On the Critical Points of Thermally Cracked Hydrocarbon Fuels under

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On the Critical Points of Thermally Cracked Hydrocarbon Fuels under High Pressure Rongpei Jiang, Guozhu Liu,* Zhiqiang You, Mingjian Luo, Xuqing Wang, Li Wang, and Xiangwen Zhang Key Laboratory for Green Chemical Technology of Ministry of Education, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, PR China

bS Supporting Information ABSTRACT: Thermal cracking of a series of model compounds (n-octane, n-decane, n-dodecane, cyclohexane, methylcyclohexane), as well as a commercial Chinese jet fuel RP-3, was performed in a flowing reactor consisting of an electrically heated tube under a pressure of 5 MPa to obtain the chemical compositions of the cracked hydrocarbon fuels at different levels of cracking conversion. The phase envelopes and critical points of the cracked hydrocarbon fuels were calculated using the PengRobinson and SoaveRedlichKwong equations. The calculation results showed that the critical points for cracked hydrocarbon fuels are strongly dependent on the hydrocarbon type and cracking conversion and that the critical temperature of cracked fuel decreases but the critical pressure increases sharply from 24 to above 10 MPa because of the appearance of many small-molecule products. Therefore, phase changes of the hydrocarbon fuel from compressed liquid phase to supercritical phase and then to gas phase possibly occurred in the electrically heated tube reactor when the cracking conversions exceeded 30%. Based on the calculation results, the supercritical cracking of hydrocarbon fuels should be carefully used at higher cracking conversions of hydrocarbon fuels under high pressure.

’ INTRODUCTION Liquid hydrocarbon fuel, except for its conventional role as a propellant to provide a power source, is taken as an ideal coolant for fuel-cooled thermal management systems to remove large amounts of heat in advanced aircraft through both physical heating (heat absorption) and chemical reaction (cracking and dehydrogenation).13 Under these conditions, the hydrocarbon fuel is heated to very high temperature (typically >500 °C) at high pressure (3.57 MPa), resulting in its decomposition into small molecules, such as methane and ethylene.4 Typically, the critical temperature and pressure of hydrocarbon fuels used in aircraft are in the ranges of 370415 °C and 1.73.3 MPa, respectively.5 Because the working temperature and pressure for fuel are higher than the corresponding critical point, the supercritical-cracking concept was proposed and widely accepted by researchers.6,7 Recently, several groups studied the supercritical-cracking behavior of hydrocarbons and found that supercritical-cracking mechanisms show dramatic differences from those of conventional cracking. Yu and Eser published a series of articles on the thermal decomposition of several hydrocarbons in the near-critical and supercritical regions and reported that the decomposition mechanism exhibits a large pressure dependence in the near- and supercritical regions.811 Similarly, Wang et al. studied the pyrolysis of the hydrocarbon fuel ZH-100 under different pressures (0.1, 1.5, 2.5, and 3.5 MPa) and found that the maximum conversion occurred at 1.5 MPa, which is near the critical pressure of ZH-100.12 They explained this result as possibly arising from a longer residence time for cracking because of the higher density of the fuel around the critical point. Stewart et al. studied the product distribution and cracking reaction mechanism of methylcyclohexane at supercritical pressure and observed that large amounts of ring-contraction products were formed because of the “cage” r 2011 American Chemical Society

effect in the high-density/supercritical environment.13 In addition, supercritical hydrocarbons also influence coke formation in the catalytic cracking process through the in situ extraction of coke precursors. Dardas and Moser investigated the cracking of n-heptane over Y-type zeolite under supercritical and subcritical conditions and observed a significant stabilization of the catalyst under supercritical conditions because of the enhanced extraction of coke within the micropores of the catalyst.1416 More recently, Xian et al. carried out the catalytic cracking of n-dodecane over ZSM-5 zeolite catalyst at 400450 °C under supercritical and subcritical conditions (0.14.0 MPa) and developed a kinetic model with a novel catalyst decay function incorporating the effect of the supercritical extraction of coke precursors. Their results indicated that extraction is significant in the near-critical region (400 °C) and insignificant in the far-supercritical region (450 °C).17 Moreover, the heat-transfer, injection, and combustion behaviors were also strongly dependent on the phase state of the hydrocarbon fuel because of the unique properties of supercritical fluids: liquid-like densities with gas-like diffusivities and viscosities.1821 In this view, it is very necessary to understand the phase state of fuel during high-pressure cracking. So far, it remains a challenge to study the phase behavior of the complexity of multicomponent reaction mixtures because of considerable difficulties in making in situ measurements. To date, very few reports have been published on the critical points of the reaction mixtures. Ke et al. investigated the critical point during the hydrogenation of propylene in supercritical CO2, consisting of the four components CO2 (solvent), C3H8 (product), Received: April 28, 2011 Accepted: June 16, 2011 Revised: June 13, 2011 Published: June 16, 2011 9456

dx.doi.org/10.1021/ie200885p | Ind. Eng. Chem. Res. 2011, 50, 9456–9465

Industrial & Engineering Chemistry Research

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Table 1. Specification Properties of Commercial Chinese Jet Fuel RP-3 Used in This Work property

value

reactant

method

Pc (MPa)

Tc (°C)

n-C8a

2.49

295.75

GB/T 18842000

n-C10a

2.11

344.65

D2887

n-C12a

1.83

385.05

109.3

Cyc-C6a

4.07

280.85

10%

143.3

MCHa

3.48

299.85

20%

157.2

RP-3b

2.15

348.16

50%

176.5

density (15 °C), g/mL ASTM distillation, °C IBPa

0.7893

90%

200.7

FBPb

227.4

hydrocarbon type, wt %

a

Table 2. Critical Points for Experimental Reactants

a

SH/T 06062005

normal paraffins total paraffins

39.20 56.80

naphthenes

42.70

aromatics

0.50

total sulfur, ppm

99% were obtained from Kermel Chemical Reagent Co., Ltd. (Tianjin, China). All materials were used as received. The commercial Chinese jet fuel RP-3 was used, and its major specification properties are listed in Table 1. The critical points of the investigated hydrocarbons are listed in Table 2. Thermal Cracking of Fuels in an Electrically Heated Tube Reactor. Cracking experiments were carried out in a flowing reactor consisting of an electrically heated tube as described by Meng et al.26 The hydrocarbon was pumped into the reactor at a rate of 50 mL/min with a P230 high-pressure liquid chromatography pump. Silicon-steel tubes (Restek) with 3.18-mm o.d, a 2.16-mm i.d., and a maximum heating length of 100 cm, were used as tube reactors. The stainless-steel reactor tube was electrically heated by passing a high current through the length of the tube. The system pressure was maintained at 5.0 MPa using a back-pressure regulator. Usually, the inlet temperature of the fuel was kept at 45 °C, and the outlet temperatures were measured by type-K thermocouples. The wall temperature was also measured by type-K thermocouples welded at 5-cm intervals along the outside of the tube. The cracked fuel was quenched to ca. 30 °C by a water-cooled heat exchanger and then flowed into a gasliquid separator. The gaseous products were analyzed online, and the liquid products were analyzed off-line. Analysis Methods. The gaseous products were analyzed online with an Agilent 3000A Micro gas chromatograph equipped with three analytical columns. The parameters of the Micro GC instrument are summarized in Table 3. The gaseous products were identified and quantified by comparison with standard gas samples. The deviation in the analysis of the gaseous products 9457

dx.doi.org/10.1021/ie200885p |Ind. Eng. Chem. Res. 2011, 50, 9456–9465


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was less than 1.5%. The liquid products were qualitatively determined with an Agilent 5795 gas chromatography/mass spectrometry (GC/MS) system. An Agilent 7890A gas chromatograph equipped with a paraffinolefinnaphthenearomatic (PONA) capillary column (50 m 200 μm 0.5 μm), and a flame ionization detector (FID) was used to quantitatively analyze the compositions of the cracked hydrocarbons. The conversion of pure hydrocarbon is defined as the mass fraction of hydrocarbon reacted with respect to the amount fed. For the complex composition of the real jet fuel, RP-3, the conversion/gas yield is defined as the ratio of the mass of gaseous products to the mass of hydrocarbons fed. Estimation of Critical Point Using EOS. The calculations of critical points of hydrocarbon mixtures have been studied extensively in chemical and petroleum engineering.2729 In this study, two popular approaches, the SoaveRedlichKwong equation of state (SRK EOS) and the PengRobinson equation of state (PR EOS), with relatively simple but surprisingly effective models, were applied to determine the critical points of the cracked hydrocarbon mixtures.3032 The PR and SRK EOS are presented here in the forms of eqs 1 and 2, respectively33,34 P¼

RT aðTÞ ðV bÞ V ðV + bÞ + bðV bÞ

ð1Þ

RT aðTÞ ðV bÞ V ðV + bÞ

ð2Þ

P¼

where P is the pressure (Pa); T is the absolute temperature (K); V is the molar volume (m3/mol); R is the gas constant (8.3145 J mol1 K1); and a and b are the energy parameter and the size parameter, respectively. The two parameters for the mixtures were evaluated using the classical one-fluid van der Waals mixing rules a¼

∑i ∑j xi xj ð1 kij Þðai aj Þ0:5

ð3Þ

∑i xi bi

ð4Þ

b¼

Ri ¼ ½1 + mi ð1 Tr 0:5 Þ2

ð5Þ

mi ¼ 0:37646 + 1:54226ωi 0:26992ωi 2

ð6Þ

mi ¼ 0:480 + 1:574ωi 0:154ωi 2

ð7Þ

aci ¼ 0:45724

R 2 Tci 2 Pci

ð8Þ

aci ¼ 0:42747

R 2 Tci 2 Pci

ð9Þ

ai ¼ aci Ri

ð10Þ

where xi is the mole fraction of component i; aci and bi are the pure-substance parameters; Tci and Pci are the pure-substance critical temperature and pressure, respectively; ωi is the acentric factor; and kij represents the binary interaction parameter for the ij pair. Note that parameters mi, aci, and bi for the PR EOS were calculated from eqs 6, 8, and 11, respectively, whereas the same parameters for the SRK EOS were estimated from eqs 7, 9, and 12, respectively. All of the required pure-substance parameters and the binary interaction parameters were taken from the ChemCAD thermodynamics databank, which contains a number of properties of pure components and more than 8000 pairs of binary interaction parameters.35 In this study, we used an efficient algorithm and procedures suggested by Heidemann and Khalil36 to calculate critical points and by Michelsen37 to obtain the phase envelopes (P versus T at fixed composition) for cracked hydrocarbons based on the SRK and PR EOS. To verify the reliability of the calculation method of the critical points using the PR and SRK equations, 55 multicomponent mixtures of hydrocarbons similar to those used in this study (as listed in Table S1 of the Supporting Information), mainly containing hydrogen, paraffins (from methane to n-decane), olefins (ethylene and propylene), and aromatic hydrocarbons (benzene and ethylbenzene), were selected from references to show the predicted accuracy of the PR and SRK EOS, and the results are presented in Table S2 (Supporting Information). Clearly, the average absolute deviations for critical temperature were found to be 0.91% and 1.13% for the PR and SRK EOS, respectively, whereas for critical pressure, the PR and SRK EOS yielded average absolute deviations of 3.45% and 3.57%, respectively. This indicates that both the PR and SRK EOS are reliable in calculating the critical points of hydrocarbon mixtures. Many researchers have observed that the critical pressures of hydrogenhydrocarbon systems show a significant dependence on the content of hydrogen and change dramatically upon addition of hydrogen.23,38,39 Thus, the uncertainty in determining the hydrogen concentration in a cracked fuel composition inevitably gives rise to some estimation errors. In addition, the critical temperature of hydrogen (239.97 °C) is rather low, whereas the calculation temperature is far above its critical temperature, resulting in binary interaction parameters that are unusually large and strongly dependent on temperature.40 Nevertheless, several researchers previously demonstrated that using an EOS to calculate of critical point of hydrocarbon systems containing relatively small amounts of hydrogen is reasonable.22,23,41 In the propylenehydrogen system (Table S2, Supporting Information), for hydrogen contents less than 8.8%, it was found that the average absolute deviation (AAD) for critical pressure as estimated using the PR and SRK EOS was 2.40% and 4.07%, respectively. For hydrogen contents greater than 9.96%, the resulting AAD was as high as 13.55% and 13.01% for the PR and SRK EOS, respectively. Similar results were also found for the ethylenehydrogen system (Table S2, Supporting Information). Because the hydrogen concentration in this study was relatively low (less than 5% for paraffin), it is anticipated that the phase envelopes and critical points calculated using the PR and SRK EOS are acceptable.

bi ¼ 0:077796

RTci Pci

ð11Þ

’ RESULTS AND DISCUSSION

bi ¼ 0:08664

RTci Pci

ð12Þ

Chemical Compositions of Cracked Hydrocarbon Fuels. To obtain the chemical compositions of cracked hydrocarbon fuels, thermal cracking runs of several model compounds, 9458



Figure 1. (a) Conversion and (b) gas yield with exit fuel temperature. (Experimental conditions: 5 MPa, 50 mL/min.)

Figure 2. Gaseous and liquid products for n-C8 with conversion: (a) 9, Hydrogen; b, methane; 2, ethylene; 1, ethane; 0, propylene; O, propane; Δ, n-butane; 3, 1-butene. (b) 9, 1-Pentene; b, 1-hexene; 2, benzene; 1, 1-heptene.

including n-dodecane (n-C12), n-decane (n-C10), n-octane (n-C8), methylcyclohexane (MCH), and cyclohexane (Cyc-C6), as well as RP-3 jet fuel, were carried out in an electrically heated tube reactor under a pressure of 5 MPa. Parts a and b of Figure 1 present the conversions and gas yields, respectively, of the different hydrocarbons as functions of the outlet fuel temperature. As can be seen from the figure, normal paraffins show lower initial cracking temperatures than cycloparaffins. In this study, the initial cracking temperatures for n-C8, n-C10, and n-C12 were found to be 550, 515, and 470 °C, respectively, whereas those for Cyc-C6 and MCH were 625 and 600 °C, respectively. Correspondingly, under identical conditions, the cracking rates of various reactants decreased in the following order: n-C12 > n-C10 > n-C8 > MCH > Cyc-C6. This result is consistent with previous observations.8,42 In addition, the cracking rate of RP-3 was found to be lower than those of normal paraffins but higher than those of cycloparaffins, as can be seen from the comparison of the gas yields of the various fuels (Figure 1b). In this study the chemical compositions of cracked fuels are plotted as a function of conversion. The major gaseous and liquid

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Figure 3. Gaseous and liquid products for n-C10 with conversion: (a) 9, Hydrogen; b, methane; 2, ethylene; 1, ethane; 0, propylene; O, propane; Δ, n-butane; 3, 1-butene. (b) 9, 1-Pentene; b, 1-hexene; 2, n-heptane; 1, benzene; 0, toluene; O, 1-octene; Δ, 1-nonene.

Figure 4. Gaseous and liquid products for n-C12 with conversion: (a) 9, Hydrogen; b, methane; 2, ethylene; 1, ethane; 0, propylene; O, propane; Δ, n-butane; 3, 1-butene. (b) 9, 1-Pentene; b, 1-hexene; 2, benzene; 1, 1-heptene; 0, toluene; O, 1-octene; Δ, 1-nonene; 3, 1-decene; g, 1-undecene.

products are presented here, and detailed compositions of thermal cracked mixture are listed in Tables S3S8 (Supporting Information). It should be noted that more than 30 components were generally identified by GC and used to calculate the critical points of cracked hydrocarbons consisting of reactant and corresponding cracked products. As shown in Figures 2a4a, the major gaseous products for normal paraffins (including n-C8, n-C10, and n-C12) were found to be methane, ethane, ethylene, propylene, propane, and 1-butene. The different gaseous products also exhibited different changing tendencies with increasing conversion. The mole fractions of methane and hydrogen increased monotonically with conversion in the interesting range, whereas propylene and 1-butene tended to level off with increasing conversion because of possible secondary pyrolysis and polymerization reactions. It was expected that the content of ethylene would reach a maximum with increasing conversion, which was not 9459



Figure 5. Gaseous and liquid products for Cyc-C6 with conversion: (a) 9, Hydrogen; b, methane; 2, ethylene; 1, ethane; 0, propylene; O, propane; Δ, n-butane; 3, i-butene; g, 1-butene; 0, 1,3-butadiene. (b) 9, 2-Methyl1-butene; b, 1,3-pentadiene; 2, 1,3-cyclopentadiene; 1, cyclopentene; 0, 1-hexene; O, methylcyclopentane; Δ, 1-methyl-1,3-cyclopentadiene; 3, 3-methylcyclopentene; g, 1,3-cyclohexadiene; 0, cyclohexene.

Figure 6. Gaseous and liquid products for MCH with conversion: (a) 9, Hydrogen; b, methane; 2, ethylene; 1, ethane; 0, propylene; O, propane; Δ, trans-2-butene; 3, 1-butene; g, 1,3-butadiene. (b) 9, 2-Pentene; b, 1,4-pentadiene; 2, benzene; 1, cyclohexene; 0, 4,4-dimethylcyclopentene; O, 4-methylcyclohexene; Δ, toluene; 3, 1-methylcyclohexene.

observed because of limitations on the experimental conditions (coking in the tube reactor) in this study. For cycloparaffins (including MCH and Cyc-C6), the major gaseous products were found to be hydrogen, methane, 1,3-butadiene, ethylene, ethane, propylene, propane, i-butene, and 1-butene, as shown in Figures 5 and 6a. According to Billaud and co-workers, cyclohexane could decompose by dehydrogenation to form cyclohexene and hydrogen or by ring-opening isomerization to form open-chain alkenes, such as ethylene and 1,3-butadiene. It can be seen from Figure 5a that significant amounts of hydrogen and 1,3-butadiene were generated, which is in accordance with the results of Billaud and co-workers.43,44 Figure 6a shows the gaseous products of RP-3 as a function of conversion. Obviously, methane, propylene, ethane, ethylene, propane, 1-butene, hydrogen, n-butane, and 1,3-butene were

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Figure 7. Gaseous and liquid products for RP-3 with conversion: (a) 9, Hydrogen; b, methane; 2, ethylene; 1, ethane; 0, propylene; O, propane; Δ, trans-2-butene; 3, 1-butene; 0, n-butane; 0, 1,3-butadiene. (b) 9, 1-Pentene; b, 1-hexene; 2, 3,3-dimethylcyclobutene; 1, 4-methylcyclopentene; 0, benzene; O, 1-heptene; Δ, toluene; 3, cyclooctane; 0, ethylbenzene.

found to be the major components. Compared with the gaseous products of normal paraffins, the content of methane was observed to be the highest among the gaseous products because of the significant amounts of branched paraffin in RP-3 jet fuels. Similarly, Zamostny et al. also observed that the pyrolysis of branched hydrocarbons leads to significant yields of methane, under standard pyrolysis conditions (810 °C, 400 kPa, and 0.20.4-s residence time).45 The liquid products are also presented in Figures 2b7b. Similarly, only major products were qualitatively identified and presented because of the considerably complicated components of liquid-phase cracked products. The liquid products obtained from the normal paraffins were the series of n-alkanes from C5 to Cn2 (where n is the number of carbons in the reactant molecule) and the series of 1-olefins from C5 to Cn1. These are the major reaction products identified from the chromatograms of the liquid products. Figures 2b4b clearly show that these 1-olefin products exhibited maxima before declining at high conversions. This phenomenon can be explained by possible secondary cracking reactions occurring at high conversion. A similar declining trend for the liquid products of n-dodecane was also observed by other researchers.46,47 Isomeric products representing branched alkanes and internal olefins also appeared in smaller quantities.48 The n-alkane products, as well as these isomeric products, were present as minor reaction products, as reported in Tables S3S8 (Supporting Information). Aromatic components, such as benzene and toluene, were also detected in the liquid products with increasing conversions. However, their contents were negligible in the liquid cracked products of normal paraffins. Compared with the liquid products of normal paraffins, those of cycloparaffins were more complicated because both cracking and dehydrogenation reactions occurred under the experimental conditions employed in this study. The major products of cyclohexane, such as 1,3-pentadiene and 1,3-cyclohexadiene, also showed maxima before declining at high conversions, indicating that these products were also consumed at high cracking conversions. The primary liquid products for methylcyclohexane were cyclohexene, 1-methylcyclohexene, and 4, 4-dimethylcyclopentene, suggesting that the formation of cyclic 9460



Figure 8. (a) Phase envelopes predicted using the PR EOS for cracked n-C8 with different conversions: L1, 549 °C, 5.23%; L2, 563 °C, 11.54%; L3, 578 °C, 15.54%; L4, 610 °C, 35.10%; L5, 633 °C, 52.18%; L6, 643 °C, 59.61%. Solid symbols represent bubble points, whereas open symbols represents dew points. (b) PT projection during the cracking of n-C8 using both the SRK and PR EOS. C1C6 denote corresponding critical points.

hydrocarbons through dehydrogenation reactions was considerable under the high-pressure conditions employed.13 Figure 7b presents the liquid product distribution of RP-3 as a function of conversion. In particular, RP-3 jet fuel was found to be a complex hydrocarbon mixture consisting of hundreds of components. Thus, it was almost impossible to identify each component, and thus, only major components are quantitatively presented here. Similarly, the contents of most liquid products increased and reached maxima before decreasing with increasing conversions. The remarkable character of RP-3 jet fuel was the significant contents of benzene, toluene, and ethylbenzene observed when the cracking conversion was greater than 30%. Phase Envelopes and Critical Points. The phase state of the cracked fuel was characterized by its phase envelope and critical point during the cracking reaction. Vaporliquid phase envelopes for different mixtures were constructed using the efficient algorithm developed by Michelsen,37 which is based on the NewtonRaphson solution of nonlinear equation and can automatically select the most convenient specification variables. The estimated critical points were calculated by the method developed by Heidemann and Khalil,36 who proposed criticality criteria using a Taylor expansion of the Helmholtz energy based on the thermodynamic concepts established by Gibbs. Figures 8a13a present the calculated phase envelopes for the cracked hydrocarbons with different cracking conversions. Typically, the bubble-point line (solid symbols) and the dew-point line (open symbols) are continuous curves meeting at the critical point, as shown in Figures 8a10a, 12a, and 13a. However, for Cyc-C6, the bubble- and dew-point lines are discontinuous at high conversion (see Figure 11a). These results can be attributed to the appearance of large amounts of permanent gas (hydrogen) in the mixtures of cracked hydrocarbons, in which the fraction of hydrogen exceeded 10% when the conversion of Cyc-C6 was higher than 40% (Figure 5a). Because of the extremely supercritical state of hydrogen, as well as the large size difference between hydrogen and hydrocarbon molecules, the phase behaviors of systems containing hydrogen are more complicated than those of hydrocarbon mixtures.38,49 Therefore, calculation of

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Figure 9. (a) Phase envelopes predicted using the PR EOS for cracked n-C10 with different conversions: L1, 388 °C, 1.79%; L2, 494 °C, 2.39%; L3, 518 °C, 4.51%; L4, 549 °C, 6.74%; L5, 573 °C, 18.19%; L6, 583 °C, 21.78%; L7, 592 °C, 28.34%; L8, 601 °C, 36.36%; L9, 611 °C, 43.94%; L10, 618 °C, 49.18%; L11, 619 °C, 49.98%; L12, 627 °C, 56.00%; L13, 631 °C, 57.12%; L14, 632 °C, 58.72%; L15, 637 °C, 63.69%. Solid symbols represent bubble points, whereas open symbols represent dew points. (b) PT projection during the cracking of n-C10 using both the SRK and PR EOS. C1C15 denote corresponding critical points.

Figure 10. (a) Phase envelopes predicted using the PR EOS for cracked n-C12 with different conversions: L1, 409 °C, 2.21%; L2, 450 °C, 3.23%; L3, 474 °C, 5.12%; L4, 512 °C, 8.82%; L5, 543 °C, 13.40%; L6, 568 °C, 25.80%; L7, 585 °C, 38.14%; L8, 599 °C, 50.43%; L9, 608 °C, 56.71%; L10, 611 °C, 60.79%. Solid symbols represent bubble points, whereas open symbols represent dew points. (b) PT projection during the cracking of n-C12 using both the SRK and PR EOS. C1C10 denote corresponding critical points.

critical points for cracked Cyc-C6 with simple mixing rules would inevitably result in some inaccuracy at high cracking conversions. Nevertheless, the calculations indeed gave similar trends of the critical point as cracking proceeded. Figures 8b13b present the PT projections for the cracked hydrocarbon mixtures. Evidently, the critical temperatures predicted with the SRK EOS were slightly higher than those predicted with the PR EOS. However, the differences between predicted critical pressures were negligible. 9461



Figure 11. (a) Phase envelopes predicted using the PR EOS for cracked Cyc-C6 with different conversions: L1, 600 °C, 0.58%; L2, 623 °C, 1.32%; L3, 625 °C, 3.80%; L4, 645 °C, 6.10%; L5, 655 °C, 20.56%; L6, 680 °C, 46.87%; L7, 699 °C, 62.52%. Solid symbols represent bubble points, whereas open symbols represent dew points. (b) PT projection during the cracking of Cyc-C6 using both the SRK and PR EOS. C1C7 denote corresponding critical points.

Figure 12. (a) Phase envelopes predicted using the PR EOS for cracked MCH with different conversions: L1, 523 °C, 0.25%; L2, 593 °C, 3.01%; L3, 623 °C, 8.81%; L4, 638 °C,16.93%; L5, 645 °C, 36.66%. Solid symbols represent bubble points, whereas open symbols represent dew points. (b) Corresponding PT projection during the cracking of MCH using both the SRK and PR EOS. C1C5 denote corresponding critical points.

Figures 14 and 15 describe the variations of the critical temperature, Tc, and critical pressure, Pc, with thermal cracking conversion, illustrating that, for all of the hydrocarbons used in this work, the calculated critical temperature decreased uniformly but the critical pressure increased with increasing cracking conversion. For example, when the conversion of n-C12 increased from 0 to 60.79%, the critical temperature decreased from 385.05 to 240.65 °C, and the critical pressure increased from 1.83 to 9.18 MPa. Because the critical temperatures of light hydrocarbons are lower than those of heavy hydrocarbons, it is anticipated that Tc decreased with increasing conversion because of increased yields

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Figure 13. (a) Phase envelopes predicted using the PR EOS for cracked RP-3 with different conversions: L1, 506 °C, 0.50%; L2, 547 °C, 1.12%; L3, 578 °C, 2.74%; L4, 605 °C, 8.05%; L5, 614 °C, 10.88%; L6, 623 °C, 15.02%; L7, 634 °C, 20.15%; L8, 644 °C,25.76%; L9, 654 °C,31.83%; L10, 666 °C, 36.37%; L11, 671 °C, 38.58%; L12, 686 °C,50.18%. Solid symbols represent bubble points, whereas open symbols represent dew points. (b) PT projection during the cracking of RP-3 using both the SRK and PR EOS. C1C12 denote corresponding critical points.

Figure 14. Critical points of thermally cracked n-C8, n-C10, and n-C12 predicted using the PR EOS: (a) critical temperature, (b) critical pressure.

of light hydrocarbons. On the other hand, the critical pressures of the mixtures usually show maxima greater than the critical pressure of any pure component. Taking n-C10 as an example, at a conversion of 63.68%, the critical pressure was 9.23 MPa, which is higher than those of n-C10 and its pyrolysis products. Actually, similar phenomena were observed for many binary and multicomponent systems because of the interactions of individual components.24,41 Compared to the obvious differences in critical temperatures for different normal paraffins, it was interesting to find that the critical pressures for cracked normal paraffins were almost independent of the number of carbon atoms when the conversion exceeded 20%. This result can be attributed to the similar contents of lighter hydrocarbons at high conversions, as seen Figures 2a4a. Figure 15 presents the variations in critical temperature and pressure for Cyc-C6, MCH, and RP-3 as functions of conversion. It seems that the 9462



Figure 15. Critical points of thermally cracked Cyc-C6, MCH, and RP-3 predicted using the PR EOS: (a) critical temperature, (b) critical pressure.

Figure 16. Phase changes of fuel along the electrically heated tube.

calculated values of both Pc and Tc for RP-3 exhibited steep changes compared to the behaviors of normal and cyclic paraffins. Indeed, the results most possibly arise from the difference in the definition of cracking conversion. From Figure 1a,b, it can be seen that the gas yield is lower than the corresponding real conversion; therefore, it is not surprising that the critical temperature and pressure change more steeply as a function of conversion (gas yield) for RP-3 than for the other samples. Analysis of Phase States of Fuel in the Cooling Channel. As discussed above, we demonstrated that the critical point for cracked hydrocarbons changes significantly during the course of cracking. It is anticipated that hydrocarbon fuels will experience different phase states along the cracking process. Because of the significant effect of phase state on cracking, heat transfer, and other operating issue involving supercritical conditions, it is necessary to determine the phase state of the cracked hydrocarbon fuel in the heat exchanger during cracking. Typically, the operating pressure of a flowing reactor is kept constant as the fuel temperature changes substantially along the reactor, which leads to considerable changes in the compositions and critical points at different positions.26,50 Figure 16 presents the bulk temperature and corresponding conversion of fuel along the tube. Generally, the hydrocarbon fuel passed through three phase regions. In the first region, the

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fuel was fed in the compressed liquid state because the temperature was lower than the critical temperature and the pressure was higher than the critical pressure. As the fuel temperature increased, both the temperature and pressure were greater than the critical point, and the liquid fuel entered the supercritical state. In this region, the system pressure was still higher than critical pressure, even at low cracking conversion. Indeed, the supercritical-cracking concept is restricted to this region. Then, the phase of the fuel eventually turned from supercritical to gas when the critical pressure exceeded the system pressure with increasing conversion. In this study, most model compounds, as well as RP-3, cracked from the supercritical to gas phase when the conversion exceeded 30% at 5 MPa. Previously, supercritical cracking was used to define the thermal or catalytic cracking of hydrocarbons in cooling channels under high pressure (approximately 3.57.0 MPa) even at very high conversions. Therefore, we must state that supercritical cracking should be carefully used at high cracking conversions, where the supercritical fuel enters the gas phase. It is important to note, however, even in the supercritical region where T is much higher than Tc, the existing phase is closer in properties to a gas than to a supercritical phase because it is far from the critical region. It should be noted that several researchers have also referred to initial supercritical conditions for instant pyrolysis in a batch reactor because the critical properties of the reaction products change depending on the changing composition.811

’ CONCLUSIONS This article described how the critical points of cracked hydrocarbon mixtures change as the reaction proceeds. High-pressure thermal cracking of a series of model compounds (n-octane, n-decane, n-dodecane, cyclohexane, and methylcyclohexane), as well as a real No. 3 Chinese jet fuel, were performed in a flowing reactor consisting of an electrically heated tube to obtain the chemical compositions of cracked hydrocarbons. The Peng Robinson (PR) and SoaveRedlichKwong (SRK) equations of state were used to calculate the phase envelopes and critical points of the cracked fuels at different cracking conversions. The calculation results clearly show that the critical temperatures of the cracked fuels generally decreased but the critical pressures sharply increased from 24 MPa for the original fuels to above 10 MPa because of the appearance of many small-molecule products. For the electrically heated tube reactor, two phase changes of hydrocarbon fuel possibly occur with increasing bulk temperature and cracking conversion: from compressed liquid phase to supercritical phase and then to gas phase when the cracking conversions exceeds 30% and the critical pressure exceeds the system pressure of 5 MPa. Based on these calculation results, we propose that high-pressure thermal cracking, rather than supercritical cracking of hydrocarbon fuels, should be used at higher cracking conversions of hydrocarbon fuels. ’ ASSOCIATED CONTENT

bS

Supporting Information. Some hydrocarbon mixtures, as well as the critical points calculated using the PR and SRK equations, to verify the reliability of calculation method (Tables S1 and S2). Detailed compositions of cracked hydrocarbon mixtures (Tables S3S8). This material is available free of charge via the Internet at http://pubs.acs.org.

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’ AUTHOR INFORMATION Corresponding Author

*Tel./Fax: +86-22-27892340. E-mail: [email protected].

’ ACKNOWLEDGMENT This article is dedicated to Prof. Zhentao Mi at School of Chemical Engineering and Technology, Tianjin University, for his 70th birthday. G.L. is grateful to him for introducing such an interesting topic and for his constant encouragements and timely inspirations during the past 10 years. The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (Grant 90916022) and the Programme of Introducing Talents of Discipline to Universities (B06006). Thanks are also given to Miss Haijing Li for her technical assistance in the product analysis. ’ REFERENCES (1) Sobel, D. R.; Spadaccini, L. J. Hydrocarbon fuel cooling technologies for advanced propulsion. J. Eng. Gas Turbines Power 1997, 119 (2), 344–351. (2) Huang, H.; Spadaccini, L. J.; Sobel, D. R. Fuel-cooled thermal management for advanced aeroengines. J. Eng. Gas Turbines Power 2004, 126 (2), 284–293. (3) Gascoin, N.; Abraham, G.; Gillard, P. Synthetic and jet fuels pyrolysis for cooling and combustion applications. J. Anal. Appl. Pyrol. 2010, 89 (2), 294–306. (4) Edwards, T. Liquid fuels and propellants for aerospace propulsion: 19032003. J. Propul. Power 2003, 19 (6), 1089–1107. (5) Edwards, T.; Zabarnick, S. Supercritical fuel deposition mechanisms. Ind. Eng. Chem. Res. 1993, 32 (12), 3117–3122. (6) Edwards, T. Cracking and deposition behavior of supercritical hydrocarbon aviation fuels. Combust. Sci. Technol. 2006, 178 (13), 307–334. (7) Liu, G. Z.; Han, Y. J.; Wang, L.; Zhang, X. W.; Mi, Z. T. Supercritical Thermal Cracking of n-Dodecane in Presence of Several Initiative Additives: Products Distribution and Kinetics. Energy Fuels 2008, 22 (6), 3960–3969. (8) Yu, J.; Eser, S. Kinetics of Supercritical-Phase Thermal Decomposition of C10C14 Normal Alkanes and Their Mixtures. Ind. Eng. Chem. Res. 1997, 36 (3), 585–591. (9) Yu, J.; Eser, S. Thermal Decomposition of C10C14 Normal Alkanes in Near-Critical and Supercritical Regions: Product Distributions and Reaction Mechanisms. Ind. Eng. Chem. Res. 1997, 36, 574–584. (10) Yu, J.; Eser, S. Thermal Decomposition of Jet Fuel Model Compounds under near-Critical and Supercritical Conditions. 1. n-Butylbenzene and n-Butylcyclohexane. Ind. Eng. Chem. Res. 1998, 37 (12), 4591–4600. (11) Yu, J.; Eser, S. Thermal Decomposition of Jet Fuel Model Compounds under near-Critical and Supercritical Conditions. 2. Decalin and Tetralin. Ind. Eng. Chem. Res. 1998, 37 (12), 4601–4608. (12) Wang, Z.; Guo, Y. S.; Lin, R. S. Pyrolysis of hydrocarbon fuel ZH-100 under different pressures. J. Anal. Appl. Pyrol. 2009, 85 (12), 534–538. (13) Stewart, J.; Glassman, I.; Brezinsky, K. Supercritical methylcyclohexane pyrolysis: A flow reactor study. Prepr. Pap.Am. Chem. Soc., Div. Fuel Chem. 1998, 43 (3), 433–437. (14) Moser, W. R.; Suer, M.; Dardas, Z.; Ma, Y. H. Mechanism of the catalytic cracking of heptane under supercritical fluid conditions. Abstr. Pap. Am. Chem. Soc. 1998, 216, 616–616. (15) Dardas, Z.; Moser, W. R.; Spadaccini, L. J.; Sobel, D. R. In situ CIR-FTIR characterization of catalytic cracking of supercritical endothermic fuels over different zeolites. Abstr. Pap. Am. Chem. Soc. 1999, 218, 641–641.

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On the Critical Points of Thermally Cracked Hydrocarbon Fuels under

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