Dual-Gas Sensor of CH₄/C₂H₆ Based on Wavelength Modulation Spectroscopy Coupled to a Home-Made Compact Dense-Pattern Multipass Cell

Abstract

A sensitive dual-gas sensor for the detection of CH₄ and C₂H₆ is demonstrated. Two tunable semiconductor lasers operating at 1.653 μm (for CH₄ monitoring) and 1.684 μm (for C₂H₆) were used as the light source for spectroscopic measurements of CH₄ and C₂H₆. Long-path absorption in a home-made compact dense-pattern multipass cell (L_eff = 29.37 m) was employed, combined with wavelength modulation and second harmonic detection. Simultaneous detection of CH₄ and C₂H₆ was achieved by separated wavelength modulations of the two lasers. Modulation frequencies and amplitudes were optimized for sensitivity detection of CH₄ and C₂H₆ simultaneously. The dual-gas sensor exhibits 1σ detection limits of 1.5 ppbv for CH₄ in 140 s averaging time and 100 ppbv for C₂H₆ in 200 s.

1. Introduction

Natural gas is the third largest source of thermal energy in the world, accounting for 22.1% of primary energy consumption after petroleum (31.9%) and coal (27.1%). The methane (CH₄) content in natural gas reaches over 90%. Biogas, which contains mainly CH₄, is a naturally occurring gas that forms from the breakdown of organic matter in the presence of anaerobic bacteria. CH₄ is also a main greenhouse gas, whose greenhouse effect is 25 times higher than that of carbon dioxide (CO₂). Ethane (C₂H₆) is the second largest component in natural gas, accounting for about 5–10%. It can be used as an indicator to discriminate whether the measured leaking gas is from natural gas, underground biogas, or other combustible gas. Monitoring C₂H₆ can be applied to diagnose leaking natural gas pipelines [1,2,3,4,5,6].

Laser spectroscopy-based gas sensors is an effective tool for environmental monitoring, medical diagnosis, industrial process control, food industry, and pollution monitoring [7], and includes quartz-enhanced photoacoustic spectroscopy (QEPAS) [8,9,10], off-axis integrated cavity output spectroscopy (OA-ICOS) [11], and tunable diode laser absorption spectroscopy (TDLAS) with a multipass cell. In general, long-path absorption is combined with wavelength modulation to improve measurement sensitivity and precision [12,13]. Krzempek demonstrated C₂H₆ concentration measurement based on 2f wavelength modulation spectroscopy (WMS) using a continuous-wave (CW) distributed feedback diode laser emitting in the mid-infrared near 3.36 µm. A 1σ minimum detectable concentration of 740 pptv with a 1 s lock-in amplifier time constant was achieved [14]. Zheng and co-workers utilized two CW interband cascade lasers (ICLs) operating at 3291 nm (CH₄) and 3337 nm (C₂H₆) for the simultaneous measurement of CH₄/C₂H₆ in the mid-infrared. Detection limits of ~1.7 ppbv for CH₄ in 9 s and ~0.36 ppbv for C₂H₆ in 65 s [15] were achieved. Li et al. realized ppbv-level measurement of C₂H₆ using 3.34 µm CW-ICL-based WMS with a detection limit of ~1.2 ppbv in a 4 s averaging time [16].

Though C₂H₆ absorption intensity is relatively weak in the near-infrared spectral region [17,18], the photonic devices in this spectral region have the characteristics of being low cost and relatively mature. Therefore, it is of great significance to develop a high-sensitivity dual-gas sensor for CH₄/C₂H₆ by TDLAS for leakage detection applications [19].

In this paper, we report on the development of an optical sensor for the simultaneous measurement of CH₄ (at 1.653 µm) and C₂H₆ (at 1.684 µm) based on long-path absorption in a newly home-made dense-pattern multipass cell combined with wavelength modulation and second harmonic detection [20].

2. Basics of Wavelength-Modulation Spectroscopy

Wavelength-modulation spectroscopy (WMS) is a spectroscopic measurement technique widely used for trace gas measurements in harsh environments owing to its high noise-rejection capability over direct absorption spectroscopy. Only a brief description of some of the fundamental theory will be given here to explain certain experimental choices (e.g., modulation index) made in this study [21,22,23]. The instantaneous laser frequency with sinusoidal modulation can be written as:

$$\nu (t)={\nu }_0+\Delta v\cos (\omega t)$$

(1)

where ν₀ (cm⁻¹) is the center laser emission frequency, ω is the angular frequency, and Δν (cm⁻¹) is the modulation depth.

The time-dependent transmission coefficient τ(ν) can be expanded in a Fourier cosine series:

$$\tau [\nu (t)]=\tau [{\nu }_0+\Delta v\cos (\omega t)]={\displaystyle \sum _{n=0}^{n=+\infty }{H}_n}({\nu }_0,\Delta v)\cos (n\omega t)$$

(2)

where H_n (ν₀, Δν) is the n-th component of the Fourier series, which can be expressed as:

$$H_0({\nu }_0,\Delta v)=\frac{1}{2\pi }{\displaystyle \underset{-\pi }{\overset{\pi }{\int }}\tau ({\nu }_0+\Delta v\cos \theta )}d\theta (\mathrm{n}=0)$$

(3)

$$H_n({\nu }_0,\Delta v)=\frac{1}{\pi }{\displaystyle \underset{-\pi }{\overset{\pi }{\int }}\tau ({\nu }_0+\Delta v\cos \theta )}\cos (n\theta )d\theta (\mathrm{n}>0)$$

(4)

In practice, second harmonic is usually used for the detection (n = 2):

$$H_2({\nu }_0,\Delta v)=\frac{1}{\pi }{\displaystyle \underset{-\pi }{\overset{\pi }{\int }}\tau ({\nu }_0+\Delta v\cos \theta )}\cos (2\theta )d\theta (\mathrm{n}=2)$$

(5)

In the case of trace gas absorption described by the Beer-Lambert law [24] (α(ν)L << 1 ), the transmission can be simplified as:

$$\tau (\nu )=\frac{I_{out}(\nu )}{I_{in}(\nu )}=\exp [-\alpha (\nu )L]\approx 1-\alpha (v)L=1-N_{0}SCL\chi (v-v_0)$$

(6)

where I_out(ν) and I_in(ν) are the transmitted and incident light intensities at frequency ν, respectively, $L$ is the optical absorption path length in [cm]. α(ν) = σ(ν)N₀C = χ(ν − ν₀)SN₀C (at standard temperature and pressure) is the absorption coefficient of the target gas with concentration C (mixing ratio) and the Loschmidt constant N₀ = 2.6868 × 10¹⁹ molecule/cm³. σ(ν) = χ(ν − ν₀)S is the absorption cross-section of the target gas with S the line strength in [cm⁻¹/(molecules/cm⁻²)] and χ(ν − ν₀) the absorption line shape function. ν₀ is the central frequency of the absorption line.

From Equations (5) and (6), the Fourier series of the second harmonic can be expressed as:

$$H_2({\nu }_0,\Delta v)=\frac{-N_{0}SCL}{\pi }{\displaystyle \underset{-\pi }{\overset{\pi }{\int }}\chi ({\nu }_0+\Delta v\cos \theta )}\cos (2\theta )d\theta$$

(7)

According to Equation (7), the harmonic signal is hence proportional to the concentration of the gas. In addition to the absorption parameters, the WMS-2f signal also depends on the modulation depth Δν. The WMS-2f signal can be maximized by choosing the optimal modulation index m, which is defined as:

m = Δν/Δν_D

(8)

where Δν_D [cm⁻¹] is the full width at half maximum (FWHM) of the absorption line shape, and the 2f signal amplitude is maximized at a modulation index m = 2.2 [25,26].

In addition, the background signal is caused by the 2f residual–amplitude–modulation (2f-RAM) signal in the presence of linear intensity modulation [27]. In the present work, we use the second harmonic signal deducting the background to determine the concentrations of CH₄ and C₂H₆.

3. Experimental Details

3.1. Design of the Dual-Gas Sensor for CH₄ and C₂H₆

The developed dual-gas sensor is shown in Figure 1. Two tunable distributed feedback (DFB) diode lasers operating at 1.653 µm and 1.684 µm were used for the measurements of CH₄ and C₂H₆, respectively. The temperature and current of both lasers were controlled by laser diode controllers LDC501 (Stanford Research Inc., Sunnyvale, CA, USA). Both lasers currents were scanned by feeding an external voltage ramp at a rate of 1 Hz from a function generator (RIGOL DG4162). Wavelength modulations (6 kHz for CH₄ and 0.6 kHz for C₂H₆) were achieved through the modulation of each laser current via a sine form wave from lock-in amplifiers #1 and #2 (SR 830 DSP, Stanford Research Systems), respectively. The voltage ramp and the sine wave were combined with a home-made adder before being coupled to the laser diode controllers.

The two laser beams were coupled together into a 2 × 1 single mode standard coupler (DWBC) with the maximum insertion loss 0.3 dB/km. The output beams were collimated through a single fiber optical collimator with the beam diameter not exceeding 0.35 mm and then injected into a home-made multipass absorption cell. The multipass cell consisted of two 2” silver-coated concave spherical mirrors separated by a distance of 12 cm, which was similar to that previously reported in [20]. An effective optical path of 29.37 m was achieved with 243 multiple reflections of laser beam inside the cell.

The transmitted beam was detected with an indium gallium arsenic photodetector (PDA20CS-ES) via a focusing lens (f = 30 mm) as shown in Figure 2. The signal detected by the photodetector was sent to lock-in amplifiers #1 and #2, respectively, for demodulations at 6 kHz for CH₄ and 0.6 kHz for C₂H₆, so as to distinguish the signals from different lasers and realize simultaneous detection of CH₄ and C₂H₆. The demodulated signals were subsequently digitalized with a data acquisition card (DA, NI-USB-6212) and displayed on a laptop via LabVIEW interface.

3.2. Spectral Line Selection

C₂H₆ shows an unresolvable absorption band near 1.684 µm [28,29]. There is no information on its spectral line parameters in the common database (such as HITRAN) for ethane in the near-infrared. In order to determine the laser temperature and the current corresponding to the maximum ethane absorption, 10,000 ppm ethane gas was filled in the multipass cell at a pressure of 0.5 atm. Direct C₂H₆ absorption spectrum was obtained by a wavelength scan of the 1.684 µm DFB laser across the C₂H₆ absorption lines, as shown in Figure 3. The laser temperature and the current needed to probe the strong absorption band of C₂H₆ near 1.684 µm were found to be 31 °C and 78 mA, respectively.

While the best CH₄ absorption lines within the spectral tuning range of the used 1.653 µm diode laser are the R₃ triplet of the 2ν₃ band near ~6046.95 cm⁻¹, they have the highest line intensities and are free of interference from other molecules (such as H₂O and CO₂). The R₃ triplet of the 2ν₃ band at ~6046.95 cm⁻¹ was selected for the measurement of CH₄ concentration. Figure 4 shows an absorption spectrum of 492 ppm CH₄ at a pressure of 0.5 atm. The laser center current was set at 85 mA with a temperature set at 22 °C for targeting the selected CH₄ absorption lines. The amplitude of the triangular ramp was 1.3 V, which scanned the laser diode current from 52.5 to 117.5 mA (50 mA/V).

The calibration curves of laser current vs. frequency were realized with the help of a wavelength meter (Bristol 621).

4. Results and Discussions

4.1. Optimization of Modulation Amplitude for WMS

In WMS, the second harmonic (2f) signal amplitude depends on the modulation amplitude [30]. In order to obtain optimal modulation amplitude for maximum second harmonic signals, a mixture of 200 ppm CH₄ and 300 ppm C₂H₆ in nitrogen was prepared using a gas diluter (Environics SERIES 4000) and then filled in the multipass cell at 1 atm. The 2f signals of 200 ppm CH₄ and 300 ppm C₂H₆ at different modulation amplitudes were investigated. The measured results of the 2f signals versus the modulation amplitudes are shown in Figure 5. As can be seen, the optimal modulation amplitude was 0.25 V for CH₄ and 0.36 V for C₂H₆. The optimal modulation amplitude of the sine wave for CH₄ detection was found to be 0.25 V, and the corresponding laser wavelength modulation amplitude was Δν_m ≈ 0.2921 cm⁻¹. According to the HITRAN database, the 200 ppm CH₄ line width (HWHM) of the targeted absorption lines was Δν_D ≈ 0.1316 cm⁻¹. The optimal modulation amplitude Δν_m ≈ 2.22 Δν_D for wavelength modulation with second harmonic demodulation was basically consistent with the theoretical result Δν_m = 2.2 Δν_D [25,26].

4.2. Optimization of Modulation Frequency and Phase for WMS

In addition to the modulation amplitude, the modulation frequency and phase may also affect the amplitude of the second harmonic signal [31,32]. Under the condition of the optimal modulation amplitude, the effects of the modulation frequency and phase on the second harmonic signal amplitude were investigated, experimentally. Figure 6 shows the phase effect and Figure 7 shows the modulation frequency effect. The optimal phase was found to be −140° for both CH₄ and C₂H₆ detections. The optimal modulation frequency was 6 kHz for CH₄ detection and 0.6 kHz for C₂H₆ detection.

4.3. Investigation on the Potential Cross-Talk

Two lasers operating at different wavelengths were injected into the same absorption cell. It might cause cross-talk effects between two signals if the selection of the modulation frequencies is not appropriate [33]. For example, cross-talk occurs when modulation frequencies are fixed at 6 kHz for CH₄ and at 5.8 kHz for C₂H₆ detection, as shown in Figure 8. The cross-talk effect was determined by the low-pass filter of the lock-in amplifier. The amplitude of the sinuous residual was determined by the stopband edge and the response of the filter.

Figure 9 shows the experimental study of the cross-talk effects in the simultaneous detection of CH₄ (190 ppmv) and C₂H₆ (170 ppmv). In order to verify that there is no cross-talk between two signal channels, two lasers work simultaneously under wavelength modulation at their specific optimal modulation frequencies, i.e., 6 kHz for CH₄ and 0.6 kHz for C₂H₆. Figure 9a plots the second harmonic signals of CH₄ with and without the operation of the laser for C₂H₆ detection. The amplitude of the CH₄ signal was 7.931 mV when the two lasers were on. When the C₂H₆ laser was turned off, the amplitude of the CH₄ signal was 7.926 mV. The difference between the peak heights of the CH₄ second harmonic signals was about 0.06%. Figure 9b compares the case for C₂H₆ detection. The amplitude of the C₂H₆ signal was 4.873 mV when the two lasers worked together. When the CH₄ laser was turned off, the amplitude of the C₂H₆ signal was 4.865 mV. The deviation between the peak heights of C₂H₆ second harmonic signals was 0.16%. It can be concluded that the cross-talk effects can be ignored when the two lasers are both operational at their specific optimal modulation frequency in the present work.

The optimal parameters used for the present work are listed in

Table 1. Optimal modulation amplitude, phase, and frequency of CH₄ and C₂H₆.

Target Gas	Optimal Modulation Amplitude	Optimal Modulation Phase	Optimal Modulation Frequency
CH4	0.25 V	−140°	6 kHz
C2H6	0.36 V	−140°	0.6 kHz

and are the default values in the subsequent experimental measurements.

4.4. Baseline Removal

Using WMS could significantly reduce the 1/f noise. However, when the baseline is not a “linear” ramp, the derivation cannot remove such “curve shape” baseline [27]. In the present work, the baseline of the sensor was investigated using high purity (99.99%) nitrogen (N₂) filled in the multipass cell. The N₂ background baselines were measured in the CH₄ and C₂H₆ channels as shown in Figure 10a,b, respectively. In the present work, the 2f signals of CH₄ and C₂H₆ were obtained by subtracting the N₂ background baselines. As an example, Figure 11a shows a 0.6 ppm CH₄ signal, obtained directly from the lock-in amplifier associated with the baseline. Figure 11b shows the 2f signal of 0.6 ppmv CH₄ after subtracting the baseline shown in Figure 10a.

The standard reference gases of 492 ppmv CH₄ and 500 ppmv C₂H₆ were mixed with high purity nitrogen to obtain a gas mixture with concentrations ranging from 10 ppmv to 100 ppmv. A gas dilution system (Model 4000, Environics Inc., Tolland, CT, USA) was used to make these mixtures. The second harmonic signals of CH₄ and C₂H₆ at different concentrations and under normal atmospheric pressure are plotted in Figure 12a,b.

Based on the results shown in Figure 12a,b, the second harmonic amplitudes vs. different concentrations are plotted in Figure 13a,b for CH₄ and C₂H₆, respectively. Good linear correlations are observed with a correlation coefficient of 99.97% for CH₄ and 99.98% for C₂H₆, which can be used for calibration of the measured 2f signal amplitudes to their corresponding concentrations.

4.5. Allan Deviation

In order to determine the sensor stability and limit of detection (LoD), analyses of Allan variance were carried out. Figure 14a,b plot time series measurements of CH₄ and C₂H₆ at a constant concentration of 2 ppmv and 32 ppmv diluted with the concentration 2.1 ppmv of CH₄ and 500 ppmv of C₂H₆ standard gas, respectively. The corresponding Allan deviations as a function of the averaging time t are plotted in Figure 14c,d. Allan variance analysis shows that the measurement precision of the developed dual-gas sensor was ~20 ppbv for CH₄ and 1.2 ppmv for C₂H₆ with an acquisition time of 1 s. A detection limit of 1.5 ppbv for CH₄ could be achieved by averaging in 140 s and 100 ppbv could be achieved for C₂H₆ by averaging 200 s.

4.6. Simultaneous Detection of Methane and Ethane Leakage

The sensor performance was evaluated by simultaneous detection of methane and ethane leakage with the current locked at the absorption peak, respectively. The outside air was pumped into an airbag (60 cm × 80 cm) and then injected into the gas cell through a long sampling tube.

Based on the calibration curves shown in Figure 13, measured second signals of CH₄ and C₂H₆ can be converted to their corresponding concentrations.

Time series measurements of the test are plotted in Figure 15. Methane and ethane in air were measured in the period of t₁. The atmospheric CH₄ concentration of about 2.1 ppmv was observed, while the C₂H₆ concentration in ambient air was lower than the detection limit of the current sensor and was not observed. CH₄ and C₂H₆ were then added in the airbag and changes in the concentrations of CH₄ and C₂H₆ were observed in the period of t₂. The CH₄ concentration varied from 2.1 to 14.1 ppmv and the C₂H₆ concentration varied from 0 to 344.7 ppmv. Subsequently, we stopped the “leakage” of CH₄ / C₂H₆ and flushed only air into the absorption cell; the concentrations of CH₄ and C₂H₆ returned to their atmospheric levels (t₃).

It is worth noting that the minimum detection limit of the commercial PGC ethane analyzer (Schutz, German) is 10 ppmv. The present experimental results of simultaneous detection of methane and ethane demonstrate the real potential of the developed dual-gas sensor of CH₄/C₂H₆ for use in leakage detection.

5. Conclusions and Outlook

In this paper, we demonstrated a compact dual-gas sensor for monitoring CH₄ and C₂H₆ based on wavelength modulation spectroscopy coupled to a compact home-made dense-pattern multipass cell using a single photodetector. Detection limits were 1.5 ppbv for CH₄ by averaging 140 s and 100 ppbv for C₂H₆ by averaging 200 s. The developed dual-gas sensor can be used to distinguish between natural gas and biogas, which has strong potential for gas sensing applications in natural gas pipeline leakage analysis.