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Fals J, Ospina-Castro ML, Ramos-Hernández A, Pacheco-Londoño L, Bocanegra S. Deactivation and regeneration dynamics in hierarchical zeolites: Coke characterization and impact on catalytic cracking of vacuum gas oil. Heliyon 2024; 10:e37813. [PMID: 39315141 PMCID: PMC11417176 DOI: 10.1016/j.heliyon.2024.e37813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2024] [Revised: 09/08/2024] [Accepted: 09/10/2024] [Indexed: 09/25/2024] Open
Abstract
This study investigated the deactivation and regeneration of hierarchical zeolites in vacuum gas oil conversion, aiming to reach the equilibrium state seen in fluidized bed catalytic cracking (FCC). The research utilized various characterization techniques to analyze the properties of zeolites before and after coking and regeneration. Zeolite Y-0.20-S was found to have the highest gasoline selectivity and quality, mirroring industrial yields, and displayed notable stability across deactivation/regeneration cycles. Higher mesopore concentration in zeolites led to increased coke selectivity and better resistance to deactivation. The study observed a dominance of aromatic coke with a higher degree of condensation in these zeolites. Despite coke deposition affecting acid and textural properties, the regeneration process effectively restored these characteristics, proving its efficiency. The zeolites with greater mesoporosity retained their fundamental properties responsible for activity and selectivity, highlighting the importance of selecting materials that provide high conversions and maintain stability and product selectivity over multiple cycles. The Y-0.20-S zeolite, in particular, was identified as a promising candidate for commercial catalyst development for gasoline production, contributing to the FCC process's energy efficiency.
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Affiliation(s)
- Jayson Fals
- Grupo de Investigación en Oxi/Hidrotratamiento Catalítico y Nuevos Materiales, Programa de Química-Ciencias Básicas, Universidad del Atlántico, Barranquilla, Colombia
| | - Maria L. Ospina-Castro
- Grupo de Investigación Química Supramolecular Aplicada, Ciencias Básicas, Universidad del Atlántico, Puerto Colombia, Colombia
| | - Andrea Ramos-Hernández
- Grupo de Investigación Química Supramolecular Aplicada, Ciencias Básicas, Universidad del Atlántico, Puerto Colombia, Colombia
| | - Leonardo Pacheco-Londoño
- Centro de Investigaciones en Ciencias de la Vida, Facultad de Ciencias Básicas y Biomédicas, Universidad Simón Bolívar, 080002, Barranquilla, Atlántico, Colombia
| | - Sonia Bocanegra
- Instituto de Investigaciones en Catálisis y Petroquímica “Ing.José M. Parera” (INCAPE)- Universidad. Nacional del Litoral, CONICET, RN 168, Km 0 Paraje El Pozo, Santa Fe, Argentina
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2
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Ramírez J, de Munck M, Liu Z, Rieder DR, Baltussen M, Buist K, Kuipers JAM. CFD-DEM Evaluation of the Clustering Behavior in a Riser-the Effect of the Drag Force Model. Ind Eng Chem Res 2023; 62:18960-18972. [PMID: 38020786 PMCID: PMC10655080 DOI: 10.1021/acs.iecr.3c00853] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Revised: 05/08/2023] [Accepted: 05/10/2023] [Indexed: 12/01/2023]
Abstract
Riser reactors are frequently applied in catalytic processes involving rapid catalyst deactivation. Typically heterogeneous flow structures prevail because of the clustering of particles, which impacts the quality of the gas-solid contact. This phenomenon results as a competition between fluid-particle interaction (i.e., drag) and particle-particle interaction (i.e., collisions). In this study, five drag force correlations were used in a combined computational fluid dynamics-discrete element method Immersed Boundary Model to predict the clustering. The simulation results were compared with experimental data obtained from a pseudo-2D riser in the fast fluidization regime. The clusters were detected on the basis of a core-wake approach using constant thresholds. Although good predictions for the global (solids volume fraction and mass flux) variables and cluster (spatial distribution, size, and number of clusters) variables were obtained with two of the approaches in most of the simulations, all the correlations show significant deviations in the onset of a pneumatic transport regime. However, the correlations of Felice (Int. J. Multiphase Flow1994, 20, 153-159) and Tang et al. [AIChE J.2015, 61 ( (2), ), 688-698] show the closest correspondence for the time-averaged quantities and the clustering behavior in the fast fluidization regime.
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Affiliation(s)
- Juan Ramírez
- Multiphase Reactors Group,
Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Martijn de Munck
- Multiphase Reactors Group,
Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Zhitao Liu
- Multiphase Reactors Group,
Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - David Raphael Rieder
- Multiphase Reactors Group,
Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Maike Baltussen
- Multiphase Reactors Group,
Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Kay Buist
- Multiphase Reactors Group,
Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Johannes A. M.
Hans Kuipers
- Multiphase Reactors Group,
Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
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3
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Shakor ZM, Al-Shafei EN. The mathematical catalyst deactivation models: a mini review. RSC Adv 2023; 13:22579-22592. [PMID: 37501777 PMCID: PMC10369042 DOI: 10.1039/d3ra02912c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 07/12/2023] [Indexed: 07/29/2023] Open
Abstract
Catalyst deactivation is a complex phenomenon and identifying an appropriate deactivation model is a key effort in the catalytic industry and plays a significant role in catalyst design. Accurate determination of the catalyst deactivation model is essential for optimizing the catalytic process. Different mechanisms of catalyst deactivation by coke and metal deposition lead to different deactivation models for catalyst activity decay. In the rigorous mathematical models of the reactors, the reaction kinetics were coupled with the deactivation kinetic equation to evaluate the product distribution with respect to conversion time. Finally, selective and nonselective deactivation kinetic models were designed to identify catalyst deactivation through the propagation of heterogeneous chemical reactions. Therefore, the present review discusses the catalyst deactivation models designed for CO2 hydrogenation, Fischer-Tropsch, biofuels and fossil fuels, which can facilitate the efforts to better represent the catalyst activities in various catalytic systems.
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Affiliation(s)
- Zaidoon M Shakor
- Chemical Engineering Department, University of Technology Baghdad Iraq
| | - Emad N Al-Shafei
- Research and Development Center, Saudi Aramco Dhahran 31311 Saudi Arabia
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5
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Puviyarasi B, Murukesh C, Alagiri M. Design and implementation of gain scheduling decentralized PI/PID controller for the fluid catalytic cracking unit. Biomed Signal Process Control 2022. [DOI: 10.1016/j.bspc.2022.103780] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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6
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Yang Y, Zhang Q, Pan T, Qu Y, Liu X, Li X, Cheng Y, Wang L, Liu W. The hydrodynamics of low-density particles and optimization of the EMMS calculation process. POWDER TECHNOL 2022. [DOI: 10.1016/j.powtec.2022.117511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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7
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Zhong H, Chen J, Gao F, Zhang J, Zhu Y, Niu B. 3D virtual full-loop CFD simulation of industrial two-stage FCC reaction–regeneration system. INTERNATIONAL JOURNAL OF CHEMICAL REACTOR ENGINEERING 2022. [DOI: 10.1515/ijcre-2021-0249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
The 3D virtual full-loop CFD simulation method with two-fluid model (TFM) was developed to model an industrial two-stage FCC reaction–regeneration system. The virtual connections (mass, species, and energy) between riser reactors, disengager, stripper, and regenerator were realized by defining user-defined functions (UDFs) for boundary conditions according to the reality. Five correction factors were used to correct the reaction rates in the 14-lump FCC reaction kinetics, and two correction factors were used to correct the FCC reaction heat in the first and second riser reactors. As a result, the whole FCC reaction–regeneration system was successfully modeled in one single CFD case. A thorough and comprehensive view of the performance of reaction–regeneration system was obtained by the 3D virtual full-loop CFD simulation, which is helpful for the operating and optimization of FCC unit. The major predicted results were in a good agreement with the industrial data. The effects of operating conditions were also investigated by changing regenerated temperature, catalyst to oil (CTO) ratio, and process capacity.
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Affiliation(s)
- Hanbin Zhong
- Engineering Research Center of Low Carbon Energy & Chemical, College of Chemistry and Chemical Engineering, Xi’an Shiyou University , Xi’an , Shaanxi , 710065 , China
| | - Jing Chen
- Petrochemical Research Institute of PetroChina , Beijing , 102206 , China
| | - Fei Gao
- Petrochemical Research Institute of PetroChina , Beijing , 102206 , China
| | - Juntao Zhang
- Engineering Research Center of Low Carbon Energy & Chemical, College of Chemistry and Chemical Engineering, Xi’an Shiyou University , Xi’an , Shaanxi , 710065 , China
| | - Yuqin Zhu
- Engineering Research Center of Low Carbon Energy & Chemical, College of Chemistry and Chemical Engineering, Xi’an Shiyou University , Xi’an , Shaanxi , 710065 , China
| | - Ben Niu
- Engineering Research Center of Low Carbon Energy & Chemical, College of Chemistry and Chemical Engineering, Xi’an Shiyou University , Xi’an , Shaanxi , 710065 , China
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Abstract
Heavy petroleum industries, including the Fluid Catalytic Cracking (FCC) unit, are among some of the biggest contributors to global greenhouse gas (GHG) emissions. The FCC unit’s regenerator is where these emissions originate mostly, meaning the operation of FCC regenerators has come under scrutiny in recent years due to the global mitigation efforts against climate change, affecting both current operations and the future of the FCC unit. As a result, it is more important than ever to develop models that are accurate and reliable at predicting emissions of various greenhouse gases to keep up with new reporting guidelines that will help optimise the unit for increased coke conversion and lower operating costs. Part 1 of this paper was dedicated to reviewing the riser section of the FCC unit. Part 2 reviews traditional modelling methodologies used in modelling and simulating the FCC regenerator. Hydrodynamics and kinetics of the regenerator are discussed in terms of experimental data and modelling. Modelling of constitutive parts that are important to the FCC unit, such as gas–solid cyclones and catalyst transport lines, are also considered. This review then identifies areas where the current generation of models of the regenerator can be improved for the future. Parts 1 and 2 are such that a comprehensive review of the literature on modelling the FCC unit is presented, showing the guidance and framework followed in building models for the unit.
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A Review of Modelling of the FCC Unit–Part I: The Riser. ENERGIES 2022. [DOI: 10.3390/en15010308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Heavy petroleum industries, including the fluid catalytic cracking (FCC) unit, are useful for producing fuels but they are among some of the biggest contributors to global greenhouse gas (GHG) emissions. The recent global push for mitigation efforts against climate change has resulted in increased legislation that affects the operations and future of these industries. In terms of the FCC unit, on the riser side, more legislation is pushing towards them switching from petroleum-driven energy sources to more renewable sources such as solar and wind, which threatens the profitability of the unit. On the regenerator side, there is more legislation aimed at reducing emissions of GHGs from such units. As a result, it is more important than ever to develop models that are accurate and reliable, that will help optimise the unit for maximisation of profits under new regulations and changing trends, and that predict emissions of various GHGs to keep up with new reporting guidelines. This article, split over two parts, reviews traditional modelling methodologies used in modelling and simulation of the FCC unit. In Part I, hydrodynamics and kinetics of the riser are discussed in terms of experimental data and modelling approaches. A brief review of the FCC feed is undertaken in terms of characterisations and cracking reaction chemistry, and how these factors have affected modelling approaches. A brief overview of how vaporisation and catalyst deactivation are addressed in the FCC modelling literature is also undertaken. Modelling of constitutive parts that are important to the FCC riser unit such as gas-solid cyclones, disengaging and stripping vessels, is also considered. This review then identifies areas where current models for the riser can be improved for the future. In Part II, a similar review is presented for the FCC regenerator system.
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10
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Li A, Wang Z, Zhu L, Wang Z, Xu X, Fang L. Numerical analysis of hydrodynamic characteristics and interphase coupling in a gas‐solid cyclone reactor. CAN J CHEM ENG 2021. [DOI: 10.1002/cjce.24079] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Anjun Li
- College of New Energy, China University of Petroleum (East China) Qindao China
| | - Zhenbo Wang
- College of New Energy, China University of Petroleum (East China) Qindao China
| | - Liyun Zhu
- College of New Energy, China University of Petroleum (East China) Qindao China
| | - Ziyi Wang
- College of New Energy, China University of Petroleum (East China) Qindao China
| | - Xiaogang Xu
- College of New Energy, China University of Petroleum (East China) Qindao China
| | - Liang Fang
- College of New Energy, China University of Petroleum (East China) Qindao China
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11
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Du S, Liu L. A bubble structure dependent drag model for
CFD
simulation of bi‐disperse gas‐solid flow in bubbling fluidizations. CAN J CHEM ENG 2021. [DOI: 10.1002/cjce.24053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Shaohua Du
- School of Chemical Engineering and Technology Xi'an Jiaotong University Xi'an China
| | - Lijun Liu
- Key Laboratory of Thermo‐Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University Xi'an China
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12
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A Model of Catalytic Cracking: Product Distribution and Catalyst Deactivation Depending on Saturates, Aromatics and Resins Content in Feed. Catalysts 2021. [DOI: 10.3390/catal11060701] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The problems of catalyst deactivation and optimization of the mixed feedstock become more relevant when the residues are involved as a catalytic cracking feedstock. Through numerical and experimental studies of catalytic cracking, we optimized the composition of the mixed feedstock in order to minimize the catalyst deactivation by coke. A pure vacuum gasoil increases the yields of the wet gas and the gasoline (56.1 and 24.9 wt%). An increase in the ratio of residues up to 50% reduces the gasoline yield due to the catalyst deactivation by 19.9%. However, this provides a rise in the RON of gasoline and the light gasoil yield by 1.9 units and 1.7 wt% Moreover, the ratio of residue may be less than 50%, since the conversion is limited by the regenerator coke burning ability.
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Predicting cold gas-solid flow in a pilot-scale dual-circulating fluidized bed: Validation of computational particle fluid dynamics model. POWDER TECHNOL 2021. [DOI: 10.1016/j.powtec.2020.11.070] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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14
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Zhang H, Li W, Ma Q, Zhang Y, Lei F. Numerical study on influence of exit geometry in gas–solid flow hydrodynamics of HDCFB riser by CPFD. ADV POWDER TECHNOL 2020. [DOI: 10.1016/j.apt.2020.08.006] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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15
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Analysis of flexible ribbon particle residence time distribution in a fluidised bed riser using three-dimensional CFD-DEM simulation. POWDER TECHNOL 2020. [DOI: 10.1016/j.powtec.2020.05.025] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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16
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Tiwari SS, Pal E, Bale S, Minocha N, Patwardhan AW, Nandakumar K, Joshi JB. Flow past a single stationary sphere, 2. Regime mapping and effect of external disturbances. POWDER TECHNOL 2020. [DOI: 10.1016/j.powtec.2019.04.032] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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17
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Wanchan W, Khongprom P, Limtrakul S. Study of wall-to-bed heat transfer in circulating fluidized bed riser based on CFD simulation. Chem Eng Res Des 2020. [DOI: 10.1016/j.cherd.2020.02.021] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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18
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A hybrid deep learning and mechanistic kinetics model for the prediction of fluid catalytic cracking performance. Chem Eng Res Des 2020. [DOI: 10.1016/j.cherd.2020.01.013] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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19
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Mu L, Buist K, Kuipers J, Deen N. Scaling method of CFD-DEM simulations for gas-solid flows in risers. CHEMICAL ENGINEERING SCIENCE: X 2020. [DOI: 10.1016/j.cesx.2019.100054] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022] Open
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20
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Wang S, Zhao X, Tian R, Chen Y, Sun Q, Fan J, Ma Y. Numerical simulation of gas-solid two-phase flow in a two-stage series riser using the filtered model. POWDER TECHNOL 2019. [DOI: 10.1016/j.powtec.2019.01.063] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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21
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Comparison of solid phase closure models in Eulerian-Eulerian simulations of a circulating fluidized bed riser. Chem Eng Sci 2019. [DOI: 10.1016/j.ces.2018.11.031] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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22
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Long J, Li T, Yang M, Hu G, Zhong W. Hybrid Strategy Integrating Variable Selection and a Neural Network for Fluid Catalytic Cracking Modeling. Ind Eng Chem Res 2018. [DOI: 10.1021/acs.iecr.8b04821] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jian Long
- Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
| | - Tianyue Li
- Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
| | - Minglei Yang
- Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
| | - Guihua Hu
- Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
| | - Weimin Zhong
- Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
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Feng X, Shen L, Wang L. Effect of baffle on hydrodynamics in the air reactor of dual circulating fluidized bed for chemical looping process. POWDER TECHNOL 2018. [DOI: 10.1016/j.powtec.2018.09.012] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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24
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Gao X, Li T, Rogers WA. Assessment of mesoscale solid stress in coarse‐grid TFM simulation of Geldart A particles in all fluidization regimes. AIChE J 2018. [DOI: 10.1002/aic.16341] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Xi Gao
- National Energy Technology Laboratory Morgantown WV, 26507
| | - Tingwen Li
- National Energy Technology Laboratory, Morgantown, WV, 26507 and AECOM Morgantown WV, 26505
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Gao X, Li T, Sarkar A, Lu L, Rogers WA. Development and validation of an enhanced filtered drag model for simulating gas-solid fluidization of Geldart A particles in all flow regimes. Chem Eng Sci 2018. [DOI: 10.1016/j.ces.2018.03.038] [Citation(s) in RCA: 98] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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26
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Numerical study of the accuracy of temperature measurement by thermocouples in small-scale reactors. Chem Eng Res Des 2018. [DOI: 10.1016/j.cherd.2017.06.003] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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27
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Lu B, Zhang J, Luo H, Wang W, Li H, Ye M, Liu Z, Li J. Numerical simulation of scale-up effects of methanol-to-olefins fluidized bed reactors. Chem Eng Sci 2017. [DOI: 10.1016/j.ces.2017.05.007] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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28
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Three-dimensional modeling of biomass fuel flow in a circulating fluidized bed furnace with an experimentally derived momentum exchange model. Chem Eng Res Des 2016. [DOI: 10.1016/j.cherd.2016.09.023] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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