Total hydrocarbon analyzers provide linear responses to methane and other hydrocarbons; however, the slope and intercept measurements are dependent on the matrix. This requires that calibration be conducted for each matrix gas. Interruptions due to the matrix effect make automation of gas analysis inefficient.
Use of data acquisition software with built-in linear transformation capability eliminates the need for multiple calibrations during the sequence of analyses, and enables a universal calibration performed in nitrogen matrix to be used for analytes in a variety of matrices.
Experimental
A Series 9000 total hydrocarbon (THC) analyzer (Mocon Inc., Minneapolis, Minn.) was used to analyze methane concentration in various matrices. The analyzer is based on a flame ionization detector (FID) with Flow-Guard electronic control that delivers a small portion of the sample gas to the detector flame.1‒4 During the combustion process, organic or hydrocarbon-based gases in the sample are ionized, detected by the instrument and reported as a concentration.
A gas mixture of 40% hydrogen and 60% helium was used as fuel for the THC analyzer. Zero-grade air was used as a supportive gas for combustion. Detector analog output signals were in the range of 0‒20 mA. The milliamp responses were converted to 0‒10 volts using a 500-ohm resistor. The converted voltages were collected by an analog-to-digital (A/D) device manufactured by National Instruments (Austin, Texas). The A/D signals were processed by data logger software (Applied Lab Automation Corp., Houston, Texas).5
Although any hydrocarbon can be used for this experiment, methane was selected due to the availability of NIST standards for comparison.6 Gas samples were prepared gravimetrically in high-pressure cylinders. Methane samples, with nominal values of 9.5 ppmv and 4 ppmv, respectively, were introduced into cylinders containing a matrix of nitrogen, helium or argon. The transfilled cylinder with pure helium, argon or nitrogen with less than 0.1 ppmv methane was used as a zero gas. The gas samples were regulated down to 30 psig and introduced to the THC analyzer via a six-port multiposition valve (Valco Instrument Co., Houston, Texas). Flow rate was maintained using a flow controller (Cole-Parmer, Vernon Hills, Ill.). A schematic diagram of the experimental setup is shown in Figure 1.
Figure 1 ‒ Schematic diagram of the experimental setup.A gas sample containing methane in a nitrogen matrix with nominal concentration of 9.5 ppmv was used to span the THC analyzer. Research-grade N2 containing less than 0.1 ppmv of methane was used to zero the THC analyzer response. Once the span and zero steps were complete, a gas sample containing methane in nitrogen matrix with a nominal concentration of 4.5 ppmv was analyzed on the calibrated THC analyzer. The analyzer responses were plotted against the concentration of methane.
Operational parameters such as sample flow rate, fuel and air pressure of the detector were kept the same during the entire process. Without performing the above span and zero steps, the same THC analyzer was used directly to analyze argon and helium zero gases as well as sample gases containing methane with nominal concentrations of 9.5 ppmv and 4 ppmv in either an argon or helium matrix.
Results and discussion
Table 1 shows the THC analyzer responses versus concentrations of methane in various matrices. The THC analyzer was first calibrated with a span gas containing 9.50 ppmv of methane in nitrogen matrix. Research-grade nitrogen was confirmed to have less than 0.01 ppmv of methane by a gas chromatography-pulsed discharge ion detector (GC-PDID), which was used to zero the THC response. Once the THC analyzer had completed the span and zero procedure, the following gases were analyzed: 4.00 ppmv methane in nitrogen, research-grade helium, 9.50 ppmv methane in helium, 4.00 ppmv methane in helium, research-grade argon, 9.48 ppmv methane in argon and 4.01 ppmv methane in argon.
Table 1 ‒ THC analyzer response vs concentrations of methane in various matrices
Figure 2 illustrates the calibration curve of analyzer response versus methane concentration in a nitrogen matrix. The curve equation was generated by running a linear regression of three data points. Similarly, Figures 3 and 4 demonstrate the calibration curves of methane in helium and argon matrices, respectively. The equation of each calibration curve is shown below:
Figure 2 ‒ Calibration curve of analyzer response vs methane concentration in nitrogen matrix.
Figure 3 ‒ THC analyzer response vs methane concentration in helium matrix.
Figure 4 ‒ THC analyzer response vs methane concentration in argon matrix.For methane in nitrogen matrix, the curve equation is:
y = 0.9878x + 0.0594 (1)
Where x = concentration of methane in nitrogen matrix; y = THC analyzer response at a given methane concentration in nitrogen matrix.
With untreated data, the curve equation for methane in helium matrix is:
y = 0.6642x ‒ 0.1132 (2)
With untreated data, the curve equation for methane in argon matrix is:
y = 0.8627x ‒ 0.2806 (3)
It is obvious that each curve has a different slope and intercept. Without additional data treatment, it was essentially impossible to accurately analyze the methane concentration in a helium or argon matrix if the THC analyzer was calibrated with methane standards prepared in nitrogen matrix.
Many laboratory instruments suffer discrepancies in analytical results based on factors associated with the matrix or the presence of contaminants. Instrument manufacturers are aware of these phenomena and can manually apply correction factors when these effects are expected. On-screen menu-selectable correction factors are available for newer models of analyzers. The simple multipliers can work well for some instruments. However, matrix effects can be more complicated, as found in THC analyzers, and thus require advanced correction techniques.
With THC analyzers, the effect is dependent on the slope and intercept of a line equation corresponding to the matrix in which the analyte is suspended. In this case, a linear transformation technique7 can be used to map the data from one calibration line to another. Methane was used as the example analyte, although any hydrocarbon should work. The linear transformation from helium matrix to nitrogen matrix can be described in the following equation:
y = ((x-b)*mN2/m) + bN2 (4)
Where y = concentration of methane in helium matrix;
x = the THC analyzer response at a given methane concentration in helium matrix while the THC was calibrated with methane standards in nitrogen matrix;
m = the slope of the methane curve in helium matrix;
mN2 = the slope of the methane curve in nitrogen matrix;
bN2 = the y-axis intercept of the methane curve in nitrogen matrix;
b = the y-axis intercept of the methane curve in helium matrix
If the values of mN2, m, b and bN2 are plugged in with the information from Eqs. (1) and (2), Eq. (4) can be rewritten as follows:
y = ((x + 0.1132)*1.4872) + 0.0594 (5)
Eq. (5) can then be rewritten as:
y = 1.4872x + 0.2269 (6)
Eq. (6) was used as a conversion tool that allows the methane concentration in helium matrix to be analyzed accurately using the same THC analyzer calibrated with the methane standards prepared in nitrogen matrix. The same logic can be applied to derive a relationship as shown in Eq. (7) for analyzing methane concentration in argon matrix using the same THC analyzer calibrated with methane standards prepared in nitrogen matrix.
ya = 1.1450xn + 0.3807 (7)
Where ya = concentration of methane in argon matrix;
xn = the THC analyzer response at a given methane concentration in argon matrix while the THC was calibrated with methane standards in nitrogen matrix
The transformation from one curve in helium matrix to the other in nitrogen matrix was accomplished within the data logger software. The instrument responses to methane concentrations were mapped from one matrix to the other using the linear transformation function provided in the software. Table 2 demonstrates the linear transformation technique applied to the THC analyzer when the analyses involved samples in multiple matrices.
Table 2 ‒ Demonstration of the linear transformation technique applied to a THC analyzer when the analyses were involved with samples in multiple matrices
Once the conversion curve was input into the data logger software, the samples in helium or argon matrix were analyzed again to confirm the feasibility of this approach. Table 3 shows the analytical results from the THC analyzer without corrections as well as the results from the data logger software with built-in linear transformation function. There is clearly a significant improvement in analytical accuracy with the linear transformation technique when the THC analyzer was utilized to determine the concentration of an analyte in various matrices. As shown in Table 3, the adjusted analytical values for methane in helium matrix agreed with the blended methane concentrations with less than a 2% difference, even if the THC analyzer was calibrated only with methane standards prepared in nitrogen matrix. The disagreement was slightly higher at around 5% when the matrix was argon. With more data points included in the calibration, the disagreement is expected to be minimized.
Table 3 ‒ Comparison of results with and without linear transformation for analyzing methane in multiple matrixes using a THC analyzer
Conclusion
It was confirmed that linear transformation can generate a universal calibration in nitrogen to be used for analysis in various matrices. This is a valuable tool when the analytes are in different matrices and the size of the test samples is large. Automation of analyses involving multiple matrices can be achieved even if a matrix-dependent analyzer such as a THC analyzer is used. Although this paper mainly discusses linear response in a THC analyzer, it can be applied to a nonlinear instrument as long as the relationship of responses in various matrices can be established experimentally.
References
- Harley, J.; Nel, W. et al. Nature 1958, 181, 177.
- McWilliams, I.G. and Dewer, R.A. Gas Chromatography; Desty, D.H., Ed.; Butterworths Scientific Publications: Oxford, U.K., 1957, p 142.
- Holm, T, J. Chromatogr. A 1999, 842, 221‒7.
- Baseline-Mocon, Series 9000 Total Hydrocarbon Analyzer, Brochure D011.4.
- Feng-Tang, G. Automation in Gaseous Sample Tests, Application No. 14/037,059, patent pending, U.S. Patent and Trademark Office.
- NIST Standard Reference Materials Catalog, 2011, 38.
- Lang, S. Linear Algebra; Springer-Verlag: New York, NY, 1987; ISBN 978-0-387-96412-6.
Michael T. Tang, Ph.D., and Greg Merideth are with Matheson Gas, Pasadena, Texas, U.S.A.; www.mathesongas.com. Grace Feng and Rui Huang are with Applied Lab Automation Corp., 6918 Corporate Dr., Ste. A16, Houston, Texas 77036, U.S.A.; tel.: 832-786-3805; e-mail: [email protected]; www.appliedlabautomation.com