Multiobjective optimization of the continuous casting process for poly (methyl methacrylate) using adapted genetic algorithm

The nondominated sorting genetic algorithm (NSGA) has been used to optimize the operation of the continuous casting of a film of poly (methyl methacrylate). This process involves two reactors, namely, an isothermal plug flow tubular reactor (PFTR) followed by a nonisothermal film reactor. Two objective functions have been used in this study: the cross‐section average value of the monomer conversion, x̄_mf , of the product is maximized, and the length, z_f , of the film reactor is minimized. Simultaneously, the cross‐section average value of the number‐average molecular weight of the product is forced to have a certain prescribed (desired) value. It is also ensured that the temperature at any location in the film being produced lies below a certain value, to avoid degradation reactions. Seven decision variables are used in this study: the temperature of the isothermal PFTR, the flow rate of the initiator in the feed to the PFTR (for a specified feed flow rate of the monomer), the film thickness, the monomer conversion at the output of the PFTR, and three coefficients describing the wall temperature to be used in the film reactor. Sets of nondominating (equally good) optimal solutions (Pareto sets) have been obtained due to the conflicting requirements for the several conditions studied. It is interesting to observe that under optimal conditions, the exothermicity of the reactions drives them to completion near the center of the film, while heat conduction and higher wall temperature help to achieve this in the outer regions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1439–1458, 2000     

Evaluation of the potential of periodically operated reactors based on the second order frequency response function

A new, fast and easy method for analysing the potential for improving reactor performance by replacing steady state by forced periodic operation is presented. The method is based on Volterra series, generalized Fourier transform and the concept of higher-order frequency response functions (FRFs). The second order frequency response function, which corresponds to the dominant term of the non-periodic (DC) component, G₂(ω, −ω), is mainly responsible for the average performance of the periodically operated processes. Based on that, in order to evaluate the potential of periodic reactor operation, it is enough to derive and analyze G₂(ω, −ω). The sign of this function defines the sign of the DC component and reveals whether a performance improvement by cycling is possible compared to optimal steady state process. The method is used to analyze the periodic performance of a continuous stirred tank reactor (CSTR), a plug flow tubular reactor (PFTR) and a dispersive flow tubular reactor (DFTR), after introducing periodic changes of the input concentrations. A homogeneous, n-th order reaction is studied under isothermal conditions.     

The effect of non‐ideal mixing on the number of steady states and dynamic behaviour for autocatalytical reactions in a CSTR

In this paper, we analyze the concentration multiplicity and dynamic behavior for an autocatalytical reaction, A + R → (n + 1)R + products with an overall rate expression given by – γ_a= kc_a^pc_r^r(p > 0 and r > 0) in a imperfectly mixed (Cholette's model) CSTR. We proved that non‐ideal mixing had an effect on the number of steady states and dynamic behavior for the reaction orders r > 1 and r = 1. However, the above‐mentioned effect does not happen for the reaction order r < 1. Furthermore, a simulated example was used to demonstrate our results.     

The effects of whey cations on the kinetic parameters of a model for the enzymic hydrolysis of lactose

The effects of whey cations (Ca²⁺, Mg²⁺) on the enzymic hydrolysis of lactose have been studied, at temperatures in the range 30–50°C, in a continuous stirred tank reactor (CSTR), using an immobilized β-galactosidase (Novozym 231). A model for the variation of V_max (the maximum rate in the Michaelis—Menten expression) in the presence of the ionic environment has been developed based on the Gouy electrical double layer concept and the liquid phase bimolecular process. In the presence of one cation (Mg²⁺), the mean value of the model parameter a_v, an approach distance including the hydration radius of the protein, was 27 × 10^?10 m, almost identical to the value obtained by the crystal density method. When two cations (Mg²⁺ and Ca²⁺) were present simultaneously the value of V_max as a function of the ionic strength showed a maximum which may be explained by the Stern adsorption modification of the Gouy theory.     

Ultralow-k hollow glass microsphere filled perfluoroalkoxy composites

Perfluoroalkoxy (PFA) composites filled with different volume fractions of hollow glass microsphere (HGM) and HGM/PFA–HGM/HBO₃–HGM/PFA sandwich layered composites were prepared by simple dry mixing and hot-pressing process. The dielectric frequency and temperature response characteristics, thermal expansion coefficient, and mechanical strength were investigated as a function of the loading fraction of HGM fillers. The obtained .6V_fHGM/.4V_fPFA composite demonstrates ultralow-k (ε_r ∼ 1,63@1 MHz; 1.57@10 GHz) with low-dielectric loss (∼7.2 × 10⁻⁴@1 MHz; ∼1.73 × 10⁻³@10 GHz), water absorption of ∼1.21%, in-plane thermal expansion coefficient of 42 ppm/°C, and temperature coefficient of dielectric permittivity (τ_εr) of ∼−92 ppm/°C. The temperature stabilities of dimension and dielectric permittivity for the .6V_fHGB/.4V_fPFA composite could be substantially improved by forming .6V_fHGM/.4V_fPFA–.6V_fHGM/.4V_fHBO₃–.6V_fHGM/.4V_fPFA sandwich–layered composite, which still maintained reasonable dielectric properties and mechanical rigidity with flexural strength of ∼8.1 MPa.     

The kinetics of cellulase-free xylanase excretion by Thermomyces lanuginosus RT9

Thermomyces lanuginosus RT9 was grown in a stirred and aerated reactor for the production of xylan-degrading enzymes and the kinetics of xylanase and β-xylosidase secretion investigated. During each fermentation, k_La decreased with increasing mycelia concentration to the point of cellular disintegration. Although both agitation and aeration rates had significant influences on the growth rate as well as on the yields and rates of enzymes (xylanase and β-xylosidase) release, the enzyme secretion kinetics showed a comparable pattern independent of the operating conditions. Enzyme secretion could be separated into a growth phase, during which extracellular xylanase was at low level, and an enzyme release phase, when there was a notable increase in the xylanase production rate accompanying cellular disintegration.     

Kinetics of the vapour-phase hydrogenation of benzene over a supported nickel catalyst in a stirred-vessel reactor

The catalytic hydrogenation of benzene was investigated over a supported nickel catalyst in a continuous stirred-vessel reactor between 260° and 450°F at atmospheric pressure. The effects of temperature, ratio of hydrogen to benzene and total feed rate (or contact time) on the conversion of benzene and yield of cyclohexane were determined. The use of the stirred reactor helped to eliminate mass transfer limitations. The investigation was carried out using surface-coated catalysts in order to eliminate pore diffusion which might otherwise mask the actual kinetics. Studies of the mixing characteristics of the reactor were carried out under both reacting and non-reacting conditions, by following conversion as a function of stirrer speed and by a tracer (pulse) technique, respectively. The kinetic data were analysed to determine the most probable model to represent the reaction. The Houghen–Watson type analysis was carried out using non-linear least squares instead of the usual linear one. The model that satisfactorily correlated the data over the entire temperature range describes the rate-controlling step as the surface reaction between adsorbed hydrogen and adsorbed benzene, the hydrogen addition being simultaneous. The following Hougen–Watson type equation was proposed: r = k_e K_H ³K_B P_H ³P_B/(1+K_HP_H+K_BP_B+K_CP_C)⁴. The constants in this rate equation were expressed as a function of temperature.     

Continuous thermal bulk copolymerization of styrene and maleic anhydride

Thermal bulk copolymerization of styrene (monomer 1) and maleic anhydride (monomer 2) was carried out in a continuous stirred tank reactor (CSTR) with a double helical ribbon-anchor impeller. A series of experimental runs under different operating conditions (average residence time, reaction temperature, and the composition in the inflow stream) were done, which showed that steady states could be approached. The effect of operating conditions on monomer conversion and copolymer composition was discussed. A CSTR model was established and the model parameters from the semicontinuous tests were used to predict conversions and copolymer compositions of the continuous process under transient and steady states. Kinetics from the semicontinuous bulk copolymerization were transferable to the continuous process. The modeling work for the continuous process showed that the same result as in a semicontinuous process could be obtained; the numerical method in which the gel effect on the copolymerization was incorporated exhibited excellent agreement between the model calculation and the experimental data. However, when using the assumption that k₂₂ = 0, k₂₁[M₁] ≫ k₁₂[M₂], (R_I/2k_t)^1/2 is a constant, and V is a constant, the predictions from the analytical solution to the model were in good agreement with the actual process data. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 615–622, 1999     

Partial oxidation of benzene catalyzed by vanadium chloride in novel reaction-extraction-regeneration system

This paper investigates the liquid-phase partial oxidation of benzene to phenol in a novel system consisting of reactor, extractor and regenerator. Since vanadium catalyst (V³⁺) is oxidized in the reactor and therefore deactivated, the regenerator with Pd or Pt catalyst and H₂ feed is employed to regenerate the deactivated vanadium. The V⁴⁺ ion can be reduced to V³⁺ and consequently the phenol production can be enhanced. Although the regenerator can regenerate vanadium catalyst and the reaction can proceed for over 100 h, some V⁴⁺ is still present. The feed position of benzene and catalyst solution have the influence on mixing condition in the reactor and interface area between benzene and catalyst solution. Counter current flow operation with the feeds of catalyst solution and benzene at the top and the bottom respectively shows the highest phenol production. The operating temperature of reactor, extractor and regenerator showed insignificant effect on phenol production rate.     

制糖废水连续流厌氧发酵制氢系统的运行特性

采用连续流搅拌槽式反应器(CSTR)作为反应装置,探讨了制糖废水厌氧发酵法生物制氢的可行性与运行特征。研究表明,在污泥接种量(以挥发性悬浮固体计)为17.74 g/L,温度为(35±1)℃,水力停留时间(HRT)为6 h,通过调节有机负荷,在12 d左右就可以快速实现生物制氢反应器中微生物的主要代谢类型为乙醇型发酵;而且此时的CSTR产氢发酵系统对负荷冲击表现出了良好的调节能力,在有机负荷(以化学需氧量COD计)从8 kg/(m3.d)提高到24 kg/(m3.d)时,反应系统可在9 d内重新达到稳定运行状态,其COD去除率和产气量由8%和3 L/d提高到20%和12 L/d,发酵气中氢气体积分数为67%。     

A comparative study of a fluidised bed reactor and a gas lift loop reactor for the IBE process: Part I. Reactor design and scale down approach

For the continuous production of isopropanol-butanol mixtures by immobilised Clostridium spp. (the IBE process) two reactor types were studied: a fluidised bed reactor with liquid recycling (FBR) and an external loop gas lift reactor (GLR). A large scale design (50–65 m³) was made for both reactors. A regime analysis, by evaluating the time constants for e.g. mixing and conversion, identified the ruling regime. Via the scale down approach two representative model reactors were developed: a 10 dm³ FBR reactor (H/D=25, D=0.08 m) and a 15 dm³ external loop GLR (H/D = 12.5, D_r=D_d=0.08 m). For both reactors the hydrodynamical behaviour and the total reactor performance were studied and are described in parts II and III of this study.     

A method for achieving inaccessible conversions by use of cascade CSTR's

The hysteresis of steady state could be found in a single isothermal, continuous stirred tank reactor (CSTR) for reaction rates of form R = kC/(1 + KC)². Clearly, a conversion (the metastable point) between the two stable solutions is never achieved. A numerical method for cascades of CSTR's to achieve this inaccessible conversion is presented along with a graphical procedure illustrating this method.     

Development of a mathematical model for Bacillus circulans growth and alkaline protease production kinetics

BACKGROUND: An unstructured mathematical model was developed to understand information on the relationship between Bacillus circulans growth and metabolism‐related protease production (using logistic and Luedeking–Piret equations respectively) in a batch reactor with respect to glucose consumption and fermentation time. The objective was to develop an indispensable tool for the optimisation, control, design and analysis of alkaline protease production. RESULTS: Biomass growth and enzyme production titres changed with a change in substrate concentration. Modelling analysis of biomass and enzyme production titres at different substrate concentrations revealed significant accuracy in terms of statistical consistency and robustness with respect to fermentation kinetic profiles. CONCLUSION: With the B. circulans strain used, an economic protease yield (2837 × 10³ U g^?1) with respect to biomass and glucose ratio was achieved at low substrate concentration (10 g L^?1). The developed model could be effectively utilised for designing, controlling and up‐scaling the protease production process in high‐density fermentation in selected bioreactors with statistical consistency. Copyright © 2008 Society of Chemical Industry     

PRODUCTION OF ETHANOL WITH SACCHAROMYCES CEREVISIAE IN A CONTINUOUS REACTOR Note III: an experimental,kinetic study with suspended,recycled biomass

By way of comparison with the kinetic investigation of the continuous production of ethanol in a tubular reactor with immobilized yeasts, a study was carried out of continuous fermentation in a stirred reactor, with final separation and recycling of the microorganisms. Flocculation with potassium ferrocyanide and zinc sulphate was used to separate the biomass. The maintenance of the metabolic activity was assessed. Next, discontinuous fermentation at various substrate and biomass concentrations was performed to determine the kinetics of glucose-ethanol transformation by flocculated and reinoculated Saccharomyces Cerevisiae.

Once again, the kinetic expression was a Michaelis-Menten equation, with un-competitive inhibition of the substrate and linear inhibition of the product.

The values observed for the various parameters were not very different from those for a biomass immobilized on an inert support or for a free biomass. Finally, the productivities of several types of reactor are compared.     

Hydrodynamic behavior of inverse fluidized bed biofilm reactor for phenol biodegradation using Pseudomonas fluorescens

The hydrodynamic characteristic performance of an internal draft tube inverse fluidized bed biofilm reactor was studied for the aerobic biodegradation of phenol (1,200 mg/l) using Pseudomonas fluorescens for various ratios of settled bed volume to reactor working volume (V _b /V _r ) under batchwise condition with respect to liquid phase. The operating parameters, such as superficial gas velocity, phase hold ups, aspect ratio and bed height, were analyzed for different ratios of (V _b /V _r ). The effect of biodegradation on synthetic phenolic effluent was determined from the reduction in chemical oxygen demand and phenol removal efficiency. The optimum value of (V _b /V _r ) _m was 0.20 for the optimal superficial gas velocity, U _gm =0.220 m/s with the COD reduction efficiency of 98.5% in 48 hours. The biomass and biofilm characteristics of P. fluorescens were determined for optimal hydrodynamic operating parameters by evaluating its biofilm dry density and thickness, bioparticle density, suspended and attached biomass concentration.     

Radial gas mixing characteristics in a downer reactor

In a downer reactor (0.1 m-I.D.x3.5 m-high), the effects of gas velocity (1.6-4.5 m/s), solids circulation rate (0–40kg/m²s) and particle size (84, 164 Μm) on the gas mixing coefficient have been determined. The radial dispersion coefficient(D _r ) decreases and the radial Peclet number (Pe_r) increases as gas velocity increases. At lower gas velocities, D_r in the bed of particles is lower than that of gas flow only, but the reverse trend is observed at higher gas velocities. Gas mixing in the reactor of smaller particle size varies significantly with gas velocity, whereas gas mixing varies smoothly in the reactor of larger particle size. At lower gas velocities, D_r increases with increasing solids circulation rate (G_s), however, D_r decreases with increasing G_s at higher gas velocities. Based on the obtained D_r values, the downer reactor is found to be a good gas-solids contacting reactor having good radial gas mixing.     

The kinetics of solution copolymerization of vinyl chloroacetate with vinyl acetate in a CSTR

The kinetics of isothermal, solution copolymerization of vinyl chloroacetate (VCLAC) with vinyl acetate (VAC) in methyl isobutyl ketone (MIBK) has been investigated using a continuous flow stirred-tank reactor (CSTR). The initiator used was 2,2′-azobis 2,4-dimethyl valeronitrile (ADVN). Polymerizations were carried out to moderately high conversions, necessitating the use of a modified parameter estimation method to determine the reactivity ratios. The copolymer composition conforms to terminal model kinetics. The values obtained for r₁ and r₂ are 1.18 and 0.80, respectively, with VCLAC as M₁ and VAC as M₂. Both values are close to unity indicating random copolymerization. The cross termination factor ? strongly depends on the composition of the comonomer feed ratio, implying that the chain-termination step is possibly diffusion controlled. The variation of ? could also be caused by chain transfer to the solvent retarding the reaction rate. Such a possibility is consistent with the observed reduction in the molecular weight of the copolymer in the presence of the solvent. The approach to steady-state in the reactor was characterized. It was not possible to obtain good agreement between experiment and simulation with a single value of the ? factor.     

Oil and fungal biomass dispersion in a stirred tank containing a simulated fermentation broth

The production of γ‐decalactone by the filamentous fungus Trichoderma harzianum involves four phases (oil–water–air–mycelium) and its dispersion is crucial during fermentation. Oil and biomass (when present) dispersion, as a function of the volumetric power drawn (P/V), was characterized, in two; three‐ and four‐phase systems agitated with Rushton turbines. Trichoderma harzianum mycelium was used as the solid phase in the four‐phase system. Two stages of the fermentation were simulated: the beginning (15% oil and 1.4 kgm^?3 of mycelium) and the end (2% oil and 10.6 kg m^?3 of mycelium). In the two‐phase system, the use of exhausted broth achieved higher oil dispersions at low P/V values as compared with distilled water. Aeration decreased the oil dispersion for the high‐oil system, but enhanced oil dispersion for the low‐oil system. Compared with the P/V used in the actual fermentation (0.2 kW m^?3), a high segregation of the system was observed for the high‐oil/low‐biomass system, due to the difficulty of mixing the thick oil–air emulsion present at the top of the tank. The system simulating the end of the fermentation reached almost complete homogeneity of oil and biomass, a phenomenon due to the high biomass/oil ratio and the biomass acting as an oil carrier. © 2001 Society of Chemical Industry     

Transformation of propene into acrylonitrile with nitric oxide over nickel oxide alumina catalyst in a continuous stirred tank reactor

Catalytic transformation of propene (C₃H₆) with nitric oxide (NO) over nickel oxide alumina catalyst (2NiO, Al₂O₃) has been investigated using a continuous stirred tank reactor at temperatures varying from 270 to 400°C, under atmospheric pressure. The main products found were acrylonitrile (C₃H₃N) and carbon dioxide (CO₂). The rate of formation of C₃H₃N and the rate of disappearance of C₃H₆ were both correlated by the same model based on a redox mechanism: r_i = k_iok_irP_NOP_HC/(k_ioP_NO + k_irP_HC) The constants in the rate equation were expressed as a function of temperature.     

Integration of CFD and polymerization for an industrial scale cis-polybutadiene reactor

A computational fluid dynamics (CFD) approach, coupled with anionic polymerization kinetics, was used to investigate the solution polymerization in a 12?m³ industrial scale cis-polybutadiene reactor. The kinetic model with double catalytic active sites was integrated with CFD by a user-defined function. The coupled model was successfully validated by the plant data and then used to investigate the key operating variables. Also, predictions of CFD model were compared with those of continuous stirred tank reactor (CSTR) model. Although the reaction mixture is well mixed in the middle and at the top of the reactor, there exists a poor mixing feeding zone at the bottom, which leads to serious deviations from the ideal CSTR. The polymerization process with nonideal mixing is very sensitive to the inlet temperature and the feeding rate. Enhancing the mixing performance in the feeding zone could be an effective way to improve the product quality.