Finite element collocation solution of tubular and packed-bed reactor two point boundary value problems

Nonlinear two point boundary value problems (TPBVP's) are frequently encountered in chemical engineering. TPBVP's describing tubular and packed-bed reactors are important and have received much attention in the literature. For certain ranges of parameter values of the reactors, the TPBVP's become stiff and pose problems in numerical solution. These problems have been efficiently solved by the finite element collocation method using Hermite and B-spline functions in conjunction with quasilinearization. Numerical results have been presented and discussed. The problems have been solved for a wide range of parameter values without encountering any numerical difficulty.     

A study of the dynamic behavior of dispersion-type tubular reactor models

The dynamic behavior of dispersion-type tubular reactors, referred to as finite and truncated models depending on the boundary condition representations at the reactor exit, was investigated through numerical simulations. It was found that the dynamic behavior of the two models can be identical or different depending on how thePéclet number changes.     

Simulation of temperature peak attenuation by catalyst dilution in a tubular packed-bed reactor

Temperature peak attenuation is an important problem for safe process control. Simulations of the axial temperature and product progression in stationary ammonia synthesis with different axial catalyst dilutions have been carried out. It is demonstrated that the requirement of temperature peak attenuation together with a maximum product yield can be met by an optimal catalyst dilution profile at the entrance of the bed.     

Phenylacetylene hydrogenation in a three-phase catalytic packed-bed reactor: experiments and model

A mathematical model was developed for the cocurrent operation of a three-phase catalytic packed-bed reactor under both trickling- and pulsing-flow regimes. The local fluctuations of liquid-solid mass transfer, liquid flow rate, and liquid holdup in unsteady pulsing-flow were simulated as periodic square-wave functions. The transport properties employed in the model were obtained using published correlations, while expressions for the intrinsic reaction kinetics were taken from our previous work. The model results were found to be in good agreement with experimental data obtained from a laboratory-scale reactor, and verified the advantage of pulsing-flow operation over trickling-flow.     

Residence time distribution of plug flow in a finite packed-bed chemical reactor

The residence time distributions in a finite packed-bed chemical reactor under plug flow conditions have been studied. Analysis was performed upon the well-known axial dispersion model in one dimension. Of paramount importance it was to construct a high order approximate solution to the corresponding initial-boundary value problem which appeared to be extremely convenient for fast numerical calculations. To this purpose singular perturbation techniq were applied using the reciprocal of the Péclet number as a small parameter. An error analysis was subsequently established for the special case of a pulse-function tracer input. The so-called “tailing phenomenon” of the response curve was simulated by an appropriate parameter-depending boundary condition of diffusion type.     

Mathematical models for a packed-bed chemical reactor

Various approaches to the mathematical representation of the simultaneous phenomena of heat transfer, mass transfer, and chemical reaction, within a packed-bed chemical reactor, are summarized and discussed from the point of view of both accuracy and practicality. After careful analysis of the ideas presented in the recent literature, a relatively simple unidimensional model is proposed for use, both for steady-state calculations and for dynamic analysis. The assumptions inherent in the use of the proposed model are carefully stated, and areas of uncertainty are pointed out. Reference is made to recent work in which the proposed model has found application.     

A stochastic flow model for a tubular solution polymerization reactor

Residence time distributions were evaluated experimentally for three tubular solution polymerization reactors to analyze aspects of the fluid‐dynamic behavior of these reactors. The analysis of the available experimental data indicates that the flow characteristics of these reactors may be subject to stochastic perturbations. A stochastic flow model is then proposed by assuming that a viscous polymer layer is formed in the proximities of the reactor walls and that plugs of polymer material are released at random during the operations. This model is able to represent the available experimental data fairly well for three tubular reactors with different configurations. POLYM. ENG. SCI., 47:1839–1846, 2007. © 2007 Society of Plastics Engineers     

Methanol oxidative dehydrogenation in a catalytic packed-bed membrane reactor: experiments and model

Methanol oxidative dehydrogenation to formaldehyde over a Fe-Mo oxide catalyst was studied experimentally in three reactor configurations: the conventional fixed-bed reactor (FBR) and the packed-bed membrane reactor (PBMR), with either methanol (PBMR-M) or oxygen (PBMR-O) as the permeating component. The kinetics of methanol and formaldehyde partial oxidation reactions were determined independently from FBR experiments. A steady state plug-flow PBMR model, utilizing these kinetics and no adjustable parameters, fit the experiments accurately. It is shown experimentally and in accordance with the model that for given overall feed conditions, the reactor performance for methanol conversion and formaldehyde yield is in the order PBMR-M < FBR < PBMR-O.     

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.     

Methanol synthesis in a forced unsteady-state reactor network

The feasibility of carrying out the low-pressure methanol-synthesis process in forced unsteady-state conditions, using a network of three catalytic fixed bed reactors with periodical change of the inlet position, has been investigated; advantages and limitations in comparison with the previously proposed reverse-flow reactor have been highlighted. The effect of the main operating parameters—inlet temperature, switching time, inlet flow rate—has been studied. A cyclic-steady-state condition and auto-thermal behaviour are possible; nevertheless, they are attainable only for switching times varying in two narrow ranges. Out of these regions, complex steady-states of high periodicity, where conversion is low, or extinction of the reactors occur. For low values of the switching time, the establishing of optimal temperature profiles along the network allows higher conversions than in the reverse flow reactor. Furthermore, the performances of the network are weakly affected by wash-out, the removal of unconverted gas in correspondence of switching, which is in intrinsic disadvantage of reverse flow operation.     

The optimum taper angle for ethanol fermentation in a packed-bed column reactor

In ethanol fermentation, tapered columns facilitate the liberation of CO₂ and, since the bed expands through a larger cross-sectional area, smaller pressure drops occur. In this work, 0°, 2°, and 4° tapered columns, containing Saccharomyces cerevisiae entrapped in beads of K-carrageenan, were operated for continuous production of ethanol from glucose. The column inlet diameters and the bead volume were maintained constant for the three columns. With decreasing taper angle, increasing feed glucose concentration, increasing feed flow rate and increasing bead volume in the reactor, the pressure drop across the bed increased. There was no significant difference between the ethanol productivities obtained in the 0°, 2°, and 4° tapered columns when a packed volume of 52% of the total volume was examined. Increasing the packed volume to 84% of the total caused the cylindrical column to become inoperable due to pressure buildup and bead compression. When the columns were packed to 84% capacity, the productivity and pressure drop values obtained on the 2° and 4° tapered columns did not significantly differ. For a feed concentration of 150 g glucose dm^?3 and a residence time range of 5.4–15.94 h, the pressure drop varied between 4.5 × 10³ and 1.28 × 10⁴ Pa in the 2° and between 4 × 10³ and 7.98 × 10³ Pa in the 4° tapered column. Conversion in the 2° tapered column varied from 94% to 78.8% and in the 4° tapered column from 92.6% to 78.8%. Defining optimum taper angle as the smallest angle which allows for stable operation without any pressure buildup, the taper angle of 2° was selected as nearest to the optimum value.     

Effect of pulsing on reaction outcome in a gas–liquid catalytic packed-bed reactor

A novel experiment is described for studying the effect of flow regime on reaction outcome for a consecutive-parallel reaction. By taking advantage of the convective nature of disturbances that grow into pulses in gas–liquid packed-bed reactors, it is shown that it is possible to compare reaction behavior for pulsing and trickling at the same flow rates. This contrasts previous studies where effects of regime were found, but at different flow rates. This experiment is accomplished by packing the column with mostly inert particles and confining the catalytically active region either near the inlet, where pulses have not yet formed, or near the end where they have developed. It is found that for the reaction of phenylacetylene to styrene and ethylbenzene over a platinum/alumina catalyst, where pulses are present in the bottom of the reactor but not at the top, about a 15% increase in styrene concentration, as an intermediate, occurs under pulsing conditions.     

Experimental, kinetic and 2-D reactor modeling for simulation of the production of hydrogen by the catalytic reforming of concentrated crude ethanol (CRCCE) over a Ni-based commercial catalyst in a packed-bed tubular reactor

Mechanistic kinetic models were formulated based on Langmuir-Hinshelwood-Hougen-Watson and Eley-Rideal approaches to describe the kinetics of hydrogen production by the catalytic reforming of concentrated crude ethanol over a Ni-based commercial catalyst at atmospheric pressure, temperature range of 673-863 K, ratio of weight of catalyst to the molar rate of crude ethanol 3472-34722 kg cat s/kmol crude in a stainless steel packed bed tubular microreactor. One of the models yielded an excellent degree of correlation, and was selected for the simulation of the reforming process which used a pseudo-homogeneous numerical model consisting of coupled material and energy balance equations with reaction. The model was solved using finite elements method without neglecting the axial dispersion term. The crude ethanol conversion predicted by the model was in good agreement with the experimental data (AAD%=4.28). Also, the predicted concentration and temperature profiles for the process in the radial direction indicate that the assumption of plug flow isothermal behavior is justified within certain reactor configurations. However, the axial dispersion term still contributed to the results, and thus, cannot be neglected.     

Optimal operation of a catalytic tubular reactor with fouling catalyst by coke deposition

The dehydrogenation of isopentane over chromia-alumina catalyst has been carried out at three isothermal levels. The catalyst fouling and the deposited coke profiles were observed in a catalytic tubular reactor. A kinetic model is proposed and the kinetic parameters have been estimated by non linear regression methods.For the dehydrogenation with catalyst fouling, the problem of finding the isothermal optimal control was formulated by a distributed maximum principle and a computational algorithm using a quasi-steady state assumption was presented. The dehydrogenation of isopentane was carried out experimentally at the evaluated isothermal optimal temperature. The observed conversion, yields and coke content profiles agreed with the evaluated ones fairly well, which suggests that the kinetic model may be useful for optimal controls.     

Prediction of packed-bed catalytic reactor performance for a complex reaction (oxidation of o-xylene to phthalic anhydride)

Statistical best-fit kinetic and transport parameters are derived from temperature and yield profiles observed in a pilot-plant catalytic reactor in which o-xylene is oxidised with air to phthalic anhydride and its precursors. Published data are used to begin the search routine and the tuned parameters are seen to be plaubible. The overall model has good extrapolative power to the point where catalyst deactivation becomes apparent.     

Optimal feed temperature for an immobilized enzyme packed-bed reactor

Optimal feed temperature was determined for a nonisothermal immobilized enzymatic reaction with enzyme deactivation in a packed-bed reactor. The optimal feed temperature was obtained by maximizing the average substrate conversion over a given reaction period. Simulation showed the optimal feed temperature to be strongly dependent on the flow dispersion, the reaction activation energy, the corresponding enzyme inactivation energy and the heat of reaction. It was also observed that in a plug flow reactor the enzyme reaction generally exhibited a lower optimal feed temperature and higher substrate conversion than in a continuously stirred tank reactor.