Random Pore Model Research Articles

Relating alkali release from a wood pellet with combustion progress: A modified random pore model supportive study

This paper concerns a miniature gasifier fed with a constant ambient-pressure flow of air to study the pyrolysis and subsequent combustion stage of a single wood pellet at T = 800 ℃. The alkali release and the concentration of simple gases were recorded simultaneously using an improved alkali surface ionisation detector and a mass spectrometer in time steps of 1 s and 1.2 s, respectively. It showed alkali release during both stages. During combustion, the MS data showed almost complete oxidation of the charred pellet to CO2. The derived alkali release, “O2 consumed”, and “CO2 produced” conversion rates all indicated very similar temporal growth and coalescence features with respect to the varying char pore surface area underlying the original random pore model of Bhatia and Perlmutter. But, also large, rapid signal accelerations near the end and marked peak-tails with O2 and CO2 after that, but not with the alkali release data. The latter features appear indicative of alkali–deprived char attributable to the preceding pyrolysis with flowing air. Except for the peak-tails, all other features were reproduced well with the modified model equations of Struis et al. and the parameter values resembled closely those reported for fir charcoal gasified with CO2 at T = 800 ℃.

Experimental and numerical investigation of water flow in different media models at multiple scales

ABSTRACT The study of the flow behavior in pores, fractures, and pore-fracture dual media plays a crucial role in understanding the mechanisms of sudden water inrush and sand flow. In this study, laboratory experiments were conducted using a custom-made transparent porous model to investigate the flow characteristics of fluids in complex media. Additionally, finite element simulations were employed to explore the flow features at multiple scales. A detailed analysis at the micrometer scale was conducted to examine the variations in the water velocity, volumetric flow rate, Reynolds number, flow field, and permeability under different porosity and pressure drop conditions. The results indicate that within the studied range of flow velocities and pressures, the fluid flow in all the media models adhered to Darcy’s law. The improvement in structural connectivity in the random pore model has made the flow channels of fluids in the random pore network more diverse, resulting in an increase in the peak water flow velocity from 4.89E–5 m/s to 4.19E–4 m/s. The fluid accelerated while bypassing the protruding solid particles, resulting in the formation of high-velocity zones in the vicinity. As the pressure drop increases, the volume flow rate of the random dual-medium model with a porosity of 0.6 can increase to 1.01E–9 m3/s, with the highest growth rate. We also simulate the fluid flow of a regular dual-medium model at different porosities and find that the permeability rapidly increases from 5.65E–13 m2 to 1.01E–11 m2, demonstrating that the presence of fractures can significantly improve the permeability performance of the medium. The research findings deepen our understanding of the migration behavior of water in complex geological environments and provide theoretical guidance for groundwater resource protection and underground engineering.

Catalytic coal gasification: mechanism, kinetics, and reactor model

Catalytic coal gasification is a promising technology in the field of clean coal utilization. A comprehensive understanding of mechanisms, reaction kinetic, and reactor model is crucial. This article summarizes and analyzes the catalytic mechanisms of key reactions, such as C–O2, C–CO2, C–H2O, and CO–H2. It also compares various kinetic models, including shrinking core model, random pore model, volume model and their respective modifications. Additionally, the article delves into mathematical modellings of catalytic coal gasification, encompassing molecular models or density functional theory, empirical model, computational fluid dynamics, Aspen modeling, and artificial neural network. The aim is to provide a roadmap for the development and scale up of reactors used in catalytic coal gasification.

Random pore model insights into structural and operational parameters for hydrogen-based iron oxide reduction

The hydrogen-based direct reduction of iron oxide (DRI) provides a sustainable approach to cleaner ironmaking. In this research, for analyzing hydrogen-based DRI in pellet scale, the random pore model (RPM), the most sophisticated non-catalytic gas-solid model, is applied to determine the effects of structural parameters, including pore-size parameter (ψ), Thiele modulus (ϕ), and product layer resistance (β), along with operational parameters such as pressure, temperature, and gas composition. The PDE equations of RPM were solved numerically using the method of lines together with a finite-difference discretization in space. The effects of parameters ψ and ϕ were investigated, revealing that the reaction rate increases with larger pores and decreases with higher values of ϕ over length and time. Kinetics resemble the unreacted shrinking core model (USCM) for small particles, while pore structure dominates for large particles. Parameter determination is influenced by ϕ changes, shifting control from chemical kinetics to diffusion, with operating conditions impacting reaction rate enhancement. Investigations revealed that as ϕ increases from 0.454 to 1.454, a 6 % conversion gradient forms from the pellet center to the surface. Additionally, at 700°C, reducing the temperature by 100°C slows conversion by 15.45 minutes while increasing it accelerates conversion by 4.55 minutes.

A Random Pore Model Approach Towards Hematite to Iron Reduction by Carbon Monoxide: A Computational and Experimental Study

A Random Pore Model Approach Towards Hematite to Iron Reduction by Carbon Monoxide: A Computational and Experimental Study

Investigation on formation and combustion process of carbon deposits from coke oven riser during waste heat recovery

In the context of carbon neutrality, the widespread application of waste heat recovery systems in steel production is crucial for energy conservation and emission reduction. This study investigates the formation and combustion removal mechanisms of carbon deposits in coke oven risers during waste heat recovery by analyzing the physicochemical structure, combustion behavior, and kinetics of different layers. The results revealed that lower temperatures near the tube wall produced higher volatile content in the lower layer. Over time, the carbon deposits gradually graphitized from bottom to top. Under long-term heating and iron catalysis, the lower carbon deposits showed a higher order degree and poorer combustion performance. The middle layer, characterized by more pores formed during polycondensation, exhibited a larger specific surface area than other samples and burned slightly faster than the upper layer. Increasing heating and airflow rates could linearly enhance the combustion efficiency of carbon deposits. The random pore model accurately described the combustion process of the upper and middle layers, whereas the multi-stage weight loss in lower deposits aligned better with a multi-stage reaction random pore model. This research could further strengthen the understanding of carbon deposits in the riser and improve the removal effect, thereby promoting waste heat recovery from coke oven gas.

Activation kinetics of biochars from peanut shells, cashew nut shells, and millet stalks under isothermal conditions in CO2 atmosphere

This study investigates the reactivity kinetics of biochar from biomass. The biochars were obtained by pyrolyzing peanut shells (PNS_800), cashew nut shells (CNS_800), and millet stalks (MS_800) at 800 °C in a fixed bed reactor. The chemical composition of the biochar samples shows that silicon (Si), potassium (K), and magnesium (Mg) are the major elements in the biochar of peanut shells (PNS_800) while potassium and magnesium are the major elements in the biochar of cashew nut shells (CNS_800) and millet stalks (MS_800). The biochars were activated in a CO2 (200 Nml/min) atmosphere at temperatures 1123 K, 1173 K, and 1223 K under atmospheric pressure. The random pore model (RPM) and a modified random pore model (MRPM) were used to correlate the reactivity profiles versus carbon conversion and to determine the kinetic parameters. It was observed that biochar reactivity increases as the temperature increases, attaining at least three times at 1173 K than those corresponding to 1123 K. Furthermore, the increase in reactivity is more pronounced with the biochar MS_800. It was observed that the RPM model cannot follow the kinetic of the experimental reactivity of all biochar samples. However, a better fitting of the reactivity is obtained when using the MRPM model. The activation energies (Ea) are distributed in the range of 98.11–148.46 kJ/mol while the pre-exponential factors (k0) are in the range of 19.31–249.53 s-1. It was observed that for the MRPM model, the lower activation energy and the lower pre-exponential factor were obtained by the biochar CNS_800. However, Ea et k0 are well evaluated for PNS_800 and MS_800 with a coefficient of determination of 99.76%. The proposed modified random pore model could be used to describe the reactivity of biochar from biomass as well as the reactivity of coal.

Pore-scale simulation of diffusion characteristics inside the bi-dispersed pore structure

The classical diffusion models fail to predict the diffusivity of bi-dispersed porous materials, particularly at low macro-porosity. In this work, a pore-scale simulation is carried out to investigate the diffusion process inside ordered and random bi-dispersed pore structures under different growth phases and shapes. The applicability of existing models is evaluated. The results reveal that Maxwell and Nield models are inadequate to predict the diffusivity of the ordered macropore structure under different growth phase types and shapes. Meanwhile, the ordered distribution of microporous spherical particles is superior to that of macropores. For random pore structure, the macropore-macropore diffusion path contributes to the error of the random pore model, which depends on the ratio of the micropore-macropore diffusivity.

Flue gas desulfurization by natural recyclable manganese ore in packed bed reactor and its performance prediction by random pore model

Various grades of manganese dioxide ores, as a natural recyclable sorbent, can be used in dry flue gas desulfurization (FGD) at moderate temperatures (350–450 °C). This research provided low- and high-grade manganese dioxide ores to examine SO2 removal in a packed bed reactor. To obtain characteristic parameters of mineral sorbents, XRD, XRF, BET, and mercury porosimetry were employed. Then, kinetic parameters of desulfurization reaction were determined using thermogravimeter analyzer (TGA) and random pore model (RPM) for a single pellet. In desulfurization experiments of simulated flue gas in a packed bed reactor and mass spectrometer (MS) apparatus, the breakthrough times were measured under various operating conditions. The onset of these breakthrough times or life-time of MnO2 reactor for the SO2 removal was predicted successfully by RPM for a packed bed reactor using related kinetic constants from TGA. In addition, reacted sorbets were recycled multiple times after washing with water. Not only does this simple method separate MnSO4 from unreacted sorbents as a valuable byproduct to reduce the FGD cost, but it also improves pore size distribution (PSD) of mineral MnO2 by creating large pores. Modified PSD of this recycled sorbent caused increased breakthrough time.

Kinetic study of sulfur dioxide removal reaction with manganese dioxide by random pore model using thermogravimetry

Kinetic study of sulfur dioxide removal reaction with manganese dioxide by random pore model using thermogravimetry

Co-combustion behavior and catalytic mechanism of high CaO/SiO2 biomass mixed with anthracite for blast furnace injection: Experiment, modeling and DFT investigation

The physical and chemical properties of apricot tree (AT), corncob (CC), and anthracite (CC) were systematically analyzed. Their combustion behaviors and blends were examined using a non-isothermal thermogravimetric method, which revealed the catalytic mechanism of biomass mineral composition in the combustion process. The presence of high CaO content resulted in better combustibility, particularly with an addition ratio of more than 50 % AT, which enhanced anthracite combustion. Kinetic analysis indicated that the random pore model had a better fit than the volume reaction model. At 75 % addition of AT and CC, the lowest apparent activation energies were observed, with values of 100.5 kJ/mol and 110.23 kJ/mol, respectively. Density functional theory calculations demonstrated that the presence of CaO caused reconfiguration in the coal's molecular structure, making it easier for aliphatic chains attached to six-membered rings to detach. The co-combustion process and catalytic combustion mechanism of biomass and coal were discussed, highlighting CaO's ability to remove oxygen-containing functional groups and aliphatic chains, while facilitating O2 diffusion within the molecular structure. Conversely, SiO2 tended to generate silicates, leading to the deactivation of CaO's catalytic effect.

Characterisation and double parallel random pore model fitting kinetic analysis of faulty coal oxygen-enriched co-combustion

This study used various analytical techniques to explore the structural characteristics of anthracite, lean coal, and bituminous coal. Thermogravimetric analysis assessed the combustion performance of individual coals and their blends. Results revealed distinct structural differences among the three coals. Although lean coal's functional groups distribution resembled bituminous coal, its carbon ordering aligned with anthracite. Increasing the proportion of bituminous coal minimally improved combustion in air. Under O2 + N2, rising oxygen levels lowered ignition and burnout temperatures, enhancing the comprehensive combustion index. At high heating rates, 30 %O2 + 70 %CO2 outperformed 30 %O2 + 70 %N2. The fitting performance of the double parallel random pore model (DRPM) was superior to that of the random pore model (RPM). Kinetic analysis suggested a DRPM for lean coal and bituminous coal co-combustion, unfolding in two stages. Activation energy increased with O2 concentration in O2 + N2 but remained lower than in O2 + CO2.

Study on the pyrolysis characteristics and char gasification kinetics of pre-separated automobile shredder residues

Automobile shredder residue (ASR) is a typical solid waste produced by the end-of-life automobile industry. The pyrolysis and gasification of ASR are effective methods to achieve reduction and resource utilization. By means of thermogravimetric analysis and fixed-bed experiments, the distribution as well as physicochemical properties of five typical ASR pyrolysis products after pre-sorting were systematically investigated, and the gasification kinetics of their pyrolysis char under CO2 as well as steam were also studied. Results showed that the pyrolysis of ASR was basically completed at 500°C, and the pyrolysis gas yield increased significantly with temperature. The tar contained mainly poly-benzene rings with carbon atoms C11–15 and their derivatives. At high temperatures, the structure of pyrolysis char tended to become more ordered, with small functional group such as - OH, - NH, - CH3, - CC -, and - COOH fracturing. The residual amounts of heavy metals such as Cr, Pb, and Ni in pyrolysis char were mostly exceed 45%, which were significantly affected by the type of heavy metals, pyrolysis temperature and material type. Hydrogen production from steam gasification accounted for up to 65%, and the gasification reactivity was better than that of CO2 gasification. The activation energy (E) calculated through shrinking core model (SCM) and random pore model (RPM) was 38.81–105.44 kJ/mol and 39.53–98.56 kJ/mol, respectively, which provided a good fit to the gasification kinetics in two gasification atmospheres. This study provides detailed data for the ASR pyrolysis and gasification technology, which is an important reference value for ASR research.

Direct Liquefaction of South African Vitrinite- and Inertinite-Rich Coal Fines.

In this investigation, coal fines enriched with inertinite were used for direct liquefaction experiments. For comparison, a vitrinite-rich coal typically utilized in coal-to-liquid processes was also employed. To assess the impact of mineral matter content, demineralization was used to remove most of the inorganic constituents. The findings revealed that the inertinite-rich coal exhibited lower liquefaction conversions due to a reduced proportion of reactive macerals and elevated levels of inorganic mineral matter. These conversion values exhibited a strong correlation with the quantity of reactive macerals present in the parent coals. For the inertinite-rich coal, the presence of inorganic mineral matter impeded the liquefaction process but facilitated the CO2 gasification reactions of the derived chars. To evaluate their potential in gasification processes, CO2 gasification experiments were conducted and the reactivities and apparent gasification activation energies of both coal chars, liquefaction residue chars, and preasphaltene and asphaltene (PAA) chars were calculated. These calculations were carried out using the random pore model (RPM) and volumetric reaction model (VRM). The chemistry, reactivity, and kinetics of residue gasification conversion are not thoroughly understood, yet they hold significant importance in optimizing syngas production within gasification processes. The findings from this work highlight significant differences in liquefaction conversion values, product distribution, and composition. These differences are influenced by factors such as maceral composition, inorganic mineral matter content, hydrogen-donor capabilities of the solvent, and liquefaction reaction temperatures. Additionally, these variables affect the CO2 gasification reactivity of liquefaction solid residue chars.

Correct Use of the Bhatia and Perlmutter Random Pore Model under Nonisothermal Conditions.

The classic random pore model (RPM) of Bhatia and Perlmutter [A random pore model for fluid-solid reactions: I. Isothermal, kinetic control. AIChE J.1980, 26, 379-386], which has been used in the kinetic analysis of numerous gas-solid processes involving porous materials under reaction control, was originally derived only for isothermal conditions. This has not prevented many researchers from using it in nonisothermal conditions, a frequent procedure whose validity has not been demonstrated until now. In this work, different questions are answered: Are the isothermal equations of the RPM valid under nonisothermal conditions? And, related to this question, is the commonly used conversion function correct? This work provides the scientific basis that was missing until now for the use of the RPM in nonisothermal conditions, as well as the correct conversion function for such use over the entire particle size range. The said RPM conversion function has been obtained from the exact formulation of the reaction rate equation, and as it should have been originally, it has the grain model function as one of its particular solutions. In this way, the gap that prevented the use of the random pore model for very low particle size values has finally been closed.

Modeling of the evolution of the porous structure during a physical activation process for the production of activated biocarbon: A novel low conversion approach

Many experimental studies have shown the feasibility of using biomass precursors to produce activated carbon, often improving the properties obtained from traditional materials. However, hardly any models focus on the development of porosity during the process. Among the so-called pore models, the random pore model (RPM) is the most popular and accurately predicts the evolution of the porous structure due to pore growth and coalescence. However, in activation processes with a low degree of conversion, in which pore formation is the dominant mechanism, the RPM does not correctly predict the evolution of the specific surface area since it does not consider the appearance and creation of new porosity. In this work, a new model is proposed that predicts the specific surface area created due to the formation of new pores. Subsequently, it is combined with the determination of the variation of the specific surface area predicted by the RPM due to the growth and coalescence of existing pores. The validation of the new pore evolution model with activated carbon samples obtained at different conversions shows that the model proposed adequately predicts the specific surface area and pore distribution evolution throughout the activation process.

The Kinetics of Semi-Coke CO2 Gasification Based on Pore Fractal Growth

The gasification kinetics of semi-coke are an important research topic in the gasification process of semi-coke. The evolution of the pore structure is one of the most important factors affecting the gasification rate of semi-coke. In this paper, the pore fractal growth model was established based on the principle of pore fractal growth and the Sierpinski sponge structure. Three kinds of semi-coke raw materials were used to prepare porous carbon with different degrees of gasification. Combined with the TG curves of raw materials, the gasification kinetics based on the fractal model were verified. The curves of the gasification reaction rate and the specific surface area as a function of carbon conversion were consistent with the random pore model and experimental data, which verified the feasibility of the model. The pore fractal dynamic model could predict the change in the pore structure with carbon conversion during semi-coke gasification, so as to reveal the kinetic law of carbon gasification.

Optimization of convection cooling by pressed brick structure and coke conversion rate in coke dry quenching furnace

Segregation of coke temperature and gas flow in Coke Dry Quenching furnace is a crucial issue in coke production, and the pressed brick structure of Coke Dry Quenching furnace plays a significant role in the problem of segregation. In this work, computational fluid dynamics simulation software Ansys Fluent and self-programmed equations were utilized to investigate the fluid flow and heat transfer processes, as well as coke particle combustion behavior, based on the No. 2 Coke Dry Quenching furnace at the Bayuquan coking plant of Ansteel. The focus was on analyzing the impact of gas flow rate and pressed brick structure on the furnace’s flow and temperature fields, as well as assessing the extent of coke particle combustion under different gas flow rates. The simulation involved the use of porous media models, pseudo-fluid models, and non-local thermal equilibrium to simulate the heat transfer processes within the CDQ furnace. The simulation results show that when the coke discharge rate was set at 160 t/h, selecting a circulating gas flow rate of 180,000 m3/h could ensure that the outlet temperature of coke meet the production requirement and reducing energy consumption. Optimizing the pressed brick structure appropriately can clearly improve the segregation in gas flow and temperature within the furnace. This led to a reduction of approximately 0.3 m in the height of coke isotherm line segregation at 500 K, while also lowered the average temperature at the coke outlet. Furthermore, we established the improved random pore model with two new equations to describe the evolution of coke porosity and the molar composition of the ambient gas, and real-time tracking of changes in coke porosity and considered the impact of variable gas concentration on coke conversion rate were provided. These findings offer valuable insights and reference for optimizing operational conditions and coke quality prediction in actual production scenarios.

First principle based rate equation (1pRE) for reduction kinetics of Fe2O3 with syngas in chemical looping

Chemical looping combustion (CLC) of solid fuel is a promising technology with inherent CO2 separation and low energy penalty for CO2 capture. Syngas is main intermediate species of solid fuel conversion in CLC, the reduction kinetics of oxygen carriers with syngas play a crucial role in CLC systems. However, the current research obtains the reaction rate constants by fitting the apparent models with the experimental data, and cannot explain the reduction kinetics behavior from a microscopic level. It remains a challenge to compute the reduction kinetics of oxygen carriers with syngas directly from first-principles density functional theory (DFT) without fitting experimental data. This study proposes a first-principle-based rate equation (1pRE) theory and integrates it into the random pore model (RPM) to predict the kinetics of Fe2O3 reduction by syngas in CLC. The developed 1pRE theory utilizes DFT calculations to search for reaction pathways and energy barriers of elementary reactions. Then the DFT data are introduced into the statistical mechanics partition function and transition state theory (TST) to calculate the reaction rate constants. Microkinetic rate equations of elementary reactions occurring at the surface scale are developed to describe the change of surface coverage of different surface species. The 1pRE theory is integrated into the RPM to account for the influence of particle-scale structural changes on the overall conversion rate during the reduction process. The theory can predict the reduction kinetics of oxygen carriers without fitting experimental data and establishes a connection between microscopic insights and macroscopic phenomena. The accuracy was validated by experimental data of Fe2O3 oxygen carriers obtained from the thermogravimetric analyzer (TGA) in the atmosphere of syngas. The developed 1pRE predicts the reduction kinetics of oxygen carriers accurately and can be used to optimize the design of oxygen carrier materials and the scale up of CLC reactors.

Dehydration kinetics of the synthesis of high-nickel cathode materials used in lithium ion batteries

Kinetics of dehydration reactions of cathode precursors such as lithium hydroxide monohydrate (LiOH·H2O) and transition metal hydroxide (NixCoyMnz(OH)2) are identified and modeled using a random pore model (RPM) method.