6EPA
United States
Environmental Protection
Agency
Environmental Sciences
Research Laboratory
Research Triangle Park NC 27711
EPA-600/2-78-214
November 1978
Research and Development
Polymeric
Interfaces for
Stack Monitoring
-------
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 ENVIRONMENTAL PROTECTION TECH-
NOLOGY series. This series describes research performed to develop and dem-
onstrate instrumentation, equipment, and methodology to repair or prevent en-
vironmental degradation from point and non-point sources of pollution. This work
provides the new or improved technology required for the control and treatment
of pollution sources to meet environmental quality standards.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/2-78-214
November 1978
POLYMERIC INTERFACES FOR STACK MONITORING
by
Richard M. Felder and James K. Ferrell
Department of Chemical Engineering
North Carolina State University
Raleigh, North Carolina 27607
Grant No. R-801578
Project Officer
James B. Homolya
Emissions Measurement and Characterization Division
Environmental Sciences Research Laboratory
Research Triangle Park, N. C. 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
-------
DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U. S. Environmental Protection Agency, and approved for
publication. Aprroval does not signify that the contents necessarily
reflect the views and policies of the U. S. Environmental Protection
Agency, nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
ii
-------
PERFACE
Traditional methods of monitoring gaseous pollutant concentrations
in process and power plant stacks involve grab sampling and wet chemical
analysis. In recent years, the need to assemble large quantities of
monitoring data to demonstrate compliance with federal emission standards
has led to the development of automatable techniques for continuous
sampling and analysis. A drawback associated with these techniques is
the need to remove particulate matter, water, and other condensable
vapors from the samples; a related problem is the difficulty of assuring
that the conditioned sample is truly representative of the stack gas, since
the conditioning steps could very likely alter the concentration of the
pollutant in the sample gas.
In 1973 a three-year developmental study was undertaken by the North •
Carolina State University Department of Chemical Engineering on the use of
polymeric interfaces for continuous monitoring. Candidate interface
materials for S0? monitoring were screened, gas transport properties needed
to design interfaces for specific applications were measured, and field
tests were performed in several stack environments. This report outlines
the experimental and calculational procedures followed in this study, and
summarizes the results and conclusions.
n
-------
ABSTRACT
This research program was undertaken with several objectives in mind.
1. To screen candidate polymeric materials for use as in-situ stack
monitoring interfaces, and to define and measure the gas transport
properties of these materials needed to design interfaces for
specific applications.
2. To design and field test interfaces in a variety of stack
environments, and to demonstrate their ability to yield accurate
monitoring data over extended periods of time.
3. To demonstrate the effects (or lack of effects) of such parameters
as stack temperature , liquid and solid particulate loading, and
stack gas humidity on the performance characteristics of polymeric
interfaces.
A laboratory system was constructed which permitted the simulation
of any desired stack gas environment at temperatures from ambient to
200°C. Polymer membranes or hollow tubes were inserted in the system, and
their SOo permeabilities and diffusivities were measured. The results were
used to design interfaces for field tests; they were also interesting in
and of themselves, since almost no S02 transport properties had previously
been reported at temperatures above about 35°C.
A portable field monitoring system based on the permeable interface
concept was designed and constructed, and was used to carry out SOg
monitoring runs in two SO- absorption tower stacks, and in oil-fired and
coal-fired power plant stacks. The Teflon interfaces used in these tests
performed extremely well, yielding continuous data in excellent agreement
with data obtained by grab sampling and wet chemical analysis using
Federal Register Method 6. The interfaces provided sample gases with SCL
concentrations that varied linearly with the SCL concentrations in the
stacks; the presence of water vapor, acid mist, and solid particulate
matter in the stack gasas had no effect on the performance of the
interfaces, and fluctuations in the stack concentrations were mirrored
accurately in the measured responses. The field test results suggest the
potential value of the in-situ polymeric interface approach for monitoring
in stack environments too dirty or corrosive for conventional continuous
monitors.
In the course of the research, a new method for measuring diffusiv-
ities of gases in polymers was developed and applied to the determination
of SCL diffusivities, and the effects of plasticizers on the permeabilities
of pofyvinylidene fluoride membranes to S02 were determined.
This report is submitted in fulfillment of Grant No. 801578 by
North Carolina State University under the sponsorship of the U. S.
Environmental Protection Agency. The report covers the period January 1,
1973 to May 31, 1976.
IV
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CONTENTS
Preface- - Hi
Abstract-- - ---1v
Figures -vi
Tables -,-—- -- -,— viii
Acknowledgements '-- - 1x
1. Introduction 1
2. Conclusions 2
3. Recommendations •. 4
4. Permeation of Sulfur Dioxide through Polymers 5
4.1 Theory and preliminary experiments 5
4.2 Compilation of permeability data 8
4.3 Humidity effects - 8
4.4 Plasticizer effects --- 10
5. Permeation of Nitrogen Oxides and Water through Polymers 17
5.1 Permeation of nitrogen oxides 17
5.2 Permeation of water 19
5.2.1 Literature Survey 19
5.2.2 Permeability measurements 19
6. Field Tests of Stack Monitoring Interfaces 20
6.1 Stack monitoring system 20
6.2 Summary of results 23
6.2.1 $03 absorption tower stack: single contact process-- 23
6.2.2 503 absorption tower stack- double contact process-- 23
6.2.3 Oil-fired power plant boiler stack 25
6.2.4 Coal-fired power plant boiler stack 25
6.3 Conclusions-- - — 28
7. Measurement of Gas Diffusivities in Polymers 29
7.1 Procedure for diffusivity measurements 29
7.2 Diffusivities of sulfur dioxide 30
References 31
Appendices'
A. Permeation of Sulfur Dioxide through Polymers T 32
B. Effect of Moisture on the Performance of Permeation Sampling
Devices 66
C. Permeation Data for NOX and H^O— - 84
D. Polymeric Interfaces for Continuous S0£ Monitoring in Process
and Power Plant Stacks - - 105
E. A Method for the Dynamic Measurement of Diffusivities of Gases
in Polymers 129
F. A Method of Moments for Measuring Diffusivities of Gases in
Polymers • 147
v
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FIGURES
Number Page
1. Schematic of laboratory apparatus 6
2. Flux vs. Ap isotherms for SO- in an FEP Teflon membrane 7.
3. Arrhenius plot of S02 permeabilities for an FEP Teflon membrane-- 9
4. Membrane permeation chamber -- 11
5. Effect of sulfolane on permeability of Kynar films 13
6. Effect of sulfolene on permeability of Kynar films- 14
7. Effect of total pressure on SCL permeability of plasticized and
unplasticized Kynar films 15
8. Schematic of stack monitoring system 21
9. Monitoring data: Single contact process stack 24
10. Monitoring data: Double contact process stack 26
11. Monitoring data: Oil-fired boiler stack 27
-------
TABLES
Number Page
1. Permeabilities of plasticized and unplasticized films 12
2. Field test parameters 22
VII
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ACKNOWLEDGMENTS
The experimental work carried out in the course of this project
was initiated by Mr. Charles Rodes and was carried on by Dr. Roger
Spence and Mssrs. James Spivey, Lanny Treece, and Chen-Chi Ma. The
contributions of the two grant monitors during the course of the
project—Mr. Rodes and Mr. James Homolya--are gratefully acknowledged.
VI 11
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SECTION 1
INTRODUCTION
Most of the work described in the abstract of this report has been
pulbished in a series of journal articles which are included as appen-
dices. The main body of the report provides a detailed summary of the
published work and an exposition of results which have not yet been
published.
The organization of the report is as follows. Sections 2 and 3 sum-
marize conclusions and recommendations. Section 4 surveys measurements
of S02 permeability, and section 5 reviews permeation of oxides of nitro-
gen and of water through polymers. Section 6 summarizes the results of
SO- monitoring field tests. Section 7 ourlines the derivation of a tech-
nique developed in this study for the measurement of gas diffusivities,
and summarizes the SO- diffusivities measured using this technique.
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SECTION 2
CONCLUSIONS
Portable systems based on in-situ polymer interfaces can be used
to monitor stack gas S02 .concentrations ranging from tens to thousands
of parts per million. The technique yields reproducible results, and
provides continuous analyses that agree well with readings obtained by
grab sampling and standard wet chemical analysis.
The presence of water vapor in a stack gas does not effect the rate
of permeation of S02 through the interface, so that the analyzer reading
need not be corrected for the stack gas humidity. Moreover, Teflon is
sufficiently impermeable to water to preclude the possibility of conden-
sation in the sample line or the analyzer. There is consequently no
need for heated sample lines, cold traps, or drying columns in the
sampling train.
The presence of liquid or solid particulate matter including acid
mist in the stack gas has no measurable effect on the performance of the
interface; using a Teflon interface, therefore, eliminates the need for
frequent filter changes, making long-term unattended continuous monitoring
in exceptionally dirty and corrosive environments a good possibility.
Responses obtained using polymer interfaces follow changes in the
stack gas S0£ concentration accurately and rapidly, suggesting the
potential applicability of such devices as feedback control loop compon-
ents.
The only observed drawback to the use of polymeric interfaces is
that the sensitivity of the interface permeability to the stack gas
temperature makes continuous correction for temperature fluctuation
necessary. However, the nature of the temperature dependence is well
established, and automatic temperature correction can easily be achieved
using modern microprocessor technology.
A gas transport model based on Henry's law for solution and Pick's
law for diffusion correlates permeation data well for pollutant concen-
tration levels characteristic of those found in stacks, making calibration
of interfaces a straightforward task.
Sulfolane, sulfolene, and N, N, N', N1, tetra-phenyl-p-phenyldiamine
(TPD) were used to plasticize polyvinylidene fluoride (Kynar) membrajjes,
and the permeabilities of the plasticized membranes to S02 were measured
over a range of temperatures. No significant permanent increase in S02
permeability was found which could be attributed to the addition of
sulfolane or TPD; when increases were observed, they were either temporary
or the results of overplasticization. Permeability increases of up to 80%
were obtained when sulfolene was used as a plasticizer.
-------
A method of moments for determining the diffusivity of a gas in a
polymer has been formulated and its validity has been verified experiment-
ally. Diffusivities are important quantities in the context of this
research, since they determine the time response of permeable interfaces;
moreover, the diffusivity is the primary variable governing the perfor-
mance of plastic grab sample containers, and of permeation tubes for
analyzer calibrations, so that the technique developed could have
benefits to environmental technology well beyond the scope of this study.
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SECTION 3
RECOMMENDATIONS
The results of the field tests performed to date suggest the
potential usefulness of polymeric interfaces for continuous stack
monitoring for S0£. Future efforts should be directed toward
exploring the range of conditions in which devices of this sort can
function, with particular emphasis on traditionally difficult-to-
monitor environments such as those found in ore smelting processes,
pulp mills, and flue gas scrubbers.
The technique should be extended to other pollutants, such as NOX,
CO, H2S, and various hydrocarbons. The use of interfaces for selective
monitoring of specific pollutants in mixtures should be studied;
included in this investigation would be the use of plasticizers or
other additives to enhance the permeabilities of polymers to selected
mixture comoonents.
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SECTION 4
PERMEATION OF SULFUR DIOXIDE THROUGH POLYMERS
4.1 THEORY AND PRELIMINARY EXPERIMENTS
The relationship between the concentration of a pollutant in a stack
gas and the rate of penetration of the pollutant into a polymeric inter-
face is governed by the permeability of the oolymer to the pollutant.
(Crank and Park, 1963) By definition, the permeability P is the ratio
J/(Ap/h), where J is the flux of the penetrating gas through a flat
membrane of thickness h, and Ap is the partial pressure difference
across the membrane. The permeability depends on temperature according
to the Arrhenius law
P =
exp(-Ep/RT)
(4.1)
where
P = permeability, cm (STP)/s.cm.cm Hg
P = preexponential factor, units of P
E = activation energy for permeation, cal/g-mole
R = gas constant, 1.987 cal/g-mole.°K
T = temperature, °K
The solution of the steady state diffusion equation yields the
relationship between the permeation rate [cm3(STP)/s] and the partial
pressure driving force Ap. For a flat membrane of cross sectional area
A (cm2) and permeability P[(cm3/STP)/s.cm-cmHg]
= PAAp
(4.2)
and for a hollow cylindrical tube of inner radius a and outer radius b,
_ 2irPAp
TnTb/a
(4.3)
In a preliminary series of experiments, SO? permeabilities were
measured for several polymers at temperatures between 120°C and 230°C,
using an apparatus shown schematically in Figure 1. Span gas mixtures
of SOo and air with S02 concentrations between 100 and 10,000 ppm were
passed on one side of a flat polymer membrane or on the outside of a
hollow tube in a thermostatically-controlled oven. S02 permeated
through the polymer into a carrier gas stream of dry air. The carrier.
gas and the S02 that permeated, into it passed to a flame photometric
detector, and the S0£ concentration was recorded. The S02 permeation
rate was calculated as the product of the carrier gas flow rate and the
S02 concentration.
Experiments of this type were carried out at a fixed temperature for
several span gas S02 concentrations, and plots of $ vs. the appropriate
function of Ap (see Eqs. 4.2 and 4.3) were used to determine the permea-
bilities. Representative plots are shown in Figure 2.
-------
CT>
Constant Head Tank
I
Water
Rotameters
Span Gas
Rotameters
Dilution Air
Rotameters
U
Hygrometer
Oven
Membrane
Chamber
Vent
Vent
Carrier Gas Rotameters
Participate Activated
Filter Carbon Desiccant
Vent
Figure 1. Schematic of laboratory apparatus
-------
p • h f cm(Hg).cm
Figure 2. Flux is Ap isotherms for SOp in an FEP Teflon membrane.
-------
Portabilities determined in this manner were plotted against
reciprocal temperature, and the slopes were used to determine the
activation energy for permeation. A representative Arrhenius plot of
this tyoe is shown in Figure 3.
Once the permeability vs. temperature functionality is known for
a polymer, Eq. (4.1) and either (4.2) or (4.3) can be used to design
an interface for any soecified stack oas temperature and S00 concen-
tration range.
Experiments of the type described above were carried out in the
research which was the precursor to the grant research. (Rodes,
Felder, and Ferrell, 1973). It was established in this work that the
theoretical relations of Eqs. (4.1)-(4.3) are valid, and therefore that
the concentration of S02 in a sample gas obtained using a polymer inter-
face can be easily and accurately correlated with the S02 concentration
in the stack qas itself.
4.2 COMPILATION OF PERMEABILITY DATA . .
An extensive series of S02 permeability measurements was undertaken
to screen candidate materials for polymer interfaces. Both thin
membranes and hollow tubes were tested; the $02 concentration in the
span gas was varied between 50 and 15,000 ppm and the temperature was
varied from roughly 30°C to 230°C.
A compilation of S0? permeabilities measured in these experiments
and other permeabilities located in the literature search through April
1974 was assembled by Spence (1975); this compilation, along with a
survey of observed temperature, pressure, humidity, and membrane
plasticizer effects on S02 permeabilities, was published by Felder,
Spence, and Ferrell (1975a).*
Several noteworthy results emerged in these studies. The SOo permea-
bilities of TFE and FEP Teflon are of comparable magnitude, contradicting
published assertions to the contrary. Silicone and fluorosilicone rubbers
are 10-100 times more permeable to S02 than is Teflon, but they are also
subject to embrittlement when exposed to acid mists. A transport model
based on Henry's law for solution and Fick's law for diffusion correlates
data well for many polymers at pressures of 1 atm or less, but deviations
are likely to occur at higher pressures.
4.3 HUMIDITY EFFECTS
A major question regarding the feasibility of polymeric stack sampling
interfaces was the potential effect of the stack gas humidity on their
performance. Two possible deleterious effects were envisioned: first,
water might permeate through the membrane, condense, and absorb SOp from
the sample gas, leading to an erroneous analyzer reading; second, the
presence of the water could alter the permeability of the interface to
SOo (possibly by swelling the oolymer), again causing an erroneous
reading.
*Attached as Appendix A
-------
*i
O
O
o
\ I I I I I I
I I
I I I I
I J | i i_ I I I
Figure 3. Arrhenius plot of SO^ permeabilities for an FEP Teflon membrane.
-------
The problem was studied by measuring Sf^ permeabilities using snan
gases containing up to 20% water by volume. In all cases studied,
neither of the anticipated effects was observed; the water permeation
rate was sufficiently low to preclude condensation in the sample gas
line, and the effective S02 permeabilities of the tubes (TFE Teflon, FEP
Teflon, and a fluorosilicone rubber) were unaffected by the presence of
the water. This work is described in detail by Spivey (1974), and is
summarized by Felder, Ferrell and Spivey (1974).*
4.4 PLASTICIZER EFFECTS
One of the potential uses of polymer interfaces is to achieve a
selective separation of components in a stack gas mixture. A way of
enhancing this effect is to incorporate a material into the polymer
which preferentially dissolves the species to be monitored, thereby
increasing the effective permeability of the polymer to that species.
This technique was investigated by Seibel and McCandless (1974),
who used polyvinylidene fluoride (Kynar) membranes plasticized with
sulfolane (tetrahydrothiophene 1,1,- dioxide) to separate S02 from
S02-N2 mixtures, and found that the addition of the plasticizers did
indeed increase the selectivity of the separation.
An additional study of this effect was carried out in our laboratory
in collaboration with James Homolya of the Environmental Protection
Agency, Research Triangle Park, N. C. Under Mr. Homolya's direction,
Kynar films were cast using three plasticizers—sulfolane, sulfolene
(2-5 dihydrothiophene 1, 1-dioxide), and N,N,N',N' tetraphenyl-p-phenyl-
diamine (TPD)--and the S02 permeabilities of these films and of
unplasticized Kynar films were measured at several temperatures. The
plasticized membranes were cast with compositions of 10$ and 25%
sulfolane (by weight), 10% and 25% sulfolene, and 5% TPD. All of the
membranes tested were cured at 75°C except the pure Kynar, which was
cured at 105°C. The thickness of each membrane was measured at 10
different points with a micrometer, and the average of the measured
values was used in the permeability calculation. The membrane thicknesses .
varied between 1 and 3 mils (0.0025-0.0075 cm).
The permeabilities of SOp through the various membranes were determined
at temperatures from 25°C to 65°C using the permeation chamber shown in
Figure 4. The results are shown in Table 1 and in Arrhenius plots in
Figures 5 (for sulfolane) and 6 (for sulfolene). In addition, Figure 7
shows permeabilities calculated from the data of Seibel and McCandless
(1974) and from our results plotted against the gauge pressure on the
high concentration side of the membrane.
The consistency between the permeabilities obtained by Seibel and
McCandless at pressures between 100 and 500 psig and those we obtained
at atmospheric pressure is excellent. The permeability of the unplasti-
cized film apparently remains independent of the chamber gas pressure up
to approximately 400 psig, while that of plasticized film begins to
increase at a much lower oressure. The increases in P due to the
Attached as Appendix B
10
-------
1-3/8"
A - Carrier gas inlet
B - Span gas inlet
C - Carrier gas inlet port (two tangential ports located diagonally)
D - Span gas inlet port (two tangential ports located diagonally )
E - Carrier gas outlet port (exits from center then bends 90° to come out
front of chamber)
F - Span gas outlet port (exits from center then bends 90° to come out
front of chamber)
G - Thermocouple tap
H - Pressure tap
I - Membrane
J - Notch for C-clamp
K - Guide posts
L - Set screw
Figure "t. Membrane permeation chamber
-------
Table 1. Permeabilities of plasticized
and unplasticized films
curing temp.
plasticizer temperature( "(')• thickness (cm)
permeability
10~iU
none
none
none
none
10% sulfolane
10% sulfolane
10% sulfolane
10% sulfolane
10% sulfolane
10% sulfolane
10% sulfolane
10% sulfolane
25% sulfolane
25% sulfolane
25% sulfolane
25% sulfolane
25% sulfolane
25% sulfolane
25% sulfolane
25% sulfolane
5% TPD
10% sulfolene
10% sulfolene
10% sulfolene
10% sulfolene
10% sulfolene
10% sulfolene
25% sulfolene
25% sulfolene
25% sulfolene
105
105
105
105
75
75
75
75
75
75
105
105
75
75
75
75
75
75
75
75
75
75
75
75
105
105
105
75
75
75
.00417
.00417
: 004 17
.00417
.00315
.00315
.00315
.00315
.00338
.00338
.00411
.00411
.00244
.00244
.00244
.00244
.00244
.00244
.00284
.00284
.00696
.00335
.00335
.00335
.00315
.00315
.00315
.00424
.00424
.00424
39
45
55
65
39
43
53
56
43
56
48
62
27
32
42
48
55
58
30
59
32
43
50
54
40
52
63
43
48
54
3.20
4.62
7.56
12.2
4.84
4.31
9.05
8.32
5.28
10.0
5.74
12.2
14.6
14.1
15.6
18.0
21.9
21.5
13.2
21.4
2840
4.22
6.09
7.77
4.53
10.2
17.3
5.27
6.79
8.61
12
-------
o
o
X
*=*k
*=**
O)
20.0
g 10.0
5
u
OJ
a.
c—
to
^aS*
CO
E
u
CN
o
to
-Q
O
Q>
E
L.
a>
a.
8.0
6.0
4.0
2.0
After 10 days
O
20 days
a
0 /o Sulfolane
10% Sulfolane
Memb. 1
10% Sulfolane
Memb. 2
25 % Sulfolane Memb. 1
25 % Sulfolane Memb. 2
10% Sulfolane Cured at 105 °C
«<— After 20 days
i
2.9
3.0 3.1 3.2 3.3
10007 T <°K"1)
Figure 5. Effect of sulfolane on permeability
of Kynar films
13
-------
40.0
o
X
V 20.0
u
0)
-------
7 50
0 % Sulfolane
8.2% Sulfolane
Seibel & McCandless, 1974
Seibel & McCandless, 1974
Experimental
Experimental
100
200 300
Permeator Pressure (psig)
400
500
Figure 7. Effect of total pressure on S02 permeability
of plasticized and unplasticized Kynar films
-------
addition of the sulfolane observed by Seibel and McCandless were
consequently due in large part to the pressure range in which they were
operating; as Figure 7 shows, the effect is much less dramatic at
atmospheric pressure.
Complete details about the experimental measurements made in these
studies are provided by Treece (1975); the principle results are
summarized below.
1. The addition of 10% sulfolane to vinylidene fluoride resins initially
increased the S02 permeability of the cast films by 25% to 50% above
that of a pure Kynar membrane. The increase was reversible, however,
and after 20 days the permeability of the plasticized film was
approximately equal to that of pure Kynar. The decrease could be
due to a deterioration of the plasticized film at the higher temper-
ature of the study, but in view of the eventual coincidence of the
plasticized and unplasticized membrane permeabilities an evaporative
loss of the plasticizer is a more likely explanation.
2. Addition of 25? sulfolane led to an increase in S02 permeability by
a factor of 3 to 8, and to an apparent decrease in the activation
energy for permeation. The increase was reproducible and irreversible.
This result is consistent with the results presented by Seibel and
McCandless, who found large flux increases for sulfolane contents of
15% and higher. This fact and the fact that these authors did not
observe any separation of S02 and N2 for membranes containing 20%
sulfolane suggests that overplasticization occurred at and above 15%
sulfolane, resulting in the occurrence of pinhole leaks.
3. The effect of sulfolane addition on S02 permeability was less in our
low pressure studies than in the higher pressure studies of Seibel
and McCandless.
4. Addition of 10% sulfolene had a negligible effect on S02 permeability,
and addition of 25% sulfolene led to a permanent increase of up to
80% in permeability.
5. Very high fluxes of S02 were observed for the membranes plasticized
with TPD, probably due to a combination of swelling and the occurrence
of pinhole leaks.
The conclusion derived from these studies is that membrane plasticiza-
tion can be used to increase selective separation, and that sulfolene is
a potentially useful plasticizer for S02 monitoring applications, but
caution must be exercised when implementing the technique since over-
plasticization can easily negate any positive effects of the plasticizer
on the interface performance.
16
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SECTION 5
PERMEATION OF NITROGEN OXIDES AND VIATER THROUGH POLYMERS
The extent to which water is screened out of a sample gas by a
polymer interface is governed by the permeability of the polymer to
water. A limited literature search on water permeabilities was
carried out, and permeabilities were measured in our laboratory for
interface materials used in the S02 measurements described in the
previous section. In addition, a literature search on NCx permeation
was carried out in anticipation of the use of polymer interfaces for
monitoring this pollutant.
The results of the literature searches are reported in detail in
Appendix C. The following sections summarize the principle findings,
and report on the results of the water permeability .measurements -carried
out in our laboratory.
5.1 PERMEATION OF NITROGEN OXIDES
Almost all reported permeation data are for the N0£ - ^4 system,
whose equilibrium under ideal conditions is given by
(PNO )2
- — = 7.1xl09 exp (-14,600/RT) • (5.1)
(Getman and Daniels, 1946). A degree of uncertainty is associated with
almost all permeation data for this system, reflecting an uncertainty
about which species was in fact permeating.
Pasternak et.al. (1970) showed that a nominal permeability
PN09 PNO, + 2 PN90, PN90,
P = - ? - 2- - L* - Li. (5.2)
Ptot
may be determined from permeation rate data, but that there is no way to
determine P..n or PM n from data taken at a temperature where both sub-
MU2 24
stances are present. The authors overcame this difficulty by carrying out
runs using TFE membranes at temperatures above 100°C, where the gas could
be assumed to be pure NOp. An Arrhenius function fit to the P^Q data was
extrapolated to lower temperatures, P.. n was determined as a function of
N2U4
temperature from the measured values of P^r. and the extrapolated values
of P,,n using Eq. (5.2), and an Arrhenius function was then fit to the
NUrt
NpO. permeabilities. The results are shown in Table 1 of Appendix C
along with other published Arrhenius parameters for NO^^O. permeation
through TFE and FEP.
17
-------
Permeability data are given in Appendix C for N0?, N?0 and NO in
dimethyl silicone membranes at 25°C. The reported NO permeability of
dimethyl silicone is seen to be an order of magnitude less than the
NOp permeability.
The remaining NO permeabilities given in Table C2 were obtained at
temperatures in the range 20 - 40°C with a vapor-liquid equilibrium
mixture of N02 - N?0. on one side of the membrane. The flux of NO
through a membrane can be calculated from the effective permeability in
the table from the following relations.
1. Flat membranes of thickness h (cm)
Fm (cm3 N02(STP)/cm2.s) = Pfi h(pNQ + PN 0 ) (5.3)
2. Hollow tubes: inner radius = r, (cm), outer radius = r2 (cm)
Ft (cm3 N02(STP)/cm.s) = 2 *Pe(PNO + PN 0 )/ln (r^) (5.4)
18
-------
5.2 PERMEATION OF HATER
5.2.1 Literature Survey
A large body of data exists for the permeation of water through
polymers. Hater oermeabilities, diffusivities and solubilities for a
number of materials are listed in Table C.3, Appendix C, and activation
energies for permeation and diffusion are given in Table C.4, Appendix C.
5.2.2 Permeability Measurements
Water permeabilities were measured in tubes of TFE Teflon, FEP Teflon,
and fluorosilicone rubber. The experimental apparatus was that shown in
Figure 1, with the addition that metered water was vaporized with
electrical heating tape, and fed into a tee in the span gas line. The
concentration of water in the sample gas was measured with a Panametrics
Model 2000 continuous flow hygrometer. Additional details are given by
Felder, Ferrell, and Spivey (1974).*
The results of these studies, which are given in Appendix C,
parallel those for SO,,. Water permeabilities in TFE and FEP Teflons are
comparable, both being an order of magnitude less than that in the fluoro-
silicone rubber. In all cases, the results show that using any of the
tested materials as a polymer interface would provide a sample gas with
a dew point well below ambient temperatures, so that condensation in the
line to the analyzer could not possibly occur. For example, if a
fluorosilicone rubber tude were used to monitor a stack gas at 177°C with
a dew point of 61°C, the dew point of a carrier gas flowing at 655 cm^
(STP)/min would be -29.5°C, and would be even lower if a Teflon tube were
used.
*Attached as Appendix B.
19
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SECTION 6
FIELD TESTS OF STACK MONITORING INTERFACES
A program of stack monitoring field tests was carried out in parallel
with the laboratory permeability measurements. In most of these tests,
Teflon tubes or membranes were used as interfaces in 1-day or 2-day S02
monitoring runs. The principal results of these tests are summarized in
this section.
6.1 STACK MONITORING SYSTEM
A portable interface system was designed and constructed for
continuous stack monitoring tests. A diagram of the interface configuration
in the stack is given in Figure 8.
The system included a central control panel with mounted pressure
gauges, flow meters, and gas cleaning and drying columns, a U-shaped
stainless steel probe with the permeable interface mounted as a segment
of one of the arms, an ambient S02 or NOX analyzer and recorder, a
thermocouple, potentiometer and recorder, an air compressor, and the
calibration gas sources required for the analyzer and the interface. A
hollow sheath mounted on the probe could be slipped over the interface,
and a span gas could then be passed over the outside of the interface for
calibration purposes. The sheath could then be withdrawn, exposing the
interface to the stack gases. The carrier gas flowing through the inside
of the tube picked up the pollutant which permeated in from the stack,
and passed out of the probe to the analyzer.
Raw data had to be corrected for variations in the stack temperature.
The thermocouple mounted on the probe provided a continuous reading of
temperature in the stack, which with the activation energy for permeation
known from the laboratory measurements permitted the corrections to be
made.
Summarizing the monitoring procedure, a polymer tube was mounted
in the probe and positioned in the stack with the sheath in the cali-
bration position. The components of the testing system were connected
and checked for leaks. Following calibration of the analyzer, the
interface was exposed to a span gas containing a known concentration of
S02» the.carrier ga§ flow rate was adjusted to its desired value,
the flow was directed to the analyzer, and the steady-state analyzer
reading was noted. A plot of span gas concentration versus analyzer
reading obtained in this manner was used as a calibration curve for the
subsequent stack monitoring. The sheath was then withdrawn, exposing
the polymer tube to the stack, and the analyzer signal was recorded
continuously. The recorded signal was later corrected for variations in
the stack temperature, and the results were used to calculate the stack
gas pollutant concentration from the calibration curve.
20.
-------
ro
carrier gas
~0 PPM S(>2
~0 PPM H2<0
100-5000
PPM SO2 > =d
flow IT
control i . ,,....-\TB •
valve
0
vent i P|
vent * i-: — — • •
ambient
SOj
analyzer
'
't
/
/
;
X
/
J
f
>
t
,
/
< stack wall
stainless steel
carrier gas line
i
! .\ < — »
••• ••••••••••
movable t 1
calibration-1
sheath ^
span gas
outlet
HI'
stack gas
^
polymer
interface
r
50-3000 PPM SOL
3
Figure 8. Permeable Stack Sampling Interface
-------
Table 2. Field Test Parameters
Stack Location
Stack Conditions
Interface
Analyzer
Carrier Gas Flow
Rate
Single-Contact Process
S(L Absorption Tower
« 2,000 ppm S02
* 80°C
FEP Teflon Tube
I.D. = 0.544 cm
O.D. = 0.604 cm
L = 75 cm
Electrochemical
Transducer
Range: 0-0.1 ppm S02
1250 cm3/min
@ 21.4°C, 1 atm
Double-Contact Process
SO., Absorption Tower
e 85 ppm S02
* 67°C
FEP Teflon Membrane
(2 mils) on a porous
stainless steel tube
Support I .D. = 1 .016 cm
Support O.D. = 1 .026 cm
L = 44 cm
Flame Photometer
Range: 0-0.5 ppm
3
300 cm /min
(9 21 ,4°C, 1 atm
Oil -Fired Power
Plant Boiler
250-1 ,045 ppm S0?
170°C - 213°C
TFE Teflon Tube
I.D. = 0.403 cm
O.D. = 0.480 cm
L = 70.5 cm
Flame Photometer
Range: 0-0.5 ppm
500 cm /min
@ 21 .4°C, 1 atm
-------
S0? monitoring runs were performed in two SO- absorption tower
stacks, an oil-fired boiler stack, and a coal-fifed boiler stack.
The experimental parameters of all but the last of these tests are
summarized in Table 2; the test in the coal-fired boiler was
preliminary in nature and only qualitative behavior was observed.
Details of these tests and plots of the data are aiven by Treece,
Felder, and Ferrell (1976)*; the principal results are summarized
below.
6.2 SUMMARY OF RESULTS
6.2.1 SO, Absorption Tower Stack: Single Contact Process
A 1-day run was carried out using an FEP Teflon sampling tube. The
stack gas contained approximately 2,000 ppm S02 and the stack temperature
was roughly 80°C. The results are shown in Figure 9. There were no
significant operating problems, and excellent agreement was obtained
between the continuous monitoring results and those obtained by
intermittent sampling and analysis using Federal Register Method 6.
A heavy acid mist was present in the stack9 and considerable dropwise
condensation on the tube took place. The SOg permeability of the
condensate-coated tube was experimentally indistinguishable from that of
the clean tube material, indicating that the condensate had no effect on
the tube performance.
In another experiment, the SO, permeability of a TFE Teflon tube was
measured, the tube was inserted in the absorption tower stack for one
year, and the permeability was then remeasured. A permeability decrease
of about 15% was found. This change would appear as a span drift, and
would easily be accounted for by periodic recalibration of the device.
This result suggests the potential usefulness of Teflon interfaces for
long-term continuous unattended monitoring in corrosive atmospheres.
On the other hand, a fluorosilicone rubber tube placed in the stack
showed obvious signs of deterioration after 12 hours, suggesting that
this material is unsuitable for use in an acid mist environment.
6.2.2 SO, Absorption Tower Stack: Double Contact Process
A 2-day monitoring run was carried out in the SO^ absorption tower
stack of a double contact process sulfuric acid plant,, The average
concentration of SO,, in the stack gas was 85 ppm9 and the stack gas
temperature was 67°c. To obtain a permeation rate sufficiently high for
the carrier gas S02 concentration to be within the operating range of the
analyzer (0.02-0.5 ppm), a tube with a very thin wall had to be constructed;
this was done by wrapping and heat-sealing a 2-mil (0.005 cm) FEP Teflon membrane
about a porous stainless steel support. The continuous readings obtained
using this device were compared with readings obtained with an on-stream
stack gas analyzer operated by plant employees.
*Attached as Appendix D.
23
-------
INi
Stock Cone. SO2 (PP™)
Carrier Cos Cone. SO2 (PPm)
4000
3000
2000
1000
.15
-JO
05
-.0
FEP Interface arrd Ambient Analyzer
Method 6
_i
j_
I
1230 1330 1430 1530
1630
Time
1730 1830 1930 2030 2130
Figure 9. Monitoring data: Single contact process stack.
-------
The results of these tests are shown in Figure 10. The data obtained
using the permeable interface exhibited less fluctuation and greater
day-to-day reliability than the results of on-stream measurements.
Moreover, the use of the plant instrument since the test has had to be
curtailed due to the effects of corrosion, a problem less likely to
occur if the in-situ interface were used on a continuing basis.
These results and those obtained in the single contact process stack
indicate that polymeric interfaces can be used to monitor stacks contain-
ing S02 at concentrations which vary over a wide range. The concentration
in the first stack, »2,000 ppm, is typical of uncontrolled emissions from
many process and power plant stacks, while that in the second stack, £85
ppm, is characteristic of a controlled emission. A system composed of
two probes and a single analyzer might therefore be used to measure the
effectiveness of an S02 removal process by monitoring both the inlet and
outlet SO^ concentrations.
6.2.3 Oil-Fired Power Plant Boiler Stack
Monitoring runs were carried out in an oil-fired power plant boiler
at North Carolina State University. A No. 6 fuel oil containing 1.9%
sulfur was burned, and the S02 content of the stack gas varied between
250 and 1,045 ppm as the load on the boiler was changed. The stack
temperature fluctuated between 170 and 213°C.
Monitoring data obtained in a 2%-hour interval are shown in Figure 11.
The feed rate of oil to the furnace, which correlates with the $62
concentration in the stack, is also shown as a function of time in Figure
11.
The results of these tests again showed excellent agreement between
measurements obtained with the permeable interface and others obtained
by direct sampling and analysis using Federal Register Method 6. More-
over, the ability of the sampling interface to follow changes in the S02
concentration in the stack is illustrated by the results: as the plots
of Figure 11 indicate, changes in the boiler loading were followed
extremely rapidly by proportional changes in the analyzer signal.
A gross measurement of the particulate concentration in the stack
using Federal Register Method 5 yielded a loading of 0.21g/m . In-
spection of the sampling tube at the conclusion of the tests revealed a
slight powdery deposit on the tube surface, but recalibration measure-
ments indicated that this layer had no effect on the S02 permeability of
the tube.
6.2.4 Coal-Fired Power Plant Boiler Stack
A 1-day monitoring run was carried out in the stack of a coal-fired
power plant boiler, under extremely heavy particulate loading conditions.
25
-------
240
200
160
120
80
40
-.15
.10
.05
Stack Cone. SCU, ppm-
Carrier Gas Cone. SC^, ppm.
On-Line Stack Gas Analyzer
FEP Interface and Ambient Analyzer
i i i i
1200 1400 1600
10/2/74
1800
*/\>
DOoK:
2000K1200
Time, hr.
1400 1600
10/3/74
1800 2000
Figure 10. Monitoring data: Double contact process stack.
-------
-10 0
10 20 30 40 50 60 70 80 90 100
t , min.
120 130 140 150 160
Figure 11. Monitoring data: Boiler stack, 1-day run.
-------
At the end of this monitoring run, the probe was withdrawn and in-
spected. The stainless steel portions of the probe were literally
invisible, caked with a layer of soot, while the Teflon interface was
almost completely clean. The ability of Teflon interfaces to resist
participate adhesion is apparent from this result; apparently mechanical
vibrating or scraping to minimize particulate adhesion during monitoring
should not be required, even under the worst of conditions.
6.3 CONCLUSIONS
1. Interfaces can be designed to monitor stack gases with SO- con-
centrations from tens to thousands of parts per million.
2 The presence of liquid or solid particulate matter in the stack gas
has no measurable effect on the performance of sampling interfaces.
Using such an interface, therefore, eliminates the need for frequent
filter changes, making long-term continuous unattended monitoring a
good possibility.
3. Teflon interfaces perform well in acid mist environments, retaining
their characteristic permeation properties for periods of a year
and up. Dropwise condensation has no apparent influence on the
SOp permeability of the interface.
4. Responses obtained using polymer interfaces follow changes in stack
gas concentrations accurately and rapidly, suggesting the potential
applicability of such devices as feedback control loop components.
28
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SFCTIOM 7
MEASUREMENT OF GAS DIFFUSIVITIES IN POLYMERS
The rate of permeation of a gas into a polymer interface is
determined by the permeability of the interface material to the gas.
The permeability is the product of the solubility and the diffusivity
of the gas in the polymer, but these terms individually have no effect
on the steady-state response of the device. The transient response of
an interface to changes in stack conditions is another matter, however;
the dissolution of the gas in the polymer can be considered instantan-
eous, so that the diffusivity alone is the prime factor in determining
the time required for the interface to respond to changes in its
environment.
Initial tests of interface response times to changes in span gas S02
concentrations were purely empirical. (Rodes et al, 1973) To better
understand the nature of the responses, it was decided to measure
diffusivities of S02 in the materials used as interfaces. A technique
was developed whereby these measurements could be made in the continuous-
flow apparatus which had been used for the permeability studies; although
this was initially done for convenience, the method proved to possess
considerable advantages over the techniques which have been traditionally
used for diffusivity measurements.
7.1 PROCEDURE FOR DIFFUSIVITY MEASUREMENTS
A polymer tube or membrane is mounted in the chamber used for
permeability measurements, and the chamber is placed in the thermo-
statically-controlled oven. The schematic diagram of Figure 1 depicts
the system.
The flow rate of the span gas with a known penetrant concentration
commences at a time t=0, and the response R(t) of the analyzer to the
carrier gas penetrant concentration is recorded. The run is terminated
when R(t) has leveled off to a value of Rs and remained there for at
least 15 minutes. The following quantities are then calculated:
(7-1)
(7-2)
where R (t) is the response of the S0« analyzer to a step change in
concentration at its inlet, and R is the asymptotic(steady-state)
value of this response. Both M ' and T are determined by numerical
integration of measured response data.
- Volume of span gas line preceding chamber (7-3)
Tl ~ Volumetric flow rate of span gas \ - )
_ Volume of span gas chamber (7-4)
T2 ~ Volumetric f1ow rate
29
-------
_ Volume of carrier gas line following chamber /-, ,-\
T3 Volumetric flow rate of carrier gas^ " '
Mo = V - (Ta + Tl + T2 + T3} (7-6>
The diffusivity can be calculated from M and geometrical parameters
of the interface. For a flat membrane of thickness h,
D = h2/6MQ (7-7)
and for a hollow cylindrical tube of inner radius a and outer radius b
D =[a2-b2 + (a2+b2) In (b/a)]/4MQ jm(b/a) (7-8)
The derivation of Eqs. (7-7) and (7-8) is given by Felder, Spence, and
Ferrell (1975b)* and Eqs. (7-1) - (7-6) for calculating M fij;om measured
response data are derived by Felder, Ma, and Ferrell (197°).
Once the diffusivity D has been determined for a polymer in the
manner indicated, and the permeability P has been measured as outlined in
Section 4, the solubility of the gas in the polymer may be calculated as
S = P/D.
7.2 DIFFUSIVITIES OF S0«
Diffusivities of SO? have been measured at temperatures from 21°C
to 227°C in Teflon and fluorosilicone rubber tubes. The results are
given by Felder, Spence and Ferrell (1975b)*and Felder, Ma, and Ferrell
(1976).*
The Arrhenius plots of the measured diffusivities shown in the figures
of Appendices E and F are linear, although variations are observed between
different tubes of the same material. Several span gas S02 concentrations
were used; the near coincidence of the diffusivities measured for the
different concentrations at a fixed temperature suggests the constancy of
D at the S02 partial pressures of 10 mm Hg and less normally encountered
in stack gases. As a test of the validity of the diffusivity estimation
technique, the theoretical expression for the transient response was
evaluated using diffusivities estimated at three different temperatures.
The close correspondence between the theoretical curves and the measured
responses at each temperature shown in Figure 3 of Appendix F validates
both the diffusivity estimation technique and the diffusion model upon
which the technique is based.
*Attached as Appendix E.
Attached as Appendix F.
30
-------
REFERENCES
Crank, J. and G, S. Park, in Diffusion in Polymers (J. Crank and
G. S. Park, eds.). Academic Press, New York (1968), p. 1.
Felder, R. M., J. K. Ferrell, and J. J. Spivey. Effects of Moisture
on the Performance of Permeation Sampling Devices. Anal. Instru-
mentation, 1_29 35 (1974).
Felder, R. M., C-C Ha and J. K. Ferrell. A Method of Moments for
Measuring Diffusivities of Gases in Polymers. A.I.Ch.E. Journals
22_, 724 (1976).
Felder, R. M., R. Do Spence and J. K. Ferrell, (a) Permeation of Sulfur
Dioxide through Polymers. J. Chem. Eng. Data, 20., 235 (1975 ); (b)
A Method for the Dynamic Measurement of Diffusivities of Gases in
Polymers. J. Appl. Poly. Sci, 19, 3193 (1975 ).
Rodes, C. E., R. M. Felder, and J. K. Ferrell. Permeation of Sulfur
Dioxide through Polymeric Stack Sampling Interfaces. Environ.
Sci. Techno!., 7., 545 (1973).
Seibel, D. R. and F. P. McCandless. Separation of Sulfur Dioxide and
Nitrogen by Permeation through a Sulfolane Plasticized Vinylidene
Fluoride Film. Ind. Eng. Chem. Proc. Des. Dev., 1_3_, 76 (1974).
Spence, R. D. Development of a Polymeric Interface as an SCL Stack
Monitor. Ph.D. Thesis, North Carolina State University, Raleigh,
N. C. (1975).
Spivey, J. J. Effects of Water Vapor on the Performance of Polymeric
Stack Sampling Interfaces. M.S. Thesis, North Carolina State
University, Raleigh, N. C. (1974).
Treece, L. C. Development and Testing of Polymeric Materials for Use
as a Stack Sampling Interface. M.S. Thesis, North Carolina State
University, Raleigh, N. C. (1975).
Treece, L. C., R. M. Felder and J. K. Ferrell. Polymeric Interfaces
for Continuous SC^ Monitoring in Process and Power Plant Stacks.
Env. Sci. Technol. 10, 457(1976).
31
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APPENDIX A
PERMEATION OF SULFUR DIOXIDE THROUGH POLYMERS*
R. M. Felder, R. D. Spence and J. K. Ferrell
Department of Chemical Engineering
North Carolina State University
Raleigh, North Carolina 27607
ABSTRACT
Permeabilities, diffusivities, solubilities and activation energies
for permeation and diffusion are reported for the permeation of S0~ through
various polymers. Effects of gas pressure and humidity and membrane plasti-
cization on S02 permeabilities are summarized.
Published as J. Chem. Eng. Data 20. 235 (1975). Reprinted by permission of
the American Chemical Society.
32
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INTRODUCTION
The permeability of a polymer to a gas or vapor is the ratio J/(Ap/h),
where J is the flux of the gas through a flat membrane of thickness h, and
Ap is the partial pressure difference across the membrane. If the equili-
brium sorption of the gas in the polymer varies linearly with the partial
pressure in the gas phase and diffusion of the gas through the polymer is
Fickian with a constant diffusivity, then
P = DS (1)
where
P = permeability, cm (STP)/s-cm.cm Hg
2
D = diffusivity, cm /s
S = solubility, cm3(STP)/cm3
The temperature dependence of gas permeabilities frequently follows an
Arrhenius relationship
p = PO exP (-EP/RT) (2)
where E is the activation energy for permeation. Techniques for the mea-
surement of P, D and S are reviewed by Crank and Park (6), and factors
which affect the values of these parameters are discussed by Stannett (34).
S02 permeabilities of a number of materials have been measured at tem-
peratures from 25°C to 232°C, and activation energies for permeation have
been calculated. This paper reports the results of these experiments. In
the course of this study, a literature search on the permeation of S02
through polymers was carried out, covering references through April 1974.
33
-------
Relatively few reported permeabilities were found, but a number of papers
presented permeation rate data from which permeabilities could be calcu-
lated. These calculations have been performed, and the results are also
reported in this paper.
34
-------
EXPERIMENTAL
Span gas mixtures of S02 in air with SOp concentrations in the range
1,000-10,000 ppm were passed on one side of a flat polymer membrane or on
the outside of a hollow tube in a thermostatically-controlled oven. SCL
permeated through the polymer into a carrier gas stream of pure air, which
passed to an SOp analyzer. The SCL permeation rate was calculated as the
product of the carrier gas flow rate and the S02 concentration in this gas
at steady-state; the permeability of the polymer to SCL was then calculated
from the permeation rate, the S02 partial pressures in the span gas and the
carrier gas, and the dimensions of the membrane or tube.
The experimental and calculational procedures for determining perme-
abilities and the permeation chamber used for hollow tubes are described in
detail by Rodes, Felder and Ferrell (23). A two-piece hollow stainless
steel cylinder with OD = 7.62 cm, ID = 5.08 cm, and outside height = 7.0 cm
was used as a permeation chamber for flat membranes. The membranes were
clamped between the two halves of the chamber, and the span gas and carrier
gas were fed into the chamber on opposite sides of the membrane. The en-
trance and exit ports were situated such that the gases entered tangentially
and swept across the entire membrane surface before exiting.
Span gas SCL concentrations were determined by passing a measured vol-
ume of the gas through a 3% Hp02 solution to absorb the SOp, and then titra-
ting with a 0.01N barium perchlorate solution in the presence of Thorin in-
dicator (9). Carrier gas S02 concentrations were measured with a Meloy
Laboratories Model SA-160 total sulfur analyzer or an Envirometrics Model
NS-300M S02 analyzer.
35
-------
PERMEABILITIES. DIFFUSIVITIES AND SOLUBILITIES
Materials for which SO- permeabilities, diffusivities and/or solu-
bilities have been found include TFE Teflon, FEP Teflon, several
silicone and fluorosilicone rubbers, polyvinyl fluoride (Tedlar), poly-
vinyl idene fluoride (Kynar), polycarbonate (Lexan), polyethylene, polypro-
pylene, polyyinyl chloride, copolymers of polyvinyl chloride and poly-
vinyl ide chloride, several natural rubbers, polyisobutene, polymethyl me-
thacrylate, polyethylterephthalate (Mylar), several cellulosic films, and
a chlorinated polyether (Penton), and a polyethylene glycol liquid mem-
brane. While most of the data are for temperatures in the range 15-30°C,
permeabilities have been measured over temperature ranges broad enough to
permit the determination of activation energies for TFE and FEP Teflon, a
fluorosilicone and a silicone rubber, polyethylene, polyvinyl fluoride,
and polyvinylidene fluoride. Measured and estimated permeabilities, dif-
fusivities and solubilities are summarized in Table 1, and Arrhenius law
parameters are listed in Table 2.
The permeabilities of TFE and FEP Teflon are similar, despite the
probable differences in the degree of crystallinity of these two substances.
This result supports a claim by Stern et. al_. (35) that the two substances
have similar permeabilities, but conflicts with assertions by Saltzman
(24,25) that TFE may be as much as 10 times more permeable than FEP at the
same temperature. '
Extended use at temperatures close to 200°C did not affect either TFE
or FEP, either in physical appearance or in permeability to S02- The fluoro-
@
silicone rubber (Dow-Corning: SILASTIC LS-631T) maintained a constant perme-
ability with extended usage, although it underwent a discoloration and de-
teriorated when subjected to an acid mist environment. The silicone rubber
36
-------
(Dow-Corning: SILAST.IC 43/j became brittle at high temperatures (23), pro-
bably due to attack by S02 (16).
Permeabilities of SCL in TFE Teflon are summarized on an Arrhenius
plot in Figure 1. The high temperature permeabilities determined in the
present study and by Rodes et_. a_l_. (23) are consistent with the permeabil-
ity reported by Jordan (15) at a temperature presumably in the range
20-30°C. Values estimated from S02 permeation tube emission rate data
(17) are substantially out of line with the other permeabilities, but the
degree of uncertainty in the tube dimensions used to obtain these values
is sufficient to account for the discrepancy.
An Arrhenius plot of SOp permeabilities in FEP Teflon is shown in
Figure 2. A single line correlates the measured and estimated permeabili-
ties reasonably well, except for values reported by Benarie and Bui-the-
Chuong (1) and estimated from permeation tube emission rates reported by
Stevens e_t. al_. (36) and Metronics, Inc. (17). Permeabilities obtained
for flat membranes 0.02-0.1 mm thick were consistently 5-20* higher than
values obtained for cylindrical tubes with wall thicknesses in the range
0.3-0.7 mm.
Stern et. al. (35) indicate that a phase change occurs in FEP Teflon
at 60°C which might affect its permeability. Figure 2 suggests that this
effect is minimal, if it exists at all.
S02 permeabilities in silicone and fluorosilicone rubbers are shown
in Figure 3. The permeability of S02 in these materials is between one and
two orders of magnitude higher than that in Teflon, and the activation
energy for permeation of the silicones is much lower than that of Teflon.
High SOp permeabilities are also found for dimethyl silicone rubbers, which
are discussed by Robb (22), Hodgson (13) and an undated General Electric
37
-------
brochure (11). Permeabilities calculated at high temperatures for a fluoro-
silicone rubber in the present study and by Rodes et. a]_. (23) do not agree
particularly well;. however, the material in question was not available com-
mercially when the latter measurements were made and the differences in the
permeabilities of different tubes might reflect a difference in fabrication
methods from one batch to another.
S02 permeabilities in polyethylene are given by several authors (1,3,
7,12,15). The permeability reported by Jordan (15) appears far too high,
assuming that it was obtained in the temperature range 20-30°C; the other
values are shown on an Arrheriius plot in Figure,4.
Studies of S02 transport in polymers which are not referenced in Table
1 have been carried out by Sano and coworkers (27-30), Stoeckli (37), and
Svoboda and coworkers (38-40). References 27-30 deal with the permeation
of S02 through polyethylene and plasticized polyvinyl chloride membranes,
Reference 37 with sorption of SOp on polyvinylidene chloride, and References
38-40 with penetration of S02 into alkyd resins.
EFFECT OF TEMPERATURE ON PERMEABILITY
The Arrhenius plots of Figures 1,2 and 4 for TFE Teflon, FEP Teflon and
polyethylene have been fit by linear regression to obtain the pre-exponen-
tial factors and activation energies listed in Table 2. The following data
points were excluded from the regressions: Figure 1 -- Metronics;
Figure 2 -- Stevens et. a!. and Benarie and Bui-the-Chuong; Figure 4 -- all
but Brubaker and Kammermeyer. Also listed in,Table 2 are published activa-
tion energies for permeation of SOp through polyvinyl fluoride, polyvinyli-
dene fluoride and polyethylene.
38
-------
The permeabilities of silicone and fluorosilicone rubbers shown in
Figure 3 are too scattered to permit meaningful regressions; however, the
following ranges for P and E may be deduced from the data:
SILASTIC 437 silicone rubber
SILASTIC LS-63U®fluorosilicone rubber
50°C < T < 232°C
EFFECT OF PRESSURE ON PERMEABILITY
10"
s-cm-cm Hg
0.1 <_ E <_ 2 kcal/g-mole
At low pressures gas permeabilities, diffusivities and solubilities are
characteristically independent of pressure (34). The high temperature permea-
tion measurements reported in Table 1 -- for which the total pressures were
close to atmospheric and partial pressures of S02 were in the range 0.08-1.3
cm Hg -- show this behavior: plots of permeation rate vs. SOp partial pres-
sure obtained by Rodes et. a_l_. (23) and in the present study were linear,
with correlation coefficients usually in excess of 0.99.
Under some circumstances, however, the effective permeability of a sub-
stance depends on the partial pressure of the permeating species and/or the
total pressure on the high concentration side of the interface. The cause
may be the departure of the solubility of the material from Henry's Law be-
havior, a concentration-dependent diffusivity, or the occurrence of permea-
tion by a mechanism other than solution followed by activated diffusion.
Pressure-dependent S02 permeabilities have been observed by Davis and
Rooney (7) for polyethylene, polycarbonate and polyamide membranes, and by
Seibel and McCandless (32) for polyvinylidene fluoride (Kynar). Seibel and
McCandless worked at total pressures of 100-500 psig -- pressures at which
any or all of the factors indicated could cause the observed pressure de-
pendence of the effective permeability.
39
-------
Solubilities of SCL in polyethylene and polymethyl methacrylate re-
ported by Jordan (15) show a considerable departure from Henry's law.
Davis and Rooney (7) report a Henry's law dependence for SOp in polyethy-
lene, deviations from this behavior in polycarbonate and pplyamide, and
concentration-dependent diffusivities for all three materials.
Davis and Rooney (7) and Perret et. aj_. (20) present diffusivity and
solubility correlations for S02 in the range 0-25°C. In the equations
that follow, pso is the SOp partial pressure in cm Hg, C— the absorbed
33
S02 concentration in cm S02(STP)/cm polymer, and D the SCL diffusivity
2
in cm /s.
1. Polyamide at 25°C (7)
0.98
PSQ
C =
1.0+ 0.169
pSQ
(3)
f= 3.63x00)
0.05 C \
DxlO
10
= 2.63x(10)°-06Cy
2. Polycarbonate at 25°C (7)
2.44
PSO,
C =
1.0 + 0.24T
PSO,
+ 0.522
(4a)
(Determinations by two different
methods)
(4b)
PSO,
(5)
40
-------
3. Polyvinyl chloride (20)
0°C : C = 0.719 pSQ + 2.155 P$0 > 3 cm Hg (6)
<£ &
20°C : C = 0.393 p$() + 1.472 P$0 > 54 cm Hg (7)
& 6f
The sorption isotherms given by Eqs. (3)5 (5)8 (6) and (7) are consist-
ent with the dual mode mechanism proposed by Michaels et. al. (18) for sorp-
tion in glassy polymers. According to this mechanism, sorption is a combin-
ation of ordinary Henry's law solution -- which leads to a linear component
of the isotherm -- and microvoid or hole-filling, which gives rise to a
Langmuir expression. Both components of the isotherm appear explicitly in
Eqs. (3) and (5). At sufficiently high pressures the isotherm becomes lin-
ear, with a slope equal to the Henry's law constant and a positive intercept
cf.Eqs. (6) and (7).
EFFECT OF HUMIDITY ON -PERMEABILITY
Stannett (34) observes that humidity has little effect on the permeabil-
ity of gases through polymers in which water is only slightly soluble, but
when water is highly sorbed the gas permeation rate may be significantly in-
creased by an increase in humidity.
The few reported studies of the effects of humidity on SOp permeation
confirm this observation. Felder, Ferrell and Spivey (10) report that the
S02 permeabilities of TFE Teflon, FEP Teflon and SILASTIC LS-63U*fluorosili-
cone rubber tubes measured for dry.gases and gases containing up to 21%
water by volume are statistically indistinguishable at temperatures up to
200°C, Hanousek and Herynk (12) found that the permeability of polyethylene
at 25°C decreased by 10-30% and the permeabilities of several types of paper
41
-------
decreased or remained unchanged when the relative humidity was raised from
0% to 84%, while the permeability of a polyamide increased by 33% and that
of polyvinyl chloride increased by 10% for the same change in humidity. On
the other hand, both Hanousek and Herynk (12) and Simril and Hershberger (33)
report increases of an order of magnitude or more in the permeability of cel-
lulosic films when the humidity was raised from Q% to 84-100X.
EFFECT OF PLASTICIZERS ON PERMEABILITY
The presence of a plasticizer in polymeric materials may
increase the solubility and hence the permeability of these materials to
water (34). Seibel and McCandless (32) utilized this principle to fabri-
cate S02 - permeable membranes by adding sulfolane (an S02 solvent) as a
plasticizer to polyvinylidene fluoride films. The addition of the sulfo-
lane increased the permeability of S02 relative to that of N2» with the
separation factor increasing with decreasing temperature.
Sano has been the author or co-author of several patents and papers
on the separation or removal of SOp by polyvinyl chloride membranes plasti-
cized with dioctyl phthalate and tricresyl phosphate (27-30).
•42
-------
SUMMARY
Permeabilities of SCL in various polymers have been measured or cal-
culated from published permeation rate data. Activation energies for
permeation have been determined by fitting Arrhenius functions to perme-
ability data for TFE Teflon, FEP Teflon, silicone and fluorosilicone rub-
bers, polyvinyl fluoride (Tedlar), polyvinylidene fluoride (Kynar) and
polyethylene.
The permeabilities of TFE and FEP have been found to be similar, con-
tradicting published assertions that TFE is considerably more permeable
than FEP. Silicone and fluorosilicone rubbers are 10 to 100 times more
permeable than Teflon, but they are also subject to embrittlement and at-
tack by acid mist.
A transport model .based on Henry's law for solution and Pick's law
for diffusion correlates permeation data well for many materials at pres-
sures of 1 atmosphere or less. At higher pressures deviations from these
laws have been reported for polyethylene, polycarbonates and polyamides,
polyvinyl chloride, polyvinylidene fluoride, and polymethyl methacrylate.
The observation of Stannett (34) that relative humidity affects the
permeability of a gas through a polymer to the extent that the polymer ab-
sorbs water is borne out by the results of several experiments. As the
humidity increases the permeabilities of TFE Teflon, FEP Teflon and fluoro-
silicone rubber tubes were unchanged, that of polyethylene decreased slight-
ly, and those of a polyamide and of polyvinyl chloride increased slightly,
while the permeabilities of cellulosic films increased substantially.
The addition of certain plasticizers to. a polymer film may increase
the permeability of the film to SOp. This effect has been observed in sul-
43
-------
•folane-plasticized polyviriylidene fluoride and dioctyl phthalate and tri-
cresyl phosphate - plasticized polyvinyl chloride films.
44
-------
ACKNOWLEDGMENTS
This work was supported by Environmental Protection Agency Grant
#801578. Mention of a commercial product or company name does not con-
stitute endorsement by the Environmental Protection Agency.
The authors acknowledge with thanks assistance with the experiments
provided by Mssrs. Chen-Chi Ma and Lanny C. Treece, helpful discussions
with Professors Harold Hopfenberg and Vivian Stannett of North Carolina
State University and Dr. James Homolya and Mr. Charles Rodes of the En-
vironmental Protection Agency, and assistance with the manuscript pre-
paration provided by Mrs. Mary Wade.
45
-------
REFERENCES FOR APPENDIX A
1. Benarie, M. and Bin-the-Chuong, Atm. Environ.. 3, 574 (1969).
2. Brocco, D. and Possanzini, M., Inquimentato. J4_, 21 (1972).
3. Brubaker, D. W. and Kammermeyer, K., Ind. Enq. Chem.. £6, 733 (1954).
4. Chappuis, Nied. Ann.. ]9_, 21 (1883), referenced in Reychler (1921).
5. Chemical Engineer's Handbook, 5th Edition, R. H. Perry and C. H. Chilton,
Editors, New York, McGraw-Hill (1973), p. 3-202.
6. Crank, J. and Park, G. S. in Diffusion in Polymers, J. Crank and G. S.
Park, Editors, New York, Academic Press (1968), p. 1.
7. Davis, E. G. and Rooney, M. L., Kolloid Z. Z. Poly.. 249, 1043 (1971).
8. Dietz, R. N., Cote, E. A., and Smith, J. D., Anal. Chem.. 46, 315 (1974).
9. Federal Register. 36, 24890 (1971).
.10. Felder, R, M., Ferrell, J. K., and Spivey, J. J., Analysis Instrum., 12,
35 (1974).
11. "General Electric Permselective Membranes,11 General Electric, Medical
Development Operation, Chemical and Medical Division, Schenectady, N. Y.
12. Hanousek, J. and Herynk, L., Chem. Listy, 56_, 376 (1962).
13. Hodgson, M. E., Filtr. and Sep.. J£, 418 (1973).
14. Hsieh, P. Y..-J. Appl. Polym. Sci.. 7., 1743 (1963).
15. Jordan, S., Staub-Reinhalt Luft. 33, 36 (1973).
16. Mclntyre, J. T., Dow Corning, Midland, Michigan, Private Communication
(1974).
17. Metronics Product Bulletin No. 20-70, Metronics Associates, Inc., Palo
Alto, California (1970).
18. Michaels, A. S., Vieth, W. R. and Barrie, J. A., J. Appl. Phys.. 34, 13
(1963). ~
19. O'Keeffe, A. E. and Ortman, G. C.. Anal. Chem.. 38, 760 (1966).
20. Perret, E. A., Stoeckli, H. F., and Jeanneret, C., Helv. Chim. Acta. 55,
1987 (1972).
46
-------
22. Robb, W. L., Ann. N. Y. Acad. Sci.. 146. 119 (1968).
23. Rodes, C. E., Felder, R. M., and Ferrell, J. K., Environ. Sci. Techno!.,
Z, 545 (1973).
24. Saltzman, B. E., Microfiche AD 727-516, Aerospace Medical Research
Laboratory, Aerospace Division (1970).
25. Saltzman, B. E., Burg, W. R., and Ramaswamy, G., Environ. Sci. Techno!.,
i, 1121 (1971). "
26. Saltzman, B. E., Feldmann, C. R. and O'Keeffe, A. E., Environ. Sci.
Techno!.. 3, 1275 (1969).
27. Sano, H., Japanese Patent 19883 (1972).
28. Sano,. H. and Otani, T.9 Osaki Kogyo Gijutsu Shikensho Kiho, |2_, 24 (1971).
29. Sano, H. and Otani, T.. Osaka Kogvo Gi.iutsu Shikensho Kiho. 22. 102 (1971),
30. Sano, H., Sakaguchi, S. and Tanaka, K., Japanese Patent 23785 (1972).
31. Scaringelli, F. P., Frey, S. A., and Saltzman, B. E., Am. Ind. Hyg. Assn.
J_._, 28, 261 (1967).
32. Seibel, D. R. and McCandless, F. P., Ind. Eng. Chem. Proc. Des. Develop.
U, 76 (1974).
33. Simril, V. L. and Hershberger, A., Mod. Plast.. 7_, 95 (1950).
34. Stannett, V., in Diffusion in Polymers, J. Crank and G. S. Park, Editors,
New York, Academic Press (1968), p. 41.
35. Stern, S. A., Sinclair, T. F., Gareis, P. J., Vahldieck, N. P., and Mohr,
P. H., Ind. Eng. Chem.. 57_, 49 (1965).
36. Stevens, R. K., O'Keeffe, A. E., and Ortman, G. C., Environ. Sci. Techno!.
3, 652 (1969).
37. Stoeckli, H. F., Helv. Chim. Acta. 55, 101 (1972).
38. Svoboda, M., Klicova, H., and Knapek, B., Prot. Steel Str. Atmos. Corr.,
Proc. Event. Eur. Fed. Corros., 57th 1970, 2., 343 (1971).
39. Svoboda, M., Knapek, B., and Smrckova, J.. Farbe und Lack. _7J_, 809 (1965).
40. Svoboda, M., Knapek, B.,and Smrckova, J., Farbe und Lack. 74^ 659 (1968).
41. van Amerongen, G. J., J. Appl. Phys.. ]7_, 972 (1946).
42. Venable, C. S. and Fuwa.T., J. Ind. Eng. Chem.. ]4_, 139 (1922).
43. Ward, W. J., Ill, U. S. Patent 3625734, Dec. 1971.
47
-------
Table I. SO- Permeabilities, Diffusivities, and Solubilities
CO
,(b)
Material Temperature (°
TFE Teflon tube
00=0.959 cm
10=0.806 cm
TFE Teflon
tube
00=0.604 cm
10=0.544 cm
99
128
131
154
154
173
175
175
179
179
202
230
241
52
68
87
127
C) PxlO'u
64.7
107.
105
157. d
147.d(21.1% H20)
212.
242.
249.
221. d
231.d(21.1% H 0)
407. d
473.
557.
14.9
17.7
34.9
55.2
DxlO
-
-
-
-
- .
- -
-
-
-
-
- •
-
-
-
Source
Present study
Felder et. al. (10)
Present study
Felder et. al. (10)
Present study
Note: Footnoteson last page of table.
-------
Table I (Cont'd)
Material
TFE Teflon
tube heat-shrunk
on a porous
sintered stain-
less steel tube
TFE Teflon
FEP Teflon
tubes
Temperature (°C)
152
175
201
20
251
30
40
93.3
121
121
149
177
177
204
232
232
127
158
175
175
180
201
PxlO'u
145.
197.
285
11.4 j'k
5.1
17.8j'k
26.5 j'k
29.9
53.9
57.6
92.3
181.
154.
234.
448.
427.
60,
124.
r\
256.
262.
H
203.
A
384.
DxlO
10
(b)
1300.
0.04
Source
Present study
Metronics (17)
Jordan (15)
Metronics (17)
II
Rodes et. al. (23)
Present study
H
Felder et. aJL (10)
Present study
Felder et. al. (10)
-------
en
O
.Table I (Cont'd)
-.••f '
Material
FEP Teflon
heat-shrunk on
a porous sinter-
ed stainless
steel tube
PEP Teflon tube
i heat-shrunk on a
stainless steel
coil
FEP Teflon tube
.heat-shrunk with
1 no support
'FEP Teflon
Membrane
0.00263 cm thick
,(a)
Temperature (°C)
126
127
152
181
196
211.5
124
125
150
179
194
24
47
48
73
85
94
97
115
122
PxlO'u
68.4
73.9
128.
242.
316..
457.
62.4
65.5
120.
219.
285.
5.84
11. 9j
13.6
26. 5j
37.4 (32.5% H20)
50.9
44.7 (32.5% H20)
91.7
85.0
DxlO
10
(b)
Source
Present study
-------
Table I (Cont'd)
Material
FtP Teflon
Membrane
0.0144 cm thick
FEP Teflon
Temperature (°C)
74
122
147
149.5
13.8
20
20
20
20.1
20.3
22
25
25
25
25
25
25
25
25
29.1
30
30
30
40
PxlOlu
22.3
96.8
103.
179.
k
1.6 K
k
2.6
3.2 k
23 J '
2.4 k
k
46. 8K
65.8
3.3 Pfk
3.4 j'k
4.0 j'k
4.2
4.0 j'k
4.0 J'k
3.3 j'k
3.5 j'k
3.6 *
7.1 J'k
3.8 ^'k
4.5
5.8 J'k
DxlO
10
(b)
•(c)
70
Source
Present study
O'Keefe & Ortman (19)
Scaringelli et. al. (31)
_ M
Metronics (17)
O'Keeffe and Ortman (19)
Stevens et. al. (36)
0.922 Benarie & Bui-the-Chuong (1)
Saltzman et. al. (26)
O'Keeffe and Ortman (19)
Dietz et. al_. (8)
Metronics .(17)
-------
Table 1 (Cont'd)
Material
01
PO
Tecsil
(silicone
rubber)
Silastic LS-63^
(silicone
rubber)
Dimethyl Silicone
(25%)
Dimethyl Silicone
Peroxide cured,
silica filler
Silastic LS-63U®
(fluorosilicone
rubber) ube
00=0.929 cm.
ID=0.521 cm.
Temperature (°
40
50.5
60
22
121
177
204
232
25
25
251
129
160
175
177
183
195
195
225
225
C) PxlOlu
7.4 j»k
17.4 j'k
24.6 j'k
11,800
2,620
2,810
3,130
3,480
11,450
13,730
43,630:i
3,180
3,330
3,130d .
3,240d(21.1X
3,350
3,290d
3,350d(21.1%
j
3,340°
3,430d(21.1%
H20)
H20)
HoO)
DxlO
10
(b)
.(c)
Source
Metronics (17)
Dietz et. al_. (8)
Benarie & Bui-the-Chuong (1)
Rodes et. al_. (23)
General Electric (11)
Robb (22)
Hodgson (1973)
Present study
n
Felder et. aj_. (10)
n
Present study
Felder et. al_. (10)
-------
table I (Cont'd)
en
CO
Material
Silastic LS-63U*
tube
00=0.848 cm.
ID=0.744 cm.
Silastic LS-63U
tubes
(a)
Polyvinyl
fluoride
(Tedlar)
njembrane
0.006196 cm thick
Polyvinylidene
fluoride
(Kynar)
membrane
0.00417 cm thick
(Kynar)
Temperature (°(
27
44
68
100
129
121
149
177
204
70
80
88
100.5
104
39
45
55
65
:) Pxio'u
2,720
2,950
3,290
3,350
3,650
2,360
2,580
2,880
3,160
15.5
23.7
31.4
61.5
54.1
3.20
4.62
7.56
12.2
DxlO
10
(b)
23
2.51 (100 psig)j
2.68 (200 psig)j
2.28 (300 psig)J'
3.47 (400 psig)j
9.49 (500 psig)j
Source
Present study
Rodes et. al. (23)
Present study
Present study
Seibel & McCandless (32)
-------
Table I (Cont'd)
Material
(Kynar + 8.2%
Sulfolane)
Temperature (°C)
13
23
en
Polycarbonate
(Lexan)
32
42
47
64
73
25
PxlO
.10
(a)
DxlO
10
(b)
7.29 (300 psig)j
15.9 (400 psig)j
3.79 (100 psig)J
5.36 (200 psig)d
13.7 (300 psig)j
19.4 (400 psig)J
36.1 (500 psig)J
16.4 (300 psig)j
26.4 (400 psig)j
42.3 (500 psig)j
18.2 (300 psig)j
24.2 (400 psig)j
38.1 (500 psig)j
16.4 (300 psig)^
27.8 (400 ps1g)J
38.8 (500 psig)J
29.3 (300 psig)J
32.6 (400 psig)j
47.2 (500 psig)j
31.9 (300 psig)^
38.8 (400 psig)J'
47.9 (500
22.4
Source
Seibel & McCandless (32)
Eq. (5)
in text
Davis & Rooney (7)
-------
Table I (Cont'd)
en
Oi
Material
Polyethylene
(Visqueen)
(Polyane)
(Visqueen)
(NSR)
(CSSR)
(Visqueen)
Polypropylene
(Maurylene)
Polyvinyl
chloride
Temperature (°C)
6.5
11.5
13
15
20.5
22
23
25
25
25'
25
25
25
25
30
41.5
42
22
0
20
22
251
PxlOlu
9.0
13.0
13.0
17.0
24.0
43.4
28.0
20. 9e
16. 2f
840.0
24.5 (0% RH)m
21.8 (84% RH)m
31.6 (0% RH)m
21.3 (84% RH)m
42.0
70.0
70.0
6.18
-
-
132.
0.042
DxlO'u
_
-
-
-
-
30.
o
1120
8549
1800
_
-
-
-
-
-
-
3.5
-
-
400.
1.4
1.45
0.0191
0.47
1.71
Eq. (6)
in text
Eq. (7)
in text
0.329
0.03
Source
Brubaker & Kammermeyer (3)
Benarie & Bui-the-Chuong (1)
Brubaker & Kammermeyer (3)
Davis & Rooney (7)
II
Jordan (15)
Hanousek & Herynk (12)
Brubaker & Kammermeyer (3)
Benarie & Bui-the-Chuong (1)
Perret et. al. (20)
Benarie & Bui-the-Chuong (1)
Jordan (15)
-------
in
01
Table I (Cont'd)
Material Temperature (°C)
25
25
Copolymer of vinyl-
idene chloride &
vinyl chloride
Polyamide
(Rilsan)
(Nylon 11)
(CSSR)
Vinyril 11
Rilsan and Saran
(cppolymer of vinyl
and vinylidene
chloride)
Vulcanized
Natural
Rubber
Buna S
25
22
25
25
25
22
0
18.5
20-22
22
25
43
25
43
PxlO
,10
(a)
412 (0% RH)m
45 (84% RH)m
0.201
21.1
6.58
8.54 (0% RH)m
11.4 (84% RH)m
1.18
DxlO
10
(b)
10.
0.6
1,450
10,000
1.84
Eqs. (3) &
(4) in text
1.97
0.528
0.322
0.256
0.158
0.311.
0.153
0.227
0.129
Source
Hanousek & Herynk (12)
n
Davis & Rooney (7)
Benarie & Bui-the-Chuong (1)
Davis & Rooney (7)
Hanousek & Herynk (12)
Benarie & Bui-the-Chuong (1)
Chappuis (4)
Reychler (21)
Venable & Fuwa (42)
Benarie & Bui-the-Chuong (1)
van Amerongen (41)
van Amerongen (41)
-------
en
Table I (Cont'd)
Material
Temperature (°C)
PxlO
10
(a)
DxlO
10
(b)
Source
Perbunan
Neoprene G
Polyisobutene
(Oppanol B 200)
Polymethyl
methacrylate
(Plexiglass)
Polyethyl terephthal ate
(Mylar)
Cellulose Films
(Cellafan, CSSR)
(.Cell of en,
English)
25
43
25
43
25
43
22
251
22
22
25
25
25
25
0.632
0.310
0.239
0.138
0.047
0.032
0.132 -
2.6 6.2 0.42
5.27 1.6 3.29
52.7 27.0 1.98
. 0.256 (Q% RH)m
7.14 (84% RH)m
2.43 (Q% RH)m
20.4 (84% RH)m
van Amerongen (41 )
II
van Amerongen (41 )
II
van Amerongen (41 )
II
Benarie & Bui-the-Chuong (1)
Jordan (15)
Benarie & Bui-the-Chuong (1)
Benarie1 & Bui-the-Chuong (1 )
Hanousek & Herynk (12)
it
Hanousek & Herynk (12)
H
(Ethylcellulose)
(Nitrocellulose)
25
25
264
176
530'
7341
7.9'
18.01
0.498"
0.3601
0.222"
0.09771
Hsieh (14)
n
Hsieh (14)
-------
en
co
Table I (Cont'd)
(a)
Material Temperature (°C)
(Nomex)
Regenerated
Cellulose Film
(22% glycerol
plasticizer)
Paper Imp II
Paper PLP II
Paper PLP I
Chlorinated
Polyether
(Penton)
22
28.1
24.5
24.5
24-25
25.
25.
25.
25.
25.1
PxlOlu
0.132
0.77xTO" 7
0.77xlO~7
0.00169 (100% 1
33.6xlO"7
3.09 (0% RH)m
3.03 (84% RH)m
6.74 (0% RH)m
1.31 (84% RH)m
< lO"15
DxlO
10
(b)
.(c)
Polyethylene
glycol liquid
membrane:porous
polymer backing
of solvinert
coated with
TFE dispersion
RH)
100. 81,300.
0.01
Source
Benarie & Bui-the-Chuong (1)
Simril & Hershberger (33)
Hanousek & Herynk (12)
Jordan (15)
Ward (43)
-------
Footnotes for Table I.
Permeability, cm (STP)/s-cm-cm Hg
K 9
Diffusivity, cm /s
cSolubility, cm3(STP)/cm3-cm Hg
Values published by Felder, et. al . (1974) were based on a nominal cylinder span gas concentra-
tion reported by the supplier. A more accurate concentration has since been obtained, and
the given value reflects the correction.
eS02 partial pressure > 25 cm Hg
Calculated as (DS)
Pso2 - o
- partial pressure -*• 0
Author measures S by a volumetric method and calculates D = P/S
Author measures S by a gravimetric method and calculates D = P/S
J Rough estimate
I/
Deduced from permeation tube emission rate
Speculation -- author did not report a temperature
Speculation -- author did not report time units
-------
Table II. Arrhenius Parameters for S02 Permeability
Material 1n Po
TFE Teflon -10.39
FEP Teflon -9.54
Silastic LS-63U®
(fluorosilicone
rubber)
Silastic LS-63^
(silicone
rubber)
PVF (Tedlar)
Membrane
Polyvinylidene
fluoride (Kynar)
+ 8.2% sulfolane
(300 psig)
(400 psig)
(500 psig)
Polyethylene
•14.65
•14.01
-6.49
-13.24"
-15.51°
-17.62C
-2.44C
S.Dva'
0.27
-
0.20
_
_
_
-
0.13
0.13
-
- _
0.28
0.97d
0.51d
0.55d
0.56d
P xlO"
0
3.07
-
7.23
_
_
—
-
0.0435
0.0826
-
_
152.
0.1 78d
0.0183d
0.00223d
8700. d
E l"'
p
6.54
6.99
7.18
7.146
9.086
9.086
8.45d
0.253
0.651
1.33
0.94
9.39
4.32d
2.67d
1.07d
10.2d
S.Dva'
0.23
0.83
0.14
_
_
_
0.86d
0.118
0.088
0.38
0.87
0.20
0.60d
0.32d
0.35d
0.33d
Source
Regression on Figure 1
Rodes e_t. al_. (23)
Regression on Figure 2
Dietz et. aj_. (8)
Saltzman et. al. (26)
Brbcco and Possanzini (2)
Present study
II
Rodes et. al_. (23)
Present study
Seibel and McCandless (32)
Regression on Figure 4
-------
Footnotes for Table II.
aStandard deviation
cm (STP)/s-cm.cm Hg
ckcal/gmole
Calculated from data reported by author
Calculated by subtracting a heat of evaporation AH „„ = 5.46 kcal/g-mole (5)
evap
from the published activation energy, which was for the combined processes of evaporation and
permeation.
-------
10
-7
X
E
o
I
7
u
I 10"
u>
I
Q
^fti
u
u
- 10"
X)
o
Q*
Q_
10
o TFE Teflon Tube
• TFE Teflon Heat Shrinkable Tube
a Rodes, et al. (23)
^ Metronicsd?)
o Jordan (15)
i i i i i i i
2.00 2.25 2.50 2.75 3.00 3.25 3.50
1000/T, °K~'
Figure 1
Permeabilities of TFE Teflon.
62
-------
10
-7
- r
I -
i
o>
I
E
u
I
E
o
I 10
o
o>
(0
I
o
u
S
,-8
v-9
- O
10
.-10
FEP Teflon Tube
FEP Teflon Heat
Shrinkable Tube
FEP Teflon Membrane
Saltzman, etgL(26)
Metronics (17)
Dietz, et gl. (8)
Scaringelli, et al.(3l)
0 Keeffe and Ortman(l9)
Stevens, et aj. (36)
Benarie and Bui-the-Chuong (I)
J 1 I I L I
1
2.00 2.25
2.50 2.75 3.00
1000 / T, °KH
3.25 3.50
Figure 2.
S02 Permeabilities of FEP Teflon.
63
-------
ID
"5
o»
o
o
tn
I
CL
(0
IO
'6
CM
O
O
I I T I I I
Fluorosilicone Rubber
• 00 = 0.336 in., ID = 0.205 in.
o OD = 0.334in., ID = 0.2935n.
A Rodes, et oj. (23)
Silicone Rubber
v Rodes et 01(23)
A Benarie and Bui-the-Chuong(l)
Dimethyl Silicone Rubber
a General Electric (I I)
• Robb (22)
* Hodgson (13)
I I
xi
%
&
I
I
1
1
1
I
I
2.00 2.25 2.50 2.75 3.00 3.25 3.50
1000/T, °KH
Figure 3. S02 Permeabilities of Silicone Rubbers.
64
-------
0»
X
o
o
•o
3
I
!?i
&
o"
CO
o
o
o
10'
-50
I I
• Brubaker and Kammermeyer(3)
Hanousek and Herynk(l2)
"NSR"
• 0% Relative Humidity
• 84% " ••
"CSSR"
a 0% Relative Humidity
o 84% •• H
BenarSe and Bui-the-Chuong(l)
Davis and Rooney (7)
8 8 8 I i I
3.1 3.2 3.3 3.4 3.5 3.6 3.7
Figure 4. SO,, Permeabilities of Polyethylene.
65
-------
APPENDIX B
EFFECTS OF MOISTURE ON THE PERFORMANCE*
OF PERMEATION SAMPLING DEVICES
R. M. Felder, J. K. Ferrell and J. J. Spivey
Department of Chemical Engineering
North Carolina State University
Raleigh, North Carolina 27607
ABSTRACT
Sampling tubes made of TFE Teflon, FEP Teflon and fluorosilicone
rubber have been.used to measure S02 concentrations in gases containing
up to 21% water by volume. Even at the highest water concentrations, the
dew point of the sample gas was well below the range in which condensation
in the sample line or the gas analyzer could occur; in addition, the S02
permeabilities of the tubes were found to be independent of the chamber
gas humidity. These results suggest that the moisture content of a stack
gas or process stream should not affect the performance of a permeation
sampling tube, either directly through condensation or indirectly by alter-
ing the permeation rate of the gas whose concentration is to be measured.
Published as Analysis Instrumentation 12, 35 (1974). Reprinted by permission
of the Instrument Society of America.
66
-------
INTRODUCTION
Continuous stack gas monitoring has a variety of process industry ap-
plications. It can be used to verify that a process is operating at a de-
sired steady-state level, to provide feedback signals to a control element
in the event of undesired changes in operating conditions, to evaluate the
performance of an add-on pollution control device, and to determine compli-
ance with federal regulations relating to source emissions.
A number of factors such as high particulate loadings and high stack
humidities can complicate the analysis of a gas sample drawn from a stack.
To minimize the effects of these factors on the performance of a continuous
monitoring device, the sample must be conditioned before being analyzed:
particulates must be filtered out, and water must be removed.
Most sample conditioning methods involve the use of particulate filters
and cold traps or water adsorption columns, devices which require relatively
frequent servicing; these methods are consequently not ideally suited to
(2)
long-term continuous monitoring. Rodes, Felder and Ferrellv ' recently re-
ported on the use of polymeric sampling tubes for SOp monitoring, a techni-
que suggested by O'Keeffe^ . A U-shaped tube which is permeable to S02 (or
whatever gas is to be monitored) is inserted into the stack, and a clean car-
rier gas is passed through the inside of the tube; the resulting S02 concen-
tration gradient from the outside of the tube to the inside leads to permea-
tion of the S02 through the tube wall into the carrier gas, which then passes
out of the stack to an analyzer.
(2\
Rodes et al. ' studied the performance of TFE Teflon, silicone rubber
and fluorosilicone rubber tubes, and showed that the concentration of SOp in
the carrier gas could be easily and well correlated with the SOp concentration
67
-------
in the stack. A subsequent study by Spence, Felder, Ferrell and Rodes
showed that TFE tubes can effectively screen out particulates under heavy
particulate loading conditions.
A major question regarding the feasibility of polymeric sampling inter-
faces is the effect of stack humidity on their performance. A high stack
moisture content can have two possible deleterious effects: (1) water might
permeate into the tube and subsequently condense, leading to erroneous analy-
zer readings; (2) water dissolved in the sampling tube could alter the tube
permeability to the gas being monitored, so that a correction for stack hu-
midity would have to be applied to the analyzer reading to determine the
stack gas concentration. This paper reports on studies of stack humidity
effects on the performance of TFE Teflon, FEP Teflon and fluorosilicone rub-
ber sampling tubes, and indicates the extent to which these two negative
phenomena are likely to affect the performance of these devices in continu-
ous S02 monitoring.
68
-------
EXPERIMENTAL
A schematic diagram of the experimental apparatus used- in this study
is shown in Figure 1.
A chamber of simulated stack gases was constructed by bolting two
six-inch square end plates to the ends of a 12-in.ch long, 3-inch I.D. Type
316 stainless steel chamber. Each end plate was tapped to accept a .125-inch
thermocouple fitting, a .125-inch pipe fitting, and a .375-inch pipe fitting.
All fittings were of Type 316 stainless steel. Each of the .375-inch fittings
was drilled internally to allow a section of .375-inch O.D. stainless steel
tubing to pass through the end plate to the interior of the chamber. The
sampling tube was connected to these sections of stainless steel tubing and
supported by a stainless steel rod. The chamber assembly was then placed in-
side a thermostatically controlled oven with a temperature adjustable to 250°C.
A mixture of 5000 ppm SOp in air and a dilution stream consisting of air
which had been passed through an activated charcoal column were fed through
rotameters into a tee. The combined stream passed through an access port in
the oven to one of the 0.125-inch taps in the chamber end plate. When desired,
water was introduced into the chamber gas by metering liquid water fed from a
constant head tank into a tee in the chamber gas line prior to its entry into
the oven. The tee was packed with sintered stainless steel, and the tee and
the line from the tee to the oven were heated gently by a heating tape control-
led by a variable transformer; the stainless steel packing provided sufficient
surface area to evaporate the water without abrupt dropwise flashing. The
water vapor concentration in the chamber was calculated from the metered flow
rates of liquid water and of the SOp-air mixture, and was checked by a hygro-
meter. After leaving the chamber, the gas passed through a sodium hydroxide
scrubber, and the scrubbed gas was vented.
69
-------
Purified air was also used as the sampling tube carrier gas. The air
passed through a rotameter and a .375-inch stainless steel tube into the
sampling tube, and upon leaving the tube, flowed through a stainless steel
line to a Meloy Labs flame photometric detector (Model SA-160) which measur-
ed the S02 concentration in the gas. When the carrier gas water vapor con-
centration was to be measured, the flow was diverted to a Panametrics hy-
grometer (Model 2000). Strip chart recorders permitted continuous monitor-
ing of both S02 and water in the exit gas.
Two thermocouples were used to monitor the temperature in the chamber,
and the temperatures of the carrier and chamber gases were monitored by
thermocouples placed just prior to the chamber. The absolute pressure of
the carrier gas and the pressure inside the chamber were measured using
water manometers.
The flame photometric detector was calibrated using purified air passed
over an S02 permeation tube with a known emission rate, varying the flow
rate of the air to generate a series of gases with known S02 concentrations.
This procedure was performed before and after each set of sampling runs at
each temperature. The drift in the analyzer calibration during any set of
measurements was never greater than 3%.
At the outset of a run the sampling tube inner and outer diameter and
length were measured. The tube was placed in the stainless steel chamber
and the lines inside the oven were connected to it. The oven thermostat was
set, and the chamber temperature was monitored until steady-state was achieved.
The chamber was then purged with gas containing the desired concentration of
SOp and/or water, and the pressures of the carrier gas and the purge gas
were regulated by throttling the appropriate lines downstream of the oven.
70
-------
The pressure of the carrier gas was kept slightly higher than that of the
purge gas to assure that a pinhole in the sampling tube would not lead to
a large bulk flow from the purge gas to the carrier gas. The carrier gas
flow was then adjusted to the desired value, and was directed from the out-
let of the oven to either the flame photometric detector or the hygrometer.
When the recorder trace indicated that steady-state diffusion of S02 or
water vapor had been achieved, the recorder signal was noted and background
concentrations of the diffusing gases were subtracted. (The concentration
of SOp in the purified air was approximately .02 PPM, while the water vapor
background concentration was approximately 50 PPM.) The fluxes of the per-
meating gases could then be calculated from the corrected concentrations of
these gases in the carrier gas stream, the carrier gas flow rate, and the
length of the sampling tube.
DATA ANALYSIS
The rate of permeation of a gas through the walls of a tube may be ex-
pressed as
In (b/a)
where
o
F = permeation rate, cm (STP)/sec-cm length
P = permeability (product of diffusivity and
solubility), cm3 CSTP)/sec-cm-cm Hg
p, ,P2 = partial pressures of the permeating species in
the carrier gas (inside the tube) and chamber
gas (outside the tube), cm Hg.
a,b = inner and outer tube diameters, cm.
71
-------
The principal assumptions which lead to Equation (1) are Fickian dif-
fusion in the tube with a constant diffusivity, and Henry's law of solu-
bility. In addition, if both the diffusivity and solubility follow an
Arrhenius law temperature dependence, then
P = PQ exp(-Ep/RgT) (2)
where
P = a pre-exponential factor, units of P
E = activation energy for permeation, kcal/g-mole
R = gas constant, kcal/g-mole«°K
T = absolute temperature, °K
Equation (1) predicts that a plot of F (obtained by multiplying the
measured concentration of the permeating species in the carrier gas by the
carrier gas volumetric flow rate) vs. 2ir(p2-p1)/ln (b/a) at a fixed tempera-
ture should be a straight line through the origin, with the slope equal to
the permeability P at that temperature. Equation (2) predicts that an
Arrhenius plot of In P vs. 1/T should be linear, with the negative of the
slope equal to the activation energy E divided by the gas constant R .
The experiments consisted of adjusting chamber concentrations of S02
and/or H20, measuring the permeation rates of these gases through the sampl-
ing tube walls, and plotting the data as indicated above. In this manner,
permeabilities of the tube materials to S02 and to water could be determined
at different temperatures.
72
-------
RESULTS AND DISCUSSION
Sulfur Dioxide Permeation
Permeation measurements were made on TFE Teflon, FEP Teflon, and
Silastic LS-63U^fluorosilicone rubber tubes, the latter manufactured by
the Dow-Corning Corporation. In all of the permeation runss the partial
pressure of the S02 in the chamber (p2 of Equation (1)) was several orders
of magnitude greater than the partial pressure in the carrier gas (p-,); con-
sequently, the permeability could be calculated from a plot of permeation
rate (F) vs. 2Trp2/ln(b/a).
Figure 2 shows plots of S02 permeation rates into a TFE Teflon tube vs.
/lrv(b/a) at three temperatures. Data points are shown both for dry
chamber gases and chamber gases containing 21.1% water by volume
(dew point = 61.5°C = 142°F).
Two principal points emerge from an inspection of Figure 2.
1. As predicted by Equation (1), the isotherms are straight lines through
the origin. The assumed model therefore correlates the permeation rate
data, and Equation (1) may accordingly be used for the design of permea-
tion sampling tubes and the interpretation of data obtained with these
devices.
2. The data obtained for dry and highly humid chamber gases are statisti-
cally indistinguishable, indicating that the presence of water in the
chamber gas does not affect the permeability of TFE Teflon to sulfur
dioxide. This is an encouraging result: it implies that for at least
this material, permeation stack sampling data need not be corrected for
variations in the stack gas humidity, so that there is no need to mea-
sure this quantity as a routine part of the stack monitoring procedure.
73
-------
Figure 3 shows the results obtained using a fluorosilicone rubber
tube. The results are qualitatively similar to those obtained for TFE:
the plots are linear, and water in the stack gas has no discernible effect
on the permeation rate of S02. The differences are that the S02 permeabi-
lity of the fluorosilicone tube is roughly an order-of-magnitude greater
than that of the Teflon tube, and is much less sensitive to temperature.
Permeation rate plots for FEP Teflon are similar to those shown for TFE.
S02 permeabilities obtained by least-squares fitting of lines through
the origin to permeation rate plots are listed in Table 1. The fluorosili-
(2)
cone permeabilities agree quite closely with those given by Rodes et a!.v '
while the TFE permeabilities are roughly 60% higher than those reported in
the earlier study, a discrepancy which we cannot now explain. Arrhenius
plots of log Pcn vs. 1/T for TFE, FEP and fluorosilicone rubber are linear,
bU2
as predicted by Equation (2); however, the temperature range of the data
obtained so far is too small and the data points are too few in number to
permit a meaningful calculation of activation energies for permeation.
Mater Permeation
Permeation rates of water through the three tube materials were also
measured. The results obtained for a TFE tube are shown in Figure 4. As
was the case for SCL permeation, the data points for specific temperatures
can be reasonably well correlated by straight lines through the origin, al-
though the scatter in the water permeation data is greater than that for S02.
Plots for FEP and fluorosilicone are similar to those of Figure 4, with the
differences paralleling those reported for S02 permeation: the permeability
of TFE at a given temperature is approximately equal to that of FEP and is
an order-of-magnitude less than that of fluorosilicone, and the permeability
74
-------
of fluorosilicone is considerably less temperature-sensitive than are the
permeabilities of TFE and FEP.
The permeabilities determined by least-squares fitting of lines through
the origin to water permeation rate plots are listed in Table 2. Again, the
temperature range and number of data points do not provide an adequate base
for accurate estimation of Arrhenius plot slopes.
The results are adequate to establish one of the principal desired re-
sults of this study, however -- namely, that a polymeric permeation sampling
device can provide a sample gas with a dew point well below the point at which
condensation in the line leading to the analyzer could occur. For example,
if the fluorosilicone tube used in this study were used to monitor a stack at
177°C with a stack gas dew point of 6l°C, the dew point of a carrier gas flow-
2
ing at 655 cm (STP)/min (a representative figure for SQy monitoring) would
be -29.5°C, and the carrier gas dew point would be even lower if a Teflon tube
were used.
Studies are currently in progress to extend the temperature range of both
the S02 and water permeation measurements so that activation energies for perme-
ation may be determined with a reasonable degree of precision, to perform per-
meation tests on additional single and composite tube materials, to extend the
tests to NO permeation measurements, to study the effects of mists (as opposed
x •
to water vapor) in the stack gas on the performance of permeation sampling
tubes, and to field-test prototype devices in process and power-plant stacks.
75
-------
CONCLUSIONS
The principal results of this study are as follows:
1. Stack sampling tubes made of TFE Teflon, FEP Teflon and fluorosilicone
rubber all provide sample gases with dew points well below normal am-
bient temperatures.
2. The permeation rates of S02 through the tube materials tested are inde-
pendent of the stack gas humidity.
Considered together, these results suggest that the moisture content
of a stack gas or process stream should not affect the performance of a
permeation sampling tube used to monitor S0«j either directly through con-
densation in the line to the analyzer or indirectly by altering the rate of
permeation of S02 into the tube.
76
-------
REFERENCES
1. O'Keeffe, A., U. S. Patent Appl., December 1970.
2. Rodes, C. E., Felder, R. M. and Ferrell, J. K., 1973, "Permeation of
Sulfur Dioxide Through Polymeric Stack Sampling Interfaces," Environ.
Sci. Technol. 7_t p. 545.
3. Spence, R. D., Felder, R. M., Ferrell, J. K. and Rodes, C. E., 1973,
"A Polymeric Interface for Monitoring SO? Emission from Stationary
Sources," paper presented at a National Meeting of the American Insti-
tute of Chemical Engineers, New Orleans, Louisiana, March 1973.
77
-------
TABLE 1. S02 Permeabilities
Material
TFE
Teflon
FEP
Teflon
Fluoro-
silicone
Rubber
Temperature, °C
154
179
202
171
175
180
197
201
153
175
200
225
S02 Permeability
P x 107
Q
(cm (STP)/sec-cm-cm Hq
0.162
0.245
0.359
0.207
0.220
0.217
0.294
0.318
2.92
3.02
3.18
3.23
78
-------
TABLE 2. Water Permeabilities
Material
TFE
Teflon
FEP
Teflon
Fluoro-
silicone
Rubber
Temperature, °C
127
171
191
217
171
180
197
130
156
177
Water Permeability
P x 107
o
(cm (STP)/sec-cm-cm Hg)
0.340
0.711
1.10
1.36
0.443
0.580
0.755
7.94
9.54
11.28
79
-------
oo
o
Constant Head Tank
I
Water
Rotameters
I
Span Gas
Rotameters
Dilution Air
Rotameters
Hygrometer
Oven
ff r *'
Sampling Tube
—{ >~
Carrier Gas Rotameters
Participate Activated
Filter Carbon Desiccant
—-D
Scrubber
Vent
Vent
Vent
Flame
Photometric
Detector
Vent
Figure 1. Experimental Apparatus.
-------
E
u
0>
M
I
cs
O
CO
x
3
5.0
4.0
3.0
2.0
1.0
TFE In (b/o)= .199
A Tube I
A Tube I with 21.1% water in
span gas
a Tube 2
• Tube 2 with 21.1% water in
span gas
2O2°C
I
I
I
8
2TT
ln(b/a)
12 14 16
cm Hg
Figure 2. Permeation rates: S02 through TFE Teflon.
81
-------
I
1 u
«
M
I
X"»
a.
i—
(A.
O
tf)
E
w
X
X
15
14
13
12
11
10
9
8
7
6
5
4
3
u
• Fluorosilicone ln(b/a)=.6O3
o
^Fluorosilicone with 21% water
in span gas
I
3
cm
225°C
195°C
ln(b/a) S02
Figure 3. Permeation rates: S02 through Fluorosilicone Rubber.
82
-------
u
I
a.
o
X
3
8.0-
7.0
6.0
5.0
4.0
3.0
2.0
1.0
TFE In (b/a)= . 2OO
171°C
127°C
1 I I I I I
1OO 2OO 3OO 4OO 5OO 6OO 7OO
2TT
ln(b/a)
Pu ^ •cm H9
Figure 4. Permeation rates: Water through TFE Teflon.
83
-------
APPENDIX C
PERMEATION DATA FOR NOV and H90
X b
The data given in the accompanying tables were obtained in a literature
search through April, 1974.
Table C-l reports Arrhenius parameters for permeation, diffusion, and
sorption of NO in FEP and TFE Teflon, and Table C-2 lists permeabilities
/\
of NO in TFE and FEP Teflon and dimethyl silicone rubber. Table C-3 gives
permeabilities, diffusivities and solubilities of water in a large number
of polymers, and Table C-4 lists activation energies for permeation and dif-
fusion of water.
84
-------
Table Cl. NO Arrhenius Parameters
J\
Material PQxl0
TFE Teflon
(N02)
(N204)
(N02-N204)
(N02-N204)
0.0116 2.55
0.00013 -0.5
- 9.91
e
(b)
Source
70. 14.0
0.4 9.54
16.6 -11.4 Pasternak et al. (1970)
_ _ H
Dietz et al. (1970)
10,900. -6.55 Johnson (1969)
FEP Teflon
(N02-N204)
(N02-N204)
10.1'
Saltzman et al. (1971)
56. 13.5 3,800 -7.15 Johnson (1969)
acra(STP)/s-cm-cm Hg
kcal/gmole
Ccm2/s
dcm3(STP)/cm3-cm Hg
Calculated by subtracting a heat of evaporations AH = 4.45 kcal/gmole
cVdp
(Yaws and Hopper,, 1974) from the published activation energy, which was
for the combined processes of evaporation and permeation.
85
-------
Table C2. Effective Permeabilities of Nitrogen Oxides
Material
TFE Teflon
(Permeation tubes)
(Film)
(Sprayed dispersion)
(Permeation tubes)
10(a)
Temperature peX1° (pNn + pN n )b'
(°r \ ' i"wo "o A
V* J ' t t *T
Source
20
21
21.4
30
30.4
39.8
40
207
175'
c.d
c.d
I93e
202d
268d
289*
268d
176d
362^
242
75C
102°
291
c'd
c,d
73.0
76.0
76.8.
116.3
117.0
177.1
177.8
Metronics (1970)
Bazarre and Petriello
(1970)
Stanford (1963)
Metronics (1970)
Dietz et.al. (1974)
Metronics (1970)
Effective permeability, cm3(STP)/s.cm.cm Hg; for N02 -N204 cm3CSTP)N02
Vapor pressure, cm Hg, of NO, - N^O. equilibrium (Handbook of Chemistry
and Physics. 1969) * * 4 .
.Rough estimate
Calculated from published flux using Eq. (3) or (4)
^Published value
Speculation -- author did not report a temperature
86
-------
Material
Temperature P.xlO
10V
Source
FEP Teflon
(Permeation tubes)
(film type A)
(film type 506)
(Permeation tubes)
TFE and FEP Teflon
Sprayed dispersion
13.8
20.
20.
20.1
21.4
40.8U
51.0C'd
41.5
54.5d
36.7d
32. Od
52.3d
35.7d
11.ld
14.2d
2.36^
16.3d
14.6d
54.8d
45.4d
71. Od
C'd
53.2
73.0
76.8
II
25.f
f
25.T
29.1
30.
30.
40.
40.
21.4
n
n
n
n
44. 3U
80. 5d
H
80. 9a
A
74. 4d
74.7c'd
59.8c'd
115. c'd
90.6c°d
A
42. 7d
A
55. 6d
A
67. r
A
56. r
!•-! /id
57.4
ii
92.7
92.7
110.2
116.3
116.3
177.8
177.8
76.8
"
•"
"
n
O'Keeffe and Ortman (1966)
Metronics (1970)
O'Keeffe and Ortman (1966)
Stanford (1963)
Saltzman et.al.(1971)
O'Keeffe and Ortman (1966)
Metronics (1970)
Stanford (1963)
" 1963)
87
-------
Material
Temperature PgXlO
10V
,(b)
Source
TFE and FEP Teflon
Codispersion
(100% TFE) 21.
(90% TFE)
(80% TFE)
(70% TFE)
(50% TFE)
(0% TFE, 100% FEP)
Laminate "
"
Dimethyl Si li cone Rubber (25%)
(Permeability to N02) 25.
( " " NO)
( " " N20)
( " " N02)
( " " NO)
( " " N20)
52. 5d 76.0 Pi
52. 5d
38. 6d
17. 5d
7.d
7 d
38. 6d
94.5c'd B,
5820. e '- Gi
458. e
3340. e
6960.e - R(
550. e
3990. e
Petriello (1968)
Bazarre and Petriello
(1970)
General Electric (undated)
Robb (1968)
88
-------
Table C3. Permeabilities, Diffusivities and Solubilities of Water in
Polymers
Material Temperature( C) PxlQ
10°
TFE
(Teflon)
(Halon G-183)
(Teflon)
(Halon G-183)
(Teflon)
20
20
23
30
38
40
50
60
127
171
24.0
46.4
33.6
8.45
38.4
14.9
13.5-28.6d
340.
711.
DxlO'u ST Source
Korte-Falinski (1962)
0.0709q Barrie (1968)
Toren (1965)
Korte-Falinski (1962)
Hadge et.al. (1972)
Korte-Falinski(1962)
Hadge et.al. (1972)
Felder et.al. (1974)
Permeability, cm (STP)/s-cm.cm Hg
h 9
Diffusivity, cm /sec
Solubility, cm3(STP)/cm3-cm Hg
Permeability depended on membrane thickness
f*i
Penneability determined with liquid water at one surface
Permeability determined with water vapor at one surface
Calculated from the reported rate data and a driving force equivalent to
the saturated vapor pressure.
Data from unoriented film
'Data from oriented film
JData from laboratory cast film
Data from commercial film
Data from calendared film
tnData from cast film
"speculation -- permeability calculated based on an inferred membrane
thickness
^Speculation -- author did not report a temperature
qUnits
g polymer-cm Hg
89
-------
Material
TKE(Cont'd)
(Teflon)
Temperature(°C)
191
PxlO10 DxlO10
1,100.
(Teflon heat-shrunk
on porous
(Teflon)
FEP
s.s) 213
217
21
23
25
25
35
35
39.5
45
45
55
55
65
65
75
75
85
85
95 1
95 1
1 ,340.
1,360.
21.3
19.4
480. e
250. f
26, 400. e
7,700.f
42.9
66, 000. e
52, 500. f
75, 500. e
72, 000. f
11.8, 000. e
108,000.f
290, 000. e
274, 000. f
898,000.e
860, 000. f
,560, 000. e
,540, 000. f
Source
Felder et.al. (1974)
Woolley(1967)
Toren (1965)
Sivadjian and Riberio
(1964)
DuPont
Sivadjian and Riberio
(1964)
90
-------
Material Temperature TO PxlOlw DxlOlu
FF.P (Cont'd )
(Teflon)
171
180
197
443.
580.
755.
Chlorotrifluoroethylene
(Kel-F)
(Halon)
23
23
30
38
2.67
2.00
0.29
3.63
Ethyl ene/Chlorotrifluorcithylene
(halar)
Poly vinyl fluoride
(Tedlar)
30
45
60
' 25 4
25 3
35 34
35 31
38
39,5
39.5 1,070
45 95
45 75
50
SS 365
55 357
60
65 809
65 537
14.8
24.1
42.1 - '
,023.®
9291.f
,700.a
8800.f
34.
41.
,,000.
,100.®
,300. f
86.8
,000. @
,000. f
181.4
8ooo.@
O000.f
Source
Felder et.al. (1974)
Toren (1965)
H
Barrie (1968)
Hadge et.al. (1972)
Hadge et.al. (1972)
Sivadjian and Riberio
(1964)
Hadge et.al. (1972)
BarHe (1968)
DuPont (undated)
Sivadjian and Riberio
(1964)
Hadge et.al. (1972)
Sivadjian and Riberio
(1964)
n
Hadge et.al. (1972)
Sivadjian and Riberio
(1964)
91
-------
Material Temperature(°C) PxlO
10°
DxlO
10C
Source
Polyvlnyl fluoride (cont'd)
(Tedlar.) 75 1,600,000.'
75 833,OOO.1
85 3,330,000.'
85 3,070,OOO.1
95 5,030,000.'
95 4,880,OOO.1
Sivadjian and Riberlo
(1964)
Fluoroplastic
(32L, type N)
(32L, type V)
(32L, type N)
(32L, type V)
(32L, type N)
(32L, type V)
Silicone Rubbers
(dimethyl s1licone)25
25
(dimethyl sllicone,
peroxide cured,
silica filler) 25
(5601) 25
(dimethyl s1licone)35
38
(5601) 48
(dimethyl silicone)65
(5601) 76
100
(Fluorosilicone 130
Silastlc LS-63U)
156
177
25
25
40
40
50
50
178.g
175.9
119.9
116.9
75.9
78.9
7,800
8,000
10,300
12,000
10,200
10,300
Shirokshlna e£.a_K(1970)
33,000
27,450
104,700.'
15,300
4,300
1,111
13,070
3,280
11,570
10,430
7,940
9,540
11,280
^70,000
100,000
Robb (1968)
General Electric(undated)
Hodgson (1973)
Kass and Andrzejewski
(1973)
Barrie (1968)
Hadge et.al. (1972)
Kass and Andrzejewski
(1973)
farrie (1968)
Kass and Andrzejewski
„ (1973)
Felder et.al. (1974)
92
-------
Material Temperature(°C) PxlO
10"
DxlO1
Polycarbonate
(Lexan)
(Unstretched)
21
23
23
(Unlaxial stretched)
23
(Kimfol)
(Kimfol & Makro-
fol)
(Lexan)
(Unstretched)
25
25"
25p
25
25
40
40
(Uniaxial stretched)
40
(Lexan)
50
100
2,800
778
1,456
1,120
2.197.3
760
370
1,170
14,000
1.047.9
1,207
933
648. g
-
-
-
-
—
84,000
-
350
6,800
93,000
-
„
96,500
600
-
-
-
—
-
—
3.34
2.22
-
-
—
-
-
Polyethylene
(Supra then NR 100) 25
(Plastin)
0
15
20
20
21
22
25
25
25
25
25
25
30
7.5'
24. 51
32.1
76.8
90.6
36.m
61. ]
73.6
39.8
12
25
90
124
-
—
-
-
-
-
-
820
122
-
-
80
-
Source
Woolley (1967)
Toren (1965)
Ito (1962)
Ito (1962)
Shirokshina et.al. (1970)
Woodgate (1971)
Spivack (1970)
Rust and Herrero (1969)
Norton (1963)
Shirokshina et.al. (1970)
Ito (1962)
Ito(1962)
Shirokshina et.al
Norton (1963)
Doty et.al. (1946)
(1970)
Korte-Falinski (1962)
Woolley (1967)
Doty et.al. (1946)
_ H n
0.0898 Rust and Herrero (1969)
0.326 ,Rust and Herrero (1969)
Barrie (1968)
93
-------
Material Temperature(°C) PxlO10 DxlO10
Polyethylene(Cont'd)
Polypropylene
(Udel)
(Block 75-80,000
M,W.)
(Emulsion
250,000 M.W.)
(Block 75-80,000
M.W.)
(Emulsion
250,000 M.W.)
(Block)
(Emu-Is Ion)
Polystyrene
(Kardel)
30
32
38
40
40
60
80
23
25
25P
25
25
25
30
40
40
50
50
23
25
25
25
25
32
32
120.1
86
110. 51
199
79.1m
222.m
500. m
39.9
22.9
39
2,925.9 Ill
3.216.9 124
51 2
68
1.213.9 110
1.457.9 131
962. 9 143
1.043.9 154
>632
1,130 1
970
895. h
835. 1
800. h
840. 1
94
-
-
_
-
-
-
49
-
,000
,000
,400
4.1
,000
,000
,000
,000
-
,400
-
-
-
...
Source
Korte-Falinsk1 (1962)
Doty et.al. (1946)
H n
Korte-Falinski (1962)
Doty et.al. (1946)
Toren (1965)
49 0.467 Rust and Herrero (1969)
Spivack (1970)
Sh1roksh1na et.al. (1970)
_ " n
Barrle (1968)
_ n
- Shlrokshina et.al. (1970)
Toren (1965)
1,400 0.807 Rust and Herrero (1969)
Barrle (1968)
Doty et.al. (1946)
-------
Material Temperature (°C) PxlO10
Polystyrene (Contd)
(Kardel)
Pol.yvlnyl chloride
(Geon 101)
(Vynan)
(Geon 101)
(Emulsion
Genotherm U.G.)
(Plastlcizer 100-
75)
(Chlorinated)
(Geon 101)
(Vynan)
(Plastlcizer
100-30)
(Geon 101)
(Vynan)
(Geon 101)
(Plastlcizer
100-75)
(Chlorinated)
(Geon 101)
38
38
45
50
0
0
10
10
20
25
25
25
25
25
30
30
30
30
35
40
45
50
50
55
870.h
835. 1
820. h
1,070
86. j
109. j
115. ^
122. j
240.
116. j
123. J
257.
2,000
207
149.J<
259
-
340
155.^
274
187. j
3,790
235
203. J"
DxlO1^ Sc
Pol.yv1n.yl chloride- acetate copolymer
(Vlnyllte) 0 199.J'
10 222. ^
230
170
Source
Doty et.al. (1946)
Barrie (1968)
Doty et.al. (1946)
Korte-Falinskl (1962)
Doty et.al. (1946)
36 7.14 Rust and Herrero (1969)
Barrie (1968)
Doty et.al. (1946)
Korte-Fallnski (1962)
Barrie (1968)
Doty et.al. (1946)
Korte-Fallnski (1962)
Doty et.al. (1946)
Barrie (1968)
Doty et.al. (1946)
Doty et.al. (1946)
95
-------
Material Temperature( C)
JO
(a)
PxlO'u DxlO'u .S
io M
Polyvinyl chloride
(Vinylite)(Contd)
(VYNS 90-10)
(Vinylite)
Polyvinylidene
Chloride - Vinyl
Chloride
Copolymer
(Saran)
25
25
25>
32
32
38
38
21
25
32
38
288J
325k
210
_
382k
324^
438k
12.1
2.0
5.2
8.2
_
r-
600
-
_
-
-
-
-
_
Polyvinylidene
Chloride 30
Polyvinylidene
Chloride
Acrylonitrile
Copolymer 25
Polyvinyl acetate 25
40
Polyvinyl alcohol 20
25
25
30
40
Polyvinyl formal-acetate-alcohol
(Formvar) 25P
Polyvinylbutyral 25
1.4-10
16
3.2
430.
6,000. 1,500.
182,000.
19. 0.51
96. 12.5
177,000.
144,000.
575.
1,850. 130
Source
Doty et.al. (1946)
n
Spivack (1970)
Barrie (1968)
Doty et.al. (1946)
Woolley (1967)
Doty et.al. (1946)
Barrie (1968)
Barrie(1968)
Korte-Falinski (1962)
Barrie (1968)
ii
,Korte-Falinski (1962)
ii
Spivack (1970)
Barrie (1968)
96
-------
Material Temperature (°Cl PxlO
Polyesters •
(Terephane)
(Mylar)
(Celanese)
(Kodar)
(Mylar)
(3-M)
(Hostaphan R50)
(Polyethylene
Terephthlate)
(Mylar)
(Terephane)
Polymethyl
Methacrylate
Polyethyl
Methylacrylat«»
Polymethacrylate
(Emulsion)
Polyarylate
(F-l)
(ITD 50:50)
(F-l)
(ITD 50:50)
(F-l)
(ITD 50:50)
Polvamide
(Nylon MB2)
(Rilsan)
20
21
23
23
23
23
25
25
25P
30
40
50
25
90
25
25
40
50
25
25
40
40
50
SO
20
20
221
115
142
130
167
146
1S3
175
60
226
230
2,500
•x-3,500
•v6,000
-
3,391.
1,491.
1,161.
2,241.
5,908.
1,207.
2,876.
910.
1,860.
9,400
235
3% DxlO10
-
-
-
-
-
-
27.
39.
-
-
-
1,300
1,050
35,000
1,200
9 135,000.
9 132,000.
9 177,000.
9 85,000.
9 230,000.
9 107,000.
9 261,000.
9 135,000.
9 284,000.
-
- •
(b) (
S(
Source
Korte-Falinski (1962)
Wool ley (1967)
Toren(1967)
5.67 Rust and Herrero(1969)
Barrie (1968)
Spivack0970)
Korte-Falinski (1962)
Barrie (1968)
Barr1e(l968)
Shlrokshina et.al. (1970)
Shirokshlna et.al. (197°)
Korte-Fal1nsk1 (1962)
97
-------
Material Temperature(°C)
10(a) 10(b) / x
PxlO10 DxlO10 SU)
Polyamide(Cont'd)
(Nylon 6)
(Rilsan)
(Nylon MB2)
(Rilsan)
(Nylon MB2)
(Nylon 6)
25
25
30
30
40
40.
60
400 9.7
1 ,400
302
8,980
403
8,400
1,900 80.
Poly(chloro-p-xylylene)
(Parylene C)
Source
Barrie (1968)
Korte-Falinski (1962)
20
Barrie (1968)
Spivack (1970)
Poly(-p-xylvlene) 25P
(Parylene N)
Polyethylene-
tetrasulphide
Phenolic
(Phenall 8700)
21
Diallyl phthalate
(Diall 51-21) 38
60
57
60
116
14.7
Barrie (1968)
Hadge et.al. (1972)
Hadge et.al. O972)
Epoxy
(Competitive)
(Experimental)
(Epiall 1970)
(Competitive)
(Experimental)
(Competitive)
(Experimental)
(Epiall 1970)
Bakelite
Ethyl Cellulose
37
38
38
50
50
60
60
60
25
25
25
83.9
21.6
34
129
35
155
49.7
82.2
1,660
21 ,000
23,800
Hadge et.al.. (1972)
Barrie (1968)
Barrie (1968)
98
-------
Material Temperature (°C) PxlOK
' DxlO10
Ethyl Cellulose (Cont'd)
Regenerated
Cellulose
(Cellophane
Impermeable IS)
(Cellophane
Permeable N)
(Cellophane)
(Cellophane Imp.
IS)
(Cellophane Perm.
N)
(Cellophane Imp.
IS)
(Cellophane Perm.
N)
Cellulose Acetate
(Triacetate KC)
(Di acetate K41)
(Triacetate)
(Triacetate KC)
(Dlacetate K41)
(Triacetate KC)
80
20
20
21
25
25
25
30
30
40
40
20
20
20
21
25
25
25
30
30
30
30
40
11,000
1,870
14,600
44,000
1,900
3,580
17,000
1,920
14,400
2,'HO
13,800
12,300
15,800
16,500
8,130
62,100
150,000
12,700
6,000
12,500
16,100
17,800
12,500
12,000
_
—
-
-
-
<10.
_
.
..
-
-
-
-
-
-
-
-
170
-
-
-
-
Source
Barrie (1968)
Korte-Falinski (1962)
it
Woolley (1967)
Barrie (1968)
Korte-Fal1nsk1 (1962)
Woolley (1967)
Barrie (1968)
Korte-Fatinski (1962)
99
-------
Material Tempera ture(C)
Cellulose Acetate
(Cont'd)
(Oiacetate K41)
(Triacetate)
Rubber
hydrochloride
(Pliofilm)
PxlO
DxlO
Natural Rubber
(Soft, Vulcan.) 25
Polyisobutene
40
40
50
20
25
25
30
38
43.5
47.5
52
25
30
37.5
16,300
i
19,200
13,800
10.2
12.4
14 4.1
20.8
41
43.5
51.5
87
2,290
71-224.4
110
Source
Korte'-Falinski (1962)
Barrie (1968)
Doty et.al. (1946)
H
Barrie (1968)
Doty et.al. (1946)
Barrie (1968)
TOO
-------
Table C4. Activation Energies for Permeation and Diffusion of Water
Material
(kcal/gmole)
ED
(kcal/gmole)
Source
Dimethyl Silicone
Polyethylene 8.0
10.2
-
-
8.0
Polystyrene 0
Polypropylene
10.0
Poly amide
(Nylon)
(Nylon 6)
a
Polyethylene-
terephthalate 0,5
Polyvinyl chloride
2.35
2.35
Polyvinyl chloride-
acetate 2.35
4.0
=
-
Polyvinyl alcohol
Polyvinyl acetate
^ 3
-
-
19.2
14.2
14.2
-
16.4
16.4
13.3
6,5
12.5
10.4
42
10
_
.
-
7.7
19.6
14.3
15.0
Barrie (1968)
Doty et.al. (1946)
"
Spencer (1965)
"
Barrie (1968)
Doty et.al. (1946)
Spencer (1965)
Barrie (1968)
Spencer (1965)
Barrie (1968)
"
Barrie (1968)
Spencer (1965)
Barrie (1968)
Doty et.al. (1946)
Doty et. aj[. (1946)
»
Spencer (1965)
"
Spancer (1965)
Soencer (1965)
101
-------
Material
Kcal/gmoTe
kcal/gmoTe
Source
Polyvinyl acetate (Cont'd)
Polyvlnylidene
chloride .
Polyvinyl1dene
chloride-
acrylonitrlle
Polyvinyl Butyral
Polymethy1 aerylate
Polymethylmethacrylate
Polyethylmethacrylate
Cellulose Acetate
17.5
10.3
-2.1
0.5
4.3
Ethyl Cellulose
-1.5
-2.8
Rubber Hydrochloride 12.8
12.5
15
20.2
10.9
11.0
11.6
11.6
8.7
15.1
12.0
5.6
6.6
14.0
6.3
9.5
17.2
14.0
Barrie (1968)
Doty et.al. (1946)
Barrie (1968)
Spencer (1965)
Barr1e(1 968)
Spencer (1968)
Barrie (1968)
Spencer (1965)
Barrie (1968)
Doty et.al. (1946)
Spencer (1965)
102
-------
References for Appendix C
1. Barrle, J. A. 1n Diffusion In Polymers. J. Crank and G. S. Park, Editors,
New York, Academic Press (1968), p. 259.
2. Bazarre, D. F. and Petriello, J., Plating, 57, 1025 (1970).
3. Dietz, R. N., Cote, E. A., and Smith, J. D., Anal. Chem., 46, 315 (1974).
4. Doty, P. M., Aiken, W. H., and Mark, H., Ind. Enq. Chem.. 38, 788 (1946).
5. DuPont Tedlar PVF Film Bulletins TD-1A, TD-2, TD-3, and TD-6, E.I.DuPont
de Nemours and Co., Inc., Film Dept., Wilmington, Del.
6. Dupont Teflon FEP fluorocarbon film bulletins T-1C, T-2D, T-3D, E.I.DuPont
de Nemours and Co., Inc., Plastics Dept., Fluorocarbon Div., Wilmington,
Del.
7. Felder, R. M., Ferrell, J. K., and Spivey, J. 0., Anal. Instrum.. 12, 35
(1974).
8. "General Electric Permselective Membranes," General Electric, Medical
Development Operation, Chemical and Medical Division, Schenectady, N. Y.
9. Getman. F. H. and Daniels, F., Physical Chemistry, New York, John Wiley
and Sons, Inc. (1946), p. 297.
10. Madge, R. G., Riddell, M. N., and 0°Toole, J. L., Soc. of Plast.. Eng.
Tech. Pap.. JjJ, 5*5 (1972).
11. Handbook of Chemistry and Physics. Fiftieth Edition, R. C. Weast, Editor,
Cleveland, Chemical Rubber Co. (1969), Sect. D, p. 145.
12. Ito, Yukio, Kobanshi Kagaku. !£, 413 (1962).
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Contract No. NAS7-505 (1969).
14. Kass, W. J. and Andrzejewski, W. J., SLA-73-718, 1973 Report NTIS.
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Alto, Calif. (1970).
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19. Pasternak, R. A., Christensen, M. V., and Heller, J..Macromolecules, 3
366 (1970). ; "
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Angeles, Calif., May 1968, Proceedings, North Hollywood, Calif.,
Western Periodicals, p. 119 (1968).
21. Robb, W. L., Ann. N. Y. Acad. Sci., 146, 119 (1968).
22. Rust, G. and Herrero, F., Materialpruf, H, 166 (1969).
23. Saltzman, B. E., Burg, W. R., and Ramaswamy, G., Environ. Sci. Tech.
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104
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APPENDIX D
POLYMERIC INTERFACES FOR CONTINUOUS STACK MONITORING*
Lanny C. Treece, Richard M. Felder and James K. Ferrell
Department of Chemical Engineering
North Carolina State University
Raleigh, North Carolina 27607
ABSTRACT
Teflon tubes have been used as interfaces between stacks containing
S02 and ambient-level S02 analyzers. Continuous monitoring runs were
carried out in process and power plant stacks in which the S02 concentra-
tion varied from 85 ppm to 2000 ppm. The interfaces provided sample gases
with S02 concentrations which varied linearly with the S02 concentrations
in the stacks. The presence of acid mist and solid particulate matter in
the stack gases had no effect on the performance of the interfaces, and
fluctuations in the stack gas S02 concentrations were accurately mirrored
in the analyzer responses. The use of such interfaces eliminates the need
for frequent manual operations usually associated with sample conditioning,
such as filter changes and cold trap or drying column replacements, and
therefore makes possible continuous unattended monitoring for extended per-
iods of time.
Published as Env. Sci. & Technology 10, 457 (1976). Reprinted by permission
of the American Chemical Society.
105
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INTRODUCTION
A growing concern about the environmental impact of industrial waste
emissions into the atmosphere led to the passage of the Clean Air Act of
1970, which specifies that air pollution control plans include emission stan-
dards and requirements for monitoring stationary sources. If emission stan-
dards are to be enforced uniformly, then methods which indicate the true
emission rates of particular pollutants must be available. Furthermore,
these methods must be relatively simple and inexpensive so that industries
which are required to comply with the standards can do so without making large
expenditures for monitoring equipment and trained personnel.
Stack gas analyses have traditionally been performed by drawing a
sample through a small tube inserted in the stack, collecting and fixing the
pollutant in a solution or on a solid by absorption or reaction, and using con-
ductimetric, colorimetric, or photometric analysis to determine the concentra-
tion of the pollutant. Some of the techniques in current use are described in
the Federal Register, the Los Angeles Pollution Control District Source Sampl-
2 3
ing Manual, and by Cooper and Rossano.
More recently, methods have been developed which provide continuous re-
cords of pollutant concentrations. A review of instrumentation for continuous
A
S02 monitoring has been compiled by Hollowell, et al.
A gas sample withdrawn directly from a stack must usually be conditioned
before passing to a continuous analyzer or a wet chemical sampling train. The
conditioning entails removing condensible vapors, mists, and solid particulates,
and chemical species which are known to interfere with the analysis of the de-
sired pollutant. A typical sample conditioning procedure might involve heating
the gas to maintain vapors above their dew point or cooling to condense and re-
move the vapors from the sample stream, filtering the sample to remove particu-
106
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lates, and bubbling the gas through a liquid solution which removes the
undesired chemical species but allows the pollutant to pass through to the
analyzer.
A. O'Keeffe of the National Environmental Research Center, E.P.A.,
proposed using a polymer tube as a stack sampling interface. In the pro-
posed method, a carrier gas is passed continuously through a polymer tube
mounted in the stack, and the pollutant permeates through the tube wall
from the stack into the carrier gas stream, which then passes to a con-
tinuous ambient analyzer. This method has several potential advantages
over traditional sample conditioning techniques: an average concentration
across the stack can be measured, polymers can be used which do not pass
interfering pollutants, vapors in the carrier gas stream should be well
above their dew points, and particulate filters are not required.
Rodes, Felder, and Ferrell investigated the feasibility of this
technique. TFE Teflon and fluorosilicone rubber tubes were tested at temp-
eratures from 93°C to 232°C with simulated S02 stack concentrations in the
range 1,000 ppm - 10,000 ppm. The conclusions of the study were that the
S02 flux through such tubes is a predictable function of the temperature
and S02 concentration in the stack, and response times can be kept reasonably
short by selecting a tube with a sufficiently thin wall.
Felder, Spence, and Ferrell measured the permeabilities of S02 for
several materials over a wide range of temperatures, and compiled a complete
summary of these results and published S02 permeability data. Felder,
Ferrell and Splvey investigated the permeation of S02 and water through TFE
Teflon, FEP Teflon, and fluorosilicone rubber tubes. S02 permeation rates
were measured over a temperature range 125°C - 225°C for simulated stack
humidities of up to 21 mole percent water. The polymer screened out water
vapor to an extent sufficient to preclude the possibility of condensation in
107
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the carrier gas stream, and the presence of water vapor in the stack gas
did not affect the S(L permeation rates.
The purpose of the present study was to develop an in-situ calibration
technique for a permeation interface, and to test this technique using pro-
totype sampling devices in several process and power plant stacks. A cali-
bration technique was designed and successfully tested. FEP Teflon, TFE
Teflon, and fluorosilicone rubber tubes were used as interfaces in contin-
uous monitoring runs of several days duration in the atmospheric exhausts of
two S(L absorption towers, and a wet chemical. technique was also used to ob-
tain intermittent measurements of the concentration of SO^ in the stack gases
for comparison with the continuous monitoring results. Another series of
experiments was carried out in the stack of an oil-fired power plant boiler.
This paper reports on the results of these field tests.
CALIBRATION FORMULAS
The rate of transport of a gas through a cylindrical polymer tube is given
8
by the following equation (Crank and Park ):
where F = flux of the diffusing gas through the polymer, cm (STP) •
sec" • cm"
P = permeability of the polymer to the diffusing gas,
cm3(STP) • cm"1 • sec"1 • cm"](Hg)
a,b = inner and outer tube radii, respectively, cm
P1 ,P2 = inner and outer bulk partial pressures of the diffusing gas,
cm(Hg)
The principle assumptions leading to Equation (1) are that diffusion is Fickian
with a concentration-independent diffusivity and that the solubility of the gas
in the polymer follows Henry's law.
108
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The permeability follows an Arrhenius relationship over a moderate
temperature range:
P = PQ exp(-Ep/RT) (2)
where E = activation energy for permeation, kcal • gmole"
R = gas constant, kcal • gmole" • °K
P = pre-exponential factor, units of P
The validity of Eqs. (1) and (2) for S02 permeating through TFE Teflon and
FEP Teflon has been demonstrated by Rodes et al. and Felder et al.
A material balance on the diffusing component in the carrier gas yields
yCG = FL/* (3)
where yCG = volume fraction of the diffusing component in the
carrier gas stream leaving the polymer tube
L = polymer tube length, cm
= carrier gas flow rate, cm (STP) • sec"
Substitution of Eq. (1) into Eq. (3) yields
D . D = *ln(b/a)
P2 pl 2TrLP yCG
If desired, the function of Eq. (2) may be substituted for the permeability
P in this equation.
Under normal operating conditions, the partial pressure of SO,, in the
stack or calibrating gas (p2) is roughly two orders of magnitude greater
than that in the carrier gas (p^); the carrier gas SCL concentration is
therefore directly proportional to the stack gas concentration, making
possible a single point calibration procedure.
EXPERIMENTAL
A portable system was designed and constructed for use in field-testing
109
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polymeric interfaces. The system, which was a modified version of an
apparatus designed by Charles E. Rodes of the Environmental Protection
Agency, included a central control panel, a probe for supporting the
polymer tube in the stack, an ambient SO^ analyzer and recorder, a thermo-
couple, potentiometer and recorder, an air compressor and an analyzer
calibration system.
The polymer tube to be tested was mounted on a probe assembly shown
in Figure 1. All parts of the probe were made from 316 stainless steel
or TFE Teflon. The assembly was mounted in the stack by means of a 1/4" x
6" x 6" plate clamped to a bolt flange located on the outside of the stack.
A 1/4" tube which passed through the inside of the 1/2" support tube served
as the carrier gas inlet. A 1" tube functioned as a movable sheath which
could be positioned over the polymer tube or withdrawn to expose the tube
to the stack gas. A span gas" of known concentration (calibration gas) was
introduced into the sheath and passed over the outside of the polymer tube
during calibration.
A 24" x 24" x 4" enclosure constructed from 1/4" plywood formed the
central control panel. Flow control valves, pressure gauges, and rotameters
were mounted on the front and side panels, as shown in Figure 2. The con-
necting 1/4" polypropylene tubes and Swagelok fittings were mounted behind
the front panel and were accessible through a hinged rear panel. A re-
movable plywood enclosure could be attached to protect the rotameters during
transport to and from the test site. A small carbon vane compressor served
as the central air supply. The air was purified by passing it through a
dessicant bed, activated charcoal, and a particulate filter.
The calibration gas was prepared by dilution of a compressed cylinder
gas (5,000 ppm SOp in air) with a stream of purified air. Both the cylinder
110
-------
gas and dilution air were metered through rotameters located on the control
panel. By varying the ratio of dilution air and cylinder gas flow rates,
a range of S0? concentrations could be obtained.
Upon leaving the probe, the carrier gas passed through an ambient SOp
analyzer. Two continuous ambient analyzers were used in this study: a
Meloy Labs Model SA-160 flame photometric detector and an Environmetrics
Model NS-300 electrochemical transducer. Both analyzers produced a con-
tinuous record of the carrier gas S02 concentration. Known concentrations
of S02 for analyzer calibration were generated by passing purified air at
a measured rate across a standard Dynacal SOo permeation tube. Either the
carrier gas or the analyzer calibration gas could be passed through the
analyzer, depending on the setting of a three-way valve on the control panel.
The stack temperature was measured using a 60-inch copper-constantan
thermocouple inserted in the carrier gas line such that the tip was posi-
tioned in the center of the polymer tube. The output emf was determined
with a potentiometer and strip chart recorder.
Measurement of low S02 stack concentrations (less than 500 ppm) re-
quired a tube with a thin wall. Since Teflon tubes with sufficiently thin
walls were not available, an FEP Teflon membrane (0.002") was wrapped and
heat sealed around a 0.40" O.D. 40p porosity stainless steel tube. The
heat sealing was performed by Livingstone Coating Corporation, Charlotte,
N. C.
The general procedure for testing a polymer interface was as follows.
A polymer tube was mounted in the probe and positioned in the stack with
the sheath in the calibration position. The components of the testing sys-
tem were connected and checked for leaks. After calibration of the analyzer,
the polymer tube was exposed to a span gas containing the desired concentra-
111
-------
tion of SOp. The carrier gas flow rate was then adjusted to its desired value,
and the flow was directed to the analyzer. When the recorder signal reached
a steady level, the carrier gas SCL concentration was noted. A plot of span
gas concentration vs. carrier gas concentration generated in this manner was
used as a calibration curve for the subsequent stack monitoring. The polymer
tube was then exposed to the stack by withdrawing the sheath, and the analyzer
signal was recorded. The signal was corrected for variations in the stack
temperature using Eq. (2), with an activation energy for permeation of 6.54
kcal/g-mole for TFE Teflon and 7.18 kcal/g-mole for FEP Teflon.
FIELD TEST RESULTS
Monitoring runs were carried out in two process stacks and a power plant
boiler stack. The stack conditions and operating parameters for these field
tests are summarized in Table 1. The sections that follow outline and discuss
the results.
Single Contact Process Sulfuric Acid Plant
A one-day monitoring run was carried out using an FEP Teflon sampling
tube in the S(L absorption tower stack of a single contact process sulfuric
acid plant. The stack gas contained approximately 2,000 ppm S02, and the
stack temperature was approximately 80°C. To check the continuous monitoring
results, gas samples were periodically withdrawn directly from the stack and
subjected to analysis by Federal Register Method 6.
Figure 3 shows a typical calibration plot obtained in the course of the
run. As anticipated, the carrier gas S02 concentration varied linearly with
the span gas concentration. Under normal circumstances a single calibration
.point should suffice, making automation of the calibration procedure relatively
straightforward.
112
-------
The results of the monitoring measurements are shown in Figure 4.
There were no significant operating problems, and excellent agreement was
obtained between the continuous monitoring results and those obtained by
intermittent direct sampling and wet chemical analysis.
A heavy acid mist was present in the stack, and considerable dropwise
condensation occurred on the tube during the run. To estimate the effect
of the condensation on the interface performance, the tube permeability
was calculated from the plot of Figure 3 and other calibration plots using
Eq. (1), and the calculated values were compared with values obtained for
clean tubes of the same material. Figure 5 shows the results. The per-
meabilities determined for the condensate-coated tubes in the stack come
quite close to a regression line on an Arrhenius plot of FEP permeabilities
reported by Felder, Spence and Ferrell, indicating that the presence of the
condensate on the tube did not alter the effective tube permeability.
In another experiment, the S(L permeability of a TFE Teflon tube was
measured, after which the tube was left in the absorption tower stack for
one year and the permeability was then remeasured. A permeability decrease
of about 15% was observed. This change would appear as a span drift, and
would easily be accounted for by periodic recalibration. This result sug-
gests the potential usefulness of Teflon interfaces as tools for long-range
unattended continuous monitoring.
Q
A fluorosilicone rubber tube (Silastic LS-63U , manufactured by Dow-
Corning) was placed in the stack for a period of twelve hours. Upon removal
from the stack the tube showed obvious signs of deterioration, indicating
that unlike Teflon, this material is unsuitable for use in an acid mist en-
vironment.
113
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Double Contact Process Sulfuric Acid Plant
Monitoring runs were carried out over a two-day period in the S(L
absorption tower stack of a double contact process sulfuric acid plant. The
average concentration of SCL in the stack gas was 85 ppm, and the stack temp-
erature was 67°C. To obtain a permeation rate sufficiently high for the
carrier gas SO^ concentration to be within the operating range of the ana-
lyzer (0.02-0.5 ppm), a tube with a very thin wall had to be constructed.
This was done by wrapping and heat-sealing a 2 mil FEP Teflon membrane about
a porous stainless steel support. The continuous readings obtained using
this device were compared with readings obtained with an on-stream stack gas
analyzer operated by plant employees.
The results of these tests are shown in Figure 6. THe stack gas analyzer
used in the normal operation of the process indicated 60 ppm on one day and
85 ppm the following day, while the continuous monitoring system indicated an
average concentration of 85 ppm both days. Since no process changes were made
during this two-day period, it can be speculated that the latter result is more
likely to be correct. Moreover, the continuous record provided by the test sys-
tem fluctuated less than the intermittent record obtained with the plant instru-
ment.
These results and those obtained in the single contact process stack indi-
cate that polymeric interfaces can be used to monitor stacks containing S0? at
concentrations which vary over a wide range. The concentration in the first
stack,
-------
Oil-Fired Power Plant Boiler Stack
Monitoring runs were carried out in an oil-fired power plant boiler
at North Carolina State University. A #6 fuel oil containing 1.9% sulfur
was burned, and the SCL content of the stack gas varied between 250 ppm
and 1,045 ppm as the load on the boiler was changed. The stack tempera-
ture fluctuated between 170°C and 213°C.
On one day, the feed to the boiler was changed from natural gas with a
negligible sulfur content to fuel oil, and 150 minutes later a change back
to natural gas was carried out. Figure 7 shows the analyzer response during
this period.
The ability of the sampling interface to follow changes in the S0« con-
centration in the stack is illustrated by Figure 7. Following each fuel
change, the analyzer signal reached its final value in approximately 10
minutes. Most of this time lag is probably attributable to the time re-
quired for the stack gas S02 concentration to reach its final value rather
than time lags of the sampling tube and analyzer. A better indication of
the sampling system dynamics is seen in the response from 120 minutes to
135 minutes, where a momentary increase in the fuel feed rate was reflected
almost instantly by a corresponding peak in the analyzer response. As in
previous runs, good agreement was achieved between measurements made with the
test system and others obtained by direct sampling and wet chemical analysis.
A four-day monitoring run was carried out in the same stack, with
results shown in Figure 8. The breaks in the analyzer signal record (the
lower curve) are due partially to periodic recalibrations, and partially
to difficulties with the strip chart recorder which occurred during un-
attended periods of operation. The results are sufficiently complete,
however, to show that the sampling interface-analyzer system provided
115
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accurate readings and responded rapidly to variations in the fuel feed rate
(and hence in the stack gas SCL concentration).
A gross measurement of the particulate concentration in the stack using
Federal Register Method 5 yielded a loading of 0.21 g/m . Inspection of
the sampling tube at the conclusion of the tests revealed a slight powdery
deposition on the tube surface, but recalibration measurements suggest that
this layer had no effect on the S02 permeability of the tube. This result is
consistent with previously reported results concerning the lack of particu-
late interference effects in tests of a TFE Teflon sampling tube in a coal-
Q
fired power plant boiler (Spence, Felder, Ferrell and Rodes ). Polymeric
interfaces are thus able to provide clean samples for analysis regardless
of the particulate loading in the stack, and to do so without a need for
filters or other particulate removal devices in the sampling train.
CONCLUSIONS
579
Previous studies ' ' have suggested the potential advantages of in-stack
polymeric interfaces for continuous stack monitoring. The field tests dis-
cussed in this report provide additional evidence of the performance capability
of such devices. Demonstrated features of TFE and FEP sampling tubes include
the following.
1. Interfaces can be designed to monitor stack gases with SOp concentrations
from tens to thousands of parts per million.
2. The presence of water vapor in the stack does not affect the rate of per-
meation of S02 through the interface, so that the analyzer reading need
not be corrected for the stack humidity. Moreover, Teflon is sufficiently
impermeable to water to eliminate the possibility of condensation in the
sample line or the analyzer. There is consequently no need for heated
sample lines, cold traps or sample drying columns in the sampling train.
116
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3. The presence of liquid or solid participate matter in the stack gas
has had no measurable effect on the performance of sampling interfaces
in tests carried out to date. Using such an interface in a sampling
train therefore eliminates the need for frequent filter changes, making
long-term unattended continuous monitoring a good possibility.
4. Responses obtained using polymer interfaces follow changes in the stack
gas SOp concentration accurately and rapidly, suggesting the potential
applicability of such devices as feedback control loop components.
ACKNOWLEDGMENTS
This work was carried out under Environmental Protection Agency
Research Grant #801578. The authors wish to express their appreciation
to James Homolya and Chen-Chi Ma for assistance with the experimentation.
Particular thanks go to Roger Spence, who carried out the field tests in
the power plant boiler stack and who has provided assistance throughout
the entire program.
117
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REFERENCES
1. "Standards of Performance for New Stationary Sources," Federal Register,
36_, 24890, December 23, 1971.
2. Source Sampling Manual, Los Angeles Air Pollution Control District, Los
Angeles, Calif., 1963.
3. H. B. H. Cooper and A. T. Rossano, Jr., Source Testing for Air Pollution
Control. New York, McGraw-Hill (1971).
4. C. D. Hoi Towel 1, G. Y. Gee and R. D. McLaughlin, "Current Instrumentation
for Continuous Monitoring for SOp," Anal. Chem., 45_, 63A (1973).
5. C. E. Rodes, R. M. Felder and J. K. Ferrell, "Permeation of Sulfur Dioxide
through Polymeric Interfaces," Env. Sci. Technol., 7_, 545 (1973).
6. R. M. Felder, R. D. Spence and J. K. Ferrell, "Permeation of Sulfur Dioxide
through Polymers," Manuscript in preparation.
7. R. M. Felder, J. K. Ferrell and J. J. Spivey, "Effects of Moisture on the
Performance of Permeation Sampling Devices," Analysis Instrum., ]2_, 35 (1974)
8. J. Crank and G. S. Park, Diffusion in Polymers, p. 5, New York, Academic
Press (1968).
9. R. D. Spence, R. M. Felder, J. K. Ferrell and C. E. Rodes, paper presented
at the National Meeting of the AIChE, New Orleans, La., March 1973.
118
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Table I. Field Test Parameters
Stack Location
Stack Conditions
Interface
Analyzer
Carrier Gas Flow
Rate
Single-Contact Process
S03 Absorption Tower
* 2,000 ppm S02
* 80°C
FEP Teflon Tube
I.D. = 0.544 cm
O.D. = 0.604 cm
L = 75 cm
Electrochemical
Transducer
Range: 0-0.1 ppm SOp
1250 cm3/min
@ 21.4°C, 1 atm
Double-Contact Process
SO., Absorption Tower
ft 85 ppm S02
* 67°C
FEP Teflon Membrane
(2 mils) on a porous
stainless steel tube
Support I.D. = 1 .016 cm
Support O.D. = 1 .026 cm
L = 44 cm
Flame Photometer
Range: 0-0.5 ppm
300 cm /min
@ 21.4°C, 1 atm
Oil -Fired Power
Plant Boiler
250-1 ,045 ppm S02
170°C - 213°C
TFE Teflon Tube
I.D. = 0.403 cm
O.D. = 0.480 cm
L = 70.5 cm
Flame Photometer
Range: 0-0.5 ppm
500 cm /min
@ 21.4°C, 1 atm
-------
LIST OF FIGURES
Figure 1. Stack sampling probe.
Figure 2. Schematic of stack sampling apparatus,
Figure 3. Probe calibration plot.
Figure 4. Monitoring data: Single contact process stack.
Figure 5. Sampling tube permeabilities.
Figure 6. Monitoring data: Double contact process stack.
Figure 7. Monitoring data: Boiler stack, 1-day run.
Figure 8. Monitoring data: Boiler stack, 4-day run.
120
-------
1/4" S.S. Tube, Carrier Gas Inlet
1/4"X6"X 6" S.S. Support Plate
1/4" S.S. Tube. Carrier Gas Outlet
1/4" S.S. Tube. Span Gas Inlet
1/2" S.S. Tube, Support
I
•Polymer Tube
1" S.S. Tube, Movable Sheath
Figure 1. Stack sampling probe.
-------
ro
ro
Analyzer
Calibrator
Stack
Probe
Thermocouple
Potentiometer
Air Pump
Span Gai
Particulate Filter
Carbon Filter
Decsicant
Figure 2. Schematic of stack sampling apparatus.
-------
PO
CO
a.3
u
c
o
U
«/»
O
U
.0
0
I
I
I
1000 2000 3000 4000
Stock Concentration
J_
5000
6000
Figure 3. Prob.e calibration plot.
-------
Stack Cone. SO2
Carrier Gas Cone. SO2 (PPm)
ro
4000
3000
2000
1000
.20
.15
.10
05
-.0
FEP Interface arrd Ambient Analyzer
Method 6
1230 1330 1430 1530
1630
Time
1730 1830 1930 2030 2130
Figure 4. Morn tor ing data; Single contact process stack.
-------
o
s«.
X
80.0
'E 40.0
u>
CJ
•a,
c-
«a
6.0
.0
Regression
FEP Teflon,
Feider, ®t d
Field Test. FEP Tube
Field Test FEP Film on
Porous S.S. Tube
2.70
3.'
figure 5. Sampling tube permeabilities.
125
-------
240
200
160
120
80
40
0 L.
-.15
.10
.05
Stack Cone. SO2,
Carrier Gas Cone. SO2, ppm.
*0* •• On-Line Stack Gas Analyzer
FEP Interface and Ambient Analyzer
t I I
i i
1200 1400 1600
10/2/74
1800 20001/1200
Time, hr.
1400 1600
10/3/74
1800 2000
Figure 6. Monitoring data: Double contact process stack.
-------
f\3
-10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
t , min.
Figure 7. Monitoring data: Boiler stack, 1-day run.
-------
fo
CO
Q) _Q
4) —
"-co
_ O
6
c
- 1000
600
400
200
0
12 18 24
I 11-9-74 I
M Method 6
6 12 18
11-10-74
24 6 12 18 24
I 11-11-74 I
Time
6 12 18
11-12 -74
24
Figure 8. Monitoring data; Boiler stack, 4-day run.
-------
APPENDIX E
A METHOD FOR THE DYNAMIC MEASUREMENT OF
DIFFUSIVITIES OF GASES IN POLYMERS*
R. M. Felder, R. D. Spence and J. K. Ferrell
Department of Chemical Engineering
North Carolina State University
Raleigh, North Carolina 27607
ABSTRACT
A method is presented for determining the diffusivity of a gas in
a polymer from the response to a step concentration change in a continu-
ous flow permeation chamber. The outlined procedure has several advan-
tages over techniques currently in use: it requires simple numerical in-
tegration rather than curve-fitting; it utilizes the complete response,
rather than a portion of the response which falls within the region of
validity of a short-time asympotic solution of the diffusion equation,
and it is applicable both to flat membranes and cylindrical tubes. An
illustration of the method is provided by the measurement of the diffusi-
vity of sulfur dioxide in a PTFE tube at several temperatures.
Published as J. Appl Polymer Sci. ]_9, 3193 (1975). Reprinted by permission
of John Wiley & Sons, Inc.
129
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INTRODUCTION
The determination of the permeability or diffusivity of a gas in a
polymer commonly involves measuring the amount of the gas which permeates
through, into or out of a sample of the polymer in a closed volume system.
Several problems are associated with experiments of this type. Measuring
the cumulative amount rather than the instantaneous rate of permeation or
sorption limits the precision of the data; moreover, in batch permeation
experiments a pressure gradient is imposed across a membrane,and conse-
2 3
quently elaborate membrane sealing and support provisions are required. '
An approach to permeation measurements in which a gas permeates through
a membrane into a flowing stream avoids these problems. Steady-state oper-
ation can be achieved in such an experiment, thereby increasing the attain-
able precision, and equal pressures can be maintained in both compartments
of the permeation chamber, minimizing the requirements for sealing and
supporting the membrane.
The continuous permeation technique has been applied extensively to
the measurement of permeabilities of gases in polymers (see, for example,
o
References 2, 4, and 5). Pasternak, Schimscheimer and Heller showed that
the continuous technique may also be used to measure the diffusivity of a
gas in a flat membrane. In the method proposed by Pasternak et a!. a step
change in the partial pressure of the penetrant is imposed on one side of the
membrane, and the rate of permeation into the gas flowing past the other
side is monitored continuously. The data are plotted such that a straight
line is obtained for a portion of the response, with the slope of the line
being a known function of the diffusivity. The method is effective, but
being based on either a short-time or long-time asymptotic solution of the
diffusion equation limits its applicability1when deviations from the an-
130
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ticipated straight line occur, it is difficult to determine whether they
are due to experimental error, or to a violation of the assumptions of
the diffusion model, or simply to the invalidity of the asymptotic solu-
tion in the range of response times where the deviations occur.
This paper outlines an alternative method for determining the dif-
fusivity of a gas in a polymer from step response data obtained in a
continuous permeation chamber. The proposed method has several advantages
over that of Pasternak et al.: it requires simple numerical integration
of response data, rather than curve-fitting; it utilizes the complete
response, rather than a portion of the response which falls within the
region of validity of an asymptotic solution of the diffusion equation,
and it is applicable to cylindrical tubes as well as flat membranes. The
method is illustrated by the experimental determination of the diffusivity
of sulfur dioxide in a PTFE tube.
THEORETICAL
A continuous permeation chamber consists of two compartments separated
by a membrane. At a time t=0 a penetrant is introduced into one compartment
(the upstream compartment), and permeates through the membrane into a stream
flowing through the other (downstream) compartment. The concentration of the
penetrant in the gas leaving the downstream compartment is monitored continu-
ously until steady-state is attained.
It is assumed that diffusion of the penetrant in the gas phase and ab-
sorption at the membrane surface are instantaneous processes, that diffusion
p
in the membrane is Fickian with a constant diffusivity D(cm /s), and that
the concentration of dissolved gas at the downstream surface of the membrane
is always sufficiently low compared to the concentration at the upstream sur-
face that it may be set equal to zero. The diffusion equation and boundary
131
-------
conditions for a flat membrane of thickness h, and for a cylindrical tube
with inner radius a and outer radius b with the penetrant introduced on
the outside of the tube, are given below:
Flat
Membrane Cylinder
3C(t,x) . n32C(t.x) 3C(t.r) _ D 3 , 9(X (1)
3t u T2 at " r 3r vr 3r;
oX
C(0,x) = 0 C(0,r) = 0 (la)
C(t,0) = C] C(t,a) = 0 (Ib)
C(t,h) = 0 C(t,b) = C1 (Ic)
The solutions of these equations may be obtained by simplifying solu-
tions given by Crank for more general boundary conditions,and the resulting
expressions for C(t,x) and C(t,r) may in turn be used to derive expressions
for the rate at which the gas permeates through the downstream membrane sur-
2
face. For a flat membrane with a surface area A(cm )
h - n^l
and for a cylinder of length L
221
(-l)nexp (JLjrW,
h* J
27rDLC,
where a-,, a^j ••• are the real positive roots of the equation
(j) is defined to be positive for flow in the negative r direction. In Eqs. (3)
and (4), J and Y are the zero-order Bessel functions of the first and second
132
(2)
-------
kind. An expression for the permeation rate applicable to both geo-
metries is
*(t) = * [1 + K I bn exp (-Un2 Dt)] (5)
n=l
where the steady-state permeation rate A is
(t) in Eq. (7) yields
<|>CCK °° b ccK * b 9
Q(t) = *sst + -^- I -7-^- Z-^expt-fto^t) (8)
n=l u) n=l a)
As t becomes large the exponential terms become negligible and a plot of
Q(t) vs. t approaches a straight line. The intersection of this line with
the time axis -- the so-called time lag tj -- is obtained by setting the
first two terms of Eq. (8) equal to zero and solving for t, with the result
t - K ? A
1 " D nil .n2
Expressions for the time lag for planar and cylindrical membranes are given
by Crank and Park
133
-------
tt\ - a2 - b2 + (a2 + b2) In (b/a) *
Ul Jc 4D In (b/a)
Eqs. (10) and (11) provide the basis for the determination of D from an
experiment in which Q(t) is measured in a closed-volume system and t-, is
determined graphically. If instead (t) is measured in a continuous per
meation apparatus the following analysis is pertinent.
The quantity (1 - 4>/ss) may easily be calculated from experimental
response data and integrated numerically from t=0 to t=°°. If the value
of this integral is designated M , then from Eq. (5)
Mo = /; [1 - 1 dt = K / bn exp (- D.n2t) dt (12)
Interchanging the order of summation and integration yields
n=1 un
which by comparison with Eq. (9) is identical to the time lag, so that the
expressions of Eqs. (10) and (11) may be equated to MQ as well as t-j. Thus.
if
then for a flat membrane
and for a cylinder
n _ a2 - b2 + (a2 + b2) In (b/a)
D 4 MQ In (b/a)
D = h2/6 MQ (15)
* 1
The expression for the cylinder given by Crank and Park erroneously omits
the D in the denominator. The correct form is given in the original deri-
vation by Jaeger.' A formula for this quantity given by Crank" is incorrect,
although it yields results which are numerically quite close to the correct
values.
134
-------
Experimental values of <|>(t) or any measured quantity proportional to 41, such
as the concentration of the penetrant in the gas stream flowing past the down-
stream side of the membrane, may be substituted into Eq. (14), and the value
of M may be obtained by numerical integration. The diffusivity D may then
be calculated from Eq. (15) or (16).
EXPERIMENTAL PROCEDURE AND RESULTS
The diffusivity of sulfur dioxide in PTFE (Teflon) was determined at 100°C.
A PTFE tube with an inner radius a=0.403 cm and an outer radius b=0.480 cm was
mounted in a chamber in a thermostatically-controlled oven. A stream of air
containing less than 0.02 ppm S02 — the carrier gas -- passed through the in-
side of the tube. At a time t=0 a gas containing 1.5% SO^ by volume and the
balance dry air -- the chamber gas -- was introduced into the chamber outside
the polymer tube. S02 permeated through the tube wall into the carrier gas,
which passed out to an electrochemical transducer S02 detector connected to a
strip chart recorder. Additional details of the experimental apparatus are
4
given by Rodes, Felder and Ferrell.
The total time lag due to the residence time of the chamber gas in the
upstream compartment, the residence time of the carrier gas between the per-
meation chamber and the detector, and the 90% response time of the detector,
was estimated to be 17 seconds. Since the 90% rise time of the measured re-
sponse was of the order of 30 minutes, the precise dynamic characteristics of
the chamber, the carrier gas lines and the analyzer were not considered im-
portant, and the 17 second lag was for simplicity assumed to be a pure time
delay. The measured response was accordingly shifted horizontally by this
amount to obtain the transient response of the polymer tube alone.
*
In process dynamics terminology, MQ is the zeroth moment of the negative unit
step response of the membrane, and the technique of estimating D from the cal-
culated value of M0 is an example of the method of moments.
135
-------
The corrected response R(t) normalized by its asymptotic (steady-state)
value R is shown in Figure 1 as a series of discrete points. The quantity
M was evaluated from Eq. (14) by replacing /<)> ss with R/RSS and using Simp-
son's rule with At = 1 minute. The calculated value of M , 17.9 minutes,
-7 2
was substituted into Eq. (16) to obtain D = 9.1 x 10" cm /second. This
value was not highly dependent on the assumption of 17 seconds for the time
lag of the system components other than the membrane: using 0 seconds or 34
seconds instead of 17 seconds made a difference of only 1.5% in the calcu-
lated diffusivity.
The theoretical curve of (t)/(|> ( = R(t)/R ) vs. t evaluated by sub-
S 5 55
stituting the tube dimensions and the calculated diffusivity into Eq. (3) is
shown as the solid curve of Figure 1. The agreement between the experimental
•
and theoretical responses is excellent, and confirms the validity of both
the diffusion model and the technique used to estimate the diffusivity.
Diffusivities have been measured at several temperatures between 22°C
and 121°C using this technique. Measurements were made using two PTFE tubes
with different wall thicknesses, and two upstream S02 concentrations for each
tube, The measured diffusivities are shown in an Arrhenius plot in Figure 2;
the S02 percentages shown in the legend on this figure are the molar per-
centages of S02 in the upstream chamber gas. Also shown in Figure 2 is an
P
S02 diffusivity reported by Jordan for PTFE at a temperature presumed to be
in the range 20°C-30°C. Jordan used a sorption technique, and calculated D
as the quotient of a measured permeability and a measured solubility; the
agreement between his value and the values obtained in the present study is
reasonable, albeit not outstanding.
S02 diffusivities measured using thick and thin-walled PTFE tubes appear
to differ by approximately 30-50%. The coincidence of data points obtained
using two different upstream concentrations at a fixed temperature suggests
136
-------
the constancy of D under the prevailing experimental conditions.
Least-squares fits to the data of Figure 2 yield an activation energy
for diffusion of 8.45 +_ 0.1 kcal/g-mole.
Future papers will report the results of diffusivity measurements for
several penetrants and polymers, and will outline applications of the con-
tinuous measurement technique to the monitoring of gaseous pollutant emis-
sions from stationary sources, the project which provided the impetus for
this study.
137
-------
DISCUSSION
Process Dynamic Considerations in Diffusivity Measurements
This study outlines a method for determining the diffusivity of a gas
in a membrane from the response at one membrane surface to a step change in
penetrant concentration at the other surface. What is actually measured,
however, is the response of a series of system components including the
chamber gas line, the chamber itself, the membrane, the carrier gas line
leading to the analyzer, and the analyzer and recorder, each of which re-
presents an additional lag or delay between the input signal and the mea-
sured response. An essential step in determining the diffusivity is to ex-
tract (deconvolute) the step response of the membrane from the response of
the entire system.
In the experiment described in this paper, the mean residence times in
the chamber and carrier gas lines and in the chamber were calculated by di-
viding each component volume by the volumetric flow rate of the chamber or
carrier gas. The response of the analyzer to a step input of S(L was measured
experimentally, and the 90% rise time was noted. The sum of the calculated
residence times and the rise time of the analyzer in the experiment of Figure 1
was 17 seconds, which was sufficiently small on the time scale of the total re-
sponse to justify approximating these lags as a single time delay.
In an experiment in which the membrane response is rapid -- as it might
be, for example, in measurements on a thin membrane at a high temperature --
the dynamics of the system components other than the membrane must be taken
138
-------
into account more explicitly in the response analysis. A reasonable approach
would be to characterize all connecting lines as pure time delays, and the
permeation chamber and (possibly) the analyzer as first-order lags, all com-
ponents being in series with the membrane. Standard deconvolution techniques
could then be used to determine the step response of the membrane alone.
Measurement of Concentration - Dependent Diffusivities
Partial pressures of gases in continuous permeation chambers are usually
1 atm or less, under which condition the diffusivity of a penetrant is likely
to be independent of the concentration of the penetrant dissolved in the mem-
brane. This independence was confirmed in this study by carrying out runs with
two significantly different penetrant partial pressures in the chamber gas and
finding essentially the same diffusivity in both cases.
A possible extension of the continuous permeation technique to conditions
at which the diffusivity varies with penetrant concentration is to pass a gas
with a penetrant concentration C0 on both sides of a membrane until equilibrium
is achieved, and then to increase the concentration on one side (upstream) to
C-, and to measure the response on the other side (downstream). Provided that
the dissolved penetrant concentration at the downstream surface of the membrane
is not significantly changed from its initial value by the amount of gas that
permeates, a simple variable transformation C' = C - C reduces the mathematical
analysis required to determine D to that given previously for the case when
C = 0. The calculated diffusivity would correspond to a concentration some-
where between the upstream and downstream concentrations C-, and C . Several
experiments of this type for different (C .C-.) pairs could in principle be
used to generate a curve of D vs. C.
CONCLUSIONS
The diffusivity of a gas in a polymer membrane or a hollow cylindrical
139
-------
tube can be conveniently measured by integrating the response to a step
change in penetrant concentration in a continuous permeation chamber. The
proposed method has been used to measure the diffusivity of S02 in PTFE
(Teflon) at temperatures from 22°C to 121°C, yielding an activation energy
for diffusion of 8.45 +_ o.l kcal/g-mole. A modified version of the method
may be used to determine concentration-dependent diffusivities.
ACKNOWLEDGMENTS
This work was supported by Environmental Protection Agency Grant
#801578. The authors acknowledge with thanks helpful discussions with
Professors Harold Hopfenberg and Vivian Stannett of North Carolina State
University, Department of Chemical Engineering, and assistance with the
experimentation provided by Mssrs. Chen-chi Ma and Lanny Treece.
140
-------
NOTATION
2
A = surface area of a flat membrane, cm
a,b = inner and outer radii of a hollow cylindrical tube, cm
bn = coefficient in Eq. (5)
C = concentration of penetrant dissolved in a membrane, moles/cm
C ,C, = initial concentration and concentration at the upstream membrane
surface, moles/cm3
2
D = diffusivity, cm /s
h . = thickness of a flat membrane, cm
J = zero-order Bessel function of the first kind
K = coefficient in Eq. (5)
L = length of cylindrical tube, cm
M = quantity defined by Eq. (14)
Q(t) = cumulative permeation up to time t, moles
R(t) = measured variable proportional to (t)
R = asymptotic (steady-state) value of R
r = radial position coordinate in a cylindrical tube, cm
t = time from imposition of a step change in penetrant partial
pressure, s
t-, = time lag, s
x = position coordinate in a flat membrane, cm.x=0 corresponds to
the upstream surface of the membrane.
YQ = zero-order Bessel function of the second kind
Greek Letters
a = n real positive root of Eq. (4)
(j)(t) = rate of permeation into the gas downstream of the membrane,
moles/s
ss = asymptotic (steady-state) value of $
w = coefficient in Eq. (5)
141
-------
S U b.Sl.i—i! p-L^-C-
c - cyttmtenr^
fnr —
142
-------
REFERENCES
1. J. Crank and 6. S. Park, Eds., Diffusion in Polymers, Academic Press,
New York, 1968.
2. T. L. Caskey, Mod. Plastics, 45_, 447 (1967).
3. R. A. Pasternak, J. F. Schimscheimer, and J. Heller, J. Polym. Sci.
A-2. 8, 467 (1970).
4. C. E. Rodes, R. M. Felder, and J. K. Terrell, Environ. Sci. Technology,
£, 1121 (1971).
5. R. M. Felder, J. K. Ferrell, and J. J. Spivey, Analysis Instrumentation,
12, 35 (1974).
6. J. Crank, The Mathematics of Diffusion, Clarendon Press, Oxford, 1956.
7. J. C. Jaeger, Proc. Roy. Soc. N.S.W., 74_, 342 (1940).
8. S. Jordan, Staub-Reinhalt Luft. 33, 36 (1973).
143
-------
LIST OF FIGURES
Figure 1. Experimental and Theoretical Step Responses of a PTFE Tube,
Figure 2. Arrhenius Plot of S02 Diffusivities in PTFE Tubes.
144
-------
-pi
tn
• Experiments
Model
PTFE Tube at 10CTC
b- 0.480 cm
a - 0.403 cm
80
Figure 1. Experimental and Theoretical Step Responses of. a PTFE Tube.
-------
10
10
f
u
10
,o8
I I I
I I T
Tubel
b=0.480cm
a=0.403 cm
Q-1.0%SO2
0-1.5% SO2
Tube 2
b: 0.302 cm
a= 0.2 72 cm
•-0.55<*b SO2-
• j 8
•—« Jordan
= 8.4 kcal/gmole
ED=8.5kca»/g
i i I I
2A 2.6 2.8 3.0 3.2 3.4
iooo/T , V1
3.6
Figure 2. Arrhenius Plot of S09 Diffusivities in PTFE Tubes.
146
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APPENDIX F
A METHOD OF MOMENTS FOR MEASURING
DIFFUSIVITIES OF GASES IN POLYMERS*
R. M. Felder, C. C. Ma, and J. K. Ferrell
Department of Chemical Engineering
North Carolina State University
Raleigh, North Carolina 27607
ABSTRACT
A method of moments has been formulated for the determination of the
diffusivity of a gas in a polymer from a step response in a continuous
permeation chamber. Contributions of system components other than the
polymer are easily factored out to determine the contribution of the poly-
mer alone, and this contribution is then analyzed to calculate the diffu-
sivity. The method has been applied to the measurement of the diffusivity
of sulfur dioxide in PTFE (Teflon) and fluorosilicone rubber tubes over a
wide temperature range.
Published as AICHE J. 22. 724 (1976). Reprinted by permission of the
American Institute of Chemical Engineers.
147
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SCOPE
Traditional methods for measuring the diffusivity of a gas in a polymer
involve either passage of the gas through a membrane into a closed chamber in
which the pressure is monitored, or sorption of the gas in a small polymer
sample suspended from a spring whose elongation is monitored. In either ex-
periment, a substantial driving force is needed to achieve measurable penetra-
tion fluxes, thereby limiting the penetrant concentrations for which data may
be obtained.
An approach in which a gas permeates through a membrane into a flowing
stream overcomes many of the experimental problems associated with closed
volume systems, and allows accurate measurements of gas transport properties
for penetrant concentrations as low as tens of parts per million. This
technique is not without its drawbacks, however. The complete solution of
the time-dependent diffusion equation is at best an infinite series, and
curve-fitting methods for estimating the diffusivity generally utilize either
short-time or long-time asymptotic solutions. When deviations from the antici-
pated straight line behavior occur, it is difficult to determine whether they
are due to experimental error, or to a violation of the assumptions of the
diffusion model, or simply to the invalidity of the asymptotic solution in the
range of response times where the deviations occur.
Felder, Spence and Ferrell (1975a) recently formulated a method for
estimating the diffusivity of a gas in a polymer from a moment of a step response
in a continuous permeation chamber. The method requires only numerical
integration rather than curve fitting, and does not depend on the existence
of a short-time or long-time asymptotic solution of the diffusion equation.
148
-------
A problem associated with this technique (and with any other dynamic
response technique) is that what is measured is the response of the entire
system—connecting line, chamber, permeable membrane, and gas analyzer--
to a step concentration change upstream of the chamber, while what is
needed to evaluate the desired diffusivity is the step response of the
membrane alone. This paper develops an extension of the moment technique
which provides a simple but accurate resolution of this problem.
149
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CONCLUSIONS AND SIGNIFICANCE
The method of moments for determining the diffusivity of a gas in a
permeable material has been found to provide several advantages over tra-
ditional closed-volume and continuous measurement techniques.
1. The use of a continuous permeation chamber rather than the closed volume
chamber of the standard time-lag experiment permits the attainment of a
true steady state, and yields data which are less susceptible to cumulative
errors.
2. Maintaining equal pressures on both sides of the membrane (which cannot be
done in a closed volume chamber) minimizes the requirements for membrane
support and sealing, and allows accurate measurements with very low pene-
trant concentrations.
3. The complete response to a step change in penetrant concentration is
utilized, rather than a portion of the response which falls within the
region of validity of a short-time or long-time asymptotic solution of
the diffusion equation.
4. Simple numerical integration of response data rather than curve-fitting
is required.
5. The method is applicable to cylindrical tubes as well as flat membranes.
6. The contributions of system components other than the membrane may be
factored out of the measured response by simple subtraction of moments
to obtain the contribution of the membrane alone.
The method has been applied to the measurement of the diffusivity of sulfur
dioxide in fluorosilicone rubber and PTFE (Teflon) tubes at temperatures from
21°e~tb 227°C. Calculated diffusivities have in several cases been substi-
tuted into the analytical solution of the diffusion equation to regenerate the
response curves from which the diffusivities were estimated. The close agree-
ment between the measured and calculated responses validates both the estimation
technique sr?d the diffusion model upon which it is based.
150
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THEORETICAL
Measurement of Transport Properties in a Continuous-Flow Permeation Chamber
In a continuous permeation experiment, a penetrant is introduced at a
partial pressure p-, (cm Hg) on one side of a flat membrane or on the outside of
a hollow cylindrical tube, and permeates through the polymer into a gas stream
flowing past the membrane or through the inside of the tube. The concentration
of the penetrant in the exiting gas is monitored continuously until a steady
state is attained.
The following assumptions are made:
1. Gas phase resistance to mass transfer is negligible.
2. Absorption of the penetrant at the polymer surface is an instantaneous pro-
cess.
3. The concentration of the dissolved gas at the downstream membrane surface
is negligible compared to that on the side where the penetrant was intro-
duced.
4. The solubility of the penetrant in the polymer is independent of the
penetrant concentration in the gas phase.
o
5. Diffusion in the polymer is Fickian with a constant diffusivity D(cm /s).
The diffusion equation may be solved for the rate of permeation of the gas
through the polymer (see Appendix A), and the solutions may in turn be used to
derive expressions for the diffusivity D. Let <|>(t) (mole/s) be the measured
permeation rate, s, the asymptotic (steady state) value of this rate, and
define
GO / \
0 w
0 TS
Felder et al. (1975a) have shown that for a flat membrane with a surface area
151
-------
2
A(cm ) and thickness h(cm),
D = h2/6M
and for a cylinder with inner radius a and outer radius b,
D . a2 - b2 + (a2 + b2) Infb/a)
4MQ ln(b/a)
If diffusivities are measured at several temperatures, an Arrhenius plot of
In D vs. 1/T yields the activation energy for diffusion of the penetrant in
the polymer (Stannett, 1968).
The analytical solution for the permeation rate (t) through the wall of a
hollow cylindrical tube is given in Appendix A, along with a numerical technique
for evaluating the infinite series which is a part of the solution.
Deconvolution of the Polymer Tube Response from the Total System Response
A difficulty associated with dynamic response measurements of the type
just described is that what is measured is the response of the entire system --
connecting lines, chamber, polymer, and gas analyzer -- to a step concentration
change upstream of the chamber, while what is needed to evaluate the diffusivity
from Eqs. (1) and (2) or (3) is the response of the polymer alone.
In the experiments described by Felder et al. (1975) this problem was solved by
assuming that the connecting lines, the chamber and the analyzer each acted as pure time
152
-------
delays, and the measured response was accordingly shifted horizontally by the
total of these delays. The values of the delays for the lines and the chamber
were taken to be the nominal mean residence times (volume/volumetric flow rate)
of the gases flowing through these units, and the time delay attributed to the
analyzer was arbitrarily set equal to the time required for the analyzer reading
to reach 90% of its final value in calibration runs.
In previous diffusivity measurements, the time lag due to the polymer
accounted for most of the total system response time, so that the particular
method used to correct for the other contributions to the response was im-
material. However, if (for example) the diffusivity of a gas in a thin
membrane at a high temperature is to be measured, the response times of the
other system components may be equal to or even greater than that of the
polymer. In such cases, representing all the time lags as pure delays would
be a serious error; the analyzer, in particular, is unlikely to be
a pure delay, or for that matter a pure first-order process or anything else
that can easily be modeled.
Fortunately, the true dynamic characteristics of the system components may
be taken into account in correcting the measured response, with little more
effort than was required for the oversimplified method used previously. The
procedure is to calculate as before the mean residence times of the gas in the
line leading to the chamber ( T, ) and in the chamber itself (T^), and the mean
residence time of the carrier gas in the line leading from the chamber to the
analyzer (^). Next, if R,(t) is the transient response of the analyzer to a
•j a
step change in the penetrant concentration at its inlet (i.e. the response measured
when the analyzer is calibrated) and Ras is the steady-state value of this response,
then the time lag due to the analyzer may be determined by numerical integration as
153
-------
R ft)
= / [1 - 4—] dt (4)
o as
Finally, if R(t) is the measured response of the entire system to a step con-
centration change (R is presumed to be proportional to the penetrant flux ), R is the
steady-state value of this response, and
0 o Rs
then the correct value of MQ to use in the diffusivity formulas (Eqs. (2) and
(3)) is
M_, = M_ - (TI+TO+TO+T,,) (6)
0 0 I i o a
The theoretical justification for this procedure is given in Appendix B.
EXPERIMENTAL
Apparatus
A permeation chamber was constructed by clamping two 6-inch square stain-
less steel endplates with Teflon gaskets to the ends of a 3-inch I.D., 24-inch
long stainless steel chamber. Each endplate was drilled and tapped to accept a
0.125-inch thermocouple bulkhead fitting, a 0.125-inch pipe fitting and a 0.375-
inch pipe fitting. All fittings were stainless steel. Each of the 0.375-inch
fittings was drilled internally to allow a length of 0.375-inch O.D. stainless
steel tubing to pass through the endplate to the interior of the chamber. The
polymer tube was connected between these internal fittings and supported by a
stainless steel rod inserted inside the tube. The chamber assembly was then
placed inside a thermostatically controlled oven.
A schematic diagram of the flow apparatus is shown in Figure 1. The feed
to the chamber is a mixture of a cylinder gas containing roughly 1.5% SOp in air
and air containing less than 0.03 ppm SOp. The precise concentration of SO- in
154
-------
the cylinder gas is determined using EPA Method 6 -- absorption of the SOU in an
isopropanol-hydrogen peroxide solution, and titration with a standardized barium
perchlorate solution (Environmental Protection Agency, 1971). The dilution air is
obtained by passing room air through a calcium chloride drying column, an acti-
vated charcoal column, and a particulate filter. The cylinder gas and dilution
air are fed through rotameters into a tee, and the combined stream passes into
the chamber on the outside of the polymer tube. A second stream of clean air
(the carrier gas) is metered and fed into the inside of the tube; the SC^ permeat-
ing through the tube wall is picked up by this stream, which passes out of the
chamber to a Meloy Laboratories Model SA-160 flame photometric sulfur detector.
The rate of permeation of SOp is calculated as the product of the concentration
read by the detector and the known volumetric flow rate of the carrier gas.
Copper-constantan thermocouples are used to monitor the temperature at two
locations near the outside surface of the polymer tube, and the pressures of the
chamber and carrier gases are measured with manometers. Strip chart recorders
are used to obtain continuous records of the signals from the S02 analyzer and
from one of the thermocouples. The analyzer is calibrated before and after each
run with a gas obtained by passing purified air at a measured rate over a cali-
brated SOo permeation tube.
This experimental system has been used to determine steady-state permeabilities
of sulfur dioxide and water in a number of polymers (Rodes et al., 1973; Felder,
Ferrell and Spivey, 1974; Felder, Spence and Ferrell, 1975b). Additional details
about its design are given in these references.
Procedures for Diffusivity Measurements
The sample tube dimensions are measured before the tube is connected to the
fitting in the chamber. The outer diameter of the tube is measured with a micro-
meter at several points around a circumference well away from an end, and an average
value is calculated. A small length of the tube is then cut axially, and the
wall thicknesses at several points are measured with the micrometer and averaged.
The inner diameter is determined from the mean outer diameter and wall thickness.
155
-------
The tube is mounted in the chamber and the chamber in turn is mounted in
the oven. The oven thermostat is set, and the chamber temperature is monitored
until it reaches a constant value. The flow rates of the cylinder gas and di-
lution air are adjusted to produce a chamber gas with a known SCL concentration,
and the flow rate of the carrier gas is adjusted to provide a sample gas with
an S02 concentration within the range of the flame photometric detector (ideally
0.1-1 ppm). The total pressure on both sides of the tube is maintained at
approximately 1 atmosphere.
The flow of the cylinder gas commences at a time t=0, and the run continues
until the measured concentration of S02 in the sample gas levels off and remains
level for at least 15 minutes. The sample gas SCL concentration is multiplied
by the volumetric flow rate of the sample gas to calculate the flow rate of
SCL leaving the tube, and the relatively small flow rate of S(L in the entering
air is subtracted to determine the SCL permeation rate 4>(t). The time lags T, ,
T2> and T3 attributable to the connecting lines and the chamber are calculated
from the known volumes of these components and volumetric flow rates of the
chamber and carrier gases, and the analyzer time lag T is determined from cali-
a
bration data using Eq. (4). The total system time lag M ' is obtained from (t)(ER(t))
using Eq. (5), and the lag due to the polymer alone is determined from Eq. (6).
Finally, the diffusivity of S02 in the polymer is calculated from Eq. (3).
RESULTS AND DISCUSSION
Fluorosilicone Rubber Tubes
Diffusivities of S02 in a fluorosil icone rubber tube (Dow Corning: SILASTIC
LS-63U^J were measured at temperatures between 74°C and 198°C, using three
different chamber gas S02 concentrations. The results are shown on an Arrhenius
156
-------
plot in Figure 2. The near coincidence of the data points obtained for the
different concentrations at a fixed temperature suggests the constancy of D
at the S02 partial pressures of 10 mm Hg and less used in these measurements.
The activation energy for diffusion obtained from Figure 2 is E, = 30.6 +
0.9 kJ/mole.
As a test of the validity of the diffusivity estimation technique, the
theoretical expression given in Appendix A for the permeation rate §(t) was
evaluated using diffusivities calculated at three different temperatures. Figure 3
shows plots of the resulting curves of R/RS(=<|>/<|>S) vs. t, along with the experimental
data. The close correspondence between the experimental and theoretical responses
at each temperature provides evidence for the validity of both the diffusivity
estimation technique and the diffusion model on which the technique is based.
PTFE Tubes
Diffusivities of sulfur dioxide in PTFE (Teflon) tubes have been measured
at temperatures from 21°C to 227°C. Figure 4 shows an Arrhenius plot of the
results obtained to date, along with a diffusivity measured by Jordan (1973) at
a temperature presumed to be in the range 20-30°C. Straight lines can be fit
quite well to the data for each individual tube, but noticeable, variations
occur-from-one tube to another. The diffusivity reported by Jordan is com*
parable*-to but higher than those measured- ifl the present work., a.result -
probably attributable to the substantially higher S02 concentrations used in
Jordan's study.
A least-squares 'Vine has been fit to the data shown in Figure 4 to obtain
the following estimation formula for the diffusivity of S02 in PTFE.
D(cm2/s) = 0.238 exp(-4760/T) (7)
157
-------
The activation energy for diffusion should not be deduced fronuEq.; (7),.
since differences between the diffusivities of the thick-walled tubes used at
the higher temperatures and those of the thin-walled tubes used at the lower
temperatures introduce a bias in the slope of a line fit to all the data points,
This point is the subject of continuing study.
ACKNOWLEDGMENT
This work was supported by Environmental Protection Agency Grant #801578.
The authors acknowledge with thanks assistance provided by Dr. Roger Spence.
A paper based on this work was presented at the 80th National Meeting of the
American Institute of Chemical Engineers, Boston, Mass., September, 1975.
158
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NOTATION
a = inner cylinder radius, cm
b = outer cylinder radius, cm
C = dissolved penetrant concentration, mole/cm
C,, C0 = penetrant concentrations at the upstream and downstream membrane surfaces,
' i mole/cm3
o
D = diffusivity, cm /s
ED = activation energy for diffusion, kJ/mole
F(t), FS = transient step response of total system and its steady-state limit
F.r(t), F. = transient step response of 1 system component and its steady-state
1 1S limit
G(s) = Laplace transform of g(t)
G. (s) = Laplace transform of g-(t)
g(t) = unit impulse response of total system
g.(t) = unit impulse response of i system component
h = thickness of flat membrane, cm
J = n -order Bessel function of the first kind
kn = V
L = length of cylinder, cm
M = zeroth moment of negative normalized step response of polymer, s
M ' =- zeroth ;.moraent of negative normalized step response of total system, s
R(t), R = transient response to a step change in penetrant concentration,
and its steady-state limit
R (t), R = transient response of the analyzer alone to a step change at its
a inlet, and its steady-state limit
r = radial coordinate, cm
s = Laplace transform variable, s
T = temperature, K
t = time, s
159
-------
U = function defined by Eq. (A6)
x = b/a
x^t) = signal at outlet of i system component
Y = n -order Bessel function of the second kind
n
Greek Letters
an = root of U0(ana) = 0
6(t) = Dirac delta function, s
u. = variable defined by Eq. (Bl), s
T = total system time lag, s
T- = time lag of i system component, s
<|>(t), = transient permeation rate and its steady-state limit, mole/s
160
-------
LITERATURE CITED
Abramowitz, M. and I. A. Stegun, eds.,Handbook of Mathematical Functions,
p. 16, National Bureau of Standards, Washington (1964).
Carslaw, H. S. and J. C. Jaeger, The Conduction of Heat in Solids, p. 489,
Clarendon Press, Oxford (1959).
Crank, J., The Mathematics of Diffusion, p. 78, Clarendon Press, Oxford (1956).
Douglas, J. M., Process Dynamics and Control, Vol. I, Prentice-Hall, Englewood
Cliffs (1972).
Environmental Protection Agency, Standards of Performance for New Stationary
Sources, Federal Register 3j5, No. 247, Part II, pp. 24890-24893 (1971).
Felder, R. M.,J. K. Ferrell, and J. J. Spivey, "Effects of Moisture on the
Performance of Permeation Sampling Devices," Anal. Instrumentation V2,
35 (1974).
Felder, R. M., R. D. Spence and J. K. Ferrell, (a) "A Method for the Dynamic
Measurement of Diffusivities of Gases in Polymers," J. Appl. Poly. Sci., 19,
3193 (1975).
Felder, R. M., R. D. Spence and J. K. Ferrell, (b) "Permeation of Sulfur Dioxide
through Polymers," J. Chem. Eng. Data. 2U, 235 (1975).
International Business Machines, System 360 Scientific Subroutine Package (360A-
CM-03X), Version III, Form H20-0205-3 (1968).
Jordan, S., "Messungen der Permeabilitat einiger Kunststoffe gegenuber Schwefeldioxid,"
Staub-Reinhalt. Luft, 33_, 36 (1973).
Rodes, C. E., R. M. Felder, and J. K. Ferrell, "Permeation of Sulfur Dioxide
through Polymeric Stack Sampling Interfaces," Environ. Sci. Technology, 7_,
545 (1973).
Stannett, V. T., "Sample Gases," in Diffusion in Polymers, J. Crank and G. S.
Park, eds., Academic Press, New York (1968).
161
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APPENDIX A
Permeation of a Gas into a Hollow Cylinder.
At a time t=0 a penetrant is introduced on the outside of a cylindrical tube
of length L, inner radius a and outer radius b. It is assumed that gas phase
mass transfer resistance is negligible, diffusion in the polymer is Fickian
with a constant diffusivity, and the partial pressure of the penetrant inside
the tube is negligible compared to that outside the tube.
Let p be the partial pressure of the penetrant in the gas phase, C the
concentration of penetrant dissolved in the polymer, D the diffusivity and S =
(C/p) f the solubility of the penetrant in the polymer. If the partial
pressures outside and inside the tube are p, and p2> the dissolved gas concen-
trations in the polymer in equilibrium with these partial pressures are C^Sp-])
and Cp^Spp), and the initial concentration of the penetrant in the polymer is
C , then the diffusion equation and its boundary conditions are
3C _ D a / aC\
~
C(0,r) = CQ (A2)
C(t,a) = C2 (A3)
C(t,b) = C1 (A4)
The solution of this equation is given by Crank (1956) as
C, ln(r/a)+C2 ln(b/r) - OJcyOUU
,
PXD, nt.
- IT I - y - * - exp(-a Dt)
n-1 J0 W ~ Jo t»nb)
162
-------
where
uo<«nr> = Jo V°nb> - Jo (<*nb> Yo Kr>
and a, ,a2> • •• are the real positive roots of the equation U (a a) = 0. J and
Y are the zero-order Bessel functions of the first and second kind.
o
In the system under consideration in this study C = 0 and C2«C,, so that
the solution simplifies to
C, ln(r/a) « J 2 (a a)Mo r) 0
The rate at which the penetrant permeates into the tube interior equals the rate
of diffusion at the inner surface
t(t) = 2TrDL(r f£)r=a (A8)
($ is defined to be positive if flow is in the negative r direction.) Substi-
tuting Eq. (A7) for C in this expression yields
Ci o - Jrt2 (ana) exp(-an2Dt) dU (ar)
Differentiation of Eq. (A6) yields
dUfctr)
where JQ (anr) = dJ0(anr)/d(anr). Since from the theory of Bessel functions
jo' =-YI and Y0' =-Jr
By definition, a-i,a2> ••• are the roots of the equation
163
-------
from which
J(ab)Y (aa)
Another result from the theory of Bessel Functions is (Carslaw and Jaeger, 19591
J0(ana)Y1(ana)-J1(ana)Y0(ana) = -^- (A14)
If this equation is multiplied by the ratio J0(ctnb)/J0(ana), and the quantity
is replaced by Y (a b) according to Eq. (A13), the result is
This expression may be substituted into Eq. (All) to yield
dU (0_r) 2 J (onb)
( 0 n ) = _ A. °, n
( dr V=a ua JQ(a a)
which may in turn be substituted into Eq. (A9) to yield
2irDL C, . Jn(«na)J«(anb) •)
C1 + 2 1n(b/a) I - exp(-aDt)] (A17)
The leading factor in Eq. CA17) is the steady-state permeation rate *s- U
follows that
00 Jn(a a)0rt(onb) 9
*(t)/* =1+2 ln(b/a) I -^ - ^n - exp(-a/Dt) (A18)
n=l 002(ana)-002(anb)
where
164
-------
Felder et al. (1975a) showed that the integral
Mn = / [1 - 4^-1 dt (A2°)
il" m
o s
is simply related to the diffusivity D through the relationship of Eq. (5), a
relationship which involves no infinite series and none of the transcendental
functions or roots of nonlinear equations which appear in Eq. (A18). To confirm
the validity of the diffusivity estimation formula and of the assumptions that
underly it, however, the estimated value of D must be substituted back into the
full expression of Eq. (A18), and the calculated curve of <|>(t)/<|>s must be com-
pared with the data used to estimate D.
The evaluation of the expression of Eq. (A18) poses two problems: finding
the roots {a }, and achieving convergence of the series. To perform the calcu-
lation, it is convenient to work with the series expressed in terms of
the variables a and x =b/a rather than a and b. Since b = ax, the equation which
defines {a } -- Eq. (A12) -- may be written in terms of modified roots k = aa as
and the normalized permeation rate is
no n
= 1+2 In x I ° n ° 2 n - exp(~Ar t) (A22)
n=1 Jo a
Newton's rule is used to estimate the roots of Eq. (A19). If
UQ(k) = J0(k)Y0(xk)-J0(xk)Y0(k) (A23)
165
-------
then
diydk = U0(k)
- J1(xk)YQ(k)] (A24)
A value of k is selected initially (the method of selection is discussed below),
and subsequent values are calculated as
o
The procedure terminates when the relative change in k is less than one part in
106. Subroutines BESJ and BESY of the IBM 360 Scientific Subroutine Package (IBM, 1968)
are used to evaluate the Bessel functions in the expressions for U and U .
The following empirical formula has been found to be effective for estimat-
ing the value of the first root k, :
(k})Q = 1.0+exp[0. 595-1 .71 In (x-l)-0.257 In2(x-l)] x < 3.5 /A26j
=1.0 x * 3.5
First guesses for subsequent roots are made as follows:
(k2)Q = 2^ (A27)
" >- 3 (A28)
Eq. (A28) appears to represent a true asymptotic relationship as n becomes large,
although this has not been formally proved. The program which implements this
root-finding procedure was checked using values of k (x) tabulated on p. 330 of
Crank (1956).
166
-------
The series of Eq. (A22) converges rapidly for moderate to large values
o
of t, but slowly or not at all for (Dt/a )«1. The Euler transformation
(Abramowitz and Stegun, 1964) has been found effective in achieving convergence
at small times. The procedure is to evaluate and add terms successively to
both the original and transformed series, and to terminate when either one con-
verges to a present tolerance. The roots kn are stored as they are calculated,
so that each need be determined only once, regardless of the number of values
of t for which <(>(t)/ is evaluated.
167
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Deconvolutlon of the Step Response of a Polymer in a Continuous-Flow
Permeation Chamber.
In the experiments described in this paper, the input signal to the system
is imposed by opening a valve which commences the flow of a gas containing the
penetrant. The gas flows through a connecting line and enters the chamber on
one side of the polymer; a portion of the penetrant dissolves in and diffuses
through the polymer into a carrier gas, which passes to an analyzer where the
penetrant concentration (the output signal) is measured.
Schematically, the system may be viewed as a series of process units, each
with its own dynamic characteristics.
xQ(t)
Inlet
Tubing
*}(t)
Chamber
x2(t)
Polymer
x3(t)
Carrier
gas
line
x4(t)
Analyzer
Hhat is measured is the response *r(t) to a step input *0(t), whereas what is
desired is related to the response of the polymer alone (x~) to a step change in
the chamber gas concentration (x2). Standard process dynamics procedures are
applicable to this problem, if it is assumed that each component behaves linearly.
This assumption is valid for the polymer if the penetrant diffusivity and solu-
bility are both independent of the penetrant concentration, and may or may not
be valid for the analyzer. Most of the theoretical foundations for the develop-
ment that follows may be found in the work of Douglas (1972).
168
-------
The terms defined below will be used to obtain the desired result.
g.(t) = the unit impulse response of the i component (i=l-5); i.e., if
xi_1 = 6(t), then x.(t) = g.(t).
g(t) = the unit impulse response of the overall system: if xQ(t) = 6(t),
then x5(t) = g(t)
y. = the zeroth moment of c
i
y. = / g.(t)dt (Bl)
o
T. = the mean of g., which is also the mean residence time for the
flow-through components (i=l,2 and 4). T has the same significance
for g(t).
/ tQjUJdt / tg(t)dt
, = _° ; T= _2 (B2)
1 00 00 V '
/ g,-(t)dt / g(t)dt
o o
G..(s) = the Laplace transform of g.j(t), or the transfer function of the i
component
G..(s) = /" e-st g.(t)dt ; G(s) = /" e'stg(t)dt (B3)
0 0
F.(t),F. = the response of the i component to a step input, and the asymp-
totic value of this response as t -> °°.
the step response
of this response.
F(t),Fs = the step response of the overall system and the asymptotic value
Mo
169
-------
F (t)
M = / [1 - 4 3 dt (B5)
0 o r3s
F,(t)
Ta • / [i - -f—3 dt (B6)
o 5s
The preceding notation follows that used in the main body of the paper: M is
calculated from the measured system response, M is the quantity needed to de-
termine the diffusivity of the penetrant in the polymer, and T is determined
a
from analyzer calibration data. The result to be proved is that
Mo = Mo' - h + T2 + T4 + Ta} ^
According to Duhamel's principle the input and output for the i component
satisfy the relationship
t
0) then from Eq. (B8)
t
F.(t) = / g.(t')dt' (B9)
o
Letting t -»• » in Eq. (B9) and noting Eq. (Bl) yields the result
Fis =Fi(») = Vj (BIO)
and differentiating Eq. (B9) with respect to t yields g^ = dF^/dt, which for con-
venience in a future calculation may be rewritten as
The quantity TI of Eq. (B2) may be rewritten with the aid of Eqs. (Bl)
and (BIO) as
170
-------
•s = r~- / Vt)dt
1 ris o
Integrating by parts with u=t, dv^dt, du=dt and from Eq. (Bll) v = ~(F.js-F.),
yields
00 00
T4 =(l/Fis){-t[Fis-F.(t)] + / [Fis-F.(t)]dt} (B13)
o o
Provided that
. Lim t[Fis-F.(t)] = 0 (B14)
t -> oo
(which must be satisfied for any real process component), Eq. (B13) becomes
F.(t)
T. = / [l-4r-3dt (BIS)
1 o ris
It follows from Eqs. (B15) and (B4) - (B6) that
T = MQ' (B16)
T3 = M0 (B17)
t5=Ta (B18)
Next, a Taylor expansion of the exponential in Eq. (B3) for the transfer
function G.(s) yields
G,(s)=/ g.(t)dt - s / tg.(t)dt + 0(s2) (B19)
o o
from which
oo
Lim G^s) = / gi(t)dt (B20)
171
-------
dG< «
.-I . / tg.(t)dt (B21)
s •*• o
and hence
--
/ g,(t)dt
o
The subscripts may be dropped to obtain the analogous result for the overall
system. The condition for the validity of (B22) is simply that the integrals
exist, which they must for any real process.
Finally, if 6(s) is the overall system transfer function, then G(s) =
6^(5)62(5) ... GC(S). Taking logs of both sides of this equation, differentiating
vyith respect to s and multiplying by -1 yields
1 dG(s) . S 1 dVs)
- G(sT
or from Eq. (B22)
T = 1 + T2 + T3 +T4 +T5
Substituting for % T. and r from Eqs. (B16) - (B18) and solving the resulting
equation for MQ yields
which is the desired result. (The time lag T4 has been relabeled T3 in
Eq. (6), to avoid an unexplained omission in the sequence of subscripts shown
in this equation.)
172'
-------
-4
10
V
ios
>
M
-6
10
T
T
Fluorosi I icone Rubber Tube
OD =0.930 cm ID = 0.520cm
A 4950 ppm SO2
• 5603 ppm SO2
• 15400 ppm SO2
2.2 2.4
1000/T
2.6
2.8
Figure 2. Diffusivities of SOp in a fluorosilicone rubber tube.
173
-------
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Fluorosi I icone rubber tube
OD = O.930 cm ID =0.520 cm
• 73.5 °C
A 101 °C
• 123 °C
Model response
50
Figure 3.
10O
250
300
150 200
Time , min.
Theoretical and experimental transient response isotherms.
350
-------
1«
v>
I
vl
E
u
>•
>
10
-7
10
-8
A
O
OD
cm
I D
cm
0,959 0.806
0.927 0.782
1.052 0.647
0.604 0.544
0.661 0.612
J o rda n
OS.
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
1000/ T , °K"1
Figure 4. Diffusivities of SCL in PTFE tubes,
175
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing}
1. REPORT NO.
EPA-6QQ/2-78-2U
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
POLYMERIC INTERFACES FOR STACK MONITORING
5. REPORT DATE
November 1978
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Richard M. Felder and James K. Ferrel
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Chemical Engineering
North Carolina State University
Raleigh, North Carolina 27607
10. PROGRAM ELEMENT NO.
1AD712
11. CONTRACT/GRANT NO.
801578
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency^RTP, NC
Office of Research and Development
Environmental Research Center
Research Triangle Park, N.C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final 1/73 - 6/76
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Research has been performed on the use of polymeric interfaces for
in-situ continuous stack monitoring of gaseous pollutants. Permeabilities
of candidate interface materials to S02 were measured at temperatures from
ambient to 200°C, and the results were used to design interfaces for field
tests. A portable field monitoring system was constructed and used to
carry out SO- monitoring runs in two SO, absorption tower stacks, and in
oil-fired and coal-fired power plant boiler stacks. The results were in ex-
cellent agreement with data obtained by standard wet chemical methods. The
S0_ concentrations in the sample gases varied linearly with the concentrations
in the stack; water vapor, acid mist, and particulates in the stack gases had
no effect on the interface performance; and fluctuations in the stack SO-
concentration were mirrored rapidly and accurately in the measured responses.
The results suggest the potential value of in-situ polymeric interfaces for
continuous monitoring in stack environments too dirty or corrosive for
conventional devices to be used.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
In-Sltu stack monitoring
* Air pollution
Sulfur dioxide
* Interfaces
* Polymers
Monitors
13B
07B
07D
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS {ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
184
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (Rev. 4-77)
PREVIOUS EDITION IS OBSOLETE
176
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