Porous Catalyst Particles Research Articles

Pore Network Modeling of Intraparticle Transport Phenomena Accompanied by Chemical Reactions.

In this work, a 3D pore network model (PNM) is introduced for modeling reaction-diffusion phenomena, with and without coupled heat transfer, in a spherical porous catalyst particle. The particle geometry is generated by packing thousands of microspheres inside a large sphere to represent the 3D geometry, porosity, and tortuosity of a spherical catalyst particle. A pore-network representation is extracted from this geometry, and a PNM for diffusion-reaction and heat conduction is constructed. This newly proposed particle-scale PNM allows for the application of realistic 3D nonuniform boundary conditions on the particle's surface, which is commonly encountered in slender packed-bed reactors. Concentration profiles inside the particle, and effectiveness of the reactions, is analyzed.

Synthesis of Porous Structured Three-way Catalyst Particles and Their Catalytic Performance Evaluation

Synthesis of Porous Structured Three-way Catalyst Particles and Their Catalytic Performance Evaluation

Controllable Synthesis of Porous and Hollow Nanostructured Catalyst Particles and Their Soot Oxidation.

The introduction of macroporous structures into three-way catalysts (TWCs) through polymer template-assisted spray drying has attracted attention because of its enhanced gas diffusion and catalytic performance. However, the surface charge effect of polymeric template components has not been investigated to control the structure of the TWC particles during synthesis. Thus, this study investigated the effect of template surface charges on the self-assembly behavior of TWC nanoparticles (NPs) during drying. The self-assembly of TWC NPs and polymer particles with different charges produced a hollow structure, whereas using the same charges generated a porous one. Consequently, the mechanism of particle self-assembly during drying and final structure particle formation is proposed in this study. Here, porous TWC particles demonstrated a faster oxidation of soot particles than that of hollow-structured particles. This occurred as a result of the larger contact area between the catalyst surface and the solid reactant. Our findings propose a fundamental self-assembly mechanism for the formation of different TWC structures, thereby enhancing soot oxidation performance using macroporous structures.

Scale-up of dry impregnation processes for porous spherical catalyst particles in a rotating drum: experiments and simulations

Catalyst impregnation is the first step and one of the most crucial steps for preparing industrial catalysts. The process is typically performed in rotating vessels with a spray-nozzle to distribute the liquid onto porous catalyst supports until the pore volume is reached. The inter-particle variability of the impregnated liquid inside the particles significantly affects the activity and selectivity of the resulting catalyst. Current scale-up practices lead to poor fluid distribution and inhomogeneity in the liquid content. The aim of this work is to understand the dynamic behavior of the particles under the spray nozzle, which is essential for desired content uniformity, and to develop a scale-up model for the dry impregnation process. In this work, we considered four dimensionless numbers in the scaling analysis. The scale-up rules require that the dimensionless numbers are kept constant for different scales. Both DEM simulations and matching experiments of dry impregnation inside the porous particles were performed for different vessel sizes. The water content of the particles was compared for different times and locations, and the relative standard deviation is calculated from the axial water content. Simulation and experimental results show that particles achieve similar content uniformity at the end of impregnation, confirming that the scale-up rules are applicable to all vessel sizes. The dimensionless numbers give very good scale-up performance since curves collapse indicating similarity in the processes. In addition, the scale-up method is validated for different particle sizes in simulations.Graphical abstract

EFFECT OF MICROSTRUCTURES ON MASS TRANSFER INSIDE A HIERARCHICALLY STRUCTURED POROUS CATALYST

In this paper, the pore network model to investigate the reaction-diffusion process in the hierarchically structured porous catalyst particle is extended to consider the phenomenon of deactivation by coking. In this framework, the interaction of internal particle pore structure and mass transfer under the condition of coke deposition is examined. Then, the effect of structural features, namely macroporosity and pore size ratio, the deactivation properties, the maximum loading of coke, as well as the transport properties, the pore Damköhler number on the net reaction rate, and deactivation of the particle have been investigated. Three deactivation mechanisms are accounted for, namely, the site coverage, the pore narrowing, and the pore blockage. It is found that the deactivation of the catalyst particle can be divided into two conditions: the kinetic deactivation and the structural deactivation. It is shown that depending on the Damköhler number, increasing the macroporosity does not necessarily improve the reactivity and deactivation resistance of the catalyst. The key finding of this work is to demonstrate and quantify how changing the typical fresh catalyst microstructure into a hierarchical one influences the reactivity and deactivation.

Intra-particle diffusion limitation for steam methane reforming over a Ni-based catalyst

This work aims to evaluate the diffusion limitation for the steam methane reforming process over spherical catalyst particles (Ni/α-Al2O). Numerical calculations based on a CFD model were conducted to determine the intrinsic and actual reaction rates. The CFD model was validated using experimental results, and good agreement was achieved. The effectiveness factor for the reaction rates was used to express the effect of diffusion limitation within the porous catalyst particle. The effectiveness factor was determined for a wide range of operational parameters, including a temperature range of 800–1300 K and a steam-to-methane ratio of 1–5. The analysis was performed for spherical catalyst particles with diameters up to 3.42 mm, and the effectiveness factor as a function of catalyst particle diameter, temperature, and steam-to-methane ratio was established. The results show that the effectiveness factor is inversely proportional to the diameter of the catalyst particle and that an increase in reaction temperature and steam-to-methane ratio leads to an increase in diffusion limitation. The limitations of the analysis are discussed and justified. The final expression for the effectiveness factor can be used in a pseudo-homogeneous steam methane reformer model where the effectiveness factor varies depending on the position in the packed bed.

Synthesis of Porous Catalyst Particles and Three-dimensional Reconstruction Analysis

In this study, porous structured three-way catalyst particles were synthesized through a spray pyrolysis followed by heating processes using template particles. When nitrogen was used as the carrier gas, porous catalyst particles were synthesized while maintaining the pore structure of the particles. In addition, the internal structure of the synthesized porous catalyst particles was analyzed by using TEM Tomography, and the interconnected pore structures were confirmed inside the particles. Furthermore, the CO2 adsorption rate results show that the introduction of porous structure contributes to the improvement of mass transfer coefficient.

The influence of dissociative adsorption on effectiveness factors of porous catalysts

AbstractThe actual concentration profile of a reacting fluid inside a porous catalyst is something of a mystery. However, there are powerful models to predict the concentration distribution, and effectiveness factor as a function of the Thiele modulus. This work provides a model for the porous catalyst particle considering heterogeneous kinetics for steady‐state Langmuir‐Hinshelwood rate expressions, including the cases when adsorption stoichiometry is other than 1:1, as for dissociative adsorption (1:2), which have not been covered by the preceding literature. The isothermal and the non‐isothermal particles are considered. Numerical solutions for the concentration profile of a limiting reactant were calculated by three methods: finite differences with Newton‐Raphson recursion, Chebyshev orthogonal collocation, and integration by Adams method as done by Weisz and Hicks. The Weisz‐Hicks method outperformed the other two. Plots show the results for specific cases, which are briefly discussed. Adsorption stoichiometry and pellet geometry are of paramount importance for the assessment of effectiveness factors. The results demonstrate that the effectiveness of a catalyst pellet with prevalent dissociative adsorption of a reactant is always inferior to the effectiveness with prevalent simple adsorption.

Fast estimation of reaction rates in spherical and non-spherical porous catalysts

We present a methodology for modeling multi-step reaction rates in porous catalyst particles for use in CFD–DEM and two fluid models. Single-step effectiveness factors based on a Thiele modulus, while useful, cannot accurately capture the cascading reaction systems common in high temperature vapor-phase chemical reactors like fluidized catalytic cracking units and catalytic biomass fast pyrolysis systems. Instead, multi-step effectiveness vectors derived from steady-state solutions to the governing reaction–diffusion equations are needed. Solutions for various catalyst shapes are presented, including spheres, cylinders, and prisms. Computational challenges inherent in repeated evaluation of reaction rates with diffusion limitations are discussed, and an efficient implementation based on pre-computed lookup tables is proposed and demonstrated on a simulation of a fluidized bed reactor. Open-source code is provided for the compilation of reaction rate tables for use in ODE, DEM, and two-fluid models.

Theoretical Analysis of Mass Transfer Behavior in Fixed-Bed Electrochemical Reactors: Akbari-Ganji’s Method

The theoretical model for a packed porous catalytic particle of the slab, cylindrical, and spherical geometries shape in fixed-bed electrochemical reactors is discussed. These particles have internal mass concentration and temperature gradients in endothermic or exothermic reactions. The model is based on a nonlinear reaction–diffusion equation containing a nonlinear term with an exponential relationship between intrinsic reaction rate and temperature. The porous catalyst particle’s concentration is obtained by solving the nonlinear equation using Akbari-Ganji’s method. A simple and closed-form analytical expression of the effectiveness factor for slab, cylindrical, and spherical geometries was also reported for all values of Thiele modulus, activation energy, and heat reaction. The accordance with results of a reliable numerical method shows the good accuracy that their approximate solution yields.

Impact of the Non-Uniform Catalyst Particle Size on Product Selectivities in Consecutive Reactions

The analysis of consecutive reactions A→B→C in porous catalyst particles, where the simultaneous processes of diffusion and chemical reactions take place and both reactant and products are subjected to diffusion limitations, was performed for catalyst particles with non-uniform sizes, a fact that has not been considered so far. The system comprises first-order consecutive irreversible reactions that proceed on spherical catalyst particles with a log-normal volume particle size distribution (PSD), which is typical in many catalytic applications. Regardless of the prevailing diffusion regime (chemical control, transition situation or intraparticle diffusion control), the yield of the intermediate product (B) reaches a maximum value as a function of the conversion of reactant (A), then decreases as a consequence of the prevalence of the secondary reaction that converts it into the secondary product (C). If intraparticle diffusion resistances affect the reactant species, given the relationship between the kinetic constants and the mean particle size, the selectivity to the intermediate product is negatively affected by the dispersion in PSD. The larger the dispersion in PSD, the stronger the negative impact.

Verification of a 0D model for the heat and mass transfer inside a moving spherical catalyst for steam methane reforming

This work is devoted to the verification of a new 0D model for the steam reforming of methane inside a spherical catalyst particle (Ni/α-Al2O3) moving in a hot methane/steam atmosphere. The submodel includes six gaseous chemical species (CH4, CO2 , CO, H2O, H2, N2) and uses experimentally defined reaction rate expressions taken from the literature. The distinguishing feature of the subgrid model is its ability to take into account the internal heat and mass transfer coupled with the heat and mass transfer on the catalyst surface influenced by convection and diffusion around the particle. The sub-model was verified against a comprehensive 1D-based model resolving diffusion and conduction processes inside the porous catalyst particle using 1D differential equations for the temperature and chemical species written in spherical coordinates. Comparisons between the 0D model and 1D model have been made for the particle diameters, d, 2 mm, 1 cm and 2.54 cm. The ambient temperature was varied between 650 K and 1000 K, respectively. Good agreement (less than 1%–2%) was achieved between predictions obtained using the new 0D model and results calculated using the 1D-based model for all particle diameter ranges for the ambient gas temperatures below 900 K. The increase in the ambient temperature and in the particle diameter leads to the deviations of up to 5%–10% between both models.

The periodic transient kinetics method for investigation of kinetic process dynamics under realistic conditions: Methanation as an example

Due to rising interest for the integration of chemical energy storage into the electrical power grid, the unsteady-state operation of chemical reactors is gaining more and more attention with emphasis on heterogeneously catalyzed reactions. The transient response of those reactions is influenced by effects on different length scales, ranging from the active surface via the individual porous catalyst particle up to the full-scale reactor. The challenge, however, is to characterize unsteady-state effects under realistic operation conditions and to assign them to distinct transport processes. Therefore, the periodic transient kinetics (PTK) method is introduced, which allows for the separation of kinetic process dynamics at different length scales experimentally under realistic operation conditions. The methodology also provides the capability for statistical analysis of the experimental results and therefore improved reliability of the derived conclusions. Therefore, the PTK method provides the experimental basis for model-based derivation of reaction kinetics valid under dynamic conditions. The applicability of the methodology is demonstrated for the methanation reaction chosen as an example process for heterogeneously catalyzed reactions relevant for chemical energy storage purposes.

Kinetic study and modeling of sulphuric acid decomposition using Cr–Fe2O3 catalyst for sulphur based water splitting processes

Sulphuric acid decomposition is the high temperature (850–900 °C) reaction step of sulphur based water splitting processes (Iodine–Sulphur and Hybrid-Sulphur processes) for hydrogen production. In this work, reaction kinetics and mass transfer data are generated experimentally, for sulphuric acid decomposition using chromium doped iron oxide, Cr–Fe2O3, catalyst in a packed bed reactor (PBR). Experiments are performed using catalyst powder, less porous catalyst particle (pellet) and high porous catalyst particle (foam), between 700 and 850 °C and 0.1–10 ml min−1 liquid feed flow rate. Activation energy and frequency factor of Cr–Fe2O3 catalyst obtained from the powder catalyst study are 74 kJ mol−1 and 183 m3 kg−1 s−1. Internal effectiveness factor (η) of pellet and foam, two industry types of Cr–Fe2O3 catalyst (5 mm size) are calculated from the experimental studies performed at external mass transfer resistance free regime. Internal effectiveness factor of pellet and foam obtained are 0.12 and 0.26 respectively, which shows strong pore diffusion resistance in these catalyst types. Overall effectiveness factor (Ω) for both the catalyst types (pellet and foam) are also obtained for the investigated range of temperatures and flow rates. Further, catalyst particle (pellet and foam) is modeled in COMSOL MULTIPHYSICS® simulation software to get an insight into concentration and temperature profiles. Significant concentration drop and smaller temperature drop are seen in less porous pellet. Small concentration drop and significant temperature drop are observed in porous foam, through simulation studies. Focus of future R&D is to optimise the size and porosity of Cr–Fe2O3 catalyst, for maximum effectiveness factor and thereby maximizing the reaction rate and conversion.

Unsteady state diffusion-adsorption-reaction. Selectivity of consecutive reactions on porous catalyst particles

Abstract The simultaneous processes of diffusion, adsorption and chemical reaction, considering the transient nature of the concentration profiles in the porous catalyst particles as applied to the analysis of consecutive reactions A → B → C, where reactant and products are subjected to diffusion limitations, are analyzed. The concentrations of the desired intermediate product B, both the average in the catalytic particles and the observed in the fluid phase, initially increase as a function of time until reaching a maximum value and then decline due to the consumption in the secondary reaction. Due to the diffusion restrictions and the adsorption effect, the observed selectivities, calculated from the concentrations in the fluid phase, are always lower than the true selectivities, which also include the amounts accumulated in the particles. Besides depending on the rates of the primary and secondary reactions, the observed yield of product B also depends on the system adsorption capacity, i.e., the relationship between the capacities of the particles and the external fluid phase to accumulate the reactant species. For a given relationship between the intrinsic rates of the primary and secondary reactions, the higher the system adsorption capacity, the lower the observed yield of B as a function of conversion. The relationship between the observed yield of B and the observed conversion of A, calculated considering the transient state of the concentration profiles in the particles, is coincident with that predicted by classical models, which assume the steady state in the particles, when the system adsorption capacity is extremely small.

A new semiempirical model for the heat and mass transfer inside a spherical catalyst in a stream of hot CH4/H2O gases

This work is devoted to the development and validation of a new 0-D model (sub-model) for the steam reforming of methane inside a spherical catalyst particle (Ni/α-Al2O3) placed in a hot methane/steam atmosphere. The particle diameter is 4 mm. The submodel includes six gaseous chemical species (CH4, CO2, CO, H2O, H2, N2) and uses experimentally defined reaction rate expressions taken from the literature. The distinguishing feature of the subgrid model is its ability to take into account the internal heat and mass transfer coupled with the heat and mass transfer on the catalyst surface influenced by convection and diffusion around the particle. The sub-model was validated against a comprehensive 3D-CFD-based model resolving the issues of bulk flow, thermal and species boundary layers around the particle and convection and diffusion processes inside the porous catalyst particle. Good agreement was achieved between the new 0-D model and the 3D CFD-based model.

Numerical simulations and modelling of mass transfer through random assemblies of catalyst particles: From dilute to dense reactive particulate regime

We study mass transfer through random assemblies of fixed spherical catalyst particles experiencing an external convective-diffusive fluid stream. Chemical species are transported through the array and are diffused from fluid to solid phase through particles surface. An internal first order irreversible chemical reaction takes place within the porous catalyst particles. We address the determination of mass transfer coefficient by performing direct numerical simulations with fully internal-external coupling using concentration and flux continuity boundary conditions at the solid-fluid interface. We derive a theoretical prediction of the profiles of cup-mixing concentration, average of mean surface and average of mean volume concentration of the particles along the height of the domain. The model for the dimensionless mass transfer coefficient (‘reactive’ Sherwood number) is accounting for the five dimensionless parameters that control the physics of the system: the Reynolds number Re, the Schmidt number Sc, the Damköhler number Da, the internal-to-external diffusion coefficient ratio γ and the solid volume fraction αs. We use a coupled Sharp Interface/ Discrete Lagrange Multiplier-Fictitious Domain Method (SIM-DLM/FD), thoroughly validated in our previous study (Sulaiman et al., 2019) to test the accuracy of the model over a wide range of dimensionless parameters and solid volume faction (from dilute αs=0.1 to dense regime αs=0.5). We show and discuss the limitations of the proposed model.

Catalyst Particle Porosity Effect upon Flameless Combustion Characteristics

The problem of heat and mass transfer of a porous catalyst particle is considered. On the her surface, including the inner surface of the pores, an irreversibly heterogeneous first-order reaction proceeds. It has been analytically shown that in a heated gas mixture, the catalyst's porosity reduces the minimum impurity's concentration of catalytic spontaneous combustion in the mixture and increases the catalyst particle's corresponding diameter. This concentration corresponds to the external kinetic and internal diffusion reaction's modes.

Secondary Effectiveness Factors and Solubility Effects for Catalytic Reactions in Series

Thiele moduli and effectiveness factors are powerful ways to account for mass transfer limitations on reactions occurring within porous catalyst particles. Effectiveness factors have been developed...

Investigation of microstructure effects on performance of hierarchically structured porous catalyst using a novel pore network model

The reaction-diffusion process in the hierarchically structured porous catalyst particle is investigated using the pore network model. A self-developed scheme is presented to generate the hierarchical pore network with a fairly low computational cost. The results were presented in the framework of a parametric sweep o f the macroporosity, the nanoporosity, the pore interconnections, and the pore size ratio, as well as the pore Damköhler number to understand the effect of different structures on the particle performance. Results showed that the benefits of the hierarchically creates from the existence of macropores inside the nanoporous network as well as their interconnections. Effect of different pore system interconnections investigated using 3D model. It was also shown that the non-physical connectivity in the 2D case is unable to describe the 3D geometries quantitatively, but may present some qualitative trends.