t-Butylation of p-cresol with t-butyl alcohol over mesoporous Al-MCM-41 molecular sieves

Selective liquid-phase t-butylation of p-cresol with t-butyl alcohol (t-BuOH) to produce 2-t-butyl-p-cresol (TBC) has been conducted over Al-MCM-41 catalysts with different Si/Al ratios. The effects of various reaction parameters such as temperature, reaction time and n_t-BuOH:n_p-cresol ratio on the conversion of p-cresol and the selectivity of TBC have been systematically investigated as well. When the Si/Al ratio of Al-MCM-41 catalysts is increased from 21 to 104 (respectively yielding Al-MCM-41(21), Al-MCM-41(42), Al-MCM-41(62), Al-MCM-41(83) and Al-MCM-41(104)), both the conversion of p-cresol and the yield and selectivity of TBC decrease due to the decrease of the number of Brønsted acid sites of the Al-MCM-41 catalysts. Al-MCM-41(21) catalyst is found to give the highest conversion of p-cresol (88.2%) and the highest selectivity of TBC (90.40%) under the optimal n_t-BuOH:n_p-cresol mole ratio of 2:1, the optimal reaction temperature of 90 °C and the optimal reaction time of 2 h. Furthermore, Al-MCM-41(21) can be recycled up to at least four times without losing its catalytic performance for butylation reaction.     

Effect of lewis number on the transient behavior of catalytic gas—solid systems

The influence of Lewis number, ρ?_pD_e/?λ_e, on the transient behavior of exothermic irreversible first-order catalytic reaction inside a spherical porous pellet is analyzed taking into account external heat and mass transport as well as initial conditions corresponding to a pellet at uniform temperature and devoid of reactant.The destabilizing effect of low Lewis number and the existence of a limit cycle are confirmed and a qualitative interpretation is put forward.In regions of multiple stationary states, the Lewis number modifies substantially the domains of attraction of the stable solutions. Moreover, for certain values of this group and over the whole range of realistic initial conditions, the system remains entirely within the domain of attraction of just one of the steady states.     

Parametric Analysis of the Simplest Model of the Theory of Thermal Explosion—the Zel''dovich—Semenov Model

Parametric analysis is performed for the Zel'dovich–Semenov model, a basic model of the theory of thermal explosion that describes the dynamics of an exothermic reaction with arbitrary kinetics in a continuous stirred tank reactor. Particular attention is given to the cases of first and nthorder reactions, oxidation reaction, and reaction with arbitrary kinetics. Parametric dependences of steady states on dimensionless parameters, curves of multiplicity and neutrality of steady states, and parametric and phase portraits of the system are constructed. Regions of multiple steady states and selfoscillations and a region of technological safety are distinguished.     

Uniqueness and multiplicity criteria for an nth order chemical reaction

New and very strong criteria are presented for a priori prediction of the conditions for which the steady-state lumped parameter model of an nth order chemical reaction (n ≥ 0) in an adiabatic CSTR has either a unique or multiple solutions. The criteria show that the higher the order of the reaction the smaller is the region in the parameters space for which multiplicity can occur.New uniqueness and multiplicity criteria are developed also for an nth order reaction in a porous catalyst using a model, which accounts for intraparticle concentration gradients, while assuming a uniform intraparticle temperature different from the ambient one. The region in the parameters space for which steady state multiplicity can occur for this model is smaller than that for a corresponding lumped model, which ignores the intraparticle concentration gradients.     

On stability of a bubble column

The goal of this contribution is to formulate the simplest possible model for the bubble column hydrodynamics and analyse it for steady states, stability, and unsteady behaviour. The governing equations are based on the mass balance of the gas phase. Two closures for the gas velocity are used and reflect two typical operational regimes, homogeneous (HoR) and heterogeneous (HeR). The model has five parameters: column height H, terminal bubble speed u₀, hindrance exponent n, enhance exponent m, gas flow rate q. Three branches of steady solutions were found for HoR, one stable, one unstable, one neutrally stable. The first two are physically relevant, are of the node-type, and merge in the turning point bifurcation at large enough gas input. Two branches of steady solutions were found for HeR, one stable and one neutrally stable. The first one is physically relevant, is of the node-type, and persists for all plausible parameter values. In both regimes, the neutrally stable solution was classified as unphysical. The transition regime (TrR) was obtained by matching the stable solutions of HoR and HeR, with help of a sigmoidal bridging function. The system stability was related to the model topology. The linear approximation of the bubble column dynamics was studied and the relaxation time estimated. The full nonlinear dynamics was demonstrated too. Both the steady and unsteady behaviour of the bubble column was compared with available experimental data.     

Steady state multiplicity depending on coalescence in liquid—liquid continuous stirred reactors with reaction in the dispersed phase

The influence of drop coalescence and breakup on the existence of multiple steady states is studied for a two-phase stirred isothermal reactor where the chemical reaction in the d?ispersed phase obeys the rate expression ? r = kC/(1 + KC)². The random coalescence model developed by Curl was simulated using a modified Spielman and Levenspiel Monte Carlo technique.For certain range of the coalescence rate, Damköhler number, and dimensionless feed concentration, multiple steady states have been investigated.A special case has also been considered wherein the existence of multiple steady states for finite values of the coalescence rate is contrasted to the unique steady state solution for an infinite coalescence rate.     

Effect of catalyst dispersion on performance of slurry bubble column reactors

Using the sedimentation-diffusion model for catalyst dispersion the steady-state performance of semi-batch bubble column reactors has been studied over a wide range of mass transfer and reaction groups for reactions that are described by power law and Langmuir-Hinshelwood (L-H) type of kinetics. The effect of catalyst dispersion on conversion is found to be a complex function of mass-transfer and reaction parameters. Nonuniform catalyst distribution has a detrimental effect on the values of conversion for systems following nth-order kinetics. However, the use of a L-H rate form predicts improved conversions for some values of model parameters in the presence of solid dispersion.Also the reactor model accounts exactly for volume change effects during reaction. It is found that volume contraction enhances conversion for reactions following the nth-order kinetics, but that the opposite is possible with the L-H kinetics.     

Multiplicity and uniqueness for binary,exothermic reaction in a non-adiabatic continuous stirred tank reactor

Exact multiplicity and uniqueness criteria for steady state in a non-adiabatic continuous stirred tank reactor are studied through simple tangent analysis for binary, exothermic reaction of the type A + bB → Products with rate expression r_A = kC_A^m C_Bⁿ, where A is the limiting reactant. Important parameters for multiplicity criteria are reaction orders m and n, stoichiometric coefficient b, the ratio p of feed concentration of A to that of B, dimensionless activation energy α, dimensionless heat of reaction β, dimensionless heat transfer coefficient γ and dimensionless coolant temperature. Necessary conditions for the system to have multiple exit conversions (temperatures) are defined in the (m, n, b, p, α, β, γ) space. Multiplicity is guaranteed by limiting the dimensionless space time ? in a proper range in addition to the necessary conditions. Effects of various parameters on multiplicity and uniqueness are numerically calculated and graphically represented. Theoretical prediction for multiplicity are further compared with multiplicity data reported in literatures.     

Transient analysis of exothermic reactions within catalyst pellets. Effect of initial conditions

The transient behavior of exothermic, irreversible, first-order catalytic reaction inside a spherical, porous pellet is analyzed using mixed type boundary conditions to represent external resistances. Calculations are performed for Lewis numbers, ?C_pD_e/?λ_e, equal to unity and a pellet initially at uniform temperature and devoid of reactant, which is considered realistic. Phenomena occurring during the evolution of transients in the region of steady external transport limitation are described.In ranges where more than one steady state exists, the effect of the initial conditions on the attainment of the different steady states is analyzed. The results include information about transient behavior when the initial condition is at the boundary between stable domains of attraction. For certain ranges of parameters it is shown that the initial conditions studied may fall outside of the domain of attraction of one of the stable steady states, demonstrating that information about domains of attraction as well as steady states should be taken into account when designing catalytic systems.     

A note on the multiplicity of the Weisz-Hicks problem for an arbitrary “geometry factor”

A general non linear equation, derived from the mass and energy balance for non isothermal nth order reaction on catalyst pellets, but with “geometry factor” s different from 0, 1 and 2, is considered.Numerical solution of this equation for the heat generation parameter β → ∞ shows that an infinite number of steady states exist when 1 <s < 9 while no more than 3 steady states exist for s ? or s > 10.44. A finite number of solutions exist when 9 <s < 10.44. Similar results are obtained for a finite β and it is proved that no more than 3 steady states can exist in cylinder geometry (s = 1) for any value of the reaction parameters.The results obtained for an Arrhenius type rate constant are discussed and explained by comparison with the simplified model that appears with an exponential approximation of the Arrhenius rate constant.Apart from their theoretical significance models with variable geometry factor may be useful in explaining results obtained with pellets in the usual geometries but with radially variable diffusivity and catalyst activity.     

Pyridylphosphine ligands for iron-based atom transfer radical polymerization of methyl methacrylate and styrene

Two pyridylphosphine ligands, 2-(diphenylphosphino)pyridine (DPPP) and 2-[(diphenylphosphino)methyl]pyridine (DPPMP), were investigated as complexing ligands in the iron-mediated atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) and styrene with various initiators and solvents. In studies of their ATRP behavior, the FeBr₂/DPPP catalytic system was a more efficient ATRP catalyst for the MMA polymerization than the other complexes studied in this paper. Most of these systems were well controlled with a linear increase in the number-average molecular weights (M_n) vs. conversion and relatively low molecular weight distributions (M_w/M_n = 1.15-1.3) being observed throughout the reactions, and the measured molecular weights matched the predicted values with the DPPP ligand. The polymerization rate of MMA attained a maximum at a ratio of ligand to metal of 2:1 in p-xylene at 80 °C. The polymerization was faster in polar solvents than in p-xylene. The 2-bromopropionitrile (BPN) initiated ATRP of MMA with the FeX₂/DPPP catalytic system (X = Cl, Br) was able to be controlled in p-xylene at 80 °C. The polymerization of styrene was able to be controlled using the PECl/FeCl₂/DPPP system in DMF at 110 °C.     

Non-premixed fluidized bed combustion of C1-C4n-alkanes

The non-premixed combustion of C₁-C₄n-alkanes with air was investigated inside a bubbling fluidized bed of inert sand particles at intermediate temperatures: 923 K ? T_B ? 1123 K. For ethane, propane and n-butane, combustion occurred mainly in the freeboard region at bed temperatures below T₁ = 923 K. On the other hand, complete conversion occurred within 0.2 m of the injector at: T₂ = 1073 K. For methane, the measured values of T₁ and T₂ were significantly higher at 1023 K and above 1123 K, respectively. The fluidized bed combustion was accurately modeled with first-order global kinetics and one PFR model to represent the main fluidized bed body. The measured global reaction rates for C₂-C₄n-alkanes were characterized by a uniform Arrhenius expression, while the global reaction rate for methane was significantly slower. Reactions in the injector region either led to significant conversion in that zone or an autoignition delay inside the main fluidized bed body. The conversion in the injector region increased with rising fluidized bed temperature and decreased with increasing jet velocity. To account for the promoting and inhibiting effects, an analogy was made with the concept of induction time: the PFR length (b_i) of the injector region was correlated to the fluidized bed temperature and jet velocity using an Arrhenius expression. These results show that the conversion of C₂-C₄n-alkanes can be estimated with one set of critical bed temperatures and modeled with one Arrhenius kinetics expression.     

Irreversible step growth polymerization having segmental diffusion limitations in HCSTRs—simulation and steady state multiplicity

The effect of various parameters on the overall rate constant, number average chain length, and polydispersity index of isothermal, irreversible, step growth polymerization of ARB monomers, exhibiting segmental diffusional limitations and carried out in HCSTRs, are studied. A phenomenological model which has proved useful for chain polymerization is adapted for step growth polymerizations and simulations for several values of the different parameters are carried out. The number average chain length μ_n and the polydispersity index ρ are obtained as a function of the dimensionless time t^*. It is found that, even though the behavior of μ_n and ρ vs. t^* depends on the values of the parameters, the plot of μ_n vs. ρ is unique as expected from statistical considerations. An attempt has been made to investigate the multiplicity of steady states under conditions of infinitely rapid heat transfer from a jacket, using singularity and bifurcation theory. It is found from the analysis that there is no multiplicity of steady states for this system, which is confirmed by simulations using a wide range of parameter values.     

Pyrolysis of wheat straw in a thermogravimetric analyzer: Effect of particle size and heating rate on devolatilization and estimation of global kinetics

The influence of different parameters such as particle size, initial weight of the sample, and heating rate on the devolatilization of wheat straw particles have been studied using thermogravimetric analysis. In addition, the variations in proximate analysis with different particle sizes of wheat straw have also been investigated. Results show that the curves corresponding to the third stage of pyrolysis differ for variations in particle size, initial weight, and heating rate of the pyrolysis process. A devolatilization model with three parallel nth-order reactions has been considered to determine the global kinetic parameters using thermogravimetric data. The kinetic parameters such as activation energy (kJ/mol), frequency factor (1/min), and order of the reaction for the three stages considered in devolatilization model were E₁ = 69, E₂ = 78, E₃ = 80; k₀₁ = 2.57 × 10¹², k₀₂ = 3.97 × 10⁷, k₀₃ = 3.17 × 10⁶; and n₁ = 2.3, n₂ = 0.65, n₃ = 2.7, respectively. It was noted from the order of the reaction that the second stage of the pyrolysis curve corresponds to the degradation of cellulose and hemicellulose, and the third stage to the lignin degradation.     

Chemical and phase equilibria calculation of α-pinene hydration in CO2-expanded liquid

Modeling of chemical and phase equilibria of α-pinene hydration in subcritical CO₂ was carried out by calculation. A simplified scheme of the conversion includes 6 reaction routes. Thermochemical and physicochemical parameters of individual compounds (T_cr, P_cr, T_b, (298.15 K), (298.15 K), C_p (T), ω) were preliminary estimated. Phase diagrams of the model reaction mixtures were calculated, coordinates of the critical point were found, and the region of subcritical parameters T and P, where the initial mixture divides into the gas phase and CO₂-expanded liquid, was located. Dependence of the products distribution and yield of CO₂-expanded liquid on the reaction temperature and pressure was studied. The reaction equilibrium as a function of temperature and pressure was determined, and heat effects of all reactions under consideration were calculated. The drift of critical parameters versus reaction mixture composition was examined. It was shown that during the hydration and alcohols accumulation the critical pressure of reaction mixture increases continuously, the critical temperature at first elevates and then begins to decrease, and the phase diagrams starts to degenerate. If amount of alcohols becomes more than 80 mol%, the mixture has no critical point and cannot pass to a supercritical state.     

Effects of nano-sized carborundum particles and amino silane coupling agent on the cure reaction kinetics of DGEBA/EMI-2,4 system

The influence of nano-sized carborundum (nano-SiC) particles and amino silane coupling agent on the curing kinetics of bisphenol-A glycidol ether epoxy resin (DGEBA) initiated with 2-ethyl-4-methylimidazole (EMI-2,4) was studied by means of non-isothermal differential scanning calorimetry (DSC). Besides decreasing the heat of reaction ΔH, the presence of nano-SiC particles results in delayed cure reactions, which is also manifested by the increased values of exothermic peak temperature T_p and cure reaction activation energy E of the filled systems. Meanwhile, the amino silane coupling agent could increase ΔH, and decrease slightly the degree of delayed cure reactions caused by nano-SiC particles, and thereby decreasing T_p of the filled systems. The presence of nano-SiC particles prevents from the occurrence of vitrification, so does the amino silane coupling agent when the nano-SiC particle content is low (?15 wt%). As the nano-SiC particle content is high (?15 wt%), the presence of amino silane coupling agent promotes the occurrence of vitrification. Besides E, the presence of nano-SiC particles could increase the overall order of reaction m+n and the frequency factor A, meanwhile, the amino silane coupling agent decreases these three parameters.     

The kinetic study of the curing reaction of mono- and di-epoxides obtained during the reaction of divinylbenzene and hydrogen peroxide with acid anhydrides

In this paper, the non-isothermal differential scanning calorimetry (DSC) was employed to investigate the cure process and to determine the kinetic parameters of the curing reactions of mono- and di-epoxides with maleic and glutaric anhydrides. The epoxides were obtained during the epoxidation process of commercially available divinylbenzene by using 60% hydrogen peroxide as the oxidant in the presence of organic solvents and magnesium oxide as the catalyst. It was found that the cure process of epoxides with maleic anhydride was described through higher values of enthalpy of polymerization (ΔH_R) and lower temperatures of the cure initiation (T_onset), the peak maximum temperature (T_max) and the final cure temperature (T_end). It can be considered to accelerate the rate of reaction and lead to an excellent network structure when maleic anhydride was used as curing agent. The kinetic analysis was firstly computed using a model free-estimation of the activation energy (Friedman, Ozawa-Flynn-Wall methods) and then the multivariate non-linear regression with a 6th degree Runge-Kutta process in a modified Marquardt procedure was employed to calculate the corresponding kinetic parameters (E_i, n_i, A_i) using the nth-order reaction f(α). The unbranched three-step process of the nth-order reaction f(α) for each step was the best to describe the cure process of mono- and di-epoxide with acid anhydrides. The determined values of the activation energies were in the range 64.7-105.2 kJ/mol for epoxides/glutaric anhydride system and 64.7-82.7 kJ/mol when maleic anhydride was used as hardening agent.     

Gas absorption with or without chemical reaction in laminar non-newtonian falling liquid films

An analytical solution is presented for gas absorption with or without a first-order or zero-order chemical reaction in a laminar non-Newtonian power-l model falling liquid film. For physical absorption, the first ten eigenvalues, series coefficients and related quantities are computed accurately by a quasinumerical method which shows considerable improvement over previous investigations. The range of applicability of the penetration theory solution is also established to indicate in what regions will the finite film thickness and complete velocity profile be important in determining the absorption rate. It is found that the range of dimensionless axial contact length X* in which the penetration theory is valid diminishes rapidly with increasi values of the power-law index n. For chemical absorption, the solution can be obtained by a linear superposition principle in terms of a “transie part” in which the effect of hydrodynamics within the liquid film is of importance and a “steady part” in which the reaction rate is controlling. In the “transient part” solution, the first ten eigenvalues and related quantities are reported for a variety of values of n and the dimensionl reaction rate parameter k_l* or k₀*. Certain asymptotic solutions from the penetration theory are also given and their range of applicab estimated. For any given n, it is estimated that only when k₁* or k₀* is less than approximately 10 will the finite film thickness and velocity profile have any effect on the absorption rate as compared to that calculated from the penetration theory with chemical reaction. The non-Newt character of the liquid film also has a significant influence on the absorption rate. At a fixed X*, the absorption enhancement due to reaction is when n = ∞ and is smallest when n = 0. The solutions obtained in this work are useful either for predicting absorption rates or for deter molecular diffusivity (and reaction rate constant) of gases in non-Newtonian falling liquid films.     

Chain extension and block copolymer synthesis using silane radical atom abstraction coupled with nitroxide mediated polymerization

Silane radicals were used to abstract bromine termini from monobrominated polystyrene (PStBr) in the presence of excess monomer and 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO), generating polymer radicals that underwent chain extension. Typically, 70-85% of the PStBr precursors were activated by silane radical atom abstraction (SRAA) and were elongated by nitroxide mediated polymerization (NMP), shifting to higher number-average molecular weight (M_n) values as observed by gel permeation chromatography (GPC). Chain extension did not occur until the temperature was elevated to 130 °C, with no increase in M_n values observed when the reaction was held at 80 °C, which is the temperature of the SRAA phase. The NMP phase of the reaction showed a linear correlation between M_n values and monomer consumption, along with first order kinetics with respect to styrene. SRAA/NMP was then applied to the synthesis of polystyrene-b-poly(n-butyl acrylate) and polystyrene-b-poly(p-methylstyrene), with analysis by GPC indicating the formation of block copolymers with a similar amount of unreacted PStBr remaining. Quantitative activation and elongation of the polymer precursors were prevented due to the ability of both the t-butoxy radicals and tris(trimethylsilyl)silane radicals to add across monomeric double bonds, competing with atom abstraction. Reactions were thus performed in which the monomer was added only after the transition to the higher temperature, which resulted in improved activation of the PStBr.