-
teristic, and the parameter which represents it, can be described by a
stationary random field in the broad sense, which is also isotropic.  Thus
the problem is the formation of a stochastic filtration model that includes
all dependencies existing between the parameters of the fabric filtration
process.
     Let us consider parameters described by the random fields f ••(?),...,
fn(p) that makeup the filtration process.  Parameters are Intercorrelated.
                                  58

-------
The relation between arbitrary parameters is expressed by the correlation
function describing the stochastic connection of these parameters.   This
correlation function can be written:
                         =  R,,   (|pD  . (i * J; 1 J = 1.  ••••  ")•    (39)
                             ' J    I  r
     We have assumed that the connections between parameters are stationary.
The relation between all parameters is expressed by a multiple correlation
function:
                                         _§n(|pq|).                (40)
In dependence (40) we have assumed stationary relations between all  param-
eters of the fabric filtration process.
     Functions (38), (39), and (40) should be chosen from classes of func-
tions which could be correlation functions of stationary, isotropic, and
stationary-related random fields.  Optimal selection of these functions will
be discussed in a later part of this section.
     Thus far the random field has been described taking into consideration
only one bale of fabric.  Now we are interested in the problem in a wider
sense.  We want to look at the filtration problem for more than one bale of
material (the same kind of fabric).  The random field defined for one bale
of material can be extended to all bales of the same fabric.   For this
purpose, we introduce the following expression:

                    M(D) = -L- /f(p)dp                               (41)
                           IV
which we call the mean of the random field f(p) over the range D, where |o| is
a field of range D, and dp is a differential of measurement in D.
     The expression (41) is considered the mean of one bale of fabric and is
estimated from the mean of a sample.  The limits are 1 and m M(D), where D
Increases without limit (the problem needs definition but here this defini-
tion 1s omitted) and 1s the expected value of the random field.  So it is a
natural extension of the mean of one fabric bale to all bales of a specific
fabric.  This definition is compatible with the generally accepted defini-
tion of a random field.  Because we cannot find the expected value of the
                                 59

-------
random field in the sense mentioned above, we will estimate it from the mean
of a sample.  In classical statistics such estimates are based on the arith-
metic mean of the random sample.  Random values (individual measurements)
are taken on the sample in order to achieve independence.  In the case of
the random field this choice is usually impossible.  We can obtain dependent
random variables but the samples from which we estimate are not random
samples.   They (random samples) do not guarantee that all parts of 0 will be
represented.  Consequently, systematic samples are used.  The problem of
optimal sampling will be discussed later in this paper.  We will be interested
in those samples which best represent the parameters of fabric filtration.
Now we will deal with the problem of estimating the mean (41) with the help
of measurements of values of the random field at points in D.
     Let f1 = f(p,)	 f  = f(P_) be values of the random field f(p) at
points pp ..., pm in D.   M(D) in (41) will be estimated by the linear
estimators given below.   It is shown that the best estimator is included
among these estimators.
     Estimator 1
                = CQ + c]f] + ... + cmfm                              (42)
where c. >  0 (i = 0, 1, ..., m)
and c  + c, + ...  + c  = 1.
     o     i          m
The error of this estimator is s,, given by
               s? = min           E[m,(D) - M(D)]2.                    (43)
                     co'cl"--'cm
     Estimator 2.
     m,(D) = c,f,  + ... + c f                                         (44)
      £       I  I           In In                                           *
where c. > 0 (i  = 1, ..., m)
and c, + ... + c  = 1.
      i          m
The error of this estimator is s2, given by
               s? = min          E[m7(D) - M(D)]2.                    (45)
                     cl	cm
                                  60

-------
     Estimator 3
     m3(D)=Clf1+... +cmfm
where c. > 0 (1 = 1, ..., m)
and c, + ...•«• c  = 1.
      i          m
and the constants are selected so that
                                 E[m3(D) -
                2
               S~ = min
                    cr
                                                                      (47)
                               m
and E[m3(D)] = M (D).
The error of this estimator is calculated from formula (47).
     Estimator 4.
     m4(D) = c(f1 +  ...-»• fm)
where c = 1/m,
     E[m4(D)] = M(D),
and constant c is selected so that
               sj = min E [m4(D) - M(D)]2.
                                                                      (49)
                                                                      (50)
                                                                      (51)


                                                                      (52)
                                             c  appearing in the estimators
The error of this estimator is calculated from formula (52).
     In all estimators, E represents the expected value operator.
     It is shown that the constants c , ..
are solutions of a set of specific linear equations of the Cramer type.   For
estimator 1 we have the equation system:
                                           , M(D))
     a(f1§
           f,)c,
                                     = 0(fm, M(D»
                                     :  = H(D)
                                                                      (53)
where a(f.,f.) (i, j = 1, ..., m) represents the covariance of the random
variables f., f.; cr(f., M(D)) is the covariance of the random variables f^
and M(D), and E(fj) is the expected value of the random variable f^.
     Constants appearing in estimator 2 are calculated from the equation
system:
     E(f1f1)c1 + ... + E(f1fm)cm = E(frM(D))
                                                                      (54)
                                  61

-------
where     E(xy) = a(x,y)  +  E(x)E(y).



     Constants appearing  In estimator 3 are calculated from the equation

system:
                                  + \ = a(frM(D))
          c, + ...  + c  =1
           I         m
                                                                     (55)
where \ is an indeterminate  Lagrange factor.

     Errors of the estimators  1, 2, 3, and 4 are calculated from the  follow-

ing equations:
                          a
     a(f,,M(D)) ...  o(f  ,M(D)) a (M(D),M(D))
        I              III
•-
     E(f,f,) ...  ECfjfJ  E(f,H(D))
E(f,M(D))
                   E(fBH(D)) E(H(D)M(D))
                                        ^) - o(fltM(D))}
        -  jot(frM(D)) + ...  + a(fm,M(D)) - a(M(D),M(D))}
                                                                     (56)
                                                                     (57)
                                                                (58)
                                 62

-------
       12                  m
            *
          mo  + 2Za(f.,f.) - 2mZa(fi ,M(D))                            (59)
       m                        =
              +m2a(M(D),M(D))l
       p                     '
where a  is a variance of the random field f(p).
     To calculate the constants c   ...,c , in estimator 1, it is sufficient
to know the correlation function of the random field and its expected value
E(f.j)(i= 1, ••-, m).  For GI , .... cm> in estimator 2, it is sufficient to
know the correlation function of the random field and the ratio M/a.   For
C1 » •••» c . in estimator 3, it is sufficient to know only the correlation
function of the random field.  The errors of the estimators 1,2,3, and 4 are
also based on the correlation functions of the random field.
     It is shown that the worst of the linear estimators are estimators 1
and 2, and that the best of all estimators are estimators 3 and 4.  For
calculation of the mean (41) we recommend first of all the use of estimator
4, which will be called the arithmetic mean.  Its calculation is very simple,
as is the calculation of the error of this estimator.
     Note the important role of correlation functions in these calculations.
Correlation functions can also be used to measure the variation in the
parameter of fabric filtration being studied.  The correlation function is
calculated from empirical data.  Let f , , ..., f  be measurements of the
random field at points p, ,  ..., p  belonging to set D.  Let t be a parameter
of the random field, i.e. an argument of the correlation function R(  pq ) =
R(t).  Let us assume that values of the parameter t, namely t1 < t,, < ...

-------
and
          «t>	W                                         (61)
                 1 + At
where A > 0; k = 0, 1, ...  are correlation functions of stationary random
fields and, in the broad sense, isotropic.  From the classes of these func-
tions, the correlation function that best describes the parameters of the
filtration process will be chosen by the Gauss least squares method.   Q is
minimized in the formula:

               Q = J I  [Pp - W]2                                (62)
                      r=l
                     (1=1,2)
     From the classes of functions (60) and (61) we should choose the best
one.  The function that best matches the empirical data (the best correla-
tion function of the random field) p,, ..., p  is the function for which Q
in formula (62) is the smallest.
     In the classical minimization problem, analogous to (62), the two sides
of the formula are partially differentiated with respect to A and k and the
derivatives are equated to zero.   This yields a set of two linear equations
with two unknowns.  In our case this method of proceeding is impossible.  We
will minimize formula (62) by trial and error.
     Let us pick an arbitrary k value.  We calculate values of the constant
A for t.|, ..., ts from equation (60).  The minimization of function (61) 1s
analogous to the one described below.
     From all values A^	Ag obtained for t^	tg from function (60)
pick the smallest value and the largest value.  Denote the smallest value by
a and the largest by b.  Now, the Interval [a,b] will be subdivided and
ordered by values a] < a2 < ••• this Interval will be divided Into m parts and formula (62)
will be used to calculate Q for these m points.  We choose the smallest Q
value from this set.  Repeating the operation as long as it 1s necessary, we
                                  64

-------
obtain the value AQ(k) for which Q in formula (62) is the smallest for that
specific k.  Repeating the procedure for all k = 0,1,... we choose the pair
AQ and kQ from the value AQ(k) for which Q in formula (62) is the smallest.
In this way we calculate the best correlation of the random field.  It
appears that this calculation method is more precise than verification
criteria of probability distributions.
     Now, we will discuss the problem of sampling.  Random field theory
sampling theory is different than sampling according to classical statis-
tics.  It is more complete and precise than in classical statistics.  In
classical statistics there is no problem of the optimum sample.  Here this
problem can solved.  In classical statistics, the sample is a random sample
so the measurements are chosen to be independent.  Generally it is recom-
mended that the distributions of these random variables be equal and normal.
So we do recognize a probability distribution that is approximately normal.
In random field theory, it is possible to distinguish an approximately-
normal distribution.
     Below we formulate the problem of the optimum sample.  It has already
been ascertained that the arithmetic mean is a "good" one.  The random
sample is assigned as follows.  Set D is established on the unfolded fabric.
From this set we choose randomly (that is, with the same probability,
according to a monotonic probability distribution) m independent points,
obtaining p,, ..., p .  At these points we measure the  values of the random
field, f(p).  The set of values f(p-|), ..., f(Pm) constitutes the random
sample.
     The stratified sample is obtained as follows.  The set D is divided
into congruent subsets A], .... Am called strata.  From each stratum we
choose a point at random, obtaining p,, ..., p .  At each point p., we
                                      I        III                   I
measure the value of the random field f(p), obtaining values f(p1), ....
f(p ), which constitute the stratified sample.
     Let the interval A,, ..., Am from set 0 be given and the sets AI, ...,
A  be congruent.  From set A, we choose at random one point p^.  From set A.
we choose the point p., so sets A^ and A.., after displacement of the vector
p,p., will overlap.  At points pi (i = 1, .... m) we measure values of the
random field f(p) obtaining fCp^), .-., f(Pm) as the systematic sample.
                                  65

-------
     We have described above the ways of obtaining the three basic samples
used in experimentation.   The statistical data collected and verified in
this project were obtained using these samples and especially the optimal
samples.
     Let

                    i m
               M1 = ^ I   f(p.)                                       (63)

be the arithmetic mean obtained using random samples;

               M2 = i ^ f(Pj)                                       (64)

be the arithmetic mean obtained using stratified samples, and

               M3 = 4 ^ f(p.)                                       (65)

be the arithmetic mean obtained using systematic samples. Let us call
               s2 = E[M(D) - M^2                      f.v            (66)

the variance of the mean estimator (41), using the arithmetic mean M,
obtained from the random sample;
               s2 = E[M(D) - M2]2                                     (67)

the variance of the mean estimator (41) using the arithmetic mean M«
obtained from the stratified sample; and
               s2 = E[M(D) - M3]2                                     (68)

the variance of the mean estimator (41) using the arithmetic mean M-
obtained from the systematic sample.
     The above theorems are proven below.
1. Equality
               sl = m C°2 " °2 
-------
2.  If set D can be divided Into separable congruent subsets A,,  ..., A  or
If the random field f(p) 1s stationary and 1n the broad sense  1sotrop1c, and
set D can be divided Into separable similar subsets A.J,  . ... A^ then

               S  =   C°2 " °2WA>)3-                               (70)
                2   m
3. If set D 1s a sum of separable congruent subsets A, .....  A ,  then
                9       m   m              9
               s* = 2-  Z   Z   RCpTpT) - D^(M(D))                    (71)
                3   mz  1=1 j-1    1 J
where p, is a center of gravity of the subset A. (1 = 1,  .... m).
                                        2
     In formulas (69), (70), and (71), a  represents the  variance of the
                    2
random field f(p); D (M(D)) is the variance of the mean (41)  in set D;
D2(M(A1)) is the variance of the mean (41) in set A^ and R(pTp^) is the
correlation coefficient of the random variables f(pp,  f(p-)  (values of the
correlation function).
     The formulas (69), (70), and (71) give us errors of  estimation of the
mean (41) with the help of the arithmetic mean obtained using random,  strati-
fied and systematic samples.  Notice that for solution of the problem  of
optimal sampling, it is sufficient to compare the variances (69), (70), and
(71).  The theorems below give this comparison.
4.  If set D is a sum of separable congruent subsets A,,  ..., A^, or if the
random field f(p) is stationary and in the broad sense isotropic, and  subsets
A,, ..., A  are similar, then
               s\ < s*                                                (72)

5.  If set D 1s a sum of separable congruent subsets AJ,  ..., Am, then the
condition

               4 < >l                                                <73)
for each 1 and j leads to the Inequality:
f
                                                   dp                 (74)
where p^ 1s the centrold of the subset AI and p. 1s the centroid of the
subset A,.  If relation (74) occurs In each set A1  - Aj U Aj (1  * j;  1, j =  1,
..., m), then Inequality (74) results.
                                 67

-------
     Theorems 4 and 5 are the criteria making it possible to choose the best
sample.  From theorem 4 it follows that the worst sample is the random
sample.  From theorem 5 it follows that under known specific conditions, the
best sample is the systematic sample.  This theorem makes it possible to
solve the problem of optimal ity of both the stratified and systematic
samples.  The problem of sample optimal ity can be solved quite easily when
we deal with a random field that is stationary and isotropic.   These kinds
of fields describe fabric filtration.  In this case it is sufficient to
examine the correlation function of this field R(pq) and to find the diameter
of the set in which R(pq) is underdamped so as to ascertain that, for a set
of this specific diameter, the stratified sample is worse than the systema-
tic one.  If the correlation function is underdamped, the stratified sample
is worse than the systematic one.   If the correlation function is overdamped
the stratified sample is better than the systematic one.
     It also appears that the stratified sample is the best for sets D of
small diameters.  The term "small  diameter" is not the same for each param-
eter or for each fabric.  It depends on the correlation function of the
random field.   But it can be proven that when the area 'of the fabric is not
               2
bigger than 2 m  and the set D is  not a zone of diameter smaller than 10 cm,
the diameter of this set is small.   A set has big diameter when it is bigger
         2
than 10 m .   But if its zone is smaller than 10 cm its area can be smaller.
In the last case the systematic sample is better than the stratified one.
These values of diameter were obtained from correlations between the veloc-
ity and pressure drop of clean air flow through fabrics.
     We examined 16 kinds of fabrics of different raw materials and struc-
ture.  We formed the correlation function for these two parameters
               R(x) = exp[- AT|]                                      (75)
        •»        f~2    2
where   x   =  yx  + y , A > 0 and is different for each fabric.
     The other parameters influencing the filtration process should also be
examined and incorporated into the correlation function.  We have reason to
suppose that the correlation functions will be similar to (75).
     This model of fabric filtration has a descriptive character and should
be considered preliminary.  The statisitical methods used in the analyses of
the empirical data also have a descriptive character.  In the final report
we will give the full mathematical-statistical description of this model and
also the mathematical -statistical and literature background.

                                  68

-------
                                 SECTION VII
                      STUDY OF FILTER MEDIUM PARAMETERS
INTRODUCTION
     As proven in section IV, obtaining a specific collection efficiency
from a specific initial aerosol state is possible only by selection of
suitable filtration parameters or filtration medium structure parameters.
Differences in the spatial composition of the filtration medium cause definite
performance differences in the filtration process.  They influence the dust
collection efficiency, filtration resistance and also the ease of regenera-
tion, the degree of filling the filtration medium with dust, etc.
     For a long time, the description of nonwoven textile materials, assum-
ing their homogeneity and isotropy, consisted of the following parameters:
          Elemental fiber diameter,
          Filtration layer thickness, and
          Porosity or packing (bulk) density.
These structural parameters of nonwoven materials have technological as well
as physical character.  Once they are specified a definite fabric structure
is produced, but the filtration performance parameters of the fabric (dust
collection efficiency and filtration resistance) are often independent of
them.
     Although the qualitative differences between fabrics (woven materials)
have been studied and the effects of various technological parameters on
their formation are known, the spatial structure of a fabric cannot be
described in a physical sense.  It is a result of the much more complicated
spatial structure of woven materials as compared to nonwoven ones.
     In woven materials, elemental fibers are not the only elements of the
structure, although they do make up the structural units of the warps and
fills, which are spatially arranged.   In the case of double fabrics the
spatial structure is even more complicated.  Because of the heterogeneity of
the yarn used for fabric production and also because of technological condi-
                                 69

-------
tions of production, woven filtration materials cannot be regarded as homo-
geneous and isotropic, but as heterogeneous and anisotropic.
     According to the above statement, characterizing the structure of woven
materials by porosity, diameter of pore and density of packing is not
consistent with the basic assumptions of the DARCY equation;  thus the appli-
cability of the Darcy equation in its unmodified form is limited.  Although
specific values of porosity can be ascribed to individual elements of the
structure of woven materials, structural variations do not allow such values
to apply to the entire volume.
     If the heterogeneity of fabrics is not taken into consideration, the
analytical determination of porosity based on fabric thickness is subject to
considerable error because of the voids between weave elements protruding
above or below the bulk structure.  This problem is illustrated in figure 4a.
     Assuming that woven and non-woven materials are characterized by the
same thickness, b, by the same weight per square meter, G, and the same
specific gravity of materials, pml = pm2, the packing density of the struc-
ture will be
          Pbl = Pb2 = G/b  (g/m3).                                    (76)
Calculating the fraction of solids in the filter and the porosity, we have:
          « = Pb/Pm                                                   (77)
and       e = 1 - «.                                                  (78)
Denoting the true thickness of the woven material by b1 (fabric thickness
does not include the voids between weave elements), we have
          pb, = G/b'>pbl = pb2,                                       (79)
and the true mean porosity of the woven material is
          e1 < e.                                                     (80)
The errors Illustrated by this calculation depend on yarn thickness and type
of weave.
     The determination of the porosity of woven materials by using measuring
methods needs additional definition of the kinds of pores that are important
in the filtration process.  An appropriate measuring method should be deter-
mined in advance.   In some cases a description of woven materials by measure-
                                  70

-------
                     a.  Bon-woven material
        VOIDS BETWEEN WEAVE
b'
                     b.  Woven material
   Figure 4a.  Geometrical  Considerations Attributed to Fabric
              Structures.
                            71

-------
ment of porosity or fraction of solids is valid, but these parameters are
not analytically related to the technological parameters, which greatly
limits their usefulness.   Any parameter characterizing the structure of
woven filtration materials should be related to the technological  parameters
of production.
     To obtain adequate data, testing was conducted on 16 kinds of Polish
fabrics instead of just 4 fabrics as originally planned.   Fabric characteris-
tics were included in the phase I report of this project.  The testing
included:
          Examination of hydraulic properties during clean air flow (labora-
          tory experiments).
          Application of mathematical methods for estimating similarities or
          differences between materials on the basis of test results and
          technological parameters.
          Description of fabric geometric structure as a function of tech-
          nological parameters.
CLEAN AIR FLOW THROUGH FILTRATION STRUCTURES
     The phase I report of this project includes the results of fabric
testing with clean air flow at two values of air-to-cloth ratio and the
corresponding ranges of pressure drop:
          Low values of flow:  AP = 0 - 10 mm of water, and
          High values of flow:   AP > 10 mm of water.
Each flow and pressure drop was measured 30 times, so each reported value
(phase I report) was the mean of 30 measurements.  Mean values of air-to-
cloth ratio for specific values of pressure drop are shown in table 27.
     The mean and the standard deviation were estimated using the following
relations:

                 1 "
          V  = n  =   qg(D                                         (81)
          CT = n\f=1(qg(i) • V2  •                                 (82)
The calculated values of the standard deviation are given in table 28.  To
verify the hypothesis of the normality of the q  distribution, the Kolmo-
                                  72

-------
                              Table 27.   CLEAN AIR #LOW THROUGH FABRICS
CO
Ap
in
mm H^O
1
5
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
Alr-to-Cloth Ratio qQm in m /m /min for fabric
ET-1
2
5.09
9.39
16.66
21,56
29.44
35.32
40.56
45.99
52.47
58.15
59.09






ET-2
3
7.98
13.66
23.60
32,16
38,55
45.83
60,41
54,16









ET-3
4
3.01
7.02
13.08
19.31
23.72
29,39
35i03
39.61
43.74
49,39
52.63
55.78





ES-4
5
5.79
10,83
19.33
26.04
33.51
39.80
48.59
53.08
55.20
58,67







ET-30
6
2.25
4.35
8.10
10,92
13.70
16.69
19.62
22,19
24,38
26,35
30.13
32.22
34.01
36.24
39.37
40.53
42,50
BT-57
7
3,17
6.87
13,04
18,09
22,94
29,04
34.61
38.41
42.97
47.57
50,51
53.11





WBT-203
8
6.50
12.85
23.77
34.42
42,59
51,54
63.70
71.22
79.23
86.34
94. U5
102.58
112.58
118.19



WBT-21 0
9
6.65
13.18
23.52
33.32
41.01
49,41
60.40
68.47
74.86
81,97
88,58
94.77
103.29
110.10
115.92



-------
Table 27 (continued)
1
170
180
190
200

5
10
20
30
40
50
60
70
80
90
100
110
120
2




ST-41
4.96
8.80
14,77
20,09
23,55
27.72
31.66
35.17
37.91
40.95
43.64
46.23
49,03
3




ST-1
12,23
19.89
31.81
39.53
46,54
53.44
52,98






4




ST-1 3
9,44
14.44
22.58
29,10
33,19
39.90
44.00
48.10
52.24
53.05
54,24


5




BWA-1 53S
4,07
8.24
15-31
21.89
28.84
35.33
41.29
46.29
51.89
55.69



6
42.50
45.58
47.80
48.82
WT-201
14-22
26.80
49.53
71.48
84.15
103.28
117.48






7




WT-203
10,90
19.89
36.70
51.64
65,43
77.88
89.83
103.80
119.38




8




WT-204
19,23
35.11
64,90
88.J>5
108.16
127.12







9




WT-207
6.94
13.34
24.78
36.10
44.86
55,78
67.06
75.72
83.99
92.69
102.80
110,63
117,07

-------
                                           Table 27 (continued)
1
130
140
150
160
170
2
50.15
51.13
52.49
52.24
53,60
3




•
4
•




' 5





6





7





8





9





U1

-------
             Table 28.    STANDARD DEVIATION  IN THE AIR-TO-CLOTH RATIO (in m3/m2/min)
01
AP
in
mm HgO
1
5
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
Kind of fabrics
ET-1
2
0.28
0.99
1.21
0.96
2.56
1.74
2,47
2,61
4.11
4,20
3.18




•

ET-2
3
1.04
0.75
0,53
0.42
0.40
0.39
0.48
0.27









ET-3
4
0.59
0.99
1.71
2.58
2.84
3.53
3.71
3.82
4,75
4.80
4,34
4,54





BT-4
5
1.21
2.29
3.12
2.82
5.24
5,32
6.53
8,20
5.28
3.73







ET-30
6
0.39
0.82
1,07
1,45
1.84
2,05
2,57
2.69
3.06
2,30
3.76
4.30
4.94
4.82
3-96
2.00
3.78
BT-57
7
0.84
1.04
1.98
2,25
2.29
2.54
1.95
2,80
3.29
3. 97
4.31
2.96





WBT-208
8
0.54
0,61
1,81
1.65
1.85
2.63
2.68
2.39
2.91
2,99
3.59
4.08
5.75
4,06



WBT-21 0
9
0,31
1.13
0.80
1.31
2.07
1.65
2.74
1.85
2.21
3-24
2.56
4.46
3.44
3.94
2.09



-------
Table 28 (continued)
1
170
180
190
200

5
10
20
30
40
50
60
70
80
90
100
110
120
2




ST-41
0.86
1.08
1.83
2.70
2,78
3.86
3.83
3.67
3.80
4,32
4.77
5.19
5,20
3




ST-1
1.36
2,33
2.73
3.65
4.78
4.81
3.20






4




ST-1 3
1,49
1,60
2.04
3,72
4,07
3.39
4,45
4,59
4.89
3.57
4.69


5




BWA-1 539
0.67
1.03
1,36
3-19
4.53
4.21
4,57
3,94
3.72
2.70



6
2.46
2,12
3,74
3.59
WT-201
1,86
2,40
3,09
4.59
4.91
7,59
4.80






7




WT-203
0.80
1.13
1.90
3.17
3,20
3.02
3.69
5,91
4.66




8




WT-204
2.37
3,08
5.65
6,65
9.55
8.67







9




WT-207
0.45
0.71
1.14
1.73
1,87
3-42
3.85
3,13
3.11
4.09
4-68
4.62
4.27

-------
Table 28 (continued)
1
130
140
150
160
170
2
5.13
4.63
4.19
3.90
4.05
3





4





5





6





7





8





9






-------
gorov test was applied (small sample size, n = 30) at the probability level
u = 0.2.  The results of this test are shown in table 29.  For all  probabil-
ity distributions except those at AP = 5 no basis is found for rejecting the
hypothesis of a normal distribution for q .   Notice that AP = 5, AP = 10,
..., AP = 200 are states of a stochastic process.  The probability distribu-
tion defines the type of stochastic process.  For individual fabrics, these
processes are normal because their probability distributions are normal.  It
should also be noticed that q   and o vary with AP, so we obtain a stochastic
process with a density function as follows:
          g [m(AP)] = -  =^  exp
                      a(AP)  V271
                                             2[a(AP]
                                                    2
                                                                      (83)
     To determine the mathematical form of the relation AP = f(q ), the
                                                                y
fabric testing data at high values of flow were used.  Using the method of
least squares, it was found that a polynomial function of the second degree
gave the best fit.  The following expression was minimized:


          ' • 5     [y1 - f(xl)]2                                     (84)
                                                and
where y. = empirical values of the variable AP,
   f(x.) = value of the function f(q_), the specific form of which
              depends on the number of parameters.
     It was assumed that the functional relationship between AP = y and q
x is a polynomial function of degree n in x.  The possible specific forms
were:
          f(x) = a0 + a,x
          f(x) = a0 + V + a2x*
          f(x) = a0 + aix + a2x2+.a3x3                               (85)
           •           •           *  n
          ffv\ -a  + a y +     + a *
          KX; - afl + ajx + ... + aRx

for n < 21 (because the number of measurements did not exceed 22).
     Equation (84) was successively minimized for each f(x) in (85).  By
differentiation of equation 84, we obtained the sets of equations from
                                  79

-------
29.  RESULTS OP AKOLMOGOROV- TEST
Range
of
AP
1
. 5
10
20
30
40
50
60
70
80
90
100
110
120
150
140
150
Fabric
ET-
1
2
1
0
1
0
1
1
1
1
1
1
1





ET-
2
3
1
1
1
1
1
1
1
1








ET-
3
4
0
1
1
1
1
1
0
1
1
1
1
1




ET-
4
5
1
1
1
0
1
1
0
1
1
1






ET-
30
6
1
1
0
0
0
1
0
1
0
1
1
1
1
\
0
1
BTr
•57
7
1
1
1
1
1
1
1
1
1
1
1 .
1




WBT-
208
8
1
1
1
1
1
1
0
1
1
1
1
1
1
1


WBT-
210
9
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1

ST-
41
10
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
ST-
1
11
1
1
1
1
1
1
1









ST-
1;
12
0
1
1
1
1
1
1
1
1
1
1





BWA-
153S
13
1
0
1
0
1
0
1
1
1
1






WT-
201
14
1
1
1
1
1
1
1









WT-
203
15
1
0
1
0
1
1
0
1
1







WT-
204
16
1
1
1
1
1
1









•

WT-
207
17
1
1
1
1
1
0
1
1
1
1
1
1
1




-------
                                              Table 29 (continued)
1
160
170
180
190
2




3




4




5




6
1
1
1
1
7




8




9




10
1
1


11




12




13




14




15




16




17




              1  -  normal distribution
              0  -  non-normal distribution
CD

-------
which to estimate the parameters a , a,,  ..., a  which minimize Q in equa-
tion 84.  The total set of equations is:

          §9=0   29  = 0       29= o
          8aQ   °«  8.,   °> ••••8an  °'
The parameters a  and a, for the first polynomial; aQ, a1 ,  and a2, for the
second polynomial, and so on were thus estimated and the corresponding
sequence of values QQ, Q1 , Q2,  .... Qn was obtained.   According to the least
squares method (the polynomial  that best fits the empirical data is that for
which the value of Q is the smallest), it was found that,  for high velocity
of flow, the best- fitting relationship was:

          AP = aqj" + bq  + c                                          (86)
                 y     y
where AP = pressure drop in mm of water,
                                  3  2
      q  = air-to-cloth ratio in m /m /hr, and
  a,b,c, = estimates of the parameters a2, a,, and a  respectively.
     Using the relationship (86), it is possible to compare the functions
and to group the fabrics into pairs with the most similar hydraulic
properties.  The quantity used to make this  comparison is:
                          supFu                                     (87)
where F^. = y. - y..   i, j = 1  	  16
      XQ  = the smallest common value of the argument x,
      xn  = the largest value of this argument for curves i and j.
     The smallest values of n^. define the fabrics that are most similar.
The obtained pairs of most similar fabrics are shown in table 30.
     The testing of fabrics at low velocity flow in the range AP <  10 mm of
water (see table 31) showed a linear relationship between velocity  and AP
(phase I report), which can be depicted analytically as:
          AP = aqg + b,                                               (88)
where AP = pressure drop,
      q  = air-to-cloth ratio,
       y
     a,b = constants.
                                  82

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    Table 30.  SIMILARITY OF TESTED FABRICS
Range of
                  Pairs of most similar fabrics
 0-5
 5-10
10 - 15
ET-1 and ET-4       WBT-21
BWA-1539 and ET-1   WBT-21
BWA-1539 and ET-4   ST-41
BT-57 and ET-3      ST-41
WBT-208 and WT-207  ST-13
ET-1 and ET-3       WBT-21
ET-2 and ET-4       WBT-21
BWA-1539 and ET-3   WBT-21
ST-1 and ET-2       ST-41
BT-57 and ET-1      ST-41
BT-57 and ET-4      ST-41
BT-57 and BWA-1539  ST-13
                    ST-13
                    ST-13
                    ST-13
                    ST-13
                    ST-30
                    ET-30
                    ST-41
                    ST-13
                    ST-13
                    ST-13
WT-207 and ET-2
WT-207 and ST-1
WBT-208 and ET-2
WBT-208 and ST-1
ET-1 and ET-2
ET-3 and ET-4
BWA-1539 and ET-2
ST-1 and ET-4
WBT-208 and ET-4
WBT-210 and ET-1
             WBT-210 and BWA-1539  ST-1
0 and WT-207
0 and WBT-208
and ET-3
and BT-57
and ET-4
0 and ET-4
0 and ST-1
0 and WT-207
and ET-1
and BWA-1539
and ET-30
and ET-1
and ET-2
and BWA-1539
and WBT-210
and ST-41
and ET-3
and BT-57
and ET-4
and ET-3
and ST-1
and BT-57
3 and WBT-208

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Table 31.   CLEAN AIR FLOW THROUGH  FABRICS AT LOW VALUES OF PRESSURE DROP.
Type of
filtration
fabric
1
ET-1
ET-2
ET-3
ET-4
ET-30
BT-57
BWA-1539
WT-201
WT-202
WT-203
WBT-21 0
ST-13
ST-1
ST-41
2 2
Air-to-Cloth Ratio, q in m /m /min, for pressure droo in mm of water
0,5
2
0.436
0.80
0.42
0.68
0.218
0.36
0.32
1.49
0.70
0.81
0.62
1.61
1.56
0.44
1 .0
3
1.00
1.54
0.74
1.52
0.42
0.69
0.56
2.69
1.08
1.65
1.05
2.84
2.67
0.81
2.0
4
2.37
3-185
1 .38
3.37
0.76
1.22
0,95
5.30
2.15
3.38
2.25
4.98
4.96
1.62
3.0
5
3.47
4.74
2.27
4.73
1 .07
1.99
1.61
7.68
3.10
5.30
3.25
6.57
6.93
2.55
4.0
6
4.78
6.23
3.03
6.17
1.54
2.70
2.14
9.99
4.04
6.89
4.39
8.03
8.80
3-25
5.0
7
5.94
7.51
3.74
7.77
2.01
3.31
2.68
12.17
5.08
8.60
5.57
900
10.38
4.02
6.0
8
6.88
8.74
4.693
9.04
2.44
3.96
3J2
14.39
6.13
10.16
6.59
10.48
11.88
4.82
7.0
9
8.00
9.397
5.50
10.38
2.81
4.63
3.68
16.84
7.049
11.73
7.56
11.55
15.36
5- 61
10.0
10
10.89
13.07
7.39(
13.19
3.97
6.30
5.41
23.29
9.89
16.54
10.59
12.25
17.30
7-49

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The coefficients a and b are shown in table 32.
     The quantity by which similarity of linear characteristics is deter-
mined is the slope of the straight lines, which over this particular range
of pressure drop, can group the fabrics according to similar hydraulic
properties.  As can be seen from tables 30 and 32, fabrics that are similar
at low flow velocity did not always show the same similarity at higher flow
velocities.  This behavior of fabrics leads to the conclusion that at higher
flows and pressure drops there are structural changes influencing the values
of permeability.  The values of the standard deviation for selected ranges
of pressure drop AP (see table 28) also show this effect of increasing q
and AP.
     The peculiarities of clean air flow through the test fabrics lead to
the conclusion that the fabrics must be regarded not as stiff bodies but as
elastic media.  Mechanical properties such as elongation under the influences
of force (elasticity) can play an important role in determining flow.  Full
confirmation of this statement requires further research.
     Recapitulating the conducted experiments and theoretical studies, it
can be concluded that:
          For clean air flow through woven filtration materials the functional
          relation AP = f(q_) appears to be parabolic except for the initial
                           y
          flow range in which it appears to be linear.
          The flow of clean air through a woven structure is a stochastic
          process of the normal type.  The change in functional form of AP =
          f(q ), from linear to parabolic, is  indicative of changing flow
          mechanisms (variation of flow type) at specific values of AP and

          V
          The increasing o values of the variable q  accompanying the increase
          of AP indicate heterogeneity of structure, i.e., the increase of
          its deformation with increase in flow velocity is not uniform over
          the whole structure.
          From a physical viewpoint, woven filtration structures cannot be
          modeled as stiff bodies because of the observed structural varia-
          tions.
                                  85

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Table 32.  VALUES OF COEFFICIENT  a  and  b  FOR EQUATION 88
Type of
filtration
fabric.
1
W-201
ET-1
ET-2
ET-4
WT-203
WBT-21 0
ST-1
ST-1 3
ET-3
WT-202
ST-41
BT-57
BWA-1 539
ET-30
Range
of coeffi-
cient "a"
2
0 - 0.5
0.5 - 1.0






1.0 - 1.5


1.5 - 2.0

2.0
Value of coefficients
"a"
3
0,44
0.89
0.76
0.73
0.60
0,94
0.59
0.77
1.32
1,02
1.32
1.57
1.37
2,49
"bw
4
-0,29
-0.07
-0.40
-0.34
-0.07
-0.08
-0.84
-1.53
0.01
-0,18
-0»23
-0.10
0.03
0.06
                              86

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ESTIMATION AND COMPARISON OF SOME FABRIC PARAMETERS
     The purpose of the following analysis is to find the common properties
among (or the the differences between) the structures of the test fabrics
based on their technological parameters and the use of statistical methods.
     Based on 40 measurements of the metric number of the yarn of the fill
and warp and of the number of threads in 10 cm, the following set of deriva-
tive parameters (based on known technological relations) was estimated:
          Dimension of inside FA between threads along warp, ko,
          Dimension of inside FA between threads along fill, kw,
          Diameter of warp, do,
          Diameter of fill, dw,
          Superficial packing with yarn, Zt,
          Relative warp packing, Zo,
          Relative fill packing, Zw,
          Complete packing of yarn in fabric along warp, Eo,
          Complete packing of yarn in fabric along fill, Ew,
          Free area, P,
                              2
          Free area per 100 cm, FA.
                                                                   2
     In the first phase of the statistical analysis, based on the x  test,
failure to reject the hypothesis of a normal probability distribution for
the individual parameters of all fabrics was shown.
     The next phase was the analysis of differences between, or common
properties of, the test structures.  Because of the large number of param-
eters analyzed, comparative analysis was judged to be of little value, and
the Student t-test was applied, using the following formulas:
                m. - m.
          t   = —	J.
           4 4    C
                  1J                                                  (89)
                 K-TZ—   I   2~72
                 frij T n^  ^/"<"     n^o
where     S,.
                                  87

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where m., m. = the average of the individual parameters in fabrics 1 and j
               OVj; i,j = 1, 2, 3, ...),
      n., n. = sample sizes,
      a., a. = standard deviations.
     From these calculations, t-Student statistics for the individual param-
eters were obtained.  Because n > 30, the following interpretation of. the t-
Student criterion was used:
when t < 4,  the fabrics do not differ significantly with respect to the
             test parameter,
when t > 4,  the fabrics differ significantly with respect to the test param-
             eter.
Based on the indicated values of t, we drew the following conclusions:
1.  According to kw, the following fabrics are similar:
          ET-3 and WT-203    (t = 1.016)
          ET-1 and WBT-208    (t = 0.208)
          WT-207 and WT-203    (t = 3.382)
          all others differ significantly.
2.  According to ko, the following fabrics are similar:
          ET-30 and WT-203    (t = 1.766)
          ET-3 and BWA-1539    (t = 3.236)
          ET-4 and ST-41    (t = 0.095)
          all others differ significantly.
3.  According to dw, the following fabrics are similar:
          ET-1 and ET-2    (t = 3.196)
          ET-1 and ET-4    (t = 3.329)
          ET-2 and ET-4    (t = 1.065)
          ST-1 and ST-13    (t  2.163)
          ST-1 and ST-41    (t = 0.363)
          ST-13 and ST-41    (t = 3.247)
          all others differ significantly.
4.  According to do, the following fabrics are similar:
          ET-3 and ET-1    (t = 1.187)
          ET-2 and WT-203    (t = 1.838)
          ST-1 and ST-41    (t = 2.997)
          all others differ significantly.
                                  88

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5.   According to Zt, the following fabrics are similar:
          ET-30 and WT-203    (t = 1.541)
          BWA-1539 and ET-4    (t = 0.696)
          ET-2 and WBT-208    (t = 0.505)
          all others differ significantly.
6.   According to Zw, the following fabrics are similar:
          ET-30 and WBT-208    (t = 2.727)
          BT-57 and WT-201    (t = 2.209)
          ET-4 and WT-203    (t = 2.435)
          all others differ significantly.
7.   According to Zo, the following fabrics are similar:
          ET-1 and BWA-1539    (t = 1.617)
          BT-57 and ST-41    (t = 1.344)
          WBT-208 and WBT-210    (t = 0.550)
          ST-1 and ST-41    (t = 2.683)
          all others differ significantly.
8.   According to Ew, the following fabrics are similar:
          ET-30 and ET-3    (t = 3.957)
          ET-30 and WT-203    (t = 1.145)
          ET-3 and WT-203    (t - 1.225)
          ET-1 and WT-207    (t = 2.427)
          ET-4 and WBT-208    (t = 1.239)
          all others differ significantly.
9.   According to Eo, the following fabrics are similar:
          ET-1 and ST-13    (t = 0.257)
          BT-57 and ST-1    (t = 0.791)
          BWA-1539 and WT-203    (t = 0.062)
          all others differ significantly.
10. According to P, the following fabrics are similar:
          ET-30 and ET-3    (t = 3.261)
          ET-30 and ET-1    (t = 3.886)
          ET-3 and ST-13    (t = 0.583)
          ET-1 and BWA-1539    (t = 0.390)
          ET-1 and WT-207    (t = 3.051)
          ET-2 and ST-41    (t = 0.172)
          all others differ significantly.
                                  89

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11. According to FA, the following fabrics are similar:
          ET-30 and WT-203    (t = 1.477)
          ET-3 and ET-1    (t = 1.707)
          BWA-1539 and ET-2    (t = 2.950)
          WBT-208 and WT-201    (t = 0.610)
          WBT-208 and ST-13    (t = 3.356)
          all others differ significantly.
     Assuming the equivalence of all  test parameters, the hypothesis can be
made that those fabrics showing the largest number of common pro-
perties are the most similar.   By this criterion the following classifica-
tion, at different levels of similarity, was obtained
          First Level of Similarity
               ET-30 and WT-203
          Second Level of Similarity
               ST-1 and ST-41
          Third Level of Similarity
               ET-30 and ET-3
               ET-3 and ET-1
               ET-3 and WT-203
               ET-1 and ET-30
               ET-1 and WT-207.
     Analyzing the influence of the measured parameters of filtration struc-
ture on the levels of similarity, it was shown that FA (Free Area) showed
the best correlation.  The values of FA for the indicated levels of similar-
ity are as follows:
                              First Level of Similarity
             ET-30 and WT-203                 FA = 6.07 and FA = 6.44
                             Second Level of Similarity
             ST-1 and ST-41                   FA=28.02 and FA = 23.58
                             Third Level of Similarity
             ET-30 and ET-3                   FA = 6.07 and FA = 1.86
             ET-3 and ET-1                    FA = 1.86 and FA = 2.79
                                  90

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             ET-3 and WT-203                  FA = 1.86 and FA = 6.44
             ET-1 and BWA-1539                FA = 2.79 and FA = 8.29
             ET-1 and WT-207                  FA = 2.79 and FA = 3.37
     Statistical analysis of the technological structural parameters leads
to the conclusions that from a statistical point of view, the best parameter
for characterizing the effect of technological parameters on fabric struc-
ture is FA (Free Area).  Also, further research should be performed to
explain the nonrepresentative values of FA characterizing clean air flow
through continuous filament fabrics.  (These values were measured during the
testing of U.S. fabrics during phase I of project 5-533-4.)
TESTING OF FABRIC GEOMETRY
     The above results of the statistical analysis of the effects of techno-
logical parameters on fabric structure served as the inspiration for develop-
ing measurements research capable of reconstructing the geometry of fabrics.
This research will be finished in 1977 and the results will be included in
the final report.
CONCLUSIONS
          Filtration fabrics can be regarded as porous, heterogeneous aniso-
          tropic media.
          Because of the mechanical properties of the material (e.g., fiber,
          yarn) the physical model cannot be approximated by a stiff body.
          The process of clean air flow through fabrics is stochastically
          normal.
          From a statistical viewpoint FA (Free Area) is at present the best
          physical parameter for incorporating the technological parameters
          which determine the spatial geometry of fabrics.
          Continuous filament fabrics display a different functional form,of
          AP = f(FA) than staple fiber fabrics.
                                  91

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                                SECTION VIII
                          STUDY OF DUST PARAMETERS

 INTRODUCTION
     Fabric filters, tested with similar fractions of different kinds of
dust, show differences in filtration resistances and efficiencies.   It can
be presumed that the kind of dust (the type of raw material  making up the
dust), its aerosol state, and the specific filtration parameters determine
the forces between the particles and the filtration structure and also
between individual particles.   In our research, we point out the dominant
character of electrostatic forces.
     Our observations lead to the conclusion that while dust layers are
usually regarded as heterogeneous,  quasi-isotropic media, the dust cake
formed on the filtration structure is an anisotropic medium.  The anisotropy
of the dust cake is caused by the presence of local variations in gas velocity
in front of the filtration surface.   These local variations  contribute to
the separation effects and give rise to dust layers with unidirectional
isotropy.
     Consequently, the development of theoretical expressions based on
geometrical models that are multidirectionally symmetrical,  result in descrip-
tions which are not confirmed by experiment.
     The dust cake problem is complicated because of the absence of practical
methods for observing and measuring the structure of the dust cake.  Attempts
to prepare cross-sections of dust cakes formed during laboratory tests
invariably suffer from displacement of dust particles during the preparation
or handling of the cross-section.  Random microscopic examination confirms
the presence of dust particle separation caused by the effects of a specific
fabric surface.
     The work conducted under this project was originally concentrated on
defining the relation between the degree of dispersion of the dust in the
aerosol stream and the properties of the dust layer formed by this dust.
                                  92

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The degree of dispersion was described by the fraction less than an arbitrary
value of diameter, d^^, and MMD (d5Q).  Dust samples from a specific separa-
tion were fractionally analyzed and the corresponding surfaces measured.
All empirical data obtained in phase I and phase II of the project were
analyzed.
EQUIPMENT AND PROCEDURES
     Two kinds of dust, cement and coal, were studied.  Particle size distri-
bution of the tested dusts was measured by use of the Bahco centrifugal
separator and on the Sartorious sedimentation balance (d < 5 urn).
     Identification of the stationary specific surface was done by the
Establishment of Catalysis and Physics of Surfaces of the Polish Academy of
Sciences in Cracow, using the BET apparatus and argon or krypton (for hydrated
lime) as an adsorbent.  Identification of the kinetic specific surface was
done by IPWMB using LEA-NURSEA apparatus.
RESULTS AND DISCUSSION
     Based on the test results shown in table 33, plots of the functions S =
f(M.) and S = fCdcn) were made.  They are shown in figures 5 and 6.
     Measurements of the degree of dispersion were made from diagrams of the
particle size distribution of the test dusts and by assumption of specific
values.  Particle size distributions are shown in figures 7 and 8.
     Tests lead to the following statements:
          The stationary specific surface, being the total area of the dust
          sample covered by a monomolecular layer of adsorbent, is for all
          kinds of dusts and for all degrees of dispersion higher than the
          kinetic specific surface.  The stationary specific surface depends
          on the kind of dust (raw material), and therefore on the surface
          structure of the dust particles (porosity of particles).
          The kinetic specific surface, being the total external surface
          without taking the pores of individual particles under considera-
          tion, is a value varying proportionally to the degree of disper-
          sion of the particles in a suspended state.
     From the above statements and applying statistical methods in interpret-
ing the empirical data, the preliminary functional relation S = f(degree of
                                  93

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Table 33.  COMPARISION OF DUST PARAMETERS.
Kind of dust
and
fraction
1
Cement:
nonfractionated
fraction 20 ^um
Coal:
nonfractionated
fractional 0 ^um
fraction<20 30 jjm
Average value
of static
specific
surface in
cm /g
2

-
-
-
36 390 ± 1 280
-

-
-
63 950 ± 2 400
-

Average value
of kinetic
specific
surface in
2
cm /g
3

7 082
27 556
19 429
11 952
1 467

7 423
24 775
15 775
11 007
1 539
HMD
in
4

22.00
2.25
4,80
6.50
48.00

30.00
5.20
7.00
10.00
80.00
Part of
fraction less
than dn. =20^um
in
percent .
5

48.0
-
100,0
99,7
15.0

40,0
100.0
98.0
78,0
6.0

-------
99.9
nnc_
yy.j
gg-
95-
go-
30-
70-
LU en
N 60
 20^01
• - Fraction d, . < 20 jjm
lim
Figure 5.  Particle Size Distribution for Cement Dust.
                             95

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    0.5

            4 5     JO    20  30 40 50    100    200 300


            PATRICLE DIAMETER, MICROMETERS



    1  - Fraction d.,.,  < 1.0 ijm      4 — Nonfractionated
                  JLUQ

    2 - Fraction dlim< 20 ^m      5 - Fraction dlin


    3 - Fraction dlim < 50 
-------
   30.000
bfl
a
o
   20,000
30
8  lo.ooo

B
-5
Cement Dust



Coal Dust
             0       20      40      60      60


                PART OP FRACTION LESS dliffl = 20
                        I


                      100


                    jm, • percent
figure  7.   Dependence of Kinetic Specific Surface On


            Degree of Dispersion Measurement H^.
                             97

-------
     30,000
 CM
  S
  o
 w
     20,000
 03


 O
     10.000
  O
                                     Cement Dust
                       	———-  Coal Dust
                    20      40      60      80     100

                               HMD,
figure 8.  Dependence of Kinetic Specific Surface On

           Degree of Dispersion Measurement HMD.
                             98

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dispersion) was developed.  The degree of dispersion measurement, Md (part
of fraction less than d^m, 1n percent), was obtained from the following
type of dependence:
               S = a(Md)b                                            (91)
where a, b = constants. The degree of dispersion measurement, d5Q (HMD), was
obtained from the following type of dependence:
               S = a (d50)'b                                          (92)
where a, b = constants.
     The functions S = f(Mrf) and S = f(d5Q) are similar for different kinds
of dust; however, they have different values that exist probably because of
differences in grain shapes.  The testing of cement and coal dust conducted
in this phase confirmed this supposition.
     The ultimate verification of the hypothesis and the verification of the
empirical relations will be done in phase III of this project using microscopic
research.
CONCLUSIONS
          The best parameter for assessing degree of dust dispersion, according
          to these tests to characterize dust in a suspended state, is dgQ
          (HMD).
          The dust layer parameter most closely related to the MMD of the
          dust sample in the suspended state 1s the kinetic specific surface.
          Development of the functional relation S = f(dg0) makes it possible
          to estimate the hydraulic properties of the dust layer from the
          degree of dust dispersion in the suspended state, defined by d&0
          (MMD).
                                  99

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                               SECTION IX
              ELECTROSTATIC PROPERTIES OF DUSTS AND FABRICS

INTRODUCTION
     Generation and concentration of electric charge are observed in many
industrial processes in which contact, friction, milling, mixing, etc.  occur
in the flow of gas, liquid, or solid streams.
     In most cases, the electrostatic phenomena accompanying industrial
processes are not desirable, because they complicate the process operation,
decrease the efficiency, or create the danger of explosion.   Commonly recog-
nized production problems exist in textile technology, cosmetics production,
food-processing, and petrochemistry.  One such problem is the electrifica-
tion of parts of machines and devices that can lead to the concentration of
electric charge, producing electric potentials of tens or hundreds of kilo-
volts.  Although electrostatic phenomena have been known for hundreds of
years, many peculiarities connected with static electrification are not yet
explained.
     The effect of electrostatic phenomena on the filtration process is
pointed out in many scientific publications, but no complete description of
it exists yet for the dust filtration process.
     Based on the many years of experience of the Institute of Physics of
Wroclaw Polytechnic on research into dust charging mechanisms, a cooperative
project was established to determine the influence of electrostatic phenomena
on the dust filtration process.
     The research concentrated on the following problems:
          Determination of the natural charges on industrial dusts,
          Determination of the resistivity of dust layers,
          Determination of the electrostatic properties of fabrics,
          Determination of the kinetics of fabric charging during the flow
     of both clean and dusty air of specific properties, and
          Development of a preliminary physical model of the dust filtration
          process, including the effect of electrostatic phenomena.
                                  100

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     The solutions to these problems required the development of suitable
methods and programs.  The basic experiments were conducted by the Institute
of Physics of Wroclaw Polytechnic, managed by Dr. Anna Szaynok; also, other
experiments of a statistical character were conducted by IPWMB.
EQUIPMENT AND PROCEDURES
Measurement of Dust Charges
     Dust charges were measured by photographing the paths of dust particles
falling between two vertical, charged capacitor plates.  This method was
first used by HOPPER and LABY to measure the charge of the elementary electron,
and was next applied by KUNKEL and HANSEN to measure the electric charges of
dust.  The diagram of the apparatus is shown in figure 9.  This apparatus
includes a thermally isolated column, 1; parallel plate capacitor, 2; optical
system, 3; Illumination system, 4; and a photographic camera, 5.
     Dust particles are fed to the upper part of the column and then fall
through the space between the vertically placed capacitor plates.  The
particles move under the influence of gravity, electric forces, and drag
forces.  Some of the particles pass through the d.c. electric field of the
capacitor and are mapped onto the film of the photographic camera by the
optical system.  A diaphragm permits the use of dark field illumination.
Illumination is chopped by a rotating disk containing small holes.
     The images of the falling particles are registered in the form of
consecutive light points on a dark background.  The frequency of disk rota-
tion is held constant for each measurement series, but it can be adjusted as
desired.  The apparatus is equiped with an extra optical system to obtain
reference mapping on each negative, which is especially important in calculat-
ing the path deviation of the falling particles.  For precise determination
by enlargement, a glass scale is placed in the visual field before each
measurement.  After the scale is photographed, the capacitor is placed in
the visual field, without changing the placement of the elements of the
optical system.  The resultant negatives are copied with the help of an
enlarger so as to facilitate the measurement of particle path coordinates.
     The diameter d. and quantity of charge q^ of the i-dust particle are
calculated from Stokes Law assuming a spherical particle:
                                 101

-------
Figure 9.  Diagram of Dust Charge Measurement.
                      102

-------
                            1/2
                                                                      (93)


                                                                      (94)

where q = kinematic viscosity of air,
      g = acceleration of gravity,
     p, = density of dust material,
     P2 = air density,
      E = intensity of electric field,
     v  = vertical component of particle velocity, and
     v  = horizontal component of particle velocity.
     Components of particle velocity are calculated from the measurement of
the distance between adjacent particle images on the photographs:
          vx = £ X                                                    (95)

          vy = £  Y                                                   (96)

where X = horizontal component of distance,
      Y = vertical component of distance,
      u = illumination frequency,
      p = enlargement.
     To obtain reliable data, it is necessary to make the measurements on at
least 1,000 dust particles.  From measured values of charge it is possible
to deduce a statistical charge distribution in the dust cloud and to calculate
the average charge and standard deviation.   The statistical charge distri-
butions in the dust clouds are similar-normal distributions.
Study of Filter Fabric Electrical Resistivity
     The measurements of filter fabric electrical resistivity were conducted
using the ring-dot set of electrodes shown in figure 10.
     The three measuring electrodes are:   (1) the upper protected (the dot);
(2) the lower; and (3) the protective ring.  They are made of brass.   The
protective ring provides the required field homogeneity for measuring the
bulk resistivity of the fabric and is also an outer electrode for measuring
the surface resistivity.

                                  103

-------
Figure 10.
Electrodes for Measurement of Fabric
         Resistivity.
                        104

-------
     Elements (5), (7), and (9) of the electrode set are made of Teflon,  a
material characterized by very high electrical resistivity and by surface
hydrophobicity, guaranteeing stable measuring conditions even under variable
air humidity.
     Weights of 1 to 10 kg of mass were placed on the weigh pan (8) in order
to examine the effect of pressure on resistivity.
     The measurement schemes for bulk and surface resistivity are shown in
figure 11.
     Both types of resistivities were measured with a type 219A electrometer
    jced by ZRK Unitra.  It has
measuring accuracy of 5 percent.
     Bulk
relations:
                                                     -5      -12
produced by ZRK Unitra.  It has a current range of 10   to 10    A and a
     Bulk resistivity p  and surface resistivity p  were calculated from the
     pv ~ Rv d                                                        (97)
where p  = bulk resistivity,
      R  = bulk resistance,
      s  = area of the protected electrode, and
      d  = thickness of the test fabric.

and   ps = Rs  in r/r                                                (98)
where p  = surface resistivity,
      R  = surface resistance,
      r, = inner radius of the ring electrode (protective ring), and
      r« = radius of the dot electrode (the protected electrode).
Study of Dust Resistivity
     Dust resistivity was measured in a chamber designed by the Institute of
Physics of Wroclaw Polytechnic.  The chamber permits measurement at a stable
value of dust compression K.
          K = 100 AV/V (X)                                            (99)
where K = the compression ratio of the dust in percent,
                                  105

-------
                TUfinUp
                                         ELECTROME-
                                         _  TSR
        Measurement of Bulk Electrical
        Resistivity.
                    TTfrfffJ
  b.   Measurement of Surface Resistivity.
Figure 11.  Measurement Schematics for Fabric
            Electrical  Properties.
                       106

-------
     AV = volume loss resulting from compression,
      V = volume of the layer after compression.
     Resistivity of the dust layer is evaluated by the formula:
          0 - R       .   = DA
          p " K In rx/r2   RA                                         (100)

where p= dust layer resistivity,
      R = measured resistance of layer,
      SL = length of dust layer,
     r1 = inner radius of ring electrode,
     r« = radius of internal electrode (the dot), and
      A = constant of the chamber.
     A TO- 2 megohm meter of Russian manufacture, with a range to 10  Mfi, was
used for the measurements.
Study of Electric Charge Leakage From Fabrics
     The system schematic is shown in figure 12.  In the figure it is shown
that a dc voltage, U = 100 V, from a constant- voltage supply, was connected
to the protected electrode of the measuring capacitor K by turning on the
switch W, .  The voltage was measured by the electrometer E.  The electrometer
was connected to the system through a coupling capacitor, C  , which, together
with the inlet capacity of the electrometer and the lead cable capacity,
formed a capacitor voltage divider, dividing the voltage U into the ratio
1:33.3.  The fabric was charged by the 100-V supply for 1 minute, and then
the switch W, was turned off.  From this moment on the capacitor K discharged
through the fabric resistance.
     The function U(t), describing the decrease of electrode voltage with
time, was traced out on recorder R (type eKB produced in East Germany),
which was connected to the outlet drive of the electrometer E.  From the
function U(t), a charge function Q(t) describing the time changes of charge
on the fabric can be deduced from the relation Q = CU (where Q is charge and
C 1s capacity).
                                  107

-------
FEEDER
                          ^
r
                                     K
ELECTRO
METEK

^^^•M

IECOHDER
                                                                     R
                                  ^HHHTIBI
              Figure 12.  Measurement of Charge Decay Time.
                                     108

-------
     From the Q(t) curves, it is possible to define a time, t1/2> at which
the charge on the fabric has decreased to half its initial value—the half
decay time.  Half decay time is a parameter describing the charge decay
process.  It is also used when the functions Q(t) or U(t) are not exponen-
tial.
     For these measurements, a lamp electrometer of 10   Q input impedance
(type 219A, produced by ZRK Unitra Poland) was used.  A vibrating reed electro-
meter of input impedance greater than 10   n (type VA-I-51 produced in East
Germany) was also used.
RESULTS AND DISCUSSION
Dust Electrical Charge
     Investigation of dust electrical charge was conducted by the Institute
of Physics of Wroclaw Polytechnic using cement and coal industrial dusts.
     The electrical charges on the non-fractionated dusts and also those on
the following fractions of dusts were determined:
          Cement dust   0  - 1.70 pm fraction I
                      1.70 - 2.94 Mm fraction II
                      2.94 - 5.95 pm fraction III
          Coal dust     0  - 2.46 Mm fraction I
                      2.46 - 4.40 Mm fraction II
     Fractionation of the dust was done by the BAHCO centrifugal device.
The results of charge measurements on non-fractionated cement dust are shown
in table 34.
          Table 34.  CHARGES ON NONFRACTIONATED CEMENT DUST
lange of particle
size
in MH>
1
4.80 - 8.40
4.80 - 5.70
5.70 - 6.70
6.70 - 8.40
d
in
Mm
2
6.31
5.43
6.12
7.53
o
in
e
3
72.5
63.4
70.1
81.5
q
in
e
4
-22
-20
-24
-27
                                  109

-------
The measurement Includes dust particles in the range of diameter 4.80 - 8.40
urn.  The standard deviation and average charge were calculated for the mean
particle diameter of the entire sample and also for the three diameter .size
ranges shown.
     The results for fractionated cement dust are shown in table 35.

          Table 35.  CHARGES ON FRACTIONATED CEMENT DUST
Fractions
in
urn
0 - 1.70



1.70 - 2.94


2.94 - 5.95
Range of
particle size
pm
4.40 - 7.90
4.40 - 5.00
5.00 - 6.00
6.00 - 7.90
4.70 - 9.99
4.70 - 6.50
6.50 - 9.00
5.60 - 7.70
d
in
urn
5.60
4.87
5.44
6.68
6.75
5.67
7.76
6.52
a
in
e
100.5
73.0
92.2
154.5
100.8
81.5
115.5
93.0
q
in
e
+2
+5
0
+5
-17.7
-17
-7
-6
The calculations conducted for the first fraction include the statistical
distributions for all the data and for three ranges of particle size; for
the second fraction, the calculations include all measurements and two
ranges of particle size.  The measurements of cement dust charging of the
third fraction showed the least variation of particle size, so the statistical
distribution of charge was made only for the entire sample.  Plots showing
particle charge dependence upon diameter for both the entire lot of cement
dust and for the three fractions are shown in figures 13 and 14.
     Additionally, measurements of the charges on non-fractionated cement
dust exposed to an electrical discharge were made.  Electrodes, between
which the electrical discharge occurs, were placed above the capacitor of
the measuring apparatus.  The dust falling down the column passed through
this discharge zone just before measurement.  The results of these charge
measurements are shown 1n table 36, and the relation between charge and
diameter size 1s shown in figure 15.
                                  110

-------
 100 -


  60


  60

  40


  20
     4.8
 -20 .,


 -40


 -60 -


 -bO •

-100
5.2
5.6
6.0
6.4
6.8
7.2
7.6
8,0
                                                 PARTICLE DIAMETER,,  microns
                    Figure 13.  Particle Charge Dependence on Diameter
                               (Non-fractionated Cement Dust).

-------
     200
150  1
     100 1
                            •Fraction     0
                            Fraction  1.70
                            JTraction  2.94
                        1.70 ym
                        2.94 yn
                        5.95 ym
 m

 8
4>
 O
 4>
H
 0)
c?
    -50



   -100  4



   -150



   -200
5.0    5.5   6.0    6.5   7.0   7.5   8.0   6.5    9.0
                      —.-«JL«_^a__l»___

            PARTICLE DIAtEBTER, microns


        .p
               Figure 14.  Particle Charge Dependence On  Diameter
                          (Fractionated Cement Dust).

-------
             a
             C
             o
             o
 120 '
 100
  60
  60 1
  40
                    5,8
 -80-
-100'
-120'
-140
-160J
             6.2
6.6
7.0
                            PARTICLE DIAMETER,  microns
                                       x
Figure 15.  Particle Charge  vs. Diameter for Non-fractionaed Cement
           Oust  Passed through an Electrical Discharge.
                              113

-------
          Table 36.  CHARGES ON NON-FRACTIONATED CEMENT AFTER
                     PASSING THROUGH AN ELECTRICAL DISCHARGE
Range of
particle size
in urn
1
5.90 - 7.10
d
in
urn
2
6.40
a
in
e
3
112.5
q
in
e
4
-25
     As with the cement dust, measurements of coal dust charges were also

made.  The results are shown in tables 37-39 and in figures 16-18.

          Table 37.   CHARGES ON NON-FRACTIONATED COAL DUST
Range of
>article size
in urn
1
9.60 - 13.00
9.60 - 11.50
11.50 - 13.00
d
in
urn
2
11.30
10.53
12.20
a
in
e
3
352
327
368
q
in
e
4
+30
+19
+31
          Table 38.   CHARGES ON FRACTIONATED COAL DUST
Fractions
in
urn
0 - 2.46
2.46 - 4.40
Range of
particle size
urn
6.60 - 9.15
6.70 - 8.50
d
in
urn
7.64
7.52
0
in
e
117.5
127
q
in
e
+9
-10
          Table 39.   CHARGES ON NON-FRACTIONATED COAL DUST
                     PASSED THROUGH AN ELECTRICAL DISCHARGE
Range of
particle size
in MID
1
7.20 - 11.80
d
in
pm
2
8.68
a
in
3
3
236
q
1n
3
4
+5
                                  114

-------
    360 .,



    340 •



    320 '
    300
n
c
o
fc
o

3 -220 1
9.8
w
  -240 .



  -260



  -280


  -300



  -320


  -340
               10.2     10.6    11,0     11.4   11.8     12.2
12,6
                            PARTICLE DIAMETER   microns
                   Figure 16.  Particle Charge Dependence On Diameter

                              (Non-fractionated Coal Dust).

-------
CO
fl
8
•P
o
0)
    140,
    120
    100
     80.
     60
     40-
     20
       6.0
 -20
 -40
 -60.
 -80-
-100
-120-
-140
                                                  x
                                                  o
                                   fraction   0 - 2,46 pm
                                   Fraction 2.46- 4.40 urn
            6.4
6,8
7.2
7.6
8.0
8.4
8,6
9.2
                         PARTICLE DIAMETER,  microns
            Figure 17.  Particle Charge Dependence On Diameter (Fractionated Coal Dust)

-------
    320



    280 •



    240 •



    200 •



    160



S   120 J
o
b
+»
u
0>

1
 ^ -120 -I

w*
C!>
| -160 •


0 -200



  -240 \



  -280



  -320



  -360 .
7,5
8.0
8.5
9.0
9,5
10.0
10,5
                   PARTICLE DIAMETER,  microns
 Figure 18.  Particle Charge vs. Diameter for Non-fractionated

            Coal Dust Passed Through an Electrical Discharge.

-------
As the measurements show, test dust particles are generally electrically
charged.  There are negative and positive charges and a comparatively small
number of uncharged particles in the dust clouds.  The average charge in a
dust cloud differs from zero and indicates the sign of the dominant charge.
     Analyzing the relationship between particle charge and diameter for the
fractionated dusts, it is clear that the measured particle diameters are
much bigger than the classified size range of the fraction.  This difference
between measured particle size and classified particle size is greatest for
the size fraction classified to have the smallest diameter particles.
Microscopic observation confirms the formation of 5 - 20 urn agglomerates,
which explains the results.  The formation of agglomerates is probably
caused by electrostatic effects.
     The preceding plots show a linear dependence between charge and particle
diameter, q = f(d).  Based on the above we can write:
          q(±) = k(±)
where k = the slope of the plotted straight line.
     The values of slope are given in table 40.
                    Table 40.  VALUES OF SLOPE k
Kind of dust
1
Non- fractionated cement
Cement - fraction I
Cement - fraction II
Cement - fraction III
Non- fractionated coal
Coal - fraction I
Coal • fraction II
SL
dm
e/um
2
15.0
22.8
10.0
23.4
8.5
27.0
18.0
t
e/um
3
16.0
30.0
14.4
14.4
36.0
19.0
9.0
Analyzing the data In table 40, we come to the conclusion that among the
classified test dusts, the largest slopes are generally shown by the smallest
dust particles.
     The standard deviation, also being a measurement of the degree of dust
charge as a function of diameter, can also be regarded as an approximately
linear relation.
                                  118

-------
     For cement dust, the strongest dependence of particle charge on diameter
was observed for the smallest dust fraction; the weakest, for the non-frac-
tionated dusts.  This charging effect is probably caused by the dust frac-
tionation process.  During this process, the probability of contact between
particles, between particles and the walls of the apparatus, and between
particles and the atmosphere, increases.  Cement dust is comparatively
difficult to charge, so that increased contact can lead to increased charg-
ing.  Because of the low electrical conduction of cement dust, any produced
charges on the cement particles have little chance to neutralize, even
during the long time of contact.
     The phenomena occuring with coal dust are quite different.  Nonfrac-
tionated coal dust shows many more charges than fractionated dust.  Dust
possessing large primary charge has a greater chance of losing that charge
than of acquiring additional charge because of contact; that is why the coal
dust charge decreases during the fractionation process.
     Electrical discharges have a similar influence on dust charge, because
they increase the ion concentration in the atmosphere.  Electrical discharges
cause an increase in the charge density of dusts of low primary charge.  For
dusts of high primary charge, electrical discharges cause a decrease in dust
charge.  These results are attributable to the partial neutralization of
charge by air ions.
     Apart from the above investigation, statistical measurements of the
charges on dusts of cement, coal, talc and fly ash, for separated and non-
separated samples, and according to the Detailed Program, were made.  In
contradistinction to the investigation conducted by Institute of Physics of
Wroclaw Polytechnic, samples of fresh, nonstored dust were used (except
talc).  The results of all series of measurements are shown in table 41.  It
was found that the average particle charge as well as the amount of particle
charging is much larger for fresh dusts than for stored dusts.  The increase
of charging during separation was also observed (except talc).
     The investigation of natural charging of industrial dusts led to the
following conclusions:
          Charging is closely connected with industrial dust generation and
          processes such as material pulverization.
                                  119

-------
Table 41.  Charges on Fresh Industrial Dusts.
Kind of dust
1
Cement - unseparated
separated
Coal (sample 1 ) - unseparated
separated
Coal (sample 2) - unseparated
separated
Talc - unseparated
separated
Ply Ash - unseparated
separated
ff
in
e
2
915.00
703.00
1347.00
1083,00
1550.00
1360.00
820.90
663-30
731.00
708.00
*
in
e
3
4-724.30
+389.00
i-82.00
+377,00
-116.90
+760.90
-274.00
+412,00
+481 .00
+200.10
                              120

-------
          Charging measured by standard deviation depends on dust history.
          The average charge of a dust cloud depends on the present state of
          the aerosol and also on the dust history.  Depending on where the
          sample is taken from an industrial installation, the same kind of
          dust can show a predominance of either negative or positive charge.
          Charges on fresh industrial dusts are very high, so their effect
          on dust cake formation and on dust collection efficiency in indus-
          trial fabric filtration can be considerable.
Electrical Resistivity of Fabrics
     Electrical resistivity across the fabrics was measured at a different
electric field intensity over the range:
          20 V/cm <_ E < 2000 V/cm
and pressure, p, over the range:
          2.5X103 N/m2 < p < 1.5X1O4 N/m2.

The measurements were conducted at an air temperature of 23 - 25° C and a
relative humidity of 40-50 percent.  For all fabrics, no changes in bulk
resistivity were observed over this range of electric field intensity.  But
a dependence of bulk resistivity on the pressure is very evident (figure
19).
     Measuring surface resistivity, the effects of interelectrode voltage on
the results were clearly observed.  We could observe the phenomena of fabric
polarization by changing electrode placement or by reversing the polarity
between the electrodes.  Current values stabilized in some cases only after
many hours.  This phenomena especially characterized fabric ET-30.   The
results of the measurements are shown in table 42.
                                 121

-------
4 .
                                              10
                    PRESSURE, x 1.25.10
                                          5
 Figure 19.  Dependence of Bulk  Resistivity On Pressure.
                           122

-------
                    Table 42.   RESISTIVITY OF FABRICS
Kind
of fabric

1
ET-4
ET-30
F-tor 5
PT-15
Thick-
ness
in mm
2
0.75
0.6
0.5
0.4
PV
in
0 cm
3
5.2X1014
4.3X1015
1.8X1014
5.8X1014
PS
in
0/sq
4
9.5X1014
3.3X1016
0.7-1.1X1014
3.0-4.5X1015
RvS
in
Ocm2
5
3.9X1013
2.6X1014
9.0X1012
2.3X1013
The last column of table 42 is a bulk resistance, calculated per unit of
area RV$, where S = the area of the protected electrode.  According to the
authors, this quantity is more suitable for estimating fabric electrical
properties.
Resistivity of Dusts
     The measurements of dust resistivity were made at a temperature of 23°
C and a relative air humidity of 51 percent.  Depending on the degree of
compression, the resistivities were as follow.
                                          9
     Cement dust
     Talc
     Coal dust
K = 10%
K = 20%
K = 10%
K = 20%
K = 10%
K = 20%
p = 9.5 X ID'
p = 5.7 X 10S
p = 9.0 X 10
p = 6.1 X 10
p = 4.5 X 10
p = 2.0 X 10
11
11
13
13
Ocm
Ocm
Ocm
Ocm
Ocm
Ocm
     To examine the effect of humidity on dust resistivity, the dust samples
were placed in desiccators along with specific saturated solutions to main-
tain the desired relative humidity.  After 48 hours of acclimatization, the
measurements of resistivity were made.  For all dusts a decrease of resist-
                                  123

-------
ivity with increased humidity was observed as is illustrated in figure 20.
The dependence of resistivity on temperature was examined after placing the
measurement chamber in a thermostatically controlled enclosure.  Stabiliza-
tion of the measured resistivities indicated the stabilization of tempera-
ture inside the measurement chamber.   The dependence of cement dust resist-
ivity on temperature is shown in figure 21.
Electric Charge Leakage From Fabrics
     In figures 22 through 25, the curves U(t) are shown describing the
decrease of voltage in time for individual kinds of clean and dusty fabrics.
     Little influence of the cover thickness on the curves was observed, so
                                                                         2
the measurements were done for only one thickness of dust cover (10 mg/cm ).
The presence of dust and the type of dust have considerable influence on
U(t), especially for fabrics covered with talc.   Different dust covers lead
to increases or decreases in half decay time.  Analyses of the U(t) curves
show considerable departure from the exponential dependence given by the
equation:
          U(t) = UQ exp (-t/eo-K-p)                                   (102)
where U  = initial value of voltage (100 V),
                  12
      e  = 8.85x10   F/m, the permittivity of a vacuum,
      K  = dielectric constant (= —),
                                  eo
      p  = dielectric resistivity, and
      e  = dielectric permittivity.
Equation 102 holds for dielectrics of constants K and p.
     Repeated measurements of the U(t) function on the same sample showed
that the half decay time, t, ,2» tended to increase for all fabrics.
     After a pause in measurements lasting a dozen or so hours, t, /2 decreased
to its initial value.  This phenomenon, as well as the difference between
the actual U(t) curve and the exponential form, can be explained by a resist-
ivity increase in the discharging process, which is caused by the displace-
ment of ions to the vicinity of the electrodes.   In the appendix (figure
A-72), a typical measurement cycle (for fabric F-tor 5) is shown.
                                     124

-------
    c
    f>
    e
 C  O
 05  
-------
 •8

      «   it
     
-------
100 ,
 n
 -p
 r-l
 o
 1
 e
 50
Pure fabric

fabric covered  with cement dust

Fabric covered  with talc dust

       covered  with coal dust
                        900

                          TIME, seconds
               1800
          Figure 22.  Function U(t) for Fabric ET-4.
                             127

-------
100
 CO
 •p
 H
 1
 50
1  -
2  -
3  -

4  -
Pure fabric
Fabric covered with cement dust
Fabric covered with talc dust
(scale  in parenthesis)
Fabric covered with coal dust
                       3000
                        (300)
                       6000
                        (600)
                           TIKE,  seconds

         Figure 23.  Function U(t) for Fabric ET-30.
                               128

-------
100 ,
                            Pure fabric
                            fabric covered with cement dust
                            Fabric covered with talc dust
                            fabric covered with coal dust
                                             100
                            TIME, seconds
        Figure 24.  Function U(t) for Fabric F-tor 5.
                              129

-------
100
                            Pure fabric
                            Fabric covered with cement  dust
                            Fabric covered with talc  dust
                            Fabric covered with coal  dust
                      900                  1800
                            TIME,  seconds
              Figure 25.  Function U(t) for Fabric PT-15.
                               130

-------
CONCLUSIONS
     Studies of the electrostatic properties of dusts and fabrics lead
to the conclusion that electrostatic effects 1n specific dust-fabric
systems under specific external conditions can determine, qualitatively
and quantitatively, the course of the dust filtration process.
     These studies are regarded as preliminary.  An Interpretation of
the Importance of these experiments upon a real dust filtration process
will be presented 1n the final report.
                                  131

-------
                               SECTION X
                            ADDITIONAL WORK
     Because of the kindness of the Project Officer, the Institute has
received for the project period a Helium-Air Pycnometer Model 1302, produced
by Micromeritics Instrument Corporation, Coulter Electronics Limited.   The
purpose of this instrument is to measure the density of dust.  Previously
the density was measured using a liquid pycnometer.
     It is an inspiration to start the additional work (not included in the
original program of the project) of comparing methods of dust density defini-
tion.   The results will be included in the final report.
                                  132

-------
APPENDIX A
   133

-------
              PARTICLE DIAMETER, MICROMETERS
                                              200 300
Figure A-1.   Particle Size Distribution for Cement Dust
              (1  - before separation;  2 - after separa-
              tion) .
                        134

-------
  99,9

  99,5
  99
                                                        UJ
                                                        N
                                                        
-------
                                                          
-------
999
gas
gg-



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go-
80:
70-
W 60
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10 50-
S 40"
< 3H
!n
on .
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r —
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r—
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fi .
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h- 4
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-10
-20
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(11
Oi
05 °
A
~Q6 o^

-Q7 t
31 -C
t^>
. v/
-cw rn
• ^^
3.


-QQ
33




                   10    20  30 40 50    100    200 300



            PARTICLE DIAMETER, MICROMETERS




Figure  A-4.   Particle  Size Distribution for Fly Ash Dust
                                                  1      ,
              (1  - before  separation; 2 -  after separa-

              tion ).
                                  137

-------
    ft
    
-------
       400
       350
       300
       250
       200
       150
        )00
        50
.  O  60m3/m2h
  X  SOm'/m'h
..A  ;20m3/m2/i
               100     2tiO    300    400     500    600    TOO
                         DUST COVER, g/m2
Figure A-6.   Pressure Difference vs. Dust Cover for Cement
              Dust and Fabric ET-4 (vnsdparated dust) .
                                    139

-------
              O ' 60 m3/m2h
              X
              A  1
         0 .   100.    200   300    400    500   600 '    TOO    500
                          DUST COVER, g/m2

Figure A-7.  Pressure Difference vs. Dust Cover  for Coal
             Dust  and Pabric ET-4  (separated  dust).
                         140

-------
       400
       350
    O
       250
       200
       150
        ]00
        50
O
X
A
          0    tOO    200    300    400    500    600    700
                           DUST COVER, g/m2
Figure A-8.   Pressure Difference vs. Dust Cover for Coal
              Dust and Fabric ET-4 (unseparated dust) .
                                    141

-------
     400
     350
•P
03
  o
     300
      250
     200
      170
      100
      50
            O 6Qr


            X 8Q


            A Wm3/m*h
        0    .100    200  ' 300    400    500    .600    TOO    600


                         DUST ClOVER,  g/m2





Figure  A-9.  Pressure Difference vs. Dust Cover for Talc

              Dust  and fabric ET-4 (separated dust).
                        142

-------
       400
       350
    H
    O
    CO
       300
        250
        200
        ISO
        JOO
        50
O  60m3/m2h

X  50m?/m2h

A
          0     100    200   300    400    500    600    700    600

                           DUST COVER,  g/m2



Figure -k-10.  Pressure Difference vs.  Dust Cover for Fly Ash

              • Dust and Fabric ET-4 ( separated dust).
                                    143

-------
    6
    4-4
    O
    en
       400
       350
       soo
       250
       200
       150
       100
        50
O  6Qm3/m2h
X  80m3/m2h
A  1ZOm3/m'h
         0     100.    200    300    400     500    600    TOO    600
                           DUST COVEfc, g/m2

Figure A-11.  Pressure Difference vs.  Dust Cover for Cement
               Dust and Fabric ET-30  (separated dust).
                          144

-------
   •8
       400
       350
       300
       250
   *i  200

    5
   P
       150
        100
        50
     O

—  x

     A
          0    100    200    300    400     500    600    700


                          DUST  COVER, g/m2
figure A^-12.  Pressure Difference vs.  Dust Cover for Cement

               Dust  and Fabric ET-3Q (unseparated dust).
                                    145

-------
                O  60m3/m2h
                X
                A  K0m3/m*h
               100    200    300.    400    500   .600    TOO    '500
                          DUST COVER,  g/m2
Figure A-13.   Pressure Difference vs.  Dust Cover for Coal
               Dust, and Fabric ET-JO  (separated dust).
                          146

-------
       400
       350
    Q) •  ,_^_
    •e   300
        250
        200
    «
    a
    p
     !.  150
        100
        50
   .  O  60m3/m2h
-"  X  80m3/m2h
   -A
          0     100    200    300    400     500    600    700    600
                           DUST COVER, g/m2

figure  A-14.  Pressiire Difference  vs. Dust Cover for Coal
               Dust  and Fabric ET-30  (unseparated dust).
                                     147

-------
    s
    1
    O
    £
    a
    CO
    CO
         0     100    200/300.   400     500    600    700   600


                          DUST COVER,  g/m2



Pigure A-15.   Pressure Difference vs. Dust Cover for Talc

               Dust and Fabric ET-30 ( separated dust ).
                          148

-------
   -100
   350
    300
p
I
    250
    200
    J50
    JOO
    50
            ~~T     r
         O

         X

         A
    0    100    200    300    400
                    .''•••
                   . BUST COVER,
                                     500    600    700
A-115.  Pressiate Difference vs.  Dust Cover for

       Dust and Fabric ET-30 (separated dust>).
                                                       Ash
                                149

-------
          0    .100    200   .300    400    500   .600   TOO   000
          • '                     • .     •                  •

                          DUST COVER, g/m



figure JU17; '  Pressure Differenpe va. Dust  Cover for Cement

               Dual.and Fabric f-tor 5 ^(separated dust) .
                          150

-------
    400
    350
    500
w
p
    250
    200
     150
     JOO
     50
                O  W


                X  80m'/m*h


                A  KOm'/m'h
       0    100    200   .300   400    500   600    700    600
                                       •y—

                       DUST COVER,  g/m
figure
           Pressure Difference vs. Dust Cover  for Cement

           Dust  and* fabric f-tor 3 (uaseparated
                                 151

-------
    M
    O
       350
       300
       250
       200
       150
       100
O  60

X  80m'/m2h

A  !20m>/m'h
         0    100.    200   300    400    500    600    700   flOO

                         DUST COVER, g/m2



Figure A-19.  Pressure Difference vs. Dust .Cover for Coal

               Dust and Fabric F-tor 5 ^separated dust^.
                          152

-------
        400
        350
    -P  300
     O .
        250
        200
        150
        100
         50
O  60
X  SOmym'h
A  I20m3/m2h
          0     100    200  .  300    400    500    600    700    600

                           DUST COVER, g/m2
Figure  A-20.  Pressure Difference vs. Dust Coyer for Coal
               Duat «ad Fabric F-tor 5 ( unseparated dust).
                                     153

-------
          0    .100    200  '  300.   400     500    .600    TDD    500
                         DUST COVER,  g/m2

Figure .A-21.   Pressure Difference vs. Dust Cover for Talc
                   , and Fabric F-tor 5  (separated dust)-,
                          154

-------
     S
     «M
     o
        400
        350
        30p
     I
        250
        200
         150
         )00
         50
O  60
X  60fn?/m2h
A  C0m%n*h
                100    200    300    400    500
                           DUST COVER,  g/m2
                                600    TOO
Figure Ar-22.  Pressure Difference  vs. Dust Cover for Ply Ash
               Dust  and Fabric F"-tpr 5 ( separated dust) .

-------
o
   400
   350
   300
   250
   200
    150
    JOO
    50
     o
—  X  80m*/m2h
     A
           100    200  '  300.   400    500

                      DUST COVBR, g/m2
                                           700   600
   Ar-23.  Pressure  Difference vs. Dust Cover for Cement
          Dust and  Fabric PT-15  .(separated dust).
                      156

-------
                O  60m3/m2h
                X  fflm'/m'h
                A
           0    100    200    300    400    500   600    700    600
                          DUST COVER,  g/m2
Figure A-24.   Pressure Difference vs.  Dust Cover for Cement
              -Dust and Fabric PT-15  {onseparated dust^).
                                     157

-------
-P
g
%H
Q
    B
       400
       350
       300
       250
       200
        150
        100
        50
            O 60m3/m2h
            X 8Qm3/m2h
            A /20my,n*/i
          0     100    200    300    400    500    600    TOO    600
                          DUST COVER, g/m2

Figure  A-25.  Pressure Difference vs.  Dust Cover for Coal
               Duet and Fabric PT-15  (separated dust) .
                          158

-------
    o
    S
    P=I
    M
       400
       350
       300
       250
       200
       150
        100
        50
O  60 m3/m2h


X  80m3/m2h


A
        "0    100     200    300    400    500    600    700    500



                          DUST COVER,  g/m





Figure  A-26.  Pressure Difference  vs.  Dust Cover for Coal


               Dust and fabric PT-15  (unseparated dust)
                                     159

-------
        400
        350
    •P  300

    g-  •
        250
    W
    O
        200
        ISO
        100
O  60

X  50

A  /20n,y,n*/i
          0    100    -200    300    400    500    600    TOO    600


                          DUST COVER, g/m2



Figure  A-27.  Pressure Difference  vs. Dust Cover for laic

               Dust  and Fabric PT-15  (separated  dust)
                           160

-------
          0    .100    200   300    400   '500   600   TOO
                         DUST COVER,  g/m2
Figure A-28.   Pressure Difference vs. Dust Cover for Ply Ash
               Dust and Pabric  PT-15-  (separated dusty.
                                    161

-------
O)
ro
               u
               h
               0)
               Pi
8
               H
               O
                    50

                    60(

                    70


                    80
       30



       95
       96

       97

       98



      990



      9513
                  99.99
                             O  - 60mJ/m*hr

                             X  -80

                             A  -
                                                                V*X
                                                                               100
                                                                                            1000
         |                            JQ

                                          DUST COVER, g/m2



Figure A^-29.  Theoretical Laboratory Efficiency for Cement Dust and Fabric ET-4 (Separated dust)

-------
•H

I
1
 O
 Vl
 0)
 Pi
O

G
      50



      70


      80


       <

      90



      95
      96

      97

      98



    99,0



    99.5
    99,90
    99,99
               O -  60m3/m*hr

               X -  80 m»/m2hr

               A -120m3/fn*hr
        1                            10                           100                          1000

                                         DUStt COVER,  g/m2

        A-20,  Theoretical Laboratory Efficiency for Cement Dust and Fabric ET-4 (unseparated dust),

-------
Ot
                    50
                    60
                    70
               £
                   99,0
o
I   9915
               o
                  99,90
                  99,99
                             O -  60m9/m2hr
                             X -  80 m'/m2hr
                             A -120 m3//n2hr
                                                  10
                                                               100
1000
                                                       DUST  COVER,  g/m2
              Figure A-J1.  Theoretical  Laboratory Efficiency for Coal Dust and Fabric ET-4  (separated dust)

-------
CT1
                                  60m3/m2hr
                                  80 ms/m2hr
                                  120
                 99.99
                                                     DUST COVER,  g/m*
                                                                                                        1000
                        Figure A-32.  Theoretical  Laboratory Efficiency for Coal  Dust  (unseparated
                                     dust) and Fabric  ET-4.

-------
O)
Ol
              I
              s
1
6
              o


              S
                                  80 ms/mzhr

                                  120 ms/m2/ir
                 99.90  —•
                 99.99
                                                                             100
          Figure  A-33.   Theoretical  Laboratory Efficiency
                                        DUST  COVER,  g/m2

                                              for Talc Dust and Fabric  ET-4 (separated dust).
                                                                                         1000

-------
$
I?
1
 n
 &

I
 M
 O
                     60m3/m2hr
                     80 ms//n2hr
                     120m3/m2hr
    99.90
    99.99
                                        DUST COVER, g/m'
                                                                                          1000
Figure A-54.  Theoretical  Laboratory Efficiency  for Fly Ash and Fabric  ET-4  (separated dust).

-------
I
 Q)
.
 0)
 o
!H

O
O
    99.90
    99,99
                                                                                           1000
                                         DUST COVER, g/m2


 Figure  A-35.  Theoretical  Laboratory Efficiency for Cement Dust and Fabric  ET-30  (separated dust)

-------
at
10
                99.99
                           o

                           X

                           A
60m3/m2hr

60 ms/m2hr

120
                    I
                10
                                                   DUST-COVER, g/m*
100
1000
           Figure A-36.  Theoretical Laboratory Efficiency for Cement Dust and Fabric  ET-30 (unseparated dust)

-------
1
      50
      6o
      70
      90

      95
      96
      97
      98

    990
o
   S9.90
   99.99
                      e
              O  - 60m3/m2hr
              X  - 50 ms/m2hr
              A  - 120 m3//n'/)r
                                    10
                                                                too
1000
                                         DUST! COVER, g/m2
Figure A-37.  Theoretical Laboratory. Efficiency for Coal  Dust and  Fabric  ET-30  (separated dust),

-------
 s
 Q>
 O
 fc
 0)
 Pi
i
60m3/m2hr

80 ms//n2hr

120 m3/m2/ir
    SS.90
    99,99
        •                           ii •

                                        DUST COVER, g/m2

Figure A-J8.  Theoretical Laboratory Efficiency  for  Coal Dust and Fabric ET-30  (unseparated dust)

-------
ro
S
•H
0>
                   50
                   60

                   70
                   90
                   95
                   96,
                   97
I
 O
 fc
 &

s
             H
             O
                  9910
9913
    99,90
                            O - 60m3/m'hr

                            X - 80 ms/m2hr

                            A -120 m3/m2Jir
                 99.99
                                                  10   DUST COVER, g/m2
                                                                  100                         1000


Figure A-39.  Theoretical Laboratory Efficiency for Talc Dust and Fabric  ET-30  (separated  dust),

-------
      M
      GO

      70
0)
•8
9>

I
Pi
0
o
      95
      96
 98


930


9915
S  99.90
    99199
                               -^
               X
               A
                60 m /m hr
                80 ms//n2hr

                120 m3//n

                                                           ^
                                                                                      S
                                                                 100
                                                                                        1000
         J                            10                     2
                                         DUST COVER,  g/m^

Figure A-40.  Theoretical  Laboratory Efficiency for Fly Ash  Dust  and  Fabric  ET-30  (separated dust)

-------
      so
      GO
      70
      90


      95
      96
      97
     990
     995
P
O
3  99.90
    99199
        I
         =   O - 60 ms/m*hr
            •   \^    on	31  21..
            .   ^ "• ou m itn nr
                                                                 s\
                                                                                         \
10
100
1000
                                                            rt
                                          TTHST COTES. t g/m                              ;

Figure A-41.    Theoretical Laboratory Efficiency for Cement Dust and Fabric F-tor 5 (separated dust).

-------
en
             I
              g   9S10
              o
              o
              M
              O
              pa
60
80
120 m*/m2hr
                 99.90
                 99.99
                                                 10                   , 2
                                                      DUST  COVER,  g/m*
             Pigure A-42t  Theoretical Laboratory Efficiency for Cement Dust and Fabric  F-tor  5  (unseparated dust)

-------
cn
                   50
                   60
                   70
 90

 95
 96
 97
             •P
             •a
             •H
             •s
             j?
             .^   930
395
             o
                 99.90
                 99,99
          O  -
          X  -
          A  -
                                  60ms/m2hr
                                  80
                                                  \
                                                  10
                                                            100
1000
                                                      DUST COVER,  g/in2
            Figure A-43.  Theoretical Laboratory Efficiency for Coal Dust and Fabric F-tor 5 (separated dust)

-------

o
fc
0)
  .
o
o
                    60m3/m2hr

                    80 m3/m2hr
                                    10
1000
        1                           IU                   .o
                                        DUST COVER,  g/nT


Figure A^-44.  'Theoretical  Laborato y Efficiency for Coal  Dust and Fabric F-tor 5  (unseparated dust)

-------
00
                                  60m3/m2hr
                                  80 ms/m2hr
                                  120 m3/jn2hr
                 99,99
                                                                                                      1000
                                                      DUST COVER,  g/m2
              Figure &-45.  Theoretical Laboratory Efficiency for Talc Dust and Fabric F-tor 5  (separated dust)

-------
s
13
o
o
p
M

O

M
                 60m3/m*hr


                 80 ms/in2hr

                 120m3/m*/ir
9190
    99.99
                                         DU13T COVER,  g/m2


 Figure A-46, 'Theoretical  Laboratory Efficiency for Fly Ash Dust and Fabric F-tor 5  (separated dust)

-------
SOj
60(
70
90
•Si 95
•H 96
$ 97
>, 98
EFFICIENCY, percent
o jg jo io
B O C* O
X

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                                   10
100
1000
                                        OUST COVER, g/m
Figure A-47. Theoretical Laboratory Efficiency  for Cement Dust and Fabric PT-15  (separated dust),

-------
§
*
3
V
o
fc
•>
p<
H
o
2  99,90
r™1
to
                    60m3/m'hr
                    80 m'/m2hr
                    120 m3/m*hr
    99,99
                                                                                         1000
                                         DUST  COVER,
 Pigure  A-48. Theoretical  Laboratory Efficiency for Cement  Dust and Fabric PT-15  (unseparated dust)

-------
00
ro
                  90


                  95
                  93
                  97
1
8
             H
             o
                99.90
                99,99
                           O
                     m   x
                     —   A
                    60m3/m*hr
                    80 m'/m2hr
                       m3//n*hr
                                                10
                                                               too
                                                     DUSI COVER,  g/m2
             Pigure  A-49.  Theoretical  Laboratory Efficiency for Coal  Dust and  Fabric PT-15 (separated .dust)

-------
00
bo
                99,99
                                                      LUST COVER,  g/V
                                                                                                      1000
            Figure A-50.  Theoretical  Laboratory Efficiency for Coal Dust and Fabric PT-15 (unseparated dust)

-------
      30
      60
      70

      80
      95
      96
      97
1
 8
 &
!«
o
FIC

jo
o
               O -  60ms/n>*hr
               X -  80 ms/ij)2hr
               A-
    99.99
              ^ s^_
                                    10
100
1000
                                         BUST COVER,  g/nr
Figure A-51,  Theoretical  Laboratory Efficiency for  Talc  Dust and  Fabric PT-15  (separated dust).

-------
U1
                                 60m3/m*hr
                                 80 m*/m2hr
                99.99
                                                     DUST COVER,  g/m'
                                                                                                     1000
            Figure A-52. Theoretical  Laboratory Efficiency for Fly Ash Dust and  Fabric PT-15 (separated dust),

-------
          a
          
          a>
          P«
                    60         SXL         120




       a.   Fabric  ET-4 and unseparated cement  dust.
        b.   Fabric ET-4 and unseparated.coal  dust.

Figure  A-53.  Dependence of Function F, and F« on  the Air

               to-Cloth Ratio, q_.
                            186

-------
  4>
  C
  9
  O
                                      ~<
                                        tt>
3
O
o
s
Pi
                                        CM
                                       fe
                 V*WA  -80
                                    -2,5
a.  Fabric ET-4 and separated fly ash dust,
     100
  .-p
  g
  o
  PI
      50
                                      CM
0)
§
Pt
                                        CM
                                   -2
                                   -2:5
           60       «L  2    GO
                 qg, m-'/m /h

b.  .Fabric ET-30 and separated cement dust,

   Ftgure A-54. Dependence of Function FI and  F»

              On the A1r-to-C1oth Ratio q,,.
                                    9
                    187

-------
o
Pi
a.   Fabric ET-30 and unseparated cement dust,
1
9
Pi
PCI
 b.   Fabric  ET-30 and separated coal dust
 Figure A-55.  Dependence of Function F^ and F^ On

             the Alr-to-Cloth Ratio, .q .
                      188

-------
     100
 1
 o
 P.
     50


-1
1
G

fc
P«
                                            CM
                                       -2
           60         60,  2,    ~W~2'5
                  qgf  mVm /h

a.   fabric  ET-JO and unseparated coal  dust,





    100
 o   50

 8
 A
-1
                                            oo
1
s
o
PI
                                            CM
                                       -2
           60         80   2     t20

                  qg, V/m /h

b.  Fabric EC-JO and  separated  talc dust,
 Figure A-56.   Dependence of Function F, and F»
             On the A1r-to-Cloth Ratto, q .
                       189

-------
   fi
   §
                                   120
                    q. m5/m2/h
a.  Fabric ET-JO  and separated fly ash dust,
   1
   o
b.  Fabric F-tor 5 and separatefl cement
  Figure A-r57.  Dependence of Function FI and
              On the A1r-to-Cloth Ratio (.
                        190

-------
  •p
   a
   o
   fe
             60
             ___       ^y
a.   Fabric  F-tor 5 and unseparated cement dust
    •  too
  1-
             60
                                        -2.5
b.  Fabric F-tor 5. and unseparated coal dust.
       c
     Figure A-58.   Dependence of Function F^  and F2

                  On the Air-to-Cloth Ratio, q .
                                          9
                         191

-------
        i
                   60        60         GO
                         qgf m5/m2/n
      a.   Fabric F-tbr 5 'and talc dust-.(separated.;);
            100
        1
         g
         PI
-t
                                                  o
                                                  fe
                                                  PI
                                              -zs
                   60         ty/a?/    ™
                          g*    •
      b.   Fabric F-tor 5 and  fly ash dust (separated )4

Figure A-59.  Dependence of Function F-, and F2  On the Air-to-
               Cloth Ratio, q .

-------
          0>
          o
          p.
                                                   
-------
         1
         o
         b
         p«
                   60         ^  2     I2°



      a. .Fabric PT-15 and  separated coal dust,
         o
         o
                    60
     • b.   Fabric PT-15  and unseparated coal dust.


Figure A-61. Dependence of Function Fiji and F2 On-the-A1r


              to Cloth Ratio, q  .
                           194

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          0)
          o
          p
          0)
               0
        a.   Fabric PT-15 and separated talc dust
          o>
          o
          Pi
           •h

          F*T
                    60        8Q . 2/v    120
                          q . m-'/m /n

        b.  Fabric PT-15 and separated fly ash

Figure A-62.   Dependence of Function FI and F2 On the Air-to-

                Cloth Ration q .
                              195

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        o

        §
        o
                                 O - 60m%n2h


                                 X - 80mf/mah


                                 A-l20m'/m»h
           0.001
                        DUST COVER, g/m'
Eigure A-6?.   Variation of Final  Concentration for
                 •  ••   '       .

               fabric ET-4 and Separated Cement Dust,
                             196

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       M
       I
       o
       a
          0,001
                             400         700
                       DUST COVER, g/m2
Figure A-64..  Variation of Final Concentration for
               Fabric BT-4 and Separated Coal Dust.
                            197

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          0,001
                       DUST COVER, g/m*
Figure A-65.  Variation of Final Concentration for
                i       •         •     .
              Fabric ET-30 and Separated Cement Dust,
                           198

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     no
    1
    o

    3
    a
    &4
        0.001
                     DUST COVER, g/m
Figure A-66.  Variation of Final Concentration for

              Fabric BT-30 and Separated Coal Dust.
                          199

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           0,001
                        •  -    400          700
                        DUST COVER, g/m*
Figure A-67.  Variation of Final Concentration for.
             . Fabric F-tor 5 and-Separated Cement Dust.1
                             200

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        §
       o
       o
       !
           0.001
                              400          700
                        DUST COVER,  g/m2
Figure A-68.   Variation of Final Concentration for
               Fabric F-tor 5 and Separated Coal Dust.
                            201

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                               O -
                               X ~
                               A -120mM»
          0,001
                        DUST COVER,  g/m*
Figure A^69.  Variation of Final Concentration for
              Fabric PT-15 and  Separated Cement Dust,
                          202

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         0.001
                       DUST COVER, g/m
Figure A-70.  Variation of Final Concentration for
              Fabric PT-15 arid Separated Coal Dust,
                          203

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AIR
OUTLET
           CONTROL VALVE
DUST FEEDER
                                          FILTER CHAMBER
                    ROTAMETER
           VACUUM PUMP
         INCLINED MANOMETERS
                  FILTER TEST STAND
                           PAPER FILTER'
         Figure A-71.  Diagram of the Laboratory Test Stand.
                               204

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   1.1
                         50
                            time (sea)
100
Figure A-72.  Loss of Charge for Fabric P-tor  5.
                          205

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APPENDIX B
     207

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                               GLOSSARY OF TERMS
     Because of the different terms used in the fabric filtration literature
concerning dust filtration through filtration media and because of the many
parameters, stages, etc., which are characteristic of the dust filtration
process, we propose to standardize the terminolgy for dust filtration.  The
proposed terms have physical sense according to the processes and phenomena
occuring during the dust filtration process (which is quite different from air
filtration).
FILTRATION  -  Process for the removal of solid particles from an aerosol
               stream by a porous medium.
AIR FILTRATION - Filtration process for atmospheric aerosols.
DUST FILTRATION - Filtration process for industrial aerosols.
DUST FILTRATION TYPE I - The initial phase of the complete dust filtration
               process when the fabric first begins operation as a filtration
               medium.  This phase ends when the pressure drop reaches a
               predetermined level.
DUST FILTRATION TYPE II- The second phase continues until the fabric is fully
               filled with dust.   This phase ends when the structure reaches
               the state of balance.
DUST FILTRATION TYPE III - This phase occurs when a stable level of filling
               of the fabric by dust has been reached and when the pressure
               drop returns to a constant level after regenerations.  This
               type operation is typical for industrial dust collectors.
GAS LOADING OF FILTRATION AREA - Mean calculated value of gas quantity, in
               cubic meters, passing through a square meter of filtration
               medium per hour (the air-to-cloth ratio).
PERMEABILITY - Gas loading of the filtration areas at a definite pressure
               drop.
                    American Standard pressure drop:  0.5 inch of water,
                    Polish Standard pressure drop:    20 mm of water.
                                      208

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DUST LOADING OF FILTRATION AREA - Mean calculated value of dust quantity on
               the filter medium per square meter of filtration medium per hour.
FILTRATION VELOCITY - The true velocity of aerosol, in meters per second
               (minute), passing through the filter medium (measured in true
               conditions).
FILL OF STRUCTURE - (Dust fill).  The dust accumulated during the filtration
                              2
               process,  in g/m  , which is retained after regeneration (without
               dust cake).
COVERED WITH DUST STRUCTURE  - (Dust cover).  The retained dust accumulated
                                                    2
               during the filtration process,  in g/m  , including the dust cake
               prior to  regeneration.
DEGREE OF  FILLING(p) - The ratio of the dust fill  for a given regeneration
               schedule  to that of the completely  filled structure, in percent.

     The full  glossary of terms will be enclosed in the final report.
                                       209

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APPENDIX C
     211

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                              METRIC CONVERSIONS

To convert from                    To                  Multiply by

     ft                       meters                      0.305
     ft2                      meters2                     0.0929
     ft3                      meters3                     0.0283
     ft/m1n                   centimeters/sec             0.508
       3                                 3
     ft /min                  centimeters /sec          471.9
     in                       centimeters                 2.54
       2                                 2
     in                       centimeters                 6.45
                                      212

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                          /»     TECHNICAL REPORT DATA
                          {Pteau read Inunction* on the reverie be?
                          fore completing)
1. REPORT NO.
 EPA-600/7-79-031
     2.
                                3. RECIPIENT'S ACCESSION'NO.
4. TITLE AND SUBTITLE
 Filtration Parameters for Dust Cleaning Fabrics
                                B. REPORT DATE
                                 January 1979
                                                      6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)               "  "
J.R.Koscianowski, Lidia Koscianowska, and
   Eugeniusz Szczepanklewicz
                                8. PERFORMING ORGANIZATION REPORT NO.
). PERFORMING ORGANIZATION NAME AND ADDRESS
Institute of Industry of Cement Building Materials
45-641 Opole
Oswiecimska Str. 21, Poland
                                10. PROGRAM ELEMENT NO.
                                EHE624
                                11. CONTRACT/GRANT NO.
                                Public Law 480 (Project
                                     P-5-533-3)
12. SPONSORING AGENCY NAME AND ADDRESS
 EPA, Office of Research and Development
 Industrial Environmental Research Laboratory
 Research Triangle Park, NC 27711
                                13. TYPE OF REPORT AND PERIOD COVERED
                                Final; 6/73 - 12/78
                                14. SPONSORING AGENCY CODE
                                 EPA/600/13
IB. SUPPLEMENTARY NOTES T£RL-RTP project officer is James H.  Turner, MD-61, 919/541-
2925. Report EPA-600/2-76-074 contains complementary information.
16. ABSTRACT
           The report describes laboratory and pilot scale testing of bag filter
fabrics. Filtration performance data and mathematical modeling parameters are
given for four Polish fabrics  tested with cement dust, coal dust, flyash, and talc.
Conclusions include: (1) The process of clean air flow, as well as the dust filtration
process, are stochastic processes of the normal type. (2) For filtration Type I
(laboratory scale), dust collection efficiency is an exponential function depending on
air-to-cloth ration, dust covering, and type of filtration structure.  (3) For filtration
Type I, resistance increases parabolically with time or dust covering. Outlet con-
centration as a function of dust covering is also parabolic. Structurally, the fabrics
are heterogeneous  anlstropic media. (4) Free area Is presently the best structural
parameter for characterizing structure of  staple fiber fabrics.  (5) Electrostatic
properties of dusts depend on their history; charge decays with time.  Dust cake
formation can be influenced by specific electrostatic properties of the fabric and
dust.
17.
                             KEY WORDS AND DOCUMENT ANALYSIS
                 DESCRIPTORS
                                           b.lDENTIFIERS/OPEN ENDED TERMS
                                            c.  COSATI Field/Group
 Pollution
 Dust Filters
 Fabrics
 Mathematical Models
 Dust
 Cements
Coal Dust
Fly Ash
Talc

Electrostatics
Pollution Control
Stationary Sources
Fabric Filters
P articulate
Polish Fabrics
13B
13K
11E
12A
11G
11B,13C
2 ID
2 IB
08G

20C
18. DISTRIBUTION STATEMENT

 Unlimited
                    19. SECURITY CLASS (TMt Report)
                    Unclassified	
                    20. SECURITY CLASS (TMtpage)
                    Unclassified
                            225
                        22. PRICE
*PA Perm 22NM ((.73)
                  213
                                                                     •* 173REGIONNO.4

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