Intraparticle Mass Transfer Resistance Research Articles

A mathematical model of a catalytic membrane reactor for the decomposition of NH 3

Catalytic NH 3 decomposition in the gas feed to the turbine is a potential method for reducing NO x emissions in coal gasification power plants. Since the decomposition reaction is equilibrium limited at gasification conditions, a membrane reactor is necessary to achieve a high conversion of NH 3 to N 2 and H 2. The objective of this study was to use a mathematical model to investigate catalytic NH 3 decomposition in a membrane reactor for both countercurrent and cocurrent flow configurations. The concurrent flow configuration was generally better in membrane reactors with Knudsen diffusion selectivities. The choice between concurrent and countercurrent flow for membranes that are more selective for H 2 depends on operating conditions. To achieve the high NH 3 conversion desired in this study, a membrane with a selectivity for H 2 over N 2 of greater than 50 is needed. The model used in this study accounts for the influence of interphase and intraparticle mass transfer resistance on membrane reactor performance. These mass transfer resistances are a concern in this study because NH 3 is present at dilute concentrations.

A mathematical model of a catalytic membrane reactor for the decomposition of NH 3

Catalytic NH3 decomposition in the gas feed to the turbine is a potential method for reducing NO, emissions in coal gasification power plants. Since the decomposition reaction is equilibrium limited at gasification conditions, a membrane reactor is necessary to achieve a high conversion of NHg to N2 and H2. The objective of this study was to use a mathematical model to investigate catalytic NH3 decomposition in a membrane reactor for both countercurrent and cocurrent flow configurations. The cocurrent flow configuration was generally better in membrane reactors with Knudsen diffusion selectivities. The choice between cocurrent and countercurrent flow for membranes that are more selective for H2 depends on operating conditions. To achieve the high NH3 conversion desired in this study, a membrane with a selectivity for H2 over N2 of greater than 50 is needed. The model used in this study accounts for the influence of interphase and intraparticle mass transfer resistance on membrane reactor performance. These mass transfer resistances are a concern in this study because NH3 is present at dilute concentrations.

Improvements to Raney copper methanol synthesis catalysts through zinc impregnation: IV. Pore structure and the influence on activity

The high activity of a Raney Cu-ZnO-Al 2O 3 methanol synthesis catalyst, produced by leaching Cu-Al-Zn (43.2-39-17.8 wt.-%) alloy pellets in a sodium zincate rich sodium hydroxide solution, has been compared with an industrial coprecipitated Cu-ZnO-Al 2O 3 catalyst. The carbon monoxide and carbon dioxide conversions for gas hourly space velocities between 11 000 h −1 and 80 000 h −1 were considerably higher for the pelleted Raney catalyst than for the coprecipitated catalyst pellets. This has been attributed to a large difference in the intra-particle mass transfer resistances of the two types of catalyst. The unique pore structure of the Raney catalyst which exhibits a well developed bimodal macro and meso pore size distribution results in low mass transfer resistances in the Raney catalyst pellets. By comparison, the coprecipitated catalyst pellets have only a small volume fraction of macro pores.

Intraparticle Diffusion/Convection Models for Pressurization and Blowdown of Adsorption Beds with Langmuir Isotherm

Abstract Intraparticle diffusion/convection and equilibrium models are used to simulate the bed dynamics of pressurization and blowdown steps of PSA processes with binary mixtures of inert and adsorbable species. The effect of the nature of the equilibrium isotherm, i.e., linear and Langmuir isotherms, is discussed. The improvement of mass transfer inside the adsorbent by increasing particle permeability or decreasing particle size is addressed. Simulation results show that using “large-pore” adsorbents, i.e., increasing permeability to cause a high intraparticle convective flow instead of decreasing particle size to reduce intraparticle mass transfer resistances, is a good choice in PSA processes.

Steady State Performance of Activated Carbon Contactors

A mathematical model for the steady state adsorption of pollutants from completely mixed activated carbon contactors is derived in this paper. In order to accurately describe these processes, a sludge age distribution is incorporated for the adsorbent. The resulting mathematical model is solvable analytically using the homogeneous surface diffusion model (HSDM) as a descriptor of intraparticle mass transfer resistance. Various examples are included in this paper to illustrate the use of this new derivation. Effects of particle size, particle size distribution of commercial carbon, surface diffusion coefficients, and solids mass flow rate, on the performance of the completely mixed adsorption system are studied in detail. Examples of multicomponent, competitive adsorption as well as an equivalent single component representation of a target component are discussed.

Regeneration strategies for coked fixed bed reactors

A two-zone grain-pellet model has been used to simulate catalyst regeneration in fixed bed reactors. Changes in coke composition during reaction and non-uniform coke distributions in the reactor have been accounted for, as well as inter- and intraparticle heat and mass transfer resistances. The model calculates the temperature rise at each axial position in the reactor during regeneration. Coke conversion profiles in the bed and temperature profiles within the catalyst particle are also calculated for different operating conditions. The results are examined in view of the regeneration rate achieved and of the extension of the high-temperature zone generated in the reactor.

Computer Simulation of Industrial Low Temperature Shift Reactor for the Purification of Syngas

A heterogneous one dimensional model for the low temperature shift converter is developed taking into consideration interphase as well as intraparticle mass and heat transfer resistances for the catalyst pellet. The model performance is checked against five industrial reactors in two different plants in Saudi Arabia. The agreement between the model results and the industrial results is very good. The model is used in an application program with the necessary data base for the the physico-chemical parameters. The program is equipped with user friendly input screens with the output obtained as tables and graphs. The package is also equipped with the facility to compute the optimal temperature porofile for constrained and unconstrained optimization. The package can be used for simulation, design and optimization as well as training.

Mathematical modelling and computer simulation of industrial water–gas shift converters

A heterogeneous one-dimensional model for the high-temperature shift converter (HTS) is developed taking into consideration interphase as well as intraparticle mass and heat transfer resistances for the catalyst pellet. The model performance is checked against four industrial reactors, one in Egypt and three in Saudi Arabia. The model is used in an application program with the necessary data base for the physico-chemical parameters. The program is equipped with user friendly input screens with the output obtained as tables and graphs. The package is also equipped with the facility to compute the optimal temperature profile for constrained and unconstrained optimization. The package can be used for simulation, design and optimization, as well as training.

Optimal feed temperature control for fixed bed catalytic reactors experiencing catalyst deactivation—A heterogeneous model

The effect of both interphase and intraparticle mass and heat transfer resistances on the optimal feed temperature policy for fixed bed catalytic reactors experiencing catalyst deactivation is investigated. The complex differential equations of the catalyst pellet are simplified using the orthogonal collocation technique, and the optimal policy is obtained using the Pontryagin maximum principle. The effect of some operating and physicochemical parameters is investigated and the results of the heterogeneous model are compared with those of the pseudo-homogeneous one.

Dynamic modelling of mass transfer phenomena with chemical reaction in immobilized-enzyme bioreactors

This paper presents a dynamic model for a fixed or liquid fluid bed immobilized-enzyme bioreactor, together with a novel method for the solution of the coupled partial differential equations in the real-time domain. Both the tanks-in-series and the dispersion models are used to describe the non-ideal axial mixing in the reactor. The solution, in its final form, comes in both cases as a system of simultaneous ordinary differential equations that can be readily solved using commercially available software packages. Based on this solution, a complete parametric analysis was performed. The analysis revealed the importance of intraparticle and external mass transfer resistances, intraparticle chemical reaction and axial dispersion on the transient behaviour of the reactor. Most important, the analysis revealed ways for parameter estimation and system identification via simple dynamic experiments. The design and optimization implications are demonstrated by using the derived solution to simulate the performance of an immobilized-urease fluidized-bed bioreactor with a recycle loop. Such a configuration is characterized by a time-varying feed concentration and can be used, as part of an extracorporeal artificial kidney device, for the treatment of uremic patients.

Intraparticle mass-transfer resistance and apparent time stability of immobilized yeast alcohol dehydrogenase

The stability and, consequently, the lifetime of immobilized enzymes (IME) are important factors in practical applications of IME, especially so far as design and operation of the enzyme reactors are concerned. In this paper a model is presented which describes the effect of intraparticle diffusion on time stability behaviour of IME, and which has been verified experimentally by the two-substrate enzymic reaction. As a model reaction the ethanol oxidation catalysed by immobilized yeast alcohol dehydrogenase was chosen. The reaction was performed in the batch-recycle reactor at 303 K and pH-value 8.9, under the conditions of high ethanol concentration and low coenzyme (NAD+) concentration, so that NAD+ was the limiting substrate. The values of the apparent and intrinsic deactivation constant as well as the apparent relative lifetime of the enzyme were calculated.

Parametric sensitivity in fixed‐bed catalytic reactors: The role of interparticle transfer resistances

AbstractThe parameteric sensitivity behavior of a plug‐flow catalytic fixed‐bed reactor with negligible intraparticle mass and heat transfer resistances is examined for any positive‐order irreversible reaction. By combining information about multiplicity and runaway, a complete picture of the steady state reactor behavior is obtained. Calculations of the parametrically sensitive region for various values of the involved dimensionless parameters are reported.

A general criterion to test the relative importance of intraparticle and external heat and mass transfer resistances in porous catalysts

AbstractA general criterion is developed for testing the relative importance of intraparticle and external, concentration and temperature gradients on the observed rates, for reactions catalyzed by porous solids. The criterion is applicable to any multiple reaction system and to reactions conforming to any rate law. The applicability of such criteria is extended to reaction systems with highly nonlinear temperature and concentration dependence, by taking into‐account the higher order terms in the Taylor expansion of the rate expressions in the derivation.

Effect of intraparticle mass transfer resistance on reactivity of immobilized yeast cells.

Effect of diffusion resistance on reaction by using an immobilized yeast entrapped by Ca-alginate gel was studied. Intraparticle effective diffusivity of substrate, De, depends upon cell density, cc, i.e. De/Do = k2(1 - k1cc)2. Here, D0 is a reference diffusivity, e.g. diffusivity in water; k1 and k2 are constants. Overall reaction rates of ethanol production by immobilized resting-yeast were measured. Experimental rates coincide well with calculated results using the effective diffusivity and reaction rate of free cells. Diffusion seemed to be restricted by cells. Thus large cell density does hot necessarily mean high reactivity. Finally, the curvature of the Lineweaver-Burk plot is pointed out.

Liquid-phase oxidation of ethylene glycol on a Pt/C catalyst. II. Kinetic studies.

Catalytic oxidation of ethylene glycol in an alkaline aqueous solution over a Pt/C catalyst by oxygen was studied in a slurry reactor at 40°C and ambient pressure. Under our experimental conditions, the interphase and intraparticle mass transfer resistances were found to be insignificant. The catalyst deactivation observed during the course of experiments can be ascribed to the formation of some oxidized species of platinum and/or to the adsorption of some by-products on the catalyst surface, and the decay of catalyst activity is consistent with a first order consecutive process, as described in the previous paper. The rate of reaction can be expressed by a power-law model under the conditions used. The orders of reaction with respect to ethylene glycol, sodium hydroxide and oxygen were estimated to be 0.20, 0.34 and zero, respectively. The mechanism of this reaction is discussed.

Rate of liquid-phase adsorption on activated carbon in the stirred tank.

A method is developed to determine the dependence of surface diffusion coefficient on the amount adsorbed, derived for Freundlich adsorption isotherm, from adsorption rates in a finite bath. The adsorption rates on activated carbon of p-nitrophenol, benzoic acid and p-chIorophenol from dilute aqueous solutions are measured, where Freundlich adsorption isotherms are applicable, and the relations between surface diffusion coefficient and the amount adsorbed are determined for three adsorbates by this method. It is proved that the external mass transfer resistance in the stirred tank has a large influence on adsorption rate as well as intraparticle mass transfer resistance in finite bath adsorption. It is also clear from these relations that the ratio of activation energy for surface diffusion to adsorption energy is nearly equal to 0.5. The time-concentration curves predicted by this method coincide well with experimental data.

Predictive Model for Design of Fixed-Bed Adsorbers: Single-Component Model Verification

A predictive mathematical model for fixed-bed adsorber design that incorporates both liquid and solid phase resistances to mass transfer is verified for four different single-component systems under normal operating conditions. The adsorbates chosen for model verification were selected on the basis of representing a broad range of diffusive and adsorptive properties. Mass transfer limitations for the adsorbates vary from primarily intraparticle mass transfer resistance to primarily liquid-phase mass transfer resistance, and adsorption capacities vary over an order of magnitude. The general agreement between model predictions and fixed-bed performance under a wide variety of conditions confirms the model validity for predicting single-component adsorber behavior. Related papers by the writers describe model development, parameter estimation, and multicomponent model verifications.

Design analysis for an ultrafilter adsorber artificial kidney

An adsorber-ultrafilter system can serve as an alternative to the conventional artificial-kidney dialysis system. To this end, the characteristics of the parametric design analysis of the absorber-ultrafilter artificial kidney and its interaction with a uraemic patient is provided. The activated-carbon adsorber is modelled as a 2-phase homogeneous system, accounting for fluid-particle and intraparticle mass-transfer resistances and the axial dispersion of solute in the interstitial fluid phase of the adsorber bed. It is assumed that the ultrafilter is highly permeable to uraemic substances, and that the ultrafiltration rate is 15–25% of the inlet blood flow rate. The detailed design analysis of the ultrafilter has been provided in an earlier paper. The uraemic patient is modelled, for solute transfer, as comprising three major compartments. The results indicate that a single activated-carbon adsorber unit, with a hold-up volume of 50 ml, is adequate for the removal of uric acid and creatinine in a 6 to 8 h treatment period. However, the poor adsorption capacity of activated carbon for urea, necessitates that the adsorber unit be switched to a freshly activated unit in a very short period of time (11 min in this example). Hence, the need for the development of a better adsorbent for urea is emphasised. A parametric design analysis of the adsorber is also presented, so as to provide the basis for arriving at an optimum size of the adsorber unit.

Analysis of haemoperfusion through fixed-bed adsorber

An attempt is made to analyse the haemoperfusion system. The patient's body is modelled as a 3-compartment system and the adsorber unit (perfusion system) is modelled as a 2-phase system with axial dispersion accounting for both the inter-particle and the intra-particle mass-transfer resistances. Results indicate that although the clearance of solute increases with an increasing blood-flow rate through the adsorber unit, the increase in clearance is not significant. The particle size (intra-particle mass-transfer resistance) and the volume of the adsorbent have a significant effect on the clearance of the solute.

Numerical solution of multicolumn adsorption processes under periodic countercurrent operation

Numerical solutions of the dimensionless equations describing multicolumn adsorption processes are presented. The columns are operated in series and move periodically countercurrent to a continuous fluid flow. Results are given for intraparticle mass transfer resistance separately and in combination with film resistance assuming a linear adsorption isotherm. Comparisons are made with columns in periodic operation and in continuous countercurrent operation. The utilization of the particles in a multicolumn arrangement, or equivalently in a pulsed bed system, compared to that in a column in continuous countercurrent operation is commonly about 80% for two columns in series and more than 90% for four columns in series, when the total column lengths and the fluid flowrates are the same.