Viscosities of Liquid Hexadecane at Temperatures Between 323 K and 673 K and Pressures up to 4 Mpa Measured Using a Dual-Capillary Viscometer

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Viscosities of Liquid Hexadecane at Temperatures between 323 K and 673 K and Pressures up to 4 MPa Measured using a Dual-Capillary Viscometer

Yolanda Sanchez-Vicente, Ian Emerson, Richard Glover, Oliver Herbage, Rodrigo Susial Martin, J. P. Martin Trusler*

Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

* Corresponding author. Email: [email protected]

ABSTRACT We report viscosities of liquid hexadecane measured at temperatures between (323 and 673) K and at pressures up to 4.0 MPa. This study significantly extends the temperature range over which viscosity data for hexadecane are available. The experiments were carried out using a dual-capillary viscometer that measures the ratio of the viscosity at the temperature in question to that at a reference temperature, 298.15 K in this work, at which the viscosity is well known. Absolute viscosities were then obtained with an estimated expanded relative uncertainty of about 3 % at 95 % confidence. An empirical function was developed to correlate the viscosity ratio with the density ratio and this fitted the experimental data within about 1 %. The results were found to agree well with the existing literature data.

1 1. INTRODUCTION Knowledge of the viscosity of hydrocarbons is critical in many technologies in the petroleum industry including various enhanced oil recovery techniques as well as carbon capture and storage.1 For example, in reservoir simulations, it has been found that variability in predicted cumulative oil production in the region of 7 % can be expected when the fluid viscosity is changed by 1 %, highlighting the economic importance of accurate knowledge of viscosity.2 Another area of increasing research interest is the field of air-breathing hypersonic vehicles. These vehicles are designed to travel at high Mach numbers and rely on their speed to compress incoming air before combustion. Since the frictional heat evolved is proportional to the square of the speed, the outer skin of these vehicles is subject to extreme temperatures. So too are the walls of the combustion chambers which can reach temperatures of over 3000 K.3 Consequently, sustained flight requires a substantial heat sink. One of the potential solutions to this problem is regenerative cooling in which the liquid hydrocarbon fuel is passed through heat-exchanger tubes embedded in the wall of the vehicle and/or its combustion chambers. In this way heat can be absorbed by the fuel as a result of temperature rise, vaporisation and ultimately endothermic cracking reactions.3 To design appropriate cooling structures for hypersonic vehicles, knowledge of the viscosity of multicomponent mixtures is essential and modelling approaches for this typically start with the viscosity of pure substances. However, there is currently a lack of experimental viscosity data of liquid hydrocarbons at temperatures above approximately 500 K. This might be due to the thermal decomposition of the sample as well as limitations of measurement techniques.

Hexadecane is often considered as a simple representative substance for diesel or aviation fuel. The available experimental data for the viscosity of hexadecane are summarised in Table 1,4-13 which details the temperatures and pressures range investigated, the measurement method employed, the uncertainty and the number of data points for each literature source. Table 1 demonstrates the relative lack of experimental data at temperatures higher than 500 K. Therefore, in this work, the viscosity of hexadecane was measured at temperatures from 323 K to 673 K and at pressures up to 4 MPa. The measurements were performed using a dual capillary viscometer, which permits short residence times in the high-temperature part of the apparatus, thereby minimising thermal decomposition. This paper follows the work of Liu et al.14 who measured the viscosities of cyclohexane and decane at temperatures up to 598 K using the same apparatus.

2 Table 1. Literature Data for the Viscosity η of Hexadecane, with Ranges of at Temperature T, Ranges of Pressures p, Number of Data Points N and Expanded Relative Uncertainty Ur(η) at 95 % Confidence.

Authors Viscometer type T/K p/MPa N Ur(η) Ref. Rolling & Vogt (1960) Rolling-ball 310-394 0.1-34.5 23 2% 4 5 Gouel (1978) Rolling-ball 300-392 0.1-40 51 5% Rastorgue & Keramidi (1980) 335-531 0.1-49.0 18 6 Dymond et al. (1980) Falling body 298-373 0.1-425 28 2% 7 Ducoulombier et al. (1986) Guided falling body 313-373 0.1-100 24 2% 8 Matthews et al. (1987) Capillary 323-564 1.4-3.5 10 3% 9 Tanaka et al. (1991) Torsionally crystal 298-348 0.1-151 16 2% 10 Rajagopal et al. (2009) Electromagnetic 318-413 6.9-62 54 3% 11 Baled et al. (2014) Rolling-Ball 304-534 3.3-227 42 3% 12 Mohammed et al.(2017) Vibrating wire 298-474 1.1-103 54 2% 13

2. EXPERIMENTAL SECTION

2.1. Apparatus The viscosity measurements were carried out using the dual-capillary viscometer described in detail in an earlier paper.14 In such an instrument, the fluid passes through two capillaries connected in series, one maintained at the reference temperature T0 and the other at the test temperature T; then, from measurements of the pressure drops across these two capillaries,

the ratio of the viscosities η at the two temperatures is obtained. If T0 is chosen such that η(T0) is already known within an acceptable uncertainty then absolute values of η(T) can be obtained.

In the present case, the reference capillary was immersed in a water bath, maintained at

T0 = 298.15 K, and the measurement capillary was enclosed in an oven, operated at the test temperature T. A preheat capillary was also installed in the oven to allow the test fluid to reach the test temperature prior to entering the measurement capillary. The reference and the measurement capillaries were nickel-clad fused-silica tubes with an inner diameter of 0.25 mm and an external diameter of 0.79 mm. One reference capillary of length 1000 mm was used for the measurements at T ≤ 623 K, and another reference capillary of 600 mm length was used when T > 623 K. Both the preheat capillary and the measurement capillary were 3000 mm in length and each was coiled with a radius of curvature of 50 mm.

The test fluid was transferred from a reservoir to the capillaries by a syringe pump (Eldex model MicroPro), which was operated in constant flow-rate mode; a filter was placed between the pump and capillaries to help prevent blockage in the capillaries. Differential pressure sensors (Keller, model PRD-33X) were connected between the inlet and outlet of both the reference and the measurement capillary. These sensors measured both the differential pressure, with a range of (0 to 100) kPa and an expanded uncertainty of 0.05 kPa (k = 2), and the upstream absolute pressure, with a range of (0 to 4) MPa and an expanded uncertainty of 0.004 MPa (k = 2).

The water bath had a capacity of 5 L and maintained the temperature of the reference capillary constant to within 0.1 K. The oven had a capacity of 30 L and a maximum operating

3 temperature of 773 K. The temperatures in the oven and the water bath were measured using 4-wire Pt100 platinum resistance thermometers (TC Direct, model 514-657) the reistances of which were measured with a data acquisition system (Agilent model 34970A). The thermometers were calibrated by the supplier against a standard platinum resistance thermometer and deviations were found to be within ± 0.1 K at T ≤ 673.15 K. Considering also the presence of temperature gradients in the oven, the standard uncertainty of the measurement temperature was taken to be 0.5 K while that of the reference temperature was taken to be 0.1 K. A back pressure regulator at the outlet of the system served to control the pressure with a precision of ± 0.1 MPa. An isolating capillary (length 500 mm, internal diameter 0.127 mm) was inserted before the back-pressure regulator to suppress pressure fluctuations upstream associated with flow instability through the regulator.

Liu et al. described the principle of a dual capillary viscometer for measurements on liquids.14 The principle is based on Poiseuille’s law and the fact that the mass flow rates of the test fluid in the two capillaries are identical at a steady state. The working equation is as follows:14

    S  SR,T  M,T  T 0  r    . (1) SS   R,TT00  M, T 0 cal

Here, ρT/ρT0 is the ratio of the densities at temperatures T and T0 at the mean absolute pressure pM in the measurement capillary, S is a derivative (d∆p/dQ) of the pressure drop Δp with respect to volumetric flow rate Q (measured at the pump conditions), and subscripts denote the reference capillary R, the measurement capillary M and the relevant temperature.

The quantity (SR,T0/SM,T0)cal is obtained in a calibration measurement with T = T0. Since the capillaries are coiled, the measured pressure drops should be corrected with a factor f(De, δ) 14, 15 to account for secondary flow; this factor is a function of the Dean number De and the ratio δ of the capillary radius to the coil radius.

2.2 Materials and Measurement Procedure The source and purity of the hexadecane sample are detailed in Table 2. The supplier’s certificate of analysis reported a sample purity of w = 0.995. The purity of the sample as received was checked by gas chromatography with flame ionisation detection (GC-FID, Shimadzu GC-2014). The GC-FID was fitted with an OV-101 packed column of length 2 m and inside diameter 2 mm operated with a temperature ramp from (308 to 473) K at a rate of 5 K min-1 and with helium carrier gas flowing at 25 ml·min-1. A test mixture was used to determine the retention times of the following components: pentane, hexane, heptane, octane, nonane, decane, dodecane, tridecane, tetradecane, pentadecane and hexadecane. Based on this analysis the mass-fraction purity was determined to be w = 0.996; the impurities detected and the relative GC peak areas are detailed in Table 2.

At the start of an experiment, the temperature of the oven was set to the desired value T and the water bath was set to T0 = 298.15 K for all the experiments. Then, the test fluid was pumped through both capillaries at a constant volumetric flow rate Q and the pressure at the inlet of the measurement capillary was set to the desired value by adjusting the setting of the back-pressure regulator. At steady-state conditions, the inlet pressure, pressure drop and temperature for each capillary recorded for at least 20 minutes. The data recorded in the final

4 Table 2. Chemical Sample Description where w is Mass Fraction. a Chemical CAS Source Purity Method of Additional name number analysis purification Hexadecane 544-76-3 Sigma w = GC-FID Vacuum Aldrich 0.996b degassed a GC-FID is gas chromatography with flame-ionisation detection. b Impurities with relative GC peak areas were: undecane, 0.04%; dedecane, 0.08 %, tridecane 0.07 %, tetradecane 0.06 %, pentadecane, 0.17 %; and heptadecane, 0.04 %.

2 p /MPa

0 300 400 500 600 700 T/K

Figure 1. Distribution of data in temperature T and pressure p for hexadecane: , experimental state points; , critical point;16 —, vapour pressure curve.17

3 min were averaged to obtain the experimental values associated with a given flow rate. This process was repeated for a minimum of four different volumetric flow rates in the range of (0.01 to 0.3) mL∙min-1, depending upon the viscosities at the reference and measurement temperature and pressure. The pressure drops at different flow rates were also measured with both capillaries at the same temperature to calculate the impedance ratio. The Reynolds number in both capillaries was also estimated for each experimental run and was found to vary in the range (0.1 to 6) for the reference capillary, and (0.6 to 150) in the case of the measurement capillary. The calculated Dean number in the reference capillary never exceeded 1, so that corrections for secondary flow there were negligible. However, the Dean numbers in the measurement capillary were higher, up to 8, due to the rapid decline of the viscosity with increasing temperature; therefore small corrections to the pressure drop were required. A linear regression analysis of the corrected pressure drops was then used to obtain the slopes S of pressure drop against flow rate at each temperature and pressure for both capillary. The measurements were performed at temperatures in the range (323 to 673) K in increments of 50 K and at nominal pressures of (1, 2, 3 and 4) MPa. The experimental conditions investigated in this work are shown in Figure 1.

5 In order to check for possible thermal decomposition, samples of the efluent liquid were collected and analysed by GC-FID using a similar procedure as followed for the fresh material. Samples collected from experiments at T = 673 K showed a mass-fraction purity of 99.3 %, only slightly changed from the fresh material. However, samples collected after trial measurements at T = 723 K showed clear evidence of thermal decomposition with a spectrum of impurities observed and an estimated mass fraction purity reduced to 96.7 %. These observations are similar to those reported by Wu et al.,18 who studied thermal cracking of hexadecane and, for small degrees of conversion, found decomposition products comprising a spectrum of alkanes and 1-alkenes with carbon number ≤ 15. Qualitatively, we also observed that the effluent always remained transparent and did not have an odour different to that of the fresh material. We conclude that a degree of thermal cracking occurred at T = 723 K but that decomposition was negligible at T ≤ 673 K. Based on this analysis, measurements at T ≥ 723 K and above were abandoned.

2.3 Uncertainty Analysis The combined standard relative uncertainty of the viscosity ratio was determined by differentiation of equation 1 and, including also the uncertainties of the density ratio, the pressure, and the two temperatures, the combined standard relative uncertainty of the viscosity ratio is:14

22 2 2 2 2 ur()()()  uS uS uS ()()(/)  uS u r rM,T rR,T0 rM,T 00 rR,T r TT 0 (2)  222  lnrTuT ( )  ln rTuT00 ( )  ln rpup  ( )  p pT 3.5

3.0

2.5 ) η r

( 2.0 r u 2

10 1.5

1.0

0.5

0.0 300 400 500 600 700 T /K

Figure 2. Estimated standard relative uncertainties ur(rη) of individual viscosity ratio measurements rη as a function of temperature T; - - - - -, root-mean-square value of ur(rη).

6 In this equation, u(X) and ur(X) refer to the standard uncertainty and the standard relative uncertainty of quantity X, respectively. The standard relative uncertainty of the density ratio for hexadecane was based on the equation of state of Romeo and Lemmon et al.19 and was taken to be 0.3 %. The standard uncertainty for the mean pressure pM in the measurement

capillary was taken to be 0.02 MPa. The temperature uncertainties were u(T0) = 0.1 K and

u(T) = 0.5 K. The standard relative uncertainties ur(rη) are shown in Figure 2 and the root-

mean-square value of ur(rη) was 1.5 %. The standard relative uncertainty of the reference viscosity was taken to be the standard uncertainty of the correlation of literature data as discussed below: ur(η0) = 0.5 %. The standard relative uncertainty of the absolute viscosities

η(T, pM), taking into account of the uncertainty of η0 = η(T0, pM), was 1.6 % and hence the overall combined expanded relative uncertainty at 95 % confidence is 3.2 %.

RESULTS AND DISCUSSION The experimental viscosity ratios are given in Table 3 at each temperature and pressure investigated, together with the corresponding density ratios calculated with the equation of state of Romeo and Lemon et al.19 In order to determine the absolute viscosities, independent

values of the viscosity of hexadecane at the reference temperature T0 and the experimental pressures were required. To address this, literature viscosity data in the ranges 293.15 ≤ T/K ≤ 303.15 K and p ≤ 10 MPa were gathered and used to establish a local correlation of low uncertainty. The data used for this correlation were critically reviewed and assessed, taking into account the measurement methods used and their respective uncertainties. The selected data,7, 10, 13, 20-23 given in Table 4, were used to obtain the parameters of the following empirical correlation:

 ln  a  bT  cp (3) μPa s

Table 3. Experimental Viscosity Ratios rη and Derived Viscosities η of Hexadecane at Temperatures T and Pressures pM, with Reference Temperature T0 = 298.15 K. Also

tabulated: Density Ratios ρT/ρT0 Calculated from the Equation of State of Romeo And a Lemmon and the Reference Viscosities, η(T0, Pm) Calculated from the Equation 3.

T /K pM /MPa ρT/ρT0 rη η(T0, pM)/(µPa⋅s) η(T, pM)/(µPa⋅s) 323.7 0.97 0.9769 0.5997 3097 1857 322.7 1.94 0.9777 0.5977 3154 1885 323.8 1.98 0.9769 0.5978 3141 1878 323.7 3.00 0.9772 0.5973 3187 1904 323.8 3.91 0.9772 0.5961 3230 1925 372.7 0.99 0.9327 0.2926 3105 909b 372.7 1.96 0.9331 0.2930 3146 922b 372.8 2.97 0.9335 0.2911 3190 929b 372.8 3.95 0.9340 0.2926 3235 947b 373.9 0.98 0.9316 0.2886 3106 896 373.9 2.00 0.9321 0.2889 3145 909 373.9 2.98 0.9326 0.2871 3187 915

7 T /K pM /MPa ρT/ρT0 rη η(T0, pM)/(µPa⋅s) η(T, pM)/(µPa⋅s) 373.9 3.90 0.9332 0.2909 3217 936 422.9 1.99 0.8883 0.1771 3127 554 422.9 2.97 0.8892 0.1759 3165 557 422.9 3.84 0.8900 0.1769 3208 568 471.9 1.00 0.8414 0.1155 3104 358 472.0 2.01 0.8429 0.1151 3153 363 472.1 2.91 0.8442 0.1163 3193 371 472.1 3.87 0.8458 0.1160 3227 374 473.7 3.99 0.8444 0.1157 3240 375b 521.9 0.97 0.7921 0.0792 3099 245 521.9 1.96 0.7946 0.0807 3152 254 521.9 2.95 0.7971 0.0812 3198 260 522.0 3.83 0.7993 0.0830 3220 267 572.2 2.00 0.7424 0.0595 3144 187 572.1 2.93 0.7462 0.0603 3187 192 572.2 3.85 0.7496 0.0605 3237 196 621.9 2.01 0.6826 0.0415 3155 131 622.0 2.89 0.6892 0.0432 3179 137 622.1 3.82 0.6951 0.0442 3221 142 623.2 3.99 0.6949 0.0441 3234 143b 673.2 2.00 0.6050 0.0288 3148 91b 673.6 3.00 0.6194 0.0305 3187 97b 672.6 3.99 0.6327 0.0321 3233 104b 672.6 3.99 0.6327 0.0321 3233 104b a Standard uncertainties are u(T) = 0.5 K; u(pM) = 0.02 MPa; ur(rη) =1.5%; ur(η) = 1.6 %. b Measured with a reference capillary of 0.6 m length; other measurements made with a reference capillary of 1 m length.

Table 4. Literature Viscosity Data η of Hexadecane at Temperatures T and Pressures p Together With Relative Uncertainties Ur(η).

Author T/K p/MPa η/(µPa∙s) Ur(η) Dymond et al.(1980) 7 298.08 0.10 3078 2 % 298.08 0.70 3109 298.08 4.50 3276 Tanaka et al.(1991) 10 298.15 0.10 3061 2 % 298.15 9.90 3490 Wu et al.(1998) 20 293.15 0.10 3447 0.1% 298.15 0.10 3061 Lal et al.(2000) 21 298.15 0.10 3039 1 % Dubey and Sharma (2008) 22 298.15 0.10 3041 0.1% 303.15 0.10 2706 Prak et al.(2013) 23 293.15 0.10 3440 0.3 % 303.15 0.10 2720 Mohammed et al.(2017) 13 298.36 1.08 3109 2 % 298.36 10.01 3497

The parameters a, b and c in eq (3) are reported in Table 5 along with the average absolute relative deviation ΔAAD and the maximum absolute relative deviation ΔMAD. Figure 3 compares the literature data from Table 4 with eq (3) and shows that the deviations are within the claimed uncertainties. Eq 3 is thereby validated for pressures between (0.1 and 10) MPa and temperatures between (293.15 and 303.15) K.

Table 5. Parameters a, b and c in Equations 3 and 4 for the Viscosity at Reference Conditions and the Viscosity Ratio, respectively, and Values of the Relative Standard Deviation σr, Average Absolute Relative Deviation ΔAAD, and the Maximum Absolute Relative Deviation ΔMAD.

Equation a b c σr ΔAAD ΔMAD 3 15.1323 -0.02384 0.01385 0.5 % 0.4 % 0.7 % 4 3.58087 3.11161 -0.13897 1.0 % 0.7 % 2.5 %

4000 (a) s)

⋅ 3500 Pa µ /(

η 3000

2500 0.8 (b) 0.4

η /

Δ 0.0 2 10

-0.4

-0.8 0.01 0.1 1 10 p/MPa

Figure 3. (a) Viscosities η and (b) relative deviations Δη/η = (ηlit – ηcalc)/ηcalc of literature viscosities ηlit from the values ηcalc calculated from equation (3) as functions of pressure p. Literature data: , Dymond et al.7; , Tanaka et al.10; , Wu et al.20; , Lal et al.21; , Dubey and Sharma22; , Prak et al.23 , Mohammed et al.13 Calculated viscosities: – ∙ – ∙ –, T = 293.15 K; – – – –, T = 298.15 K; ————, T = 303.15 K.

9 Values of η(T0,p) calculated from eq (3) are listed in Table 3, together with the absolute viscosities obtained by combining these values with the measured viscosity ratios at each state point investigated. The viscosities are plotted as a function of inverse temperature along isobars in Figure 4. From the near linearity of the isobars on the semi-logarithmic scale, it is clear that hexadecane behaves as a ‘first-order’ fluid over most of the temperature range investigated. Furthermore, the spacing of the isobars demonstrates that the effect of pressure is very modest, except at the higher temperatures where the free volume is larger and the 24 viscosity-pressure coefficient αη = (∂lnη/∂p)T increases. Nevertheless, it is well established that the viscosity of dense liquids can be represented precisely as a function of relative 25 density. In the present case, we see that the viscosity ratios r  (,)/( Tp T0 ,) p can be represented as a function of the density ratio (,)Tp ( T0 ,) p alone. This is illustrated in Figure

5(a) where we plot rη against /  (,)/(,)Tp  T p, with T0 = 298.15 K. The curve shown in TT0 0 Figure 5(a) is calculated from the following empirical relation:

ax bx2   r  exp  (4)  cx 

in which

x1 (,) Tp ( T0 ,) p. (5)

2560

1280

640 s) ⋅

320 / (µPa

160

80 0.4 0.5 0.6 0.7 0.8 0.9 1.0 T0/T

Figure 4. Viscosity η of hexadecane as functions of the inverse temperatures ratio T0/T along isobars: black, p = 1 MPa; red, p = 2 MPa; blue, p = 3 MPa; green, p = 4 MPa. Curves calculated from equations 4 and 5 with parameters from Table 5.

The parameters of eq (4) were fitted to the experimental data, making use of density ratios calculated from the equation of state of Romeo and Lemmon et al.,19 and the values are given

in Table 5, along with ΔAAD and ΔMAD. Figure 5(b) shows the deviations of the experimental

10 data from this correlation and demonstrates that it fits the data to within the expanded uncertainty. Eq 4 with the parameters in Table 5 is valid at temperatures between (298.15 and 723.15) K and at pressures up to 4 MPa.

1.00 (a) η r 0.10

0.01 4 (b)

η 2 r )/ η r 0 ( ∆ 2

10 -2

-4 0.5 0.6 0.7 0.8 0.9 1.0 ρT /ρT 0

Figure 5. (a) Experimental viscosity ratios rη as a function of density ratio ρT/ρT0 for hexadecane (); black continuous curves calculated with equation 4 with parameters from Table 5; (b) relative deviations Δrη/rη = (rη − rη,calc)/rη between experimental viscosity ratios, rη,exp and values rη,calc calculated from equation 4 with parameters from Table 5: ---, ± 1.5 %.

Absolute viscosities can be obtained at specified temperature and pressure by combining rη from eq 4, where x is calculated from the equation of state, with the corresponding value of

η(T0, p) calculated from eq (3). Figure 6 compares the available literature data for the viscosity of hexadecane at p ≤ 7 MPa with this model. The data of Gouel5 were not considered in the analysis since uncertainties of their measurements were about 5 %. It is clear that our experimental results are in generally good agreement with the majority of the literature data; an AAD of 2 % was obtained across all literature sources plotted in Figure 6. However, the data of Matthew et al.9 deviate significantly at temperatures above 500 K. The rest of the literature data with deviation higher than 3 % were measured at pressure above 4 MPa.

8.0

6.0

4.0

2.0 η /

∆ 0.0 2 10 -2.0

-4.0

-6.0

-8.0 300 400 500 600 700 T/K

Figure 6. Relative deviations Δη/η = (ηexp − ηcalc)/ηcalc of experimental viscosities of hexadecane from those calculated from eqs 3 and 4 with densities fromt equation of state of Romeo and Lemmon et al.,19: , this work; , Rastorguev and Keramidi 11 (re , Dymond et al.;7 , Ducoulombier et al.;8 , Matthews et al.;9 , Tanaka et al.;10 , Rolling and Vogt;24 , Rajagopal et al.;11 , Baled et al.;12 , Mohammed et al.13

CONCLUSION The viscosities of liquid hexadecane were measured using a dual-capillary viscometer at temperatures between (323 and 673) K and pressures between (0.1 and 4.0) MPa, thereby substantially extending the temperature range of existing data. The combined expanded relative uncertainty of the results was estimated to be 3.2 % at 95 % confidence. A new correlation was developed as a function of relative density and this fitted the data within the reported uncertainty, with an average absolute relative deviation of 1 %. These results agree well with existing literature data with an average absolute relative deviation 2 % of across all selected literature sources. The experimental data obtained here may be useful in the development of a more wide-ranging correlation for the viscosity of hexadecane.26

Acknowledgement This work was carried out as part of the Qatar Carbonates and Carbon Storage research Centre (QCCSRC). The authors gratefully acknowledge the funding of QCCSRC provided

12 jointly by Qatar Petroleum, Shell, and the Qatar Science & Technology Park and for supporting the present project and the permission to publish this research.

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