Catalytic Bed Research Articles

Batch to Continuous Flow Visible‐Light Photooxidations Using Alumina Supported Hydroxyanthraquinones

AbstractThe discovery of new environmentally friendly recyclable photosensitizers is key to develop future applications in photooxidation chemistry. We report here the evaluation of a set of differently substituted biobased hydroxyanthraquinones in the context of visible light mediated singlet oxygen (1O2) photochemistry. This class of compounds is efficiently immobilized on alumina supports, which offers a simple way of removing them from the reaction mixture downstream. An integrated process using a flow reactor with a fixed catalytic bed is also evaluated and its performance is compared with homogeneous conditions.

Intensifying Cyclopentanone Synthesis from Furfural Using Supported Copper Catalysts.

This work addresses catalytic strategies to intensify the synthesis of cyclopentanone, a bio-based platform chemical and a potential SAF precursor, via Cu-catalyzed furfural hydrogenation in aqueous media. When performed in a single step, using either uniform or staged catalytic bed configuration, high temperature and hydrogen pressures (180 °C and 38 bar) are necessary for maximum CPO yields (37 and 49 %, respectively). Parallel furanic ring hydrogenation of furfural and polymerisation of intermediates, namely furfuryl alcohol (FFA), limit CPO yields. Employing a two step configuration with optimal catalyst bed can curb this limitation. First, the furanic ring hydrogenation can be suppressed by using milder conditions (i. e., 150 °C and 7 bar, and 14 seconds of residence time). Second, FFA hydrogenation using tandem catalysis, i. e., a mix of β-zeolite and Cu/ZrO2, at 180 °C, 38 bar and 0.6, allows sufficient time for CPO formation and minimises polymerisation of FFA, thereby resulting in 60 % CPO yield. Therefore, this work recommends a split strategy to produce CPO from furfural. Such modularity may aid in addressing flexible market needs.

Hydrodynamic and Temperature Profile Analysis in a Gas-Solid Fluidized Bed with Liquid Atomization to Convert Fructose to Value-Added Chemicals

Carbohydrates specified C6 sugars dehydrate to produce platform chemicals like 5-hydroxymethyl furfural and furfural that further oxidize to chemicals 2,5-diformyl furan and 2,5-furan dicarboxylic acid. Here we propose a gas-phase in which a two-fluid nozzle atomizes a 0:1 ▪ fructose in water solution into a fluidized bed of Mo–V–▪/▪. However, the imperfect interaction between droplet and catalyst increases the agglomeration, which destroys the heat transfer efficiency and hydrodynamic stability. We evaluated the temperature and gas residence time distribution in catalytic bed to improve reaction and process performance by modifying the bed temperature, bed height, and gas velocity. A high mass of catalyst (>▪) degrades fructose and reduces the selectivity. At ▪ temperature distributes homogeneously within bed and with time on process it shifts toward higher values. Velocity in the range of ▪ to ▪ yield product with the highest selectivity (16%). These results demonstrate the potential of optimizing gas-phase catalytic processes to improve the selective production of platform chemicals from carbohydrates, supporting more sustainable chemical manufacturing.

Improvement of Properties of Bio-Oil from Biomass Pyrolysis in Auger Reactor Coupled to Fluidized Catalytic Bed Reactor

The goal of this research work was to investigate the improvement of bio-oil issued from beechwood biomass through catalytic de-oxygenation. Pyrolysis was conducted in an auger reactor and the catalytic treatment was performed in a fluidized catalytic bed reactor. Lab-synthesized Fe-HZSM-5 catalysts with different iron concentrations were tested. BET specific surface area, BJH pore size distribution, and FT-IR technologies were used to characterize the catalysts. Thermogravimetric analysis was used to measure the amount of coke deposited on the catalysts after use. Gas chromatography coupled to mass spectrometry (GC-MS), flame ionization detection (GC-FID), and thermal conductivity detection (GC-TCD) were used to identify and quantify the liquid and gaseous products. The pyrolysis temperature proved to be the most influential factor on the final products. It was observed that a pyrolysis temperature of 500 °C, vapor residence time of 18 s, and solid residence time of 2 min resulted in a maximum bio-oil yield of 53 wt%. A high percentage of oxygenated compounds, such as phenolic compounds, guaiacols, and the carboxylic acid group, was present in this bio-oil. Catalytic treatment with the Fe-HZSM-5 catalysts promoted gas production at the expense of the bio-oil yield, however, the composition of the bio-oil was strongly modified. These properties of the treated bio-oil changed as a function of the Fe loading on the catalyst, with 5%Fe-HZSM-5 giving the best performance. A higher iron loading of 5%Fe-HZSM-5 could have a negative impact on the catalyst performance due to increased coke formation.

Atmospheric Pressure Portable Catalytic Thermal Plasma System for Fast Synthesis of Aqueous NO3 and NO2 Fertilizer from Air and Water

AbstractMeaningful deployment of plasma water-based nitrogen fixation in agricultural application is hindered primarily due to its poor synthesis rate in compact systems. The study reports a directly deployable thermal plasma based portable catalytic compact system, offering typical synthesis rate as high as 1035 mg/min for nitrate and 635 mg/min for nitrite directly from naturally abundant atmospheric air and water. Developed technology is clean, sustainable, easily decentralizable, and completely free from fossil fuels and harmful intermediates like ammonia. The system avoids safety hazards and costs related to the requirements of continuous energy resources, pressurized environment for synthesis, regulated storage, refrigeration need, transportation of raw materials and distribution of fertilizer, as may be required by other competing technologies. Described system, consisting of air plasma torch, reaction chamber, water injection manifold and catalytic bed creates a unique nascent reactive plasma environment at ambient pressure that auto activates the catalyst in the field of thermal plasma for highly efficient fixation of nitrogen. Presented results indicate that use of combination catalysts with mechanically enhanced surface area allows drastic enhancement in the nitrogen fixation. Possible reaction chemistries, results of trials with different catalysts, time evolution of concentration, auto-conversion from nitrite to nitrate in aqueous media, time stability of concentration of the synthesized nitrate and observed remarkable effectiveness in the actual field trials are presented. Achieved synthesis rates are compared with those reported in literature in the area of thermal and non-thermal plasma.

Low pressure-drop CuO/CeO2/UiO-66 catalysts for H2 purification

Pressure drop is responsible of a great part of the energy cost in industry due the energy consumed by pumps driving a fluid through the installation, and heterogeneous catalysis industrial processes suffer from this pressure drop penalty. This study demonstrates that UiO-66 significantly improves the catalytic performance of the CuO/CeO2 active phase for preferential CO oxidation in H2 streams with regard to a conventional γ-Al2O3 carrier due to the particular porous and crystalline properties of MOF materials. A packed bed of UiO-66 produces very low-pressure drop in comparison to conventional catalytic carriers, such as γ-Al2O3 or beta zeolite, being 4 times lower for UiO-66 than for γ-Al2O3 under 2 L/min flow of N2, and this ratio increases and approaches ∞ for lower gas flow rates. This feature of UiO-66 not only decreases the energy required to pump gases through the catalytic bed, but also improves catalytic performance of UiO-66-supported catalysts due to the enhanced gas diffusion into the catalytic bed. The reaction gases flow through the interparticle space left by the catalyst in a packed bed of CuO/CeO2/γ-Al2O3, and this produces high pressure drop, preferential gas pathways and mass transport limitations, negatively affecting the reaction rate. On the contrary, the reaction gases are able to flow through the UiO-66 material without channel constrictions, and the CuO/CeO2/UiO-66 catalysts avoid the gas diffusion restrictions of conventional catalysts.

Modeling & experimental studies on enhancement of H2S conversion using catalytic membrane reactor for hydrogen production

Abstract Acidic gases such as H2S and CO2 are generated in the refineries during coal gasification. These pollutant gases need to be treated before releasing to the atmosphere. Conventionally, H2S gas is treated by Claus process in which H2S is converted to elemental S and H2O, in presence of O2 at ∼1,200 K. In the present energy scenarios, hydrogen has got importance as a source of clean fuel for industrial application. The H2S generated in the refineries can be a potential precursor of hydrogen. If this hydrogen can be obtained by thermal decomposition of H2S, that can increase the overall economic value of the H2S containing streams and the produced hydrogen can be used for hydrocracking and hydro-treating in refineries, as well as to synthesize value-added products for chemical industries. However, H2S thermal decomposition is an endothermic and equilibrium limited reaction (equilibrium conversion is only ∼15 % at 1,000 K), requiring a very high temperature (∼1,500 K) to achieve even a conversion of greater than 40 %. Packed Bed Catalytic Membrane Reactor (PBCMR) for thermal decomposition of H2S can be a potential technology augmentation and process intensification to increase this equilibrium conversion. In this work, modeling and experimental studies of H2S thermal decomposition using in-house designed & developed PBCMR have been carried out. The modeling studies were validated with experimental data. Clay-alumina ceramic tubular membrane (L: 250 mm; OD: 12 mm; thickness: 2 mm) was fabricated using extrusion process having an average membrane pore size of ∼1 μm and with a porosity of ∼20 %. Pt (2 %) coated alumina extrudes were used as catalyst to accelerate the reaction kinetics. Experimental studies showed that H2S to hydrogen conversion of ∼90 % is achieved using PBCMR at ∼1,523 K, compared to only ∼40 % conversion in a conventional packed bed tubular reactor (without membrane). Modelling studies were carried out to study the influence of operating parameters such as, reactor wall temperature, feed temperature, pressure and feed velocity. Studies showed that reactor wall temperature is having the most dominant effect on H2S conversion, which is confirmed by experimental findings. The studies offer useful insights into the application of PBCMR technology for management of waste gas stream containing H2S and recovery of hydrogen.

Single feed droplet–catalyst particle collision in a liquid containing gas–solid fluidized bed to convert fructose to value-added chemicals

Carbohydrates, comprising C6 sugars, dehydrate to form furfural (FUR) and 5- hydroxymethyl furfural (HMF). HMF is an intermediate for value-added specialty chemicals like 2,5-diformyl furan (DFF) and 2,5-furandi carboxylic acid, a monomer for polyethylene furaonate. Atomizing sugar solutions into catalytic fluidized beds operating beyond the caramelization temperature, Tcarm, accelerates reaction rates while avoiding humins, which are color forming agents characteristic of liquid phase processes. However, droplets partially coat particles in the spray zone and agglomerate due to liquid cohesive forces, which reduces heat transfer rates at the micro-scale and degrades reaction rates at the macro-scale. Here, we developed a CFD model to study the collision between a single feed droplet and a catalytic particle above Tcarm. We focused on evaluating the evaporation rate and heat transfer between the droplet and particle to promote vaporization the liquid feed, and assessing the impact of bed temperature, liquid feed rate, and superficial gas velocity. The highest DFF and furfural selectivity obtained are 17% and 24%, respectively, and these values are correlated to the maximum coke formation and agglomeration of 0.6% and 12g. However, the corresponding heat transfer and mass transfer are among the lowest values of 40% and 0.5W.

Multilayer polyelectrolyte and palladium nanoparticle decorated porous materials as fixed-bed reactors for efficient reduction of 4-NP

In this study, a continuous flow catalytic reactor based on three-dimensional porous sponge bed with the uniform distribution of catalyst to treat 4-NP wastewater efficiently. The porous sponge is used as a support to construct polyelectrolyte multilayers by loading dopamine. And the multilayer polyelectrolyte is closely bound to dopamine to form polyelectrolyte film, and the nanocatalysts are synthesized by electrostatic adsorption of precursors. The reactor realizes the uniform and stable distribution of the catalyst in the three-dimensional porous sponge, and the reactant transfers from bulk solution to catalyst surface by the way of convection and diffusion, which enhances mass transfer and further improves the reaction efficiency. Under the operating conditions of a catalytic bed as small as 3 cm, a 4-NP concentration up to 4.5 mM, and a flow rate of 300 μL min−1, the conversion rate remained above 96 % for up to 200 h, indicating that the reactor has good catalytic efficiency. The results showed that this continuous flow catalytic system structure has excellent performance in wastewater treatment.

Hydrocarbon generation through pyrolysis of high-lipid-content microalgae within a dual-catalyst bed

The presence of oxygenated and nitrogenated compounds formed during the pyrolysis of microalgae poses challenges for utilizing bio-oil as a competitive alternative to fossil fuels. In an effort to mitigate the formation of these undesirable substances and enhance the production of aromatic hydrocarbons, this study delved into the catalytic analytical pyrolysis of Schizochytrium limacinum using a tandem catalytic bed. The research involved the characterization of Schizochytrium limacinum biomass and examining the impact of reaction temperature and the dual-catalytic bed (hydrotalcite followed by zeolite) on the formation of pyrolytic compounds and hydrocarbons. In the analytical pyrolysis, the dual-catalytic bed comprising NiHTC followed by NiHZSM-5 showed superior efficiency in deacidification and deoxygenation. Through the calcination and reduction/passivation of both catalysts, hydrocarbon production achieved noteworthy levels, reaching 89 % and 92 %, respectively, with a catalyst-to-biomass ratio set at 5:1. Under these optimized conditions, aromatic formation consistently remained between 60 % and 70 %. Furthermore, pathways were delineated to elucidate potential chemical reaction routes. The satisfactory results suggest that high-lipid content microalgae can serve as successful feedstock for hydrocarbon generation.

Exothermic characteristics evaluation of the Pt coated α-Al2O3 catalyst in bed for passive airborne radioactive material reduction system under forced flow conditions

After the severe accident at the Fukushima nuclear power plant, there has been heightened interest in the development of severe accident countermeasures. As part of these efforts, a passive filtration system capable of passive operation during power loss is under development.This paper focuses on evaluating the performance of a catalyst-filled bed designed to create a temperature gradient through exothermic reactions between combustible gases generated during accidents and a catalyst. The temperature gradient facilitates the formation of natural convection within the system, enabling passive operation. The catalytic bed is designed in a bed-type configuration filled with exothermic catalysts. To ensure physical and chemical stability under severe accident conditions, heat resistance tests were conducted using inorganic materials as a base to select an optimized exothermic catalyst. A test apparatus was designed for unit evaluation testing of the catalyst-filled bed equipped with the catalytic bed. Exothermic characteristics evaluation tests were conducted by varying the hydrogen volume fraction and face velocity, measuring heat generation in the catalytic bed under each condition. The correlation between these variables and the heat generation performance of the catalytic bed was determined. These findings will be utilized to inform the design parameters of the passive airborne radioactive material reduction system.

Mixed metal oxide bronzes as catalysts for the gas-phase aerobic transformation of glycerol to acrylic acid: Single or double catalytic bed approaches

Metal-doped hexagonal tungsten oxide bronzes (h-WVOx and h-WNbOx) and metal-doped orthorhombic molybdenum oxide bronzes-M1 type (MoVOx, MoVTeOx and MoVTeNbOx) have been synthesized hydrothermally and heat-treated at 400, 550 or 600 °C in N2. The catalysts were characterized by several techniques and tested in the one-pot aerobic transformation of glycerol at 350 °C. From all of them, h-WNbOx resulted as the most selective to acrolein (80 % yield), whereas both h-WVOx and MoVTeNbOx were more effective to acrylic acid (with a yield lower than 25 %). Subsequently, a double-bed reactor comparative study was conducted, with h-WNbOx acting as the first catalytic bed. In this case, the yield to acrylic acid decreased as follows: MoVTeNbOx > MoVTeOx > MoVOx >h-WVOx. IR spectroscopy of acrolein adsorbed on these catalysts allows to explain the catalytic performance of these catalysts.

Selective H2 production from plastic waste through pyrolysis and in-line oxidative steam reforming

This study deals with the proposal of pyrolysis and in-line oxidative steam reforming (P-OSR) for plastic waste valorization and assesses the potential of this strategy for the selective production of H2. Overall, the study aims at progressing towards the fine-tuning of the pyrolysis-reforming technology by co-feeding O2. Thus, a multi-point O2 injection system has been developed to ensure a suitable O2 distribution in the reforming reactor and avoid the formation of hot spots, as they may cause catalyst deactivation by metal sintering. Moreover, as O2 is directly supplied into the catalytic bed, pre-combustion of the volatile stream before contacting the catalyst is avoided and in-situ coke combustion is promoted. The P-OSR of HDPE was carried out in a two-step reaction system, which combines CSBR (conical spouted bed reactor) and FBR (fluidized bed reactor) technologies. The experiments were conducted in continuous mode and the influence of the main process conditions at zero time on stream was analyzed. Thus, the effect of reforming temperature was studied in the 550–750 °C range, that of the space time from 3.12 to 15.62 gcat min gHDPE−1, steam to plastic (S/P) ratio between 2 and 5 and equivalence ratio (ER) from 0 to 0.3. Under the optimum conditions (700 °C, S/P of 3, 12.5 gcat min gHDPE−1 and ER of 0.2), a H2 production of 25.0 wt% was obtained, which is only 28.6 % lower than that obtained in the conventional pyrolysis-steam reforming (P-SR) process. The results obtained confirm the potential of continuous P-OSR process for the selective production of H2.

Investigation and Control of Fluidized Bed Catalytic Cracking Unit

The fluidized catalytic cracking (FCC) unit is one the main unit of the oil refinery, its objective is upgraded heavy low value petroleum streams into higher value products, mainly gasoline and olefin. In this process the catalyst is circulated into the regenerator, the coke is burned, and the catalyst is regenerated. Many parameters are used to control FCC, the most importantare temperature, which should be kept at (505? C ) and the catalyst temperature (655? C). Other parameters are the level and flow rate of the catalyst. In this work, control strategy was build and the transfer functions were detected, so, the characteristic equations were calculated as well as the open- loop transfer functions. Tuning, stability analysis and simulation response of the system were achieved by using Routh, direct substitution, RootLocus and bode methods

Co-Gasification of Polyethylene and Biomass in Catalytic Bed Material

In this work, a simplified comprehensive three-dimensional numerical model is developed to study the effect of hydrogen production on co-gasification of biomass and low-density polyethylene (LDPE). CFD software AVL Fire 2020 inbuilt algorithms were employed to develop the gas phase while the solid phase was developed by user-defined FORTRAN subroutines. Solid hydrodynamics, fuel conversion, homogenous and non-homogenous chemical reactions, and heat transfer, including radiation, subroutines were defined and incorporated into AVL FIRE explicitly. Species concentrations of the syngas were analyzed for co-gasification of Beechwood and LDPE for three distinct types of bed materials (silica sand, Na-Y zeolite, and ZSM-5 zeolite). Then, the model is validated with experiment results available in the literature for a lab-scale fluidized bed reactor. The highest hydrogen production was observed in Na-Y zeolite followed by ZSM-5 zeolite and silica in both numerical and experimental analysis for the co-gasification of Beechwood and LDPE, providing a reasonable agreement between the numerical and the experimental results. Therefore, the current model predicts the enhancement of the quality of hydrogen-rich syngas through the application of co-pyrolysis within a fluidized bed reactor, incorporating a catalytic bed material.

Experimental Analysis of Inductive Heating of Catalytic Beds

AbstractTo reduce CO2 emissions in the chemical industry, already established endothermic reactors should be heated with electrical energy. One promising possibility is inductive heating, in which electrical energy can be transferred to the susceptor (material to be heated). The uniform heating of the susceptor material is necessary for stable operation in chemical reactors and is therefore investigated in this work. For this purpose, a non‐reactive test setup was built that enables the investigation of inductive heating of different susceptor materials and measurement of the temperature distribution under defined non‐reactive conditions. In the first tests, temperatures of up to 800 °C were reached and an uneven heat input in a bed of stainless‐steel rings was observed.

Performance assessment of a novel porous catalytic reactor with a hydrogen-selective membrane for enhanced methane dry reforming process – CFD investigation

This manuscript offers a thorough examination of the efficiency of a reactor-assisted membrane system for the production of syngas through a process of methane dry reforming (DRM). The proposed strategy aims to bring attention to the optimization of the DRM and reverse water gas shift (RWGS) reactions, towards achieving increased conversions of methane and carbon dioxide, as well as increased purity in syngas production. This goal will be accomplished by integrating a selectively permeable membrane within the central region of the tubular catalytic porous bed reactor. The primary objective of the current research is to quantitatively assess the impact of operational parameters on both the hydrogen flux and concentration distribution of the various components residing in the reactor. This study highlights the impact of inlet feed pressure on hydrogen flux. It is found that an elevation in the inlet feed pressure from 1 to 4 bar yields an average increase in hydrogen flux from 2.60 to 4.21 kg/(m2.h), particularly when the inlet feed pressure is set at 2 bar. However, a subsequent increase to attain a pressure of 4 bar results in a decline in hydrogen flux to a rate of 2.78 kg/(m2.h). Moreover, increasing the inlet feed temperature from 900 to 1100 K leads to a substantial augmentation in the average hydrogen flux, from 7.08 to 8.56 kg/(m2.h), while maintaining a reactor wall temperature of 1000 K. As another finding, a molar ratio of CH4/CO2 of 1 leads to the greatest mean hydrogen flux of 4.73 kg/(m2.h) across the membrane interface. The current research work could provide useful tips/guidelines for efficient reactor design and optimization; it also enhances comprehension of reactor-assisted membrane systems in the context of syngas production.

Evaluation of Heterogeneous Catalytic Ozonation for Micropollutants Removal from Wastewater: Application of a Pre-Industrial-Scale Unit

The present study evaluates the application of heterogeneous catalytic ozonation for the removal of micropollutants from wastewater effluent in a pre-industrial-scale unit, consisting of a post-filtration, an ozone dilution, a catalytic ozonation, and a final biological stabilization step. The important step of ozone dilution is optimized by the use of a hollow fiber membrane that minimizes the loss of ozone gas due to the transfer of ozone to the liquid phase mainly by diffusion. It is observed that the efficiency of this sub-system is maximized for the dead-end operation of the membrane and the introduction of ozone gas to the shell side and liquid phase to the lumen side of the membrane module. Under these conditions, the concentration of dissolved ozone is directly dependent on the ratio of ozone gas feed to the wastewater flow subjected to post-treatment. Regarding the removal of MPs, part of their degradation already takes place at this stage (i.e., during ozone dilution), while after the post-treatment of wastewater effluent in the catalytic ozonation bed, the MP degradation yield ranges from 35% up to complete removal, depending on the type and properties of the specific MP. The addition of a final biological filtration bed to the overall treatment unit significantly increased its performance, regarding the removal of MPs, enhancing it by an additional removal rate that can reach up to 30%.

Thermally manageable and scalable reactor configurations towards efficient hydrogen release from liquid organic hydrogen carriers

In the global pursuit to minimize carbon emissions, hydrogen has emerged as a prominent alternative energy solution. This research introduces a thermally efficient, scalable, and potentially carbon–neutral system for releasing hydrogen, employing methylcyclohexane as a liquid organic hydrogen carrier (LOHC). Our heat supply mechanism utilizes benzyltoluene as a liquid–gas phase change material (PCM) to facilitate effective heat transfer from the heating units to the reactor. We have developed catalysts with high dispersion and Pt loading of Pt/γ-Al2O3 that maintain performance over extended periods, achieving a hydrogen extraction rate of 2.3 Nm3H2(g)/h (equivalent to 5 kgH2/day) in a bench-scale reactor. The bench-scale setup achieves near-equilibrium conversion at a space velocity of 2 LLOHC/(Lcat-h) and 310 °C. The PCM-enhanced system supports a scalable catalytic bed design and simplifies heat supply and startup through the use of various heating methods. We then compare catalytic dehydrogenation reactor setups using single and hybrid heat sources; the former includes an internal Joule heater, offering simplicity and reduced heat loss but depends heavily on electrical energy, while the latter combines the internal Joule heater with an external fuel combustor, facilitating rapid startup albeit with increased heat loss. Lastly, we suggest future research directions to address existing technological hurdles and to expand the application of this system in scaling up hydrogen release processes.

Profile of the Effectiveness Factor under Optimal Operating Conditions for the Conversion of Ortho-Xylene to Phthalic Anhydride in a Fixed-Bed Tubular Reactor

The objective of this research is to find the effectiveness factor of the catalyst particles for the most favorable conditions of the phthalic anhydride production in a fixed bed reactor, with the aim of achieving the highest rate of phthalic anhydride production compared to other secondary products and analyzing the areas of lower effectiveness for the modification of the reactor design. Initially, the material and the energy balances in the catalytic bed are solved to obtain the concentration and temperature profiles based on the radius and length of the reactor, using polymath software(Polymath® v6.2 Software Minitab 19 Matlab 2019) with the data from literature. Once the profiles reproducibility was verified using the initial data (inlet temperature, pressure in the reactor, reactor wall temperature, reactor radius and mass flow rate) the experimental design 35 carry out, which generates 243 “experiments”, whose response variable (phthalic anhydride concentration) was obtained using Matlab. Subsequently, the variables were analyzed using the Minitab 18® that, through the response surface analysis method, allowed us to obtain the optimal values of the tested variables. Then, Subsequently, material and energy balances coupled with Fourier and Fick’s laws, along with the effectiveness factor equation, were applied, resulting in the generation of 9 coupled differential equations. Upon implementing the finite difference method, this yielded 90 nonlinear algebraic equations, which were solved using the Polymath software. A total of 78 particles were preselected based on their radial and axial positions to determine the effectiveness factor profile, with values ranging from 0.83 to near unity. The lower values correspond to the points with higher temperature, as evidenced by the calculations performed.