Modeling of transfer phenomena on heterogeneous ziegler catalysts. II. Experimental investigation of intraparticle mass transfer resistance during the polymerization of ethylene in slurry

An experimental investigation of mass transfer limitations on a single batch of high activity, heterogeneous catalysts used in the slurry polymerization of ethylene is presented. The viscosity of the continuous phase was varied, using trace amounts of inert copolymer in order to reduce the monomer diffusivity, and the activity levels were varied using hexene as an activator. These changes were intended to clearly identify situations in which the polymerization becomes mass-transfer-limited due to diffusion resistance in the pores of the catalyst. Increasing the observed activity of the catalyst from approximately 9000 to 40,000 grams of polymer per gram of catalyst per hour (g/g/h) revealed no evidence of mass transfer resistance, even when the diffusivity of the monomer in solution was reduced by a factor of six. Analysis of the molecular weight as a function of particle size supported this conclusion but did suggest that there might be slight chemical differences between large and small particles. © 1996 John Wiley & Sons, Inc.     

Evaluation of the effect of reaction and mass transfer on the growth of polymer particles in olefin polymerization

The process of the growth of polymer particles in olefin polymerization is studied. The regions of the possible overheating of particles due to the polymerization reaction in the gas and liquid phases of a monomer and in a solvent are estimated. It is shown how the rates of external mass transfer, internal diffusion, and reaction in the polymer particle vary with its growth. The cause of unusual transition of the reaction from the diffusion region to the kinetic one with the growth of particles is clearly explained. A model for the dynamics of the polymerization process is proposed that takes into account the diffusion of active component ions of a catalyst (chlorine in Ti _x Cl _y and oxygen in Cr _x O _y ). The results of the study are used in the application of high-activity catalysts to the slurry process of propylene polymerization.     

Study on process parameters in metallocene polymerizations,I. Apparent viscosity and macro-scale mass transfer

A heat balance reaction calorimeter was used to obtain information about the most informative process parameters in polymerizations carried out with Et[Ind]₂ZrCl₂-methylaluminoxane catalyst. The viscosity of the reaction mixture was found to increase dramatically during the homopolymerization of ethylene, but it could be controlled through appropriate selection of the reaction mixture medium. The mass transfer between the gas and liquid phases was the rate-determining step for the polymerization when the reaction mixture-based Reynolds number was below 2.500. The limited mass transfer between the gas and liquid phases was caused by the intensive activity of the metallocene catalyst and the increased viscosity of the reaction mixture.     

Mass transfer effects in emulsion polymerization systems. I. Diffusional behavior of chain transfer agents in the emulsion polymerization of styrene

On the basis of the so-called two-films theory for mass transfer, a mathematical model for transfer of chain transfer agents from monomer droplets to polymer particles, where chain transfer agent molecules are consumed by the chain transfer reaction, is developed for an emulsion polymerization system. It is shown by the model that the concentration of chain transfer agent in the polymer particles during the polymerization is decreased to a value much less than that which would be attained if thermodynamic equilibrium for chain transfer agent were reached between the polymer particles and the monomer droplets, due mainly to the resistance to transfer of chain transfer agent molecules across the diffusion films at the interface between the monomer droplets and the water phase. The validity and utility of the model developed for predicting the diffusion and consumption rates for chain transfer agent are demonstrated experimentally using five normal aliphatic mercaptans from n-C₇ to n-C₁₂ as chain transfer agents in the seeded emulsion polymerization of styrene. © 1994 John Wiley & Sons, Inc.     

Assessment of kinetics of photoinduced Fe‐based atom transfer radical polymerization under conditions using modeling approach

Kinetic insight into photoinduced Fe‐based atom transfer radical polymerization (ATRP) involving monomer‐mediated photoreduction was performed by modeling approach for the first time. Preliminary numerical analysis of number‐average molar mass (M_n) derivation in this specific system was given. Simulation results provided a full picture of reactant concentration and reaction rate throughout the entire polymerization. Methyl 2,3‐dibromoisobutyrate (MibBr₂) generated from methyl methacrylate (MMA)‐mediated photoreduction as the leading factor for the deviation of M_n from theoretical value was confirmed by reaction contributions in α‐bromophenylacetate (EBPA) containing system. Reasonable predictions were made with respect to the polymerizations under a variety of initial conditions. Results show that increasing light intensity will shorten transition period and increase steady state polymerization rate; decreasing catalyst loading will cause the decrease in polymerization rate and M_n deviation; varying initiation activity will slightly increase the time to attain steady state of dispersity (M_w/M_n) evolution and enormously change the fraction of reaction contributions; increasing targeted chain length will extend transition period, decrease steady state polymerization rate, increase M_n deviation degree with same reaction contributions, and decrease the time to attain the steady state of M_w/M_n. The numerical analysis presented in this work clearly demonstrates the unique ability of our modeling approach in describing the kinetics of photoinduced Fe‐based ATRP of MMA. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

A unified conjugate mass transfer model of VOC emission

This paper develops a unified conjugate mass transfer model for VOC (Volatile Organic Compound) emission, which implies conjugate boundary condition for mass transfer at the material-air interface. Thus, no special treatment is needed at the material-air interface and numerical methods for conjugate heat transfer problem can be applied directly. The material-air partition coefficient has been taken into account and its effect is the same as specific heat in the energy equation. The equivalent diffusion coefficient in the material K_maD_m instead of D_m characterizes the rate of mass transfer. The ratioK _ma D _m /D _a indicates whether VOC emission is controlled by the internal diffusion or not. The equivalent air-phase initial concentration C₀/K_ma determines the order of maximum concentration in the air. VOC emission contains two stages: the initial stage and the pseudo-steady stage when the emission rate nearly equals mass rate through the outlet of the air. Diffusion coefficient of VOC in the material has a significant effect on VOC emission in the two stages. The effect of partition coefficient on VOC emission depends on the value of K_maD_m/D_a.     

Mass transfer in olefin polymerization: estimative of macro- and microscale diffusion coefficients through the swollen polymer

Diffusion coefficient of propylene through polypropylene and ethylene through polyethylene, both in toluene and n-hexane, were estimated taking into account structural parameters of polymer chain and diffusing compound. In order to evaluate the influence of the structural variables considered in the prediction of the diffusivity and the swelling effects of the solvents, dynamic simulations of the metallocene-based slurry polymerization of propylene were performed using the assumptions of the multigrain model. The solvent influence was found to be more pronounced on the MAO diffusion, which is a larger molecule than the monomers propylene and ethylene. For n-hexane, the screening effects of the polymer chains were shown to hinder the diffusion of large molecules. The monomer concentration along the macro- and microscale particles was found to be quite constant, what can be attributed to the slight influence of the monomer diffusive transport in slurry polymerization of olefins, which is in agreement with the literature.     

Experimental proof of the existence of mass‐transfer resistance during early stages of ethylene polymerization with silica supported metallocene/MAO catalysts

The size of a silica supported metallocene/MAO (methylaluminoxane) catalyst plays an important role in determining its productivity during ethylene polymerization. From a chemical engineering point of view, this size dependency of catalytic activity of supported metallocenes is mathematically connected with the different levels of mass‐transfer resistance in big and small catalyst particles but no experimental evidence has been provided to date. The results of this systematic experimental study clearly demonstrate that the intraparticle monomer diffusion resistance is high in bigger catalyst particles during initial instants of ethylene polymerization and diminishes with the polymer particle growth. Two different silica supported metallocene/MAO catalysts provided the same results while highlighting the fact that catalyst chemistry should be carefully considered while studying complex chemical engineering problems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4476–4490, 2017     

Modeling of transfer phenomena on heterogeneous Ziegler catalysts: Differences between theory and experiment in olefin polymerization (an introduction)

This article begins by briefly reviewing the more important contributions to the area of modeling heat and mass transfer, and particle growth during the polymerization of olefins on Ziegler–Natta catalysts. It is shown that these models are capable of identifying the critical areas involved in heat and mass transfer, and of modeling polymerizations where the observed activity is less than approximately 5,000 g of polymer per gram of catalyst per hour (g/g/h). However, it is not possible to use these models “as-is” to model more modern catalysts whose activity levels can surpass the 50,000 g/g/h mark because they predict prohibitively large concentration gradients inside the growing particles during slurry polymerizations, and temperature gradients outside the particles during polymerization in the gas phase. An analysis of the mass and heat transfer Peclet numbers (Pe) reveals that certain simplifying assumptions may not always be valid. Pe values in the transition range suggest that convection inside the particles during polymerization in the liquid phase may help to explain why observed mass transfer rates are higher than the predicted rates. In an opposite vein, a Pe analysis shows that conductive heat transfer may play an important role at length scales characteristic of those in the early stages of polymerization. A new mechanism for heat transfer at reduced length scales is proposed. © 1995 John Wiley & Sons, Inc.     

Pore diffusion: Dependence of the effective diffusivity on the initial sorbate concentration in single and multisolute batch adsorption systems

The present work studies the intraparticle diffusivity in batch adsorption systems as a function of the initial sorbate concentration. The systems under investigation are basic dyes, namely Basic Blue 69, Basic Red 22 and Basic Yellow 21 and their binary and ternary combinations, all adsorbing onto activated carbon Filtrasorb 400. They study is based on the film-pore diffusion model and the output is a combination of the external mass transfer coefficient, k_f and the effective diffusivity, D_eff that yields congruent experimental and theoretical kinetic data. It has been found the D_eff varies with C_o in an exponential decay function. Furthermore. D_eff values undergo a general reduction in the multisolute systems compared to the single component systems. Also, the relative diffusion rates in the multisolute systems are found to change such that D_eff of the slower diffuser is enhanced and that D_eff of the faster diffuser is inhibited.     

Morphological development of impact polypropylene produced in gas phase with a TiCl4/MgCl2 catalyst

This article reports on a comprehensive study of the reaction kinetics, particle morphology development, and polymer properties of impact polypropylene produced in gas phase with a TiCl₄/MgCl₂ catalyst. Experiments were conducted over a range of copolymerization times, temperatures, monomer compositions, and hydrogen levels. The catalyst was found to exhibit a decay-type reaction rate for ethylene and propylene, but the presence of both monomers together caused an activation of the catalyst. Copolymer composition was constant over reaction time. Hydrogen was found to reversibly enhance the rate of propylene polymerization but to have no effect on ethylene. Microscopy provided evidence that the copolymer phase segregates from the homopolymer during polymerization. As copolymer content increased, product bulk density decreased because of the presence of sticky material on the particle surface. However, even at 70 wt % copolymer, enough pores were present in the particle to prevent monomer diffusion limitations. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 3085–3106, 2001     

Simulation of packed bed reactors using lattice Boltzmann methods

Lattice Boltzmann (LB) methods are used to simulate hydrodynamics, reaction and subsequent mass transfer in a disordered packed bed of catalyst particles at sub-pore length-scales. In contrast to previous studies, a variety of modifications are introduced in the LB method enabling particle Pe numbers up to 10⁸, and hence realistic values of diffusivity, to be accessed. These include decoupling the hydrodynamics from mass transfer and the use of a rest fraction in the LB formulation of mass transfer. In addition the mass transfer simulations are modified to permit spatially varying values of diffusivity, essential to differentiate between intra- and inter-particle diffusivity (D_intra and D_inter, respectively). The simulation method is applied to both a disordered and ordered 2D packing for a range of Pe (15.6-1557.8) and Re (0.16-1.56) numbers, as well as various ratios of D_intra/D_inter (0-1), whilst simulating an esterfication reaction catalyzed by an ion-exchange resin. The value of D_intra is found to have limited effect, whilst reducing Pe number results in a considerable increase in overall conversion. The simulation method is then applied to a 3D lattice for which experimental conversion data is available. This experimental data is straddled by the simulation case of D_intra=0 and D_intra=D_inter, as expected.     

Comparison of Selective Gas Phase‐ and Liquid Phase Hydrogenation of (Cyclo‐)Alkadienes towards Cycloalkenes on Pd/Alumina Egg‐Shell Catalysts

The hydrogenation of dienes such as 1,3‐butadiene, cyclooctadiene, and of acetylenic hydrocarbons on Pd catalysts shows high reaction rates and consequently, a strong influence of mass transfer on the selectivity of the intermediate alkene or cycloalkene product. 100 % selectivity towards (cyclo)‐alkene hydrogenation is achieved for the gas phase when the Thiele modulus is , where L is the thickness of the active layer and D_eff is the effective diffusion coefficient of the diene. The interdependencies expressed by this formula were studied in detail using model catalysts with regular pores of uniform length and diameter and perpendicular to the surface. These catalysts were prepared by anodic oxidation of aluminium wires and immobilization of the active Pd. For the liquid phase procedure of selective hydrogenation, a reaction mass transfer model has been derived in order to compare the gas phase and liquid phase procedures, in particular with respect to the selectivity. The hydrogenation of 1,3‐cyclooctadiene and of 1,3‐butadiene were studied for both procedures employing the same catalyst. The rate of hydrogenation can be represented for both cases by the identical kinetic equation r₁ = k₁ c_H2. This result is interpreted by assuming that the access of hydrogen to the surface through the dense layer of adsorbed diene is the rate determining step.     

Restricted diffusion of residual molecules in catalyst pores under reactive conditions

The restricted diffusion of residual molecules under catalytic conversion conditions was investigated using commercial catalysts. The effectiveness factor, η, and the effective diffusion coefficient, D_e, for residual molecules were evaluated and explicitly compared based on a pseudo-first-order reaction kinetic model and the Thiele modulus. The experimental results showed that the restrictive diffusion of heavy oil molecules is affected by the joint functions of several factors, such as the operating conditions, the size and configuration of the reactant molecules, and the average pore diameter of the catalyst. The reaction temperature has a greater influence on restrictive diffusion than the other operating factors, and the ratio of reactant molecular size to catalyst pore size is the most critical factor that determines the degree of restrictive diffusion. Moreover, a mathematical expression was derived for the restrictive factors in order to describe the relationship between the effective diffusivity and ratio of molecule-to-pore size.     

Modeling separation of proteins by inert core adsorbent in a batch adsorber

Adsorption/desorption kinetics of protein on the binding ligand of inert core adsorbent in a batch adsorber is analyzed theoretically for Langmuir isotherm coupled with the intraparticle diffusion and film mass transfer resistances. For the two limiting cases of Langmuir isotherm, there are analytical solutions. New analytical solutions are derived for Henry isotherm, and the analytical solution of shrinking core model is recommended for rectangular isotherm. The effects of the inert core radius, equilibrium constant, intraparticle diffusion and film mass transfer resistances on the time evolution of bulk concentration and particle radial profiles were investigated. The applicable range of the analytical solution with rectangular isotherm is given. A new method to estimate both film mass transfer coefficient, k_f, and effective pore diffusivity, D_pe, from a single bulk concentration-time curve in batch adsorber is given and tested with literature data for the adsorption of BSA on CB-6AS inert core adsorbent.     

The Proper Use of Mass Diffusion Equations in Drying Modeling: Introducing the Drying Intensity Number

This article intends to clearly define the possibilities and limitations offered by a simple diffusion approach of drying. Actually, many works use a simple diffusion equation to model mass transfer during drying, probably because a simple analytical solution of this equation does exist in the case of simple boundary conditions. However, one has to be aware of the limitations of this approach. Using a comprehensive formulation and a relevant computational solution, the most frequent assumptions of the diffusion approach were rigorously tested. It is concluded that analytical solutions must be discarded for several reasons: analytical solutions, either using Dirichlet or third kind boundary conditions, are often misleading and should be avoided; in the drying process, the coupling between heat and mass transfer is mandatory; nonlinearity (variation of diffusivity with moisture content) can hardly be avoided for mass transfer. In order to reach a verdict, a dimensionless number, the Drying Intensity Number (N_DI), is introduced. It allows the level of coupling between heat and mass transfer to be easily assessed. Thanks to this number, a guide is proposed for choosing the right level of modeling, depending on the drying configuration.     

Color removal from dye wastewaters by adsorption using powdered activated carbon: Mass transfer studies

Color removal from synthetic dye wastewater which typically emanates from the Taiwan textile industry has been studied using powdered activated carbon (PAC) as an adsorbent. The CIE colorimetric system has been used in the measurement of color for the treatment of disperse-red-60 dye wastewater. The effect of contact time, dye concentrations and PAC dosage on color and color removal has been investigated. A film-pore double resistance diffusion model for mass transfer has also been used in this study to determine the effective diffusivity, D_eff, for the adsorption of disperse-red-60 dye wastewater to PAC.     

Simplified treatment of mass transfer for gas-phase hydrogenation/dehydrogenation of heavy compounds

Using single catalyst pellets (5 mm) 15% Ptγ–Al₂O₃, we experimentally studied gas-phase benzene hydrogenation at normal pressure by thermocouple measurements of gas flow and the pellet center. Temperature of gas flow was varied in the range of 20 ‡C / 350 ‡C for three molar fractions of benzene vapor (0.1, 0.2, and 0.3) mixed with hydrogen. The ignition/extinction behavior of the flow-pellet temperature rise (maximum values up to 100 ‡C/ 200 dgC) is explained by internal-external mass transport limitations of the reaction rate and reaction reversibility at high pellet temperature. A simplified pseudobinary treatment of both multicomponent intrapellet mass transfer (in bimodal porous media) and multicomponent external mass transfer (under forced convection) is proposed on the basis of the analytical estimation. The validity of the suggested approach is confirmed by comparing the experimental data for benzene hydrogenation with rigorous (multicomponent) and approximated (pseudobinary) calculations obtained by using a mathematical model of a spherically symmetric pellet. The simplified approach appears to be quite accurate for reactions A+nH₂=B of hydrogenation (n>0) or dehydrogenation (n<0) of sufficiently heavy compounds, i.e. if D _AH ≈D _BH >>D _AB      

Reverse atom transfer radical polymerization of methyl methacrylate in different solvents

The reverse atom transfer radical polymerization of methyl methacrylate was investigated in different solvents: xylene, N,N‐dimethylformamide, and pyridine. The polymerizations were uncontrolled, using 2,2′‐bipyridine as a ligand in xylene and pyridine because the catalyst (CuBr₂/2,2′‐bipyridine complex) had poor solubility in the xylene system. In the pyridine system, the solubility of the catalyst increased, but the solvent could complex with CuBr₂, which influenced the control of the polymerization. In the N,N‐dimethylformamide system, the catalyst could be dissolved in the solvent completely, but the ? N(CH₃)₂ group in N,N‐dimethylformamide could also complex with CuBr₂, so the polymerization could not be well controlled. The ligand of 4,4′‐di(5‐nonyl)‐2,2′‐bipyridine was also investigated in xylene; the introduction of the ? CH(C₄H₉)₂ group enabled the CuBr₂/4,4′‐di(5‐nonyl)‐2,2′‐bipyridine complex to easily dissolve in xylene, and the polymerizations were well controlled. The number‐average molecular weight increased linearly with the monomer conversion from 4280 to 14,700. During the whole polymerization, the polydispersities were quite low (1.07–1.10). © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

Experimental study of mass transfer limitations in Fe- and Cu-zeolite-based NH3-SCR monolithic catalysts

An experimental study of steady-state selective catalytic reduction (SCR) of NO_x with NH₃ on both Fe-ZSM-5 and Cu-ZSM-5 monolithic catalysts was carried out to investigate the extent of mass transfer limitations in various SCR reactions. Catalysts with different washcoat loadings, washcoat thicknesses and lengths were synthesized for this purpose. SCR system reactions examined included NO oxidation, NH₃ oxidation, standard SCR, fast SCR and NO₂ SCR. Comparisons of conversions obtained on catalysts with the same washcoat volumes but different washcoat thicknesses indicated the presence of washcoat diffusion limitations. NH₃ oxidation, an important side reaction in SCR system, showed the presence of washcoat diffusion limitations starting at 350 °C on Fe-zeolite and 300 °C on Cu-zeolite catalysts. Washcoat diffusion limitations were observed for the standard SCR reaction (NH₃+NO+O₂) on both Fe-zeolite (≥350 °C) and Cu-zeolite (≥250 °C). For the fast (NH₃+NO+NO₂) and NO₂ SCR (NH₃+NO₂) reactions, diffusion limitations were observed throughout the temperature range explored (200–550 °C). The experimental findings are corroborated by theoretical analyses. Even though the experimentally observed differences in conversions clearly indicate the presence of washcoat diffusion limitations, the contribution of external mass transfer was also found to be important under certain conditions. The transition temperatures for shifts in controlling regimes from kinetic to washcoat diffusion to external mass transfer are determined using simplified kinetics. The findings indicate the necessity of inclusion of mass transfer limitations in SCR modeling, catalyst design and optimization.