Investigation on the solidification of several pure cyclic and aromatic hydrocarbons at pressures to 300 MPa

Fuel 111 (2013) 75–80

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Investigation on the solidification of several pure cyclic and aromatic hydrocarbons at pressures to 300 MPa Yue Wu ⇑, Kun Liu, Babatunde A. Bamgbade, Mark A. McHugh National Energy Technology Laboratory, Office of Research and Development, Department of Energy, Pittsburgh, PA, USA Department of Chemical and Life Science Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA

h i g h l i g h t s  A technique for solidification determination at high pressures.  High-pressure solidification data reported for cyclic and aromatic hydrocarbons.  Experimental data well represented by quadratic and Simon equations.

a r t i c l e

i n f o

Article history: Received 20 December 2012 Received in revised form 30 March 2013 Accepted 24 April 2013 Available online 9 May 2013 Keywords: Melting points Saturated cyclic hydrocarbon Xylene Aromatic High pressure

a b s t r a c t The effect of pressure on the solidification of several saturated cyclic hydrocarbons and three xylene isomers are experimentally determined with a variable-volume view cell at pressures to 300 MPa and temperatures starting at 293.15 K. Solid–liquid transitions are observed for cyclooctane, cis-1,2-dimethylcyclohexane, trans-1,4-dimethylcyclohexane, p-xylene, o-xylene, and 2-methylnaphthalene. However, methylcyclohexane, ethylcyclohexane, cis-1,4-dimethylcyclohexane, and m-xylene remained liquid over the same operating pressure and temperature ranges. The experimental solid–liquid transition data are well represented with two empirical equations, the Simon equation and a 2nd-order polynomial equation. Data obtained in this study agree with literature data within ±0.4% for 2-methylnaphthalene and ±0.2% for p-xylene. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The undesired formation of solid deposits in crude and lube oils leads to problems in their storage, transportation, and end use since these deposits can clog processing lines, which can subsequently damages sensitive equipment [1]. Several methods are used to suppress the formation of solid crystals when processing crude and lube oils [2–7]. For example, Ray et al. [7] found that the pour point of a lube oil depends on the distribution and average chain length of the n-alkanes in solution and also on the other compounds in solution, such as aromatics and iso-paraffins, that can inhibit wax crystal formation. Applied hydrostatic pressure is another factor that determines the solidification temperatures of hydrocarbons and their mixtures. Higher pressure results in a higher solidification temperature for a pure hydrocarbon [8]. However, it should be noted that an increase in pressure could cause a decrease in the solidification temperature if the hydrocarbon is a ⇑ Corresponding author. Address: Department of Chemical and Life Science Engineering, Virginia Commonwealth University, 601 West Main St., Richmond, VA 23284, USA. Tel.: +1 804 822 7136. E-mail address: [email protected] (Y. Wu). 0016-2361/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.fuel.2013.04.067

mixture rather than a pure component [8–16]. A number of studies investigated the composition effect with a binary mixture of a normal alkane with a cyclic or aromatic hydrocarbon at a constant pressure [11,17]. The solidification temperature first decreases to a minimum value (eutectic point) and then increases with the increase in the mole fraction of one component. For example, the solidification temperature decreases by 5 K when adding 3 mol% (i.e. 6 wt%) tridecane to cyclohexane at 300 MPa [17]. Given that the temperatures and pressures in an ultra-deep petroleum reservoir can reach as high as 533 K (260 °C) and 275 MPa, respectively [18], it is reasonable to expect that many of the hydrocarbon compounds in the petroleum reservoir could form solid deposits during the petroleum recovery process [19]. Hence, high-pressure solid–liquid phase transition data for heavy n-alkane, cyclic, and aromatic hydrocarbons provide fundamental information needed to determine the operating conditions that promote the formation of waxes in petroleum reservoirs. Purecomponent solidification data are also valuable from the perspective of modeling. Several thermodynamic models for the formation of wax have been reported for petroleum component mixtures [8,12,20–26] and the verification and improvement of these

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models requires pure component solidification temperature–pressure data similar to the data reported here. There is a substantial amount of literature [1,10–12,14,17,27– 31] reporting high-pressure solid–liquid phase equilibrium data for n-paraffins up to carbon number 60. These studies also report that the solid crystal structure of an n-paraffin depends not only on the number of carbons in the paraffin but also whether the number of carbons is odd or even [4,8,20,32,33]. There are fewer available literature studies on the effect of pressure on the solidification behavior of cyclic and aromatic hydrocarbons with the exception of several high-pressure studies on cyclohexane and benzene [9,11,17,34]. To the best of our knowledge there are no reported solid–liquid phase behavior data for cyclooctane (cycloC8), cis-1,2-dimethylcyclohexane (cis-1,2-dimethylcC6), and trans-1,4dimethylcyclohexane (trans-1,4-dimethylcC6) above 0.1 MPa, and for 2-methylnaphthalene (2-MN) above 200 MPa, which are compounds investigated in this study. There are a limited number of xylene solidification studies reported in the literature but these studies are constrained to pressures below 100 MPa. However, Bridgman [35] does report solid– liquid phase equilibrium data for xylene isomers at 298 K (25 °C) and 348 K (75 °C) and pressures to 539 MPa, although Bridgman characterized these data as ‘‘approximate values’’ [35]. Isaacs [36] reports solid–liquid phase transition data for p-xylene to 228 MPa, m-xylene to 354 MPa, and o-xylene up to 251 MPa, although the data for each of these xylenes are determined at only three temperatures. In the present study, a high-pressure, variable-volume view cell is used to determine the solid–liquid phase boundary of pure cycloC8, methylcyclohexane, ethylcyclohexane, cis-1,2-dimethylcC6, cis-1,4-dimethylcyclohexane, trans-1,4-dimethylcC6, p-xylene, mxylene, o-xylene, and 2-MN to pressures of 300 MPa and at temperatures starting at 293 K. The experimental solid–liquid phase transition data are fit to two empirical equations, the Simon equation and a 2nd-order polynomial equation, which facilitates a comparison to available literature data for p-xylene and 2-MN. 2. Experimental 2.1. Materials Cyclooctane (P99 wt% purity), methylcyclohexane (P99 wt% purity), ethylcyclohexane (P99 wt% purity), cis-1,2-dimethylcyclohexane (99 wt% purity), cis-1,4-dimethylcyclohexane (99 wt% purity), trans-1,4-dimethylcyclohexane (P98 wt% purity), p-xylene (P99 wt% purity), o-xylene (P99 wt% purity), m-xylene (P99 wt% purity), and 2-methylnaphthalene (97 wt% purity) were purchased from Sigma–Aldrich. All of the chemicals were used as received. 2.2. Experimental procedure Solid–liquid phase transitions are measured visually using a high-pressure, variable-volume cell (Nitronic 50, 7.0 cm OD  1.5 cm ID, 15 cm3 working volume) shown in Fig. 1 and described in detail elsewhere [18,37]. The internal volume of the cell is adjusted with a pressure generator that injects water behind the oring-sealed piston. The cell is loaded with the hydrocarbon of interest and the gas volume in the cell is eliminated by moving the piston forward until liquid hydrocarbon is ejected from the top port of the cell. The cell contents are viewed on a TV monitor using a camera (Olympus Corporation, model STC-N63CJ) connected to a borescope (Olympus Corporation, model F100-024-000-55) placed against a sapphire window secured at one end of the cell. This apparatus allows for visual determination of any water leakage

Fig. 1. Schematic diagram of the high-pressure view cell system used in this study.

around the piston o-ring since water has a very small solubility in the hydrocarbons considered in this study. If water is detected, the apparatus is disassembled, cleaned, and reloaded. The temperature of the fluid inside the cell, held constant to within ±0.2 K, is measured with a type-k thermocouple calibrated against an immersion thermometer (Fisher Scientific, precision to ±0.1 K, accurate to better than ±0.1 K, recalibrated by ThermoFisher Scientific Company at four different temperatures using methods traceable to NIST standards). The system pressure is measured on the water side of the piston with a pressure transducer (Viatran Corporation, Model 245, 0–345 MPa, accurate to ±0.35 MPa) and, therefore, a correction of one bar is added to the reported pressure to account for the pressure needed to move the piston [18,37]. The transducer is recalibrated at pressures to 55 MPa using a Heise pressure gauge (Heise Corporation, Model CC, 0–68.9 MPa, accurate to ±0.07 MPa). Therefore, the transducer is considered accurate to ±0.07 MPa to pressures of 55 MPa and to ±0.35 MPa for pressures from 55 to 300 MPa. Initially the temperature and pressure is adjusted until the hydrocarbon liquid phase in the cell is clear. The pressure is then isothermally increased and held constant for approximately 10 min. If the liquid remains clear, the pressure is increased until it becomes opaque and solid crystals are observed. The pressure is then decreased to obtain a clear liquid phase. This process is repeated until the interval between a clear phase and one where the solution becomes slightly opaque and contains solid crystals is less than 0.34 MPa. This procedure is repeated at a new temperature to determine the new solidification pressure. 3. Results and discussion 3.1. Experimental data Tables 1 and 2 list the solidification data for cycloC8, cis-1,2dimethylcycC6, trans-1,4-dimethylcC6, p-xylene, o-xylene, and Table 1 Solidification data for cycloC8, cis-1,2-dimethylcC6, and trans-1,4-dimethylcC6 obtained in this study. The temperature uncertainty is 0.1 K and the pressure uncertainty is 0.07 MPa below 55 MPa and 0.35 MPa from 55 to 300 MPa. CycloC8

cis-1,2-DimethylcycloC6

trans-1,4-DimethylcycloC6

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

18.4 63.4 103.7 143.5 196.2 247.6 300.8

294.9 314.9 333.5 351.4 373.8 394.4 413.4

202.7 212.4 217.2 219.9 230.2 242.2

295.7 298.6 300.5 301.5 304.8 309.1

172.1 181.3 193.5 199.3 216.0 227.9 236.7 252.3 266.7 273.3

295.2 298.3 302.1 303.9 309.1 312.6 315.6 320.3 324.5 326.3

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2-MN in the temperature range of 293 to 413 K and pressures to 300 MPa. Solid–liquid phase transitions are not observed for methylcyclohexane, ethylcyclohexane, cis-1,4-dimethylcyclohexane, and m-xylene when operating at the same the temperature and pressure ranges. Table 3 compares the data obtained in this study to available literature data and the experimental methods used to determine the solidification boundary. The abbreviations of the experimental methods are those used by Fonseca et al. [38]. SynVis means phase transition determination with visual observation, while SynNon means phase phase transition determination without visual observation. For example, the present study uses the SynVis method. In contrast, Takagi [39] determined the solidification boundary using an ultrasonic method, which is a SynNon method. Isaacs [36] did not report the method used to determine solidification data, hence ‘‘N/A’’ is used in the table. It should be noted that several researchers, such as Bridgman [35] and Isaacs [36], only reported two or three solidification temperatures at high pressures, which limits the accuracy of their solidification temperatures estimated at other pressures. Note, also, that this table does not list literature data that only report solidification temperatures at atmospheric pressure. In contrast, there are a fair amount of solid–liquid literature data for 2-methyl naphthalene and p-xylene to compare to the data obtained in this study, as shown in the next paragraphs.

Fig. 2 shows the solid–liquid data for 2-MN obtained in this study are in good agreement with literature data. Kulkarni et al. [43] report data to within ±0.1 K and ±1.3 MPa, Nagaoka and Makita [41,44] report data to within ±0.1 K and ±0.5 MPa, and although Yokoyama et al. [45] also report data for 2-MN, they do not report any accuracy for the temperatures and pressures. Fig. 3 shows the solid–liquid data for p-xylene obtained in this study are in good agreement with literature data. Castro et al. [40] report data to within ±0.01 K and ±0.01 MPa, Isaacs [36] reports data with no accuracy on the temperatures and pressures, Nagaoka and Makita [41,44] report data to within ±0.1 K and ±0.5 MPa, and Takagi [39] also report data without any accuracy listed for the temperatures and pressures. Although the comparisons in Figs. 2 and 3 show very good agreement between literature data and data obtained in the present study for these few compounds, a more meaningful comparison can be made using a deviation graph showing the percent deviation between the two sets of solidification data. To facilitate the construction of a deviation graph, the experimental solidification temperatures obtained in this study are fit to a quadratic function of pressure so the data reported here can be compared directly to literature data at any temperature and pressure. Likewise, deviation graphs are constructed using the Simon equation fit to data obtained in the present study. The deviation graphs are presented in the next section of this paper. 3.2. Correlations

Table 2 Solidification data for p-xylene, o-xylene, and 2-MN obtained in this study. The temperature uncertainty is 0.1 K and the pressure uncertainty is 0.07 MPa below 55 MPa and 0.35 MPa from 55 to 300 MPa. p-Xylene

o-Xylene

2-MN

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

26.9 53.3 87.8 120.3 150.5 185.5 213.1 226.8 246.3 261.4

295.1 304.0 315.2 325.6 335.0 345.6 353.8 357.7 363.2 367.1

210.2 211.6 212.4 220.6 223.4 223.7 223.8 228.4 238.5 243.7 251.0 262.5

295.0 295.4 295.6 297.4 298.1 298.2 298.3 299.4 301.9 303.1 304.7 307.1

19.2 30.1 52.3 77.2 124.1 153.9 188.1 209.2 227.8 245.1 265.6

312.3 314.8 320.3 326.4 339.1 346.4 355.0 359.6 364.2 368.1 372.6

3.2.1. Simon equation The Simon equation, shown in Eq. (4), is a popular empirical equation used to describe the relationship between solidification temperatures and pressures [45–47].

 c P  P0 T ¼ 1 T0 a

ð1Þ

where P is the system pressure in MPa, P0 is the ambient pressure equal to 0.1 MPa, T and T0 are solidification temperatures in K at pressures P and P0, respectively, and a and c are fitted parameters. The parameters in Eq. (1) are listed in Table 4 together with the absolute average deviation (AAD, Eq. (2)) and absolute average percent deviation (AAPD, Eq. (3)) for the solidification data obtained in this study. Note that the maximum AAD and AAPD values are 0.55 K and 0.16%, respectively, for the fit of solid–liquid transition data for these six compounds.

Table 3 Comparison of the solid–liquid transition data obtained in this study to that available in the literature. Literature

p-Xylene Bridgman [35] Castro et al. [40] Isaacs [36] Nagaoka and Makita [41,42] Takagi [39] o-Xylene Bridgman [35] Isaacs [36]

Literature data points

Literature temperatures (K)

Literature maximum pressure (MPa)

Literature experimental method

Pressures (MPa) for solid–liquid transition data obtained in this study differing from literature data

2 20 3 4 1

303.2, 348.2 285.3–297.7 298.2, 319.2, 353.2 293.2–323.2 303.2

186a 38 228 114 52

SynNon SynNon N/A SynVis SynNon

186 < P < 260 38 < P < 260 228 < P < 260 114 < P < 260 52 < P < 260

2 3

303.2, 348.2 269.7, 298.2, 303.2

539a 251

SynNon N/A

P < 263 251 < P < 263

203 137 155

SynVis SynVis SynVis

203 < P < 266 137 < P < 266 155 < P < 266

2-MN Kulkarni et al. [43] 3 323.2, 342.4, 357.2 Nagaoka and Makita [44] 5 308.2–343.2 Yokoyama et al. [45] 3 307.1–347.6 CycloC8, cis-1,2-DimethylcC6, and trans-1,4-DimethylcC6 No available data at P > 0.1 MPa a

The pressure is an approximate value [35].

P < 300

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Y. Wu et al. / Fuel 111 (2013) 75–80 Table 4 Values for the solidification temperature at ambient pressure, T0 [48], coefficients of the Simon equation (Eq. (4)), a and c, and the absolute average deviation (AAD, Eq. (2)) and the absolute average percent deviation (AAPD, Eq. (3)). CycloC8

Fig. 2. Solidification behavior of 2-MN to high pressures. The filled symbols represent the experimental data obtained in this study (d). The open symbols are literature data from Kulkarni et al. [43] (h), Nagaoka and Makita [44] (s), and Yokoyama et al. [45] (4). The solid line is used to guide the eyes.

AAD ¼

1 n

AAPD ¼

n X

jT exp  T calc j

ð2Þ

i¼1

n 1X jT exp  T calc j  100% n i¼1 T exp

ð3Þ

where Texp is the experimental solidification temperature, Tcalc is the calculated solidification temperature using the quadratic equation, and n is the number of data points. Fig. 4 shows the deviation graph with the percent deviation between calculated and available literature data for 2-MN. The percent deviation varies uniformly around the zero baseline for all pressures and is within ±0.5% except for one data point at approximately 70 MPa, verifying the good fit of the data obtained in this study to that available in the literature. This deviation graph confirms the good agreement with lower pressure data reported in previous studies by Kulkarni et al. [43], Nagaoka and Makita [44], and Yokoyama et al. [45]. Fig. 5 shows the deviation graph with the percent deviation between calculated and available literature data for p-xylene. The percent deviation varies uniformly around the zero baseline for all pressures and is within ±0.2%, except for the study by Castro et al. [40] whose data are always 0.4–0.8% lower than the data obtained in this study. As previously mentioned, Castro et al. [40] report temperatures within ±0.01 K and pressures within ±0.01 MPa

Fig. 3. Solidification behavior of p-xylene to high pressures. The filled symbols represent the experimental data obtained in this study (d). The open symbols are literature data from Castro et al. [40] (s), Isaacs [36] (h), Nagaoka et al. [41] (4), and Takagi et al. [39] (}). Note that there is only one data point from Takagi et al. [39], which overlays the data of this study at 52 MPa.

cis-1,2DimethylcycloC6

trans-1,4DimethylcycloC6

T0 (K) a (MPa) c AAD (K) AAPD (%)

285.0 316.2 1.786 0.55 0.16

223.1 367.5 1.558 0.16 0.05

236.2 374.5 1.692 0.08 0.02

T0 (K) a (MPa) c AAD (K) AAPD (%)

p-Xylene 286.4 441.7 1.859 0.16 0.05

o-Xylene 248.0 1050.6 1.046 0.17 0.06

2-MN 307.7 762.7 1.554 0.23 0.07

for p-xylene system. It is unlikely that this deviation comes from of the impurity in p-xylene samples in the study by Castro et al., who reported a p-xylene purity of 99.6%, which we presume is a weight percentage. If the impurity has a similar chemical structure to pxylene, the p-xylene + impurity should form an ideal liquid mixture. If we further assume that the amount of the impurity is 0.4 mol%, not 0.4 wt%, the melting point depression, DT, is estimated to be less than 0.2 K following the equation in Sandler’s book [49], which is 0.06% of the p-xylene solidification temperature at 0.1 MPa and will be even lower at higher pressure. Given that the percent deviation ranges from 0.4% to 0.8% between Castro’s data and the data obtained in the present study, it is unreasonable to assume the low concentration of impurity causes such a large deviation from our experimental results. The reason for the consistent deviation with Castro’s data is still not apparent especially given that the present data are within ±0.2% of the other literature data shown in Fig. 5 [36,39,41]. 3.2.2. Quadratic equation Over a modest pressure range the solid–liquid phase transition temperature of a pure substance can be fit to a quadratic function in pressure shown in Eq. (4) [9,11,36]. The quadratic equation is fit to experimental data of each hydrocarbon obtained in this study and to literature data for solidification at 0.1 MPa [48].

T ¼ A0 þ A1 P þ A2 P 2

ð4Þ

where T is the phase transition temperature in K, P is pressure in MPa, and A0, A1, and A2 are empirical coefficients. The three coeffi-

Fig. 4. Percent deviation of solidification temperatures obtained in the present study represented with the Simon equation, Tcorr, to available literature data, Tlit, of Nagaoka and Makita [44] (j), Kulkarni et al. [43] (d), and Yokoyama et al. [45] (N) for 2-MN.

Y. Wu et al. / Fuel 111 (2013) 75–80

Fig. 5. Percent deviation of solidification temperatures obtained in the present study represented with the Simon equation, Tcorr, to available literature data, Tlit, of Castro et al. [40] (d), Isaacs [36] (j), Nagaoka et al. [41] (N), and Takagi et al. [39] () for p-xylene.

cients can be found in the Supplementary data section along with AAD and AAPD for each hydrocarbon considered in this study. The section also shows the percent deviation of the data calculated with the quadratic equation from the available literature data for 2-MN and p-xylene, respectively. The empirical quadratic equation adequately represents the effect of pressure on the melting point given the small values for AAD and AAPD. Unfortunately it is not apparent how to estimate values for A0, A1, and A2, which obviates the predictive capabilities of this approach. The trends observed with the fit of the Simon equation are also observed with the fit of the quadratic equation as shown in the percent deviation graphs in the Supplementary data section. The percent deviation between the 2-MN data calculated with the Simon equation and literature data is within ±0.4% except for one data point at 70 MPa. The percent deviation for p-xylene is within ±0.2% except for the data reported by Castro et al. [40]. As previously mentioned, there appears to be no apparent reason for the discrepancy with the data of Castro and coworkers. 4. Conclusion To improve our understanding of the solution behavior of petroleum fluids in ultra-deep reservoirs at extreme pressures and temperatures, solidification temperatures of pure cycloC8, cis1,2-dimethylcC6, trans-1,4-dimethylcC6, p-xylene, o-xylene, and 2-MN are reported to pressures of 300 MPa. The Simon equation and empirical quadratic equation are fit to the data and they provide a means to estimate solidification conditions within the range presented in this study. Acknowledgments This technical effort was performed in support of the National Energy Technology Laboratory’s Office of Research and Development support of the Strategic Center for Natural Gas and Oil under RES Contract DE-FE0004000. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.fuel.2013.04.067. References [1] Machado JJB, de Loos TW, Ihmels EC, Fischer K, Gmehling J. High pressure solid–solid and solid–liquid transition data for long chain alkanes. J Chem Thermodyn 2008;40:1632–7.

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