Envlron. Scl. Technol. 1984, 18, 88-92
Influence of Mass Transport and Quenching on Nitric Oxide Chemiluminescent Analysis Martin F. Zabielski,* Daniel J. Seery, and Lee G. Dodge7 United Technologies Research Center, East Hartford, Connecticut 06108 ~~
~
H Data indicating the influence of carrier or bulk gases
on the calibration of low-pressure chemiluminescent NO analyzers are presented. A theory of instrument performance incorporating both capillary flow theory and quenching theory is developed. The predictions of a model based on this theory are compared with these data and the predictions of quenching theory alone. The limitations of using only quenching theory to predict instrument response for binary mixtures are demonstrated. Data useful for estimating measurement errors are given.
Introduction The most popular method of analyzing for NO/NO, pollutants in combustion exhausts is the chemiluminescent analyzer. Normally, this device is calibrated by using standard mixtures of NO in N2 In practice, however, these measurements are made in mixtures of combustion products wliich have compositions far different from the calibration mixtures. Several investigations (1-3) have attempted to account for differences in carrier or bulk gases and their effect on the quenching of NOz*. The focus of most of these studies has been to determine the effect of diluent gases on the reactions NO
+ 0 3 -k NOz* + 0 2
NO2* + M NO2*
+M
NOz + M
(2)
+ hv
(3)
kS
(1)
NO2
The results of these quenching studies have been used to predict instrument correction factors ( I ) . A detailed study of chemiluminescent analysis data obtained at this laboratory, however, revealed that the use of quenching efficiencies to predict correction factors yields erroneous results. The study of Folsom and Courtney (4) also indicated that quenching data alone were inadequate for describing the performance of two different commercial analyzers when the carrier gas was varied, but no detailed explanation of their data was given. The errors introduced can be as large as 20% for instruments with low-pressure reaction chambers. The purpose of this work is (1)to present additional experimental data showing the influence of carrier gas on instrument response, (2) to demonstrate that the transport properties of the span and sample gases govern how much NO is available for reaction 1and hence must be considered along with quenching, and (3) to describe a detailed model that can be used to predict response factors for chemiluminescent analyzers with lowpressure (- 10 torr) reaction chambers.
Experimental Section The gas standards employed in this study were gravimetrically prepared by Scott Research to f l % accuracy. Present address: Southwest Research Institute, S a n x o n i o , TX. 88
Environ. Sci. Technol., Vol. 18, No. 2, 1984
These standards were cross-referenced with other standards by using both mass spectrometry and chemiluminescent analysis. Mixtures of gas were prepared by flowing standards and high-purity carrier gases through choked orifices followed by counterflow mixing. To ensure that choked flow was maintained through the orifices, both upstream and downstream pressures were monitored with Wallace & Tiernan Model 62B gauges. The NO concentrations in the mixtures ranged from 100 to lo00 ppm. The estimated accuracy of the gas blending system was *3% or better. The chemiluminescent analyzer was a Scott Model 125 which is shown schematically in Figure 1. Although there are some significant differences in some instrument features, e.g., capillary dimensions and electronics, this instrument is generally similar to the widely used TECO Model 10A, especially its sample introduction method and reaction chamber pressure. Pressures PI and P3 measured upstream of the sample and Oz/03 capillaries, respectively, were typically 101 kPa (760 torr). The thermal conductivity gauge provided with the instrument at Pz was replaced with a capacitance manometer (Barocel Model 1173) so that the reaction chamber pressure could be measured to f2%. Unlike the thermal conductivity gauge, the response of this manometer is not sensitive to gas composition. The pressure in the reaction chamber without sample flow was typically 800 Pa (6 torr) while with sample flow the pressure was typically 930 Pa (7 torr).
Theory When a chemiluminescent analyzer is spanned with a calibration gas, i.e., with a known concentration of NO in Nz, it is usually assumed that the sample gas will have similar quenching and transport properties. This assumption is not always valid ( 4 ) . In developing a theory of instrument behavior to cope with nonideal conditions, several factors must be considered. First, the act of spanning the instrument electronically sets an absolute emission intensity against which all subsequent measurements are referenced. Second, the bulk transport properties of the sample gas control the amount of NO entering the reaction chamber through the capillary and, hence, the amount of NO available to participate in reaction 1. Third, even though the principal quenching agent is Oz, the contribution of the carrier gas to quenching is significant and is dependent on the composition and amount flowing through the sample capillary. Fourth, the flow of O2 into the reaction chamber is maintained constant by keeping P3 constant, Other details such as the center wavelength of the optical filter, its band-pass, vacuum pump efficiency, etc., can be important in comparing the performance of two different instruments. To predict the amount of gas passing through a capillary is difficult for the conditions of continuum flow and large pressure gradients ( 1 atm). Poiseuille’s theory is not applicable because the Mach number at the exit of the capillary is much larger than the maximum 0.3 required for the validity of this theory (5). An a priori choice of whether isothermal or adiabatic compressible flow is ob-
-
0013-936X/84/0918-0088$01.50/0
@ 1984 American Chemical Society
SAMPLE INLET
4ij = 81/2(1
(0.127 mm ID.)
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0 2 INLET
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P.M. TUBE FILTER
-
REACTIONCHAMBER
CAPILLARY N0.2
)(
(0.203 mm I.D.)
-
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(? VACUUM
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Flgure 1. Schematic diagram of Scott Model 125 NO chemllurninescent analyzer.
tained in the capillary is not obvious. This choice is dependent upon the pressure gradient, length, and-radius of the capillary. For adiabatic, laminar conditions, the flow equations for a constant area tube given by Shapiro (6)(eq 2.26, 3.5, 3.7,4.14a, and 4.14b and Figure 6.15 and Table 8.1) can be used. These equations must be solved iteratively by varying the entrance Mach number until the flow chokes at the capillary exit; i.e., the Mach number is unity at the exit. Shapiro (6)also presents a detailed theory for flow through tubes under isothermal conditions. A more convenient treatment using approximations, however, has been developed by Roffman (7) for compressible fluid flow in capillary tubes. By use of the treatment, the mass flow is given by -16RTpL m = ( 7rMr4
(6)
+ i=lCUiPi)
(7)
where F is the emission signal, B is a proportionality and Piare the partial pressure of NOz and constant, PNoz the ith component, and ai is the quenching constant for the ith component given by the ratio of its rate constants, k2(O to k#). The sample mass flow predicted by eq 4 influences the emission signal F through the terms P N Oand ~ Pi.The amount of NO entering the reaction chamber and, hence, the amount of NO2* formed via reaction 1 are controlled by the bulk sample flow. Exclusive of the O2 and O3 in the reaction chamber, the pressures of the remaining constituents in the reaction chamber depend on both the sample mass flow and their mole fractions in this flow. Quenching data are given in the literature ( 1 , l l - 1 4 ) . Although the measured values of the quenching constants differ according to excitation process (aNz= 44 torr1 by 435.8 Hg-line (11) and uNz= 119 torr-' by reaction 1 (2, 13)),the relative values are consistent. The excited electronic states of NO2 are the same for either chemical or photon excitation, except the photon process populates higher vibrational levels (11). A model including quenching and mass transport was developed from the theory given above. The required input data are (1)molecular weights of the reference and diluent gases, (2) viscosities of reference and diluent gases, (3) the length and diameter of the sample capillary, (4) the pressures upstream and downstream of the sample capillary, (5) the partial pressure of oxygen in the reaction chamber, (6) the quenching coefficients of oxygen, reference, and diluent gases, and (7) the concentration of NO in the reference gas. The model is divided into two sections: In the first section, the mass flow of the reference gas through the sample capillary is calculated by using eq 4. This mass flow rate is converted to molar flow rate. Equation 7 is then employed to calculate the reference emission. The proportionality constant B is arbitrarily set equal to unity since ultimately the model is used to predict relative instrument response. In addition, the values 4ij,which are calculated only once, are determined in this first section by using eq 6. The second section of the model treats all cases where the diluent gas is added to the reference gas, e.g., Nz diluted with Ar. For all the calculations given below, N2was the reference gas, and only binary mixtures were considered. The viscosity of the mixtures is calculated from eq 5 given the mole fractions of the mixture. The mass flow is determined by using eq 4 and transformed into molar flow. The Stern-Volmer relationship (eq 7) is used to predict the emission intensity F. The emission intensity of the mixture is then divided by that of the reference gas to give the relative response R. The mole fraction of the diluent gas is typically incremented by 0.1, and the calculations of the second section are repeated until only the diluent remains. The model was entered into a TI59 programmable calculator. Typically 4 min were required
+[(=)lt4(m) 16RTpL
17RT
17RT where L and r are the length and radius of the capillary, respectively, M is the molecular mass, R is the universal gas constant, T i s the temperature, p is the viscosity, and PIand P2are the upstream and downstream pressures. For mixtures of gases, the mean molecular mass is employed, and the viscosity can be calculated from the Chapman-Enskog theory ( 4 9 ) which can be summarized by (5)
and
rn
B(1
ELECTRONICS
q4]2
pN02
F=
-
) (cA%Yy1'""
(E)"(
where X denotes the mole fraction of ith or jth component and the remainder of the terms have been defined above. The effect of variations of sample composition and reaction chamber pressure on reaction 3 follows the well-known Stern-Volmer relation (10)
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+ $)'"[ 1+
Envlron. Scl. Technol., Vol. 18, No. 2, 1984
89
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0.80
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I
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I
I
1
0.0
0.2
0.8
8.4
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xd
1.3
for the computation of a response curve.
Results To facilitate the demonstration of the model, only results for binary mixtures are given. No data are presented for H 2 0 for the following reasons. First, significant discrepancies exist in the literature values for the quenching of NO2*by H20 (1,14) even after normalization to account for different excitation processes. Second, in most combustion exhaust measurements, samples are usually dried to H20 concentrations of 0.5% or less. The contribution of the term aH#H,O in eq 7 in this situation is numerically insignificant. In Figure 2, predictions from the model are compared with experimental data for N2/Ar mixtures. The relative response R is defined as the ratio of the indicated NO concentration to the known NO concentration for a given mole fraction Xd of diluent gas. Included in Figure 2 are data from Folsom and Courtney (4)obtained with a TECO Model 10A instrument and data from this laboratory by using the Scott Model 125. As seen from these data the behavior of the TECO instrument is similar to that of the Scott instrument. Although this agreement must be regarded as fortuitous, parallel behavior is also observed for C02 and will be assumed to continue for other gases used by Folsom and Courtney (4). The results of Stern-Volmer calculations ignoring the effects of flow through the capillary are also shown for comparison. Consequently, if one of these instruments was spanned with a NO in N2 standard and then used to measure NO in Ar, an 18% error would occur. If a correction factor based on quenching alone were used, a 22% error would result. The following two items should be noted about the sensitivity of the model to the input data. First, for a capillary of given diameter and length, the mass flow is principally a function of viscosity, molecular weight, and the upstream pressure PI but only weakly dependent on P2. For the Scott instrument, a 1-torr (133 Pa) change in P2 produces a change in the differences term (P: - P12) of 0.003 5%. Second, the quenching coefficients (ai) used were those of Myers et al. (14). Since in the Stern-Volmer equation the summation term is much greater than unity, the relative response is not strongly dependent on the absolute value of ai. For example, if the quenching coefficients are normalized to a N 2 = 119 torr-' of Clough and Thrush (13))for Xd(Ar) = 1 the response R = 0.8524 vs. 90
Environ. Sci. Technol., Vol. 18, No. 2, 1984
I
1.2
1.1 R
0.8
0.0
8.2
0.4
0.6
0.8
I
.e
xd
Flgure 4. Response (R) vs. mole fraction (X,) of diluent CH,. Quenchin theory (0), model with a = 82 torr-' (0),model wlth a = 140 torr- (V),and data (Folsom and Courtney) (A).
B
0.8523 for normalization to aNq= 44 torr-' from Myers et al. (14). This difference is obviously negligible relative to the uncertainties in the measurements of the quenching coefficient. Data for C 0 2 are given in Figure 3. The model predictions for a quenching coefficient C02 = 105 torr-' are -7% higher than both the experimental data and the predictions for only quenching. The reason that the model values are higher than for the quenching only case is that the mixtures of C02and N2have a viscosity less than that of N2and, hence, more NO arrives in the reaction chamber offsetting the increased quenching of C02. It should be noted that if aco is increased by 3090,excellent agreement between the model predictions and the experimental data is obtained. Such an increase is outside the stated experimental uncertainty of the quenching data, but there are significant differences (e.g., mode of excitation, peak wavelength, and band-pass) between the experiments in ref 14 and the Scott instrument so that a 30% difference in quenching is not unreasonable. The agreement between the quenching theory and the data is regarded as fortuitous. Given in Figure 4 are data for CHI from Folsom and Courtney (4) along with the model predictions and
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1
+/I I .e4
R I .82
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I
I
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8.4
I 8.8
1
1 e.8
I
e
I
t
.e
m 8.8
8.2
e
Xd
Figure 5. Response ( R ) vs. mole fraction (xd)of diluent CO and 02. CO: model (0) and data (Folsom and Courtney) (+). 0,: quenchlng theory (0),model (V),and data (Foisom and Courtney) (A).
Conclusions The consideration of only quenching phenomena to predict the response of low-pressure chemiluminescent analyzers can result in significant errors. A comprehensive
8.8
\
.e
Xd
Flgure 6. Response (R) vs. mole fraction (X,) of diluent He. Quenching theory (O), model (V),and data (this study (+).
,
t 1.8
quenching calculations. Unlike the quenching calculations, the trend of the model predictions is correct. The quenching coefficient for CH4from Myers et al. (14) is UCH, = 82 torr-' which is somewhat lower than we would expect for a molecule which has several channels through which energy can be transferred from NO2*. If the Scott and the TECO instruments were identical, a quenching coefficient of 140 torr-l would produce agreement between data and the model predictions. This value is most likely an upper bound for uCH,. Nevertheless, the trend of the response curve for quenching theory alone is incorrect. In Figure 5, CO and O2data from Folsom and Courtney are compared with model predictions. The behavior for CO is expected because its viscosity and quenching efficiency are similar to that of N2. Quenching theory predictions lie on top of the model predictions and are not presented to maintain the clarity of the figure. The data for 02,however, show major deviations from the model predictions and quenching theory calculations but are much closer to the model predictions. Part of the discrepancy between the data and model predictions is due to the fact that the TECO instrument's capillary and operating conditions were assumed to be the same as those of the Scott instruments. Another potential source of error is the loss of NO by reaction with 02. Data for light gases are given in Figures 6 and 7. The somewhat unusual shape of the He model curve results form the Chapman-Enskog computation of the viscosity of the mixture. The data for He were taken at this laboratory. Although the predictions of the model and quenching theory lie within the uncertainty of the data (-3%) for dilutions up to 85%, only the model predicts a rapid increase in R as the dilution approaches 100%. The response measured at 90% dilation indicates the onset of this rapid increase. The data for H2 are from Folsom and Courtney. The model calculations were made again by assuming the two instruments are identical. The trend of the response curve is incorrect for the quenching theory; however, the data are in good agreement with the model through X , I0.5. The rapid rise in the curve Xd > 0.8 is due to the low viscosity of Hz.
B.6
8.4
l
I
1.4
2 I .2
1 .e
8.8
8.2
8.4
B.6
8.8
I
xd
Figure 7. Response (R) vs. mole fraction (X,) of diluent H., Quenching theory (0), model (A), and data (Folsom and Courtney) (0).
treatment must include both quenching and transport effects. Of critical importance is the influence of viscosity on the amount of NO introduced into the reaction chamber. Table I lists typical errors at specified dilutions that can be encountered with binary mixtures if the analyzer is spanned with NO in N2and (1)unit response is assumed, (2) quenching theory alone is used to predict response, and (3) quenching theory and transport properties are used to predict response. The model, which was specifically developed to predict the response of instruments like the Scott 125 or the TECO 10A, includes Chapman-Enskog relations to estimate the viscosities of mixtures, the capillary flow theory of Roffman (7), and the Stern-Volmer relation to estimate emission intensity. A program describing this model has been written for the TI59 programmable calculator. Where data are available, the model predictions are in good agreement with the data. Only binary mixtures, however, can be treated with this program because of calculator memory limitations. The theory upon which the model is based is not limited to binary mixtures. It is planned to place this model on a small computer so that the response of such instruments to combustion gases can be made. With this expandable model and a knowledge of key instrument parameters, it should be possible to predict the response factors of comEnviron. Sci. Technol., Vol. 18, No. 2, 1984 91
Table I. Analysis Errorsa for Binary Mixtures Using a Low-Pressure Chemiluminescent Analyzer Spanned with NO in N,
Registry No. Nitric oxide, 10102-43-9;nitrogen, 7727-37-9; carbon dioxide, 124-38-9; carbon monoxide, 630-08-0; oxygen, 7782-44-7; helium, 7440-59-7; hydrogen, 1333-74-0.
Literature Cited
model (quenching unit quenching and theory transport) response A €%
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