Optimal temperature profiles for heterogeneous catalytic parallel reactions

The problem of determination of the optimal temperature profiles in a fixed-bed catalytic reactor for the catalytic parallel reactions including transport phenomena (external or internal diffusion) has been worked out.Special attention was given to predict the shapes of the optimal temperature profiles. The general considerations are illustrated by some numerical examples. It has been found that for every studied case the optimal temperature profile need not to end by the isotherm T = T_max.     

Sequential experimental design for estimation and analysis of thermal parameters in a fixed bed

The analysis of the effective radial thermal conductivity and the film heat transfer coefficient were carried out in a fixed bed. The temperature profiles were described by two‐dimensional pseudo‐homogeneous model. The thermal parameters were estimated using a sequential experimental design technique. The minimum volume criterion was used to design the next point for temperature measurement in the bed. The utilization of T = T₀ (constant) as the boundary condition at the bed inlet resulted in an axial variation of thermal parameters, which was the factor responsible for the inadequacy of the model in fitting experimental data of different bed heights simultaneously. Using T = T(r) as the boundary condition makes the thermal parameters independent of the axial position and the model statiscally adequate to describe the axial and radial temperature profiles throughout the bed.     

Extracting kinetic parameters of aniline polymerization from thermal data of a batch reactor. simulation of the thermal behavior of a reactor

A simulation model of the thermal behavior of a reactor during aniline polymerization is proposed. The model takes into account the polymerization mechanism together with heat production and dissipation. The temperature–time profiles can be simulated with different kinetic parameters. The model is used for two purposes: to extract kinetic parameters by fitting experimental temperature–time profiles of a cooled agitated batch reactor; and to estimate the temperatures changes occurring in a reactor under different experimental conditions to find the best conditions for industrial production of polyaniline. The rate equation used includes two rate constants: one in the absence of polymer (k₁) and another in the presence of polymer (k₂). The thermal factors, such as the heat transfer coefficient and the reaction enthalpy, are experimentally measured. A computer program is written that fits the experimental data using different kinetic parameters. The data analysis shows a temperature peak (T_max) whose magnitude decreases when k₂ decreases, whereas it is not affected by k₁. The time to reach the T_max is inversely proportional to k₁ and k₂. The model allows obtaining the kinetic parameters in different reaction media, e.g. varying the concentration of acid. The model is used to simulate the thermal behavior, to polymerize 1M of aniline: in one step the temperature of the reactor will increase till 82ºC, such thermal runaway will cause polymer degradation, successive additions of portions of the total oxidant amount, paced at defined time intervals, is devised to maintain low temperatures while producing the same amount of polymer. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 39409.     

On‐line optimizing control of bulk polymerization of methyl methacrylate: Some experimental results for heater failure

An experimental unit has been assembled to carry out on‐line optimizing control of the bulk polymerization of methyl methacrylate (MMA). A rheometer‐reactor assembly is used. Temperature and viscosity measurements are used to describe the state of the system. The polymerization is carried out under an off‐line computed optimal temperature history, T_op(t). A planned disturbance (heating system failure) is introduced at time t₁. This disturbance leads to a fall in the temperature of the reaction mass. A new optimal temperature history, T_reop(t), is re‐computed on‐line and is implemented on the reaction mass at time t₂, when the heating is resumed. This procedure helps ‘save the batch’. A genetic algorithm is used to compute this reoptimized temperature history in a short period of ～2 min of real time. The feasibility of the on‐line optimizing control scheme has been demonstrated experimentally. Replicable results for the viscosity history, η(t), of the polymerizing mass under several non‐isothermal conditions have been obtained. These experimental results are quite trustworthy, even though the model predictions are only in approximate agreement with them, perhaps because of the extreme sensitivity of results to the values of the model parameters. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2350–2360, 2002     

Cure modeling and monitoring of epoxy/amine resin systems. II. Network formation and chemoviscosity modeling

The glass transition temperature (T_g) advancement and the chemoviscosity development under isothermal conditions have been investigated for four epoxy/amine systems, including commercial RTM6 and F934 resins. Differential scanning calorimetry (DSC) was the thermoanalytical technique used to determine the T_g advancement and rheometry the technique for the determination of the chemoviscosity profiles of these resin systems. The complex cure kinetics were correlated to the T_g advancement via an one‐to‐one relationship using Di Benedetto's formula. It was revealed that the three‐dimensional network formation follows a single activated mechanism independent of whether the cure kinetics follow a single or several activation mechanisms. The viscosity profiles showed the typical characteristics of epoxy/amine cure. A modified version of the Williams‐Landel‐Ferry equation (WLF) was adequate to model the viscosity profiles of all the resin systems, in the temperature range 130 to 170°C, with a very good degree of accuracy. The parameters of the WLF equation were found to vary in a systematic manner with cure temperature. Further correlation between T_g and viscosity showed that gelation, defined as the point where viscosity reaches 10⁴ Pas, occurs at a unique T_g value for each resin system, which is independent of the cure conditions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 2178–2188, 2000     

Experimental study and simulation of the polymerization of methyl methacrylate at high temperature in a continuous reactor

The bulk polymerization of MMA at high temperature (120–180°C) in a continuous pilot‐plant reactor has been studied. The polymerization is initiated by diterbutyle peroxide and the chain transfer agent is 1‐butanethiol. A simulation program has been developed to predict the steady state behavior of the reactor. The particular features of the kinetic at above‐T_g temperature are included in the model, especially the thermal initiation of the reation and the attenuation of the autoacceleration effect. For the flow and mixing model, the actual vessel cannot be approximated to a single ideal reactor because of its design and of the moderate agitation imposed by the high viscosity of the reacting fluid. A tanks in series model with a recycle stream between tanks is proposed to evaluate the backmixing caused by the special design of the agitator. The parameters of the model are determined with the help of the experimental residence time distribution measured on the reactor. The data collected on the actual reactor, i.e., operation, conversion, molecular weight, temperature, are compared to the calculated one. The agreement is satisfactory but the tendencies are slightly underestimated. The program is a tool to evaluate the effect of modifications of the design of the reactor or changes on the operation parameters like input rate, temperature, and agitation on its behavior. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 2038–2051, 2001     

Optimization of nylon 6 reactors with end-point constraints

Optimal temperature profiles for nylon 6 polymerization in plug–flow reactors have been obtained with end-point constraints involving the degree of polymerization and the cyclic dimer concentration, using the most recent kinetic information. Computations suggest that the temperature at the feed end of the reactor must be maintained close to the highest permissible level (determined by the boiling point of the ?-caprolactam). The temperatures in this region control the degree of polymerization more than other variables. Thereafter, the temperature should be reduced. This second zone controls the undesirable cyclic dimer concentration. The effect of a systematic change of values of the various design variables is studied. The profiles obtained herein are qualitatively similar to those obtained by earlier workers using similar formulations. However, they differ significantly from the profiles obtained by us earlier, using different objective functions which are more relevant to the design of new reactors. Attempts have also been made to obtain a global optimal scheme to produce polymer of a desired degree of polymerization and cyclic dimer content, using as short a reactor as possible, and using the water content and the modifier concentration in the feed as the independent variables.     

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     

A priori modelling of an adiabatic spouted bed catalytic reactor

An a priori reactor model for an adiabatic spouted bed reactor has been developed. This model uses first-principles mass and energy balances to predict the concentration and temperature profiles in the spout, annulus and fountain regions of the reactor. The particle circulation and voidage profiles in the spout are calculated using previously developed analytical techniques. Particle circulation patterns in the annulus are determined by a minimum path-length analysis. The spout and fountain are shown to contribute significantly to the overall conversion in the bed. Predicted and experimental conversions at flowrates up to 1.2U_ms show that extension of the fountain reaction zone and increased particle circulation with increasing inlet flow makes up for the higher average voidage in the spout and fountain. Experimental data confirm the calculated results for a stably spouting bed with CO oxidation over a Co₃O₄/αAl₂O₃ catalyst. The effects of flowrate and inlet reactant concentration are confirmed.     

Dielectric studies of poly(vinyl chloride)

Measurements of the dielectric constant and loss factor of polyvinyl chloride (PVC) have been made over a wide range of temperature and frequency. Maxima in dielectric loss were observed at a temperature corresponding to the α or glass transition temperature and secondary β transition temperature. The sensitivity of these maxima to both frequency and thermal pretreatment was investigated. It was found that the position of the β peak on the temperature axis changed markedly with frequency, while the glass transition or α peak showed only small variations. Neither the α nor the β peak were very sensitive to thermal pretreatment, but interesting changes in the minimum between these peaks were observed. In quenched samples a distinct shoulder peak at T_β < T_s < T_α was observed; it was possible to eliminate it by a slow cooling of the samples. The effect of plasticizer content was also studied.     

Optimization of nonvaporizing nylon 6 reactors with stopping conditions

In this study, optimal temperature profiles or histories T(t) are obtained for nonvaporizing plug-flow or batch Nylon 6 reactors using the minimum principle. Two objective functions are studied, one in which the monomer conversion is maximized, and the other in which the undesirable cyclic dimer concentration in the product stream is minimized. The control variable, temperature, is constrained to lie between 220 and 270°C in order to ensure single-phase polymerization. The most significant difference between this study and earlier ones is that the residence or reaction time t_f is not specified a priori, but is determined optimally by the use of a “stopping” condition such that the polymer product has a number-average chain length μ, equal to some desired value μ_n,d. This makes the algorithm considerably more complex, but the results are more meaningful. Qualitatively different optimal temperature profiles are obtained for the two objective functions studied, representing the complex interplay of several opposing factors in determining optimal conditions. This study also lays the foundation for even more complex, but relevant, optimization studies.     

Differential scanning calorimetric analysis of edible oils: Comparison of thermal properties and chemical composition

The thermal profiles of 17 edible oil samples from different plant origins were examined by differential scanning calorimetry (DSC). Two other confirmatory analytical techniques, namely gas-liquid chromatography (GLC) and high-performance liquid chromatography (HPLC), were used to determine fatty acid (FA) and triacylglycerol (TAG) compositions. The FA and TAG compositions were used to complement the DSC data. Iodine value (IV) analysis was carried out to measure the degree of unsaturation in these oil samples. The DSC melting and crystallization curves of the oil samples are reported. The contrasting DSC thermal curves provide a way of distinguishing among these oil samples. Generally, the oil samples with a high degree of saturation (IV<65) showed DSC melting and crystallization profiles at higher temperature regions than the oil samples with high degree of unsaturation (IV>65). Each thermal curve was used to determine three DSC parameters, namely, onset temperature (T _o ), offset temperature (T _f ) and temperature range (difference between T _o and T _f ). Reproducibility of DSC curves was evaluated based on these parameters. Satisfactory reproducibility was achieved for quantitation of these DSC parameters. The results show that T _o of the crystallization curve and T _f of the melting curve differed significantly (P<0.01) in all oil samples. Our observations strengthen the premise that DSC is an efficient and accurate method for characterizing edible oils.     

Optimal oxygen concentration strategy through an isothermal oxidative coupling of methane plug flow reactor to obtain a high yield of C2 hydrocarbons

An optimal oxygen concentration trajectory in an isothermal OCM plug flow reactor for maximizing C₂ production was determined by the algorithm of piecewise linear continuous optimal control by iterative dynamic programming (PLCOCIDP). The best performance of the reactor was obtained at 1,085 K with a yield of 53.9%; while, at its maximum value, it only reached 12.7% in case of having no control on the oxygen concentration along the reactor. Also, the effects of different parameters such as reactor temperature, contact time, and dilution ratio (N₂/CH₄) on the yield of C₂ hydrocarbons and corresponding optimal profile of oxygen concentration were studied. The results showed an improvement of C₂ production at higher contact times or lower dilution ratios. Furthermore, in the process of oxidative coupling of methane, controlling oxygen concentration along the reactor was more important than controlling the reactor temperature. In addition, oxygen feeding strategy had almost no effect on the optimum temperature of the reactor. Finally, using the optimal oxygen strategy along the reactor has more effect on ethylene selectivity compared to ethane.     

The kinetics modeling and reactor simulation of propylene chlorination reaction process

The kinetics experiments of fast reaction process of propylene chlorination at low temperature (30–90°C) and high temperature (420–480°C) are respectively conducted, and the corresponding reaction mechanisms and kinetics models are proposed. The radical mechanism at high temperature and the molecular mechanism at low temperature are found to be most likely with the experimental results. Specifically, the kinetics model, firstly considering the reversible reaction step of forming C₃H₆Cl · and direct hydrogen abstraction of forming C₃H₅ · , shows better agreement with the experimental data. Furthermore, the critical reaction temperature T_critical is firstly proposed to determine the dominant reaction mechanism in different conditions, and correspondingly the combination method of the high-temperature and low-temperature kinetics models has been adopted for tubular reactor simulation, which can reasonably reflect the influence of wide variation range of temperature in the reactor and guide the industrial reactor design in the further work.     

The effect of composition on the properties of nylon 612 copolymers

The series of nylon 612 copolymers was synthesized from caprolactam (C) and laurolactam (L) at 145°C. The 50/50 C/L molar ratio copolymer was found to have the minimum melting temperature (T_m ) for the series. The glass transition temperatures (T_g 's) of the copolymers were affected by the crystallinity of the copolymers. The T_g was at a minimum for the 50/50 copolymer for crystalline samples. However, for amorphous samples there was a decrease in T_g with increasing L content. Percent crystallinity was determined by differential scanning calorimetry and X-ray techniques. It was found that the degree of crystallinity was at a minimum for copolymers of 70/30 to 40/60 C/L ratios. Coefficients of linear thermal expansion (CLTE) were obtained for the copolymers at 10°C intervals from 20 to 70°C for dry and from 20 to 50°C for samples conditioned at 50% relative humidity and 50°C. The dry samples gave lower initial values, but had a greater temperature dependence than the conditioned samples. As expected, the CLTE was found to be lowest for samples exhibiting the highest crystallinity. The tensile strengths and moduli decreased rapidly with increasing L up to the 70/30 C/L ratio after which they remained relatively constant. Elongations reached maximums between 70/30 and 40/60 C/L ratios. An inverse relationship was found between crystallinity and impact strength.     

Pressure-Induced densification in injection molding

The effect of pressure on the densification of amorphous polymers in the Injection-molding process is examined. Density distributions in molded polystyrene slabs were measured for several well-defined molding histories. In all cases the density of the molded part was spatially inhomogeneous, and its distribution in the slab was closely related to the pressure and temperature histories that prevailed in the molding cavity during the process cycle. The density profile in the gapwise direction followed a characteristic “parabolic” pattern with a minimum at the midplane of the slab. A simple phenomenological model, based on the pressure-induced densification effect, was constructed to explain the observed density profiles, and close agreement with experimental data was found. Annealing of the molded article at a high temperature (<T_g) caused the density to decrease overall and become more uniform across the part. This is generally consistent with volume-recovery data for the densified material, which were generated independently in a controlled pressure-densification experiment.     

Plasticating single-screw extrusion of amorphous polymers: Development of a mathematical model and comparison with experiment

A mathematical model was developed for plasticating single-screw extrusion of amorphous polymers. We considered a standard metering screw design. By introducing a ‘critical flow temperature’ (T_cf), below which an amorphous polymer may be regarded as a ‘rubber-like’ solid, we modified the Lee-Han melting model, which had been developed earlier for the extrusion of crystalline polymers, to model the flow of an amorphous polymer in the screw channel. T_cf is de facto a temperature equivalent to the melting point of a crystalline polymer. The introduction of T_cf was necessary for defining the interface between the solid bed and the melt pool, and between the solid bed and thin melt films surrounding the solid bed. We found from numerical simulations that (1) when the T_cf was assumed to be close to its glass transition temperature (T_g), the viscosity of the polymer became so high that no numerical solutions of the system of equations could be obtained, and (2) when the value of T_cf was assumed to be much higher than T_g, the extrusion pressure did not develop inside the screw channel. Thus, an optimum modeling value of T_cf appears to exist, enabling us to predict pressure profiles along the extruder axis. We found that for both polystyrene and polycarbonate, T_cf lies about 55°C above their respective T_gs. In carrying out the numerical simulation we employed (1) the WLF equation to describe the temperature dependence of the shear modulus of the bulk solid bed at temperatures between T_g and T_cf, (2) the WLF equation to describe the temperature dependence of the viscosity of molten polymer at temperatures between T_cf and T_g + 100°C, (3) the Arrhenius relationship to describe the temperature dependence of the viscosity of molten polymer at temperatures above T_g + 100°C, and (4) the truncated power-law model to describe the shear-rate dependence of the viscosity of molten polymer. We have shown that the T_g of an amorphous polymer cannot be regarded as being equal to the T_m of a crystalline polymer, because the viscosities of an amorphous polymer at or near its T_g are too large to flow like a crystalline polymer above its T_m. Also conducted was an experimental study for polystyrene and polycarbonate, using both a standard metering screw and a barrier screw design having a length-to-diameter ratio of 24. For the study, nine pressure transducers were mounted on the barrel along the extruder axis, and the pressure signal patterns and axial pressure profiles were measured at various screw speeds, throughputs, and head pressures. In addition to significantly higher rates, we found that the barrier screw design gives rise to much more stable pressure signals, thus minimizing surging, than the metering screw design. The experimentally measured axial pressure profiles were compared with prediction.     

A comparison of induction time and crystallization rate for syndiotactic polystyrene

One objective of this study was to measure the crystallization parameters for syndiotactic polystyrene (M_W = 244,000) to support a computer simulation of this material in an injection molding application. A second objective was to introduce a new crystallization rate equation that adequately predicts crystallization rates over a broader temperature range than the Hoffman‐Lauritzen equation. A third objective was to establish a new clearly defined method for determining the true induction time of a semicrystalline polymer as a function of temperature. The new crystallization rate equation introduced in this study has been formulated to give appropriate crystallization rate constants for all the temperatures currently usable with the Hoffman‐Lauritzen equation. In addition, this new equation also predicts appropriate crystallization rate constants outside the range of the Hoffman‐Lauritzen equation from temperatures significantly below the glass transition temperature, T_g, to temperatures significantly above the melting point, T_m. Interestingly, the isolation of the true isothermal induction times from apparent induction times in this study nicely mirrored the isothermal crystallization rates at each specific temperature. Both the true induction time and the crystallization rate curves were found to be similarly unsymmetrical as a function of temperature. Also, the temperature at the minimum induction time and the temperature at the peak crystallization rate determined from nonisothermal crystallization rate measurements were found to be nearly identical. Consequently, the results from this study strongly suggest that there is a significant and potentially very useful relationship between induction time analysis and crystallization rate kinetics.     

Improved thermoelectric properties of layered Ti1−xNbxS2−ySey solid solutions

The thermoelectric properties of a series of the polycrystalline samples of titanium dichalcogenides with partial substitution of Ti for Nb and S for Se were investigated. It was found that sintering of the samples improved the thermoelectric efficiency (ZT), and the maximum ZT was achieved at sintering temperature of 600°C. A further increase in the sintering temperature (850°C and 950°C) led to the recrystallization of the samples, as a result, the Seebeck coefficient sharply decreased and electrical conductivity dramatically increased. The temperature dependences of electrical conductivity σ(T) in the temperature range from 4.2 to 300 K and Seebeck coefficient S(T) in the temperature range from 77 to 300 K were investigated in order to determine the nature of the observed improvements in thermoelectric properties due to double substitutions and sintering. Two-dimensionalization of electron transport properties of Ti_1−xNb_xS_2−ySe_y solid solutions was found. The Fermi energy E_F2D was estimated using the temperature dependences of Seebeck coefficient. The relationship between the Fermi energy E_F2D and figure of merit ZT was established. The effect of sintering on parameters σ(T), S(T), charge carrier concentration (n_2D), mobility (µ), and thermal conductivity (k) was found. The optimal value of Fermi energy E_F2D in terms of figure of merit ZT = 0.31 at room temperature (T = 300 K) was found for Ti_0.98Nb_0.02S_1.3Se_0.7 sample sintered at 600°C.