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Ind. Eng. Chem. Res. 2008, 47, 8940–8946
Solubility of Ethylene in the Presence of Hydrogen in Process Solvents under Polymerization Conditions G. Sivalingam,* V. Natarajan, K. R. Sarma, and U. Parasuveera Polymer Research and Technology Center, Reliance Industries Ltd, V. N. PuraV Marg, Chembur, Mumbai, 400 071, India
The concentration of ethylene in the solvent of slurry polymerization process is important as it determines the extent of reaction, reaction temperature, heat duty, and molecular weight. In the present study, gas liquid behavior of ethylene, in the presence and absence of hydrogen, was studied in two process solvents namely, hexane and Varsol at various process pressures and temperatures. Solubility of ethylene increases with increase in pressure and decreases with increase in temperature in both the solvents. Ethylene solubility decreases with increase in carbon number of solvent at identical conditions. The presence of hydrogen strongly influences the solubility of ethylene in hexane and varsol. The solubility of ethylene in hexane decreases in the presence of hydrogen compared to its binary solubility, while the presence of hydrogen increases the solubility of ethylene in varsol compared to its binary solubility. A heterogeneous thermodynamic model based on the Chao-Seader method was adopted for modeling the solubility of ethylene, in the presence and absence of hydrogen, in hexane and varsol. Chao-Seader method uses the Redlich-Kwong equation of state for vapor phase fugacity, Chao-Seader correlation for pure component/reference state fugacity, Scatchard-Hildebrand model for liquid activity coefficient, and Lee-Kesler method for molar volume, Gibbs free energy departure and enthalpy departure of the mixtures. The model could explain the ethylene solubility closely in both solvents with the presence and absence of hydrogen over the entire range of process conditions studied. 1. Introduction Polyolefin is commonly produced with Ziegler-Natta catalysts in gas phase,1-3 slurry phase,4-8 and solution processes9,10 in continuous scale. The slurry process possesses inherent advantages over other processes such as mild operating conditions, higher monomer conversions, ease of heat removal, and simpler processing. These make the slurry process a more common method of production.11,4-8 In this process, solvent is used as a diluent and also for reaction temperature control and hydrogen is used as chain transfer agent to control molecular weight.7,11,12 If polymer of interest is high molecular weight, controlling heat of reaction becomes crucial as high temperatures deactivate the catalyst. For highly active catalysts, heat of reaction can be controlled by either manipulating the concentration of ethylene in solvent in such a way that mass transfer from either gas to liquid (and thus liquid to solid) is limited or by decreasing the catalyst loading. The decrease of catalyst loading is not a common method to control the reaction heat, and the concentration of ethylene is used as a tool. Hence a detailed understanding of ethylene at various pressures, temperatures, and in the presence of chain transfer agents is crucial for a successful slurry reactor operation.7,13 Absorption data of ethylene in hexane is available in open literature.11,14-17 However absorption data in varsol, which is practiced as a diluent/solvent in industrial practice, is very scarce. The molar ratio of hydrogen to ethylene is one of the controlled parameters for grade change and reactor operation in HDPE production using the slurry process,7,18 and a detailed understanding of their interactions is vital. To the best of our knowledge, experimental data on the influence of hydrogen on the equilibrium absorption of ethylene in various process solvents is not available in the literature. * To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: 091-22-67677364. Fax: 09122-67677080.
Mechanically agitated gas-liquid contactors can be used to determine the solubilities of the gases in liquids19-21 and is adopted in the present investigation. In the present study the solubility of ethylene under various process conditions (temperature, pressure, and hydrogen) is investigated in the two process solvents, namely, varsol (boiling range 140-200°C) and n-hexane using mechanical agitated gas-liquid contactors. The solubility of ethylene was determined experimentally in the pure solvents at various pressures and temperatures. The solubility behavior of ethylene in the presence of a chain transfer agent (hydrogen) was also experimentally studied. The solubility of ethylene under polymerization conditions would strongly influence the polymerization behavior. A predictive model for ethylene solubility at various conditions would be needed for process developmental studies. The solubility modeling significantly depends on the knowledge of pure components and their interactions as it will lead to the determination of thermodynamic, phase equilibrium, and transport properties. The results’ accuracy, rigor, reliability, and validity depend on the kind of thermodynamic models chosen to represent the system. Hence choosing an appropriate thermodynamic model is very critical for solubility modeling. The solubility predictions can be further used to develop kinetic, heat, and mass transfer models and thus the reactor model. Various thermodynamic models were screened, and a method proposed by Chao-Seader for hydrocarbon mixtures22 based on a heterogeneous approach was found satisfactory for our system investigated in the present study. The objectives of the present investigation are two fold: 1. To measure the solubility of ethylene in the presence or absence of hydrogen in n-hexane and varsol under various process conditions. 2. To develop a predictive model for estimating solubility of ethylene over the wide range of experimental conditions.
10.1021/ie801236m CCC: $40.75 2008 American Chemical Society Published on Web 10/28/2008
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of gas absorbed at equilibrium temperature and pressure and can be written as: GC ) (ES - AS) + (OHVETP - OHVRTP)
Figure 1. Experimental setup for solubility measurement used in the present study.
(1)
where GC is the number of moles of gas collected in the metering vessel, ES is number of moles of gas dissolved in the solvent at ETP, AS is number of moles of gas dissolved in the solvent at RTP, OHVETP is the number of moles of gas in the overhead space at ETP and OHVRTP is the number of moles of gas in the overhead space at RTP. Redlich-Kwong equation of state23 was used to calculate the number of moles of gas present in overhead space at ETP (OHVETP) and RTP (OHVRTP). AS was obtained by gas chromatographic analysis. ES is then estimated using eq 1. Ethylene solubility at ETP is calculated using ES and the amount of solvent used in the experiment. Further details of experimental procedure to calculate the solubility are given elsewhere24 Experiments were repeated at least three times for all the conditions and the experimental standard deviation was less than 5%.
2. Experimental Section
3. Solubility Model
Polymerizable grade ethylene, hydrogen, and varsol were obtained from the polyethylene plant, and laboratory grade hexane was used in the present study. Hexane, varsol, ethylene, and hydrogen were completely demoisturized before used for experiments. A 5 L Buchi reactor was used to carry out solubility experiments. Experiments were carried out with 60% operating volume of reactor amounting to 3 L of the solvent. At desired temperature, the Buchi reactor was pressurized with ethylene at a set agitation speed, and constant pressure was maintained by constantly feeding the ethylene to compensate the amount of ethylene absorbed in the solvent. Agitation speed was kept sufficiently high such that mass transfer limitation is minimal in the reactor. This will also ensure that the equilibrium absorption is reached in a reasonable amount of time. Once the system reached equilibrium, agitation was stopped, and the mixture was brought down to room temperature. After cooling to room temperature, the absorbed and overhead gases at equilibrium temperature and pressure are collected by venting through a flow meter to a metering vessel. The solution is well agitated to remove all the gases in excess of equilibrium solubility at room temperature and pressure. The amount of gas collected is equal to the amount of gas absorbed and the amount of gases in vapor phase at equilibrium temperature and pressure (ETP) minus the equilibrium amount of gases in the solvent and vapor phase volume at room temperature and pressure (RTP). For binary mixtures, solubility is calculated by mass balance of gases collected in excess or deficit of atmospheric solubility. For ternary mixtures, in addition to flow analysis, a composition of gas and liquid phase was measured using a GC at equilibrium temperature and pressure. Experimental setup is shown in Figure 1, and temperature and pressure ranges are 25-75°C and 2-6 bara, respectively. Agitator speed was between 200 and 500 rpm. A method to measure the solubility from the experimental procedure was developed. In the experimental setup, the gases coming out of the solution by agitating at room temperature and pressure are measured. The gas collected in the metering vessel is the difference between the total amount of gas (in the solvent as dissolved gas and in the overhead space as gas) in the Buchi reactor at ETP and the total amount of gas (in the solvent as dissolved gas and in the gas in the overhead volume as gas) in the Buchi reactor at RTP. The solubility is the amount
Khare et al.,18 have modeled slurry polymerization of ethylene to produce HDPE (high density polyethylene). Thermodynamic behavior of the polymerization system was studied using two thermodynamic approaches: Sanchez Lacombe property method and Chao-Seader property method. These two property methods were used to predict the pure component properties and binary properties of ethylene, hydrogen, hexane, and comonomers. The predictions of the property methods were compared at various temperatures and pressures. It was concluded on the basis of the prediction capabilities that the Chao-Seader method gives an accurate description of the phase behavior of mixtures of light hydrocarbons and the Sanchez-Lacombe method provides good predictions of the phase behavior of polymeric mixtures.18 Hence the Chao-Seader method would best describe ethylene solubility in the present conditions of investigations. Recently, Nagy et al25 have used the modified SanchezLacombe (MSL) equation of state to predict the solubility of ethylene at high temperatures (117-237°C) and pressures (15-100 bar) targeting the solution polymerization range. MSL binary interaction parameters obtained from their experimental study were also used in Peng-Robinson and Soave-RedlichKwong equation of states to predict the ethylene solubility. It was concluded that all three methods produce similar results in the range of investigation. Since the current study involves phase behavior of light hydrocarbons18 with no polymers, Chao-Seader property method is selected as a thermodynamic model to predict the solubility. A heterogeneous model proposed by Chao and Seader22 for hydrocarbon mixtures was used in the present study. For liquid phase, Chao Seader correlation for the reference state fugacity coefficient, Scatchard-Hildebrand model for activity coefficient were used. For vapor phase, Redlich-Kwong equation of state23 was used to predict properties. Lee-Kesler equation of state for liquid and vapor enthalpy and API method for liquid molar volume, viscosity, and surface tension were used to predict for both the phases. Chao-Seader method uses all the above listed methods/models to predict the solubility of ethylene at various process conditions. This method was developed for systems containing hydrocarbons and light gases, such as carbon dioxide and hydrogen sulfide, but with the exception of hydrogen. However, in the present investigation, Chao-Seader approach was satisfactory enough to explain the ternary ethylene solubility
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even in the presence of hydrogen. Chao-Seader method is readily available in commercial simulation software Aspen Plus and was used in the present study. 3.1. Liquid Phase Modeling. The general Chao-Seader correlation for pure component/ reference state fugacity is given as22 (0) (1) ln φL* i ) ln υi + ω ln υi
(2)
where φi is the liquid fugacity of pure component i, ω is the acentric factor of the component, and υi(0), υi(1) are the Chao-Seader parameters for the component i. (1) υ(0) i , υi ) f (T, Tci, P, Pci)
(3)
where Tci and Pci are the critical temperature and pressure of component i. Scatchard-Hildebrand model for calculating the liquid activity coefficient is given by ln γi ) where
V l,* i RT
∑ ∑ φ φ (A j k
j
k
ji - 0.5Ajk)
(4)
Aij ) (δi - δj)2 + 2kijδiδj,
φi )
xiV l* i V mL
V mL )
,
∑xV i
l* i
i
and δ is the solubility parameter; V’s are molar volumes. 3.2. Vapor Phase Modeling. Redlich-Kwong equation of state23 (RK EOS) is used to calculate the vapor phase behavior. RK EOS is applicable for systems at low to moderate pressures and extent of non-ideality in the vapor phase are small. The EOS is given as24 P)
a RT Vm - b T 0.5V (V + b) m m
(5)
where
√a )
∑ i
xi√ai, b )
∑ i
xibi, ai ) 0.42748023
R2T 2.5 ci , and Pci
bi ) 0.08664035
RTci Pci
Lee-Kesler method is used to calculate the molar volume, enthalpy departure, Gibbs free energy departure, and enthalpy departure of a mixture at a given temperature and pressure for any phase through the compressibility factor.
Figure 2. (a) Plot of binary ethylene solubility in hexane at various temperatures and pressures: (9) 30, (b) 55, (2) 75°C, and solid lines are Henry’s law fits. (b) Plot showing the experimental Henry’s constants at various temperatures with the literature data: ([) experimental data; (1) literature data (Lit et al., 1996). (c) Plot showing the high temperature and pressures solubility of ethylene in hexane from the literature (Zhure and Zhurba, 1960, and Nagy et al., 2005). These confirm the present investigation experimental trends: (9) 30, (b) 50, (2) 75°C from Zhure and Zhurba, 1960; (1) 117, (left triangle) 137, (right triangle) 152, ([) 177, (0) 202°C from Nagy et al., 2005. (d) Plot showing the solubility of ethylene at atmospheric pressure in hexane from the literature and from the present study: (9) Waters et al., 1970, (b) present study, (2) Sahgal et al., 1978.
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Z ) Z + ωZ (0)
(0)
(1)
(6)
(1)
Where Z and Z are the compressibility factors of a simple fluid and real fluid, respectively, and are assumed to be a universal function of reduced temperature and pressure. 4. Results and Discussion This section is divided into two parts. In the first part, solubility of ethylene in hexane with the presence and absence of hydrogen at various temperatures and pressures would be discussed along with Chao-Seader method prediction. In the second part, solubility of ethylene in varsol with the presence or absence of hydrogen at various temperatures and pressures along with Chao-Seader method prediction will be discussed. And also a comparison between binary and ternary solubility of hexane and varsol will be discussed. 4.1. Binary and Ternary Solubility of Ethylene in Hexane. Figure 2a shows the solubility of ethylene as a function of pressure and temperature in hexane.24 One can note that, solubility of ethylene decreases steeply with increase in temperature at a given pressure. The solubility increases with increase pressure at a given temperature. Prior to modeling of
Figure 3. (a) Plot showing the model prediction for binary solubility of ethylene at various temperatures and pressures: (9) 30, (b) 55, (2) 75°C, and solid lines are Chao-Seader model predictions. (b) Plot showing the Chao-Seader model prediction of ethylene solubility at high pressures reported by Zhuze and Zhurba et al., 1960. Also shows the experimental data measured in the present study at low pressures: (9) 30, (b) 50, (2) 75°C from Zhure and Zhurba, 1960; (0) 30, (O) 55, (∆) 75°C from the present study and the solid lines are model predictions.
solubility of ethylene in hexane, validity of simpler approaches such as Henry’s approach (P ) Hx, where P is the partial pressure of ethylene, x is the mole fraction of ethylene in solvent, and H is the Henry’s constant) was checked. For Henry’s law, the gas should have zero solubility at zero pressure. But, in the present case, experimental data were fitted with Henry’s law equation and found a non-zero intercept at zero pressure. Though the magnitude of intercept is smaller, it will be significant at low pressure or high temperature experiments and an accurate thermodynamic model was proposed to explain these data. To check the validity of present experimental data, Henry constants were calculated by ignoring the intercept and compared with Henry constants reported in the literature. The solid lines in Figure 3a are Henry’s law fits. Figure 3b shows the Henry’s constants of present study with data available in the literature. The Henry’s constants for ethylene in hexane reported in literature are 7.5, 9.4, and 11.3 bar m3/kmole at 40, 60, and 80°C, respectively.11 Our measured Henry’s constants are 5.7, 8.6, and 13.6 bar m3/kmole at 30, 55, and 75°C, respectively. It can be noted from Figure 2b that the Henry constants values measured in the present study compare well with the data reported in the literature and validates the present experimental method to determine solubility. However, the non-zero intercept in the Henry’s equation implies that the system does not behave ideally, and the requirement of the appropriate thermodynamic model is very essential to explain the data. Ethylene solubility in hexane at high pressures and temperatures are reported in the literature,25,26 and these would be useful for solubility under solution polymerization conditions. Figure 2c shows the ethylene solubility variation with pressures at different temperatures25,26 It also clearly indicates that the solubility of ethylene decreases with increase in temperature at high pressures and solubility increases with pressure at high temperatures. The ethylene solubility at low temperatures around atmospheric pressure or lesser are reported in the literature.16,27 Figure 2d shows the solubility of ethylene in the temperature range of -10 to 25 °C at atmospheric pressure. The solubility measured at atmospheric pressure in the present study is also shown for comparison. It can be seen from the figure that solubility decreases with increase in temperature and the present data is in line with the literature. This indicates the further validation of present experimental data and trends observed on ethylene solubility in hexane with literature. The distribution of hexane in liquid and vapor phases is very important for modeling and for estimating the partial pressure of ethylene and for calculating the solubility of ethylene in hexane. If the amount of hexane in vapor phase is significant, the resultant partial pressure of ethylene, thus absorption rate, would be very different. We have calculated the amount of hexane in vapor phase as well as the amount/fraction of total hexane used for the experiment. The maximum amount of hexane seen in vapor phase is less than 0.5 mole % of total hexane and hence partial pressure of hexane in vapor phase was ignored. Hence the total pressure was assumed as equilibrium pressure of ethylene. The model explained in the previous section was used to predict the binary solubility of ethylene in hexane. Figure 3a shows the Chao-Seader model predictions for solubility of ethylene in hexane. It can be seen from the figure that the Chao-Seader model could explain the experimental data closely over all the temperature and pressure range studied in the present study. Figure 3b shows the Chao-Seader model predictions for the data reported in literature26 at high pressures in the slurry polymerization temperature range. The present experimental data
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Figure 5. Parity plot showing the experimental solubility of ethylene in hexane and Chao-Seader model prediction in binary and ternary system: (b) binary solubility, (O) ternary solubility, solid line is a parity line.
Figure 4. (a) Plot showing the effect of hydrogen on the solubility of ethylene at 30 °C in hexane at various pressures: (9) binary ethylene solubility; (b) ternary ethylene solubility with 5 vol % hydrogen; (2) ternary ethylene solubility with 10 vol % hydrogen. (b) Plot showing the effect of hydrogen on the solubility of ethylene at 55 °C in hexane at various pressures: (9) binary ethylene solubility; (b) ternary ethylene solubility with 5 vol % hydrogen; (2) ternary ethylene solubility with 10 vol % hydrogen.
is also shown in the same figure to establish the model capability to predict the solubility of ethylene over the pressure ranges of 2-90 bara and temperature range of 30-75 °C. It can be seen from the figure that the model satisfactorily explains the present and the literature data. Thus the model can be used for modeling the solubility of ethylene under slurry polymerization conditions. Hydrogen is used as a chain transfer agent to control molecular weight in most of the polymerization reactions. Hence, the effect of hydrogen on the solubility of ethylene was studied over a wide range of temperatures and pressures. It is interesting to note that the presence of hydrogen reduces the solubility of ethylene in hexane significantly. Figure 4a shows the effect of hydrogen concentration on the solubility of ethylene at 30 °C with two levels of hydrogen concentrations (5 and 10 volume %). The extent of decrease in the solubility of ethylene with 5 vol % hydrogen over no hydrogen is nearly 50%. It can be further noted that the extent of decrease in ethylene solubility with increase in hydrogen is not linear. The extent of decrease with 5% hydrogen and with 10% hydrogen is not significantly different, while the amount of solubility decrease due to 5% hydrogen against 0% hydrogen is significant. Figure 4b shows the effect of hydrogen on the solubility of ethylene at 55 °C. The presence of hydrogen (5 and 10 volume %) significantly
reduces the solubility of ethylene in hexane. Similar to 30 °C observation, the extent of decrease in the ethylene solubility with hydrogen concentration is also not linear at 55 °C. It can be seen from the figure that the trend of reduction in ethylene solubility with hydrogen concentration is similar to that of the observation at 30 °C. Experiments were also carried out at 75 °C and 6 bara with 5 volume % hydrogen. The solubility (mole fraction) of ethylene in the presence of hydrogen was 0.032 while the ethylene solubility (mole fraction) in the absence of hydrogen was 0.044. This implies that presence of hydrogen, under polymerization conditions, not only deactivates the active polymerization sites of the catalyst18 and also effectively brings down the ethylene available for polymerization thus the polymerization rate. In literature,26 ethylene solubility was studied with various solvents with same carbon number such as hexane, cyclohexane, and benzene and found that ethylene solubility is higher in hexane compared to cyclohexane and benzene. Chao-Seader method could also explain the ethylene solubility in the ternary system closely. The decrease in the solubility of ethylene due to the presence of hydrogen was captured reasonably with the present model. Figure 5 shows a parity plot of experimental ethylene solubility with and without hydrogen with the Chao-Seader method prediction with various pressures and temperatures. It can be implied from the figure that all the data are close to a parity line indicating the applicability of Chao-Seader method for solubility of ethylene in binary and ternary system. This model can be used to develop an overall reactor model and any further studies. 4.2. Binary and Ternary Solubility of Ethylene in Varsol. Varsol, an industrial solvent, is a mixture of saturated linear hydrocarbons with almost negligible aromatics and waxes. The carbon number range for varsol is C8-C11, boiling point range is 140-200 °C, melting point is -58 °C, and specific gravity is 0.76 g/cc. A true boiling point (TBP) method (boiling point as a function of amount distilled) was used to get the composition of the varsol. Varsol is represented as a mixture of linear alkanes (C8-C11) and typical composition is C8, 4; C9, 19; C10, 70; and C11, 7 wt %. This was used to represent the varsol in our experimental and modeling studies. Figure 6a shows the experimental binary solubility of ethylene in varsol.24 The experimental binary solubility behavior of ethylene in varsol is very similar compared to its solubility in hexane. Figure 6a shows the experimental solubility with Henry’s law fits. Even in this case, there is a
Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8945
Figure 7. Plot showing the solubility of ethylene in binary and ternary conditions in varsol at different pressures and temperatures: (9) binary ethylene solubility at 30 °C, (0) ternary ethylene solubility at 30 °C with 5 vol % hydrogen, (!) ternary ethylene solubility at 30 °C with 10 vol % hydrogen, (b) binary ethylene solubility at 55 °C, (0) ternary ethylene solubility at 55 °C with 5 vol % hydrogen, (y) ternary ethylene solubility at 55 °C with 10 vol % hydrogen.
Figure 6. (a) Plot showing the ethylene solubility in varsol under various temperatures and pressures: (9) 30, (b) 55, (2) 75 °C, and solid lines are Henry’s law fits. (b) Plot showing the ratio of binary ethylene solubility in hexane and varsol and various process conditions: (9) 30, (b) 55, (2) 75 °C, and solid lines are Henry’s law fits.
non-zero intercept indicating the non-applicability of Henry’s law as seen with hexane. The approximate Henry constants for ethylene in varsol at 30, 55, and 75 °C are 10.8, 14.2, and 20.2 bar m3/kmole, respectively. While the Henry constants for ethylene in hexane at 30, 55, and 75 °C are 5.7, 8.6, and 13.6 bar m3/kmole, respectively. These indicate that varsol is relatively poorer solvent compared to hexane. It can be seen that the extent of ethylene dissolved in varsol is much lesser than ethylene solubility in hexane for similar conditions. The number of carbons for hexane is 6 and the average number of carbons for varsol is 9.8. Figure 6b shows the ratio of ethylene solubility in hexane to varsol over various process conditions. On average, the solubility of ethylene in hexane under binary conditions is 1.5-2 times that of varsol under the same operating conditions. The presence of hydrogen significantly influences the solubility of ethylene in a varsol. Figure 7 shows the solubility of ethylene at 30 °C and 55 °C with and without the presence of hydrogen. It can be seen from the figure that presence of hydrogen increases the ethylene solubility significantly. Experiments were also conducted at 75 °C at 3 bara with 5 volume % hydrogen; the solubility of ethylene (mole fraction) in varsol was 0.0048 and while in the presence of 5 volume % hydrogen, the ethylene solubility (mole fraction) was 0.022. Since hydrogen is used as a molecular
Figure 8. Parity plot showing the experimental solubility of ethylene in varsol and Chao-Seader model prediction in binary and ternary system: (b) binary solubility, (0) ternary solubility, solid line is a parity line.
weight controlling agent, this behavior will have critical impact on the polymerization rates. Under polymerization conditions, hydrogen will play an interesting part. On one hand, hydrogen deactivates the active polymerization sites and on another end, it provides more reactant concentration to the polymerization in varsol. This will have serious implications on the way the reactors are operated with these solvents/diluents. Since the concentration of ethylene in the solvent is one of the important factors that decides the rate of polymerization and hence the molecular weight, accurate control of the hydrogen concentration is utmost critical. Figure 8 shows the parity plot of ethylene solubility in varsol in the presence and absence of hydrogen with various temperatures and pressures. It can be seen from the figure that the Chao-Seader model predictions for ethylene solubility in varsol with the presence or absence of hydrogen under various process conditions are satisfactorily close. The increase in ethylene solubility due to the presence of hydrogen is captured by this model (vide Figure 8).
8946 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
5. Conclusion Solubility of ethylene in hexane and varsol was measured with and without hydrogen under various temperatures and pressures. In both the solvents, ethylene solubility decreased with increase in temperature and increased with increase in pressure. Solubility of ethylene was significantly lower in varsol compared to hexane. The presence of hydrogen significantly changed the solubilities of ethylene in hexane and varsol. A comprehensive model based on the Chao-Seader method explained the entire spectrum of data satisfactorily. Acknowledgment The authors would like to thank Reliance Industries Limited for allowing us to publish this work. We also thank Kamal Kataria for help with carrying out some of the experimental works. Literature Cited (1) Choi, K. Y.; Ray, W. H. The dynamic behavior of continuous stirredbed reactors for the solid catalyzed gas phase polymerization of propylene. Chem. Eng. Sci. 1988, 43, 2587. (2) McAuley, K. B.; Talbot, J. P.; Harris, T. J. A comparison of twophase and well-mixed models for fluidized-bed polyethylene reactors. Chem. Eng. Sci. 1994, 49, 2035. (3) Xie, T.; McAuley, K. B.; Hsu, J. C. C.; Bacon, D. W. Gas phase ethylene polymerization: Production processes, polymer properties, and reactor modeling. Ind. Eng. Chem. Res. 1994, 33, 449. (4) Neto, A. G. M.; Pinto, J. C. Steady state modeling of slurry and bulk propylene polymerizations. Chem. Eng. Sci. 2001, 56, 4043. (5) Bohm, L. L.; Goebel, P.; Schoneborn, P. R. Detailed reaction engineering as a basis of modern slurry technology for PE-HD-production. Angew. Makromol. Chem. 1990, 174, 189. (6) Wolf, S. D.; Cuypers, R. L. E.; Zullo, L. C.; Vos, B. J.; Bax, B. J. Model predictive control of a slurry polymerization reactor. Comp. Chem. Eng. 1996, 20, S955. (7) Alt, F. P.; Bohm, L. L.; Endrele, H. F.; Berthold, J. Bimodal polyethylene: interplay of catalyst and process. Macromol. Symp. 2001, 163, 135. (8) Fontes, C. H.; Mendes, M. J. Analysis of an industrial continuous slurry reactor for ethylene-butene copolymerization. Polymer 2005, 46, 2922. (9) Hinchliffe, M.; Montague, G.; Willis, M.; Burke, A. Hybrid approach to modeling an industrial polyethylene process. AIChE J. 2003, 49, 3127. (10) Young, M. J.; Ma, C. C. M. Polymerization kinetics and modeling of PE solution process with metallocene catalysts. J. Polym. Eng. 2002, 22, 75.
(11) Li, J.; Tekie, Z.; Mizan, T. I.; Morsi, B. I.; Maier, E. E.; Singh, C. P. P. Gas-liquid mass transfer in a slurry reactor operating under olefinc polymerization process condition. Chem. Eng. Sci. 1996, 51, 549. (12) Brockmeier, N. F. Latest commercial technology for propylene polymerization, Transition Metal Catalyzed Polymerizations: Alkenes and Dienes; Quirk, R. P., Ed.; Harwood Academic: New York, 1983; Vol. 4. (13) Alper, E.; Wichtendahl, B.; Deckwer, W. D. Gas, absorption mechanism in catalytic slurry reactors. Chem. Eng. Sci. 1980, 35, 217. (14) Albert, L. F.; Smith, C. F. Reactions of ethylene with triethyl aluminum: Effect of operating variables and kinetics of reaction. AIChE. J. 1968, 14, 325. (15) Chang, M. Y.; Eiras, J. G.; Morsi, B. I. Mass transfer characteristics of gases in n-hexane at elevated pressures and temperatures in agitated reactors. Chem. Eng. Process. 1991, 29, 49. (16) Waters, J. A.; Mortimer, G. A.; Clements, H. E. Solubility of some light hydrocarbons and hydrogen in some organic solvents. J. Chem. Eng. Data 1970, 15, 174. (17) Battino, R.; Clever, H. L. The Solubility of Gases in Liquids. Chem. ReV. 1966, 66, 395. (18) Khare, N. P.; Seavey, K. C.; Liu, Y. A.; Ramanathan, S.; Lingard, S.; Chen, C. Steady state and dynamic modeling of commercial slurry highdensity polyethylene (HDPE) processes. Ind. Eng. Chem. Res. 2002, 41, 5601. (19) Mehta, V. D.; Sharma, M. M. Mass transfer in mechanically agitated gas liquid contactors. Chem. Eng. Sci. 1971, 26, 461. (20) Joshi, J. B.; Pandit, A. B.; Sharma, M. M. Mechanically agitated gas liquid reactors. Chem. Eng. Sci. 1982, 37, 813. (21) Oguz, H.; Brehm, A.; Deckwer, W. D. Gas/liquid mass transfer in sparged agitated slurries. Chem. Eng. Sci. 1987, 42, 1815. (22) Chao, K. C.; Seader, J. D. A general correlation of vapor-liquid equilibria in hydrocarbon mixtures. AIChE. J 1961, 7, 598. (23) Redlich, O.; Kwong, J. N. S. On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions. Chem. ReV. 1949, 44, 233. (24) Kataria, K. L.; Sivalingam, G.; Sarma, K. R.; Venkateswaran, N.; Parasuveera, U. Solubility of ethylene, hydrogen and their mixture in process solvents under ethylene polymerization conditions. Sixth International Symposium on Catalysis in Multiphase Reactors (CAMURE-6): National Chemical Laboratory-Pune, 14-17th January, 2007, P44, 538. (25) Nagy, I.; Krentz, R. A.; Heidemann, R. A.; Loos, T. W. D. Vaporliquid equilibrium data for the ethylene-hexane system. J. Chem. Eng. Data. 2005, 50, 1492. (26) Zhuze, T. P.; Zhurba, A. S. Solubilities of ethylene in hexane, cyclohexane, benzene under pressure. Russ. Chem. Bull. 1960, 9, 335. (27) Saghal, A.; La, H. M.; Hayduk, W. Solubility of Ethylene in Several Polar and Non-Polar Solvents. Can. J. Chem. Eng. 1978, 56, 354.
ReceiVed for reView August 12, 2008 ReVised manuscript receiVed September 26, 2008 Accepted September 29, 2008 IE801236M
