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Online Continuous Trace Process Analytics Using Multiplexing Gas Chromatography Marco R. Wunsch,†,¶ Rudolf Lehnig,†,¶ and Oliver Trapp*,§ †

BASF SE, Carl-Bosch-Str. 38, 67056 Ludwigshafen, Germany Department Chemie, Ludwig-Maximilians-Universität München, Butenandtstr. 5-13, Haus F, 81377 Munich, Germany

§

S Supporting Information *

ABSTRACT: The analysis of impurities at a trace level in chemical products, nutrition additives, and drugs is highly important to guarantee safe products suitable for consumption. However, trace analysis in the presence of a dominating component can be a challenging task because of noncompatible linear detection ranges or strong signal overlap that suppresses the signal of interest. Here, we developed a technique for quantitative analysis using multiplexing gas chromatography (mpGC) for continuous and completely automated process trace analytics exemplified for the analysis of a CO2 stream in a production plant for detection of benzene, toluene, ethylbenzene, and the three structural isomers of xylene (BTEX) in the concentration range of 0−10 ppb. Additional minor components are methane and methanol with concentrations up to 100 ppm. The sample is injected up to 512 times according to a pseudorandom binary sequence (PRBS) with a mean frequency of 0.1 Hz into a gas chromatograph equipped with a flame ionization detector (FID). A superimposed chromatogram is recorded which is deconvoluted into an averaged chromatogram with Hadamard transformation. Novel algorithms to maintain the data acquisition rate of the detector by application of Hadamard transformation and to suppress correlation noise induced by components with much higher concentrations than the target substances are shown. Compared to conventional GC-FID, the signal-to-noise ratio has been increased by a factor of 10 with mpGC-FID. Correspondingly, the detection limits for BTEX in CO2 have been lowered from 10 to 1 ppb each. This has been achieved despite the presence of detectable components (methane and methanol) with a concentration about 1000 times higher than the target substances. The robustness and reliability of mpGC has been proven in a two-month field test in a chemical production plant.

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ion mode is used. The usage of such detectors or trapping techniques usually narrows the variety of detectable target substances. Trapping techniques require additional instrumental effort, which increases the risk of failure when operated continuously. Multiplexing techniques, well established in spectroscopy, can also be used in chromatography to enhance the signal-to-noise ratio (SNR) and to improve detection limits (multiplex advantage).3 It is advantageous that there is no discrimination through sample pretreatment or usage of special detectors by application of multiplexing techniques.4 Multiplexing gas chromatography (mpGC) was introduced in 1967 by Izawa et al.5 Multiplexing chromatography in general is currently the subject of intensive research.6−19 When multiplexing chromatography is applied, the sample is injected according to the pattern of an n-bit (m = 2n − 1 elements) pseudorandom binary sequence (PRBS) into the chromatograph.5 A “1” in this binary sequence stands for injection, and a “0” stands for no injection. The time span between two

o manufacture products at high purity standards and to maintain a clean environment, trace amounts of impurities have to be detected in consumer products and in the environment. For example, volatile organic compounds (VOC) such as benzene, toluene, ethylbenzene, and xylenes (BTEX) are harmful substances and classified as hazardous air pollutants (HAPs).1 The detection of such chemicals in the low parts per billion (ppb) range in consumer products and in the environment requires highly sensitive measurement technology. Trace analysis is therefore becoming increasingly important also for process analytical technology.2 We are presenting a method for online trace analysis of BTEX in the low ppb range in a CO2 stream optimized for an application in process analytical measurements. For a continuous online measurement in an industrial environment, a reliable and fully automatic operation of the measuring equipment over a period of several weeks without manual intervention is expected. Trace analysis using chromatography usually requires trapping techniques or application of detectors with high sensitivity for the target substances. For example, an electron capture detector for halogenated compounds, a thermionic specific detector for nitrogen and phosphorus, or a mass selective detector in single © XXXX American Chemical Society

Received: November 25, 2016 Accepted: March 8, 2017 Published: March 8, 2017 A

DOI: 10.1021/acs.analchem.6b04674 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry

grams on the separation column. In practice, from one injection to the other, peak heights could vary or retention times could shift. These effects introduce so-called nonlinearities during linear superposition of the single chromatograms.22 The result is that low-frequency noise and ghost peaks, respectively, are observed in the deconvoluted chromatogram. This kind of lowfrequency noise was termed correlation noise by Annino and Bullock.24 Simulations prove that PRBS from linear feedback shift registers (LFSR) are especially suited for correcting such errors in multiplexing chromatography.21,25 Such kinds of PRBS are also used for the current application. However, for the analysis presented in this paper (BTEX in the ppb range and methane and methanol in the parts per million (ppm) range in a CO2 stream), correlation noise induced by methane and methanol is in the same order of magnitude as the intensity of the BTEX-peaks. Therefore, the peaks of interest are nearly buried by the correlation noise. Thus, the multiplexing advantage is lost if detectable high-concentration components are present because of the huge contribution of the corresponding peaks to the correlation noise as already reported previously.25,26 The standard deviation of the correlation noise grows linearly with the mean square error of the detected signals.27 Therefore, suppression of correlation noise is a key factor for a successful application of mpGC for trace analysis. An experimental approach to overcome this effect, termed differential cross correlation chromatography, has been published by Laeven et al.28 Here, in the current paper, an algorithm for the suppression of correlation noise induced by high-concentration components is presented for Hadamard transformation. The signals of these components are eliminated from the convoluted raw data prior to Hadamard transformation. This allows one to apply mpGC for trace analysis despite the presence of detectable components (here, highly concentrated methane and methanol) with concentrations much higher than that of the target substances. The injection technique and algorithms were developed for a continuous and reliable measurement and tested for trace analysis of BTEX (ppb range) in a CO2 gas stream containing methane and methanol (ppm range). Automated measuring equipment with software for control and data analysis was tested for two months in a chemical plant as a process analytical instrument.

elements of the PRBS is referred to as time interval (Δt). Because the duration of a chromatogram (time scale: minutes) is considerably longer than the time interval between two injections (time scale: seconds), a superimposed (convoluted) chromatogram is recorded. Multiplexing chromatography can be described by Hadamard transformation.20 Within this model, the convoluted chromatogram is the result of the forward Hadamard transformation according to eq 1. ⎡ deconvoluted ⎤ ⎡ convoluted ⎤ [S] × ⎢ ⎥=⎢ ⎥ ⎣ chromatogram ⎦ ⎣ chromatogram ⎦

(1)

where S (m × m matrix) is the convolution matrix derived from the PRBS.20 The inverse convolution matrix multiplied with the convoluted chromatogram produces the deconvoluted chromatogram, shown in eq 2 (inverse Hadamard transformation). ⎡ convoluted ⎤ ⎡ deconvoluted ⎤ [S]−1 × ⎢ ⎥=⎢ ⎥ ⎣ chromatogram ⎦ ⎣ chromatogram ⎦

(2)

Alternatively, the deconvoluted chromatogram, called correlogram R in this case, can be obtained by cross-correlation between the PRBS and the convoluted chromatogram according to eq 3.5 Both computational methods lead to identical deconvoluted chromatograms.21 m

R (v ) =

∑ [PRBS]j j=1

⎡ convoluted ⎤ ×⎢ ⎥ ⎣ chromatogram ⎦ j + v

(3)

Applying eq 2 or 3 to real data requires data pretreatment. The reason is that the equations can only be applied if the dimension of the chromatogram is the same as that of the PRBS. There are basically 3 ways to fulfill this prerequisite. First, the data acquisition rate of the convoluted chromatogram (frequency > 1 Hz) is reduced to the injection frequency (frequency < 1 Hz).22 That can be achieved by reducing the number of elements in the convoluted chromatogram with a moving average to match the dimension size of the PRBS. Thus, the convoluted chromatogram and the deconvoluted chromatogram possess only one data point per time interval. Since chromatographic peaks are usually narrower than the time intervals between two injections, the reduction of data points in the convoluted chromatogram leads to a substantial loss of information.23 A second option for using eq 2 or 3 for deconvolution without loss of information is to extend the PRBS or the convolution matrix until the number of elements in the PRBS (eq 3) or the dimension of the inverse convolution matrix (square matrix in eq 2) is equal to the number of data points in the convoluted chromatogram.23 A third way of deconvolution also without loss of information is presented in this paper. Instead of extending the convolution matrices, the convoluted chromatogram is arranged as a matrix having the same dimension as the convolution matrix S. The Hadamard transformation is then carried out as matrix multiplication, which will be referred to as high definition Hadamard transformation. This method is less computationally expensive than previous proposals; however, it may only be used for Hadamard transformation, not the cross-correlation according to eq 3. When applying eq 1 for describing the formation of the convoluted chromatogram, it is assumed that each injection leads to a linear superposition of identical single chromato-

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EXPERIMENTAL SECTION Material. The reference gas for calibration and application development was purchased from Linde (Munich, Germany). The reference gas contains benzene, toluene, ethylbenzene, o-, p-, and m-xylene, and methanol in a CO2 matrix. The concentrations are 120, 122, 126, 125, 125, and 115 ppb and 110 ppm, respectively. CO2 of analytical grade (4.5) from Basi (Rastatt, Germany) was used as carrier gas and for dilution of the reference gas up to a factor of 100. Instrumentation. The mpGC experiments were carried out with a commercially available gas chromatograph (model 7890B by Agilent) equipped with a flame ionization detector (FID). Separation of methane, methanol, and the BTEX (isothermal and isobaric at 60 °C and 60 kPa) was conducted on a CP SIL 5 CB capillary column with 0.53 mm inner diameter and 30 m length, also from Agilent. Since the sample, containing mainly CO2, is injected every few seconds, the column is filled with a significant amount of CO2 during one multiplexing experiment consisting of a few hundred injections. If a standard carrier gas such as helium, hydrogen, or nitrogen is B


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Analytical Chemistry chosen, it will be diluted by CO2 to such an extent that the retention times of all components will shift over the course of one multiplexing experiment causing correlation noise.26 To avoid this effect, CO2 was used as carrier gas. The sample was injected with a solenoid valve together with a patented injector design29 according to a n-bit PRBS (m = 2n − 1 elements) generated with a virtual LFSR. The sample is injected with a slight overpressure (∼3 kPa) into the system to guarantee equilibration of the chromatographic system within the time interval. The solenoid valve is opened for 1.5 s for every injection in order to obtain high injection volumes. Data Acquisition and Analysis. Multiplexed chromatograms were acquired with the software ChemStation by Agilent (data acquisition rate of 50 Hz). A post run macro for ASCII export of the data was used. Automated data analysis with Hadamard transformation and suppression of correlation noise, as described in this paper, was carried out with a self-written algorithm in MATLAB.

Figure 1. High definition Hadamard transformation illustrated with computer simulated data: Multiplication of all red values in the convoluted chromatogram with the inverse convolution matrix gives the red values in the deconvoluted chromatogram. The same holds for all green, gray, and blue values, respectively. Multiple Hadamard transformation maintains the data acquisition rate in the deconvoluted chromatogram.

deconvoluted chromatogram. In this way, all values of the time intervals (red, green, gray, and blue) can be deconvoluted consecutively. Suppression of Correlation Noise [Algorithm II]. Components with concentrations much higher than the target substances induce a significant level of correlation noise originating from varying peak heights or peak shapes.25,26 If the correlation noise is of the same intensity as the target peaks, suppression of correlation noise will be the key for application of mpGC for trace analysis. The basic concept of algorithm II is eliminating the peaks of the high-concentration components from the convoluted chromatogram by setting the corresponding data points to zero. The remaining data set only contains the superimposed peaks of the target substances. This modified chromatogram will be Hadamard transformed according to algorithm I to obtain a deconvoluted chromatogram without correlation noise induced from high-concentration components but with the peaks of the target substances. For the first injection, the data points recorded at the beginning and the end of the elution of the high-concentration components are determined from the convoluted chromatogram. These values can then be used to predict from the PRBS the ranges when all following peaks of the high-concentration components in the convoluted chromatogram elute. Depending on the position and shape of the peaks that have to be eliminated, a certain number of consecutive data points is set to zero. The consecutive data points, which are set to zero, will be referred to as the elimination interval. For each of the 2n/2 injections, the high-concentration components are eliminated resulting in a total of 2n/2 elimination intervals. The start and end of an elimination interval correspond to two cuts in the chromatogram, respectively. The elimination of peaks in the convoluted chromatogram may lead to changes of the baseline level of the deconvoluted chromatogram. The reason is that the elimination of peaks leads to elements which are equal to zero in the matrix M. The number and arrangement of those elements depend on the position of the cuts. It turns out that there are columns with the same number of identically arranged zero elements in matrix M. Each of these columns of matrix M results in a uniform baseline level in the corresponding columns of matrix H after Hadamard transformation. The two cuts of each elimination interval cause two different sets of columns in matrix M. Therefore, two sets of columns with different baseline levels occur in matrix H. Since matrix H is dissembled row by row into a vector, the baseline level changes periodically in every time interval of the deconvoluted chromatogram. The

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ALGORITHMS Maintaining the Data Acquisition Rate: High Definition Hadamard Transformation [Algorithm I]. The algorithm for application of high definition Hadamard transformation on convoluted data can be described as follows. In the first step, after offset correction, all data points that are acquired after finishing the injection sequence are added to the first data points of the raw data (cyclization of raw data).9 The total number of data points in the cyclized raw chromatogram N is given by eq 4. N = m × Δt × f (4) where m is the number of elements in the PRBS, Δt is the length of a time interval, and f is the data acquisition rate. Every time interval has Δt times f data points (T = Δt × f). In a second step, the elements of the cyclized raw chromatogram are arranged as a matrix M (m × T). All first data points of each time interval of the cyclized raw chromatogram form the first column of matrix M. The second and third points of each time interval will form the second and third column, respectively. This goes on for all consecutive data points of each time interval. In the third step, the Hadamard transformation is carried out according to eq 5.

H = [S]−1 × M

(5)

In the fourth step, matrix H is dissembled to form a vector in the inverse way as matrix M was formed from the cyclized chromatogram. This vector contains the high definition deconvoluted chromatogram with a time distance between two data points identical to the time distance between two data points of the convoluted chromatogram. The idea of high definition Hadamard transformation is illustrated in Figure 1 with computer simulated data. A cyclized convoluted chromatogram is multiplied with the inverse convolution matrix to obtain the deconvoluted chromatogram. A 3-bit PRBS has been used for multiplexing. Accordingly, the cyclized convoluted chromatogram can be divided into seven time intervals (m = 2n − 1). The time intervals which are separated with dashed lines contain 400 data points each. For a simplified illustration, just 4 ranges of these 400 data points are marked with 4 different colors per time interval in Figure 1 (red, green, gray, and blue). For deconvolution, the inverse of the convolution matrix is multiplied with all red values of the convoluted chromatogram to get all the red values of the C


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Figure 2. Illustration of the suppression of correlation noise with algorithm II for a convoluted chromatogram of undiluted reference gas (concentration of BTEX: 100 ppb each; concentration of methanol: 100 ppm). (a) High definition Hadamard transformation of the unmodified raw data (50× baseline zoom). (b) High definition Hadamard transformation of the modified raw data consisting of methanol peaks with superimposed BTEX peaks (50× baseline zoom). The data in-between the methanol peaks are set to zero. (c) High definition Hadamard transformation of the modified raw data consisting of superimposed BTEX peaks. The methanol peaks are set to zero.

is equal to T, the results for A′ and B′ will be identical. Elimination intervals having the length of one time interval (Δt) have been applied in the experiments shown. For baseline correction, the different ranges with equal baseline level each are shifted up or down until a common baseline level is obtained. The new baseline level has no physical meaning, but the chromatograms can be interpreted and integrated as conventional chromatograms. The baseline correction has been carried out for all deconvoluted chromatograms shown in this paper. A significant level of correlation noise is induced in the deconvoluted chromatogram if the elimination interval is too small so that the front or the tail of the high-concentration component is not eliminated. The shape of the target peaks starts to degrade if the elimination interval is longer than a time interval because too much information on the target peaks is lost. It has been observed that gradual changes of the baseline level in the order of magnitude of the size of the target peaks are erratically distributed in the deconvoluted chromatogram

corresponding data points can be predicted for baseline correction. Let A be the data point of the first injection where the elution of the high-concentration component starts and B be the point of the first injection where the elution ends. Thus, the elimination interval is [A; B]. The data points A′ at which the baseline level changes in the deconvoluted chromatogram can be calculated with eq 6. The modulo operation (mod) gives the remainder when dividing A by (Δt × f). A′ = j × (Δt × f ) + A mod(Δt × f ) for{j ∈ |0 ≤ j < m}

(6)

Correspondingly, B′ values are the data points where the baseline level changes in the deconvoluted chromatogram due to the cuts at the data points where the elution of the highconcentration components ends and can be calculated with eq 6 by exchanging A against B. If the difference between A and B D


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correction, the chromatogram in Figure 2c.3 is produced. Subtraction of the chromatogram in Figure 2b.3 from the chromatogram in Figure 2a.3 also results in the chromatogram in Figure 2c.3. Both, direct deconvolution of the BTEX peaks and subtraction of the deconvoluted methanol peaks from the deconvoluted unmodified data, lead to identical chromatograms. The BTEX peaks without correlation noise as presented in Figure 2c.3 can be quantified. Although all methanol peaks have been removed from the convoluted chromatogram, a small signal between 44.2 and 49.2 s (retention time of methanol), corresponding to the elimination interval [2210; 2460], is observed in the deconvoluted chromatogram seen in Figure 2c.3. This signal is interpreted as an artifact of the elimination procedure; therefore, quantification of methanol has to be done from the chromatogram seen in Figure 2a.3 (high definition Hadamard transformation of the unmodified raw data). The application of algorithm II, as illustrated in Figure 2, has been completely automated for the field test with constant values A and B for start and end of the elution of the highconcentration components. The retention time was stable for the whole test period of 2 months. With the proposed algorithm, only correlation noise that is induced from the components inside the elimination intervals will be suppressed.

over the entire retention time. Since the length of the single chromatogram is much shorter than the measurement time, most of the deconvoluted chromatogram, which has the same length as the convoluted chromatogram, contains no analytical information (i.e., chromatographic peaks of interest). Accordingly, modulation parameters and chromatographic parameters can be adjusted to shift the resulting gradual changes of the baseline level to those retention time ranges without analytical information. The chromatograms shown in Figure 2 illustrate the effects of applying algorithms I and II to a convoluted chromatogram of undiluted reference gas (see Figure 2a.1). For the reference gas, methanol is a component with a concentration 1000 times higher than the concentrations of the target substances BTEX. For the convoluted chromatogram shown in Figure 2a.1, a 10bit PRBS (m = 1023 matrix elements/512 injections) has been chosen. The time interval was Δt = 5 s at 50 Hz data acquisition rate. The elution order of the substances is methanol, benzene, toluene, ethylbenzene, and p-, m-, and oxylene. The para and meta isomers of xylene are not separated from each other and are observed as one peak. The peak of ethylbenzene is not baseline separated from the p- and mxylene peak. The first methanol peak of the convoluted chromatogram elutes between the data points 3710 and 3960 corresponding to the retention time between 74.2 and 79.2 s. Since six time intervals without injection (six 0 elements in the PRBS) pass before the first injection, these six time intervals (6 × Δt × f = 1500 data points corresponding to 30 s) have to be subtracted to obtain the retention time range of the methanol peak (44.2 to 49.2 s corresponding to an elimination interval [A; B] of A = 2210 and B = 2460). For elimination of all other methanol peaks, their positions were predicted from the PRBS. Figure 2a.2 shows the retention time range from 7 to 8 min of the raw data shown in Figure 2a.1. In Figure 2a.3, finally, the deconvoluted chromatogram of the raw data depicted in Figure 2a.1 is presented. The BTEX peaks can hardly be recognized since they are almost buried under the correlation noise induced by the methanol peaks. Figure 2b.1 shows those data of the chromatogram presented in Figure 2a.1 that will be set to zero according to algorithm II. In Figure 2b.2, again the retention time range from 7 to 8 min is shown at a larger scale. It can be seen that the convoluted chromatogram just contains the ranges where the methanol peaks with superimposed BTEX peaks are present and that the areas in-between the methanol peaks are set to zero. To demonstrate which information is lost when the peaks of the high-concentration components are set to zero, a Hadamard transformation of the data shown in Figure 2b.1 with subsequent baseline correction is presented in Figure 2b.3. The BTEX peaks are visible in Figure 2b.3 (with a smaller intensity than in Figure 2a.3) although the time intervals between the methanol peaks have been set to zero before deconvolution. The reason is that BTEX signals are superimposed with the methanol peaks, so deconvolution of the chromatogram presented in Figure 2b.1 yields both the methanol and the BTEX peaks. The chromatogram displayed in Figure 2c.1 consists of those data of the chromatogram depicted in Figure 2a.1 where the ranges containing the methanol peaks are set to zero, according to algorithm II. The retention time range from 7 to 8 min of the chromatogram shown in Figure 2c.1 is depicted in Figure 2c.2. It can be seen that the retention time ranges where the methanol peaks are found have been set to zero. When algorithm I is applied to the chromatogram shown in Figure 2c.1 with subsequent baseline

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RESULTS AND DISCUSSION For direct comparison of conventional GC-FID with mpGCFID, chromatograms measured with both methods are presented in Figure 3. The chromatograms of identical samples are shown in Figure 3a−f, respectively. Conventional GC-FID chromatograms are shown to the left (Figure 3a,c,e). The peaks of the BTEX are observed at retention times between 1 and 5 min; therefore, this range is also shown at a larger scale. For Figure 3a,c, a magnification factor of 100 and for Figure 3e, a factor of 20 has been chosen, respectively. The results of the multiplexing experiments obtained by deconvolution of the raw data with algorithms I and II are shown to the right (Figure 3b,d,f). The modulation for the mpGC-FID measurements was performed according to a 10-bit (m = 1023 matrix elements/ 512 injections) PRBS while the time interval was Δt = 5 s at 50 Hz data acquisition rate. This results in a total measurement time of 90 min consisting of 85 min for the injections and the length of the chromatogram of 5 min. Two chromatograms are shown in each of these figures: The deconvoluted chromatogram of the unmodified raw data (below) is shown in Figure 2a.3 and the deconvoluted chromatogram of the BTEX peaks only with 150 times magnification of the intensity is depicted in Figure 2c.3. The methanol peak elutes for the first time in the convoluted chromatograms of Figure 3b,d between the data points A = 2210 and B = 2460. Since the start time of the data acquisition has been modified in Figure 3f, the values are changed to A = 2185 and B = 2435. The chromatogram of undiluted reference gas recorded with GC-FID is shown in Figure 3a. The corresponding chromatogram obtained with mpGC-FID for the same sample (Figure 3b) shows a larger signal-to-noise ratio than the chromatogram measured with GC-FID (Figure 3a). In Figure 3c, a conventional chromatogram of reference gas diluted by a factor of 10 is presented. The peaks of the BTEX with a concentration of 10 ppb each are at the detection limit. The mpGC-FID chromatogram of the same sample (Figure 3d) shows distinct BTEX peaks that can be analyzed quantitatively. Figure 3e shows a conventional GCFID chromatogram of reference gas diluted by a factor of 100. No peaks are visible for the BTEX with a concentration of 1 E


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adsorbed to the walls of the steel pipes guiding the sample to the GC. Changing methanol concentrations in the gas phase leads to adsorption of methanol to the walls or to desorption from the walls until an equilibrium is reached. For the BTEX, adsorption and desorption does not take place to such an extent as for methanol. Injecting a sample before equilibration of the methanol distribution will therefore result in different relative peak intensities for samples of methanol and BTEX diluted with CO2. For the multiplexing experiments, a constant relative intensity of methanol and BTEX peaks is observed for different absolute concentrations (see Figure 3b,d,f). The reason is that, for the measurement over 90 min of time, the equilibrium between the methanol concentration in the gas phase and the amount of methanol adsorbed to the walls has been reached shortly after the start of the measurement. Therefore, most of the samples injected represent the correct relative concentrations of methanol and BTEX leading to correct relative intensities of the corresponding peaks in the deconvoluted chromatogram. For validation of the mpGC-FID method, also, the relative area deviation of the peaks in the deconvoluted chromatogram was determined from 30 consecutive measurements of the undiluted reference gas over a total measurement time of 48 h and was found to be less than 2% for every BTEX peak. A fivepoint calibration with three single measurements per point in the range of 1−10 ppb BTEX was carried out. The coefficients of determination for the BTEX concentrations as obtained from linear regression are higher than 0.99 for all peaks. The linearity of the FID is maintained by mpGC. The gas chromatograph (model 7890B by Agilent) was fully automated for the field test measurements. In the field test, additionally, methane occurs with a concentration in the ppm range. The correlation noise caused by methane also has to be suppressed. Methane and methanol elute directly one after another. The elimination interval has to be increased compared to the experiments with reference gas containing just methanol. Therefore, longer time intervals have to be chosen to prevent the loss of too much information by peak elimination. For example, if the elimination interval is twice the time interval, the data set will be eliminated almost completely. In the field test, the modulation of the sample injection was performed according to an 8-bit (m = 255 matrix elements/128 injections) PRBS while the time interval was Δt = 13 s at 50 Hz data acquisition rate. Methane and methanol elute one after another and can therefore be eliminated with one elimination interval per injection. In the convoluted chromatogram, the start and end of elution of the first methane peak is recorded at the data points A = 2235 and B = 2885, respectively. The improvement of SNR is reduced by a factor of 2 in comparison to the measurement with the reference gas because the number of injections has been reduced to a quarter compared to the mpGC measurements with the reference gas.30 The total measurement time for one multiplexing experiment in the field test was 60 min. The field test was carried out over a period of two months. Over this period, the BTEX in a CO2 stream could be monitored with mpGC-FID with a fully automated setup also including sample injection and data analysis. There was no need for human interaction. The elimination interval [2235; 2885] did not have to be adjusted proving that the retention time of methane and methanol were stable. Figure 4 shows the comparison of a typical chromatogram of a field test sample (black line) and one with diluted reference gas (blue line; dilution factor of 20) measured with identical modulation

Figure 3. (a, c, and e) Conventional GC-FID chromatograms. (b, d, and f) Deconvoluted chromatograms from mpGC-FID. (a) 100 ppb BTEX each and 100 ppm methanol (GC-FID). (b) Same sample as (a) measured with mpGC-FID. (c) 10 ppb BTEX each and 10 ppm methanol (GC-FID). (d) Same sample as (c) measured with mpGCFID. (e) 1 ppb BTEX each and 1 ppm methanol (GC-FID). (f) Same sample as (e) measured with mpGC-FID.

ppb each. The deconvoluted mpGC-FID data for the identical sample is depicted in Figure 3f. The BTEX peaks are at the detection limit but can clearly be identified. For the modulation parameters chosen for this experiment, the mpGC technique shows an improvement of the signal-tonoise ratio by a factor of 10. For a modulation with a 10-bit PRBS, the improvement of the SNR of a mpGC measurement compared to a conventional GC measurement can be calculated to be 16 (eqs 1−17 in ref 30). Thus, the observed improvement is lower than expected.30 This effect can be seen in Figure 3. The intensity scale of the conventional chromatograms in Figure 3a,c has to be increased by a factor of 100 to make the BTEX peaks visible. To obtain almost the same height for the BTEX peaks in the deconvoluted mpGC-FID data in Figure 3b,d, a magnification factor of 150 is needed. The reason for this effect is application of algorithm II. For deconvolution of the target substances, about half of the raw data is set to zero since in the current case each of the 2n/2 elimination intervals had the length of one time interval. Therefore, in this case, the signal strength decreases with the application of algorithm II to about 50%. This effect diminishes the improvement of the SNR compared to the theoretical value. The relative size of the methanol peaks compared to the BTEX peaks in Figure 3a,c,e varies. An explanation might be that a certain fraction of methanol is F


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significance of the data will allow for more stable control loops and therefore for keeping the process at a more efficient point. Maintaining the data acquisition rate by application of algorithm I can be done online and fully automated by today’s available computing capacity. Nowadays, usually, more data points than elements in the PRBS are acquired. Therefore, application of algorithm I is always recommended. The idea of algorithm II can be generally applied for Hadamard transform applications to improve the signal-to-noise ratio. The whole method is designed to operate without any human interaction as required for process analytical measurements. Online trace analytics is needed for quality control of products requiring high purity standards. Nowadays, such measurements are often done in the lab; therefore, mpGC offers the possibility to set up such measurements as a fully automated system. Errors introduced by manual sampling can thereby be avoided, and the operators are relieved of routine work. The presented method opens new possibilities for continuous trace analysis, not only in an industrial environment. Algorithms I and II are important tools for the development of efficient and user-friendly measurement systems for trace analysis with chromatography or time-of-flight mass spectrometry, based on Hadamard transformation.31

Figure 4. Comparison of a typical deconvoluted mpGC-FID chromatogram of a field test sample (black line, below) with a deconvoluted chromatogram of calibration standard with a BTEX concentration of 5 ppb each and a methanol concentration of 5 ppm (blue line on top). The vertical arrows indicate the retention times of the BTEX peaks.

parameters. An additional peak can be observed in the chromatogram of the reference gas with a retention time of 87 s that was not present in the chromatograms of reference gas measured in the lab (see Figure 3b,d,f). At the same retention time, a peak is also observed in the chromatogram of the field test sample. Most probably, the sample line guiding either the field test sample or the reference gas to the GC was not purged enough to completely remove this substance from the line before the chromatogram of the reference gas was recorded. No peaks can be found in the field test sample at the retention times of the BTEX as indicated by the vertical arrows in Figure 4. The detection limit of the mpGC-FID method chosen for the field test is 2 ppb. It can be concluded that the sample obtained from the process does not contain BTEX with concentrations larger than 2 ppb. However, besides methane and methanol in the ppm range, further substances are present with retention times at 73, 78, and 176 s. When a similar response factor of these components as for the BTEX is assumed, the concentrations of these additional components are also in the ppb range.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.6b04674. MATLAB source code and further explanations of algorithms I and II (PDF) Convoluted raw data (Figure 2a.1) (XLSX) 10-bit PRBS used for injection (XLSX) Deconvoluted raw data obtained by applying both algorithms (Figure 2c.3) (XLSX)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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ORCID

CONCLUSION A fast computation method for high definition Hadamard transformation (algorithm I) and a new approach for the suppression of correlation noise induced by components with a concentration much higher compared to the target substances (algorithm II) are presented. Both algorithms allow application of mpGC-FID for process analytical measurements of trace components in the presence of detectable high-concentration components. A process stream can be analyzed in the low ppb range with a mpGC-FID setup, without discrimination of substances as is typical for trapping techniques or special detectors. Low and high concentrated components can be measured simultaneously with one mpGC application. In comparison to a conventional GC setup, the detection limits are decreased significantly (up to a factor of 10 with the modulation parameters chosen for the mpGC measurements shown in Figure 3). The deconvoluted chromatograms have a higher statistical significance than a single chromatogram because the deconvoluted chromatograms are averaged over many injections. If the results of the process analytical measurements are used for process control, the higher statistical

Oliver Trapp: 0000-0002-3594-5181 Author Contributions ¶

M.R.W. and R.L. contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been funded by BASF SE. REFERENCES

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