Transient analysis of isothermal fluid—solid reaction systems: Modeling the sigmoidal conversion—time behavior of a gas—solid reaction

Development of Solid–Fluid Reaction Models—A Literature Review

“…More research efforts should be dedicated to this important area in the future; (4) 1D homogeneous plug-flow model is most commonly used in practical engineering applications to simulate particle reactions in a fixed bed, while 3D discrete particle model requires significant computational time though attracting increasing academic research interest recently; (5) The critical particle size below which the particle internal heat and mass transfer becomes insignificant depends on the specific application conditions; (6) The flow rate of reactant fluid, can increase, decrease, or have negligible influence on the reaction rate in the fixed bed, depending on the specific application conditions; (7) There is a lack of a general correlation for voidage of bed for practical particles, which normally have irregular shapes. Therefore, more research efforts are needed in this area; (8) The hydrodynamic behaviors of the fluidized bed reactor have a significant influence on the performance of the reactor, such as fluid dynamics affects both heat and mass transfer. In a fluidized bed reactor, the smaller the particle size, the stronger the heat and mass transfer, and the higher the conversion rate; (9) Fluidization velocity can increase the heat and mass transfer and thus enhance the conversion rate.…”

“…The reaction rate depends on several parameters, including particle shape, particle size, particle morphology, particle pore structure, chemical kinetics, fluid flow condition, and heat and mass transfer, etc. [8][9][10][11][12][13][14][15][16]. Furthermore, more complexity is added when the reactions occur in different types of reactors, including a reactor where papers published with keywords "solid reaction modelling" plus "single-particle model" versus "solid reaction modelling" plus "Computational Fluid Dynamics/CFD" according to Web of Science.…”

Development of Solid–Fluid Reaction Models—A Literature Review

“…More research efforts should be dedicated to this important area in the future; (4) 1D homogeneous plug-flow model is most commonly used in practical engineering applications to simulate particle reactions in a fixed bed, while 3D discrete particle model requires significant computational time though attracting increasing academic research interest recently; (5) The critical particle size below which the particle internal heat and mass transfer becomes insignificant depends on the specific application conditions; (6) The flow rate of reactant fluid, can increase, decrease, or have negligible influence on the reaction rate in the fixed bed, depending on the specific application conditions; (7) There is a lack of a general correlation for voidage of bed for practical particles, which normally have irregular shapes. Therefore, more research efforts are needed in this area; (8) The hydrodynamic behaviors of the fluidized bed reactor have a significant influence on the performance of the reactor, such as fluid dynamics affects both heat and mass transfer. In a fluidized bed reactor, the smaller the particle size, the stronger the heat and mass transfer, and the higher the conversion rate; (9) Fluidization velocity can increase the heat and mass transfer and thus enhance the conversion rate.…”

“…The reaction rate depends on several parameters, including particle shape, particle size, particle morphology, particle pore structure, chemical kinetics, fluid flow condition, and heat and mass transfer, etc. [8][9][10][11][12][13][14][15][16]. Furthermore, more complexity is added when the reactions occur in different types of reactors, including a reactor where papers published with keywords "solid reaction modelling" plus "single-particle model" versus "solid reaction modelling" plus "Computational Fluid Dynamics/CFD" according to Web of Science.…”

Dry Regenerable Metal Oxide Sorbents for SO2 Removal from Flue Gases. 2. Modeling of the Sulfation Reaction Involving Copper Oxide Sorbents

“…A comprehensive list of empirical models for effective diffusivity can be found elsewhere. [10][11][12] In this study, an exponential function [i.e., exp(RX O )] was used to describe the tortuosity parameter R. A similar functional form has also been used by Shaaban 13 and Karnik, 14 while modeling the sulfation of calcined limestone. Therefore, the dependence of effective diffusivity on the sorbent conversion is determined from Equations 1 and 2 were approximated by finite difference formulation and solved as a boundary value problem.…”

“…Therefore, the effective diffusivity of the SO 2 through the solid particle and its dependence on the particle conversion is modeled using empirical equations with adjustable parameters that are determined from the experimental data. A comprehensive list of empirical models for effective diffusivity can be found elsewhere. − In this study, an exponential function [i.e., exp(α X O )] was used to describe the tortuosity parameter α. A similar functional form has also been used by Shaaban and Karnik, while modeling the sulfation of calcined limestone.…”

Noncatalytic gas‐solid reactions in a vertical pneumatic transport reactor

“…3 is the void fraction of the particle. It is assumed that over a given range of the solid conversion, relationship between dC2 br r = ro; D e~ __ = kd(C1 -Cz) E and the solid concentration can be approximated by (Wen, 1968;Fan et al, 1977): where €0 is the void fraction of the particle at the initial condition.…”

Development of Solid–Fluid Reaction Models—A Literature Review

“…More research efforts should be dedicated to this important area in the future; (4) 1D homogeneous plug-flow model is most commonly used in practical engineering applications to simulate particle reactions in a fixed bed, while 3D discrete particle model requires significant computational time though attracting increasing academic research interest recently; (5) The critical particle size below which the particle internal heat and mass transfer becomes insignificant depends on the specific application conditions; (6) The flow rate of reactant fluid, can increase, decrease, or have negligible influence on the reaction rate in the fixed bed, depending on the specific application conditions; (7) There is a lack of a general correlation for voidage of bed for practical particles, which normally have irregular shapes. Therefore, more research efforts are needed in this area; (8) The hydrodynamic behaviors of the fluidized bed reactor have a significant influence on the performance of the reactor, such as fluid dynamics affects both heat and mass transfer. In a fluidized bed reactor, the smaller the particle size, the stronger the heat and mass transfer, and the higher the conversion rate; (9) Fluidization velocity can increase the heat and mass transfer and thus enhance the conversion rate.…”

“…The reaction rate depends on several parameters, including particle shape, particle size, particle morphology, particle pore structure, chemical kinetics, fluid flow condition, and heat and mass transfer, etc. [8][9][10][11][12][13][14][15][16]. Furthermore, more complexity is added when the reactions occur in different types of reactors, including a reactor where papers published with keywords "solid reaction modelling" plus "single-particle model" versus "solid reaction modelling" plus "Computational Fluid Dynamics/CFD" according to Web of Science.…”

Dry Regenerable Metal Oxide Sorbents for SO2 Removal from Flue Gases. 2. Modeling of the Sulfation Reaction Involving Copper Oxide Sorbents

“…A comprehensive list of empirical models for effective diffusivity can be found elsewhere. [10][11][12] In this study, an exponential function [i.e., exp(RX O )] was used to describe the tortuosity parameter R. A similar functional form has also been used by Shaaban 13 and Karnik, 14 while modeling the sulfation of calcined limestone. Therefore, the dependence of effective diffusivity on the sorbent conversion is determined from Equations 1 and 2 were approximated by finite difference formulation and solved as a boundary value problem.…”

“…Therefore, the effective diffusivity of the SO 2 through the solid particle and its dependence on the particle conversion is modeled using empirical equations with adjustable parameters that are determined from the experimental data. A comprehensive list of empirical models for effective diffusivity can be found elsewhere. − In this study, an exponential function [i.e., exp(α X O )] was used to describe the tortuosity parameter α. A similar functional form has also been used by Shaaban and Karnik, while modeling the sulfation of calcined limestone.…”

Noncatalytic gas‐solid reactions in a vertical pneumatic transport reactor

“…3 is the void fraction of the particle. It is assumed that over a given range of the solid conversion, relationship between dC2 br r = ro; D e~ __ = kd(C1 -Cz) E and the solid concentration can be approximated by (Wen, 1968;Fan et al, 1977): where €0 is the void fraction of the particle at the initial condition.…”

Development of Solid–Fluid Reaction Models—A Literature Review

“…More research efforts should be dedicated to this important area in the future; (4) 1D homogeneous plug-flow model is most commonly used in practical engineering applications to simulate particle reactions in a fixed bed, while 3D discrete particle model requires significant computational time though attracting increasing academic research interest recently; (5) The critical particle size below which the particle internal heat and mass transfer becomes insignificant depends on the specific application conditions; (6) The flow rate of reactant fluid, can increase, decrease, or have negligible influence on the reaction rate in the fixed bed, depending on the specific application conditions; (7) There is a lack of a general correlation for voidage of bed for practical particles, which normally have irregular shapes. Therefore, more research efforts are needed in this area; (8) The hydrodynamic behaviors of the fluidized bed reactor have a significant influence on the performance of the reactor, such as fluid dynamics affects both heat and mass transfer. In a fluidized bed reactor, the smaller the particle size, the stronger the heat and mass transfer, and the higher the conversion rate; (9) Fluidization velocity can increase the heat and mass transfer and thus enhance the conversion rate.…”

“…The reaction rate depends on several parameters, including particle shape, particle size, particle morphology, particle pore structure, chemical kinetics, fluid flow condition, and heat and mass transfer, etc. [8][9][10][11][12][13][14][15][16]. Furthermore, more complexity is added when the reactions occur in different types of reactors, including a reactor where papers published with keywords "solid reaction modelling" plus "single-particle model" versus "solid reaction modelling" plus "Computational Fluid Dynamics/CFD" according to Web of Science.…”

Dry Regenerable Metal Oxide Sorbents for SO2 Removal from Flue Gases. 2. Modeling of the Sulfation Reaction Involving Copper Oxide Sorbents

“…A comprehensive list of empirical models for effective diffusivity can be found elsewhere. [10][11][12] In this study, an exponential function [i.e., exp(RX O )] was used to describe the tortuosity parameter R. A similar functional form has also been used by Shaaban 13 and Karnik, 14 while modeling the sulfation of calcined limestone. Therefore, the dependence of effective diffusivity on the sorbent conversion is determined from Equations 1 and 2 were approximated by finite difference formulation and solved as a boundary value problem.…”

“…Therefore, the effective diffusivity of the SO 2 through the solid particle and its dependence on the particle conversion is modeled using empirical equations with adjustable parameters that are determined from the experimental data. A comprehensive list of empirical models for effective diffusivity can be found elsewhere. − In this study, an exponential function [i.e., exp(α X O )] was used to describe the tortuosity parameter α. A similar functional form has also been used by Shaaban and Karnik, while modeling the sulfation of calcined limestone.…”

Noncatalytic gas‐solid reactions in a vertical pneumatic transport reactor

“…3 is the void fraction of the particle. It is assumed that over a given range of the solid conversion, relationship between dC2 br r = ro; D e~ __ = kd(C1 -Cz) E and the solid concentration can be approximated by (Wen, 1968;Fan et al, 1977): where €0 is the void fraction of the particle at the initial condition.…”