Fuel Processing Technology 110 (2013) 133–140

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Fuel Processing Technology

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Assessment test of sulfur content of gases

Ali Eslamimanesh a, Farhad Gharagheizi b, Amir H. Mohammadi c,d,⁎, Dominique Richon d,e

a Department of Chemical & Biomolecular Engineering, Clarkson University, Potsdam, NY 13699-5705, USAb Department of Chemical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iranc Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, Franced Thermodynamics Research Unit, School of Chemical Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africae Department of Biotechnology and Chemical Technology, School of Science and Technology, Aalto University, Aalto, Finland

⁎ Corresponding author at: Institut de Recherche enGénParis Cedex, France.

E-mail address: a.h.m@irgcp.fr (A.H. Mohammadi).

0378-3820/$ – see front matter © 2012 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.fuproc.2012.12.005

a b s t r a c t

a r t i c l e i n f o

Article history:Received 2 October 2012Accepted 5 December 2012Available online 5 February 2013

Keywords:Data evaluationSulfur contentGasLeverage approachOutlier diagnosticsSolubility

The experimental sulfur content data of various gases are evaluated in this work for outlier diagnostics. Theleverage statistical algorithm is applied for this purpose, which includes determination of the statistical Hatmatrix, sketching the Williams plot, and calculation of the residuals of selected correlation results. Moreover,the applicability domains of the employed correlation and the quality of the existing experimental data arechecked along with the outlier detection. The previously proposed del Valle and Aguilera correlation is ap-plied for representation/prediction of the sulfur content of several gas samples. It is found that the appliedcorrelation for representation of the corresponding solubilities is statistically valid and correct, three datapoints are not within its applicability domain and one datum is a probable outlier of the evaluateddatasets.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Several natural gas field observations demonstrate that there ispossibility of sulfur precipitation (or deposition) in the formation, wellbores, flow control valves, nozzles, orifices, and other production facili-ties [1–5]. High temperatures, pressures, and hydrogen sulfide concen-trations (particularly in sour gases) would increase the probability ofthis phenomenon [1–5]. The drawbacks of sulfur deposition have beenalready well argued [1–8].

Sulfur may exist as a number of polymeric species (up to S8) inthe gaseous state and may combine with other gases to producepolysulfides or sulfanes such as H2S9 [1,2,5,9–19]. The amount of eachspecies in the final complex generally depends on pressure and temper-ature [2,4,5,13–18]. Under atmospheric pressure and at temperaturesgreater than the fusion temperature, liquid sulfur is composed of about99% (mole basis) S8 and traces of lighter molecules [1,2,5,12–16,20,21].Nevertheless, if temperature increases, the ring molecules of sulfurpolymerize. Liquid sulfur begins to polymerize at about 430 K[1,2,5,13–18,22].

Regarding the significance of the sulfur content of different gases,several experimental studies have been reported in open literature. Apreviously performed literature review [2,18] is herein presented asSupporting information.

ie Chimique et Pétrolier (IRGCP),

rights reserved.

To propose accurate thermodynamic models for estimation of thesulfur content of various gases, accurate experimental datasets are re-quired. However, measuring such data is generally difficult because ofthe low sulfur content of gas samples. Additionally, sulfur contentdata are normally measured at high temperatures and high pressures(similar to that of the natural gas operation conditions) [1,2]. Thesefactors may result in unreliable experimental data or high uncer-tainties. It can be stated that only the best data must be retained toadjust the parameters of the corresponding thermodynamic modelsfor further calculations/estimations [23].

Consequently, there is indeed a need to evaluate the available ex-perimental data for the sulfur content of various gases. In a previouswork [2], the thermodynamic consistency of the experimental solubilitydata of sulfur in hydrogen sulfide vapor was checked using thermody-namic assessment test (consistency test) method. It is, therefore, of inter-est to use another approach on the basis of a statistically-correct method[24–28] for simultaneous diagnostics of the doubtful data and check fortheir quality alongwith determination of the validity and domain of appli-cability of a proposed correlation in the literature for their representation.

2. Theory

2.1. Hat matrix and Williams plot

Evaluation of the experimental datasets may be of priority in devel-oping the models, as discussed in our previous studies [23–25], due tothe diagnosis of individual datum (or groups of data) that may differ

Table 1The ranges of experimental sulfur content data [30–34] evaluated in this work.

Set no. Temperatureranges/K

Pressureranges/MPa

Sulfur content ranges/molefraction×106

Na Fluid compositions/mole fraction Ref.b

H2S N2 CO2 C1 C2 C3 i-C4 n-C4

1 303.2–363.2 30–45 0.049–2.48 8 0.0495 0 0.074 0.8765 0 0 0 0 [31]2 303.2–363.2 30–45 0.078–3.11 8 0.0993 0 0.0716 0.8291 0 0 0 03 303.2–363.2 30–45 1.03–5.820 8 0.1498 0 0.0731 0.7771 0 0 0 04 303.2–363.2 20–45 0.011–7.11 9 0.1771 0 0.0681 0.7584 0 0 0 05 303.2–363.2 30–45 1.69–12.70 8 0.2662 0 0.07 0.6638 0 0 0 06 303.2–363.2 30–45 0.0712–2.77 8 0.1 0 0.0086 0.8914 0 0 0 07 303.2–363.2 30–45 0.079–3.20 8 0.1003 0 0.1039 0.7958 0 0 0 08 316.3–383.2 7.03–31.14 1670–1020 21 1 0 0 0 0 0 0 0 [32]9 363.2 11.83–36.21 4830–10,500 6 1 0 0 0 0 0 0 0 [33]10 363.2–383.2 12.07–40.52 5.34–201 12 0 0 1 0 0 0 0 011 363.2 11.47–32.78 2340–8150 6 0.9509 0.0001 0.0372 0.0103 0.0009 0.0004 0.0001 0.000112 363.2 18.38–34.71 10.20–225 6 0.4411 0.0068 0.0072 0.4797 0.0409 0.0191 0.0028 0.002413 398 12.85–48.8 23.7–8270 10 0.84 0 0.09 0.07 0 0 0 0 [34]14 473 8–155 117–8680 9 0.42 0 0.02 0.56 0 0 0 015 485 7.5–76 95.20–1050 9 0.09 0 0.05 0.86 0 0 0 016 398–458 6.7–134.2 62.20–5110 11 0.35 0 0.08 0.57 0 0 0 017 398 7.00–43.00 1.84–687 8 0.35 0 0.08 0.45 0.12 0 0 018 398 7.00–43.50 4.62–952 8 0.35 0 0.08 0.45 0 0 0.12 019 373.15–433.15 10.0–60.0 1421–26,857 28 1 0 0 0 0 0 0 0 [35]20 373.15–433.15 10.0–60.0 9.39–301 18 0.07 0.08 0.2 0.65 0 0 0 021 373.15–433.15 10.0–60.0 3.67–281 20 0.06 0.04 0.09 0.81 0 0 0 022 373.15–433.15 10.0–60.0 8.36–594 15 0.01 0.04 0.14 0.81 0 0 0 023 373.15–433.15 10.0–60.0 1011–63,873 16 0.2 0.04 0.1 0.66 0 0 0 0Total 260

a Number of experimental data.b Reference number of experimental data.

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from the bulk of the data present in a dataset. The leverage statisticalapproach [26–28], which is employed here, includes numerical+graphical steps [23–25]. The calculation procedure of this method con-sists of determination of the residual values (i.e. the deviations of amodel results from the experimental data) and a matrix known as theHat matrix composed of the experimental data and the calculatedvalues obtained from a correlation (model) [23–28]. An appropriatemodel is therefore needed to employ the aforementioned strategy[23–28].

Fig. 1. Detection of the probable doubtful experimental sulfur content data (set no. 1)and check for the applicability domain of the del Valle and Aguilera correlation [29].The H* value is 1.125.

The following relation is generally used to form the Hat matrix (H)and its indices [23–28]:

H ¼ X XtX� �−1

Xt ð1Þ

where X is a two-dimensional matrix composing n data (rows) and kparameters of the model (columns) and t stands for the transpose

Fig. 2. Detection of the probable doubtful experimental sulfur content data (set no. 2)and check for the applicability domain of the del Valle and Aguilera correlation [29].The H* value is 1.125.

Fig. 3. Detection of the probable doubtful experimental sulfur content data (set no. 3)and check for the applicability domain of the del Valle and Aguilera correlation [29].The H* value is 1.125.

Fig. 5. Detection of the probable doubtful experimental sulfur content data (set no. 5)and check for the applicability domain of the del Valle and Aguilera correlation [29].The H* value is 1.125.

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matrix. The Hat values in the feasible region of the problem are thediagonal elements of the H matrix [23–28].

The graphical detection of the suspended (doubtful) data or out-liers is undertaken through sketching the Williams plot on the basisof the calculated H values through Eq. (1). This plot indicates the cor-relation of Hat indices and standardized cross-validated residuals(SR), which are defined as the difference between the representedvalues and the implemented data [23–28]. A warning leverage (H*)is normally equal to 3n/p, where n is the number of training points(represented data) and p is the number of model (correlation) inputparameters plus one [23–28]. The leverage of 3 is generally consid-ered as a “cut-off” value to accept the points within ±3 range (twohorizontal red lines in the figures) standard deviations from the

Fig. 4. Detection of the probable doubtful experimental sulfur content data (set no. 4)and check for the applicability domain of the del Valle and Aguilera correlation [29].The H* value is 1.000.

mean (to cover 99% normally distributed data) [25–28]. The existenceof the majority of data points in the ranges 0≤H≤H* and −3≤R≤3reveals that the model has a wide applicability domain to includethese points. In addition, it contributes to the conclusion that themodel is a statistically valid one [23–28]. “Good high leverage” pointsare located in the domain of H*≤H and−3≤R≤3 . The good high le-verage can be designated as the ones, which are outside of the appli-cability domain of the applied model [26–28]. In other words, themodel is not able to represent or predict the following data. Thepoints located in the range of Rb−3 or 3bR (whether they are largeror smaller than the H* value) are designated as outliers of the modelor “bad high leverage” points. These inaccurate representations/predictions can be attributed to the doubtful data [26–28].

Fig. 6. Detection of the probable doubtful experimental sulfur content data (set no. 6)and check for the applicability domain of the del Valle and Aguilera correlation [29].The H* value is 1.125.

Fig. 9. Detection of the probable doubtful experimental sulfur content data (set no. 9)and check for the applicability domain of the del Valle and Aguilera correlation [29].The H* value is 0.429.

Fig. 7. Detection of the probable doubtful experimental sulfur content data (set no. 7)and check for the applicability domain of the del Valle and Aguilera correlation [29].The H* value is 1.125.

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As the leverage approach [26–28] is generally used for checkingthe applicability domains of the models based on the numerical re-gressions, we have used a previously recommended del Valle andAguilera correlation [29] to correlate the sulfur content data.

2.2. del Valle and Aguilera correlation

Fitting the experimental values of solubilities of vegetable oils insupercritical carbon dioxide, del Valle and Aguilera [29] proposedthe following equation:

c=g:dm−3 ¼ ρ=g:dm−3� �k

exp aþ bT=K

þ dT=Kð Þ2

� �ð2Þ

Fig. 8. Detection of the probable doubtful experimental sulfur content data (set no. 8)and check for the applicability domain of the del Valle and Aguilera correlation [29].The H* value is 0.429.

where c is the concentration of a solute in a gas (solvent), ρ denotesthe density of the gas, k stands for the association term (in a complexformed from solution of a solute in a solvent), T is temperature, and a,b, and d are the adjustable parameters determined for a system of in-terest [29,30]. Application of Eq. (2) has contributed to acceptable re-sults for correlating the sulfur content data of various gases (with theassumption that sulfur is present as the molecule S8) [5].

3. Experimental data

Table 1 reports the ranges of the evaluated sulfur content data ofdifferent gases [31–35].

Fig. 10. Detection of the probable doubtful experimental sulfur content data (set no. 10)and check for the applicability domain of the del Valle and Aguilera correlation [29]. TheH* value is 0.750.

Fig. 11. Detection of the probable doubtful experimental sulfur content data (set no. 11)and check for the applicability domain of the del Valle and Aguilera correlation [29]. TheH* value is 1.500.

Fig. 13. Detection of the probable doubtful experimental sulfur content data (set no. 13)and check for the applicability domain of the del Valle and Aguilera correlation [29]. TheH* value is 1.500.

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4. Results and discussion

The recommended parameters of the correlation, and the absoluterelative deviations (ARD) of the correlation results from the experi-mental values [31–35] are presented as Supporting information.

To achieve our objectives, the H values have been calculated usingEq. (1) and theWilliams plots have been sketched in Figs. 1 to 23. Thecalculated H and R values are presented in the Supporting information.The warning leverages (H*) have been fixed at 3n/p for the whole data.Furthermore, the recommended cut-off value of 3 has been used, as al-ready mentioned [26–28].

Fig. 12. Detection of the probable doubtful experimental sulfur content data (set no. 12)and check for the applicability domain of the del Valle and Aguilera correlation [29]. TheH* value is 1.500.

The following results are interpreted from the application of thedescribed statistical strategy:

1. Accumulation of the data points in the ranges 0≤H≤H* and−3≤R≤3 for each dataset reveals that the applied correlation[29] is statistically correct and valid for representation of theseexperimental values.

2. The whole sulfur content data [31–35] can be declared to within theapplicability domains of the correlation [29], except three data points.

3. There is only one datum located in the range of Rb−3 or 3bR(ignoring their H values) to be designated as outliers or bad high

Fig. 14. Detection of the probable doubtful experimental sulfur content data (set no. 14)and check for the applicability domain of the del Valle and Aguilera correlation [29]. TheH* value is 0.900.

Fig. 15. Detection of the probable doubtful experimental sulfur content data (set no.15) and check for the applicability domain of the del Valle and Aguilera correlation[29]. The H* value is 1.000.

Fig. 17. Detection of the probable doubtful experimental sulfur content data (set no.17) and check for the applicability domain of the del Valle and Aguilera correlation[29]. The H* value is 1.125.

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leverage points. Thus, all of the other investigated experimental sul-fur content data [31–35] are statistically valid (not outliers) andmaynot be declared as doubtful or suspended ones.

4. The quality of the treated data (even those belonging to thesame dataset source) is inhomogeneous. Normally, the experi-mental data with lower absolute R values (near R=0 line) andlower H values may be considered as the more reliable ones[26–28].

5. The results of this work is in agreement with the conclusions of theprevious consistency test [2] performed on the experimental sulfurcontent data of hydrogen sulfide vapor.

Fig. 16. Detection of the probable doubtful experimental sulfur content data (set no.16) and check for the applicability domain of the del Valle and Aguilera correlation[29]. The H* value is 0.818.

It is worth pointing out that our objective in this work has been toconclude about the quality of the investigated data [31–35] in a statis-tical way. Conclusion about the accuracy and reliability of the pursuedexperimental techniques and procedures for obtaining these datashould be checked through complementary and independent methodsbefore a complete justification of their quality.

5. Conclusion

The leverage mathematical strategy [26–28] was applied to detectthe outliers in the experimental sulfur content data of several gases.

Fig. 18. Detection of the probable doubtful experimental sulfur content data (set no.18) and check for the applicability domain of the del Valle and Aguilera correlation[29]. The H* value is 1.125.

Fig. 19. Detection of the probable doubtful experimental sulfur content data (set no.19) and check for the applicability domain of the del Valle and Aguilera correlation[29]. The H* value is 0.321.

Fig. 21. Detection of the probable doubtful experimental sulfur content data (set no.21) and check for the applicability domain of the del Valle and Aguilera correlation[29]. The H* value is 0.450.

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The graphical method was performed on the basis of the Hat matrixand the Williams plot [23–28]. The existing solubility datasets fromthe literature [31–35] were represented by del Valle and Aguilera'scorrelation [29]. The results show that:

I. The applied correlation [29] is valid and statistically correct;II. There are three data points to be assigned as being out of the

applicability domains of the applied correlation [29];III. Only one outlier was diagnosed in the experimental datasets

[31–35];IV. The obtained results confirm the conclusions of the previous

thermodynamic consistency test [2] on the experimental sulfurcontent data of hydrogen sulfide.

Fig. 20. Detection of the probable doubtful experimental sulfur content data (set no.20) and check for the applicability domain of the del Valle and Aguilera correlation[29]. The H* value is 0.563.

A literature review on experimental studies of sulfur content ofvarious gases, the absolute relative deviations of the correlation[29] results from the experimental values [31–35] accompanied bythe standardized residual and Hat values, and the recommendedvalues of the correlation parameters are presented in the Supporting in-formation. Supplementary data related to this article can be found on-line at http://dx.doi.org/10.1016/j.fuproc.2012.12.005.

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Fig. 22. Detection of the probable doubtful experimental sulfur content data (set no.22) and check for the applicability domain of the del Valle and Aguilera correlation[29]. The H* value is 0.500.

Fig. 23. Detection of the probable doubtful experimental sulfur content data (set no. 23) andcheck for the applicability domain of the del Valle and Aguilera correlation [29]. The H* valueis 0.563.

140 A. Eslamimanesh et al. / Fuel Processing Technology 110 (2013) 133–140

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