Catalyst Effectiveness Factor Research Articles

Modeling catalyst effectiveness factor with space-fractional derivative using Haar wavelet collocation method

Abstract Mass transfer limitations may considerably affect the rate of a heterogeneous catalytic process. The catalyst effectiveness factor is a quantitative measure of the impact of the diffusion process inside a catalyst particle. The effectiveness factor is derived from the solution of the steady-state reaction-diffusion problem. Herein, we simulate the steady-state reaction-diffusion equation with space-fractional derivative and linear reaction kinetics. The solution to the problem is obtained numerically using the Haar wavelet collocation method. The effect of the anomalous diffusion exponent on the catalyst effectiveness factor and process parameters, e.g. reactor volume and catalyst mass, is demonstrated. We anticipate that the process efficiency will be notably improved by changing the diffusion regime from standard to superdiffusive.

Assessment of transport phenomena in catalyst effectiveness for chemical polyolefin recycling

Since the dawn of agitated brewing in the Paleolithic era, effective mixing has enabled efficient reactions. Emerging catalytic chemical polyolefin recycling processes present unique challenges, considering that the polymer melt has a viscosity three orders of magnitude higher than that of honey. The lack of protocols to achieve effective mixing may have resulted in suboptimal catalyst effectiveness. In this study, we have tackled the hydrogenolysis of commercial-grade high-density polyethylene and polypropylene to show how different stirring strategies can create differences of up to 85% and 40% in catalyst effectiveness and selectivity, respectively. The reaction develops near the H2–melt interface, with the extension of the interface and access to catalyst particles the main performance drivers. Leveraging computational fluid dynamics simulations, we have identified a power number of 15,000–40,000 to maximize the catalyst effectiveness factor and optimize stirring parameters. This temperature- and pressure-independent model holds across a viscosity range of 1–1,000 Pa s. Temperature gradients may quickly become relevant for reactor scale-up.

Catalytic decomposition of sulphuric acid in Iodine-Sulphur and Hybrid-Sulphur processes for Hydrogen production: Estimation of effectiveness factor of catalyst

High endothermic heat of SO3 decomposition reaction (ΔHR∼+98 kJ mol−1) can lead to significant thermal gradients (lower temperatures) inside the catalyst particle, depending up on mass diffusion, heat conduction and intrinsic reaction kinetics in the particle. The lower catalyst effectiveness (due to thermal gradients) leads to lower decomposition conversions in Packed Bed Reactors (PBR), which has to be maximized. In this study, a multi-scale model (Double Porosity Model, DPM) is used for the estimation of non-isothermal effectiveness factor (η) of Cr-Fe2O3 catalyst types; less porous pellet and porous foam types. η obtained using DPM (foam∼0.249 and pellet∼0.147) are found to be in good agreement with experimental data and also with the results of derived model (Weisz model). Further, effect of porosity and size/diameter on η are studied and obtained the optimum porosity required for maximum η. The present study is useful for estimation and optimization of non-isothermal η of catalysts.

Development of Simplified One-dimensional Model for Microchannel Steam/Methane Reformers based on Catalyst Effectiveness Factor Correlations

Development of Simplified One-dimensional Model for Microchannel Steam/Methane Reformers based on Catalyst Effectiveness Factor Correlations

Process Simulation and Performance Models for Enhanced Modular Refinery Operations in Nigeria

The study aimed at availability of petroleum products in Nigeria through the operation of enhanced modular refinery process due to inefficient conventional major refineries. The enhanced modular refinery converts or processes residue product from conventional modular refinery as feedstock to the hydrocracker reactor for viable and desired products such as liquefied petroleum gas, naphtha and diesel. Therefore, twenty Nigerian crude oil types were classified as sweet, light and medium crude oil, and these crude oil types were categorized based on their recovery volume at true boiling point of 370oC as Group A, Group B and Group C respectively. Thus, based on product output and equipment cost, a modular refinery with 29 trays was used in this study, as light and medium sweet crude oil types were simulated in a modular refinery of various column trays prior to the desired tray. A topping plant with a 30,000 barrel per day capacity and a modified topping plant with 29 trays respectively were used to process different types of Nigerian crude oil. using Aspen Hysys to evaluate their products yield and tray compositions. The modified modular refinery with hydrocracker yielded more valuable from the residue of conventional modular refinery with minimal bottom fraction. Performance models for hydrocracker reactor was developed based on the nature of reaction, kinetic parameters estimated and results compared with experimental data with minimum deviations. The developed performance models predicted feedstock conversion and product yield along the hydrocracker reactor’s dimensionless length by solving a set of ordinary differential equation models. Thus, the hydrocracking process was simulated to evaluate the effects of catalyst effectiveness factor on feedstock conversion and products yield.

Optimization of the Striping Section of Modular Refinery Operations in Nigeria

Nigerian crude oil type Okoro 2012 was applied in this study owing to its low API value 23.54 and high residual percentage value of 42.16% from conventional modular refinery operations in Nigeria. The residue acted as a precursor or feedstock to the hydrocracker reactor of the modified modular refinery operation, which is an hydrogenation catalytic process at operating conditions of 380°C and 183 bar respectively and the hydrogen gas applied is produced via steam-methane reforming since the operational feedstocks are available as methane is the first gaseous product from the modified modular refinery process. Thus, more valuable products such as liquefied petroleum gas, naphtha and diesel were produced from modified modular refinery thereby resolving the residue or bottom product issue associated with conventional modular refinery operation in Nigeria. Models were developed from the first principle through the application of the principle of conservation of mass to predict the performance of the hydrocracker reactor and the developed models were sets of ordinary differential equations, which were solved using MatLab ODE45 solver and validated using simulation data of Aspen Hysys software for the hydrocracker reactor. The results gave a minimum percentage absolute error (deviation) between model predictions and Aspen Hysys results of 4.45%, 5.0% and 2.02% for liquefied petroleum gas, naphtha and diesel products respectively. Hence, the model developed predicted the output performance of the hydrocracker reactor very closely and was applied in studying or simulation of the effects of catalyst effectiveness factor on the overall performance of the hydrocracker reactor.

Experimental verification of kinetics and internal diffusion impact on low temperature steam reforming of a propane-methane mixture over Ni-based catalyst

Experiments were made on three fractions (0.5–1, 2–2.5 and 3–5 mm) of a Ni/Cr2O3/Al2O3 catalyst in order to verify the kinetics and influence of internal diffusion transport on the apparent reaction rate of low-temperature steam reforming of a propane-methane mixture. Feed gas composition was: C3H8 = 22.6%, CH4 = 77.4%, H2O/C = 0.51, GHSV = 11600 h−1, temperature 300–370 °C. To analyze the experimental data, a plug-flow reactor model with fixed temperature profiles was used; the profiles were obtained by interpolating the measurements of a moving thermocouple placed along the axis of the catalyst bed. The global kinetic scheme included the parallel reactions of propane steam reforming and propane hydrogenolysis. The catalyst effectiveness factor was calculated with the effective diffusion coefficient based on the Wilke formula, Thiele modulus and experimental pore size distribution. Experimental data for all catalyst fractions are described well by the proposed model at a porous catalyst tortuosity factor 1.53 and permeability coefficient 0.26.

Diffusion and catalyst efficiency in hierarchical zeolite catalysts.

The preparation of hierarchical zeolites with reduced diffusion limitation and enhanced catalyst efficiency has become a vital focus in the field of zeolites and porous materials chemistry within the past decades. This review will focus on the diffusion and catalyst efficiency of hierarchical zeolites and industrial catalysts. The benefits of diffusion and catalyst efficiency at two levels of hierarchies (zeolitic component level and industrial catalyst level) from a chemical reaction engineering point of view will be analysed. At zeolitic component level, three types of mesopores based on the strategies applied toward enhancing the catalyst effectiveness factor are presented: (i) ‘functional mesopores’ (raising effective diffusivity); (ii) ‘auxiliary mesopores’ (decreasing diffusion length); and (iii) ‘integrated mesopores’ (a combination thereof). At industrial catalyst level, location and interconnectivity among the constitutive components are revealed. The hierarchical pore interconnectivity in multi-component zeolite based industrial catalysts is exemplified by fluid catalytic cracking and bi-functional hydroisomerization catalysts. The rational design of industrial zeolite catalysts at both hierarchical zeolitic component and catalyst body levels can be fully comprehended using the advanced in situ and/or operando spectroscopic, microscopic and diffraction techniques.

Kinetic Parameter Calculation and Trickle Bed Reactor Simulation Based on Pilot-Scale Hydrodesulfurization Test of High-Temperature Coal Tar.

At present, a few chemicals can be separated after further processing of high-temperature coal tar (HTCT) distillates, which have a lower utilization. However, hydrogenation to produce clean fuel oil has not been widely reported in literature. Thus, due to the use of new feedstocks and the implementation of more severe environmental legislations, deep hydrodesulfurization (HDS) of HTCT will face formidable challenges. A series of HDS experiments were performed in a continuous isothermal trickle bed reactor in which the reactor temperature was varied from 648 to 678 K, the pressure from 12 to 16 MPa, and the liquid hourly space velocity (LHSV) from 0.25 to 0.35 h–1, and hydrogen-to-oil ratio kept constant at 2000 L/L. Based on the experimental data, possible reaction pathways of HDS reaction were investigated, and a modified Langmuir–Hinshelwood (LH) HTCT desulfurization kinetic model was established. gPROMS software was used to obtain optimal kinetic parameters that are as follows: EA = 26,842, K0 = 93,958, α = −1.14, n = 1.65, and m = 0.86. The model can well reproduce various working conditions and has better prediction accuracy. Some characteristics of HTCT HDS reactions were discovered; the reaction order (n) of HTCT HDS is slightly higher than that of crude oil and medium/low-temperature coal tar (M/LTCT), but the activation energy (EA) is relatively smaller. The established reactor model was used to predict the changes of the concentration of hydrogen, hydrogen sulfide, and sulfur compounds in the gas, liquid, and solid phases along the length of the reactor, respectively. The model was also used to predict the effects of pressure, temperature, and LHSV on the conversion rate of sulfur and catalyst effectiveness factors. The results showed that the LHSV has a greater impact on the conversion rate, and the pressure and temperature are less pronounced at high-severity operating conditions; the effectiveness factor is significantly smaller than that of other HDS processes, temperature has a greater effect on the effectiveness factor, followed by pressure and LHSV. The conclusion can provide a basis for further understanding the HTCT hydrotreating process.

Coupling non-isothermal trickle-bed reactor with catalyst pellet models to understand the reaction and diffusion in gas oil hydrodesulfurization

Abstract In this work, a trickle-bed reactor coupled with catalyst pellet model is employed to understand the effects of the temperature and catalyst pellet structures on the reaction–diffusion behaviors in gas oil hydrodesulfurization (HDS). The non-isothermal reactor model is determined to be reasonable due to non-negligible temperature variation caused by the reaction heat. The reaction rate along the reactor is mainly dominated by the temperature, and the sulfur concentration gradient in the catalyst pellet decreases gradually along the reactor, leading to the increased internal effectiveness factor. For the fixed catalyst bed volume, there exists a compromise between the catalyst reaction rate and effectiveness factor. Under commonly studied catalyst pellet size of 0.8–3 mm and porosity of 0.4–0.8, an optimization of the temperature and catalyst pellet structures is carried out, and the optimized outlet sulfur content decreases to 7.6 wppm better than the commercial level at 0.96 mm of the catalyst pellet size and 0.40 of the catalyst porosity.

Mathematical Modeling of the Stefan Flow Effect on Process in a Catalyst Grain Using Mathcad

Weekman and Gorring [2] considered the problem of the influence of the Stefan flow in a catalyst grain for mth order gas-phase chemical reaction A → nB. Special numerical methods were used to solve the problem. This paper proposes a simple method for solving the problem of a first-order gas-phase chemical reaction A → 2B using the Mathcad program. As an illustration of the method, the profiles of dimensionless reagent concentration and gas velocity of the Stefan flow at the Thiele parameter ψ = 1 and the molar fraction of reagent A outside the grain θ = 1, the dependence of the catalyst effectiveness factor on the parameters ψ and θ in the ranges ψ = 0.1–10 and θ = 0.1–1, and the dependence of a ratio between the catalyst effectiveness factor at θ = 1 and an analogous parameter in the absence of the Stefan flow on the Thiele parameter were calculated.

Multi-scale two-dimensional packed bed reactor model for industrial steam methane reforming

A non-isothermal heterogeneous steady-state model was developed for a packed bed reactor for steam methane reforming employing a multi-scale approach. The model consists of two-dimensional fluid-phase mass and heat transport equations accounting for axial and radial dispersion in the reactor tube, as well as accounting for mass and heat transfer resistances at the fluid-solid phase boundary, calculated using empirical equations. Reaction, mass and heat transfer in the catalyst particle are directly coupled with the fluid-phase equations using a 1D pellet model, thus avoiding the use of a catalyst effectiveness factor for reaction. The performance of the packed-bed reactor is compared using three pressure drop equations: the Ergun equation which neglects wall effects and the Eisfeld-Schnitzlein and Di Felice-Gibilaro correlations which include them. This multi-scale model also accounts for the effects of temperature, pressure and molar change of gas species due to reaction on superficial velocity using a separate equation. The impact of neglecting these effects through simplified models is evaluated.

Kinetic modeling and simulation of catalyst pellet in the high temperature sulfuric acid decomposition section of Iodine-Sulfur process

In the iodine-sulfur (I-S) thermochemical process for hydrogen production, the most endothermic high temperature step is the sulfuric acid decomposition which is catalytic process. Here, we introduce a model-based framework to address the effect of model uncertainty on catalyst identification, designing and optimization. To investigate the kinetic parameters, the experiments are performed in the packed bed reactor under the conditions of diffusion free regime. Further, the kinetic model is implemented in a two-dimensional heterogeneous model of the catalytic packed bed reactor developed in Multiphysics software in order to investigate the effects of catalyst composition, support material, catalyst pellet shapes, sizes (i.e., diffusional length), pellet intrinsic properties (i.e., porosity and thermal conductivity) and temperature on the catalyst effectiveness factor. The 7-hole cylindrical shapes with 0.75 and 1.5 mm principle dimension at 1073 K has been found to have negligible diffusional limitation and temperature gradients across their cross sections.

Analyzing the impact of implementing different approaches of the approximation of the catalyst effectiveness factor on the prediction of the performance of trickle bed reactors

Abstract A steady-state diffusion model comprising of diffusion and reaction in a catalyst pellet was used to study and understand the effect of the approximation of the catalyst effectiveness factor in the modeling of trickle bed reactors. The hydrogenation of alpha-methylstyrene was chosen as the case study reaction from literature for liquid-limited reaction conditions. The effectiveness factor values in this study were sensitive to reactor scale equations during the prediction of reactor performance. The approximation of accounting for the overall catalyst effectiveness factor in the reactor scale model equations from different models and solving the reactor scale model equations by different modeling approaches was assessed. It was observed that evaluating the overall effectiveness factor from pellet scale model equations and integrating the parameter in the reactor scale axial dispersion model at every local axial collocation point to simulate the reactor performance showed better agreement to the experimental data. This approach evaluates the effectiveness factor locally with the variation of the reactant concentration at different axial points across the reactor rather than using one value for the entire reactor. The approach of using a single effectiveness factor for the whole bed and using the effectiveness factor approximated as a fitted polynomial to the reactant concentrations did not properly predict the reactor performance.

Optimal Kinetic Parameters of Trickle bed Reactor for Oxidation of 2-Proplymercaptan in Naphtha

The best kinetic of the reaction are estimated based on experimental data obtained from the literature using parameter estimation technique. The best mathematical model for oxidative 2-proplymercaption via oxygen is taking into account the apparent intrinsic kinetics considering internal diffusion and TBR hydrodynamic effect on the reaction process mainly , catalyst wetting efficiency, catalyst effectiveness factor, Thiele model and the effective diffusivity. The optimal operating condition for oxidative process is carried out utilizing. The optimization technique based upon the minimization of the sum squared error between experimental and predicted composition of naphtha oxidative process to determine the best parameters of kinetics models. The predicted product compositions for oxidation process found to be a good agreement with the experimental data for wide range of operating conditions (2.5-10 hr-1, 75-300 ppm and 293-353K) with minimum error 5% among all results

Multiscale model based design of an energy‐intensified novel adsorptive reactor process for the water gas shift reaction

AbstractIn this work, an adsorptive reactor (AR) process is considered that can energetically intensify the water gas shift reaction (WGSR). To best understand AR process behavior, a multiscale, dynamic, process model is developed. This multiscale model enables the quantification of catalyst and adsorbent effectiveness factors within the reactor environment, obliviating the commonly employed assumption that these factors are constant. Simulations of the AR's alternating adsorption‐reaction/desorption operation, using the proposed model, illustrate rapid convergence to a long‐term periodic solution. The obtained simulation results quantify the influence of key operating conditions and design parameters (e.g., reactor temperature/pressure, Wcat/FCO, Wad/FCO, FH2O/FCO ratios, and pellet size) on the AR's behavior. They also demonstrate, for pellet diameters used at the industrial scale, significant temporal and axial variation of the catalyst/adsorbent pellet effectiveness factors. Finally, the energetic intensification benefits of the proposed AR process over conventional WGSR packed‐bed reactors are quantified.

Approximating Catalyst Effectiveness Factors with Reaction Rate Profiles

A novel approximate solution for catalyst effectiveness factors is presented. It is based on carefully selected approximate reaction rate profiles, instead of typical assumption of composition profiles inside the catalyst. This formulation allows analytical solution of the approximate model, leading to a very simple iterative solution for effectiveness factor for general nonlinear reaction stoichiometry and arbitrary catalyst particle shape. The same model can be used with all practical Thiele modulus values, including multicomponent systems with inert compounds. Furthermore, the correct formulation of the underlying physical model equation is discussed. It is shown that an incorrect but often-used model formulation where convective mass transfer has been neglected may lead to much higher errors than the present approximation. Even with a correctly formulated physical model, rigorous discretization of the catalyst particle volume may have unexpectedly high numerical errors, even exceeding those with the present approximate solution. The proposed approximate solution was tested with a number of examples. The first was an equimolar reaction with first order kinetics, for which analytical solutions are available for the standard catalyst particle geometries (slab, long cylinder, and sphere). Then, the method was tested with a second order reaction in three cases: 1) with one pure reactant, 2) with inert present, and 3) with two reactants and non-stoichiometric surface concentrations. Finally, the method was tested with an industrially relevant catalytic toluene hydrogenation including Maxwell-Stefan formulation for the diffusion fluxes. In all the tested systems, the results were practically identical when compared to the analytical solutions or rigorous finite volume solution of the same problem.

Pore diffusion effects on catalyst effectiveness and selectivity of cobalt based Fischer-Tropsch catalyst

Abstract In this study we investigate performance characteristics (catalyst effectiveness, CH4 selectivity, and hydrocarbon product distribution) of with a highly active Co/Re/Al2O3 catalyst particle for Fischer-Tropsch synthesis. In numerical simulations we utilize kinetic parameters for CO consumption rate, CH4 formation rate and hydrocarbon formation rates (C2+ hydrocarbons) determined from experiments with this catalyst to study effects of catalyst activity, catalyst particle shape (sphere, slab, solid and hollow cylinder), size (i.e. diffusion length), catalyst distribution (uniform vs. eggshell type distribution for a spherical particle) and process conditions (temperature, pressure, syngas composition and conversion level) on the catalyst performance. With increase in Thiele modulus (i.e. particle size at a fixed set of process conditions) we observe increasing H2/CO ratio profile towards the center of the particle resulting in increase of local and average CH4 selectivity. The goal is to find conditions which allow one to use sufficiently large particles to reduce pressure drop, while avoiding negative influence of diffusional limitations on selectivity and activity. For each catalyst particle shape we determined values of Thiele modulus, i.e. characteristic length of diffusion, corresponding to the upper limit of the kinetic region, and investigated how it changes with operating conditions. We found that simultaneous increase of pressure and the use of syngas with H2/CO feed ratio of 1.4–1.7 is the best strategy for mitigating the negative impact of intraparticle diffusional limitations on CH4 selectivity. For a spherical particle of 1 mm in diameter, one can achieve CH4 selectivity of 5.6% with catalyst effectiveness factor of 1.07 at the reactor inlet by operating at 50 bar, 473 K and H2/CO = 1.4.

A Monte-Carlo-based sensitivity analysis of multicomponent diffusion in porous catalysts

Molar fluxes inside porous catalysts can be calculated by means of multicomponent diffusion models. The state-of-the-art dusty-gas model competes with several alternatives, best-known the mean-transport pore model and the binary friction model. All three approaches combine Maxwell-Stefan-based transport with Knudsen diffusion and viscous Darcy flow. However, the models have not yet been compared theoretically, when applied to actual diffusion-reaction problems. Here we successively show that these diffusion models result in very similar behavior when applied to CO2 methanation, methanol synthesis and oxidative dehydrogenation of ethane. By comparing molar fractions, temperature and pressure profiles, latter revealed the most striking deviations between the models. Monte-Carlo-based, global sensitivity analyses on the catalyst effectiveness factors exhibit significant impact of catalyst properties, even at low uncertainties. At equal uncertainty levels, highest sensitivity was observed for the pellet porosity, followed by the tortuosity factor and the pore diameter. Overall, the choice of the diffusion model appears to have low influence on the regarded reaction-diffusion models. Hence, we recommend the binary friction model as most reliable, since both other approaches suffer from inconsistencies in the treatment of the viscous flux terms. These findings can be used as valuable basis for modeling multicomponent diffusion inside porous catalysts employed in heterogeneously-catalyzed gas-phase reactions.This work has been selected by the Editors as a Featured Cover Article for this issue.

Interfacial reactions between DBD and porous catalyst in dry methane reforming

Interaction between dielectric barrier discharge (DBD) and porous catalyst in dry methane reforming (CH4 + CO2 = 2H2 + 2CO) was studied. Coke formation behavior and coke morphology, as well as material conversion and selectivity, over the cross-section of porous pellets was investigated comprehensively by SEM analysis, Raman spectroscopy and pulsed reforming diagnosis, showing DBD and porous pellet interaction is possible only in the interfacial region (the external surface of the pellet): neither generation of DBD nor the diffusion of plasma generated reactive species in the internal micropores is possible. Coke formation and gasification mechanism in nonthermal plasma catalysis of DMR were discussed based on the catalyst effectiveness factor: low-temperature plasma catalysis is equivalent to the high-temperature thermal catalysis.