A  TECHNIQUE  FOR  CALCULATING

        OVERALL  EFFICIENCIES

OF PARTICULATE CONTROL  DEVICES
                    by
              William M. Vatavuk
       Monitoring and Data Analysis Division
        ENVIRONMENTAL PROTECTION AGENCY
        Office of Air and Water Programs
    Office of Air Quality Planning and Standards
    Research Triangle Park, North Carolina 27711
                August 1973

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This report is issued by the Environmental Protection Agency to report technical
data of interest to a limited number of readers.   Copies are available free of
charge to Federal employees, current contractors  and grantees, and nonprofit
organizations - as supplies permit - from the Air Pollution Technical Information
Center, Environmental Protection Agency, Research Triangle Park, North Carolina
27711, or from the National Technical Information Service, 5285 Port Royal Road,
Springfield, Virginia 22151.
                          Publication No. EPA-450/2-73-002
                                         11

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                                    CONTENTS

LIST OF ABBREVIATIONS	   i.v
ABSTRACT	    v
BASIC DEVELOPMENT 	    1
APPLICATIONS TO SINGLE CONTROL DEVICES	    3
    Gravity Settling Chambers  	    3
    Cyclones	    6
    Venturi Scrubbers  	    7
    Electrostatic Precipitators  	   11
APPLICATIONS TO CONTROL DEVICES  OPERATED IN SERIES	   14
REFERENCES	   17
                                LIST  OF FIGURES
Figure                                                                        Page
  1  Cumulative Distribution Versus  Particle  Diameter  	  5
  2  Reciprocal Efficiency Versus Ratio  of Cut Size to Mean Diameter for Cyclone 8
  3  Reciprocal Efficiency Versus e/y  for  Venturi Scrubber	10
  4  Reciprocal Efficiency versus B/CT  for  Electrostatic Precipitator	12
  5  n Control Devices Operated in Series  	 14
                                        m

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                            LIST  OF ABBREVIATIONS

   A  Electrostatic precipitator collecting  surface, ft2
  Bc  Width of gravity settling chamber,  ft
   C  Gravity settling chamber empirical  factor,  dimensionless
  C'  Venturi scrubber correlation  coefficient, dimensionless
   D  Particle diameter,  microns
  Dc  Cut size, microns
  Dm  Mean particle diameter,  microns
 esu  Electrostatic units
  Ej  Overall collection  efficiency of a  single control device
 Ejn  Overall collection  efficiency of n  control  devices operated  in series
   F  Electrostatic precipitator migration velocity constant, microns"!
f(D)  Frequency size distribution  of particles
   g  Gravitational acceleration,  ft/sec2
   L  Venturi scrubber:  liquid injection rate, ft3/1000 ft3
  Lc  Length of gravity settling chamber, ft
 MCi  Total mass of particles  collected by a control device, Ib
  M-J  Total mass of particles  entering a  control  device, Ib
  NC  Number of parallel  chambers  in gravity settling  chamber
Q(D)  Size collection efficiency of a control device
   V  Gas volumetric flow rate, ft3/sec
  Vj.  Venturi scrubber:  gas  stream throat velocity, ft/sec
W(D)  Migration velocity  of a  particle of diameter D in an electrostatic  precipita-
        tor, ft/sec
Y(D)  Cumulative size distribution  of particles
   a  Cyclone empirical size  efficiency parameter, micron~l
   3  Slope of a semi logarithmic particle cumulative distribution, micron-1
   y  Gas viscosity, Ib/ft-sec
   p  Gas density, lb/ft3
  Pp  Particle density, lb/ft3
  W-j  Width of the cyclone gas inlet, ft
  N£  Number of revolutions the gas stream makes  in the cyclone
  Vj  Inlet gas velocity to cyclone, ft/sec
  En  Charging field in electrostatic precipitator, kV/cm
  E0  Collecting field in electrostatic precipitator,  kV/cm
   K  Dielectric constant of particles collected  in electrostatic  precipitator
                                         i v

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                                     ABSTRACT

      A  generalized mathematical technique is developed to calculate the overall  col-
 lection efficiency of particulate control devices.  Equipment operating parameters
 and  the size distribution of the particles in the inlet gas stream are used in the
 calculation.  The technique is successively applied to efficiency calculations for
 settling chambers, cyclones, venturi scrubbers, and electrostatic precipitators.
 Extension of this mathematical method is made to encompass control devices operated
 in series.  Specific examples are also included to illustrate the technique when  it
 is applied  to single and multiple devices.

!
jKey  words:  control efficiency, particle size, settling chamber, cyclone, venturi
iscrubber, electrostatic precipitator, mathematical technique

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                 A TECHNIQUE  FOR  CALCULATING

                        OVERALL  EFFICIENCIES

               OF  PARTICULATE  CONTROL  DEVICES


                            BASIC  DEVELOPMENT
     Before the effectiveness of a given participate control device can be deter-
mined,  it is necessary that its  overall collection efficiency be calculated under
existing operating conditions.   Collection efficiency is a function of such operating
conditions as temperature, pressure, and velocity of the gas stream entering the
device; dimensions of the control device; and statistical  size distribution of the
incoming particles.  For most devices it is possible to determine either the theo-
retical or empirical functional  relationship between efficiency and particle size.
That is:
                        Size collection efficiency = Q(D)                     (1)
                    Where:  D = diameter of particle, microns
In many cases, the cumulative size distribution of the particles in the incoming gas
stream  can be readily determined from a few measurements.   The cumulative distribu-
tion i:; the function used to calculate the mass or weight fraction of particles in a
given sample having diameters greater than a stated diameter, D:
                       Cumulative size distribution = Y(D)                    (2)
Once known, the cumulative distribution can be used to determine the frequency dis-
tribution, which is used to calculate the masses of particulates that fall within
the various ranges of size (size-fractions).

     The following mathematical  development shows how the frequency size distribution,
f(D), can be found from the cumulative distribution, Y(D). Consider a particulate
sample of mass, M(lb), with diameters ranging from 0 to <=•. By definition, Y(D)
equals the mass fraction of particles larger than diameter D.
                                 r°          /*D
                          Y(D) =J  f(x)dx = -/ f(x)dx                      (3)
                                 D            «•

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This relationship holds because Y(D) is the integral  of f(D).   Differentiating Y(D)
with respect to D:
                                             /•D
                       d/dD [Y(D)1 = d/dD [-/  f(x)dx] = -f(D)                   (4)
                                            oo
Now, consider all the particles in the size interval  D to D + dD.   The mass of these
particles collected by the device, dMc, would equal  the mass of incoming particles in
the interval, Mf(D) dD, multiplied by the collection efficiency at size D, Q(D):
                                dMc = Mf(D) Q(D)  dD                               (5)
To determine the overall  collection efficiency, Ej,  one would simply integrate dMc
from 0 to M and divide by the total incoming mass, M:

                            ET =!/ dMc =/ f(D)Q(D)dD                        (6)
                                 " 0        0
This is the basic equation for overall collection efficiency.   Equation 6 can be
further simplified by the substitution of f(D).  For many, if not  most, particulate
streams, the weight distribution very closely follows a log-normal curve, which is
a normal distribution skewed toward very small  or very large particle sizes.  Sub-
stitution of the log-normal distribution function into equation 6  would result in an
expression that probably could not be integrated to  yield a closed-form function.
Either numeric or graphic integration would have to  be used to calculate the overall
efficiency (see Example 1).  A simpler approach can  be taken if one recognizes that
for values of Y(D) ranging from about 0.15 to 0.85,  the distribution approximates an
exponential of the form:
                                     Y(D) = e-eD                                 (7)
              Where:  6 = slope of the semilog distribution, micron"'
     The parameter @ can be obtained by plotting the log of the cumulative distribu-
tion of particle size-fractions against the particle diameters.  These size-fraction
measurements can be obtained from one or more particle separation  procedures such as
sieving (for coarse particles), elutriation, and sedimentation (for fine particles).
(It must be emphasized that equation 7 deviates from the actual weight distribution
for relatively small and relatively large particles.)
     Recalling equation 4:  f(D) = -d/dD [Y(D)j.   Then, substituting equation 7 into
equation 4:
                     f(D) = -d/dD [Y(D)] = -d/dD [e^D] = 6e-6D                  (8)
Substitution into equation 6 yields:
                                                   dD                            (9)

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                APPLICATIONS TO SINGLE CONTROL  DEVICES
     To obtain  efficiencies, the above equations  can be  applied to some of the com-
monly used parti cul ate control devices; e.g., gravity settling chambers, cyclones,
venturi scrubbers, and electrostatic precipitators.

GRAVITY SETTLING CHAMBERS
     According  to R. T. Shigehara,  the size efficiency  of  a  settling chamber is
based on Stoke's  settling law and such parameters as the spatial dimensions of the
device and the  characteristics of the gas stream:
                                [Cg(pD - P)LCBCNC]D2
                         Q(D) -  — P      CCC    - [k]D2                    (10)
Where :
      C = dimensionless empirical factor (use 0.5  if no  other  information is
            available)
      g = gravitational acceleration, ft/sec2
     Pp = particle density,
      p = gas  density,
      p = gas  viscosity, Ib/ft-sec
      V = volumetric  flow rate, ft3/sec
     Bc = chamber width, ft
     Lc = chamber length, ft
     Nc = number of parallel chambers:  1  for a simple chamber  and N trays + 1 for a
            Howard setting chamber
For a given set of operating conditions, the terms  in brackets  are considered to be
constants.   Thus, substitution into equation 9 yields the overall collection effi-
ciency:                                /%
                                ET = 3/ kD2 e-SD  dD
                                 T    0                                       (11)
This integral  must be evaluated in two parts:  first, between the limits of D = 0 and
D = /Vk and second,  between the limits of  D = A/k and D =  °°.  This is necessary
because the size efficiency remains at a constant value of 100  percent for all par-
ticles  having  diameters greater than or equal to /Vk. Thus:

        ET = fey     kD2 e-SD do) + (e/  e-^D dD]  = ^-{l - e-eM[l + 0//k] )  (12)
             \ o                /    \ vVk        /    e2 \                   /
Example 1 :
     A settling chamber, operated as the primary cleaner  on  a heating plant spreader
     stoker, has the  following parameters:

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     Empirical  factor, C = 0.60
     Particle density, pp = 150 lb/ft3
     Number of parallel  chambers, Nc = 1  (simple  chamber)
     Gas viscosity,  y =  1.68-10'5 lb./ft-sec at 400°  Fahrenheit,  1  atmosphere
     Gas density, p  = 0.0462 lb/ft3
     Volumetric flow rate, V = 120 acf/sec
     Chamber length, Lc  = 20 ft
     Chamber width,  Bc = 10 ft
     Gravitational  constant, g = 32.2 ft/sec2
     Slope of the semi logarithmic  particle distribution,  B =0.025micron~'
     Substituting these  values into equation 10:
     k = Cg (pp - p) LCBCNC = ["(0.60)(32.2 ft/sec2)(150 1b/ft3)(20 ft)1
                                     .68-10-5 lb/ft-sec)(120 ft3/sec) J
                                       (10
18yV
                  [
                  [(
                                 J(30.48-104 microns/ft)
     k = 1.719-10-4 micron-2
                      /                     \
     And:     ET = ^n  - e-3//k" [l  + e//k~]j = 0.3131  or 31.31  percent

     It is interesting to compare this calculated efficiency with the value obtained
from a numerical integration method.  In Figure 1  the cumulative  distribution function,
Y(D), is plotted against  the particle diameter.  As the dotted lines on the graph
indicate, the weight fraction of particles falling between 10 and 20 microns, AY(D),
is 0.1723.  The average size collection efficiency for  this size interval  corresponds
to the average particle size, 15 microns:
   Q(15) = kD^v =  (1.719-10'4 micron"2) (15 microns)2  =0.0387 or 3.87 percent  (13)
From this equation, Table 1  can be constructed.

                 Table 1.   AVERAGE OVERALL COLLECTION  EFFICIENCIES
Size range,
microns
0 to 5
5 to 10
10 to 20
20 to 30
30 to 40
40 to 50
50 to 60
60 to 70
70 to 76
>76
DAV»
microns
2.5
7.5
15.0
25.0
35.0
45.0
55.0
65.0
73.0
--
AY(D)
0.1175
0.1037
0.1723
0.1341
0.1045
0.0814
0.0634
0.0493
0.0242
0.1496
Q(DAV)
0.00107
0.00967
0.0387
0.1074
0.2106
0.3481
0.5200
0.7263
0.9161
1.0000
Q(DAV)-AY(D)
0.00013
0.00100
0.00667
0.01440
0.02201
0.02834
0.03297
0.03581
0.02217
0.14960

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    100

     90

     80


     70


     60


     50



     40




     30
20
                                                  \
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hg
(£
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f-
.-i
10

 9

 8

 7


 6

                                                                                     \
              10      20      30      40     50     60      70      80     90     100    110    120     130    140


                                         PARTICLE DIAMETER, microns
                     Figure 1.  Cumulative distribution versus particle diameter.

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The overall efficiency is given by the sum of the products  of AY(D)  and
                             Ey =0.3131 or 31.31  percent                        (14)
Note that this is exactly equal to the calculated value.

CYCLONES
     Unlike gravity settling chambers, no useful  theoretical  expression  has  ever been
developed for cyclones that ties operating parameters,  equipment dimensions, etc.  to
particle size to yield a size efficiency function.   However,  several  attempts have
                                                                2
been made at deriving empirical functions.  For example, Gallaer  determined that the
cyclone size efficiency curve, when plotted on semi logarithmic paper, results in a
straight line, the equation of which is:
                                   Q(D) = 1  - e-<*D                              (15)
      Where:  a = a constant for the particular cyclone in  question,  micron-1
Direct substitution of equation 15 into the basic equation  results in:
                               /""
                               0             6         a +  e                     (16)
     3 4
Grove '  developed a method for replacing the constants a and e in this  expression
with two commonly measured particle parameters, the  cut size, Dc, expressed  in
microns, and the mean particle diameter, Dm, also given in  microns.   By  definition,
the cut size is the diameter corresponding to a size efficiency of 50 percent, or:
                                 Q(D) = 0.50 = e"BDc                            (17)
The cut size can, in turn, be calculated from the following expression:

                                DC = -,
Where:
     W-j = width of the cyclone gas inlet, ft
     Nt = number of revolutions the gas stream makes in the cyclone  (5 to  10 is
            typical)
     V-j = inlet gas velocity, ft/sec
     Pp = particle density, Ib/ft3
      p = gas density, Ib/ft3
      y = gas viscosity, Ib/ft-sec
The mean particle diameter is defined as the size above which 50 percent of  the
particles lie or where the cumulative distribution equals 0.50:
                                 Y(D) = 0.50 = e"30"1                            (19)
Combining equations 16 and 17, and solving for a yields:

                                           ft)
(20)

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Finally, substitution of this expression for a into the Ej relationship yields:

                                    p
The reciprocal efficiency, 1/Ey, is plotted against the ratio Dc/Dm = 6/a irvFigure 2,

Example 2:
     A dry cyclone is used as a secondary cleaner following the gravity settling
     chamber in Example 1.  The device has the following operating characteristics:
     Width of gas inlet, Uj = 1 ft
     Number of revolutions, Nj- = 10
     Inlet gas velocity, V-j = 41.4 ft/sec
     Substitution of these parameters into equation 18 yields:
       r  *   •    tn \    I 9 (1.68-10-5 Ib/ft-sec) 1 ft    „  .. ,..4   .      ...
       Cut size  (Dc) =  /—     L «m>	4 	.1... i. n».  i  -30.48-10^ microns/ft
                       V2TT.10 (150 Ib/ft3)(41.4 ft/sec)
                     - 6 microns
     Because the size distribution is semi logarithmic, equation 19 can be rearranged
     to yield:

             Mean particle diameter (Dj =   0.025" micron'1  = ?'8 m1crons

     Hence, the efficiency of the cyclone alone would be:
              .  _     1            1            1
                                                        = 82-37 percent
VENTURI SCRUBBERS
     The collection mechanism of venturi scrubbers is based on the impingement of
the particles on a spray of liquid (usually water) droplets.  The efficiency of
collection is a function of water droplet size, velocity and viscosity of the gas
stream, and rate of liquid injection to the scrubber, as well as particle diameter and
                                            5
density.  The combined work of Ranz and Wong  has resulted in a theoretical size
efficiency function, similar in form to that of the cyclone:

                             Q(D)  = 1  - exp f-C'LD /VtPP 1                      (22)
f
Where:
      C'= dimensionless correlation coefficient (varies from 1 to 2; 1.5 is a
            reasonable estimate)
      L = liquid injection rate, ft3/!000 ft3
     Vt = gas stream velocity through venturi throat, ft/sec
     Pp = particle density, lb/ft3

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                       0.5
2.5
                              1.0              1.5              2.0


                          RATIO OF CUT SIZE TO MEAN DIAMETER


Figure 2. Reciprocal efficiency versus ratio of cut size to mean diameter for cyclone.

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     DW = average liquid droplet diameter, microns
      u = gas viscosity, Ib/ft-sec
      D = particle diameter, microns

For a given venturi, all of the terms above become constants, except D, so that
equation 22 can be simplified to:
                                   Q(D) = 1 - e'YD                              (23)

                               Where:  Y = C'L |VtpP                            (24)
                                              \ 18DwM
     The average liquid droplet diameter can, in  turn, be calculated from the fol-
lowing relationship:
                              D    1^+28.51.1.5
                                     Vt                                         (25)

Substitution into the basic equation results in an expression for overall efficiency
identical in form to that of the cyclone:

                               r  -   Y   _     1    __
                                TTT   i  +  3/Y)

     Refer to Figure 3 for a graphic representation of equation 26.

Example 3:
     Because the spreader stoker described in  Example 1 emitted fairly large quanti
     ties of small-diameter particulates, it became necessary to install a venturi
     water scrubber to follow the settling chamber and cyclone.  The operating para
     meters of this device were:
     Correlation coefficient, C'=1.40
     L-quid injection rate, L = 1.50 ft3/!000  ft3
     Throat velocity, Vt = 250 ft/sec
     Average liquid droplet diameter, Dyy = 100 microns
     From equation 24:
      y - (1.40)0.50) J	(250 ft/sec) (150 1b/ft3)
                         18-100 microns (30.48-104 microns/ft)(l.68.10"5 Ib/ft-sec))
      Y = 1.40 microns"^

     The overall efficiency for the venturi is calculated from equation 26:

                  ET = 1 + (S/Y) = 1 + (0.025/1.40)= 98'25 percent

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       3.5
       3.0
       2.5
  o
  z
  UJ

  o
  o
  o
  a:
  o_
       2.0
       1.5
       1.0
       0.5
                          0.5
1.0
1.5
2.0
2.5
                                                      ft/y
                      Figure 3.  Reciprocal efficiency versus /?/y for venturi scrubber.
10

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ELECTROSTATIC PRECIPITATORS
     According to Engelbrecht,  the size collection efficiency of an electrostatic
precipitator also follows the familiar exponential function:

                              Q(D) = 1 - exp

Where:
        A = collecting surface of the precipitator, ft2
        V = volumetric flow rate of the gas stream through the device, ft^/sec
     W(D) = migration velocity of a particle of diameter D in the precipitator,
              ft/sec
This migration velocity is, in turn, dependent on several operating parameters, as
well as on the particle size:
                       W(D) =
12irw
                                              -
                                             
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                                 (3/5
Figure 4.  Reciprocal efficiency versus /3/8 for electrostatic precipitator.

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Average effective collecting field, EQ ~ 1.15 kV/cm
Dielectric constant of particle, K = 7
Gas stream viscosity, y = 1.68-10"5 Ib/ft.  - sec
Precipitator collecting surface, A = 2,000  ft2
Gas stream volumetric flow rate, V = 120 ft-Vsec

Therefore:
F -   (1.92 kV/cm)(1.15 kV/on)(3.33 esu-cm/kV)2  L + 2J7-l( ] g/cm_sec2_esu2
    (12ir)(l. 68-10-5 lb/ft-sec)(14.88 g-ft/lb-cm) |_     (7+2) J

F = 0.269 sec"1

According to equation 29:

        x   AF        (2,000 ft2)(0.269 sec-T)                .      .-,
        6 " 7" = (120 ft3/sec)(30. 48-104 microns/ft)  = °'333 microns

Thus,  the overall efficiency is:
                               1^(0.025/0. 333)
                                                                             13

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        APPLICATIONS TO CONTROL  DEVICES OPERATED  IN  SERIES

     Because it is  necessary in certain operations to remove  a  higher percentage of
the incoming particulates than is possible with a single  control device, two or more
                                                  o
devices are  often operated in series.  Van Der Kolk  evaluated  the overall efficiency
of series-connected cyclones.  The following development  extends his argument to
cases where  different devices are operated in series.   First, consider n devices
arranged as  illustrated  in Figure 5:
                       Figure 5.  n control devices operated in series.

In this arrangement,  the outlet stream of device 1  becomes  the  inlet  stream of
device 2, and so forth.
     Now, let the total mass of particulates entering each  device  be  designated as
MI for device 1, M2  for device 2, etc., and the respective  masses  collected be
     Again, consider  the  differential size interval  D to D + dD.   The mass of par-
ticulate entering device  1  in this size interval is:
                                      = Mif(D)dD                               (31)
The amount collected  by  device 1, dMc, , simply equals its  size  efficiency, Q-|(D),
times the entering quantity, or:
                               dMq = M1Qi(D)f(D)dD                            (32)
The amount leaving device  1 and entering device 2 is:
                      dM2 = dMi - dMq = MI [1 - Q!(D)]f(D)dD                   (33)

Extending this argument  to the nth device:
             dMn = MT[I  -  Qn-i(D)] [1 - Qn-2(D)] ... [1  - Q](D)]  f(D)dD        (34)
14

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          dMCn = M1Qn(D)[l  - Qn-i(D)]  [1  -  Qn.2(D)]  ...  [1  - Q1(D)]f(D)dD      (35)
The total mass collected by n devices  would be:
                    dMCj =    dMCi = dMq + dMC2 + . . . + dMCn,
                           i ~ I
or, by equation 35:
dMCT = Mif(D)dD {QT(D) + q2(D) [i  - Q^D)] + .  .  .  + qn(D)  [i  -  qn_i(D)]
         [1 - Qn-2(D)] ...Cl-  Ql(D)]}                                       (37)

Integration of equation 36  over all particle sizes  (0 to  °°)  and  division by the
inlet mass, M] , yields thj  overall  collection efficiency  for the n devices:
       1
   'n   MI^
J>C1
                        or
       /""
 ETn =J  (Ql(D) + Q?(D)n - Ql(D)] + .  .  .  + Qn(D)  [1  -  Qn  ,
   n   0                                                  N-I
            ...  [1 - Q1(D)]}{f(D)dD}                                          (38)

Application of equation  38 to a specific case illustrates its  properties.   For
example, consider the series arrangement of  a cyclone,  followed  by  a  venturi.   In
this case, the respective size efficiency  functions  are:
                             Ql(D) = 1  - e-«D (cyclone)                          (39)
                             Q2(D) = 1  - e-YD (venturi)                          (40)
Substituting these into  equation 38, and assuming that  the frequency  distribution  is
represented by equation  8:
                           /oo
                            {1  _  e-«D +  e-«D  +  [1 -  e-YD]} 66-^° dD              (41)
                         u
Simplifying, and substituting for a:
                         F   _   a + Y    _    BDm +  YDC                          (,9}
                          T2 ' a + 6 +  Y " 6(Dm + Dc) + vD,                      ^'
Example 5:
     Again consider the spreader stoker and its  various  control  devices  described  in
     Examples 1 through 4.  Suppose it were necessary to know the  overall  collection
     efficiency of the cyclone and venturi  operated in series.   This  can be done by
     merely substituting the previously calculated  values for a,  e, and  Y  into
     equation 42:
    -  (0.025 micron"')(28 microns) + (1.40 microns"^)(6 microns)      _„  ,_
      (0.025 micron-l)(28 + 6 microns) + (1.40 microns ^(6  microns)     '    Percen
                                                                                 15

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     As this calculation shows,  the operation  of these  two  control  devices  results
     in an overall  efficiency of 98.38 percent—only 0.13 percent  higher than  that
     obtained when  the venturi  is used alone.
     As equation 40 indicates,  the overall  efficiency for the  devices  is a  function
of their operating  parameters,  k, a, and  y, and the  frequency  distribution  parameter,
3.
     In conclusion, one important point should be emphasized.   That is,  there  is  no
assurance that the  operating parameters (a, Y> <$» and k) for control devices operated
singly would remain constant for the same devices arranged  in  a series.  For instance,
experience has shown that the cyclone parameter a is directly  dependent  on, among
other things, the inlet dust concentration. This concentration, in turn, varies  with
the number of devices used and  the operating configuration.  Therefore,  the equations
developed for series operations  cannot be used to accurately calculate the  control
efficiency unless the respective equipment parameters remain constant.  In  any case,
actual field testing at operating conditions should  be  performed to adequately
evaluate the system.
16

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                                   REFERENCES

1.  Shigehara, R.T.  Settling Chambers.   In:   Control  of Particulate  Emissions.
    U.S. Environmental  Protection Agency,  Office  of Air Programs,  Air Pollution
    Training Institute, Research Triangle  Park, N.C.   January 1970.

2.  Gallaer, C.A. and J.W.  Schindler.   Mechanical  Dust Collectors.  J.  Air  Poll.
    Control  Assn.  1:3:574-580, December 1963.

3.  Grove, D.J.   Cyclones.   In:   Control  of Particulate Emissions.  U.S.  Environ-
    mental Protection Agency, Office  of Air Programs,  Air Pollution Training  Insti-
    tute, Research Triangle Park, N.C.   1971.

4.  Personal communication  with  W. Smith and D.J.  Grove.   U.S.  Environmental  Pro-
    tection  Agency, Office  of Air Programs, Air Pollution Training Institute,
    Research Triangle Park, N.C.  April  1972.

5.  Ranz, W.E. and. J.B. Wong.  Industrial  Engineering  Chemistry.   44:1371ff.   1952.

6.  Englebrecht, H.L.  Electrostatic  Precipitators:  Control  and  Industrial Appli-
    cation.   In:  Control of Particulate Emissions.  U.S. Environmental  Protection
    Agency,  Office of Air Programs, Air Pollution  Training Institute, Research
    Triangle Park, N.C.  1971.

7.  White, H.J.   Industrial Electrostatic  Precipitation.   Addison-Wesley  Publishing
    Co., Inc.  Reading, Mass.  1963.

8.  Van Der  Kolk, H.   Linking Cyclones  in  Series  and  Its  Effect on Total  Separation,
    Communication to  Second Symposium on Cyclones.   Utrecht,  The  Netherlands.
    December 10, 1968.
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