Are 3‐D models necessary to simulate packed bed reactors? analysis and 3‐D simulations of adiabatic and cooled reactors

Simulations and analysis of transversal patterns in a homogeneous three‐dimensional (3‐D) model of adiabatic or cooled packed bed reactors (PBRs) catalyzing a first‐order exothermic reaction were presented. In the adiabatic case the simulation verify previous criteria, claiming the emergence of such patterns when (ΔT_ad/ΔT_m)/(Pe_C/Pe_T) surpasses a critical value larger than unity, where ΔT_ad and ΔT_m are adiabatic and maximal temperature rise, respectively. The reactor radius required for such patterns should be larger than a bifurcation value, calculated here from the linear analysis. With increasing radius new patterned branches, corresponding to eigenfunction of the problem emerge, whereas other branches become unstable. The maximal temperature of the 3‐D simulations may exceed the 1‐D prediction, which may affect design procedures. Cooled reactor may exhibit patterns, usually axisymmetric ones that can be characterized by two anomalies: the peak temperature may exceed the corresponding value of an adiabatic reactor and may increase with wall heat‐transfer coefficient, and the peak temperature in a sufficiently wide reactor need not lie at the center but rather on a ring away from it. In conclusions, we argue that transversal patterns are highly unlikely to emerge in practical adiabatic PBRs with a single exothermic reaction, as in practice Pe_C/Pe_T > 1. That eliminates patterns in stationary and downstream‐moving fronts, whereas patterns may emerge in upstream‐moving fronts, as shown here. This conclusion may not hold for microkinetic models, for which stationary modes may be established over a domain of parameters. This suggests that a 1‐D model may be sufficient to analyze a single reaction in an adiabatic reactor and a 2‐D axisymmetric model is sufficient for a cooled reactor. The predictions of a 2‐D cylindrical thin reactor with those of a 3‐D reactor were compared, to show many similarities but some notable differences. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Transversal moving-front patterns: Criteria and simulations for two-bed and cylindrical shell packed-bed reactors

We show that a moving-front solution in a cylindrical shell packed-bed catalyzing a first-order activated reaction may bifurcate into transversal patterns when Pe_C/Pe_T<ΔT_ad/ΔT_m, i.e. when the ratio of the mass to heat Pe numbers is smaller than the ratio of the adiabatic to maximal temperature rises. This coincides with the previous condition of transversal patterns to emerge in stationary fronts [Pe_C/Pe_T<1 [Viswanathan, G., Bindal, A., Khinast, J., Luss, D., 2005. Stationary transversal hot zones in adiabatic packed-bed reactors. A.I.Ch.E. Journal 51, 3028-3038]] and extends the bifurcations condition to the case of moving fronts. The novel condition cannot be satisfied in a downstream propagating front (ΔT_m/ΔT_ad>1), but for an upstream propagating front (toward the cold reactor inlet) ΔT_m/ΔT_ad<1 and the symmetry breaking can be obtained within a feasible domain of operating conditions (Pe_C/Pe_T>1). It was also assumed that the axial and the transversal Pe numbers vary consistently, i.e. κ_C=Pe_C⊥/Pe_C=κ_T=Pe_T⊥/Pe_T. A similar condition was also obtained using a simplified model composed of two 1-D beds with heat and mass exchange between them.Bifurcation diagram showing domains of transversal patterns is constructed using a learning two-bed model. These predictions are verified by direct numerical simulations of the continuous 2-D cylindrical shell model showing various types of moving transversal patterns within a feasible domain of the state parameters with Pe_C>Pe_T. In the case of varying ratio (κ_C≠κ_T) the pattern domain can be significantly extended toward larger Pe_C/Pe_T.     

Solution-combustion synthesis of oxide nanoparticles from nitrate solutions containing glycine and urea: Thermodynamic aspects

Solution-combustion synthesis (SCS) of nanoparticles was characterized by the temperature effect (ΔT _ad) calculated upon neglect by the temperature dependence of heat capacity. Thus calculated ΔT _ad values were found to be a linear function of the inverse radius of metal ions. Our calculations have shown that SCS reactions may yield not only oxides but also hydroxides and carbonates. Suggested was a simple formula for evaluating the ΔT _ad values attained in SCS of complex oxides.     

Transversal patterns in three‐dimensional packed bed reactors: Oscillatory kinetics

Formation of transversal patterns in a 3D cylindrical reactor is studied with a catalytic reactor model in which an exothermic first‐order reaction of Arrhenius kinetics occurs with a variable catalytic activity. Under these oscillatory kinetics, the system exhibits a planar front (1D) solution with the front position oscillating in the axial direction. Three types of patterns were simulated in the 3D system: rotating fronts, oscillating fronts with superimposed transversal (nonrotating) oscillations, and mixed rotating–oscillating fronts. These solutions coexist with the planar front solution and require special initial conditions. We map bifurcation diagrams showing domains of different modes using the reactor radius as a bifurcation parameter. The possible reduction of the 3D model to the 2D cylindrical shell model is discussed. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Effects of enzyme microcapsule shape on the performance of a nonisothermal packed-bed tubular reactor

The effects of enzyme microcapsule shape (spherical, cylindrical and flat plate) on the performance of a nonisothermal, packed-bed reactor have been modeled as a function of Biot number and Peclet number for mass and heat transfer (Bi_m, Bi_h, Pe_m and Pe_h), and dimensionless heat of reaction α. Under the given simulation conditions, only higher values of Bi_m and Bi_h (>2·5) confirm the influence of microcapsule shape on the reactor performance such that the axial and overall conversion and bulk temperature decrease as follows: spherical > cylindrical > flat plate. In terms of the shape-independent modified Biot number, Bi* = Bi/{(n + 1)/3}, this order is retained for 2 < Bi* < 8. The influence of increasing Pe_m, Pe_h, and α on conversion and bulk temperature also follows the above order. For the flat plate, the exit conversion and temperature are not influenced by Pe_m and Pe_h, that is, mass transfer and thermal backmixing effects, respectively. On the other hand, for the spherical and cylindrical microcapsules, overall backmixing effects are negligible only beyond a critical value of Pe_m (∼7) and Pe_h (∼1·75). The conversion and bulk temperature increase with the increase in α, independent of the microcapsule shape. The spherical and cylindrical microcapsules, unlike the flat plate, cannot be considered isothermal.     

Some thermodynamic properties of tetrafluoroethene-hexafluoropropene copolymers

Copolymers of tetrafluoroethene (TFE) with hexafluoropropene (HFP) have been prepared in the 0-14mol% HFP composition range. Their melting temperatures (T_m), enthalpies (ΔH_f) and entropies (ΔS_f) of first and second fusion, and crystallinities (X) according to x-ray diffraction(x.r.d.) and differential scanning calorimetry (d.s.c.) have been determined. The results indicate that ΔH_f/X_x.r.d of the polymer crystals decreases with higher HFP content.     

Polymeric surfactants for enhanced oil recovery. IV—Thermodynamic properties of ethoxylated alkylphenol formaldehyde polymeric surfactants

The thermodynamic properties of some low molecular weight ethoxylated alkylphenol formaldehyde polymeric surfactants have been investigated. Surface tension as a function of concentration of the surfactants in aqueous solutions was measured at 28, 38, 48 and 58°C, using the spinning drop technique. From these measurements, the minimum area per molecule at the aqueous solution/air interface (A_min) was determined. The thermodynamic parameters of micellization (ΔG_mic, ΔH_mic, ΔS_mic) and of adsorption (ΔG_ad, ΔH_ad, ΔS_ad) for these polymeric nonionics were calculated. Micellization is more sensitive to ethylene oxide chain length while adsorption is more dependent on the length of the alkyl chain.     

Thermal stability of polyacrylonitrile in the melt formed by hydration

Differential scanning calorimetry (DSC) and intrinsic viscosity measurement have been used to investigate the thermal stability of PAN-based copolymer in the melt formed by hydration. Samples containing various water contents were annealed at temperatures between 160 and 180°C for periods up to 60 min. The melting point (T_m) and crystallization temperature (T_c) increased with annealing time, irrespective of annealing temperature and water content. The increase in T_m with annealing time was interpreted in terms of thermodynamic parameters. The decrease in the heat of fusion (ΔH_f) with the increase of annealing time implies that the number of nitrile groups is reduced during annealing in the melt. The decrease in the entropy of fusion (ΔS_f) calculated from T_m and ΔH_f suggests that the polymer chain becomes more rigid as the annealing time (or temperature) increases; however, the intrinsic viscosity does not increase during annealing. From both thermodynamic analysis and intrinsic viscosity, it is concluded that the increase in T_m is caused by chain rigidity mainly due to the intramolecular cyclization of nitrile groups. © 1992 John Wiley & Sons, Inc.     

Melting parameters of poly(glycolic acid)

Equilibrium melting temperature T_m⁰, heat of fusion ΔH_f, and entropy of fusion ΔS_f of poly(glycolic acid) (PGA) was determined by using Clapeyron-Clausius equation. Equilibrium melting temperature T_m⁰ was 504.6 K which was determined by Hoffman-Weeks plots. The pressure dependence of T_m⁰ was determined by high pressure DTA up to 150 MPa. Volume change ΔV_f at melting was determined by using dilatometer. Heat of fusion in PGA was 183.2 (J g⁻¹), which is very close to the value reported by Chujo et al. who determined it by using T_m depression in copolymer with poly(lactic acid). ΔS_f of PGA was 0.363 (J g⁻¹ K⁻¹), which is about twice that of PLA, and the reason was discussed on the basis of the elastic modulus below T_m.     

Thermogravimetric investigations in prediction of coking behaviour and coke properties derived from inertinite rich coals

The coal quality, temperature, pressure, heating rate, various processes and reactor type affect coking behaviour of coal and resulting coke properties. Several petrographic and chemical methods were proposed earlier for prediction of coking behaviour of coals. Inertinite rich coal samples (I^mmf>30 vol%) having different petrographic compositions were selected for thermogravimetric investigations (DTA, DTG and TGA) and their coking behaviour was studied. The petrographic build up, micro-structural properties (porosity and cell wall thickness) and mechanical strength of the resulted cokes were also investigated. ΔH and ΔH_max (the main endothermic area of heat absorption and fast absorbing main endothermic area, respectively) were distinguished in DTA curves. ΔA and ΔA_max (the main decomposition area and fast disintegrating main decomposition area) under DTG curves were identified. ΔH_max/ΔA_max shows good correlation with Roga's indices (RI, caking properties) as well as with petrographic caking ratio (PCR). The coarse mosaic content of cokes seem to depend on LΔT_max/ΔT_max (ratio of weight loss during fast decomposing main reaction to temperature difference) under DTG. L^mΔT/ΔT (ratio of weight loss during main decomposing reaction to temperature difference) under DTG exhibits correlation with p₁ (mean pore size) and t₁ (mean cell wall thickness) of cokes. ΔA_max/(L^mΔT_max) also indicates good relationship with mechanical strength of cokes. (L^mΔT_A−T_B)/(L^mΔT) (i.e. ratio of weight loss during main endothermic reaction under DTA to weight loss during main decomposing reaction) appears to have relationship with DD (compactness) of cokes. The course of main endothermic reaction/main decomposition reaction under DTA, DTG and TGA seems to govern coking behaviour and the resulting coke strength, which in turn is controlled by microlithotypes.     

Polymerization of acrylic bone cement investigated by differential scanning calorimetry: Effects of heating rate and TCP content

The polymerization reaction of a bone cement (standard Surgical Simplex-P Radiopaque) upon heating has been investigated by differential scanning calorimetry (DSC). The effects of the addition of tricalcium phosphate (TCP) on the rate and the heat of polymerization during DSC heating were evaluated. The rate and polymerization heat (ΔH) were characterized by the initial curing temperature (T_i), peak temperature (T_p), completing curing temperature (T_f), the curing range (ΔT = T_f ? T_i) and the area of the DSC exotherm. It was found that T_i, T_p, T_f, ΔT, and ΔH all increase with increasing heating rate. Increasing TCP content also induced increases in T_i, T_p, T_f, ΔT, and ΔH. From the kinetic analysis, the polymerization of acrylic bone cement was found to be a first order reaction. The effects of heating rate and TCP contents on the rate and the heat of polymerization could be explained based on the frequency factor and the activation energy extracted from the kinetic analysis. Increases in both heating rate and TCP content depressed the frequency factor and the activation energy.     

Theoretical Study on Thermodynamic and Detonation Properties of Polynitrocubanes

We investigated the heat of formation (Δ_fH) of polynitrocubanes using density functional theory B3LYP and HF methods with 6‐31G*, 6‐311+G**, and cc‐pVDZ basis sets. The results indicate that Δ_fH firstly decreases (nitro number m=0–2) and then increases (m=4–8) with each additional nitro group being introduced to the cubane skeleton. Δ_fH of octanitrocubane is predicted to be 808.08 kJ mol⁻¹ at the B3LYP/6‐311+G** level. The Gibbs free energy of formation (Δ_fG) increases by about 40–60 kJ mol⁻¹ with each nitro group being added to the cubane when the substituent number is fewer than 4, then Δ_fG increases by about 100–110 kJ mol⁻¹ with each additional group being attached to the cubic skeleton. Both the detonation velocity and the pressure for polynitrocubanes increase as the number of substituents increases. Detonation velocity and pressure of octanitrocubane are substantially larger than the famous widely used explosive cyclotetramethylenetetranitramine (HMX).     

Nonisothermal crystallization of s‐PP fractions

Syndiotactic polypropylene (s‐PP) was prepared by metallocene catalyst and was fractionated with the temperature rising elution fractionation (TREF) technique. The nonisothermal behavior of the obtained fractions was investigated. Fractions was first cooled at different rates and then heated at a constant rate. The parameters such as the peak crystallization temperature (T_c), the onset crystallization temperature (T_on), the difference between T_on and T_c (ΔT₁ = T_on − T_c), the crystallization enthalpy (ΔH), the peak melting temperatures (T_m1, T_m2), and the difference between the T_m1 and T_m2 (ΔT₂ = T_m2 − T_m1) were obtained. The dependence of these parameters on cooling rate, syndiotacticity, and molecular weight was discussed. It is found that T_c, T_on, ΔH, T_m1, and T_m2 systematically increase with increasing syndiotacticity and are depressed on increasing the cooling rate. Cooling rate, syndiotacticity, and molecular weight show different influences on ΔT₁. In the melting process of s‐PP, double peaks were observed. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 897–901, 1999     

Reversibility of Thermal Transitions in Dilute Dioctadecyl-Dimethyl-Ammonium Bromide Vesicles

Dioctadecyl-dimethyl-ammonium bromide (DODAB) vesicles can be characterized by their differential scanning calorimetry (DSC) thermograms comprised of two endotherms at T _s ≈ 36 °C and T _m ≈ 45 °C in the heating, ascribed respectively to the subgel-to-gel and gel-to-liquid crystalline transitions, and two exotherms at T′_m ≈ 40 °C and T′_s ≈ 16 °C in the cooling, ascribed respectively to the liquid crystalline-to-gel and gel-to-subgel transitions. It has been reported but not proved that the T _m-transitions, the T′_m-transitions, the T _s-transitions, and the T′_s-transitions are reverse to each other, displaying hystheresis ΔT _m ≈ 5 °C and ΔT _s ≈ 20–25 °C, respectively. By investigating the effects of the initial scanning temperature (T _i) on the transition enthalpies (ΔH _m, ΔH _s, ΔH′_m and ΔH′_s), we have seen that these transitions are the reverse to each other and display different kinetics.     

Moisture Uptake Behavior,Antibacterial Property,and Heat of Sorption of Nano Silver-Loaded Calcium Alginate Films

This work describes preparation, characterization, and a moisture uptake study of silver nanoparticle-loaded calcium alginate films. The equilibrium uptake data was interpreted by various isotherm models. In the lower moisture content range of 0.02 to 0.06, the enthalpy of sorption (ΔH) and differential entropy (ΔS) were 25.25 to 4.82 kJ/mol and 0.07521 to 0.01371 kJ/mol/K, respectively. There was fair correlation between ΔH and ΔS values. Finally, the higher value of isokinetic temperature, T_B (i.e., 336.77), as compared to the harmonic mean temperature, T_m (i.e., 302.05), indicated that moisture uptake mechanism was enthalpy driven.     

Effect of the melting temperature on the crystallization behavior of a poly(l‐lactide)/poly(d‐lactide) equimolar mixture

The effect of the final melting temperature (T_f) on the crystallization of poly(l ‐lactide) (PLLA)/poly(d ‐lactide) (PDLA) was studied via a combination of differential scanning calorimetry, wide‐angle X‐ray scattering, polarized optical microscopy, and Fourier transform infrared (FTIR) spectroscopy. We observed that a residual stereocomplex (SC) crystal induced the formation of SC crystals during cooling from a T_f (230°C) just above the melting peak of the SC crystals. On cooling from a T_f (240°C) just above the endset temperature of SC crystal melting [T_m(S)(E)], the possible order structure and the strong interchain interaction promoted the preferential crystallization of SC crystals; this enhanced the formation of α crystals. During cooling from a T_f (≥250°C) far above T_m(S)(E), the crystallization peaks of α and SC crystals converged. The FTIR results indicated that the residual SC crystals, possible ordered structure, and interchain interactions in the melt might have been the key factors for the different crystallization of PLLA/PDLA. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43015.     

Overall map and correlation of dispersion data for flow through granular packed beds

Measured values of the coefficients of transverse and longitudinal dispersion (D_T and D_L, respectively) are reported for liquid flow through granular packed beds. Measurements of D_T were made for 50<Sc<1950 and 300<Pe_m<10⁵, working with water at temperatures between 278 and 373 K, and values of D_L were measured for Sc≅750 and 1<Pe_m<45, working with water at 293 K; nearly two hundred new data points are reported.The data obtained, together with data from other sources, both for gas and liquid flow, are reported in plots of Pe_T vs Pe_m and Pe_L vs. Pe_m, in order to stress the influence of Sc on dispersion and elucidate the difference between liquid and gas behaviour.Empirical correlations are presented for the prediction of the dispersion coefficients (D_T and D_L) over the entire range of practical values of Sc and Pe_m, and they are shown to give the dispersion coefficients with very good accuracy.     

Generalized warpage parameter

A warpage index (Δψ_m) was introduced for studying warpage characteristics of a plastic part injection molded from PA66 compounded with 30 wt% glass fiber. Δψ_m is defined as Δψ_m = (Δψ_m)_max – (Δψ_m)_min, where ψ_m = ψ(θ)_max, where ψ(θ) = (ε(θ) – α(θ)ΔT)/| α(θ)ΔT|, where ε is the total strain, α is the linear thermal expansion coefficient, ΔT is temperature difference, and θ is the angle along which ε and α are calculated. Finite element analysis was used for calculating flow field in injection, fiber orientation, material anisotropy and warpage. ψ_m is calculated in each finite element, and Δψ_m is calculated in a whole finite element model. Δψ_m is a measure of the ratio of actual shrinkage to the amount of shrinkage that would occur if an element freely shrank. The characteristics of Δψ_m were studied. It has been found that warpage is null if Δψ_m = 0, but that null warpage generally does not indicate Δψ_m = 0. It is shown that Δψ_m quantitatively represents the warped and unwarped state. Δψ_m distinguishes the null warpage state with possible buckling from the null warpage state without possible buckling. It has been shown that material anisotropy is possibly described with Δψ_m, and that the cause of warpage is self-restrictive deformation in an injection molded part. It has been deduced that it is generally not possible to eliminate warpage only by controlling material properties. Δψ_m is obtainable for a plastic part with complex geometry and complex fiber orientation state, and for arbitrary materials. Applications of Δψ_m are left for future study.     

Synthesis and Physico-Chemical Properties of Sodium 3-Oxo-2-(3-(4-sulphonatophenyl)triaz-2-enyl)octadecanoate Anionic Surfactant

The novel anionic surfactant sodium 3‐oxo‐2‐(3‐(4‐sulphonatophenyl)triaz‐2‐enyl)octadecanoate (SSTO) was prepared from renewable raw materials; glycine and palmitic acid. Surface and bulk properties of SSTO were investigated by surface tension and electrical conductivity techniques at 298, 308, 318 and 328 K. Surface properties including critical micelle concentration (CMC), maximum surface excess concentration (Γ_max), minimum area per molecule (A_min), surface tension at CMC (γ_CMC), effectiveness of surface tension reduction (Π_CMC), efficiency of surface adsorption (pC₂₀), and degree of counterion dissociation (α) were determined. The thermodynamic parameters of micellization (ΔG°_mic, ΔH°_mic and ΔS°_mic) and adsorption (ΔG°_ad, ΔH°_ad and ΔS°_ad) were also investigated at 298, 308, 318 and 328 K. The effect of 3 wt% n‐propanol, n‐butanol and n‐pentanol on surface tension and conductivity at 298 K was also determined.     

Taming the Beast: Measurement of the Enthalpies of Combustion and Formation of Triacetone Triperoxide (TATP) and Diacetone Diperoxide (DADP) by Oxygen Bomb Calorimetry

Low‐melting paraffin wax was successfully used as a phlegmatizing agent to perform semi‐micro oxygen bomb calorimetry of spectroscopically pure samples of the sensitive explosive peroxides TATP and DADP. The energies of combustion (Δ_cU) were measured and the standard enthalpies of formation (Δ_fH°) were derived using the CODATA values for the standard enthalpies of formation of the combustion products. Whilst the measured Δ_fH° of DADP (Δ_fH°=−598.5 ± 39.7 kJ mol⁻¹) could not be compared to any existing literature value, the measured Δ_fH° value of TATP (Δ_fH°=+151.4 ± 32.7 kJ mol⁻¹) did not correlate well with the only existing experimental value and confirmed that TATP is an endothermic cyclic peroxide.