Temperature and Pressure Insensitive Spectroscopic Method for Measuring 13CH4 during Oil and Natural Gas Drilling Operations

A novel rugged two-section driving NIR TDLAS scheme was implemented to reduce temperature and pressure sensitivity of methane carbon isotope measurement during oil and natural gas drilling operations. Isotope spectra line groups with same lower energy levels were selected to derive the concentration of 13CH4 and 12CH4. Dynamic pressure linewidth broadening was introduced in the absorbance curve fitting. Various uncontrollable factors such as spectra shift, stretching, and baseline trending were incorporated in the comprehensive multi-peak fitting. The results showed that the sensitivity of isotope ratios to temperature and pressure variation was greatly suppressed. The δ13CH4 uncertainty in the temperature test was 2.8‰ with fitted δ13CH4-T slope of 0.021‰/°C in 25 ± 5°C range. The δ13CH4 uncertainty in the pressure test was 1.4‰ with fitted δ13CH4-P slope of <0.001‰/mbar from 400 to 1000 mbar. The limit standard deviation of long-term test was 0.15‰ (@135 s). The results indicate that our scheme is a promising solution for δ13CH4 measurement during drilling operations due to the enhanced robustness.


INTRODUCTION
The natural gases' carbon isotopes composition provides an effective basis for quantitatively describing the migration, transformation, and traceability of chemical substances in oil and gas resources [1][2][3][4][5]. Therefore, it is necessary to develop an efficient and stable technique for in situ detecting the carbon isotopes during oil and natural gas drilling operations [6,7]. Isotopic abundance can be expressed as the relative ratio between the heavy isotopic component and the light isotopic components. δ 13 CH 4 is determined by measuring the concentration ratio of 13 CH 4 and 12 CH 4 . The δ 13 CH 4 detection in the drilling site requires in situ measurement, robustness in the harsh operating conditions, and better than 1‰ accuracy.
Other spectroscopic δ 13 CH 4 measurement in trace environmental methane used mid-infrared lasers such as interband cascade laser (ICL) [16], nonlinear differential frequency generation (DFG) through LiNO 3 crystal [17,18], with accuracy ranging from 0.7‰ to 12‰. Due to increased optical pathlength in multiple reflection gas cell, tunable diode laser absorption spectroscopy (TDLAS) with NIR laser is feasible to measure δ 13 CH 4 in natural gas. In 2019, Zhang et al. used a 1.658 µm DFB laser to detect δ 13 CH 4 in coal bed methane (CBM) and achieved standard deviation of 0.47‰ [19]. However, their control accuracy of temperature and pressure was very tight, i.e., P < ±1 mbar and T < ±0.05 K.
Thus, the temperature and pressure sensitivities are common issues of current spectroscopic isotope measurement techniques which hinder their applications in drilling operations. In present work, we proposed a novel single laser TDLAS technique by selecting isotope spectral lines with the same lower energy level to suppress the temperature variation impact on absorption strength. In addition, two-section laser driving, and comprehensive multi-peak fitting model were used to compensate the pressure dependence. The experimental result was around 1‰ precision without tight control of temperature and pressure.

Selection of Isotope Spectra Lines
Concentration of gaseous 13 CH 4 and 12 CH 4 can be derived through their absorption spectra based on Beer-Lambert's Law. When selecting 13 CH 4 and 12 CH 4 absorption spectral lines near 1.65 µm through HITRAN2016 database [20], the line separation, line strength, and temperature sensitivity should be considered. Eventually, four lines of 5E, F→6E, F transition belonging to the 2ν 3 R5 line were chosen for 13 CH 4 , listed as A1-A4 in Table 1 and plotted in Figure 1 (blue A1-A4 dots). Two lines of 5F2,1→5F1,2 transition belonging to the 2ν 3 Q5 line were chosen for 12 CH 4 , listed as B1-B2 in Table 1 and plotted in Figure 1 (red B1-B2 dots). They are ∼1.8 nm apart, which is close to the tuning limit of a DFB laser. For spectral strength, the line strength of 12 CH 4 is about twice of 13 CH 4 under natural abundance. Thus, the 12 CH 4 spectra provide a stable reference for measuring the 13 CH 4 spectra and concentration of subtle isotope variation. The lower level vibration quantum numbers of A and B lines are (0,0,0,0), the rotational quantum numbers are 5, and the energies are ∼157.1 cm −1 . Thus, the influence of temperature on the absorption spectra is canceled per Boltzmann distribution. The detection result is insensitive to temperature variation. The candidate spectral lines A and B with important spectral parameters are shown in Table 1. Besides A and B lines, suboptimal 12 CH 4 candidate lines C1-C2 with least spectral interference are also listed in Table 1 and plotted in Figure 1(red C1-C2 dots). Three congested 12 CH 4 peaks at 6046.94, 6046.95, and 6046.96 cm −1 with corresponding 3F, A→4F, A transitions belonging to the 2ν 3 R4 line are located in the middle of the wavelength range, listed in Table 1 as O1-O3. Their line intensities are 2-3 orders of magnitude stronger, which are out of Figure 1 scope.

Spectroscopy Theory for Isotope Measurement
Isotopic abundance can be expressed as the relative ratio between the heavy isotopic component and the light isotopic components. For example, the carbon isotope abundance value ( 13 C) of a sample can be described by δ 13 C [4] i.e., Where, ( 13 C/ 12 C) Sample is the concentration ratio 13 C to 12 C of test sample; ( 13 C/ 12 C) PDB is the ratio of standard substance-Pee Dee Belemnite. By definition, δ 13 C for PDB is 0, and the corresponding 13 C: 12 C ratio is 0.01118. δ 13 CH 4 was determined by measuring the concentrations of 13 CH 4 and 12 CH 4 . The concentration was derived by fitting the absorbance curve which was transformed from the normalized transmission spectra [20].
The target test sample is natural gas. But only its major component methane is used in our experiment for simplicity. The tested methane was in a 30 L stainless steel cylinder at a starting pressure of 1500 psi and was provided by Yantai Deyi Specialty Gas. Before we ran the spectra test, gas was sampled twice and was analyzed by a Thermo Fisher Scientific isotope analyzing system consisting of TRACE1310

Experiment Setup
The experiment was carried out in an automatic gas mixing station ( Figure 2) which was controlled through a LabVIEW program. The station consists of mass flow controllers (MFC, Sevenstar CS200), pressure controller (PC, TESCOM ER5000), vacuum pump and temperature chamber. The gas cell was placed inside the temperature chamber where experiment can run from 0 to 50°C. The MFCs' ranges are in 100-5000 SCCM with an accuracy of 1%. The pressure range is 400-1000 mbar with an accuracy of about 2 mbar. The tests ran automatically with different gas mixture in four dimensions including flow rate, ratio, temperature and pressure. The TDLAS apparatus' scheme is shown in Figure 3. A butterfly NIR DFB diode laser (Wuhan 69 Sensors, SN18020801) was used for direct absorption measurement. The wavelength scan was controlled by a periodical waveform current to cover both the target absorption lines of 13 CH 4 and 12 CH 4 . The laser output was coupled into a multi-pass Chernin cell with 20 m pathlength through its pigtail fiber. A built in InGaAs photon detector was used to collect the transmitted light. The detector signal went through I-V conversion and low-pass filtering before analog digital convertor (DAC) acquisition.
By using Hewlett Packard 86120B wavelength meter and Fabry-Perot (F-P) scanning interferometer (SA210-12B) to study the tuning parameters of the laser, the tuning curve is shown in Figure 4. The current tuning coefficient and temperature tuning coefficient of the laser are 0.03025 nm/mA and 0.0699 nm/°C respectively. The average wavelength-current tuning coefficient is larger than that of ordinary DFB lasers (typically 0.005-0.01 nm/mA). This laser diode was specifically chosen for its large tuning coefficient, so that all target absorption lines of 13 CH 4 and 12 CH 4 were covered.
In order to verify the stability of the laser light source, the laser temperature was stabilized at 34.3°C and the driving current were set at 25-35 mA and 90-116 mA, the stability of the absorption spectrum of the laser light intensity absorbed by 10% methane gas has been researched, the test time was 1 h, and extracted 100 absorption spectra, as shown in Figure 2. The maximum deviation was 0.0847, so it is indirectly proved that the laser has good stability.

Two-Section Driving of DFB Laser
However, there are still challenges in spectra analysis due to the following reasons. First, there are lots of lines in between the two target line groups and some lines are adjacent to the target lines  ( Figure 1 insets). Second, there is strong linearity due to the large wavelength separation (Figure 4). Thus, it brings extra uncertainty in absorbance calculation. There is too much trivial information in the collected spectra for continuous nonstop scan ( Figure 5A).
A two-section current driving scheme was proposed and implemented to address these challenges. In this scheme, the two isotope target spectra lines were aimed by two sections of driving current (I 1 25-35 mA, I 2 90-100 mA) at laser operating T of 34.3°C ( Figure 5B). The overall scan period was 200 ms. The strong peak in conventional one large section (I 25-100 mA) driving scheme ( Figure 5A O) was eliminated. As a result, the spectra gain setting is now restricted by the target lines rather than by the strong background lines, which increase the spectra signal strength by more 100 times. In addition, the data length representing target lines increased from 260 points to approximately 900 points, with resolution increased 3.5 times. Thus, the features in experimental absorbance have better resemblance with HITRAN2016 simulated absorbance. The wavelength linearity in each section was also improved.

Spectra Preprocess
In order to improve the signal to noise ratio of spectra, the spectra were averaged after every 10 scans. In order to calculate the absorbance, the transmitted light I 0 with no absorbing gas (pure nitrogen) in the cell was collected and was used as the normalization basis. When the sample gas was guided into the cell, real time transmitted light I s was collected. In each section, the absorbance curve A i was calculated separately.
Where, i 1,2 is the current section index, I si , I oi are the transmitted light power in the ith section with and without absorbing gases.

Multi-Peak Fitting
For the temperature and pressure range in the experiment, a Gaussian waveshape was adopted in the absorbance spectra fitting. In fact, there are more peaks in the absorbance curve other than the target peaks in the designated section. A multipeak fitting model was introduced,  Where, C j (j 1,2) is the coefficients proportional to the 13 CH 4 and 12 CH 4 concentration and is further used to calculate δ 13 CH 4 , S j i is the absorbance strength of the ith line of the jth isotope molecules, μ i is the center wavelength of the ith line, σ i is the linewidth of ith line, m is total number of lines. In order to improve the fitting accuracy, all lines listed in HITRAN2016 including the weak ones were included. Based on the HITRAN2016 database, the self-broadening coefficient of all absorption lines within the scanning range of the laser is almost similar to the pressure broadening coefficient, all of which are in the same order of magnitude. In particular, the self-broadening coefficient of the target absorption line is completely same with the pressure broadening coefficient. Even if the line width of the absorption line is slightly different, it is negligible. So the linewidth of ith line (σ i ) was kept constant.
The initial values of the peak center, line width, line amplitude and line separations are linearly related to the spectral parameters in HITRAN2016. There is a scale transformation from the database with absolute wavelength to experimental spectra with discrete data points by, Where, μ 1 is the position of first peak in the experimental absorbance curve, h i is the wavelength difference in database between the ith line and the first line, b is the scale transformation coefficients. By this formula, the spectra shift the horizontal direction can be automatically adjusted and compensated. However, there are many practical factors affecting the performance in experiment. Due to laser/detector aging, gas flow turbulence, mirror contamination or optical alignment change, thermal drift of amplifier's gain, there are uncontrollable fluctuations in the transmitted light, which will result in the whole absorbance curve upward or downward shift. The strong nonlinear wavelength-current relation causes the nonlinear shift (i.e., stretch) of the absorbance spectra. Furthermore, there is also nonlinear detector response at different laser power level which makes the absorbance curve having a trending baseline. So, we have to build a comprehensive fitting model by introducing more parameters, Where, the extra terms c, k 1 x, and k 2 x are used to compensate baseline trending, horizontal scale stretching and the vertical shift in the absorbance curve. The curve fitting model was implemented in a MATLAB program. The detection accuracy of δ 13 C is determined by Eq. 5. The parameters that affect the error of comprehensive fitting model φ(x) mainly include fitting coefficients (C j ), absorbance strength of the ith line the jth isotope molecules (S j i ), the center wavelength of the ith line (μ i ) the linewidth of ith line (σ i ), total number of lines(m), baseline trending(c), horizontal scale stretching (k 1 x) and vertical shift (k 2 x). Among the above parameters, absorbance strength of the ith line the jth isotope molecules (S j i ) can be found in HITRAN2016 database, and the rest of variables are need to be determined. In order to reduce the error, the relative positions of all the target absorption peaks from the HITRAN2016 database were obtained. So once the center wavelength of the ith line (μ i ) was determined, and so on, the other center wavelength of the lines were determined. The remaining variables change within a certain range, so that comprehensive fitting model φ(x) is very close to the collected absorption spectrum, so as to determine the optimal value of the variable. The optimal fitting coefficients were obtained iteratively with multiple nonlinear constraints. The fitting result is demonstrated in Figure 6. The transmitted light with and without absorbing gas in two sections are shown in (a). The calculated absorbance and model fitted absorbance in two sections are shown in (b). The spectra fitting residue was 1% of the signal amplitude and shown in (c). After the fitting coefficients C j were obtained, their ratio is correlated to the concentration ratio in Eq. 1 by the GC-MS analysis of test sample. For a selected sample, the ratio should remain constant under any conditions. Thus, the repeatability and robustness against environmental factors' variation are important indicators of the measurement techniques.

EXPERIMENTS AND RESULTS
The isotope ratio measurement performance was experimentally evaluated in terms of temperature sensitivity, pressure sensitivity and repeatability. The experimental details are listed in Table 2. The repeatability was characterized by standard deviation of δ 13 CH 4 in the long-term test. The spectroscopic ratio values of 10% CH 4 at 25°C, 400 mbar were used as the reference, corresponding to δ 13 CH 4 of −41.04‰.

Pressure Dependence
Simulated absorbance curves for each wavelength region at 400, 700, and 1000 mbar based on the HITRAN2016 are plotted in Figures  7A,B. As a comparison, the experimental absorbance curves from pressure test are plotted in Figures 7C,D for each driving section. The Simulated absorbance curve for 13 CH 4 and 12 CH 4 data are derived from HITRAN2016, the carbon isotope abundance value (δ 13 C) for simulation data is different from δ 13 C for the experimental data. Thus, simulated absorbance curve for 13 CH 4 and 12 CH 4 do not agree with experimental absorbance curve for 13 CH 4 and 12 CH 4 in Figure 7. As the pressure changes, the pressure broadening effect becomes more obvious. With the decrease of the pressure, the full width at half maximum of absorbance curve for 13 CH 4 and 12 CH 4 decreases gradually. Absorption spectrum mixing effect is less apparent. Thus, experiment running at lower pressure can help to improve δ 13 C detection accuracy.
To extend pressure range coverage, the pressure broadened linewidth was included in the curve fitting Eq. 4. The linewidth for each peak was calculated by, Where, P is gas pressure in ATM, nCH 4 and nN 2 are the relative concentrations of methane and nitrogen in the gas mixture, δ self and δ air are self and air pressure broadening coefficients from HITRAN2016. For the selected 13 CH 4 spectra lines, their self and air broadening coefficients are 0.06 and 0.077 cm −1 /ATM. For the selected 12 CH 4 spectra lines (Choice B), their self and air broadening coefficients are 0.066 and 0.077 cm −1 /ATM. The δ 13 CH 4 in the pressure test is plotted in Figure 8. The standard deviation for the overall test is 1.4‰ ( Figure 8A). The δ 13 CH 4 shows no pressure dependence with linear fit slope <0.001‰/mbar ( Figure 8B). Introduction of dynamic pressure linewidth broadening by Eq. 5 is the key to maintain good δ 13 CH 4 accuracy in pressure test.

Temperature Dependence
For the two choices of measuring 12 CH 4 , choice B is the target line with same lower energy levels, but it is congested with other lines. Choice C is more isolated and less affected by the interference. As a comparison, we used both choices to fit the coefficients of 12 CH 4 . The calculated δ 13 CH 4 during temperature test with same flowing gas for choice B and C was plotted in Figure 8C red and blue curve. The choice C is clearly more sensitive to temperature change. The      Figure 8D red curve) is 0.021‰/°C which is 2 orders weaker than that of choice C (1.55‰/°C, Figure 8D blue curve). This proved that the selection of same lower energy state was more effective than spectra interference in terms of reducing temperature dependence.

Long Term Test
During the 3-hour long term test, the gas cell was placed inside the test chamber with T set at 25°C. The pressure was maintained at 400 mbar. The gas mixture of 10% CH 4 and 90% N 2 flowed through the cell at 100 ml/min rate. Totally 500 spectra were collected. We applied the multi-peak Gaussian waveshape fitting with absorbance curve. The calculated δ 13 CH 4 are plotted in Figure 9A with standard deviation of 0.95‰ at update time of 2 s. Allan analysis of δ 13 CH 4 measurement in long-term test gives the limit standard deviation is 0.14‰ (@135 s) ( Figure 9B).

CONCLUSION
We proposed and implemented a rugged two-section laser driving TDLAS system in which a broad tuning NIR DFB laser was used to cover spectra lines for both isotope molecules. Isotope spectra lines with same lower energy levels were selected to derive the 13 CH 4 and 12 CH 4 concentrations. In addition to dynamic pressure broadening linewidth, various uncontrollable factors such as spectra shift, stretching, and trending were addressed in the comprehensive multi-peak absorbance curve fitting by introducing the corresponding terms.
The δ 13 CH 4 uncertainty in the temperature test was 2.8‰ with fitted δ 13 CH 4 -temperature slope of 0.021‰/°C in 25 ± 5°C range. The δ 13 CH 4 uncertainty in the pressure test was 1.4‰ with fitted δ 13 CH 4 -pressure slope of <0.001‰/mbar from 400 to 1000 mbar. The limit standard deviation of longterm test was 0.15‰ (@135 s). The δ 13 CH 4 precisions of a few research groups were better. But their apparatuses were more complicated and delicate mainly due to stringent requirement of pressure and temperature control. Our NIR TDLAS scheme is a promising solution for δ 13 CH 4 measurement during drilling operations.

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.