A correlation to the solution of the two-phase dispersion model

A correlation to the solution of the two-phase dispersion model has been developed for gas-solid fluidized bed reactors operating in the bubbling regime. An analytical solution was obtained for fractional gas conversion by using an exponential function to characterize the dense phase gas concentration profile. The coefficient of the exponential function was found to depend on gas axial dispersion and, in order to determine this parameter, a Peclet number correlation was developed. Model predicted gas conversions were in excellent agreement with experimental conversions for a variety of fluidized bed reaction data over a conversion range from 2.5 to 99%.     

Analysis and performance of a countercurrent moving-bed chromatographic reactor

A theoretical and experimental investigation of a countercurrent moving-bed chromatographic reactor is the subject of this paper. In this reactor a reversible heterogeneous reaction takes place on catalyst particles passing downward through an upcoming gas stream. The behaviour of an ideal reactor model was examined for different values of feed concentrations and reactor length. It is predicted that reaction and separation can be achieved simultaneously and that under appropriate operating conditions, a reactor fed at the bottom with the species more favoured by thermodynamic equilibrium can lead to 100% product purity with overall conversions lower than a conventional fixed bed reactor. The effect of nonidealities on the reactor performance is also discussed. Finite adsorption and axial dispersion have a generally deteriorating effect on overall conversion and product purity. An improved reactor configuration with a bottom stripping section is suggested. Its operating conditions can be tailored so that predicted performance exceeds that of a fixed bed both in yield and product purity. The hydrogenation of mesitylene with excess hydrogen over a Pt on alumina catalyst was used for an experimental investigation of the reactor. The experiments, performed in a 1/2″ i.d., 7′ long column, resulted in products of higher purity than the equilibrium prediction, and overall conversions comparable to a fixed bed reactor.     

Modeling and simulation of non-isothermal catalytic packed bed membrane reactor for H2S decomposition

The recovery of H₂ from H₂S is an economical alternative to the Claus process in petroleum and minerals processing industries. Previous studies [React. Kinet. Catal. Lett. 62 (1997) 55; Catal. Lett. 37 (1996) 167] have demonstrated that catalytic decomposition of H₂S over bimetallic sulfide can proceed at relatively higher rates than over mono-metallic systems due to chemical synergism although conversions are still thermodynamically limited. In the present study, the performance of a catalytic membrane reactor containing a packed bed of Ru–Mo sulfide catalyst has been investigated with a view to improving H₂ yield beyond the equilibrium ceiling. A system of differential equations describing the non-isothermal reactor model has been solved to examine the effect of important hydrodynamic and transport properties on conversion. The results were obtained using a Pt-coated Nb membrane tube as the catalytic reactor enclosed in a quartz shell cylinder. Reynolds number for shell and tube side (Re^s and Re^t) as well as the modified wall Peclet number, Pe_m, dramatically affect H₂S conversions. Membrane reactor conversion rose monotonically with axial distance exceeding the equilibrium conversion by as much as eight times under some conditions.     

Effect of kinetic regime and axial dispersion on the dynamic response of counter flow extractive reactors

Plug flow as well as axial dispersion dynamic models for counter-flow extractive reactors are formulated and solved to investigate the frequency response characteristics of such reactors. The reactions considered are taken to be either infinitely fast, taking place at the interface between the two phases or within a thin film in one of the phases, or slow taking place in the bulk of one of the phases. The results demonstrate the effect of the kinetic regime as well as axial dispersion (Peclet number) of the continuous phase on the dynamic behaviour of the two phase reactor. For the plug flow case (Pe → ∞) it is shown that for some input-output relations the kinetic regime affects the functional forms of the transfer functions. The complex transfer functions are approximated, using simple fitting techniques, to simpler ones suitable for the design of the reactor's control loops. For the axial dispersion case the results show that the continuous phase Peclet number affects the frequency response of the reactor in a complicated manner giving rise, for some input-output relations and small values of the Peclet number, to complex oscillations in both amplitude ratio and phase angle.     

Estimation of liquid phase mixing due to solids in a turbulent bed contactor

The mixing in two-phase gas-liquid and three-phase gas-liquid-solid system (turbulent bed contactor) is evaluated through residence time distribution (RTD) studies in terms of Peclet number. RTD experiments are conducted for various gas and liquid velocities, and number of stages for two- and three-phase systems. Since the mean residence time is very short in both the systems, a mixed flow tank with exponential decay RTD is used in series. After deconvolution, the RTD of the system is obtained. The experimental RTD curves are satisfactorily compared with the axial dispersion model and Peclet numbers are evaluated for all the experiments. The axial dispersion coefficients are calculated from Peclet numbers. With this study, it is thought that liquid phase mixing may be controlled by changing the quantity of solid particles in the bed.     

Liquid phase mixing in turbulent bed contactor

Axial mixing of the liquid phase in turbulent bed contactor (TBC) is studied through residence time distribution (RTD) experiments over a large range of variables such as flow rate of gas and liquid phases, static bed heights, diameter and density of particles and number of stages in presence of downcomer using air water system. Since all the liquid exits only through the downcomer, it enables the correct estimation of exit concentration of the tracer. The experimental RTD curves are satisfactorily compared with the axial dispersion model. The Peclet numbers evaluated by axial dispersion model and the Peclet numbers reported in the literature are used to propose a unified correlation in terms of operating and geometric parameters. Correlation is also developed for predicting the axial dispersion coefficient. It was observed in the present study that almost plug flow conditions can be achieved in multistage TBC.     

Sorption dynamics in fixed‐beds of inert core spherical adsorbents including axial dispersion and Langmuir isotherm

The effects of axial dispersion and Langmuir isotherm on transient behavior of sorption and intraparticle diffusion in fixed‐beds packed with monodisperse shell‐type/inert core spherical sorbents are studied. The system of partial differential equations of the mathematical model is solved numerically using finite difference methods. Results are presented in the form of breakthrough curves for adsorption and desorption processes. Results reveal that the shape of the breakthrough curves is influenced by both hydrodynamic and kinetic factors. Hydrodynamic factor is governed by axial dispersion and is controlled by changes of Peclet number. Simulation results reveal that when linear adsorption isotherm is used, the effect of axial dispersion on breakthrough curves of the system is important for Peclet numbers smaller than 50, whereas, for Langmuir isotherm axial dispersion is considerable for Peclet numbers less than 80. In addition, effects of type of adsorption isotherms and size of adsorbents on breakthrough curves are investigated, and results are compared with existing reports in the pertinent literature. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Fluid dynamic characteristics of a structured bed spiral mini-reactor

The fluid dynamic characteristics of a structured bed type multiphase mini-scale reactor are investigated in this work. This type of reactor, which is called spiral reactor, consists of a small tube with an internal diameter a little larger than the catalyst extrudate diameter where the catalyst particles are introduced one by one forming a string bed in the spiral tube. Mock up tests were performed at ambient conditions using water and nitrogen as liquid and gaseous phase, respectively, in upflow and downflow operation mode. The effect of the gas and the liquid superficial velocities, the reactor internal diameter to catalyst diameter ratio and the length of the reactor on the axial dispersion, liquid hold-up and pressure drop were studied. The liquid dispersion is not extended and its impact on the spiral reactor performance is expected to be not significant.     

The spherical reverse flow reactor

A packed bed reactor made up of two hemispheres separated by an orifice plate can be operated as an adiabatic reverse flow reactor with nearly spherical symmetry. The reactor requires little or no insulation with external temperatures limited to the adiabatic temperature rise, but much higher internal temperatures. The operational characteristics of this type of reactor have been studied using a dynamic model and the steady state model obtained for fast switching of the flow direction. Due to the large cooling region, higher conversions than the conventional reverse flow reactor are predicted for reversible exothermic reactions.     

Axial dispersion coefficients in packed beds at low reynolds numbers

Peclet numbers describing axial dispersion in gas flow through packed beds of spheres were obtained using a two measurement point, pulse technique in a test section four inches inside diameter and 5.14 feet high. Three packing sizes were investigated, corresponding to tube to particle diameter ratios of 6.4, 17, and 66 In the experiments the contribution of the velocity profile to axial spreading was reduced by using thermal conductivity detectors which responded to dispersion only in the central part of the bed cross-section. In this region of a packed bed the velocity profile is relatively flat. The results point to a particle diameter effect which is more pronounced than has been previously reported. This is in accord with the diffusive mechanism of axial dispersion in a packed bed provided dispersion caused by the velocity profile does not affect the measured pulse response. In the absence of velocity profile effects, the spreading of residence times in void cells is caused primarily by the shedding of the decelerated boundary layers on the downstream side of the particles. At low velocities however, molecular diffusion predominates. Implicit in this discussion is the hypothesis that the uniformity of shape and size of packing particles has an important bearing on the manner in which the Peclet number approaches its limiting value as the gas velocity is increased.     

Axial dispersion in two phase co-current flow with fast and instantaneous reactions

Approximate solutions to the governing equations for two phase co-current flow with fast and instantaneous reactions between a gaseous and a liquid species are considered. These solutions are obtained by perturbation technique for large Peclet numbers of the gas and the liquid phases and by Galerkin's method for small and intermediate values of the gas and liquid Peclet numbers. The approximate solutions are compared with a numerical solution obtained under the limiting condition of the gas phase Peclet number becoming infinite. Criteria for axial dispersion in a two phase column are also obtained based on the perturbation solutions.     

The behaviour of an adiabatic fixed bed reactor for the oxidation of carbon monoxide—I: General parametric studies

An experimental study of an adiabatic catalytic fixed bed reactor has been made under both transient and steady state operation. Temperature measurements have been made within the bed and within two instrumented pellets placed inside the bed. Concentration profiles have also been measured in the bed under steady state conditions. A general parametric investigation was made which also included the effect of reverse operation. Intraparticle temperatures were small even in the ignition zone but could be adequately predicted if local variables were used. Good agreement was obtained between the experimental results and a heterogeneous dispersion model.     

A combined method to facilitate the high dispersion modeling for wastewater treatment bioreactors with closed boundaries

Two tanks in series and axial dispersion models are used frequently for bioreactors flow regime modeling, especially the wastewater treatment reactors. Using the tanks in series model is simple, but the axial dispersion model is dependent on the boundary conditions. In case of high dispersion and closed boundaries, axial dispersion model will be a complicated method. In this paper by combination of tanks in series and axial dispersion models, a new simple model is presented to facilitate the axial dispersion solution for closed boundary condition. For the various studied Peclet numbers, the maximum peak concentration error is calculated by combined method equal to 3% in comparison with the error for open solution that increases progressively and exceeds 14%. Furthermore the combined model peak time errors are zero for all the Peclet numbers while are more than 10% for the open solution.     

中心气升式气-固环流反应器与自由流化床流动特性对比

对中心气升式气固环流反应器和自由床流化反应器的流动特性进行了对比. 结果表明,在同样的操作条件下,在轴向高度h=112~512 mm范围内,环流反应器导流筒区的径向不均匀指数RNI比自由床的RNI减小27%~36%;与自由床相比,环流反应器导流筒区的局部不均匀指数减小20%~59%,整体不均匀指数减小17%~43%,环流反应器的流化质量较高;环流反应器导流筒区和自由床内均存在气体返混现象,导流筒区各采样点示踪气体的浓度和轴向扩散系数Da,g比自由床均有所降低,在表观气速0.2~0.4 m/s范围内,导流筒区Peclet准数的绝对值比自由床增大12%~58%,说明导流筒区气体返混程度小于自由床,气-固两相流向上的宏观流动可有效抑制气体的轴向返混.     

Radioisotope tracer study in trickle bed reactors

The residence time distribution (RTD) of liquid phase in trickle bed reactors has been measured for air‐water system using radioisotope tracer technique. Experiments were carried out in a glass column of internal diameter of 0.152 m packed with glass beads and actual catalyst particles of two different shapes. From the measured RTD curves, mean residence time of liquid was calculated and used to estimate liquid holdup. The axial dispersion model was used to simulate the experimental data and estimate mixing index, ie. Peclet number. The effect of liquid and gas flow rates on total liquid holdup and Peclet number has been investigated. Results of the study indicated that shape of the packing has significant effect on holdup and axial dispersion. Bodenstein number has been correlated to Reynolds number, Galileo number, shape and size of the packing.     

Multi-objective optimization of industrial styrene reactor: Adiabatic and pseudo-isothermal operation

Multi-objective differential evolution (MODE) is used to optimize an industrial styrene reactor considering productivity, selectivity and yield as the main objectives. Two reactor configurations (single bed adiabatic operation and steam injected pseudo-isothermal operation) and four combinations of objectives consisting of 5 and 7 variables respectively are considered. Pareto optimal solutions are obtained for all combinations of objective functions for both the configurations. The results are compared with those reported in the literature and an industrial operating point. For all the cases considered, MODE is able to give a Pareto front better (in terms of wider range and a better spread) than that obtained using NSGA for both the configurations. Steam injected reactor configuration is better than the adiabatic reactor configuration in terms of performance. The Pareto optimal solutions obtained from such studies provide a wide range of optimal operating conditions from which an appropriate operating point can be selected based on the requirements of the decision maker.     

The gas–liquid contacting effect on the operation of small scale upflow hydrotreaters

The effect of reactor geometry and bed dilution on the extent of gas oil hydrodesulfurization was tested by conducting hydrodesulfurization experiments in two laboratory reactors of different scale with non-diluted and diluted beds in ascending flow. The superficial gas and liquid velocities and the catalyst bed height were kept constant while the main difference between the two reactor scales was the reactor diameter. The diluted bed of the mini-reactor showed the best performance and its results were identical in upflow and downflow mode. The differences between the performance of the mini- and the bench-scale reactor operating in upflow mode have been investigated. Reactor performance simulation was attempted by a mathematical model that takes into account axial dispersion of the liquid phase and gas–liquid mass transfer. Bench-scale reactor operation was characterized by lower mass transfer rates than the corresponding mini-scale one. Combining model predictions and mock up operation it is concluded that the stronger mass transfer resistances calculated for the bench-scale reactor are associated with poorer gas distribution through the catalyst bed. Reduction of the bed diameter results in better gas–liquid contact by forcing the gas bubbles to distribute more effectively into the liquid phase.     

Axial dispersion characteristics in three phase fluidized beds

Axial dispersion coefficients in three-phase fluidized beds have been measured in a 0.152 m-ID x 1.8 m high column by the two points measuring technique with the axially dispersed plug flow model. The effects of liquid velocity (0.05–0.13 m/s), gas velocity (0.02–0.16 m/s) and particle size (3-8 mm) on the axial dispersion coefficient at the different axial positions (0.06–0.46 m) in the bed have been determined. The axial dispersion coefficient increases with increasing gas velocity but it decreases with an increase in particle size and exhibits a maximum value with an increase in the axial position from the distributor. The axial dispersion coefficients in terms of the Peclet number have been correlated in terms of the ratio of fluid velocities, the ratio of the panicle size to column diameter, and the dimensionless axial position in the bed based on the isotropic turbulence theory.     

DYNAMICS OF A RESIDUE HYDRODESULFURIZATION TRICKLE BED REACTOR SYSTEM

An adiabatic residue hydrodesulfurization trickle bed reactor packed with a porous catalyst undergoing deactivation is simulated numerically in order to examine the dynamic behavior of this specific reaction system. One dimensional pseudo-homogeneous model incorporating the effects of mass and heat dispersion is used in the mathematical derivation. The parameters used in the simulation are primarily based on the experimental data of Shoji Kodama and other correlations. The method of orthogonal collocation is used to obtain the solution of coupled mass and energy balance equations. The catalyst deactivation model adopted was proposed by Shoji Kodama to include the interaction of demetallization and coking reaction on a catalyst. The performance of the reactor during start-up period and that for long time operation are examined. Meanwhile, step-wise changes of feed composition, feed rate, inlet temperature on the dynamic behavior of the reactor @KEYWORDS: Residue hydrodesulfurization, Dynamics, Trickle bed reactor, Simulation Orthogonal collocation.