Axial Dispersion Model Research Articles

Effect of Gas- and Liquid-Phase Axial Mixing on the Rate of Mass Transfer in a Pilot-Scale Distillation Column Packed with Mellapak 250Y

Using the profile method, the vapor- and liquid-side volumetric mass-transfer coefficients (k V a, k L a) were evaluated by comparing the vapor and liquid concentration profiles with those calculated from a rate-based distillation model taking into account axial mixing in both phases. The method was applied for the atmospheric distillation of three different mixtures of primary alcohols: methanol-ethanol, ethanol-propanol, and methanol-propanol on structured packing Mellapak 250Y. The column was operated at total reflux; liquid and vapor samples were withdrawn at seven sampling points distributed regularly along the column. Bodenstein numbers Bo were determined by means of the cold air-water dynamic experiments performed under hydraulic conditions, by which the concentration profiles were measured in the distillation column. The mass-transfer coefficients were compared with those obtained in our previous work (Rejl et al. Ind. Eng. Chem.. Res, 2010, 49, 4383) using the plug flow model for their evaluation. The axial dispersion model reproduces the experimental profiles with a 2-fold decreased relative difference between the experimental and the calculated concentrations in comparison with the plug flow model. The individual transport coefficients are higher (by up to 2 times) and are less dependent on the phase flow rate in comparison with the plug flow model. The correspondence with the mass-transfer correlations designed for the packed columns (Rocha et al. Ind. Eng. Chem. Res. 1996, 35, 1660; Billet and Schultes TransIChemE 1999, 77,498; Olujic et al. Chem. Eng. Process. 1999, 38, 683) is not improved by using the dispersion model: the differences reach multiples of the measured values. The parameters k L a, k V a, Bo L , and Bo V were studied for their relative influences on the separation efficiency of the column. The relative contribution of k V a is predominant (60%), whereas the axial mixing of vapor Bo V has practically no effect. The contribution of k L a constitutes about 25%, and the one of the axial mixing of the liquid Bo L . increases from about 15 to 40% with a decrease in the liquid flow rate at the expense of the contribution of k V a.

Optimization of making pure oxygen with the electrical analogue model

Based on the electrical analogue model, an optimization process is presented and investigated for making pure oxygen by a two stage pressure swing adsorption. The system performance is affected by important parameters such as valve parameters, the purge rate and the operating time. By a simulating process, carbon molecule sieve adsorbs Ar and N 2 with outlet gas of about 70% oxygen to start with the in feed gas to the zeolite molecule sieve, which can make oxygen with a purity of 99.06% and a recovery rate of 28.4%. Compared to the axial dispersion model, it takes less time for the electrical analogue model to reach the cyclic steady state.

Hydrodynamics and reaction studies in a layered herringbone channel

AbstractThe performance of a consecutive reaction of the type A→k1B→k2C was studied in two reactor configurations. A layered herringbone channel, which consists of two rectangular channels and a middle layer containing machined-through herringbone structures, is compared with an unstructured rectangular channel. It was found that when the reactants are not premixed before the inlet, the layered herringbone configuration shows an improved performance compared to the rectangular channel giving a 40% increase in the maximum amount of intermediate produced. The maximum concentration of intermediate is obtained at lower residence times, which indicates that reactor volume could be decreased compared to the rectangular channel. The maximum amount of intermediate and the conversion at which this maximum occurs is dependent also on the ratio (k2/k1) which in this work is 0.05. Good mixing characteristics and narrow residence time distribution (RTD) are responsible for the improved behaviour in the layered herringbone channel. When the reactants are premixed before the inlet the differences are more subtle, indicating that the improved reaction behaviour in the layered herringbone channel is mainly due to good mixing and to a smaller extent to narrow RTDs. Residence time distributions were calculated numerically via CFD and particle tracking methods. The RTDs for the layered herringbone channel were found to be narrower as compared to the rectangular one. The model of axial dispersion exchanging mass with a stagnant zone was used for the modelling of the RTD. It was found that the model parameters could be calculated directly from hydrodynamic data obtained from CFD calculations, without the need of particle tracking algorithms. Concepts from turbulent theory were employed for the calculation of an effective diffusion coefficient that replaced the stirring effect of the herringbones. This procedure greatly simplifies the theoretical calculation of RTDs and reaction conversions.

Analysis and interpretation of residence time distribution experimental curves in FM01-LC reactor using axial dispersion and plug dispersion exchange models with closed–closed boundary conditions

The liquid phase mixing flow pattern at low (20 < Re < 120) and intermediate liquid flow rate (120 < Re < 400) was studied by means of residence time distribution (RTD) experimental curve in an up-flow Filter Press electrochemical reactor (FM01-LC) bench scale. For this purpose, a plastic turbulence promoter was used with stainless-steel and platinised titanium structural meshes as electrodes in channel configuration. To visualize and determine the mixing flow pattern in the liquid phase, the stimulus-response technique was employed using dextran blue ( D M = 1.058 × 10 −11 m 2 s −1, 25 °C, in water) as model tracer. A theoretical analysis and approximation RTD experimental curves with axial dispersion model (ADM) and plug dispersion exchange model (PDE), with “closed–closed vessel” boundary conditions were used in order to establish a better approximation of the axial dispersion, stagnant zones, channelling and by-pass (preference flow) effects present at low and intermediate Re. RTD curves show that the liquid flow pattern in the FM01-LC deviates considerably from axial dispersion model at low Re, where the FM01-LC exhibits large channelling, stagnant zones, and dead zone. The PDE model represents fairly this deviation from ideal flow (less dead zone).

Single Pellet String Reactor for Intensification of Catalyst Testing in Gas/Liquid/Solid Configuration

Catalyst improvement is a key route toward process improvement in terms of yield, energy efficiency and selectivity optimization. The catalyst development strategy includes catalyst testing on a model or real feedstock. This key step has been the focus of many studies during the last decades concerning reactor design, analytical tool development and operating procedures. Most studies aim to determine catalytic grain activity in isothermal conditions so as to be able to understand and predict the kinetics. With catalyst improvement, in the lab-scale reactors available, the mass transfer rate can become the limiting step compared with the reaction rate, especially for fast exothermic reactions. A new reactor geometry is proposed to intensify the mass transfer and to accelerate the fluid superficial velocities: the single pellet string reactor. To characterize this new geometry, a hydrodynamic study was carried out in a horizontal single pellet string reactor with a 4.0 × 4.0 mm<sup>2<sup/> square section, filled with spherical particles of diameter varying between 2.0 and 4.0 mm. In this hydrodynamic study, visual observations of the flow patterns were performed, as well as pressure drop measurements and residence time distribution analysis in single liquid phase flow and two-phase flows. In every configuration tested, two main regimes were identified: the “isolated bubbles” regime and the “stratified” regime. Peclet number and liquid hold-up were deduced from the residence time distribution analysis. The measured liquid hold-ups are always higher than 0.6, which indicates, in addition to the visual observations and colorimetric tests, that the catalyst is always fully wetted by the liquid film. The axial dispersion measurements showed that the single liquid phase flow cannot be interpreted by a classical axial dispersion model. However, when a gas phase is added, the flow becomes closer to plug flow, with Peclet numbers always higher than 40. It has been shown that the pressure drop is controlled by the liquid/solid friction surface and that the pressure drop is not a limiting parameter in the reactor’s operation (values always lower than 0.1 bar). So, from a hydrodynamic point of view, this new reactor exhibits characteristics suitable for its use in catalytic tests. Finally, this reactor was implemented under reaction conditions to study hydrogenation reactions with a real industrial catalyst. The selective hydrogenation of allene was studied. The string reactor was shown to run isothermal kinetic tests with a very small amount of industrial-sized catalyst particles (less than 2 cc) and to explore kinetics of fast reaction at high space velocities impossible to achieve in standard fixed bed units with appropriate hydrodynamic conditions. For constant residence time, the allene conversion does not vary with pressure and feed flow rate, which confirms that the string reactor allows one to perform catalytic tests with such a fast reaction without external mass transfer resistance.

Copper extraction from ammoniacal medium in a pulsed sieve-plate column with LIX 84-I

This article reports on a study of copper removal from ammoniacal aqueous solution (1.0 kg m −3 Cu, pH 9.5) by liquid–liquid extraction using a pulsed sieve-plate column. The extractant tested was the hydroxyoxime LIX 84-I (2-hydroxy-5-nonylacetophenone oxime) in the aliphatic diluent Shellsol D-70. The results of the pilot plant experiments demonstrated the feasibility of operating the extraction process in this type of column, with efficiencies of copper removal in the range of 90.5–99.5%. Several effects on the column performance were examined, namely the aqueous and organic flow rates and the pulse velocity. The axial dispersion model was applied to simulate the concentration profiles, which reasonably predicted the experimental data. The overall mass transfer coefficient was evaluated from the experimental data and was found to be between 9 × 10 −6 and 1.2 × 10 −5 m s −1. These data were compared with the ones obtained from the resistances in series model, which indicated that the resistance due to chemical reaction was 84–91% of the overall resistance to mass transfer. The extraction using a hollow fiber contactor was also carried out to compare the membrane process performance with the one of conventional process.

Investigation of the effect of impeller rotation rate, powder flow rate, and cohesion on powder flow behavior in a continuous blender using PEPT

In this paper, we examine the movement of particles within a continuous powder mixer using PEPT (Positron Emission Particle Tracking). The benefit of the approach is that the particle movement along the vessel can be measured non-invasively. The effect of impeller rotation rate, powder flow rate, and powder cohesion on the particle trajectory, dispersive axial transport coefficient, and residence time is examined. Increase in the impeller rotation rate decreased the residence time, increased the axial dispersion coefficient, and resulted in longer total path length. Effect of flow rate was different at two different rotation rates. At lower rotation rate, increase in flow rate increased the residence time, decreased the axial dispersion, and resulted in longer total path length. At higher rotation rate, increase in flow rate decreased the residence time, increased the total path length and showed a complex dependence on the axial dispersion coefficient. Increasing cohesion (measured using the flow index, dilation, and the Hausner ratio) did not affect the axial dispersion coefficient significantly, but had significant effects on the total particle path length traveled and the residence time. These results, relevant to pharmaceutical powders, provide better physical understanding of the influence of operating parameters on the flow behavior in the continuous mixer. In addition, one of the main obstacles of modeling continuous mixing of particles is to know the appropriate values for the modeling parameters as well as validate modeling approaches. One example is the dispersion coefficient which leads to an analytical solution for the axial dispersion model of a continuous blending process.

Kinetic modelling and performance prediction of a hybrid anaerobic baffled reactor treating synthetic wastewater at mesophilic temperature

A modelling study on the anaerobic digestion process of a synthetic medium-strength wastewater containing molasses as a carbon source was carried out at different influent conditions. The digestion was conducted in a laboratory-scale hybrid anaerobic baffled reactor with three compartments and a working volume of 54 L, which operated at mesophilic temperature (35 °C). Two different kinetic models (one model was based on completely stirred tank reactors (CSTR) in series and the other an axial diffusion or dispersion model typical of deviations of plug-flow reactors), were assessed and compared to simulate the organic matter removal or fractional conversion. The kinetic constant ( k) obtained by using the CSTR in series model was 0.60 ± 0.07 h −1, while the kinetic parameter achieved with the dispersion model was 0.67 ± 0.06 h −1, the dispersion coefficient ( D) being 46. The flow pattern observed in the reactor studied was intermediate between plug-flow and CSTR in series systems, although the plug-flow system was somewhat predominant. The dispersion model allowed for a better fit of the experimental results of fractional conversions with deviations lower than 8% between the experimental and theoretical values. By contrast, the CSTR in series model predicted the behaviour of the reactor somewhat less accurately showing deviations lower than 10% between the experimental and theoretical values of the fractional conversion.

Simulation of chemical reactors using the least-squares spectral element method

In this work, we address the issue of solving detailed mathematical models of chemical reactors by using a method based on the least-squares formulation. The article presents the resolution of an axial dispersion model, and makes an analysis of relevant issues that are involved when solving this type of models using the least-squares spectral element method. A central issue is that C 1 elements are required if no additional variables are to be defined. We analyze two different alternatives for achieving global first-order differentiability without increasing the number of variables: using C 1 Hermite elements and imposing the constraint weakly using C 0 elements. We include numerical examples for the case of the transformation of natural gas into synthesis gas. The least-squares spectral element method showed no major difficulties in solving the model equations of the model, in spite of the steep variations obtained. We conclude that the optimal choice for achieving global first-order differentiability depends on the problem and the objectives of the calculation. For the model presented here, the Hermite approach gave the fastest results, although it required a high condition number of the problem matrix.

Numerical Studies of Catalyst Wetting and Total Organic Carbon Reaction on Environmentally Based Trickle-Bed Reactors

This work is devoted to the computational fluid dynamics (CFD) simulation of trickle-bed reactors (TBRs) with environmentally based applications on advanced wastewater remediation technologies. Recently, TBRs have assumed a major role in industrial wastewater treatment plants being envisaged as a breakthrough paraphernalia to move forward superseded decontamination processes. According to the literature, the generous research in environmental reaction engineering has indicated that scale-up of TBRs is erroneous if one considers isothermal operation and uses either a pseudohomogeneous or a heterogeneous model with plug flow for gas and liquid phases. Even though an axial dispersion model may account for liquid distribution nonuniformity, the reaction parameters are strongly dependent on the reactor fluid dynamics. In our case-study, first we developed a volume-of-fluid CFD framework which accounts for the surface tension and wall adhesion effects. A three-dimensional computational domain was employed to in...

Cascade Control Scheme for Tubular Reactors with Multiple Temperature Measurements

In this work, we introduce a new structure for cascade control scheme based on a weighted average temperature of three-temperature measurement distributed along the axial position of the tubular reactor. The control configuration exploits the information provided by two additional temperature sensors located close to the feed and the output positions of the tubular reactor. The configuration with the averaged temperature improves the behavior of the classical cascade control scheme by enhancing the disturbance rejection. Numerical simulations of two axial dispersion models of tubular reactors are used to illustrate and compare the control performance.

Assessment of CFD Euler–Euler method for trickle-bed reactor modelling in the catalytic wet oxidation of phenolic wastewaters

Trickle-bed reactors (TBRs) are envisaged as a breakthrough technology in industrial wastewater treatment plants. According to the literature, the generous research in environmental reaction engineering has indicated that scale-up of TBR is erroneous if one considers isothermal operation and uses either a pseudo-homogeneous or a heterogeneous model with plug flow for gas and liquid phases. Even though axial dispersion model may account for liquid distribution non-uniformity, the reaction parameters are strongly dependent on the reactor fluid dynamics. In our case study, we develop an Eulerian CFD (computational fluid dynamics) framework based on empirical interphase coupling parameters in the momentum balance equation. After the hydrodynamic validation, the catalytic wet oxidation of phenolic wastewaters was taken as an example to evaluate axial and radial profiles for the total organic carbon depletion and temperature along the packed bed. The theoretical calculations were compared against experimental data taken from a trickle-bed reactor pilot plant. The Eulerian computations have shown promising results on how fluid dynamics can be correlated with chemical reaction, namely on the prediction of total organic carbon conversions attained at different temperatures.

Solids Flow Models for Gas - Flowing Solids - Fixed Bed Contactors

Three solids flow models for gas – flowing solids – fixed bed contactors are analyzed. They all presume axial dispersion in the dynamic, freely flowing zone, but they differ in the interpretation of the stagnant zone. The models have been examined and the model parameters have been optimized on the basis of two types of tracer experiments. One provides step response curves for flowing solids at the exit and the other presents the response curves of the static flowing solids holdup. The model which assumes axial dispersion and exchange between dynamic and two active static zones, most accurately describes the solids flow pattern. A simpler model which presumes exchange between dynamic and one static zone can be used if there is no need for a precise description of the behavior of stagnant particles. The most simple axial dispersion model is not realistic, as it does not explain stagnancy at all, which was experimentally observed for the gas – flowing solids – fixed bed contactors.

Protein adsorption‐dependent electro‐kinetic pore flow: Modeling of ion‐exchange electrochromatography with an oscillatory transverse electric field

Electro-kinetic acceleration of protein mass transfer was studied by dynamic chromatographic experiments and computer simulations on IEC with an oscillatory transverse electric field (EF) perpendicular to the mobile-phase flow (pIEEC). The breakthrough behavior of BSA was investigated at different electric current densities. A two-dimensional mathematical model has been established to describe the electro-kinetic convection-diffusion behavior of protein adsorption in a single adsorbent particle. The equation was coupled with the axial dispersion model to simulate the dynamic adsorption process in the pIEEC. The model parameters were determined by independent experiments or calculations. It was found that protein adsorption led to an exponential decrease of intraparticle electro-kinetic flow with increasing protein adsorption. Taking this effect into consideration, the model calculations could well describe dynamic breakthrough curves. Moreover, protein distribution in adsorbents was observed to present excursion along the periodical oscillatory EF direction. At the beginning of pIEEC, intraparticle convection caused by the EF contributed more to the enhancement of dynamic binding capacity. Finally, it was confirmed that both the EOF and electrophoresis contributed to the acceleration of mass transfer.

Dynamical modelling of a reactive extrusion process: Focus on residence time distribution in a fully intermeshing co-rotating twin-screw extruder and application to an alginate extraction process

The context of this study is the modelling of reactive extrusion process based on an alginate extraction protocol. Residence Time Distribution (RTD) is one important part to predict the kinetics of reactive compounds. A simple model is proposed to predict RTD in fully intermeshing co-rotating twin-screw extruders without reaction. This model, which can be easily extended to reactive case in a future work, is based on the extension of an axial dispersion model, including control parameters (screw speed and flow rate) and geometrical parameters (screw profile and die design). Simulations were performed for various operating and geometrical conditions so as to illustrate possibilities offered by the proposed model. Validation was conducted for two different extrusion applications, seaweed extrusion and polymer extrusion. This highlighted the model ability to predict RTD for various kinds of materials after adjusting only one parameter thanks to a unique experimental RTD curve.

Axial dispersion/population balance model of heat transfer in gas–solid turbulent fluidized beds

An axial dispersion/population balance model is presented for describing heat transfer processes in gas–solid turbulent fluidized beds. In the model, the gas and particle transport is described by the axial dispersion model, while the particle–particle and particle–wall heat transfers are modeled as collisional random events, characterized by the collision frequencies and random variables with probability density functions determined on interval [0,1]. An infinite hierarchy of moment equations is derived from the population balance equation, which can be closed at any order of moments. The properties of the model and the effects of process parameters are examined by numerical experimentation.

The effect of flow maldistribution on the evaluation of axial dispersion and thermal performance during the single-blow testing of plate heat exchangers

A single-blow transient test technique based on axial dispersion model is proposed for the determination of both heat transfer coefficient and axial dispersion coefficient in plate heat exchangers, characterized by NTU and dispersive Peclet number respectively. The present experimental analysis deals with the effect of flow maldistribution on the transient temperature response for U-type plate heat exchangers. The experiments are carried out with uniform and non-uniform flow distributions for various flow rates and two different numbers of plates. Special effort has been made to differentiate the deviation from plug flow due to flow maldistribution and fluid backmixing. The fluid axial dispersion is used to characterize the backmixing and other deviations from plug flow. Due to unequal distribution of the fluid, the velocity of the fluid varies from channel to channel and hence the heat transfer coefficient variations are also taken into consideration. The computed outlet fluid temperatures are compared with experimental outlet temperatures, and the values of dispersive Peclet numbers are estimated. The results indicate that in order to get parameters independent of the number of plate used in single-blow experiment, it is essential to isolate flow maldistribution from backmixing. This paper has brought out a practical way in which this isolation can be done in the process of data reduction through suitable computational model.

Modeling in Multiphase Reactor Design: Solid Phase Residence Time Distribution in Three-Phase Sparged Reactors

Gas−liquid−noncatalytic solid reactions are typically conducted in three phase sparged reactors. Modeling of the particle size residence time distribution (RTD) and verification/validation of the models is essential for fundamental understanding and design of these multiphase reactors. A brief review and analysis of the RTD models reported in the literature is presented in this paper. Earlier investigations in this field typically employ the axial dispersion model to describe the RTD. It is shown that the tanks-in-series model can equally be applied in such cases. These single-parameter models are simplistic in nature and do not reflect accurately the flow behavior of solids in the three phase sparged reactors. Recent phenomenological approaches to modeling involve using a tanks-in-series model in parallel or countercurrent recycle mode with a plug flow reactor. These models have better accuracy but are also more complex and require specifications of several more parameters. Further developments in the field will be based on these models.

Modelling of displacement washing of packed bed of fibers

The mechanism of displacement washing of packed bed of porous, compressible and cylindrical particles, e.g., fibers, is presented with the help of an axial dispersion model involving Peclet number (Pe) and Biot number (Bi). Bulk fluid concentration, intra-pore solute concentration and concentration of solute adsorbed on the fiber surface are taken to be the function of washing time and position in the bed. Concentration of solute adsorbed on the fiber surface and intra-pore solute concentration are related by a Langmuir adsorption isotherm. Experiments have been performed on pulp beds formed from unbeaten, unbleached kraft fibers. Displacement washing has been simulated using a laboratory washing cell. Model equations are solved by using orthogonal collocation on finite elements (OCFE). Model predicted values are compared with the experimental values and key industrial parameters such as displacement ratio and efficiency are expressed in terms of exit and average solute concentrations.

Adsorption kinetics and performance of packed bed adsorber for phenol removal using activated carbon from dates’ stones

Kinetic studies of phenol adsorption on activated carbon (AC) produced from waste dates’ stone (DS) were performed using four different AC particle sizes (1.47, 0.8, 0.45 and 0.225 mm) and initial concentration of phenol of 200 and 400 ppm. Breakthrough data for phenol removal using a packed bed of AC produced from DS were collected over a wide range of operating conditions: bed height = 5, 10, 15, 20, and 25 cm, initial phenol concentration = 50, 100 and 150 ppm, flow rate = 23.3–141.5 ml/min and particle size = 0.45, 0.8, and 1.50 mm. It was found that adsorption kinetics of phenol can be very well represented by the pseudo-second order equation. The initial rate of adsorption ( h) predicted from the pseudo-second order model, decreased with increasing particle diameter ( d p) as a result of higher interfacial surface area provided by particles with smaller d p. The obtained breakthrough curves were very well fitted using an axial dispersion model (correlation coefficient of 0.997 or better), which enabled the determination of the axial dispersion coefficient and Peclet number ( Pe). Additionally, breakthrough data were analyzed using the Equivalent Length of Unused Bed (LUB) approach. Defining the Fractional Equivalent Length of Unused Bed (FLUB) as LUB divided by the bed height it was found that FLUB can be correlated with Pe with fairly good accuracy using the relation: FLUB = e −0.0713( Pe) for the whole range of experimental parameters explored. It was also shown that the film mass transfer coefficient obtained from the analysis of breakthrough curves for small particle size and short bed at applicable conditions agreed fairly well with that obtained from mass transfer correlation available in literature.