Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method

This paper presents a new method for multiphase equilibria calculation by direct minimization of the Gibbs free energy of multicomponent systems. The methods for multiphase equilibria calculation based on the equality of chemical potentials cannot guarantee the convergence to the correct solution since the problem is non-convex (with several local minima), and they can find only one for a given initial guess. The global optimization methods currently available are generally very expensive. A global optimization method called Tunneling, able to escape from local minima and saddle points is used here, and has shown to be able to find efficiently the global solution for all the hypothetical and real problems tested. The Tunneling method has two phases. In phase one, a local bounded optimization method is used to minimize the objective function. In phase two (tunnelization), either global optimality is ascertained, or a feasible initial estimate for a new minimization is generated. For the minimization step, a limited-memory quasi-Newton method is used. The calculation of multiphase equilibria is organized in a stepwise manner, combining phase stability analysis by minimization of the tangent plane distance function with phase splitting calculations. The problems addressed here are the vapor–liquid and liquid–liquid two-phase equilibria, three-phase vapor–liquid–liquid equilibria, and three-phase vapor–liquid–solid equilibria, for a variety of representative systems. The examples show the robustness of the proposed method even in the most difficult situations. The Tunneling method is found to be more efficient than other global optimization methods. The results showed the efficiency and reliability of the novel method for solving the multiphase equilibria and the global stability problems. Although we have used here a cubic equation of state model for Gibbs free energy, any other approach can be used, as the method is model independent.     

Kinetics and phase equilibria of competing aldolization and elimination in a three-phase reactor

Butyraldehyde was aldolized with formaldehyde over a weakly basic anion-exchange resin catalyst in aqueous solvent in a batch reactor operating at atmospheric pressure and at temperatures 50–70°C. The reaction mixture was a liquid–liquid–solid system, an emulsion, the phase equilibria of which were studied through chemical analysis of the organic and aqueous phase as well as of the mixed emulsion. Simplified rate equations were derived starting from molecular reaction mechanisms on the catalyst surface. A liquid–liquid reactor model for the fitting of the experimental results was developed on the basis of the rate equations and the phase equilibria. The model described very well the experimental data.     

Local hydrodynamics of gas–liquid-nanoparticles three-phase fluidization

The laser Doppler anemometer (LDA) and conductivity probes were used for measuring the local hydrodynamic performances such as gas holdup and liquid velocity in a lab-scale gas–liquid–TiO₂ nanoparticles three-phase bubble column. Effects of operating parameters on the local gas holdup and liquid velocity were investigated systematically. Experimental results showed that local averaged axial liquid velocity and local averaged gas holdup increased with increasing superficial gas velocity but decreased with increasing TiO₂ nanoparticles loading and the axial distance from the bottom of the bubble column. A three-dimensional computational fluid dynamic (CFD) model was developed in this paper to simulate the structure of gas–liquid–TiO₂ nanoparticles three-phase flow in the bubble column. The time-averaged and time-dependent predictions were compared with experimental data for model validation. A successful prediction of instantaneous local gas holdup, gas velocity, and liquid velocity were also presented.     

Phase transition phenomena of the adsorbed 1-dodecanol monolayer at the air–water interface

Phase transition phenomenon of the 1-dodecanol monolayer at the air/water interface was studied by the dynamic γ(t) curves and the adsorption isotherm obtained by ellipsometry at 20 °C. The surface-concentration adsorption isotherm clearly showed three abrupt increases at bulk concentration C of 1.3 × 10⁻⁹, 2 × 10⁻⁹ and 3.7 × 10⁻⁹ mol/mL, respectively. The 1st and the 3rd transitions observed herein, that were typical 2D first-order transitions, were consistent with the gas to liquid expanded (G–LE) and the liquid expanded to liquid condensed (LE–LC) phase transitions observed in a previous tensiometry study. The 2nd transition that occurred at C = 2 × 10⁻⁹ mol/mL was not identified from any previous dynamic surface-tension profiles. Judging from the substantial increase in the film thickness of the transition, it was believed that the orientation change of the adsorbed molecule was involved in the LE phase. A LE_h and a LE_v phase, that denoted the “lie-down” and “stand-up” types of adsorption, respectively, was used to describe this transition and a cusp, instead of a constant surface-tension region, was observed in the dynamic γ(t) curves for this transition. This suggested that, since the surface tension varied during the transition process, the newly identified LE_h and LE_v transition might not be the typical first-order type of phase transition.     

Liquid–liquid equilibrium correlations using lattice fluid equation of state with hydrogen bonding

The nonrandom lattice equation of state with hydrogen bonding (NLF-HB EOS) was examined for the correlation of liquid–liquid equilibria (LLE) for binary alcohol and hydrocarbon mixture in a wide pressure range. For hydrocarbon + alcohol mixtures the consideration of a hydrogen-bonding term in the lattice equation of state clearly improves the prediction for vapor–liquid equilibrium (VLE) as shown in previous works, but the prediction of LLE is still in question. In this paper, LLE data for alcohols (methanol and ethanol) + hydrocarbons (n-hexane to n-hexadecane) were correlated by NLF-HB EOS and results were compared with a cubic equation of state (Peng–Robinson EOS with the T–K Wilson based G^E model). Both equations of state showed similar degree of accuracies but with different number of adjustable parameters. The Peng–Robinson EOS based approach requires six temperature dependent coefficients for accurate calculation whereas NLF-HB EOS requires only two temperature dependent coefficients. The effects of varying hydrogen-bonding energies for NLF-HB EOS are discussed.     

Effect of cooling rate and frequency on the calorimetric measurement of the glass transition

The glass transition of thermoplastics of different polydispersity and thermosets of different network structure has been studied by conventional differential scanning calorimetry (DSC) and temperature modulated DSC (TMDSC). The cooling rate dependence of the thermal glass transition temperature T_g measured by DSC, and the frequency dependence of the dynamic glass transition temperature T measured by TMDSC have been investigated. The relation between the cooling rate and the frequency necessary to achieve the same glass transition temperature has been quantified in terms of a logarithmic difference Δ=log₁₀[|q|]−log₁₀(ω), where |q| is the absolute value of the cooling rate in K s⁻¹ and ω is the angular frequency in rad s⁻¹ necessary to obtain T_g(q)=T(ω). The values of Δ obtained for various polymers at a modulation period of 120 s (frequency of 8.3 mHz) are between 0.14 and 0.81. These values agree reasonably well with the theoretical prediction [Hutchinson JM, Montserrat S. Thermochim Acta 2001;377:63 [6]] based on the model of Tool–Narayanaswamy–Moynihan with a distribution of relaxation times. The results are discussed and compared with those obtained by other authors in polymeric and other glass-forming systems.     

Drop properties and pressure fluctuations in liquid–liquid–solid fluidized-bed reactors

Characteristics of size, rising velocity and distribution of liquid drops were investigated in an immiscible liquid–liquid–solid fluidized-bed reactor whose diameter was 0.102 and 2.5 m in height. In addition, pressure fluctuations were measured and analyzed by adopting the theory of chaos, to discuss the relation between the properties of liquid drops and the resultant flow behavior of three (liquid–liquid–solid) phase in the reactor. Effects of velocities of dispersed (0–0.04 m s⁻¹) and continuous (0.02–0.14 m s⁻¹) liquid phases and fluidized particle size (1, 2.1, 3 or 6 mm) on the liquid drop properties and pressure fluctuations in the reactor were determined. The resultant flow behavior of liquid drops became more irregular and complicated with increasing the velocity of dispersed or continuous liquid phase, but less complicated with increasing fluidized particle size, in the beds of 1.0 or 2.1 mm glass beads. In the beds of 3.0 or 6.0 mm glass beads, the effects of continuous phase velocity was marginal. The resultant flow behavior of liquid drops was dependent strongly upon the drop size and its distribution. The drop size increased with increasing dispersed phase velocity, but decreased with increasing particle size. The drop size tended to increase with approaching to the center or increasing the height from the distributor. The size and rising velocity of liquid drops and correlation dimension of pressure fluctuations have been well correlated in terms of operating variables.     

Simulation of industrial catalytic-distillation process for production of methyl tert-butyl ether by developing user’s model on Aspen plus platform

The industrial catalytic-distillation process for the production of methyl tert-butyl ether (MTBE) from methanol and isobutylene was simulated by developing the process model as a user modular on Aspen plus platform. The model utilizes the Aspen plus system and retains the characteristics of the self-designed model, which has been verified in various scale-up processes. The experimentally determined reaction kinetics was applied in the model. NRTL and Redlick–Kwong–Soave equations were selected for the vapor–liquid equilibrium calculation. The NRTL binary interaction parameters were estimated from the experimental data of the two-component vapor–liquid equilibrium. Two typical industrial plants for the MTBE production, one using the loose-stack-type package technology and the other using the bale-type package technology in the catalytic-distillation column, were chosen as the sample processes to demonstrate the validity of the model. The flowsheet simulations of the two industrial plants were done on Aspen plus platform, in which the simulation of the catalytic-distillation column used the developed user modular. The results show that fair agreements between the calculated and operating data were obtained.     

The synthesis of nearly optimal on-off controllers with application to chemical processes

A new technique is presented for designing a set of on-off controllers for processes which can be approximated by linear-lumped parameter models of any order. The design is based on the minimization of a quadratic function of the process outputs. Each higher member of the set of systems approaches optimal control ever more closely. Our major concern, however, is with the lowest member of the set which is implemented by using only a relay and a simple summing device. Several analog computer examples are presented using this control scheme. In all cases, the system response is excellent from both quantitative and qualitative viewpoints.

One of the examples presented is the control of a simulated six stage liquid—liquid extraction unit. Here, the lowest level control is shown to outperform an experimentally tuned standard three-mode type of control as well as a control strategy based on dynamic programming which was developed for the same process by a previous investigator.     

Modeling and simulation of a liquid extraction column with structured packing

In this work mass transfer phenomenon of liquid–liquid extraction process with structured packing was modeled. The model was validated by means of fluid-dynamic and mass transfer tests, for mass transfer from the continuous to the disperse phase with n-butanol/succinic acid/water system. The effect on hold-up and outlet concentration profiles of each phase were evaluated when the incoming flow of the disperse phase was disturbed between 10 and 30%. Surface velocity of each phase and hold-up were considered in the model as functions of time. The continuous phase dispersion phenomenon was also taken into account. Deviation percentage average of 8% between the experimental data and the simulation results of the disperse phase composition in steady state were obtained. For the dynamic model the inclusion of the dispersion effect of the disperse phase and more experimental tests are recommended.     

Simultaneous liquid–liquid demixing and crystallization and its effect on the spherulite growth in poly(ethylene terephthalate)/poly(ether imide) blends

Poly(ethylene terephthalate) (PET)/poly(ether imide) (PEI) blends were miscible in the melt, but exhibited simultaneous liquid–liquid phase separation and crystallization over a wide range of temperature and composition. The interplay between these two processes is expected to dominate the morphological formation in the blends. In this study, the phase diagram of PET/PEI blend was determined to evaluate the envelop within which liquid–liquid phase separation was operative with crystallization. A UCST phase diagram below 240°C was identified for this system. The effect of liquid–liquid phase separation on the growth of PET spherulites was studied by small-angle light scattering (SALS). Nonlinear spherulite growths were observed for the blends at higher crystallization temperatures of 210°C and 220°C, while the growths were basically linear below 210°C. The nonlinear growth behaviour was discussed based on the competition between spherulite growth and spinodal decomposition.     

Novelties of liquid–liquid–liquid phase transfer catalysis Alkoxylation of p-chloronitrobenzene

Liquid–liquid–liquid phase transfer catalysis (L–L–L PTC) offers orders of magnitude intensification of rates of reaction and better selectivities than the biphasic PTC. The catalyst-rich middle phase is the main reaction phase. The etherification or alkoxylation of p-chloronitrobenzene (PCNB) was conducted by using alkanol and alkali instead of the metal alkoxide. A kinetic model is presented and validated.     

Determination of intrinsic viscosity of polymeric compounds through a single specific viscosity measurement

A modified method based on a combination of the Huggins and Schulz–Blaschke equations is proposed which enables the determination of intrinsic viscosity [η] from the measurement of a single specific viscosity. The method has been verified for different polymer samples having a wide range of [η] values and showed a variation of <±6×10⁻³% from the values obtained by Huggins extrapolation method     

Mass transfer effects on hydroformylation catalyzed by a water soluble complex

The rate of hydroformylation of 1-octene catalyzed by a water soluble catalyst is measured in mechanically agitated batch reactor at various stirrer speeds and organic phase holdups. The data have been analyzed by coupling reaction kinetics to a pseudo-homogeneous gas–liquid–liquid model based on Higbie's penetration theory which takes into account the presence of the dispersed organic phase. A rapid liquid–liquid mass transfer of the reactants is assumed leading to an equilibrium between the continuous and the dispersed phases. The predicted values of the rate are in good agreement with the experimental one. The depletion of the organic substrate in the continuous phase is found negligible.     

Spectroscopic ellipsometry characterization of TiO2 thin films prepared by the sol–gel method

TiO₂ thin films were prepared on SiO₂/Si(100) substrates by the sol–gel process. XRD results indicate that the major phase of TiO₂ thin films is anatase. The surface morphology and cross-section are observed by FE-SEM. The surface of thin films is dense, free of cracks and flat. The average grain size is about 60–100 nm in diameter. The thickness of single layer TiO₂ thin films is about 60 nm, which increases with the concentration of solution. Ellipsometric angles ψ, Δ are investigated by spectroscopic ellipsometry. The optical constant and the thickness of TiO₂ thin films are fitted according to Cauchy dispersion model. The results reveal that the refractive index and the extinction coefficient of TiO₂ thin films in wavelength above 800 nm are about 2.09–2.20 and 0.026, respectively. The influences of processing conditions on the optical constants and thicknesses of TiO₂ thin films are also discussed.     

Mathematical modelling of fixed bed adsorption of aromatics and sulphur compounds in kerosene deodorisation

A mathematical model that adequately predicts the effluent concentration and breakthrough profiles of aromatic and sulphur compounds in kerosene deodorisation has been developed. The contributions of radial transport (pore and surface diffusion) were incorporated in the mathematical formulations. Thus, the final model took into account the overall effect of both the solid and liquid phase mass transfer resistances. The resulting model expressions were coupled partial differential equations which were resolved into first order ordinary differential equations using the orthogonal collocation technique. The roots of the Jacobi orthogonal polynomials (P_N^,β) with N=8 and =β=0 were taken as the interior collocation points while the exterior points were ζ=1, z=0 and z=1. The fourth-order Runge Kutta method was then used to integrate the 4N differential equations and the resulting functions were solved simultaneously to obtain the effluent and breakthrough profiles. Theoretical predictions from the model were compared with column adsorption data to ascertain the authenticity of the model. The agreement was good for both cases of aromatics and sulphur breakthroughs. The experimental breakthrough time of 8 h was predicted by the model. The breakthrough profiles also confirmed the formation of multiple adsorption layers.     

Application of an extended Tool–Narayanaswamy–Moynihan model.Part 2. Frequency and cooling rate dependence of glass transition from temperature modulated DSC

In the first part of this paper a Tool–Narayanaswamy–Moynihan-model (TNM) extended by non-Arrhenius temperature dependence of the relaxation time was applied to describe results from temperature modulated DSC (TMDSC). The model is capable to describe the features of the heat capacities measured in TMDSC scan experiments in the glass transition region of polystyrene (PS). In this part the model is applied to bisphenol A-polycarbonate (PC). Both aspects of glass transition, vitrification as well as the dynamic glass transition are again well described by the model. The dynamic glass transition above T_g can be considered as a process in thermodynamic equilibrium. The non-linearity parameter (x) of the TNM model is not needed to describe complex heat capacity as long as the dynamic glass transition is well separated from vitrification. Under such conditions the relation between cooling rate (q₀), and the corresponding frequency (ω) can be found from the two independently observed glass transitions. Fictive temperature and the maximum of the imaginary part of complex heat capacity are used for comparison here. The measurement as well as the TNM-model confirm the relation derived from Donth's fluctuation approach to glass transition, ω=q₀/aδT, where a=5.5±0.1 (confirmed previously experimentally as 6±3) and δT is mean temperature fluctuation of the cooperatively rearranging regions (CRRs).     

CO2, NOx and SO2 emissions from the combustion of coal with high oxygen concentration gases

The emissions of CO₂, NO_x and SO₂ from the combustion of a high-volatile coal with N₂- and CO₂-based, high O₂ concentration (20, 50, 80, 100%) inlet gases were investigated in an electrically heated up-flow-tube furnace at elevated gas temperatures (1123–1573 K). The fuel equivalence ratio, φ, was varied in the range of 0.4–1.6. Results showed that CO₂ concentrations in flue gas were higher than 95% for the processes with O₂ and CO₂-based inlet gases. NO_x emissions increased with φ under fuel-lean conditions, then declined dramatically after φ=0.8, and the peak values increased from about 1000 ppm for the air combustion process and 500 ppm for the O₂(20%)+CO₂(80%) inlet gas process to about 4500 ppm for the oxygen combustion process. When φ>1.4 the emissions decreased to the same level for different O₂ concentration inlet gas processes. On the other hand, NO_x emission indexes decreased monotonically with φ under both fuel-lean and fuel-rich combustion. SO₂ emissions increased with φ under fuel-lean conditions, then declined slightly after φ>1.2. Temperature has a large effect on the NO_x emission. Peak values of the NO_x emission increased by 50–70% for the N₂-based inlet gas processes and by 30–50% for the CO₂-based inlet gas process from 1123 to 1573 K. However, there was only a small effect of temperature on the SO₂ emission.     

Deactivation behavior of ruthenium promoted Co/γ-Al2O3 catalysts in Fischer–Tropsch synthesis

Heterogeneous catalytic hydrogenation of cyclohexene, catalyzed by Pt/Al₂O₃, was carried out in solutions of 2-hydroxyethylammonium formate (a room temperature ionic liquid, RTIL) mixed with methanol, ethanol and propan-2-ol at 25 °C. The rate constants of the reaction in ionic liquid alcohol mixtures were higher than alcohol alone. First-order rate constant of the reaction in the RTIL relative to propan-2-ol is approximately 28. Furthermore, the rate constant of the reaction increases with the mole fraction of the ionic liquid. Single-parameter correlations of log k vs. normalized polarity parameter (), hydrogen-bond acceptor basicity (β) and hydrogen-bond donor acidity () do not give acceptable results in the solutions. In addition, log k does not show an acceptable dual-parameter correlation with π* (dipolarity/polarizibility, one of the Kamlet–Taft parameters for solvent that shows the dipolarity of the solvent) and , π* and β and and β. However single-parameter correlation of log k vs. π^* gives reasonable results. The increase of the reaction rate with π^* is attributed to the non-polar nature of the reactants.