EPA AA-EOD-82-1
Technical Report
July 1982
Gas Divider Evaluation
By
Sherman D. Funk
Notice
NOTICE
Technical reports do not necessarily represent final EPA
decisions or positions. Their publication or distribution does not
constitute any endorsement of equipment or instrumentation that may
have been evaluated. They are intended to present technical
analysis of issues using data which are currently available. The
purpose in the release of such reports is to facilitate the exchange
of technical information and to inform the public of technical
developments which may form the basis for improvements in emissions
measurement.
Engineering Staff
Engineering Operations Division
Office of Mobile Sources
Environmental Protection Agency
2565 Plymouth Road
Ann Arbor, Michigan 48105
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ABSTRACT
This project was conducted to evaluate the characteristics of a
gas divider used to generate the calibration data for exhaust
emission gas analyzers. HC, C02, CO and 02 calibration curves
generated by gravimetric standard gases were compared with gas
mixtures using the divider. The divider was found to provide
acceptable results of comparability for HC and CO. However, the
viscosity of the C02 and 02 at the higher concentrations
affected the gas flow, which caused a 1-2% error in the theoretical
gas mixture. This report relates the work that has been done by
this lab and others toward establishing a reliable dividing ratio
factor that can be used with C02 and 02 to achieve accurate
results when calibrating the analyzers with a gas divider.
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INTRODUCTION
The Engineering Staff of EOD investigated the feasibility of
using a gas divider for generating and/or checking emission analyzer
calibration standard gases. Gordon Becker and Dave Turner of the
Gas and Chemical Analysis Group supported the Staff by performing
the specified tests. A calibration gas divider was loaned by
National Environmental Systems of Livonia, Michigan, for these tests
and evaluation. The intent of this project was to investigate and
possibly answer some of the questions that have arisen in regard to
viscosity effects on the flow of C02 gas through a capillary,
thereby causing an effect on the concentration of the gas mixture.
The results of this series of tests would be to qualify the concept
and quantify the calculations needed to use a divider as an on-site
curve generator or checker.
BACKGROUND AND THEORY
The measurement of mobile exhaust emissions requires a
significant expense for the acquisition and maintenance of
calibration gases for the analyzers. The use of gas dividers by
many laboratories has been one way of reducing that cost. A gas
divider uses the principle of capillary flow to accurately divide or
dilute a calibration gas of known value to set proportions by
selecting combinations of capillaries to flow a diluent gas or a
span gas.
This principle is expressed in the Hagen-Poiseuille law of
capillary flow that states
Q = r4 . P1-P2
8y L
Q = flow rate
where y =
viscosity
r = radius
Pl= inlet pressure
P2= outlet pressure
L = length
in this case, L, PI, P2 and r are constant. Thus, Q is a function
of viscosity y and the formula can be rewritten
Q = K
y
where K = r4 (P1-P2) = constant
8L
Using this law the divider ratio can be expressed as follows:
-------
See Figure 4 for capillaries' flow formula and flow path diagram of
the divider.
Since Q = K
y
the formula for divider output concentration is CT= Qs . Cs
Qs + Qz
and the divider ratio is related to the number of capillaries flowing
K
by di = Ns us
NS K + NZ K
ys vz
or \ di = Ns
Ns + Ns-10(jy_s_)
(yz)
where Of = Theoretical concentration
Cs = Concentration of span gas
Q = Flow rate
Ns = Number of capillaries flowing span gas
Nz = Number of capillaries flowing zero gas
K = Constant or TT r4 (PI - P2)
8L
ys = Viscosity of span mixture gas
yz = Viscosity of zero or balance gas
The dividers usually use 6-10 "matched" capillaries depending on
the number of points needed to be checked. The Model CGD-11 that
was used in this project contained ten capillaries.
Many emissions testing laboratories in the U.S. and foreign
countries use gas dividers as a calibration tool for vehicle
certification and enforcement testing under the provisions of the
Federal Register 40 CFR 86.114-79 (a)(7). In all cases that have
been reported and reviewed, all units provide acceptable results on
all gases except C02 where in some instances marginal results of
acceptable accuracy are experienced. It is generally believed that
the viscosity effects of a C02/N2 mixture at the ranges of
concentrations in use can cause errors to the point that a dividing
ratio correction factor must be developed (reference Nissan report
to Andy Kaupert, dated June 23, 1981). One of the most significant
questions that came out of this report was the disagreement between
the theoretical data derived from Wilke's viscosity equation for gas
mixtures (reference Journal of Chemical Physics, Vol 18 No. 4, April
1950) together with the Hagen-Poiseuille law regarding viscosity and
flow and actual measurements made on different concentration levels
of C02« This report discussed those tests and their results, and
comments on possible ways to relate these data to the use of a gas
divider.
-------
EVAULATION TEST PLAN
Three major areas were addressed in assessing the gas divider as
a calibration tool: 1) comparative curves and general operation, 2)
capillary flow tests for viscosity effects, and 3) viscosity
correction factor development.
Each area is described as follows:
1. A gas divider evaluation test which included:
a. Comparisons of gravimetric versus divider curves of
C02» CO, C3Hs, and Q£ were made to assess accuracy.
b. Response measurements were made from time of gas valve
change to 90% of full scale and to stable reading on chart.
c. A series of runs made both in forward and reverse
order to check for hysteresis effects and precision.
d. Lowering the zero and span input pressures from 25
PSIG (zero) and 35 PSIG (span) to 15 PSIG and 20 PSIG, respectively
to assess pressure affects.
2. The comparison tests of actual flow versus
concentration/viscosity consisted of using the flow arrangement in
Figure 5 in two parts. The first was to run N2 and six
concentrations of C02 from 1 % to 100% at 40 PSIG for a period of
1000 seconds through a Beckman 400 capillary into a Brooks prover.
The prover is a volumetric displacement measuring device by which
the actual volume of gas is measured for a specific time. The
second part was to run the same C0£ arrangement again and similar
blends of 02 and C3Hg. By using actual volume and time
measurements, flow rates were calculated. Theoretical flow rates
were derived from viscosity calculations and a dividing ratio factor
for the specific concentration. The actual and theoretical flow
rates of C02, 02 and C3Hg are listed on Table 9 and plotted
on Figure 3.
3. Measurements and curve data were analyzed to develop
an applicable viscosity mixture formula for gas blends. Wilke's
equation in attachment 1 (10), which used concentration ratios,
viscosity of individual gases, density and molecular weights was
evaluated. See Discussion of Test Results Section for symbol
definitions. This equation was implemented on a basic computer
program in order that these properties for various gases and
concentrations could be entered and the viscosity mixture could be
calculated quickly.
-------
DISCUSSION OF TEST RESULTS
The major portion of this project was to evaluate the gas
divider for use as a calibration tool. The two issues that were
addressed secondarily were the effects of concentration or viscosity
change on flow rate together with the investigation and search for
an applicable viscosity mixture formula for gas blends.
The response, hysteresis effect, and pressure change checks gave
excellent results and are expected to cause no problems.
Other laboratories have run tests on various models of gas
dividers and have gotten excellent results. However, most all have
expressed a concern over the apparent viscosity effect on CC>2
mixtures. In order to see and possibly quantify some of these
effects, a series of gravimetrically-referenced curves was
established using 0-100 PPM C3Hg/air, 0-24% 02/N2, 0-5%
C02/N2, 0-15% C02/N2, 0-1000 PPM CO/N2 and 0-2500 PPM
CO/N2. For each gas and range the top gas was run through the ten
points of the divider, the response was read on the analyzer, and
the data were processed for deviation comparison. The curve
comparisons are shown in Tables 1-8. The HC (0-100 PPM) was
selected because it is a linear range on which there would be no
significant viscosity effect. A number of problems were revealed in
that a higher than expected error was seen. The curve appeared to
be linear. By running additional fit and non-zero intercept curves,
it could be seen that there seemed to be a flow, pressure or drift
problem with the analyzer and not the fault of the divider. Changes
were recommended to improve the HC flow controller.
The 02 was run to look at viscosity effect since the viscosity
of oxygen is considerably higher than nitrogen as opposed to carbon
dioxide being lower. In the case of oxygen the predicted
(theoretical) and the actual measured deviation from linear were in
the same direction but not the same magnitude. It could be seen
that there were some effects at the different divider points,
possibly from viscosity. See Figure 1 for divider ratio variance
from linear. The curve for 02 can be seen on Table 4.
-------
The formulas used in establishing these plots are:
CDR = Calculated Divider Ratio
LDR = Linear Divider Ratio
MDR = Measured Divider Ratio
A = Difference
Calculated A from linear = CDR - LDR
Measured A from linear = MDR - LDR
Calculated %A = CDR - LDR x
LDR
Measured %A = MDR - LDR x 100
LDR
where
CDR =
Ns
where Ns
ys
yz
10
MDR =
10 - Ns (jjs) + Ns
(yz)
number of capillaries flowing component gas
viscosity of component gas mixture or span
viscosity of balance gas or zero
total number of capillaries
Ct
where
Cp
Ct = Component gas concentration at the top undiluted
Cp = Concentration read at that specific divider point
Carbon monoxide in nitrogen C02/N2 curves were run at two
ranges, 0-1000 PPM and 0-2500 PPM. CO was selected since the
viscosities and molecular weights are mainly the same as N2 and no
viscosity effect should be seen. We again incurred a curve problem
with the 0-1000 PPM curve (Bendix). It was 8.8% non-linear and
could have been defined better on the low end (Table 5). However
the 0-2500 PPM range (MSA), Table 6, showed a very good fit and
comparability down to a maximum of + 0.5% of point deviation. To
prove further viscosity or non-viscosity effect, a range of 0-10% CO
should be run in the future.
If viscosity is a definite factor, there should be considerably
better comparability on the CO than C02 or 02« Carbon dioxide
in nitrogen curves were run in two ranges, 0-5% (table 7) and 0-15%
(Table 8). While a slight effect could be seen on the 5% range,
there was a significant effect on the 15% range with deviations as
high as -1.5% of point. Also, for the 0-15% range refer to the
divider ratio comparisons on Figure 2, where the calculated ratio is
the direct opposite direction as opposed to measured. Even though
the magnitude of deviation from linear was not as great as
calculated, it was greater than any of the other gases run. An
empirically-derived curve of divider deviation from an S-Tec
instrument (Japanese) was plotted and was near the same magnitude
and direction as the instrument we used.
-------
To better see the concentration/viscosity curves' flow rate
effects, a series of flow measurements were made using an
arrangement as seen on Figure 5. Gases used were C02, CsHg
and 02. The results were tabulated on Table 9 and plotted on
Figure 3. The theoretical values were calculated by comparing
ratios of viscosity of the various mixtures to the balance gas or
N£. The measured values were derived by a volumetric displacement
measurement versus a time period of flow. Viscosity of mixtures
were calculated by using Wilke's equation as seen on Attachment 1.
The symbols for this equation are defined as:
X^ = concentration of gas 1
X2 = concentration of gas 2
yi = viscosity of gas 1
U2 = viscosity of gas 2
MI = molecular weight of gas 1
M2 = molecular weight of gas 2
P! = density of gas 1
?2 = density of gas 2
All the viscosity mixture values were calculated from this
formula.
It is interesting to note that for propane and carbon dioxide
the theoretical and measured disagreed in both magnitude and
direction, whereas the oxygen agreed in direction and very nearly in
magnitude. In the curve comparisons, the C02 and C^Hg actual
measured deviations were in the opposite direction of the calculated
based on viscosity and the 02 agreed in the same direction. Some
questions remain as to why the actual flow rates and deviations
measured do not agree with the theoretical and could possibly
warrant further investigation.
The response checks that were made were from time of valve
change to 90% of full scale (3-5 seconds) and to full stable reading
(10-12 seconds).
The runs made in both forward and reverse order to check for any
hysteresis effect showed no significant effect (+0.2% FS or less).
Lowering the zero and span input pressure showed no discernible
effect.
The capillary flow rate versus concentration/viscosity tests are
plotted on Figure 3 for C3H8, C02 and 02« The C3Hg and
C02 calculated effects from viscosity do not agree in magnitude or
direction with the measured. The same gases differed in the same
manner in the curve comparisons and will be discussed later in the
section. Table 9 lists the values used for the plots on Figure 3.
-------
It has been seen that different gases act differently from
viscosity or other effects and that from the amount of data we have,
it is difficult to state that viscosity is the sole cause of these
deviations, although it appears to be the major cause. The fact
that 02 which has a viscosity considerably higher than that of
N£, the balance gas, as opposed to CC>2 which has a viscosity
considerably lower than N£, yet both gases have the same result in
direction of deviation on the divider causes some concern in
applying the total effect to viscosity.
CONCLUSIONS AND RECOMMENDATIONS
1. Conclusions
A. It can be clearly seen that, in the ranges of gas analyzers
we use, the gas divider can be used as an accurate tool for
calibration with deviations of generally less than 0.5% of point on
all instruments except C02 where a useable divider ratio should be
developed empirically.
B. The instrument is easy to use from an operational
standpoint, provides a reasonable response and has no significant
hysteresis effect from forward or reverse order runs.
C. This report is in general agreement with the Nissan study
report to A. Kaupert dated June 23, 1981 in that C02, which was
the prime concern of their study, has properties that in actual
practice will necessitate using an increasingly negative divider
ratio with increasing concentration while the theoretical predicts
that the ratio should increase in the opposite (positive) direction.
D. The data indicate that it would not be appropriate to use
the available theoretical formulas to develop a divider ratio. Any
divider ratio correction should be empirically developed.
2. Recommendations
A. It is recommended that a gas divider be purcahsed and used
as an alternative gas analysis tool.
B. It is recommended that by testing this divider, a set of
empirical divider ratios be developed.
C. It is recommended that a plan be developed to implement
these units as a calibration tool for our analyzers.
D. It is also recommended that some additional work be
considered in the future to more clearly define these effects.'
-------
References
1. Journal of Chemical Physics, Vol. 18, Number 4, April 1950.
2. Memo and Report, Nissan Motor Co., to Andy Kaupert, June
23, 1981.
3. S-TEC Instruction Manual, Standard Technology, Inc., Japan.
4. Viscosity Behavior of Gases, T. A. Bromley and C.P. Wilke,
Univ. of California Industrial and Engineering Chemistry,
Vol. 43, No. 7, 1950.
5. Memo to D. Paulsell from T. Penninga re Horiba Gas Blender,
11-1-78.
6. Memo to D. Paulsell from J. Batchelder, State of
California, re evaluation of Horiba Gas Divider, 5-25-78.
7. Handbook of Chemistry and Physics, Weast 60th Edition,
1979-80.
-------
INDEX OF APPENDICES
Table 1 0-100 PPM HC curve (2nd degree fit)
2 0-100 PPM HC curve (1st degree fit)
3 0-100 PPM HC curve (non-zero intercept)
4 0-24% 02 curve
5 0-1000 PPM CO curve
6 0-2500 PPM CO curve
7 0-5% CP2 curve
8 0-15% C02 curve
9 Gas Flow Measurement Tabulation
Figure 1 02 Divider Ratio Plots
2 C02 Divider Ratio Plots
3 Flow Rate vs. Concentration Plots
4 Capillary Flow Mixing Method and Formula
5 Gas Flow Measurement Set-Up
6 S-TEC Model SED-78 Gas Divider Ratio Plots
Attachment 1 Wilke's Equation for Viscosity Mixture Calculation
-------
PAGE 2
ffC
**** PROCESSED: 15!32:28 03-10-82
CAL, NUMBER (UTI)
EUUIPMENT 1» NO.
CALIBRATION NAME
TEST SITE NUMBER
END i: A I...tli. AT
MINOR HAH
820310153228
038284
HCAN-CR16
A251
11M.5 03-10-82
C3H8
if******************************************
*******#***********##*******#**************
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*** ANALYZER CALIBRATION CURVE ANALYSIS ***
*** ***
*********#********!)(*****)(<**************** + *
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PAGE 2
**** PROCESSED: .1.1:11:37 05-29-82
CAL. NUMBER (UTI)
EQUIPMENT ID NO.
CALIBRATION NAME
TEST SITE NUMBER
END CALIB. AT
MINOR GAS
: 820528111137
: 030284
J HCAN-CR16
5 A251
: 09:20 05-27-82
: C3H8
if******************************************
*******************************************
*** ***
*** ANALYZER CALIBRATION CURVE ANALYSIS ***
*** ***
*******************************************
*******************************************
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I G11831
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-------
PAGE 2
*#** PROCESSED: 10:57:50 06-03-82
CAL. NUMBER (IJTI)
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CAL I BRA [.TON NAME.
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END CALIB. AT
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820603105750
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I f!2hU.b NOME (1
1 i»0-S?.5 MONEd
I IB?M.S tJt).>JEd
1 lb^b.1 NONE d
I li»i».<» NONtd
1 1110. 3 MdiviEd
I 91 a. ?. ,tWf.il
1 b«1.2 NUNEd.
I *«bb.l NOMEd)
?aei.e
1D75.1
lb5d.M
I«b5.9
\2tt. J
967.S
e?7.a
6bb.7
/
I 22H1.8
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1 Irtl9.8
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» I3h7.9
d«^.fl
91)9.9
b»7.7
1SH.7
I iJiftt.l MONE(l) 8i?V.l
I
1) CYLINDER NUf DEFINED IN THE EQUIPMENT FILF. 3YS1EM.
ANALYZER DEFL. I I CUKVE FIT DEVIATIONS
MEAS. CORK. I DATA TYPE I FROM N AKEO/NOMI N AL X FROM LAST
X XI
91.250 91.250 ICYL CURVE INPUT
7b.5bO 76.^50 ICYL CURVE INPUT
68.300 66. SOU ICYL CURVE INPUT
61.100 61.100 ICYL CURVE INPUT
52.350 52.150 ICYL CURVE INPUT
11.350 11.350 ICYL CURVE INPUT
35.600 35.t>00 ICYL CURVE INPUT
28.500 28.500 ICYL CURVE INPUT
1
91.250 91.d50 ICYL TO HE NAMED
82.850 82.B50 ICYL TO BE NAMED
71.500 71.500 JCYL TO BE NAMED
66.150 66.150 ICYL TO BE NAMED
57.300 57.300 ICYL TO BE NAMED
40.100 18.100 ICYL TO BE NAMED
39.000 39.000 ICYL TO Bf NAMED
29.600 29.800 ICYL TU BE NAMED
20.100 20.100 ICYL TU BE NAMED
10.150 10.150 ICYL TO BE NAM£0
1
AVERAGE INPUT DATA POIN1
DEVIATION FROM 1 HE CUKVE
X POINT X FbLL-Sr.L ANL/CYL CAL
0.051 0.019 NONtd)
-0.212 -0.157 NOMEd)
0.155 0.101 NONEd)
-0.011 -0.025 NONE(I)
0.170 0.081 NUNEd)
-0.159 -0.061 NONEd)
0.020 0.006 NONEd)
0.009 0.002 NUNEd)
0.051 0.019 NUNEd)
-0.257 -0.208 NUNEd)
-0.258 -0. 18b NONE (1)
0,079 0.050 NONEd)
-0.032 -0.017 NONEd)
0.183 O.OH3 NONEd)
-0.259 -0.093 NUNEd)
0.506 0.137 MONE(l)
0.560 0.101 NONEd)
0.158 0.011 NONEd) I
I
I
0.103 0.061 0.000 I
___.__.._-._-_.__.._.--__-..__-..._____-.---_-_----- . ....... T
(-4) Nil "LAlESr" ANALYZER CALIBRATION ON FILE IN THE t.FS.
/"//
-------
l o : -j i : e. 4
IV.KCAL
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CAI. . MJMrlEW (III I )
NO.
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CAL lUKAl ION
It: SI SUE NI
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C02A-CH24
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) 1 - - 1 1 . 'l b '1 0
1 . I -- I 1. H200
) I 1 0./c>bl>
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1 -- i l.hbrlU
I -- I 5.19bS
I -- I 2.M90
1 -- I ..!.^')2')
) 1 -- 1 1.-V6.I
) I -- I l.it>9b
) I 1 0.9131,
) 1 -- I '. i' .'i'it>';>
1 1
OEKINEl) IN fHE EUUlPKEi'i 1 F
M1HAI10MS I ANALYZE
LAIEST M-'.'i i ME AS.
CYI. CAL CUKVE 1 X
NOi-Jt (
NOME I
mii'./665 I 16.000
I !
) 4. Si. Wi I 90.000-
) '1. 1 !"<«' I HI .700 !
) 3.6VK I 73.000.
) ' 3. l9/'i 1 04.300 '
) rr./r":>9 I 5*>.20il
) ? . <' 1 b 9 I 4 6 . 4 0 0
) 1 . >< ,' 1 i> I 37.400
) 1 .3* 0.6SO
SO. 100
59.HOO
50.0bO
21 .200
16.000
90.000
« 1 . 7 0 0
73.000
64.300
bb.200
46.400
37.400
2«.200
19.000
9.600
I
I
I
ICYL
1CYL
Ii:YL
ICYL
ICYL
ICYL
ICYL
ICYL
I
JCYL
ICYL
ICYL
1 C Y 1-
ICYL
ICYL
ICYL
ICYL
ICYL
ICYL
I
ILC r.YSTtM. 1 AVEHAPE INPUT
I OH
VI AT10N
J-HUM
1
DATA TYPE 1
I
CllKVE INPUT I
CukVE INPUT I
LUKVE INPUT I
CUKVE INPUT I
CURVE INPUT I
CUKVE INPUT 1
CUKVE INPUT I
CUKVE INPUT 1
I
TO bE NAMED I
TO BE NAN'EU I
TU BE NAMED i
10 I»K NAMED I
TO BE NAMED 1
TO HE NAMED I
TO BE NAMED 1
TO BE NAMED I
TO BE NAMED I
TO BE NAMED I
1
DATA POINT I
FHE CURVE I
CUKVt
Fll LH:ViATl(Jf;S
FHOM NAllEU/lMOMJfvAL
X POINT Z
-0.034
0.060
0.007
-0. 1 07
-0.147
O.Otib
-0.046
0. 169
-0,054
0.202
0.063
0.064
-0.479
(t VJ Q t>
0 <* ^1 0
-0^427
-0.09/4
0.207
O.OS2
FULL-bCL
-0.030
0 . o 4 b
O.ob J
-O.Obl
-0 ,0b(>
0 . 0 2 'l
-0.009
0.0»;b
-0.030
0.163
0 . 0 4 b
0.040
-0.256
-0.150
-0,006
-0.114
-0.017
0 . 0 1 «
0.037
t FKOM LAST
ANI./CYL CAL
NONE (4)
WOfJE ( 4 )
KUlJt (4)
MUl»E ( 4 J
MUMt- ( 4)
NUliE (4)
NONE (4)
NONE (4)
NUM: ( 1 )
NCiiMfc ( i J
NONE ( 1 )
MONh ( 1 )
NONE ( 1 )
NONE ( 1 )
NONE ( 1)
N0(;l. ( 1)
NONL ( 1 )
NONE ( 1)
0.000
MI 'LAiFsr11 ANALYZEK CALIHKATJON ON FU.E iu THE QFS.
-------
PAGE 2
**** PROCESSED:
CAL.
EQUIPMENT TO
CAI. IBRiVi I ilf-l i-
TEST SITF ?".;
F:XO CAL ((<, 0
MINOR ivAS
**t **** -** + ** ****#**##**** *+*.>. + *.) **********
** t***+ * + + *##*.*###*#*#####** +***;< *.***;****.*,*
* + 4 * < *
*** ANALY7ER CALIBRATION CURVE ANALYSTS ***
t .* * *. * +
****.* *** .*******#*.**# *.** #.******** ***********
***#*****##***##*.#*. *.##*.**.***.#***. ****:**:#***#
i
I'
.1. ....
I EPA
I CYL .
I NUMl-.iEK
I A 10? 2
I 0.11£i:.'.9
[ ni.ii?1,'!
I 11:10. -.:';:;
i G lift ail!
I GllB'50
I l'mP62
I HI 06! 16
I H89462
I Gil 85 3
I 011858
I
I DO
I BIO
I B9
I B8
I B7
I F<6
I B5
I B4
I B3
I
I B2
I Bl
I
I VFfHMR
I CYL I;;OKR
I MUiU'il-.F'1
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I l.lr'l i-JlH-M.' ( 1 )
I. iif.i|-.iMiii.i,-i < i >
I UHK,"!i".!i-' ( 1 )
I LINK NO WM ( 1 )
1 UNK'WOWN ( 1 )
I UNKNOWN (!)
I UNKNOWN ( .1 )
I UNKNOWN (.1)
I UNKNOWN ( 1 )
I UNKNOWN ( 1 )
I
I UNKNOWN < 1 )
I UNKNOWN ( 1 >
I UNKNOWN ( 1 )
I JINK NO WM <1>
I UNKNOWN < 1 )
I UNKNOWN < t )
I UNKNOWN ( 1 )
I UNKNOWN ( 1 >
1 UNKNOWN < 1 )
I
I UNKNOWN < 1 )
I UNKNOWN ( 1 >
I
I
I
T
.1.
I
.1
1
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
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1
(1) CYLINDER NOT DEFINED
I
CONCENTRATIONS
KLEND I NAMED OR
K A l.i II I
- . - 'I
.1.
I
I
I
I
T
> T
T
T
I
-r
I
I
._ ._ 'I'
T
I
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I
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T
I
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I
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. T
I
N 1.1(1 IN At.
14.360
13.577
1 1. i 550
10.303
8.675
6.719
5.141
4.637
3.848
3 . 005
1,454
0 . 000
14.360
12.924
11.488
10.052
8.616
7.180
5.744
4 . 308
2.872
1.436
IN THE EQUIPMENT
LATEST
CYL. CAL
NONE < 1 )
NONE < 1. )
NONE ( 1 )
NONE ( 1 )
NONE ( 1 )
NONEU)
NONE < 1 )
NONE ( 1 )
NONE ( .1. )
NONEU)
NONEU)
NONEU)
NONE ( 1 )
NONE ( 1 )
NONEU)
NONE ( 1 )
NONE < 1 )
NONE ( 1 )
NONEU)
NONE ( 1 )
NONEU)
NONEU)
FILE SYSTEM
I
NEW I
CURVE I
_ r
14.360 I
13.581 I
11.532 I
10.320 I
8.673 I
6.718 I
5.139 I
4.635 I
3.854 I
3.002 I
1.455 I
I
0.00,0 I
14.360 I
12.911 I
11.434 I
9.992 I
8.523 I
7.078 I
5.664 I
4.243 I
I
2.842 I
1.427 I
I
I
I
I
T-
ANALY/ER DEFL. . I
MEAS.
X
- M
90.000
85.900
74.700
67.800
58.100
46.100
36 . 000
32.700
27.500
21.700
10.800
0.000
90.000
82.300
74.150
65.900
57.200
48.350
39.400
30.100
20.600
10.600
CORR. I
X I
C* T
* ~ .1
90.000 ICYL.
85.900 ICYL
74.700 ICYL
67.800 ICYL
58.100 ICYL
46.100 ICYL
36.000 ICYL
32.700 ICYL.
27.500 ICYL
21.700 ICYL.
10.800 ICYL
I
0.000 ICYL
90.000 ICYL
82.300 ICYL
74.150 ICYL
65.900 ICYL
57.200 ICYL
48.350 ICYL
39.400 ICYL
30.100 ICYL.
I
I'
DATA TYPE I
I
"
CURVE INPUT I
CURVE INPUT I
IMJRUF INPUT I
CURVE INPUT I
CURVE INPUT M
CURVE INPUT I
CURVE INPUT I
CURVE INPUT I
CURVE INPUT I
CURVE INPUT I
CURVE INPUT I
I
TO BE NAMED I
TO BE NAMED I
TO BE NAMED I
TO BE NAMED I
TO BE NAMED I
TO BE NAMED I
TO BE NAMED I
TO BE NAMED I
TO BE NAMED I
I
20.600 IOTHER CYL. PT. I
10.600 IOTHER CYL. PT. I
I
AVERAGE INPUT
DEVIATION FROM
I
DATA POINT I
THE CURVE I
CURVE FIT DEMI
FROM NAHED.-'NOM FNAI
'/. POINT 7.
-0.001
0.032
-0. 155
0. 165
-0.022
-0 . 000
- 0 .045
-0.041
0.159
-0.115
0.042
0 . 000
-0.001
-0. 102
-0.471
-0.597
-1 .086
-1 .436
-1.413
-1 .540
-1 .052
-0.635
0.071
I-ULI. -SCI.
--0. < >.>:!
0.027
-0. .1 1.0
0. 104
-0.01.2
-0.003
-0.014
-0,012
0.038
-0.021
0.004
0 . 000
-0.001
-0.081
-0.330
-0.365
-0.567
-0.622
-0.490
-0. -100
-0. 183
-0.055
0.031
AT '10 US
Z I-POM 1 A'M
ANI ,'CYI. C..I
Mi 'if-' Ft 4 )
r'. W< s)
f.'MHF'. !)
I'H WE* 4)
MI 'HE '. 0)
MI Ir-fE ( 4 )
N'.iME(4)
MODE < 4 )
KiiiHL- \ 1)
MOHE<4)
Mi)HE(-1)
NOME (I )
MOMEU )
NONEU )
NONEU )
Ml iNE < I )
llil^F i I >
NONE.U )
MI iNE ( 1 )
Mi INE ( 1 )
HONE< 1 )
NONE ( 1 )
0 . 000
(4) NO "LATEST' ANALYZER CALIBRATION ON FILE IN THE EPS.
PR I PI
SET THE TERMINAL 70 THE TOP OF PAGE AT THE BEGINNING OF EACH REPORT PAGE
PRESS TO START PRINTING. PRESS OR TO PREVENT PRINTING.
-------
02%
0
3.112
9.914
18.253
23.903
99.5
100
C3H8%
0
0.833
2.069
15.097
99.7
100%
C02%
0
0.9503
2.113
4.351
8.28
14.36
99.99
100
GAS
N2%
100
96.888
90.086
81.747
76.097
0.50
0
N2
100
99.167
97.931
84.903
0.3
0
N2%
100
99.049
97.887 >
95.649
91.72
85.64
0.01
VOLUME
(CO
1000
1000
1000
1000
1000
1000
11
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
MEASURED
TIME
(SEC)
104.90
105.05
105.47
106.12
106.75
112.66
"
104.39
104.60
104.86
108.00
121.20
105.7
105.8
106.1
106.7
107.5
109.5
129.5
THEORETICAL
FLOW RATE
(Q)CM3/SEC
9.533
9.519
9.481
9.423
9.369
8.876
'*
9.579
9.560
9.536
9.259
8.251
9.461
9.451
9.425
9.372
9.302
9.132
7.722
VIS (umix).
POISE @ 21 C
.1760 E-3
.176953 E-3
.1788015 E-3
.1815293 E-3
.1832114 E-3
.2044667 E-3
.206064 E-3
"
.1760 E-3
.1735742 E-3
.1701142 E-3
.141585 E-3
.0803749 E-3
.08029 E-3
.1760 E-3
.175349 E-3
.1746291 E-3
.1732498 E-3
.1709951 E-3
.1678784 E-3
.148001 E-3
.1480 E-3
RATIO
umix-UN2
0.0
0.9946
0.9843
0.9695
0.9606
0.8607
ft
0.0
1.013
1.035
1.243
2.190
0.0
1.003
1.007
1.016
1.029
1.048
1.189
RATIOxQN2
CM3/SEC
9.533
9.482
9.383
9.243
9.158
8.206
ft
9.579
9.713
9.910
11.907
20.130
9.461
9.495
9.535
9.611
9.738
9.919
11.251
NOTE: The viscosi-
ties of the gas
mixtures were
calculated using
Wilke's equation 10
from the Journal of
Chemical Physics,
Volume 18, Number 4
April 1950, "A Vis-
cosity Equation for
Gas Mixtures".
Table 9
-------
O
.01
V
V
i
...
.U/i
! i
i i
(]
1 !-
~r-
I
TT
! I
I I
tl
i i
~r
T+f-
\
\
M (')
(I ( J
in co
ro cxj
3 ^
7
9
C'J I I
-------
y
/
3<
-------
-------
Capillary Flow Mixing Method
Cm
Q2
./vvv\_
Qi
.cs
Ql + Q2
CM
Ql
./VVW.
Cm = concentration of mixture out
Cs = concentration of span or component gas
CZ = concentration of zero or balance gas
Ql = Flow rate of balance gas
Q2 = Flow rate of component gas
Figure 4
-------
'-Of
-------
C02 High Concentration Calibration Curve
__f pr_ S-TEC_ ?.:odol SG5-78 _Sj.;ir,d^rji C-* D1 vi fjg
u;::'i--.!-:;J:": :.. ;::..V±L'..::.
f^JiL:.::-::- « v 71". :..:::.:. '
^r^iCto- full_scale)_
-0.
34-
. ;.- - -i -::-;-: <- ..\^-.- }
This "curve 'shows "applicable' calibration curve-" when hicjh"Concenti'atiort
' staiidaTd-ga5"i'?"us'eit'l:oir.';rodqr-SGD=7S-Standa-rd- Gas-Dividcr-r
o ID* i\'.
~i P'OTian inr-tanccr '-vhcn'fi standard"ints-of !&?& CO^ is-uscd-and-thc
vidinv^-iacror-is-soi -at- 5,thc-coriC-c-.tration-ratio rc.iil*- as-0-f'0t>
.i.-frum the curve, ao thru the conccncrucion which is actually generated-.A j,L
determined fi-om 10 x O.if.'Go = S.L't",")^.
STANDAT\D T^CJINOT.f)C',V INC
- .. Kvnrrn. -IAI-.'.:;
-------
518
C . R . \V I L K E
* All data at atmospheric pressure.
M. Trauu and H. E. BenUele. Ann. d. Phytik 5. 561 (1930).
» M. Trauu and K. F. Kipphan. Ann. d. Pliysik 2. 743 (1929).
M. Trauu and A. Melster. Ann. d. Physik 7. 409 (1930).
« M. Trauu and K. G. Sore. Ann. d. Physilt 10. SI (1931).
J. \V. Buddenbers. M.S. thesis. University oi California (1948). Data
determined relative to Ns.
' M. Trauu and F. Kurz. Ann. d. Physik 9. 992 (1931).
bined* to eliminate the diffusion coefficient from the
1*1
1+-
1+
(10)
To offer a severe test of Eq. (11) a number of binary
systems exhibiting highly irregular and dissimilar vis-
cosity-concentration curves were selected from the
literature. These data are plotted and compared with
the calculated curves in Fig. 1. Properties of the pure
components and literature sources for these systems
are given in Table I. It is believed that the close corre-
pbndence between these calculated and observed data
indicates the ability of Eq. (11) to reproduce gas
viscosity behavior with sufficient precision for most
purposes. The average deviation between calculation
and experiment for the data shown in Fig. 1, excluding
terminal points, is 0.97 percent. Prediction of the hy-
drogen-argon curve is the least satisfactory, and by ex-
cluding these data the average deviation between calcu-
lated and experimental points is reduced to 0.49 percent
For ideal gas behavior, Eq. (10) may be reduced to the
relatively simple expression:
240
Equation (11) constitutes the final recommended rela-
tion for binary mixtures. This relation is relatively
convenient to use, requiring only the molecular weights
and viscosities of the pure components for the predic-
tion of the entire viscosity concentration curve. It
should be noted that the equation contains no empirical
Values of ft; and 5: need not necessarily be viewed as equal
to a single value of 3 in corr.binini; (3) and' (9;, hut rather that
l3 = 3\, in Calculating D;-.. and ^ = 3: ir. calculating D-\. Thus it is
possible that errors due to deviations between 0i and £» may for-
tuitously cancel in each of the partial viscosity terrus in (3).
Colculoled Curves
0 0 £ '+ Eiperirrientol Dot a
.2 A .6 .8 1.0
Mole Fraction of Firs! Gas
Fic. 1. Comparison of calculated and experimental
viscosities for some binary mixtures.
w> 1O
TABLE I.
Gas pair
He-A
NVO-
C;Hc-C>Hs
H-CCi:F.
H-C»H,
HrA
Ne-A
Xe-He
He- A
XYCO:
HrCO:
HrNt
Ne-CO.
Xe-CCl:F.
Xe-X.
COrCCl.F;
XrCCljF.
Properties of gases used in Fig.
,oc
.20
27
250
25
26.9
20
200
200
200
25
25
25
25
25
25
25
25
1 and Table II.'
TABLE II. Calculated and experimental data for
: muiticomDonent mixtures.
it\ X101 M:X10* *» . *r viscosity data
197.3
178.1
152.6
SS.4
89.1
87.5
422.0
422.0
267.2
176.8
S8.4
8S.4
313.3
313.3
313.3
176\8
221.1
205.7
136.3
124.0
81.7
221.1
320.8
267.2
320.8
147.8
147.8
176.8
147.8
124.0
176.8
124.0
124.0
2.417
0.994
1.276
3.943
3.674
1.S70
1.606
0.4862
2.318
1.368
2.470
1.903
2.250
3.987
1.612
1.751
2.358
0.2716
1.014
0.779
0.0920
0.1539
0.23S4
0.6166
1.552
0.2789
0.7281
0.1977
0.2750
0.5011
0.2628
0.6552
0.5351
0.3830
a,b
c
d
e
f
a
a
a
a
e
e
i.°C Ne
Volume percent 01
A He H:
components
CO: X: CChF.
200 31.93 32.13 . 35.94
25 33.33
25
25
25 25.00
25
See Table I
» See Tabie I
. reference b.
. reference e.
numerical constants,
the kinetic
theory-
33.33
33.33
25.00
25.00
the
33.33
33.33 33.33
33.33 33.33 33.33
25.00 25.00
25.00 25.00 25.00
Viscosity X101.
"calc ^exp
360.0 3S7 4.
190.2 18j!7» !
145.7 Hb9a {
144.6 Usi8» '
159.3 168 >
146.7 U7!l»
constant 4/V2 coming from
1
COMPARISON OF CALCULATED WITH
EXPERIMENTAL DATA
-------
02%
0
3.112
9.914
18.253
23.903
99.5
100
C3H8%
0
0.833
2.069
15.097
99.7
100%
C02%
0
0.9503
2.113
4.351
8.28
14.36
99.99
100
GAS
N2%
100
96.888
90.086
81.747
76.097
0.50
0
N2
100
99.167
97.931
84.903
0.3
0
N2%
100
99.049
97.887
95.649
91.72
85.64
0.01
VOLUME
(CO
1000
1000
1000
1000
1000
1000
11
1000
1000
1000
1000
1000
1000
(I
1000
1000
1000
1000
1000
1000
1000
MEASURED
TIME
(SEC)
104.90
105.05
105.47
106.12
106.75
112.66
M
104.39
104.60
104.86
108.00
121.20
it
105.7
105.8
106.1
106.7
107.5
109.5
129.5
THEORETICAL
FLOW RATE
(Q)CM3/SEC
9.533
9.519
9.481
9.423
9.369
8.876
11
9.579
9.560
9.536
9.259
8.251
ti
9.461
9.451
9.425
9.372
9.302
9.132
7.722
VIS (Umix)d
POISE @ 21 C
.1760 E-3
.176953 E-3
.1788015 E-3
.1815293 E-3
.1832114 E-3
.2044667 E-3
.206064 E-3
i*
.1760 E-3
.1735742 E-3
.1701142 E-3
.141585 E-3
.0803749 E-3
.08029 E-3
.1760 E-3
.175349 E-3
.1746291 E-3
.1732498 E-3
.1709951 E-3
.1678784 E-3
.148001 E-3
.1480 E-3
£/ RATIQ4/
ifmix-jjNJ
0.0
0.9946
0.9843
0.9695
0.9606
0.8607
f*
0.0
1.013
1.035
1.243
2.190
ii
0.0
1.003
1.007
1.016
1.029
1.048
1.189
' !/- (L<
RATfl5xON2
GM3/SEC
9.533
9.482
9.383
9.243
9.158
8.206
"
9.579
9.713
9.910
11.907
20.130
9.461
9.495
9.535
9.611
9.738
9.919
11.251
sty/ /S £ ^~
NOTE: The viscosi-
ties of the gas
mixtures were
calculated using
Wilke's equation 10
from the Journal of
Chemical Physics,
Volume 18, Number 4
April 1950, "A Vis-
cosity Equation for
Gas Mixtures".
Table 9
-------
UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
ANN ARBOR. MICHIGAN 48105
OFFICE OF
AIR. NOISE AND RADIATION
June 18, 1982
SUBJECT: Gas Divider Evaluation
FROM: Sherman D. Funk tp"'
Engineering Staff
MEMO TO: C. Don Paulsell
Chief, Engineering Staff
An evaluation project and report have been completed on the gas
divider for use as a calibration device for our exhaust analyzers.
It has been determined that this type of instrument may be used
instead of a full complement of gas cylinders to produce accurate
calibration curves. An empirically-established divider ratio is
needed for C02- Use of a divider can result in considerable
savings in manpower and funds. Potential accuracy is on the order
of +0.5% of point.
It is recommended that EOD pursue the development of new
analyzer calibration procedures using the gas divider.
A copy of the report on this project will be circulated and will
be available from the Gas & Chemical Analysis Group or the
Engineering Staff.
cc: G. Reschke
J. Carpenter
R. Lawrence
R. Gilkey
K. Heiss
------- |