Current address: Rutherford Consulting Service, 5012 E Budlong Street, Anaheim, CA 92807, USA.

This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Two methods were described to estimate interference in the measurements of infrared (IR) photoacoustic multi-gas analyzer (PAMGA). One is IR spectroscopic analysis (IRSA) and the other is mathematical simulation. An Innova 1412 analyzer (AirTech Instruments, Ballerup, Denmark) with two different filter configurations was used to provide examples that demonstrate the two methods. The filter configuration in Example #1 consists of methane (CH_{4}), methanol (MeOH), ethanol (EtOH), nitrous oxide (N_{2}O), carbon dioxide (CO_{2}), and water vapor (H_{2}O), and in Example #2 of ammonia (NH_{3}), MeOH, EtOH, N_{2}O, CO_{2}, and H_{2}O. The interferences of NH_{3} as a non-target gas in Example #1 were measured to validate the two methods. The interferences of H_{2}O and NH_{3} as target gases in Example #2 were also measured to evaluate the analyzer’s internal cross compensation algorithm. Both simulation and experimental results showed that the interference between the target gases could be eliminated by the internal cross compensation algorithm. But the interferences of non-target gases on target gases could not be addressed by the internal cross compensation, while they could be assessed by the IRSA and mathematical simulation methods. If the IR spectrum of a non-target gas overlaps with that of target gas A at filter A, it could affect not only gas A (primary interference), but also other target gases by secondary interference (because the IR spectrum of gas A overlaps with gas B at filter B and thus affects gas B measurements). The IRSA and mathematical simulation methods can be used to estimate the interference in IR PAMGA measurements prior to purchase or calibration of the unit.

Agriculture is an important source of air emissions, including greenhouse gases, volatile organic compounds, and ammonia (NH_{3}) [

It is well known that interference exists in IR spectroscopic measurements and causes large uncertainties in observational data if it is not treated properly. Therefore, understanding of IR PAMGA interference is a critical step to ensure accurate air emission monitoring when using such instrumentation.

The principle of the IR PAMGA and IR photoacoustic technology were described in detail by Christensen [

Each gas molecule has its own set of characteristic quantum energies. When a molecule absorbs external energy (such as photons in light), it transits from a lower to a higher energy level. When the molecule returns back to its lower energy level, it either emits a photon or releases heat or both. During the transition from one energy level to another, the difference between the higher energy level E_{high} and the lower level E_{low} of the molecule must be equal to the photon energy (

where ν is the wavenumber of the photon in cm^{−1} and ^{−1}), in which the mid-IR region (670–4,000 cm^{−1}) is widely used in the IR detection of gas molecules. When an IR monochromatic light with single wavenumber enters a chamber that contains a single gas absorbing the light at the same wavenumber, the light intensity decreases after passing through the chamber. The change in light intensity before and after the chamber obeys Beer’s law (e.g., [

or

where _{0} and ^{−1}∙m^{−1}. _{0},

The gas concentration inside the chamber can be determined from Equations (2) or (2a) based on the change in light intensity, when the absorption coefficient _{0}(

When the gas absorption is small (

Simplification from Equation (2a) to (2b) is reasonable as long as the gas concentrations are in the linear measurement range because the IR gas analyzers provide a linear response to the gas concentrations. When an IR light intensity is modulated at an “audio” frequency, the heat released by the molecule when transiting from a higher to a lower energy level produces a sound signal at the same frequency inside the chamber that can be detected by microphones. Intensity of the microphone signal is proportional to the absorbed light intensity

_{4}, CO_{2}, MeOH, EtOH, N_{2}O, NH_{3} and H_{2}O in the IR region of 600–2,400 cm^{−1}. The IR spectral data of these molecules were obtained from the IR spectral library of the Pacific Northwest National Laboratory [^{−1} resolution. Each gas molecule has its characteristic spectrum in terms of wavenumber region, absorption intensity, and structure (

Example of infrared (IR) absorption spectra of CH_{4}, CO_{2}, MeOH, EtOH, N_{2}O, NH_{3} and H_{2}O (black solid lines). Locations and bandpass of filters corresponding to each gas are shown in orange rectangles on each plot. In Example #1, CH_{4}, CO_{2}, MeOH, EtOH, N_{2}O and H_{2}O are target gases and NH_{3} is the non-target gas. In Example #2, CO_{2}, MeOH, EtOH, N_{2}O, NH_{3} and H_{2}O are target gases and CH_{4} is the non-target gas.

If there are multiple gases inside the chamber and some of them absorb light at the same wavenumber

where

When the gas absorption is small (

It is almost impossible to derive gas concentrations from Equations (3)–(3b) at a single IR wavenumber because the change in IR light intensity is due to absorption by several gases, but it may be possible to do so in multiple IR regions. For example, the Innova 1412 (AirTech Instruments, Ballerup, Denmark), an IR PAMGA, uses up to six filters to select IR light in up to six spectral regions to detect up to six gases sequentially. Because there are multiple gases in the monitoring environment in this case, overlaps of gas IR spectra may cause interference in gas detection and therefore may introduce measurement errors if the interference is not properly treated.

Because the IR PAMGA employs an IR spectroscopic technique to measure multiple gases, interference between the gases is likely to occur due to the overlaps of IR spectra. In order to reduce the interference, the first step is to properly configure the filters in IR PAMGA based on the IR absorption of all gases of interest in the monitoring environment. In the present study, two filter configurations were used as examples and are listed in _{2}O, CO_{2}, CH_{4} and H_{2}O in channels A, B, C, D, E, and W, respectively. In Example #2, the target gases were MeOH, EtOH, N_{2}O, CO_{2}, NH_{3} and H_{2}O in channels A, B, C, D, E, and W, respectively. The IR absorption spectra of these gases are shown in _{4}, 5 ppm for MeOH, EtOH, and NH_{3}, 1 ppm for N_{2}O, 500 ppm for CO_{2}, and 10,000 ppm for H_{2}O. Because of the wide range in agricultural air emissions from very low (ppb level) in open sources to extremely high (thousands ppm level) in the enclosed animal housing, the vertical scale of the IR spectra in _{2} and H_{2}O and linear for other gases.

First, the selected filters must be located in the absorption regions of their target gases, away from the strong absorption for high concentration gases, and close to the central peak for low concentration gases. _{2}O filter was located at the far wings of a water vapor absorption band to avoid saturation caused by strong absorption near the band center. The CO_{2} filter was located at a weak absorption band to avoid saturation as well. For other target gases, the filters were located near the band center to achieve stronger absorption.

Filter configurations and filter/target gas combinations in Example #1 and #2.

Channel in Example #1 | Channel in Example #2 | Filter Name | Target Gas | Filter Center (cm^{−1}) |
FilterBandpass (cm^{−1}) |
||
---|---|---|---|---|---|---|---|

A | A | UA 0936 | MeOH | 1,020 | 989–1,053 | ||

B | B | UA 0974 | EtOH | 1,061 | 1,027–1,096 | ||

C | C | UA 0985 | N_{2}O |
2,215 | 2,193–2,237 | ||

D | D | UA 0982 | CO_{2} |
710 | 683–737 | ||

E | - | UA 0969 | CH_{4} |
1,254 | 1,220–1,289 | ||

- | E | UA 0976 | NH_{3} |
941 | 908–974 | ||

W | W | SB 0527 | H_{2}O |
1,985 | 1,965–2,205 |

Secondly, the selected filters should be located at the spectral regions where overlaps between the IR spectra are as few as possible because spectra overlaps would cause interference in multiple gas measurements. The overlaps between the gas IR spectra can be easily identified by aligning the IR spectra of all gases in one graph. _{3} interference at the MeOH and EtOH filters, the MeOH interference at the EtOH filter, and the EtOH interference at the MeOH filter. By contrast, the CH_{4} interference on other gases is not likely to occur because the CH_{4} absorption band is located far away from other filters. Because the IR spectra of water vapor cover a wide spectral range, water vapor interferes with most gases unless the air sample is dry. Therefore, a H_{2}O filter must be included in the filter configuration when the PAMGA is used in atmospheric applications. In _{2}O filter was installed in channel W for both Examples #1 and #2. Although

In order to quantitatively compare the absorption of the selected gases at an IR PAMGA filter, absorption coefficients measured at the standard ambient pressure and temperature of 101.3 kPa and 25 °C by the PNNL [^{−1}) of a gas at a filter bandpass was an integration of individual absorption coefficients from the PNNL database over the entire filter bandpass and then multiplied by the gas concentration. _{4} (10 ppm), MeOH (5 ppm), EtOH (5 ppm), N_{2}O (1 ppm), CO_{2} (500 ppm), H_{2}O (10,000 ppm) and a non-target gas NH_{3} (5 ppm) at the six filters of Example #1. _{3} (5 ppm), MeOH (5 ppm), EtOH (5 ppm), N_{2}O (1 ppm), CO_{2} (500 ppm), H_{2}O (10,000 ppm), and a non-target gas CH_{4} (10 ppm) at the six filters of the Example #2. It is seen in

Absorption of Example #1 target gases (CH_{4} = 10 ppm, CO_{2} = 500 ppm, MeOH = 5 ppm, EtOH = 5 ppm, N_{2}O = 1 ppm, and H_{2}O = 10,000 ppm) and non-target gas (NH_{3} = 5 ppm) at each filter.

Absorption of Example #2 target gases (NH_{3} = 5 ppm, CO_{2} = 500 ppm, MeOH = 5 ppm, EtOH = 5 ppm, N_{2}O = 1 ppm, and H_{2}O = 10,000 ppm) and non-target gas (CH_{4} = 10 ppm) at each filter.

Figures 2 and 3 were produced for selected filter configurations and gas concentrations to show the possible interference between these gases. Similar plots can be made for different filter configurations at various gas concentrations after the total absorption at each filter are computed from the PNNL IR spectral database. Because gas concentrations vary in the real world, it is impossible to make graphs for every gas concentration to perform the IRSA. It would be better to have a single plot or table for a given filter configuration which can be used for IRSA at variable gas concentrations. For this purpose, total absorptions of these gases at a concentration of 1 ppm are provided in _{4}, MeOH, EtOH, N_{2}O, CO_{2}, and H_{2}O in Example #1 with the introduction of 1 ppm non-target gas NH_{3}. _{3}, MeOH, EtOH, N_{2}O, CO_{2}, and H_{2}O in Example #2 with the introduction of 1 ppm non-target gas CH_{4}. _{3} on the target gases MeOH and EtOH, less interference on CH_{4} and CO_{2}, and much less interference on N_{2}O. The relative absorption shown in _{3} on 1 ppm target gases MeOH, EtOH, N_{2}O, CO_{2}, and CH_{4} are 349, 432, 0, 78, and 11 ppb per ppm NH_{3}, respectively, which were derived from _{3} could cause about 3.5, 4.3, 0, 0.8, and 0.1 ppm interference, respectively, in the measurements of MeOH, EtOH, N_{2}O, CO_{2}, and CH_{4}. Either the relative absorption in _{3} appears to be at elevated concentrations.

As another example, the IRSA was applied to _{4} on 1 ppm target gases NH_{3}, MeOH, EtOH, N_{2}O, and CO_{2} in Example #2 were hardly observed in _{4}, respectively, therefore can be neglected when the CH_{4} concentration is low. When CH_{4} was as high as 1,000 ppm, the errors caused directly by CH_{4} would be 11, 12, 21, 4, and 362 ppb, respectively, in the NH_{3}, MeOH, EtOH, N_{2}O and CO_{2} measurements. So, the CH_{4} interference in Example #2 was still negligible even if the CH_{4} was up to thousands of ppm, while the target gases were at a few ppm.

Relative absorption of 1 ppm non-target NH_{3} and 1 ppm target gases at each filter in Example #1.

Relative absorption of 1 ppm non-target CH_{4} and 1ppm target gases at each filter in Example #2.

Total absorption of 1 ppm gas at each filter, NH_{3} relative interferenceon target gases in Examples #1, and CH_{4} relative interference on target gases in Example #2.

Filter | Total Absorption of 1 ppm Gas (m_{−1}) |
NH_{3} RIF*ppbper ppm |
CH_{4} RIF *pptper pm |
||||||
---|---|---|---|---|---|---|---|---|---|

MeOH | EtOH | N_{2}O |
CO_{2} |
CH_{4} |
H_{2}O |
NH_{3} |
|||

MeOH | 2.2 × 10^{−1} |
1.2 × 10^{−1} |
5.0 × 10^{−6} |
1.5 × 10^{−5} |
2.6 × 10^{−6} |
5.2 × 10^{−6} |
7.6 × 10^{−2} |
349 | 12 |

EtOH | 1.9 × 10^{−1} |
2.3 × 10^{−1} |
1.3 × 10^{−5} |
3.2 × 10^{−5} |
4.7 × 10^{−6} |
9.8 × 10^{−6} |
9.8 × 10^{−2} |
432 | 21 |

N_{2}O |
3.9 × 10^{−4} |
5.4 × 10^{−4} |
6.6 × 10^{−1} |
1.4 × 10^{−4} |
2.5 × 10^{−6} |
4.0 × 10^{−6} |
2.6 × 10^{−6} |
4 × 10^{−3} |
4 |

CO_{2} |
2.7 × 10^{−4} |
9.3 × 10^{−5} |
4.9 × 10^{−5} |
2.5 × 10^{−2} |
9.1 × 10^{−6} |
7.6 × 10^{−5} |
2.0 × 10^{−3} |
78 | 362 |

CH_{4} |
1.4 × 10^{−2} |
5.8 × 10^{−2} |
8.5 × 10^{−2} |
8.0 × 10^{−6} |
2.5 × 10^{−2} |
1.9 × 10^{−4} |
2.9 × 10^{−4} |
11 | - |

H_{2}O |
3.2 × 10^{−4} |
4.5 × 10^{−4} |
5.6 × 10^{−6} |
4.3 × 10^{−6} |
7.3 × 10^{−7} |
4.8 × 10^{−4} |
3.8 × 10^{−9} |
8 × 10^{−3} |
1517 |

NH_{3} |
5.8 × 10^{−3} |
6.9 × 10^{−3} |
2.2 × 10^{−5} |
1.1 × 10^{−5} |
1.9 × 10^{−6} |
6.0 × 10^{−6} |
1.8 × 10^{−1} |
- | 11 |

* RIF: Relative Interference.

In order to validate the IRSA method, experimental tests were conducted at California Analytical Instruments, Inc (CAI) using an Innova 1412 analyzer with two configurations as shown in _{3} interferences as a non-target gas in Example #1 (because the NH_{3} filter was not installed) are shown in _{3} filter was installed) are shown in

Interference of NH_{3} in Example #1 as a non-target gas. Black solid lines with closed circles are experimental responses to NH_{3} only (NH_{3} = variable, other gases = 0 ppm), blue dash lines with open circles are experimental responses to NH_{3} in the presence of MeOH (12.8 ppm) and EtOH (4.5 ppm), and red thin-lines with crosses are estimation by the IRSA method for the NH_{3} only test. All gas mixtures were in N_{2} balance and not humidified.

Interference of NH_{3} in Example #2 as a target gas. Black solid lines with closed circles are experimental responses to NH_{3} only (NH_{3} = variable and other gases = 0 ppm) and blue dash lines with open circles are experimental responses to NH_{3} in the presence of MeOH (35.2 ppm) and EtOH (12.2 ppm). All gas mixtures were in N_{2} balance and not humidified. Analytical results of the interference of NH_{3} as a target gas were not available because the IRSA method is used to estimate the interference of non-target gases.

There are two tests shown in _{3} only was fed to the analyzer in various concentrations while all target gas concentrations were zero and (2) the non-target gas NH_{3} was mixed with MeOH (12.8 ppm) and EtOH (4.5 ppm) in various concentrations before the mixture was fed to the analyzer while the other gas concentrations were zero. Experiment (1) was titled the “NH_{3} only test” and experiment (2) the “tri-gas test”, which was the simplest case of a multi-gas test. In both experiments, the sample gases were obtained from standard gas cylinders in N_{2} balance and were not humidified (H_{2}O = 0 ppm). The analyzer’s internal cross compensation algorithm was used in both experiments. The interference of non-target gas NH_{3} on target gases MeOH, EtOH, N_{2}O, CO_{2}, and CH_{4} were calculated based on the relative interference given in _{3} concentrations in the absence of other gases (NH_{3} only test). The IRSA results are also shown in _{3} interference as non-target gas on the IR PAMGA measurements seem independent of the target gas concentrations because the line slopes in each graph are very close between the NH_{3} only and tri-gas tests.

Comparisons between the experimental results and IRSA results in _{2}O and an overestimation for MeOH and EtOH. However, the negative interference of the non-target gas NH_{3} on the target gas CH_{4} measurements in _{3} and CH_{4} at the CH_{4} filter, NH_{3} did not directly interfere with CH_{4} (primary interference), but NH_{3} had a secondary interference on CH_{4}, _{3} had a primary interference on EtOH at the EtOH filter and in turn EtOH had a primary interference on CH_{4} at the CH_{4} filter. The similar secondary inference of NH_{3} on CH_{4} via MeOH also happened due to the same procedure. It may be difficult to understand the negative interference of NH_{3} on CH_{4} as shown in _{3} in Example #1 absorbed light at both MeOH and EtOH filters (Figures 1, 2, and 4) contributing a positive artifact in both MeOH and EtOH measurements. This positive artifact was then transferred to the CH_{4} filter because MeOH and EtOH absorbed light at the CH_{4} filter. In order to compensate for these positive artifacts at the CH_{4} filter, the analyzer erroneously deduced a negative concentration of CH_{4} through the internal cross compensation procedure. Because the IRSA method did not involve any cross compensation, it could not predict the secondary interference. Therefore, an algebraic matrix calculation is needed to estimate both primary and secondary interference, which will be discussed in

The “NH_{3} only” and “tri-gas” experiments were also conducted using the Example #2 analyzer, except that the NH_{3} was a target gas because the NH_{3} filter was installed in Example #2, and the results are shown in _{3} on MeOH and EtOH was eliminated by the analyzer’s built-in cross compensation algorithm. No IRSA was performed for the NH_{3} interference as a target gas because the IRSA method can only estimate the interference of non-target gases. Again, in order to simulate the interference of both target gas and non-target gas, an algebraic matrix is needed as described in

Because the IR spectrum of water vapor covers a wide spectral range and overlaps with that of many other gases, water vapor is a very important gas in terms of interference with other gas measurements. Therefore, water vapor must be measured as a target gas. This means that a H_{2}O filter must be included in the filter configuration. The interference of water vapor as a target gas in Example #2 was experimentally tested and the results are shown in _{2} gas at a constant concentration was humidified before entering the IR PAMGA using Nafion tubing over a heated water bath. The concentration of water vapor was adjusted by changing the water bath temperature. Two concentrations of CO_{2} at 520 ppm and 1,250 ppm in ultra-zero air were used respectively in the tests, while all other gases were 0 ppm.

Interference of H_{2}O in Example #2 as a target gas. Black solid lines with closed circles are experimental responses to 520 ppm CO_{2} and blue dashed lines with open circles are experimental responses to 1,250 ppm CO_{2}. All other gases were 0 ppm. Analytical results of the interference of H_{2}O as a target gas were not available because the IRSA method is used to estimate the interference of non-target gases.

As discussed in

Assuming that six filters were installed in the IR PAMGA to measure six target gases including H_{2}O, _{i} represents the microphone signal in μV from filter i (i = 1, 2, …, 6), _{j} is the concentration in ppm of target gas j (j = 1, 2, …, 6), and α_{i,j} is the contribution of target gas j to the microphone signal _{i}. The α_{i,j} is referred to as sensitivity coefficient in μV/ppm. Because of the overlaps of gas IR spectra, α_{i≠j} may not be zero, the target gas j would contribute to microphone signal _{i} (i ≠ j) and cause interference on the measurement of the target gas i. In theory, the microphone signal _{i} of IR PAMGA can be expressed as functions of the target gas concentrations _{j}:

These linear algebraic Equations can also be expressed with an algebraic matrix Equation:

or simply

where both [_{i}] and [_{i}] are a 1 × 6 matrix and [α_{i,j}] a 6 × 6 matrix, respectively. Equation (4b) can be solved using an algebraic matrix Equation.

where matrix [α_{i,j}]^{−1} is the inverse of the matrix [α_{i,j}]. Because the method to calculate Equation (4c) can be found in any textbook of linear algebraic theory, it is not described here. In addition, there are many software packages with built-in programs to solve such linear algebra problems, so it is straightforward to calculate the variables [_{i}] when microphone signals [_{i}] and sensitivity coefficients [α_{i,j}] are known. The sensitivity coefficients [α_{i,j}] can be obtained by calibrating the IR PAMGA. Although six filters were assumed to derive Equations (4a)–(4c), the Equations can be applied to any number of filters in the PAMGA.

In order to introduce the interference of non-target gases, Equation (4) can also be expressed as:

In the real monitoring environments, there may be other gases as well as random electronic noise that, in addition to the target gases, contribute to the microphone signals. Considering all these factors, Equation (5) becomes

where, φ_{i} is the total contribution of all non-target gases to the microphone signal _{i} and _{i} is the electronic noise (zero offset) at filter i. It is obvious that, for the same microphone signals _{i} (i = 1, 2, 3,…6), the solutions _{j} would be different between Equations (5) and (5a) if non-target gases and electronic noise exist (φ_{i}≠0 and _{i}≠0). The differences in solution _{j} between Equations (5) and (5b) are errors caused by non-target gas interference φ_{i} and noise _{i}. In general, when the interference and electronic noise increase, the difference in solution between Equations (5a) and (5) also increases and therefore the uncertainty of the IR PAMGA measurements increases. There are several ways to reduce measurement errors. One is to decrease the electronic noise _{i} by increasing the measurement interval. As mentioned in previous sections, properly configuring the filters in IR PAMGA based on the presence of all possible gases and their IR absorption properties is a key procedure to reduce the contribution of the non-target gas interference φ_{i.}

When the sensitivity coefficients α_{i,j} are available after calibration, the interference between the target gases can be simulated by solving Equation (5). It is also possible to evaluate the interference of non-target gases on IR PAMGA measurements by solving Equation (5a) when the non-target gases have also been calibrated. In some cases, when the calibrated sensitivity coefficients are not available, a simulation of the interference may be needed to assess its effect in the IR PAMGA measurements. Next we will discuss this possibility. Because the microphone signal of a single gas is proportional to the absorbed light intensity [

where β is a factor that includes the combined effects of temperature, pressure, thermal property of gases in the gas chamber, and geometry of the gas chamber,

Or using Equation (3b) when gas absorption is low, Equation (6) becomes:

or:

Now, it can be seen that Equation (6c) is similar to the algebraic matrix Equation (5). Defining _{i}' = S_{i}/βI_{0}L (m^{−1}) as simulation signal, the simulation signals at the six filters in IR PAMGA are:

Equation (7) is also an algebraic matrix Equation similar to Equation (5). Thus, variables _{j} can be solved from Equations (7) only if the simulation signals are known because absorption coefficients can be computed from available databases [_{i},_{j} instead of sensitivity coefficients α_{i},_{j}, using the simulation signal S_{i}' instead of the microphone signal _{i} to simulate the interference in IR PAMGA.

If we only consider the interference of one non-target gas without electronic noise (_{i} = 0), then Equation (5a) becomes:

where _{i}^{n} and ^{n} are the absorption coefficient at filter i and the concentration of the non-target gas, respectively. From Equations (7) and (7a), the interference of the non-target gas in IR PAMGA measurements can be mathematically estimated based on the selected filters and the IR absorption coefficients of all gases in the monitoring environment without calibrating the analyzer. This method might prove beneficial for IR PAMGA users when planning a new filter configuration for their analyzers. The procedure to simulate the interference using Equations (7) and (7a) is described below:

Use initial concentrations of the target gas _{i}^{I} and their absorption coefficients _{i},_{j} to calculate initial simulation signals _{i}^{I} using Equation (7), where superscript “I” represent initial values.

Add non-target gas absorption _{i}^{n}^{n} in Equation (7a).

Subtract _{i}^{n}^{n} from the initial signals _{i}^{I} to produce disturbed signals _{i}^{d}, where superscript “d” represents disturbed values.

Solve Equation (7) again using _{i},_{j} and _{i}^{d} to obtain disturbed target gas concentrations _{i}^{d}.

The differences in target gas concentrations between initial _{i}^{I} and disturbed _{i}^{d} values reveal the interference of the non-target gas in IR PAMGA measurements.

_{3} interference on IR PAMGA measurements was assessed by the mathematical simulation using Equations (7) and (7a) instead of the IRSA method. The NH_{3} interference on target gases is almost independent of the target gas concentrations because the changes in interference with the NH_{3} concentrations (line slopes) were very similar between the NH_{3} only (NH_{3} = variable and other gases = 0 ppm) and the tri-gas (MeOH = 12.8 ppm, EtOH = 4.5 ppm, NH_{3} = variable, and other gases = 0 ppm) tests. Actually, the simulation was also conducted for multiple target gases at various concentrations in addition to the tri-gas (MeOH, EtOH and NH_{3}) in _{3} relative interference (ppb per ppm NH_{3}) on target gases in Example #1 as a non-target gas. The relative interferences in

Comparison of NH_{3} relative interference on target gases in Example #1 as a non-target gas (ppb per ppm NH_{3}).

Target Gas | IRSA | Mathematical Simulation | Experiment (NH_{3} Only) |
Experiment (Tri-Gas) |
---|---|---|---|---|

MeOH | 349 | 212 | 182 ± 10 | 215 ± 42 |

EtOH | 432 | 250 | 174 ± 8 | 172 ± 58 |

N_{2}O |
0.004 | −0.4 | 0 ± 0.3 | 0 ± 0.4 |

CO_{2} |
78 | 76 | 103 ± 42 | 122 ± 28 |

CH_{4} |
11 | −686 | −377 ± 9 | −302 ± 145 |

Interference of NH_{3} on target gases in Example #1 as a non-target gas. Black solid lines with closed circles are experimental responses to NH_{3} only (NH_{3} = variable, other gases = 0 ppm), blue dash lines with open circles are experimental responses to NH_{3} in the presence of MeOH (12.8 ppm) and EtOH (4.5 ppm), red squares are results of mathematical simulation for the NH_{3} only test, and green crosses are simulation for the tri-gas test. All gas mixtures were in N_{2} balance and not humidified.

The agreement between predictions and experiments for MeOH and EtOH were improved significantly by the mathematical simulation in comparison with the IRSA results (Figures 6 and 9 and _{3} relative interferences on N_{2}O and CO_{2} predicted by both IRSA and mathematical simulation were similar. They agreed well with experiments for N_{2}O (almost zero), but the prediction was lower than the experimental results for CO_{2}. The negative effect of the NH_{3} interference on CH_{4} measurements was successfully predicted by the mathematical simulation, which was due to the secondary interference but could not be predicted by the IRSA method (Figures 6 and 9 and _{i} in the IR PAMGA which was ignored in the simplified Equation (7a). The rectangle simplification of the filter bandpass shape may result in some difference in calculating the absorption coefficients and therefore cause simulating errors in Equations (7) and (7a). The dependence of microphone signals on temperature and pressure was ignored when the sensitivity coefficients α_{i},_{j} in Equations (5) and (5a) were replaced with gas IR absorption coefficients _{i},_{j} in Equations (7) and (7a) and the simulation signal _{i}' was used, which might cause some simulation errors. The simulation accuracy could be improved if all target and non-target gases were calibrated and the calibration data were used in the mathematical simulation. But the calibration data of non-target gases were usually not available because the manufacturers rarely provided this information. This is one of the reasons why the gas absorption coefficients were used in this study instead of the calibration data to simulate the interference. Although both IRSA and mathematical simulation methods are not ready yet for use to correct the errors caused by the interference of non-target gases because of their accuracy, they still can be used to select filters, simulate the interference of non-target gases, and therefore would be helpful for properly using the IR PANGA. A significant advantage is that the two methods can be performed prior to the instrument calibration, which would be very convenient for IR PAMGA users.

The simulations of CH_{4} interference in the Example #2 measurements as a non-target gas were also conducted at various target gas concentrations. It was predicted by the IRSA that the CH_{4} interferences in the Example #2 measurements were nearly zero at all 6 filters because the absorption of CH_{4} at any of these filters was almost zero. The mathematical simulation using Equations (7) and (7a) came to the same conclusion.

Two methods, IRSA and mathematical simulation, were introduced to estimate the interference in IR PAMGA measurements. The methods were also validated by experimental results. An Innova 1412 analyzer with two filter configurations was used as an example to demonstrate the IRSA and mathematical simulation methods. The filter configurations were (1) six filters for CH_{4}, MeOH, EtOH, N_{2}O, CO_{2}, and H_{2}O in Example #1, and (2) six filters for NH_{3}, MeOH, EtOH, N_{2}O, CO_{2}, and H_{2}O in Example #2.

The internal cross compensation algorithm of IR PAMGA can eliminate the interference between target gases but cannot address the interference of non-target gases. The possibilities of interference in IR PAMGA measurements can be visualized by graphing and aligning the IR absorption spectra of all target gases, the locations of their corresponding bandpass filters, and the IR spectra of all possible non-target gases. The IRSA method is useful in configuring the filters and predicting the interference for IR PAMGA. Basically, if the IR spectrum of a non-target gas overlaps with that of a target gas in that filter, interference would occur. For example, the filter configuration of Example #1 restricted its use to monitoring environments where NH_{3} was not present, because NH_{3} absorbed light at several filters of Example #1 but was not a target gas. The filter configuration of the Example #2 allowed its use in the presence of non-target gas CH_{4} because CH_{4} hardly absorbed light at any filters. The IRSA was able to estimate the primary interference due to the direct spectra overlapping but could not predict the secondary interference that resulted from overlaps of multiple gas IR spectra.

Mathematical simulation using absorption coefficients and simulation signals in Equations (7) and (7a) instead of sensitivity coefficients and the microphone signals in Equations (5) and (5a) made it possible to evaluate the interference in PAMGA measurements prior to purchase and calibration of the analyzers. Although both IRSA and mathematical simulation methods can predict the interference, the simulation method is more accurate because the algebraic matrix calculation involves cross compensation. The simulation results agreed with the experimental results better than the IRSA method (Figures 6 and 8). The mathematical simulation also predicted the secondary interference due to the overlapping IR spectra of multiple gases (see the negative effects of NH_{3} interference on CH_{4} measurements in

The mathematical simulation might be more accurate should the calibrated sensitivity coefficients be used to solve Equations (5) and (5a) rather than using absorption coefficients to solve Equations (7) and (7a). Although the Innova 1412 calibration data can be downloaded from the analyzer or provided by the manufacturer, the calibration data (such as the span conversion factor, the humidity gain factor, and the concentration offset factor) cannot be directly used in Equations (5) and (5a) because the relationship between sensitivity coefficients and the calibration data could not be determined. The raw calibration data were internally converted to the factors of span conversion, humidity gain, and offset for the built-in cross compensation algorithm. This is one of the reasons why absorption coefficients and simulation signals were used to simulate the interference in the present study.

Although an Innova 1412 analyzer with two filter configurations was used in this paper as an example to demonstrate the IRSA and mathematical simulation methods, the two methods can be applied to any filter configurations of Innova 1412 and other types of IR PAMGA (such as Innova 1312 and its older versions) to assess interferences. It may be possible to perform post measurement adjustment to correct the errors caused by non-target gas interferences using the algebraic matrix calculation which would be the ultimate goal for IR PAMGA users. To reach this goal, a wider range of mathematical theory, more experimental tests, and closer collaboration with instrument manufacturers are needed. The IRSA and mathematical simulation methods are very important approaches to this goal.

The authors would like to acknowledge the infrared spectral library of the Pacific Northwest National Laboratory.