U.S. Environmental Protection Agency Industrial Environmental Research EPA~600/7~78-026
Office of Research and Development Laboratory
Research Triangle Park, North Carolina 27711 MdfCn 1978
SR 52 PROGRAMMABLE
CALCULATOR PROGRAMS
FOR VENTURI SCRUBBERS
AND ELECTROSTATIC
PRECIPITATORS
Interagency
Energy-Environment
Research and Development
Program Report
s_
-------
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research-
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects; assessments of. and development of, control technologies for energy
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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-600/7-78-026
March 1978
SR-52 PROGRAMMABLE
CALCULATOR PROGRAMS
FOR VENTURI SCRUBBERS
AND ELECTROSTATIC PRECIPITATORS
by
Leslie E. Sparks
U.S. Environmental Protection Agency
Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, N.C. 27711
Program Element No. EHE624
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, D.C. 20460
-------
ABSTRACT
This report is intended to provide useful tools for estimating
particulate removal by venturi scrubbers and electrostatic precipitators.
Detailed descriptions are given for programs to predict the penetration
(1 minus efficiency) for each device. These programs are written specifically
for the Texas Instruments SR-52 programmable calculator. Each program
includes a general description of the mathematical model upon which the
program is based and the formulas and numerical techniques used in
adapting the model to the SR-52. Numerical examples, program listing,
and user instructions are included.
-------
TABLE OF CONTENTS
Page
Abstract ii
List of Figures iv
List of Tables iv
Nomenclature v
Introduction 1
Notes on the Programs 2
Venturi Scrubber 3
Mathematical Model 3
Scrubber Pressure Drop 3
Particle Penetration 4
SR-52 Program 6
Card 1 6
Card 2 9
Use of the SR-52 Program 12
Example 1 14
Example 2 18
Example 3 22
Comparison with Experimental Data 26
Electrostatic Precipitator 29
Mathematical Model 29
SR-52 Program 31
Card 1 34
Card 2 35
Use of the SR-52 Program 37
Example 4 39
Example 5 43
Example 6 48
Example 7 51
Example 8 54
Cautions on Using SR-52 Program Results 59
References 60
Appendix A - User Instructions and Program Listing for Venturi Scrubber
Program 61
Appendix B - User Instructions and Program Listing for ESP Program . . 66
m
-------
FIGURES
Number Page
1 PC-100A printer output for example I—overall
penetration and scrubber pressure drop 17
2 PC-100A printer output for example 2--scrubber pressure
drop vs outlet emission 23
3 PC-100A printer output for example 3--changing scrubber
size distribution parameters 27
4 PC-100A printer output for example 4--overall penetration
through ESP 42
5 PC-100A printer output for example 5--specific collector
area vs. ESP emission standard 47
6 PC-100A printer output for example 6--changing ESP size
distribution parameters 52
1 PC-100A printer output for example 7--ESP penetration vs.
dust resistivity 55
8 PC-100A printer output for example 8--changing normalized
standard deviation of ESP gas flow distribution 58
TABLES
Number Page
1 Comparison Between SR-52 Scrubber Program Predicted
Results and Experimental Data 28
2 Migration Velocity vs. Particle Diameter Curve Fit
Parameters for Various ESP Current Densities 33
IV
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NOMENCLATURE
A - Collector plate area in electrostatic precipitator (ESP)
2
a - First curve fit parameter for w(d) = a + bd + cd
B - Correction factor sneakage and reentrainment in ESP
2
b - Second curve fit parameter for w(d) = a + bd + cd
C' - Cunningham correction factor
2
c - Third curve fit parameter for w(d) = a + bd + cd
D - Drop diameter
d - Particle diameter
d. - Initial particle diameter for integration
df - Final particle diameter for integration
d - Mass mean particle diameter
E - Overall collection efficiency
E - Electric field at plate
F - Correction factor for non-uniform gas flow in ESP
f - Empirical factor in scrubber model
f(d) - Fraction of particles with diameters between d and d + dd
j - Current density
K,, Kp - Constants used in scrubber program
K . - Inertia! impaction parameter evaluated at throat of
venturi scrubber
L/G - Non-dimensional liquid/gas flow rate ratio for venturi
scrubber
N - Number of baffled sections in ESP
h - Number of steps in numerical integration
Pt(d) - Penetration (1 minus efficiency) of particles of
diameter d
Pt'(d) - Corrected penetration of particles of diameter d used in
ESP model
Pt - Overall particle penetration
-------
q - Particle electrical charge
R.. - Storage register ij
S - Fraction of particles that are reentrained and that bypass
electrified region per section
T - Temperature
UG - Gas velocity
V - Volumetric flow rate of gas
w(d) - Electrical migration velocity of particles with diameter d
Ad - Particle diameter increment for numerical integration
Ap - Pressure drop
p - Gas viscosity
P - Dust electrical resistivity
p. - Liquid density
p - Particle density
a - Normalized standard deviation of gas flow
a - Geometric standard deviation of log normal size distribution
VI
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INTRODUCTION
Computer models for particle collection in venturi scrubbers and
2
electrostatic precipitators have been developed under EPA sponsorship.
These models, which are fully described in referenced reports, provide
useful tools for the design, specification, selection, and troubleshooting
of particulate control devices.
Recent advances in calculator technology make it possible to use
these models without a large computer. The scrubber model described by
Calvert et al. has been fully programmed for a Texas Instruments SR-52
programmable calculator. Results of calculations made with the ESP
2
computer model described by Gooch et al. have been incorporated in an
SR-52 program which has much of the power and usefulness of the full
computer model.
These SR-52 programs and examples of their use are presented in
this report. These programs are written for the SR-52 and the PC-100A
printer. Instructions on how to use the programs without the printer
are also presented.
Typical uses of the SR-52 programs are presented in the example
problems. Several examples for both the scrubber and the ESP program
are presented to enable the user to get a "feel" for the programs before
he tries to solve his own problems.
-------
NOTES ON THE PROGRAMS
In the user instructions and examples, a convention of underline
letters or numbers has been adopted to denote the key or keys on the SR-
52 keyboard which should be pressed to conduct the operation discussed.
For example: in the instruction Press A, the underline indicates that
the A button on the keyboard should be pressed. Storage registers are
indicated by R^ .. For example: RQ, refers to storage register 01.
The programs all make extensive use of the indirect recall and
indirect store features of the SR-52. Thus, it is essential that the
counter for the indirect recall and indirect store register be set at
the proper initial value and advanced at the required times. Anyone who
wishes to modify the programs should remember that the programs as
written depend on indirect recall and indirect store instructions.
Cards are entered into the SR-52 calculator by:
Step Procedure Press
1 Enter side A 2nd rst 2nd read
2 Enter side B 2nd read
In the program listing, the use of the 2nd key is denoted by asterisk,
Thus, the notation, for example, B1* means press 2nc[ B'.
-------
VENTURI SCRUBBER
MATHEMATICAL MODEL
The mathematical model used in the SR-52 program was developed by
Calvert and is fully described by Calvert et al. Therefore, only a
brief discussion of the model will be given here.
The mathematical model of a venturi scrubber consists of two parts:
one to predict scrubber pressure drop; the other to predict scrubber
particle collection efficiency.
Scrubber Pressure Drop
Pressure drop in a venturi scrubber is caused by acceleration and
by wall friction. The pressure drop due to acceleration is generally
the larger. Therefore, pressure drop due to wall friction will be
neglected.
The pressure drop due to acceleration is reasonably insensitive to
scrubber geometry and can be predicted from hydrodynamics. Calvert
derived the following equation for venturi scrubber pressure drop:
AP (cm water) = 1.03 x 10~3 [UG -t~c)]2 ^ (1)
where u£ is the gas velocity in the venturi throat, and L/G is the
dimensionless liquid to gas flow rate ratio.
-------
Calvert et al. have compared the predictions of equation (1) with
experimental data and concluded that the equation consistently overpredicts
pressure drop in a venturi scrubber by about 20%. They suggest that
equation (2) below gives better agreement with the data.
AP (cm water) = 8.24 x 10~4 [UQ (^ )]2 | (2)
Equation (2) is the equation used to predict pressure drop in the SR-52
model.
Particle Penetration
The overall particle penetration (1 minus efficiency) through a
venturi scrubber is given by:
PtQ = o/°Pt(d)f(d)dd (3)
where Pt is the overall particle penetration, Pt(d) is the penetration of
particles with diameter d, and f(d) the fraction of particles with
diameters between d and d + dd.
Calvert et al. derived equation (4) for Pt(d):
Pt(d) = exp [|g. jr UG PL D F(K f)] (4)
M
-------
where UG is the velocity of the gas, p, is the density of the liquid, D
is the diameter of the collecting drops, p is the viscosity of the gas,
and F (K .f) is given by:
F(Kptf) = [0.7 Kptf * 1.4 in
where f is an empirical parameter (usually f = 0.5), and K .is the
inertial impaction parameter calculated at conditions in the throat:
Kpt = UG Pp C'
where UG is the gas velocity in the throat, p is the particle density,
C' is the Cunningham correction factor, and d is the diameter of the
particles.
The diameter of the drops can be calculated from an empirical
correlation by Nukiyama and Tanasawa.
91.8( )'
The assumptions used to derive all these equations are given by
Calvert et al. and the interested reader is referred there for additional
information.
It should be noted that equation (4) is valid only when inertial
impaction is the dominant particle collection mechanism. Inertial
impaction is the dominant mechanism for particles with diameters greater
-------
than about 0.1 microns. Thus equation (4) is valid in most situations
of practical interest.
The parameter "f" in equation (5) is an empirical parameter which
includes all unmodelled effects. Experimental data for industrial scale
scrubbers indicate that f is essentially a constant with a value of 0.5.
SR-52 PROGRAM
The SR-52 program is a two card program which provides a numerical
solution to equation (3) for a log-normal particle size distribution.
Card 1 is used to enter the data, calculate pressure drop, and calculate
constants used in calculations performed using Card 2. Card 2 uses a
trapezoidal rule numerical integration to solve equation (3) over the
11mits dinitialto dfinaT
Card 1
The program on Card 1 is used to carry out three activities:
1. Enter and store data on scrubber parameters,
gas conditions, and particle size distribution.
2. Calculate constants used in the program contained
on Card 2.
3. Calculate pressure drop across the scrubber.
-------
Each of these activities is discussed below.
The data on scrubber parameters, gas conditions, and particle size
distribution are entered in a specific order.
T - Gas temperature (°C) stored in RQ3
f - Empirical parameter (usually 0.5) stored in RQ^
d - Mass mean particle diameter (microns) stored in RQQ
a - Geometric standard deviation stored in R-,Q
d- - Initial particle diameter for integration (micron)
stored in R,,
df - Final particle diameter for integration (micron)
stored in R^
Ad - Particle diameter increment for integration (micron)
stored in R,.,
2
p. - Density of liquid (gm/cm ) stored in R-,,
3 3
L/G - Liquid to gas flow rate ratio (m /m ) stored in R-j5
UG - Gas velocity in venturi throat (cm/sec) stored in R-]6
P - gas viscosity (poise) stored in R,^
o
P - Density of the particles (gm/cm )stored in R-,g
Data entry is accomplished by entering gas temperature then pushing A_.
All other data are entered using RUN key. Each one of the entered data
is printed as it is entered.
As soon as the last entry p is made, the constants for Card 2 are
calculated, drop diameter is calculated and printed intern, and pressure
drop is calculated and printed in cm water.
-------
Calculation of Constants for Card 2
As soon as p is entered the program automatically calculates and
stores the following constants for use in the program on Card 2:
9uD
- 2 In2 ag
/2V In
an
2 L ur P. D
55 G -£ L
v
In order to calculate these constants, the program twice calculates
and prints drop diameter, D, in cm.
The calculation routine to calculate constants can be called from
the keyboard by pressing £._ The calculator will then calculate all the
constants, and calculate and print drop diameter and pressure drop.
This procedure is especially useful (as is discussed in the section on
the use of the program) when it is necessary to perform several calculations
where only a few variables, such as gas velocity, are changed from run
to run.
NOTE: This procedure cannot be used in cases where
•*'*" the log-normal size distribution parameters
are changed.
Calculation of Pressure Drop
After the calculation of constants is complete, the calculator
4 ^
-------
automatically calculates and prints the pressure drop across the venturi
in cm of water. The pressure drop calculation routine can be called
from the keyboard by pressing 2nd A'. The effects of various combinations
of gas velocity and liquid/gas flow rate ratio on pressure drop can be
investigated by storing UG in R,g and L/G in R15, then pressing 2nd A'.
Card 2
Card 2 is used to calculate the overall penetration for a log-
normal particle size distribution. The method of solution is discussed
below.
Equation (1) can be approximated by:
d
Pt = /°Pt(d)f(d)dd = ./f Pt(d)f(d)dd (8)
0 o QJ
where d^ is the initial particle diameter and d^ is the final particle
diameter.
The solution to equation (8), for the case where the particle size
distribution is log-normal, is accomplished by the program carried on
Card 2. Equation (8) is solved using a trapezoidal rule numerical
integration:
PtQ = Ad [lii^-i^iil + pt (d1 + Ad)f(di + Ad) + Pt (d1 + 2 Ad)f(d + 2Ad)
) ] (9)
where Pt(d) is given by:
-------
y K?C' d2f + 0.7
Pt(d) = exp ( K1 [ - 0.7 - K2C' d^f + 1.4 In (——^ )
+ 0.49 _ , 1
0.7 ± KC' dZf J KC' d2
where KI = | UGPL D and K2 = u
Gp
both are calculated using Card 1,
C1 is the Cunningham correction factor and is calculated in the
program by:
C' = 1 +-ilLjO F2.79 + 0.894 exp (2.47 x 1Q7 d( m)1 (11)
D(um) x 10 TJ
Pt(d) is calculated in subroutine E.
For a log-normal size distribution, f(d) is given by:
f(d) * 1 exp ["1n 2( /dg^- 3 (12)
^"V 2 1n CTg
where d is the geometric mass mean particle diameter (ym) and og is
the geometric standard deviation.
f(d) is calculated in subroutine D.
At the completion of the numerical solution, the calculator will
print Pt , d- and df. Pt is stored in Rgg.
Because particle size distributions span several orders of magnitude
of particle diameter, it is useful to break equation (8) into increments,
10
-------
each with its own Ad, and sum the solutions to the increments to obtain
the overall solution; i.e.,
Pt =/df Pt(d)f(d)dd =/dl Pt(d)f(d)dd +/d2 Pt(d)f(d)dd (13)
di di dl
+ A Pt(d)f(d)dd
dn
The summation is automatically carried out in Rgg. In order to use
Rgg for the summation the user must store 0 in Rgg when beginning a
problem.
The user must determine his own total integration limits, how many
increments to divide the total integral into, and the A.d for each increment.
In general overall integration from 0.1 to 20 microns with increments
of
0.1 to 1.0 microns (Ad =0.1)
1.0 to 10 microns (Ad = 0.5)
10 to 20 microns (Ad = 2)
is more than adequate. For particle size distributions with small d
and large a , the lower limit should be reduced. For cases where the
pressure drop exceeds, say, 40 cm of water, integration past 5 ym is
generally not necessary. When the mass mean particle diameter is small,
say, less than 2 ym, Ad should not exceed 0.2 until integration is past
V
11
-------
Use of the SR-52 Program
The SR-52 program provides a quick way to determine venturi scrubber
performance. Three possible uses are:
1. Determine pressure drop and penetration through
a given scrubber on a given aerosol. (See
Example 1.)
2. Determine pressure drop required to meet a given
outlet emission. (See Example 2.)
3. Determine effects of changes in particle size
distribution on penetration through a given
scrubber. (See Example 3.)
The SR-52 program as written will print all input data, drop diameter,
pressure drop, overall penetration, and integration limits using the PC-
100A printer.
The printer output is arranged as follows:
T,°C
d ,
°g
12
-------
d.p, ym
Ad, ym
PL, gm/cm
L/G, m3/m3 or cm3/cm3
UQ, cm/ sec
y, poise
D, ym
D, ym
Space
Ap, cm water
Space
Pto
d.j , ym
d.p, ym
All the above are automatically printed.
Pt for all increments is manually printed by pressing RCL 98 2nd
prt and follows df.
The program can be used without the printer as follows:
1. Card 1
Pressure drop is displayed at end of calculation.
Drop diameter can be displayed by pressing £.
13
-------
2. Card 2
Penetration due to particles between d, and d~ can be
displayed by the following steps:
Press RCL 19.
Press X.
Press RCL 13.
Press f_
Penetration will then be displayed.
Overall penetration can be displayed by pressing RCL 9(3, the same
step as required when using the printer.
Example 1
Calculate overall penetration and pressure drop of a scrubber
operating under given conditions.
Given:
Temperature = 65°C
Particle size distribution--
mass mean diameter, = 1.5 pm
geometric standard deviation = 2.0
-433
Liquid/gas ratio = 9 x 10 cm /cm
2
Gas velocity = 100 x 10 cm/sec
-4
Gas viscosity = 1.8 x 10 poise
3
Liquid viscosity = 1.0 gm/cm
Particle density = 2.0 gm/cm
Empirical factor = 0.5
14
-------
Solution:
Divide integration into two increments:
Pt
,1.5 Pt(d)f(d)dd
0.1
Enter Card 1, sides A and B:
1.5
Pt(d)f(d)dd
Step Procedure
1 Enter Card 10
2 Enter data
Enter
T (65)
f (.5)
dg
og (2)
d1 (-1)
df (1.5)
Ad (.1)
PL (1)
L/G (9EE ± 4)
UQ (100EE2)
n (1.8EE + 4)
Pp(2)
Press
STO 98
A
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
Display
0
3.38-02
5.01
1.01
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
7.41601
Print
65.
5.01
1.5 00
2.
0.1
1.5
0.1
1.
9. -04
1. 04
1.8-04
2. 00
7.4786-03
7.4786-03
7.416 01
15
-------
Step Procedure
3 Enter Card 2
Enter
Press Display Print
5
6
7
8
9
10
11
Calculate Pt 0.1
-------
65. PRT
5. -01 PRT
1. 5 00 PRT
2. PRT
0. 1 PRT
1.5 PRT
0. 1 PRT
1. PRT
9. -04 PRT
1. 04 PRT
1.8-04 PRT
2. 00 PRT
7.4736-03 PRT
7.4736-03 PRT
7. 416 01 PRT
1.614021433-02 PRT
1.-01 PRT
1. 5 00 PRT
.0012172657 PRT
1.5 PRT
5. PRT
.0173574305 PPT
Figure 1. PC-100A printer output for example I—overall penetration
and scrubber pressure drop.
17
-------
Example
This example shows how to use the program to estimate pressure drop
required for a given outlet emission.
Given:
3*
Allowable emissions = 0.01 mg/dNm
Inlet loading = 1 mg/dNm
Gas temperature = 65°C
Particle size distribution--
mass mean diameter = 3 urn
geometric standard deviation = 2
Particle density = 2 gm/cm
Solution:
Required penetration = 0.01.
(Required efficiency = 1-0.01 = 0.99.)
Assume f = 0.5.
For first guess let L/G = 9 x 104 m3/m3, and
4
UG = 1.2 x 10 cm/sec.
Integrate over two intervals:
0.1 to 1 with Ad =0.1, and
1 to 5 with Ad = 0.2.
*dNm is dry normal cubic meters; normal conditions are 1 atm and 20°C
18
-------
Step Procedure Enter
1 Enter Card 1
2 Enter data T(65)
f (-5)
dg(3)
°g(2)
d1 (.1)
df (1)
Ad (.1)
PL (1)
L/G(9EE ± 4)
UQ (1.2EE4)
v (1.8EE ± 4)
P<2)
3 Clear Rg8 0
4 Enter Card 2
5 Calculate Pt 0.1< d< 1 Mm
6 Carry integration past 1.0 m
7 Clear R]g 0
8 Store new d. 1.
Press Display
A 3.38-02
RUN 5. -01
RUN 1 . 01
RUN 7.00
RUN 6.00
RUN 5.00
RUN 4.00
RUN 3.00
RUN 2.00
RUN 1 . 00
RUN 0.00
RUN
1.06790402
STO 98 0
A 1.
STO 19 0
STO 11 1.
Print
65.
5. -01
3. 00
2. 00
1. -01
1. 00
1. -01
1. 00
9. -04
1.2 04
1.8 -04
2. 00
6.645266667-03
6.645266667-03
Space
1.067904 02
Space
8.787862447-04
1. -01
1. 00
19
-------
Step
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Procedure Enter Press Display
Store new cL 5.
Store new Ad 0.2
Calculate Pt 1.0
-------
Step
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
Procedure Enter
Store new Ad 0.1
Calculate Pt
0
1.0
-------
Step Procedure Enter Press Display Print
45 Calculate Pt A 5.0 .0051689409
o —
1.0
-------
• 65.
5. -01
3. 00
2. 00
1. -01
1. 00
1. -01
1. 00
9. -04
1. 2 04
1. 3-04
2. 00
6. fi4526A£A7-ns
6. &4^2i->f'f--f'7 -03
1. 067904 02
8. 787862447-04
1. -01
1. 00
. 0010940953
1.
5.
. 0019728815
1.081193333-02
. uy 1 lyoooJ-Ui!
2. 66976 01
. 0081657664
0. 1
1.
0. 003565109
1.
5.
. 0167303754
9. 423044444-03
9. 423044444-03
3. 8444544 01
. 0049534354
0. 1
1.
. 0051639409
1.
5.
. 0101223763
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
Fi l~i "T*
RT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
Figure 2. PC-100A printer output for example 2--scrubber pressure drop
vs. outlet emission.
i w • w * f* • i t i w *— i xxvi wfi
vs. outlet emission.
23
-------
Liquid density
Gas viscosity
Liquid/gas ratio
= 1 gm/cnT
-4
= 1.8 x 10 n poise
= 1 x 10~3 m3/m3
Solution:
Integrate over two intervals:
Step
1
2
3
di = 0.1 df = 1.0
di = 1.0 df = 5.0
Procedure Enter
Enter Card 1
Enter data T(65)
f(.5)
dg
°g
d^.l)
Ad(.l)
PL(D
L/G(1EE ±3)
UG (1EE4)
n (1.8EE ±. 4)
Pp(2)
Clear Rno 0
Ad =
Ad =
Press
A
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
STO 98
0.1
0.2
Display
3.38-02
5. -01
1.01
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
8.24 01
Print
65
5. -01
3. 00
2. 00
1. -01
1. 00
1. -01
1. 00
1. -03
1. 04
1.8-04
2. 00
7.902970892-03
7.902970892-03
8.24 01
24
-------
Step Procedure
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Enter Card
Calculate
Enter
Press Display
2
Pt 0.1
-------
Step Procedure
22 Enter Card 2
Enter
Press
23 Calculate PtQ 0.1< d< 1 ym
24
25
26
27
28
29
30
Carry integration past 1.0
Clear R^g 0
Store new d^ 1.
Store new df 5.
Store new Ad 0.2
Calculate Pt 1.0
-------
9 02'?
65.
5. -
3.
kl D
1. -
1.
1. -
1.
1. -
1.
1.8-
2.
^! 9 7 U 3 9 ii -
2970392-
31
JO
JO
31
30
31
30
33
34
34
"ifi
Jo
33
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
8.24 01 PRT
1. 144193314-03
1. -01
1. 00
7.66 9 02 3 6 3 9 - 0 4
1. 00
5. 00
1.911101177-03
.0079029709
7.902970392-03
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
8.24 01 PRT
0116402343 PRT
0.1 PRT
1. PRT
0006463332 PRT
1. PRT
5. PRT
0122366724 PRT
Figure 3. PC-100A printer output for example 3—changing scrubber
size distribution parameters.
27
-------
Table 1. COMPARISON BETWEEN SR-52 SCRUBBER PROGRAM PREDICTED
RESULTS AND EXPERIMENTAL DATA
Measured Calculated
28
Plant Ap, cm water Pt Ap, cm water Pt
1 45.7 0.015 46 0.016
2 25 0.025 25 0.028
3 100 0.005 105 0.004
-------
ELECTROSTATIC PRECIPITATOR
MATHEMATICAL MODEL
The SR-52 program is based on the Environmental Protection Agency/Southern
Research Institute (EPA/SoRI) mathematical model of electrostatic precipitation
2
described by Gooch et al. Only a brief discussion of the model will be
given here.
The theoretical overall penetration (1 minus efficiency) through an
electrostatic precipitator (ESP) is given by:
PtQ = o/°°Pt(d)f(d)dd (14)
where Pt(d) is the penetration of particles with diameter d, and
f(d) is the fraction of the particles with diameters between
d and d + dd.
The EPA/SoRI model is based on the Deutch-Andersen equation for
particle penetration through an ESP:
Pt(d) = exp [-w(d)A/V] (15)
where Pt(d) is the theoretical penetration of particles with diameter
d, w(d) is the electrical migration velocity of particles with
diameter d, A is the collector plate area, and V is the volumetric
flow rate of gas.
29
-------
For the situation where the particle charge, c[, and the electric field
at the plate, E , are known, w(d) can be calculated from:
w(d) = (<± E C')/(3Tr dy ) (16)
where C1 is the Cunningham correction factor and y is the gas viscosity.
The calculations necessary to determine £ and E are beyond the
capabilities of the SR-52. These calculations were carried out in the
EPA/SoRI model for a typical ESP collecting fly ash, and the results are
incorporated into the SR-52 program.
The penetration predicted by equation (15) is generally less than
the penetration measured in industrial ESP because certain non-ideal
factors (e.g., non-uniform gas flow, sneakage, and reentrainment) act to
increase penetration. Methods for estimating the effects of non-uniform
2
gas flow, sneakage, and reentrainment are described by Gooch et al.
whose method is used in the SR-52 program.
Gooch et al. have shown that the effects of these non-ideal factors
can be estimated by:
Pt'(d) = exp [ ™^up (17)
where Pt'(d) is the corrected penetration, B is the correction factor
for sneakage and reentrainment, and F is the correction factor for non-
uniform gas flow.
30
-------
B =
1.nPt(d)
Nsln LS + (l-S)Pt(d)1/INs]
where N$ = number of baffled sections, and S is the fraction of
particles that are reentrained and that bypass the electrified
region per section.
F = 1.0 + 0.766 [l-Pt(d)]o1<786 + 0.0755 aln [l/Pt(d)] (19)
where a is the normalized standard deviation of the gas flow (a = 0.25
is generally considered good).
Note that both B and F are particle size dependent.
The overall penetration is given by:
Pt0 =o/roPt'(d)f(d)dd (20)
It is this equation that is solved by the SR-52 program.
SR-52 PROGRAM
The SR-52 program solves equation (20) over the finite limits of d^
to d.c using a trapezoidal rule numerical integration.
Pt(d) is calculated based on second order polynomial curve fits to
2
W(d) vs d curves given by Gooch et al. These curves are based on
typical electrical conditions for an ESP collecting fly ash.
31
-------
Curves for the following cases were used to develop the least squares
curve fit parameters shown in Table 2:
2
Cold-side ESP current density 5 na/cm
2
Cold-side ESP current density 20 na/cm
2
Cold-side ESP current density 40 na/cm
2
Hot-side ESP current density 30 na/cm
Gas temperatures are 150°C and 370°C for cold- and hot-side ESP's,
respectively.
The current density that should be used in the calculations depends
on the dust resistivity. The relationship between allowable current
density (cold-side ESP) and dust resistivity is based on empirical data
reported by Hall. Hall's relationship can be written:
. = 6.31 x 1011
J
pO.987
2
where j is current density (in na/cm ) and pis the dust resistivity (in
ohm-cm).
When the current density predicted by the equation above is less than 5
2
na/cm , a hot-side ESP should be considered and the hot-side parameters
should be used.
This is a two card program: Card 1 is used to enter and store data
and to calculate constants; Card 2 is used to perform the numerical
integration.
32
-------
00
CO
Table 2. MIGRATION VELOCITY VS. PARTICLE DIAMETER CURVE FIT PARAMETERS
FOR VARIOUS ESP CURRENT DENSITIES
Current Density Temperature Particle Diameter Limi
na/cm °C pm
5 150
5 150
20 150
20 150
40 150
40 150
30 370
30 370
d <
d >
d <
d >
d <
d >
d <
d >
2
2
2
2
2
2
2
2
ts Curve Fit Parameters for Migration Velocity0
First, a Second, b Third, c
1.15987
0.94818
2.85176
2.2525
4.2029
2.8475
3.9943
2.5917
0.3
0.811698
1.06416
2.3348
1.5294
3.6296
-1.2175
1.5032
0.21188
-0.0003504
0.48567
0.002652
0.6956
0.01137
1.02250
0.005790
Parameters for w(d) = a + bd + cd cm/sec
-------
Card 1
The program on Card 1 is used to:
1. Enter and store data on ESP parameters, gas
conditions, and particle size distribution.
2. Calculate constants used in Card 2.
The following data are entered and stored by pressing the indicated
buttons:
Enter Data Press
Mass mean particle diameter, d (ym) A
Geometric standard deviation, a RUN
9
First curve fit parameter for migration velocity, a B^
Second " " " , b RUN
Third " " " , c RUN
2 3
Specific collector area, A/V (cm /Acm /sec), or C_ _^
Specific collector area, A/V (ft2/1000 ACFM) stflg 1 C
Normalized standard deviation of gas velocity distribution D^
Number of baffled sections, NS E^
Sneakage-reentrainment fraction, S RUN
Initial particle diameter, d. (ym) 2nd A'
Final particle diameter, df (ym) RUN
Particle diameter increment, Ad (ym) RUN
Each of the input data is printed as it is entered.
34
-------
Card 2
Card 2 is used to perform the numerical integration of equation
(20) for a log-normal size distribution over the finite limits d. to d.
using the trapezoidal rule numerical integration technique:
Pt = / f Pt'(d)f(d)dd = Ad -{Pt'(dj) + (21)
di "2~
Pt'(d. + Ad) + Pt1 (d. + 2 Ad) + ...Pt'(df))
i i —
where Pt'(d) is given by equation (17) and w(d) is given by:
w(d) = a + bd + cd2. (22)
Data a, b, and c are input using Card 1.
Pt'(d) is calculated in routine E.
For a log-normal size distribution, f(d) is given by:
f(d) = -J— exp [ -1" (d/V ] (23)
where d is the mass mean particle diameter, ym, and a is the geometric
j j
standard deviation.
Fraction of particles with diameter d, f(d), is calculated in subroutine
D.
At the completion of the numerical solution, the calculator will
print PtQ, d^ and df. PtQ is stored in Rg£.
35
-------
Because particle size distributions span several orders of magnitude
of particle diameter, it is useful to break equation (8) into increments
(each with its own Ad) and sum the solutions to the increments to obtain
the overall solution; i.e.,
Pt = /df Pt(d)f(d)dd = / ] Pt(d)f(d)dd + / 2 Pt(d)f(d)dd (24)
di dk di
df
+ / T Pt(d)f(d)dd
The summation is automatically carried out in Rgg. The results of
the summation must be manually recalled and printed by pressing RCL 98
2nd prt.
The user must determine: his own total integration limits, the
number of increments into which to divide the total integral, and the Ad
for each integral.
In general, overall integration from 0.1 to 20 microns with increments
of
0.1 to 1.0 microns (Ad =0.1)
1.0 to 10 microns (Ad = 0.5)
10 to 20 microns (Ad = 2)
is more than adequate.
36
-------
Use of the SR-52 Program
The SR-52 program provides a quick way to estimate ESP performance.
Five possible uses of the program are to:
1. Determine penetration of a given aerosol through
a given outlet emission standard for a given
aerosol. (See Example 4.)
2. Determine specific collector area required to
meet a given outlet emission standard for a
given aerosol. (See Example 5.)
3. Determine effects of changes in particle size distribution
on penetration through a given ESP. (See Example 6.)
4. Determine effects of changes in dust resistivity on
penetration through a given ESP. (See Example 7.)
5. Determine effects of changes in non-ideal factors on
penetration through a given ESP. (See Example 8.)
The SR-52 program as written will print all input data and penetration
through a given increment using the PC-100A printer. The overall penetration
summed over all increments must be recovered and printed manually by
pressing RCL 913 2nd prt.
37
-------
The printer output is arranged as follows:
V ym
0
g
a ) 2
b > parameters for w(d) = a + bd + cd
A/V, cm2/Acm3/sec or ft2/103KACFM
a
Ns
S
di
df
Ad .
space
A/V, cm2/Acm3/sec
space
Pt_
The program can be used without the printer with no changes. PtQ
for each increment will be displayed at end of calculation. Pt summed
over all increments can be displayed by pressing RCL 98.
Steps to follow in using program:
1. Determine dust resistivity, p, in ohm-cm.
2
2. Determine allowable current density, j, in na/cm from
r.
Hall'sj empirical correlation:
38
-------
. = 6.31 x 1011
J 0.987
P
3. Determine least squares parameters for w(d) =
2
a + bd + cd from Table 2 using current density
nearest to but not exceeding that calculated in
Step 2.
4. Determine A/V.
5. Enter data using Card 1.
6. Determine Pt using Card 2.
Example 4
Calculate overall penetration through an ESP for given conditions.
Given:
Cold-side ESP A/V = 0.7 cm2/Acm3/sec (356 ft2/103 ACFM)
Dust resistivity = 4 x 10 ohm-cm
Mass mean particle diameter = 15 ym
Geometric standard deviation = 4
Normalized standard deviation of
gas velocity distribution = 0.25
Number of baffled sections = 4
Fractional sneakage/reentrainment = 0.1
Cold-side ESP T = 150°C
39
-------
Solution:
PtQ =o/mPt'(d)f(d)dd
Divide integration into two increments
0.1 to 2 ym with Ad = 0.1, and
2.0 to 20 ym with Ad = 1.
Calculate allowable current density:
6.31 x 10
11
= 22 na/cm
J (4 x lo10)0'987
2
Use a, b, c for 20 na/cm
Step Procedure Enter
1 Enter Card 1
2 Enter all data d (15)
og(4)
a(2. 85176)
b(l. 06416)
c(0. 48567)
A/V (0.7)
o(0.25)
Ns(4)
S(O.l)
d.(O.l)
df(2.0)
Ad(O.l)
•
Press
A
RUN
B_
RUN
RUN
£
D_
£
RUN
2nd A1
RUN
RUN
Display
15
3.474924643
2.85176
1.06416
0.48567
-0.7
0.018875
4.
0.1
0.1
2.0
0.7
Print
15.
4.
2.85176
1.06416
0.48567
0.7
0.25
4.
0.1
0.1
2.
0.1
space
0.7
40
-------
Enter
11
'19
Store new d^
Step Procedure
3 Enter Card 2
4 Calculate Pt 0.1 ..2.0 ym
2.2525
2.3348
0.0026252
Calculate PtQ for 2< d< 20 ym
Press
5
6
7
8
9
10
STO 05
STO 06
STO 07
A
12 Recover and print
PtQ 0.1 < d < 20 ym
RCL 98
2nd Prt
Display
2.
Print
• 0060170031
2.
STO 19
STO 16
STO 17
STO 18
0.
2.
20.
1.
2.2525
2.3348
0.0026252
20. 0.002792262
20.
.0088092652
.0088092652
It is not useful to carry the integration past 20
In summary:
PtQ = 0.0088,
EQ = (1 - PtQ) - 0.9912,
A/V =0.7 cm2/Acm3/sec, and
T = 150°C.
Sample printer output for example 4 is shown in Figure 4.
41
-------
15. PRT
4. PRT
-2.85176 PRT
1.06416 PRT
0. 48567 PRT
0. 7 PR
0. 25 FRT
4. PRT
0. 1 PRT
0. 1 PRT
2. PRT
0. 1 PRT
0. 7 PRT
. 0060170031 PRT
2. PRT
0. 002792262 PRT
20. PRT
. 0088092652 PRT
Figure 4. PC-100A printer output for example 4—overall penetration
through ESP.
42
-------
Example 5
Determine the required specific collector .area, A/V, required for
an ESP to meet an emission standard of 0.02 mg/m under given conditions.
Given:
Inlet loading = 2 mg/m
Mass median particle diameter = 15 ym
Geometric standard deviation = 4
Dust electrical resistivity = 10 ohm-cm
Normalized standard deviation of gas velocity
distribution = 0.25
Number of baffled sections = 4.0
Fraction of particles that are reentrained and that bypass
electrified region per section = 0.1
Cold-side ESP T = 150°C
Solution:
Required PtQ - °-02 = 0.01.
Allowable current density, j = 6'31 x 10 = 8.8 na/cm2.
2
Use a, b, c for 5 na/cm .
Divide integration into two increments:
0.1 to 2 ym with Ad = 0.1, and
2.0 to 20 ym with Ad = 1.0.
First guess for A/V = 1.0 cm2/cm3/sec (500 ft2/103ACFM)
43
-------
Step Procedure
1 Enter Card 1
2 Enter all data
3 Enter Card 2
4 Calculate Pt
0.1 < d < 2.0 um
Enter
dg(15)
«g(4)
a(l. 15987)
b(0.3000)
c(0. 211888)
A/V(1.0)
o(0.25)
Ns(4.0)
S(.l)
d.(O.l)
df(2.0)
Ad(O.l)
Press
A
RUN
B_
RUN
RUN
C
D
I
RUN
2nd A
RUN
RUN
A
Display
15
3.474924643
1.15987
0.3
0.211888
-1.
0.018875
4.
0.1
0.1
2.
1.
2.
Print
15
4
1.15987
0.3
0.211888
1.
0.25
4.
0.1
0.1
2.
0.1
space
1.
.0167131954
2.
6
7
Penetration is already too high so there is no benefit in
continuing the calculation.
Increase A/V Enter Card 1
New A/V =2 2.
Calculate constants
for Card 2
Enter Card 2
Calculate PtQ 0.1 < d< 2.0 ym
C. -2.
2nd B1 2.
A 2.
2.
space
2.
.0049972136
2.
44
-------
Step Procedure
Enter
Press
Display Print
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Carry integration
Clear RIQ
Store new d^
Store new d.r
Store new Ad
Store new a, b, c
Calculate PtQ 2. <
Recover Pt 0.1 < d
This is too low.
Enter Card 1
Enter new A/V
Enter a, b, c for
Enter d.
Enter df
Enter Ad
past 2.0 ym
0.
2.
20.
1.
for b > 2.0 ym
.94818
.811698
-.0003504
d< 20. um
< 20 ym RCL
A/V needs to be
1.78
d< 2.0 ym
1.15987
0.3
0.211888
0.1
2.0
0.1
STO 19 0.
STO 16 2.
STO 17 20.
STO 18 1.
STO 05 .94818
STO 06 .811698
STO 07 .0003504
A 20. .0025482646
20.
98 2nd Prt .0075454782 .0075454781
decreased.
C_ -1.78 1.78
B_ 1.1 5987 1 . 1 5987
RUN 0.3 0.3
RUN 0.211888 0.211888
2nd A 0.1 0.1
RUN 2.0 2.
RUN 1.78 0.1
space
1.78
45
-------
Step Procedure
22 Enter Card 2
Enter
Press
23
24
25
26
27
28
29
30
31
Calculate PtQ 0.1 < d< 2 ym
Carry integration past 2.0 ym
Clear R
19
Store new d.
Store new d,.
0
2.
20.
Store new Ad 1.
Store a, b, c for d >2.0 ym
0.94818
0.811698
-0.0003504
Display
2.
Calculate Pt 2.0
-------
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PR i
2. PRT
0. 1 PRT
1. PRT
0167131954 PRT
2. PRT
2. PRT
2. PRT
. U04yy7L:liob
Cl. B
. 0 0 2 5 4 8 2646
20.
. 00754547S1
1. 78
1. 15987
0. 3
0. 211333
0. 1
Ll >
0. 1
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
1.73 PRT
. nfib4011292 PRT
2. PRT
. fifr:-: 1990565. PRT
20. PRT
.0096001857 PRT
Figure 5. PC-100A printer output for example 5--specific collector
area vs. ESP emission standard.
47
-------
Example 6
Determine the effects of changing the size distribution parameters
from
to
d = 25 ym, O = 4
dg = 25
Og = 3.
for the given conditions.
Given:
A/V (cold-side)
Current density
2 3
= 0.7 cm /cm /sec
= 20 na/cm
Normalized standard deviation of gas velocity
distribution = 0.25
Number of baffled sections = 4
Fraction of particles that are reentrained and that
bypass electrified region per section = 0.1
Solution:
Divide integration into two increments:
0.1 to 2 pm, with Ad
2 to 20 ym, with Ad
0.1, and
1.0.
Step Procedure
1 Enter Card 1
2 Enter all data
Enter
Press
25
4
2.85176
1.06416
0.48567
0.7
0.25
A
RUN
B_
RUN
RUN
C
D
Display
25.
Print
25.
3.474924643 4.
2.85176 2.85176
1.06416 1.06416
0.48567 0.48567
-0.7 0.7
0.018875 0.25
48
-------
Step Procedure Enter
4
0
0
2
0
3 Enter Card 2
.1
.1
.0
.1
4 Calculate Pt 0.1 < d< 2.0 ym
(calculation requires about 5
5 Continue integration
6 Clear R-jg 0
7 Store new d- 2
8 Store new df 20
9 Store new Ad 1
10 Enter new a, b, c for
2.
2.
0.
11 Calculate Pt 2. < d <
12 Recover and print
Pt 0.1 2 ym
2525
3348
002652
20 ym
Press
E
RUN
2nd A
RUN
RUN
A
minutes)
ym
STO 19
STO 16
STO 17
STO 18
STO 05
STO 06
STO 07
A
RCL 98 2nd
Prt
Display Print
4. 4.
.1 0.1
.1 0.1
2. 2.0
0.7 0.1
space
0.7
2. .0026480641
2.
0
2.
20.
1.
2.2525
2.3348
0.002652
20 .0019190628
20.
.0045671269 .0045671269
This is the overall penetration for d = 25 ym and o = 4.
-------
For d = 25 ym and a = 3:
.7 ;J
Step Procedure Enter
1 Enter Card 1
2 Enter data 25
3
2.85176
1.06416
0.48567
0.1
2.0
0.1
3 Enter Card 2
4 Calculate Pt 0.1 2.0
2.2525
2.3348
0.002652
11 Calculate Pt
0
2.
-------
In summary:
T = 150°C,
A/V = 0.7 cm2/Acm3/sec,
for d = 25 and a = 4, PtQ = 0.0046, and
for d = 25 and o = 3, PtQ = 0.0023.
Note**the large effect that an increase in a has on overall penetration.
Printer output for example 6 is shown in Figure 6.
Example 7
Determine penetration for the ESP in Example 4 for the case where
dust resistivity is increased from 4 x 10 ohm-cm to 10 ohm-cm.
Given: All conditons, except dust resistivity, are as for example 4.
Solution:
Allowable current density, j = 6'3],x IS-, = 8.8 na/cm2.
do11)'987
2
Use a, b, c for 5 na/cm .
Divide integration into two increments:
0.1 to 2.0 pm with Ad = 0.1, and
2.0 to 20 ym with Ad = 1.0.
51
-------
25. PRT
4. PRT
2.85176 PRT
1.06416 PRT
0.48567 PRT
0. 7 PRT
0.25 PRT
4. PRT
0. 1 PRT
0.1 PRT
2. PRT
0. 1 PRT
0.7 PRT
.0026480641 PRT
2. PRT
.0019190628 PRT
20. PRT
.0045671269 PRT
25. PRT
3. PRT
2.85176 PRT
1.06416 PRT
0.48567 PRT
0. 1 PRT
2. PRT
0. 1 • PRT
0.7 PRT
.0006880736 PRT
2. PRT
0.001589385. PRT
20. PRT
.0022774587 PRT
Figure 6. PC-100A printer output for example 6—changing ESP size
distribution parameters.
distribution parameters
52
-------
Step Procedure
Enter
Press
Display
Print
1 Enter Card 1
2 Enter all data 15 A
4 RUN
1.15987 B_
0.3 RUN
0.211888 RUN
0.7 C
0.25 D
4 E.
0. 1 RUN
0.1 2nd A
2.0 RUN
0.1 RUN
3 Enter Card 2
*%
4 Calculate Pt " A 2.
0.1 2.0 vm
11 0.94818 STO 05
12 0.811698 STO 06
13 -0.0003504 STO 07
15 15.
3.474924643 4.
1.15987 1.15987
0.3 0.3
0.211888 0.211888
-0.7 0.7
0.018875 0.25
4. 4.
0.1 0.1
0.1 0.1
2.0 2.
0.7 0.1
space
0.7
.0251019171
2.
0.
2.
20.
1.
0.94818
0.811698
-0.0003504
53
-------
Step Procedure
14 Calculate Pt
2. < d< 20.0 ym
15 Recover and print
Pt 0.1 < d< 20 ym
Enter
Press
A
RCL 98
2nd Prt
Display
20.
.0524198854
Print
.0273179683
20.
.0524198854
In summary:
for p = 4x10 ohm-cm,
,11
Pt = 0.008, and
PtQ = 0.052.
for p = 10 ohm-cm,
Printer output for example 7 is shown in Figure 7.
Example 8
Determine the effect of increasing the normalized standard deviation
of the gas flow distribution in Example 4 from 0.25 to 0.5.
Given: All conditions, except normalized standard deviation of the gas
flow distribution, are as for example 4.
Solution:
Divide integration into two increments:
0.1 to 2.0 um with Ad = 0.1 ym, and
2.0 to 20 ym with Ad = 1.0 ym.
-------
15. PRT
4. PRT
1. 15937 PRT
0. 3 PRT
0.211333 PRT
0. 7 PRT
0. £5 PRT
4. PRT
0. 1 PRT
0. 1 PRT
2. PRT
0. 1 PRT
PRT
.0251019171 PRT
2. PRT
. 0273179633 PRT
20. PRT
.0524193354 PRT
Figure 7. PC-100A printer output for example 7--ESP
penetration vs. dust resistivity.
55
-------
Step Procedure
Enter
Press
Display
Print
1 Enter Card 1
2 Enter all data 15
4
2.85176
1.06416
0.48567
0.7
0.5
4.
0.1
0.1
2.0
0.1
3 Enter Card 2
4 Calculate Pt
0
0.1 < d< 2.0 ym
5 Continue integration past 2.0 ym
6 Clear R,Q 0.
i y
7 Store new d. 2.
i
8 Store new df 20.
9 Store new Ad 1 .
10 Store new a, b, c for d> 2.0 ym
2.2525
2.3348
0.002652
A
RUN
B_
RUN
RUN
C_
D_
E_
RUN
2nd A1
RUN
RUN
A
'"""
STO 19
STO 16
"~
STO 17
STO 18
STO 05
STO 06
STO 07
15 15.
3.474924643 4.
2.85176 2.85176
1.06416 1.06416
0.48567 0.48567
-0.7 0.7
0.03775 0.5
4. 4.
0.1 0.1
0.1 0.1
2.0 2.
0.7 0.1
space
0.7
2. .0088151441
2.
0.
2.
20.
1.
2.2525
2.3348
0.002652
56
-------
Step Procedure Enter Press Display Print
11 Calculate Pt
2. < d < 20 ym A 20. .0088824589
20.
12 Recover and print RCL 98 .017697603
PtQ 0.1
-------
15. PRT
4. PRT
2.35176 PRT
1.06416 PRT
0.43567 PRT
0. 7 PRT
0. 5 PRT
4. PRT
0. 1 PRT
0. 1 PRT
2. PRT
0. 1 PRT
PRT
.0088151441 PRT
2. PRT
.0088324589 PRT
20. PRT
0.017697603 PRT
Figure 8. PC-100A printer output for example 8--changing normalized
standard deviation of ESP gas flow distribution.
58
-------
CAUTIONS ON USING SR-52 PROGRAM RESULTS
The SR-52 program is based on results calculated using the EPA/SoRI
ESP computer model for typical ESP used to collect fly ash. Thus, the
calculated results are most accurate when the dust concentrations,
particle size distributions, and voltage/current relationships are close
to those used in the computer model calculations. Even in those cases
the SR-52 results will predict values of penetration somewhat higher
than those predicted by the computer model for large specific collector
area ESP.
The correction factors for non-ideal effects have not been subjected
to rigorous experimental evaluation. These correction factors, however,
in combination with the rest of the model do give useful results which
are in line with available experimental data.
Note that although the absolute accuracy of the SR-52 calculations
may not be high when conditions other than those used in the computer
model calculations are of interest, the trends predicted by the SR-52
program are still correct and provide useful information.
59
-------
REFERENCES
1. Calvert, S., Goldshmid, J., Leith, D.f and Meta, D., "Scrubber
Handbook—Volume I of Wet Scrubber Systems Study," EPA-R2-72-118a (NTIS
PB 213-016), August 1972.
2. Gooch, J. P., McDonald, J. R., and Oglesby, S., Jr., "A
Mathematical Model of Electrostatic Precipitation," EPA-650/2-75-037
(NTIS PB 246-188/AS), April 1975.
3. Calvert S., "Source Control by Liquid Scrubbing," Chapter 46
in Air Pollution. A. Stern ed. Academic Press, 1968.
4. Calvert, S., Yung, S., and Barbarika, H., "Venturi Scrubber
Performance Model," EPA-600/2-77-172 (NTIS PB 271-515/AS), August 1977.
5. Hall, H. J., "Trends in Electrical Energization of Electrostatic
Precipitators." Presented at the Electrostatic Precipitator Symposium,
February 23-25, 1971. Birmingham, Alabama.
60
-------
APPENDIX A
USER INSTRUCTIONS AND PROGRAM LISTING FOR VENTURI SCRUBBER PROGRAM
USER INSTRUCTIONS
Enter Card 1, sides A and B. Enter data as follows:
Enter
T °C
f (usually 0.5)
d,, ym
g
ag
d . ym
d.p ym
Ad ym (if known)
2nd stfl 1 (if number n
of steps n known)
p. gm/cm
L/G m3/m3
UG cm/sec
y poise
Pp gm/cm
0
Press
A
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
RUN
Display
T°K x 10"4
f
1.01
7.00
6.00
5.00
4.00
4.00
3.00
2.00
1.00
0.00
Ap cm water
0
Enter Card 2 and press A. Display
61
-------
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-------
APPENDIX B
USER INSTRUCTIONS AND PROGRAM LISTING FOR ESP PROGRAM
USER INSTRUCTIONS
Enter Card 1, sides A and B. Enter data as follows:
Enter Press Display
dg ym A dg
ag RUN ag
a i a
b RUN b
c RUN c
A/V cm2/Acm3/sec C^ -A/V**
or A/V ft2/103 ACFM 2nd stfl 1 C -A/V cm2/Acm3/sec
0 2. a
Ns E Ns
S RUN S
di ym 2nd A' d..
df ym RUN df
Ad ym RUN Ad
or n (number of steps) 2nd stflg 2 RUN Ad
Enter Card 2. Press A. Display df.
Recover PtQ by pressing RCL 98.
**A/V in cm /Acm /sec is displayed because the program uses A/V in the
calculations.
-------
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-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/7-78-026
2.
4. TITLE AND SUBTITLE
SR-52 Programmable Calculator Programs for
Venturi Scrubbers and Electrostatic Precipitators
7. AUTHOR(S)
Leslie E. Sparks
9. PERFORMING ORGANIZATION NAME AN
See Block 12.
D ADDRESS
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
3. RECIPIENT'S ACCESSION NO.
5. REPORT DATE
March 1978
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO.
EHE624
11. CONTRACT/GRANT NO.
NA (Inhouse Report)
13. TYPE OF REPORT AND PERIOD COVERED
Final; 6-8/77
14. SPONSORING AGENCY CODE
EPA/600/13
,5. SUPPLEMENTARY NOTES Dr . Sparks ' mail drop is 61; his phone is 919/541-2925.
16. ABSTRACT The rep()rt provides useful tools for estimating particulate removal by
venturi scrubbers and electrostatic precipitators. Detailed descriptions are given for
programs to predict the penetration (one minus efficiency) for each device. These
programs are written specifically for the Texas Instruments SR-52 programmable
calculator. Each program includes a general description of the mathematical model
on which the program is based and the formulas and numerical techniques used in
adapting the model to the SR-52. Numerical examples, program listing, and user
instructions are included.
17.
a. DESCRIPTORS
KEY WORDS AND DOCUMENT ANALYSIS
b.lDENTIFIERS/OPEN ENDED TERMS
Air Pollution Programming Air Pollution Control
Dust Manuals Stationary Sources
Estimating Calculators Particulate
Scrubbers Mathematical Venturi Scrubbers
Venturi Tubes Models SR-52 Calculator
Electrostatic Precipitators
18. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS (This page)
Unclassified
c. COSATI Field/Group
13B
11G 05B,09B
14B
07A
12A
21. NO. OF PAGES
77
22. PRICE
EPA Form 2220-1 (9-73)
71
------- |