SL EOS Research Articles

Dynamic Modeling of Industrial Loop Reactors for Catalytic Ethylene (Co)polymerization: Pressure Safety Valves

AbstractIn industrial loop reactors, for catalytic ethylene (co)polymerization, the heat produced by polymerization can result in temperature and pressure increase, which in turn can lead to reactor breakage, explosion, and consequent release of toxic/flammable fluids in the environment. To predict the reactor temperature and pressure during ethylene (co)polymerization and assess the performance of presure safety valves (PSVs) in response to emergency accidents, an integrated mathematical approach is followed including catalyst kinetics, thermodynamics, and transport properties modeling. A catalytic ethylene (co)polymerization kinetic model is used to predict the catalyst activity variation with respect to reactor temperature and the heat produced by the polymerization reaction during a reaction runaway. The Sanchez–Lacombe equation of state (SL EOS) is utilized in order to predict the reactor pressure for different slurry mixture compositions and the slurry densities at different temperatures, pressures and solids weight fractions. Dynamic macroscopic mass and energy balances are derived to calculate the dynamic evolution of concentrations of the various molecular species as well as the temperature changes in the loop reactor. The model can predict the temperature and pressure increase rates and the maximum flow rate at the PSVs during the runaway.

Pressure-volume-temperature relationships of diisononyl phthalate and phase behavior of carbon dioxide/diisononyl phthalate binary system

The pressure-volume-temperature (PVT) relationships of pure diisononyl phthalate (DINP) were measured at temperatures of 303.15–363.15 K and pressures up to 160 MPa by a variable-volume method. Using a synthetic method that involved observing the bubble point, the phase behavior of the CO2/DINP binary system was also measured. The phase boundaries were determined at temperatures of 313.15–393.15 K and CO2 molar fractions of 0.3–0.9. The characteristic parameters of DINP were obtained by correlating the measured PVT data using the Sanchez-Lacombe equation of state (SL EoS), and the bubble points of the system were correlated using the SL EoS with the determined characteristic parameters. The interaction parameter exhibited temperature dependence, and the introduction of the temperature dependence improved the correlation.

A novel approach for the estimation of the Sanchez-Lacombe interaction parameters for the solubility of ternary polyolefins systems

The total solubility of ethylene in LLDPE in presence of propane, isobutane and 1-butene is measured using a gravimetric technique at 70 °C and pressures up to 5 bars. In order to overcome the lack of experimental partial solubility data in ternary systems, a novel approach for the estimation of the Sanchez-Lacombe interaction parameters is proposed. The total solubility measurements combined with the independent estimate of the compressibility factor for a mixture of gases using Peng-Robinson EoS as a second “data source” were fitted to SL EoS in order to identify its interaction parameters. This makes it possible to calculate individual component solubility data for the two penetrants in a non-ideal ternary system where the third phase is polyethylene. The observed trends were theoretically interpreted because no available data can be found in the literature for these studied systems. Good agreement was observed between the experimental overall solubility and SL EoS combined to PR EoS, with a difference of 1–4% for the overall solubilities and a maximum of 0.8% for the compressibility factor.

Applied Thermodynamics for Process Modeling in Catalytic Gas Phase Olefin Polymerization Reactors

AbstractThe Sanchez–Lacombe Equation of State (SL EoS) is used to model the solubility of different industrial alkane penetrants in polyethylene to explain the importance of considering different diluents for different processes, and the impact that this choice can have on operating conditions, especially for the production of linear low density polyethylene (LLDPE). Extension of this approach to ternary (ethylene/penetrant/LLDPE) systems shows the effect of composition of penetrant/ethylene mixtures on the solubility of such mixtures in LLDPE and swelling of the polymer phase at conditions of industrial relevance. This analysis reveals that using a constant polymer density instead of that predicted by the SL EoS can result in erroneous calculations of the particle size distribution developments in an olefin polymerization reactor.

Measurement and prediction of phase equilibria of ethylene + methyl acrylate + poly(ethylene-co-methyl acrylate) systems

The solubilities of ethylene in the methyl acetate (MA) solutions of poly (ethylene-co-methyl acrylate) (EMA) were investigated according to conditions applicable to polymerization. The bubble point pressure (BP) for vapor-liquid equilibrium (VLE) and the cloud point pressure (CP) for liquid-liquid equilibrium (LLE) of ethylene + MA + EMA ternary system (weight ratio of MA: EMA, 9: 1) were measured at temperatures of 373 K and 393 K and at pressures up to 25 MPa with a synthetic method. The BP and CP increased with increasing temperature and ethylene weight fraction, especially the slope of CP against ethylene weight fraction was large. The Sanchez-Lacombe equation of state (SL EoS) could correlate VLE data of ethylene + MA and ethylene + EMA systems by fitting a corresponding binary interaction parameters for each binary to within about 4.7% in pressure. The phase equilibria of the ternary system could be predicted with the SL EoS from binary interaction parameters determined from the binary systems.

Modeling Condensed Mode Cooling for Ethylene Polymerization: Part II. Impact of Induced Condensing Agents on Ethylene Polymerization in an FBR Operating in Super-Dry Mode

The Sanchez–Lacombe equation of state (SL EoS) was used to estimate the concentration of ethylene and different induced condensing agents (ICAs) in polyethylene, and the effects of adding an ICA on parameters such as reactor temperature, production rate, and particle size were discussed. A simple continuous stirred tank reactor (CSTR)-like reactor model was validated from production data, and the results reveal that serious errors will be found in the prediction of the reactor temperature and production rate if the interaction between ethylene and ICA is not taken into account. It is also shown that adding an ICA can lead to increased production rates at the cost of decreased catalyst mileage.

Phase behavior of Carbon dioxide/Trimethoxy(methyl)silane and Methylsilicate 51 system

The phase behaviors of carbon dioxide (CO2)/trimethoxy(methyl)silane (MTMS) and CO2/Methylsilicate 51 (MS-51: methylsilicate tetramer) binary systems were determined. The experiments were performed using a synthetic method by observing the bubble point. The phase boundaries were determined at temperatures of 313.2 K–393.2 K and CO2 molar fractions of 0.2–0.9. The experimentally obtained bubble points of the CO2/MTMS binary system were correlated using the Peng-Robinson equation of state (PR EoS), and the molecular interaction parameters kij and lij were determined. The results of the CO2/MS-51 binary system were correlated using the PR EoS and the Sanchez-Lacombe equation of state (SL EoS). In the SL EoS, two types of mixing rules, originally proposed by Sanchez et al. which uses kij as a fitting parameter and modified by McHugh et al. which uses two fitting parameters kij and lij, were used. For this system, the experimental results were correlated better using the SL EoS than using the PR EoS, and the latter mixing rule was more suitable than the former.

High pressure densities for mixed ionic liquids having different functionalities: 1-butyl-3-methylimidazolium chloride and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

In this work, high pressure density measurements were made of mixed ionic liquid systems (1-butyl-3-methylimidazolium chloride ([bmim]Cl) and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([bmim][Tf2N])) for the purpose of developing efficient reaction and separation systems for processing biomass. The mixed ionic liquids were prepared at mole ratios, [bmim]Cl:[bmim][Tf2N] of 0.75: 0.25, 0.50: 0.50 and 0.25: 0.75. Density data were measured (10–200MPa, 312–392K) and correlated (up to 100MPa) with the ε∗-modified Sanchez-Lacombe equation of state (ε∗-mod SL EoS). The density of the binary mixed ionic liquid system was modeled in two ways: (i) as a single pseudo-component or (ii) as two discrete components. By treating the mixed ionic liquids as a single pseudo-component, the ε∗-mod SL EoS could correlate the high pressure density data to within a maximum average relative deviation (ARD) of 0.06%. On the other hand, by treating the mixed ionic liquids as discrete components, higher ARD values (0.15%) were obtained from the ε∗-mod SL EoS that can be attributed to the EoS mixing rules. Both approaches for modeling the ionic liquid mixtures had sufficiently low deviations and will be applied to multicomponent CO2-containing systems in future works.

Measurement and prediction of phase equilibria of ethylene + vinyl acetate + methanol + poly(ethylene-co-vinyl acetate) systems

This work investigated the solubilities of ethylene in the 10 wt% poly (ethylene-co-vinyl acetate) (EVA) solutions including vinyl acetate (VA) and methanol which are related to production of EVA. The bubble point pressure (BP) for vapor-liquid equilibrium (VLE) and the cloud point pressure (CP) for liquid-liquid equilibrium (LLE) of ethylene + VA + EVA ternary and ethylene + VA + EVA + methanol quaternary systems were measured at temperatures of 313 K, 343 K, 373 K and at pressures up to 20 MPa with a synthetic method. The experimental results revealed that the BP and CP increased with increasing temperature and ethylene weight fraction, especially the influence of ethylene weight fraction on CP was found to be drastic. The Sanchez-Lacombe equation of state (SL EOS) could correlate the BP data of ethylene + VA + EVA ternary and ethylene + VA + EVA + methanol quaternary systems within 3.6% an average relative deviation. The phase equilibria of the EVA + VA + ethylene ternary system could be predicted over wide polymer concentration ranges by the SL EOS with the determined parameters in the correlations. With increasing pressure, phase behavior changed from VLE at low pressure to vapor-liquid-liquid equilibrium (VLLE) and LLE at high pressures.

Combined EoS and elastic constraints models to predict thermodynamic properties for systems involving semi-crystalline polyolefins

In the present study, an equation of state model (i.e., Sanchez–Lacombe equation of state-SL EoS) and an Activity coefficient model (i.e., UNIFAC-FV) are combined with elastic constraints models to assess the effect of polymer crystallinity on solubility of penetrants (e.g., α-olefins, diluents, light gases, etc.) in polyolefins (i.e., binary and ternary mixtures). It is shown that the predictive capabilities of the employed solubility models can be significantly improved when combined with corresponding models accounting for the elastic constraints effects on polymer chains (i.e., Michaels–Hausslein, Banaszak modification of Michaels–Hausslein). More specifically, it is illustrated that for the SL EoS, the fraction of elastically effective chains (f) is the only adjustable parameter which has to be considered to accurately predict the solubility of penetrants in semi-crystalline polyolefins at conditions of industrial importance. In addition, such a combined model results in reduction of the adjustable parameters (i.e., binary interaction parameters, kij), particularly in multi-component mixtures. It is also depicted that the parameter f is a function of polymer crystallinity and temperature in a way that f increases with increasing crystallinity and decreasing temperature. Moreover, it is demonstrated that the incorporation of elastic constraints models in UNIFAC-FV improves its predictive capabilities by about 25%. Finally, a comprehensive sensitivity analysis is carried out to investigate the effect of parameter f on the predictive capabilities of the SL-EoS combined with elastic constraints models.

Hydrogen storage in a series of Zn-based MOFs studied by Sanchez–Lacombe equation of state

One of the most famous porous adsorbents used for separation and storage of hydrogen is metal organic framework (MOF). In this study, the experimental data related to hydrogen adsorption on and desorption from five adsorbents including MOF-5, MOF-177, MOF-200, MOF-205 and MOF-210 is adopted. Then, the hydrogen sorption is modeled by applying Sanchez–Lacombe Equation of State (SL EoS). The amount of hydrogen uptake in the adsorbents is obtained through hydrogen-adsorbents phase equilibrium calculations at temperature 77 K and various pressures up to 80 × 105 Pa. The result is compared with the experimental data to show the precision of SL equation of state in predicting the hydrogen sorption trend. SL EoS predicts the experimental results satisfactorily, even though in comparison with PHSC EoS, the latter shows a little reduction in average absolute deviation.

Modelling of multicomponent olefins solubility in polyolefins using Sanchez–Lacombe equation of state

The Sanchez–Lacombe equations of state (SL EoS) was employed to predict the solubility of different α-olefins in their corresponding mixtures with polyolefins. Its predictive capabilities depend on binary α-olefin/polyolefin interaction parameters, which are extracted from the corresponding binary systems. These parameters can be used directly unless polymer crystallinity is high where fine adjustment is needed. It was found that model predictions were in excellent agreement with the available experimental data for different multicomponent systems over a wide range of pressure, temperature and mixture composition. An accurate quantitative knowledge of olefins solubility in polyolefins is essential for the detailed design and modelling of polymerization reactors. Nevertheless, there are a limited number of studies that deal with modelling of multicomponent α-olefins/polyolefin systems. This work can be considered as a part of a comprehensive plant-scale modelling approach for industrial polyolefin manufacturing processes.

The Effect of Pure Component Characteristic Parameters on Sanchez–Lacombe Equation‐of‐State Predictive Capabilities

AbstractThe dependence of predictive capabilities of SL EOS on the pure characteristic parameters of monomers and polymers is investigated. A sensitivity analysis study is carried out to understand the effect of these parameters on the predictive capability of SL EOS for different α‐olefin/polyolefins systems. Among all pure component characteristic parameters, the monomer characteristic temperature (T*monomer) has the largest impact on SL EOS predictive capability; whereas the polymer characteristic density (ρ*polymer) is found to have the smallest impact. magnified image

Partition coefficients of furan derivative compounds in 1-n-butyl-3-methylimidazolium chloride ([bmim][Cl])–supercritical CO2 biphasic systems and their correlation and prediction with the LSER-δ model

Infinite dilution partition coefficients of furan and furan derivative compounds (2-methylfuran, 2-ethylfuran, furfural and furfuryl alcohol) between ionic liquid ([bmim][Cl]: 1-n-butyl-3-methylimidazolium chloride) and supercritical carbon dioxide (scCO2) were measured at temperatures from 313 to 353K and at pressures from 9 to 21MPa with a chromatographic method. A linear solvation energy relationship-solubility parameter (LSER-δ) model was applied to available data and was compared with a proposed entropic term and with the Sanchez–Lacombe equation of state (SL EoS). The average relative deviations (ARDs) of furan derivative compounds, which were newly measured, for SL EoS model, LSER-δ model and modified LSER-δ model were within 3.2%, 14.9% and 14.7%, respectively. The LSER-δ model can be applied as prediction model for Kw3∞ of ionic liquid–CO2 systems for which solute descriptors are available.

Correlation of supercritical CO2–ionic liquid vapor–liquid equilibria with the ε*‐modified Sanchez–Lacombe equation of state

ABSTRACTThe ε*‐modified Sanchez–Lacombe equation of state (ε*‐modified SL EOS) contains a temperature‐dependent interaction energy that allows it to provide better pure component ionic liquid pressure–volume–temperature representation than the original SL EOS. In this work, we applied the ε*‐modified SL EOS to correlate available high pressure CO2–ionic liquid vapor–liquid equilibrium (VLE) data, which are important for developing viscosity correlations. Usual SL EOS mixing rules were applied with one interaction parameter, kij, which was fitted to the data. For the case of kij equal to zero, the ε*‐modified SL EOS could greatly improve the average relative deviation (ARD) of the VLE (ARD 14.6%) over that of the original SL EOS (ARD 44.0%). For the case of kij being fitted for both EOS, representation of the VLE of both equations was similar (ARD ≤ 9%). The ε*‐modified SL EOS is able to describe the vapor–liquid equilibria data over a wide range of pressures (0.1 < P < 100 MPa) and gives semi‐quantitative (ARD < 15%) representation of CO2 solubilities in many ionic liquids from knowledge of only the pure component properties. © 2012 Curtin University of Technology and John Wiley & Sons, Ltd.

Solubility of Subcritical and Supercritical Propylene in Semicrystalline Polypropylene

The solubility of propylene in semicrystalline isotactic polypropylene (iPP) was measured at temperatures from (348.15 to 383.15) K and pressures up to 8 MPa by a pressure-decay method. The results demonstrated that solubility of propylene in iPP is increased with elevated pressure and decreased with elevated temperature. The results could be correlated using the Sanchez−Lacombe equation of state (SL EOS) with temperature-dependent binary interaction parameters kij. It was shown that the SL EOS can well predict the solubility of propylene in polypropylene over a wide range even above the critical temperature and pressure. The deviations between experimental data and calculated results were within 5 %. It is important to point out that the value of kij varied almost linearly with respect to temperature, and the solubility of propylene in semicrystalline polypropylene in other conditions can be estimated.

Compatibility analysis of Nylon 6 and poly(ethylene- n-butyl acrylate-maleic anhydride) elastomer blends using isothermal crystallization kinetics

Nylon 6 is a widely used engineering polymer, and has relatively poor impact strength. Ethylene, n-Butyl acrylate, maleic anhydride (E- nBA-MAH) terpolymer is blended with Nylon 6 to enhance its impact strength. Mixture should be compatible to be used in applications. The bare interaction energy between Nylon 6 and E- nBA-MAH terpolymer is calculated according to melting point depression approach using both Flory–Huggins (FH) Theory and Sanchez–Lacombe Equation of State (SL EOS). It demonstrates that blends are thermodynamically favorable to any arrangements. Yet, isothermal crystallization kinetics and WAXS crystallization peaks of blends reveal that mixtures of various compositions have different crystallization behaviors and require alternating crystallization energy due to crystalline structures of individual polymers. Also, SEM images support that after 5% addition of elastomeric terpolymer, interaction loosens due to strong crystalline structure of Nylon 6.

Simple modification of the temperature dependence of the Sanchez–Lacombe equation of state

In this work, the interaction energy term of the Sanchez–Lacombe equation of state (SL EOS) was modified to take into account the temperature dependence of hydrogen bonding and ionic interactions. A simple function was used in the form of the Langmuir equation that reduces to the original SL EOS at high temperature. Comparisons are shown between the ɛ*-modified SL EOS and the original SL EOS. The ɛ*-modified SL EOS could represent volumetric data for the group of non-polar fluids, polar fluids and ionic liquids to within an absolute average deviation (AAD) of 0.85%, 0.51%, and 0.054%, respectively whereas, the original Sanchez–Lacombe EOS gave AAD values of 0.99%, 1.2%, and 0.21%, respectively. The ɛ*-modified SL EOS provides remarkably better PVT representation and can be readily applied to mixtures.

Mathematical modelling of the solubility of supercritical CO 2 in poly( l-lactide) and poly( d,l-lactide-co-glycolide)

Two mathematical models, Sanchez–Lacombe equation of state and the Perturbed-Chain Statistical Associating Fluid Theory were applied for modelling the phase equilibrium for the poly( l-lactide)–CO 2 and poly( d,l-lactide-co-glycolide)–CO 2 systems. Aspen Polymer Plus software was used. The results were compared with previously obtained experimental values for solubility. The solubility of scCO 2 in the two biodegradable polymers was calculated for three different temperatures (308, 313 and 323 K) in the pressure range (10–30 MPa). The characteristic parameters for the components and the binary interaction parameters for the models were optimized in order to obtain the best fit between the estimated and the experimental gas solubility data. The results suggest that both SL EOS and PC-SAFT are reliable models in describing the phase equilibrium of the PLLA–CO 2 and PLGA–CO 2 systems at the proposed working conditions.

Polymer solution and lattice theory applications for modeling of asphaltene precipitation in petroleum mixtures

Here asphaltene precipitation in petroleum reservoirs during natural depletion and miscible gas injection is modeled via two distinct and new methods (polymer solution and lattice theories). The first model is based on the polymer solution theory, which is a combination of Miller's combinatorial term with a modified residual term of the original Flory-Huggins theory. The second one is the application of the well-known Sanchez-Lacombe equation of state (SL EOS) to describe the phase behavior of asphaltene compounds in crude oil. The results of both models show an acceptable and good agreement between the real data (field and experimental) and these two models. As it can be seen from the obtained results of these two models, it seems application of the lattice or polymer solution theories (based on The Miller's combinatorial term) could give the better and more close to real data.