Vapor-liquid equilibrium data were measured using an automatic static total pressure apparatus fo... more Vapor-liquid equilibrium data were measured using an automatic static total pressure apparatus for binary mixtures of 2-methylpropene + methanol, + 1-propanol, + 2-propanol, + 2-butanol, and + 2-methyl-2-propanol at 364.5 K. The measured p, T, z data were fitted against Legendre polynomials and reduced using Barker's method to obtain phase equilibrium data. In addition to Legendre polynomials, binary interaction parameters were also optimized for Wilson, UNIQUAC, and NRTL activity coefficient models. All binary data showed a positive deviation from the Raoult's law. In addition, azeotropic behavior was observed for the 2-methylpropene + methanol binary mixture.
Industrial Engineering Chemistry Research, Oct 3, 2008
ABSTRACT An improved hydrodynamic model is developed for estimating wetting efficiency, pressure ... more ABSTRACT An improved hydrodynamic model is developed for estimating wetting efficiency, pressure drop, and liquid holdup in trickle-bed reactors. The model is based on the hydrodynamic model presented in Alopaeus et al. [Alopaeus, V.; Hynynen, K.; Aittamaa, J.; Manninen, M. Modeling of Gas−Liquid Packed-Bed Reactor with Momentum Equations and Local Interactions Closures. Ind. Eng. Chem. Res. 2006, 45, 8189.], which is extended to take into account partial wetting of the packing. In addition, the applicability of the 1D model for three-dimensional situations is considered in the process of model development. The wetting efficiency model is formulated on the basis of dimensional analysis and carrying out systematic tests with varying combinations of dimensionless groups. In addition, the wetting efficiency model is not evaluated solely on the wetting efficiency data, but also it is tested systematically with the hydrodynamic model. Furthermore the consistency of the model characteristics to common experimental observations is discussed. Finally, the model’s ability to predict wetting efficiency, dimensionless pressure drop, and liquid saturation was compared to other existing models and improvements were found in all areas. The resulting hydrodynamic model can be used equally as a tool for design and modeling of large scale industrial reactors as well as a tool for complicated three-dimensional simulations.
Modelling is one of the most significant prospective tools for design and analysis of trickle-bed... more Modelling is one of the most significant prospective tools for design and analysis of trickle-bed reactors. Unfortunately, current hydrodynamic models, developed on laboratory experiments, often work poorly in industrial scale. Therefore, physically, more authentic ...
Capillary pressure is considered in packed-beds of spherical particles. In the case of gas–liquid... more Capillary pressure is considered in packed-beds of spherical particles. In the case of gas–liquid flows in packed-bed reactors, capillary pressure gradients can have a significant influence on liquid distribution and, consequently, on the overall reactor performance. In particular, capillary pressure is important for non-uniform liquid distribution, causing liquid spreading as it flows down the packing. An analytical model for capillary pressure–saturation relation is developed for the pendular and funicular regions and the factors affecting capillary pressure in the capillary region are discussed. The present model is compared to the capillary pressure models of Grosser et al. (AIChE J., 34:1850–1860, 1988) and Attou and Ferschneider (Chem. Eng. Sci., 55:491–511, 2000) and to the experiments of Dodds and Srivastava (Part Part Syst. Charact., 23:29–39, 2006) and Dullien et al. (J. Colloid Interface Sci., 127:362–372, 1989). The non-homogeneity of real packings is considered through particle size and porosity distributions. The model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity. This makes the model more suitable for porous or rough particles than for non-porous smooth particles. The main improvements of the present model are found in the pendular region, where the liquid dispersion due to capillary pressure gradients is most significant. The model can be used to improve the hydrodynamic models (e.g., CFD and cellular automata models) for packed-bed reactors, such as trickle-bed reactors, where gas, liquid, and solid phases are present. Models for such reactors have become quite common lately (Sáez and Carbonell, AIChE J., 31:52–62, 1985; Holub et al., Chem. Eng. Sci, 47, 2343–2348, 1992; Attou et al., Chem. Eng. Sci., 54:785–802, 1999; Iliuta and Larachi, Chem. Eng. Sci., 54:5039–5045, 1999, IJCRE 3:R4, 2005; Narasimhan et al., AIChE J., 48:2459–2474, 2002), but they still lack proper terms causing liquid dispersion.
ABSTRACT An algebraic model for the estimation of gas−liquid packed-bed hydrodynamic parameters i... more ABSTRACT An algebraic model for the estimation of gas−liquid packed-bed hydrodynamic parameters is developed, based on one-dimensional material and momentum balances for gas and liquid phases. Underlying momentum exchange closures are critically analyzed, which leads to discarding some interaction models between the phases and development of new models based on local hydrodynamics. The present approach is based on more-relevant assumptions for the particle scale geometry than the slit models presented in the literature. The resulting model requires a one-parameter iterative solution, from which both pressure drop and liquid holdup are obtained. The model can be used without any extra complication in situations where the boundary conditions are specified either at the inlet or at the outlet of the reactor. It is suitable for modeling both low- and high-pressure operations, trickling as well as pulsing flow, upflow and downflow arrangements, and processes with Newtonian as well as non-Newtonian liquids. Finally, the present model is compared to its differential counterpart, and to available experimental data from open literature. Reasonably good agreement was observed for both pressure drop and liquid holdup data from a wide range of operating conditions, using only a single set of Ergun parameters.
ABSTRACT An improved hydrodynamic model is developed for estimating wetting efficiency, pressure ... more ABSTRACT An improved hydrodynamic model is developed for estimating wetting efficiency, pressure drop, and liquid holdup in trickle-bed reactors. The model is based on the hydrodynamic model presented in Alopaeus et al. [Alopaeus, V.; Hynynen, K.; Aittamaa, J.; Manninen, M. Modeling of Gas−Liquid Packed-Bed Reactor with Momentum Equations and Local Interactions Closures. Ind. Eng. Chem. Res. 2006, 45, 8189.], which is extended to take into account partial wetting of the packing. In addition, the applicability of the 1D model for three-dimensional situations is considered in the process of model development. The wetting efficiency model is formulated on the basis of dimensional analysis and carrying out systematic tests with varying combinations of dimensionless groups. In addition, the wetting efficiency model is not evaluated solely on the wetting efficiency data, but also it is tested systematically with the hydrodynamic model. Furthermore the consistency of the model characteristics to common experimental observations is discussed. Finally, the model’s ability to predict wetting efficiency, dimensionless pressure drop, and liquid saturation was compared to other existing models and improvements were found in all areas. The resulting hydrodynamic model can be used equally as a tool for design and modeling of large scale industrial reactors as well as a tool for complicated three-dimensional simulations.
CFD simulations of trickle-bed reactors are presented with radial spreading of the liquid due to ... more CFD simulations of trickle-bed reactors are presented with radial spreading of the liquid due to mechanical and capillary dispersion. Simulations are performed with various particle sizes and the significance of the dispersion mechanisms at the industrially relevant particle size range is analyzed. The effect of the bed porosity distribution and particle size to the simulation results is also discussed. The choice of the radial porosity profile is found to have a significant impact to the simulation results, especially when the column to particle diameter ratio, D/d p , is small, in which case the wall flow is important. The dependence of the standard deviation of porosity on the sample size is determined experimentally. Introducing just random variation of porosity to the model is found to describe inadequately the dispersive flow behavior. The presented hydrodynamic model with proper capillary and mechanical dispersion terms succeeds in capturing the features of the two independent physical phenomena. Separate models are presented for each dispersion mechanisms and it is shown that they both can have a significant contribution to the overall dispersion of liquid flowing through a packed bed. The hydrodynamic model is validated against the experimental dispersion profiles from Herskowitz and Smith [1978. Liquid distribution in trickle-bed reactors. A.I.Ch.E Journal 24, 739-454], Boyer et al. [2005. Study of liquid spreading from a point source in trickle-bed via gamma-ray tomography and CFD simulation. Chemical Engineering Science 60, 6279-6288] and Ravindra et al. [1997. Liquid flow texture in trickle-bed reactors: an experimental study. Industrial & Engineering Chemistry Research, 36, 5133-5145]. The extent of liquid dispersion predicted by the presented hydrodynamic model is in excellent agreement with the experiments.
A cellular automata model for liquid distribution studies in trickle bed reactors is presented. I... more A cellular automata model for liquid distribution studies in trickle bed reactors is presented. It is a potential tool for describing non-uniform distribution of gas and liquid in a trickle bed. This non-uniformity may arise from a wide range of potential sources, such as improper distribution of the feed, random or radial porosity variation, wall effect, partial wetting of the catalyst, and gas-liquid surface tension related effects. Axial and radial dispersion of the liquid flow are inherently included in the model, since the fundamental model probability parameters are directly related to the dispersion coefficients. The present model is extremely fast due to simple single-event modeling, and it is well suited for parallelization. Three examples of the model performance are shown. In the first a liquid jet spreading from a point source is followed, and in the second, effect of radial porosity profile to wall flow is examined. The third example illustrates the potential of the model to predict pulsing flow regime. ᭧
Vapor-liquid equilibrium data were measured using an automatic static total pressure apparatus fo... more Vapor-liquid equilibrium data were measured using an automatic static total pressure apparatus for binary mixtures of 2-methylpropene + methanol, + 1-propanol, + 2-propanol, + 2-butanol, and + 2-methyl-2-propanol at 364.5 K. The measured p, T, z data were fitted against Legendre polynomials and reduced using Barker's method to obtain phase equilibrium data. In addition to Legendre polynomials, binary interaction parameters were also optimized for Wilson, UNIQUAC, and NRTL activity coefficient models. All binary data showed a positive deviation from the Raoult's law. In addition, azeotropic behavior was observed for the 2-methylpropene + methanol binary mixture.
Vapor-liquid equilibrium data were measured using an automatic static total pressure apparatus fo... more Vapor-liquid equilibrium data were measured using an automatic static total pressure apparatus for binary mixtures of 2-methylpropene + methanol, + 1-propanol, + 2-propanol, + 2-butanol, and + 2-methyl-2-propanol at 364.5 K. The measured p, T, z data were fitted against Legendre polynomials and reduced using Barker's method to obtain phase equilibrium data. In addition to Legendre polynomials, binary interaction parameters were also optimized for Wilson, UNIQUAC, and NRTL activity coefficient models. All binary data showed a positive deviation from the Raoult's law. In addition, azeotropic behavior was observed for the 2-methylpropene + methanol binary mixture.
Industrial Engineering Chemistry Research, Oct 3, 2008
ABSTRACT An improved hydrodynamic model is developed for estimating wetting efficiency, pressure ... more ABSTRACT An improved hydrodynamic model is developed for estimating wetting efficiency, pressure drop, and liquid holdup in trickle-bed reactors. The model is based on the hydrodynamic model presented in Alopaeus et al. [Alopaeus, V.; Hynynen, K.; Aittamaa, J.; Manninen, M. Modeling of Gas−Liquid Packed-Bed Reactor with Momentum Equations and Local Interactions Closures. Ind. Eng. Chem. Res. 2006, 45, 8189.], which is extended to take into account partial wetting of the packing. In addition, the applicability of the 1D model for three-dimensional situations is considered in the process of model development. The wetting efficiency model is formulated on the basis of dimensional analysis and carrying out systematic tests with varying combinations of dimensionless groups. In addition, the wetting efficiency model is not evaluated solely on the wetting efficiency data, but also it is tested systematically with the hydrodynamic model. Furthermore the consistency of the model characteristics to common experimental observations is discussed. Finally, the model’s ability to predict wetting efficiency, dimensionless pressure drop, and liquid saturation was compared to other existing models and improvements were found in all areas. The resulting hydrodynamic model can be used equally as a tool for design and modeling of large scale industrial reactors as well as a tool for complicated three-dimensional simulations.
Modelling is one of the most significant prospective tools for design and analysis of trickle-bed... more Modelling is one of the most significant prospective tools for design and analysis of trickle-bed reactors. Unfortunately, current hydrodynamic models, developed on laboratory experiments, often work poorly in industrial scale. Therefore, physically, more authentic ...
Capillary pressure is considered in packed-beds of spherical particles. In the case of gas–liquid... more Capillary pressure is considered in packed-beds of spherical particles. In the case of gas–liquid flows in packed-bed reactors, capillary pressure gradients can have a significant influence on liquid distribution and, consequently, on the overall reactor performance. In particular, capillary pressure is important for non-uniform liquid distribution, causing liquid spreading as it flows down the packing. An analytical model for capillary pressure–saturation relation is developed for the pendular and funicular regions and the factors affecting capillary pressure in the capillary region are discussed. The present model is compared to the capillary pressure models of Grosser et al. (AIChE J., 34:1850–1860, 1988) and Attou and Ferschneider (Chem. Eng. Sci., 55:491–511, 2000) and to the experiments of Dodds and Srivastava (Part Part Syst. Charact., 23:29–39, 2006) and Dullien et al. (J. Colloid Interface Sci., 127:362–372, 1989). The non-homogeneity of real packings is considered through particle size and porosity distributions. The model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity. This makes the model more suitable for porous or rough particles than for non-porous smooth particles. The main improvements of the present model are found in the pendular region, where the liquid dispersion due to capillary pressure gradients is most significant. The model can be used to improve the hydrodynamic models (e.g., CFD and cellular automata models) for packed-bed reactors, such as trickle-bed reactors, where gas, liquid, and solid phases are present. Models for such reactors have become quite common lately (Sáez and Carbonell, AIChE J., 31:52–62, 1985; Holub et al., Chem. Eng. Sci, 47, 2343–2348, 1992; Attou et al., Chem. Eng. Sci., 54:785–802, 1999; Iliuta and Larachi, Chem. Eng. Sci., 54:5039–5045, 1999, IJCRE 3:R4, 2005; Narasimhan et al., AIChE J., 48:2459–2474, 2002), but they still lack proper terms causing liquid dispersion.
ABSTRACT An algebraic model for the estimation of gas−liquid packed-bed hydrodynamic parameters i... more ABSTRACT An algebraic model for the estimation of gas−liquid packed-bed hydrodynamic parameters is developed, based on one-dimensional material and momentum balances for gas and liquid phases. Underlying momentum exchange closures are critically analyzed, which leads to discarding some interaction models between the phases and development of new models based on local hydrodynamics. The present approach is based on more-relevant assumptions for the particle scale geometry than the slit models presented in the literature. The resulting model requires a one-parameter iterative solution, from which both pressure drop and liquid holdup are obtained. The model can be used without any extra complication in situations where the boundary conditions are specified either at the inlet or at the outlet of the reactor. It is suitable for modeling both low- and high-pressure operations, trickling as well as pulsing flow, upflow and downflow arrangements, and processes with Newtonian as well as non-Newtonian liquids. Finally, the present model is compared to its differential counterpart, and to available experimental data from open literature. Reasonably good agreement was observed for both pressure drop and liquid holdup data from a wide range of operating conditions, using only a single set of Ergun parameters.
ABSTRACT An improved hydrodynamic model is developed for estimating wetting efficiency, pressure ... more ABSTRACT An improved hydrodynamic model is developed for estimating wetting efficiency, pressure drop, and liquid holdup in trickle-bed reactors. The model is based on the hydrodynamic model presented in Alopaeus et al. [Alopaeus, V.; Hynynen, K.; Aittamaa, J.; Manninen, M. Modeling of Gas−Liquid Packed-Bed Reactor with Momentum Equations and Local Interactions Closures. Ind. Eng. Chem. Res. 2006, 45, 8189.], which is extended to take into account partial wetting of the packing. In addition, the applicability of the 1D model for three-dimensional situations is considered in the process of model development. The wetting efficiency model is formulated on the basis of dimensional analysis and carrying out systematic tests with varying combinations of dimensionless groups. In addition, the wetting efficiency model is not evaluated solely on the wetting efficiency data, but also it is tested systematically with the hydrodynamic model. Furthermore the consistency of the model characteristics to common experimental observations is discussed. Finally, the model’s ability to predict wetting efficiency, dimensionless pressure drop, and liquid saturation was compared to other existing models and improvements were found in all areas. The resulting hydrodynamic model can be used equally as a tool for design and modeling of large scale industrial reactors as well as a tool for complicated three-dimensional simulations.
CFD simulations of trickle-bed reactors are presented with radial spreading of the liquid due to ... more CFD simulations of trickle-bed reactors are presented with radial spreading of the liquid due to mechanical and capillary dispersion. Simulations are performed with various particle sizes and the significance of the dispersion mechanisms at the industrially relevant particle size range is analyzed. The effect of the bed porosity distribution and particle size to the simulation results is also discussed. The choice of the radial porosity profile is found to have a significant impact to the simulation results, especially when the column to particle diameter ratio, D/d p , is small, in which case the wall flow is important. The dependence of the standard deviation of porosity on the sample size is determined experimentally. Introducing just random variation of porosity to the model is found to describe inadequately the dispersive flow behavior. The presented hydrodynamic model with proper capillary and mechanical dispersion terms succeeds in capturing the features of the two independent physical phenomena. Separate models are presented for each dispersion mechanisms and it is shown that they both can have a significant contribution to the overall dispersion of liquid flowing through a packed bed. The hydrodynamic model is validated against the experimental dispersion profiles from Herskowitz and Smith [1978. Liquid distribution in trickle-bed reactors. A.I.Ch.E Journal 24, 739-454], Boyer et al. [2005. Study of liquid spreading from a point source in trickle-bed via gamma-ray tomography and CFD simulation. Chemical Engineering Science 60, 6279-6288] and Ravindra et al. [1997. Liquid flow texture in trickle-bed reactors: an experimental study. Industrial & Engineering Chemistry Research, 36, 5133-5145]. The extent of liquid dispersion predicted by the presented hydrodynamic model is in excellent agreement with the experiments.
A cellular automata model for liquid distribution studies in trickle bed reactors is presented. I... more A cellular automata model for liquid distribution studies in trickle bed reactors is presented. It is a potential tool for describing non-uniform distribution of gas and liquid in a trickle bed. This non-uniformity may arise from a wide range of potential sources, such as improper distribution of the feed, random or radial porosity variation, wall effect, partial wetting of the catalyst, and gas-liquid surface tension related effects. Axial and radial dispersion of the liquid flow are inherently included in the model, since the fundamental model probability parameters are directly related to the dispersion coefficients. The present model is extremely fast due to simple single-event modeling, and it is well suited for parallelization. Three examples of the model performance are shown. In the first a liquid jet spreading from a point source is followed, and in the second, effect of radial porosity profile to wall flow is examined. The third example illustrates the potential of the model to predict pulsing flow regime. ᭧
Vapor-liquid equilibrium data were measured using an automatic static total pressure apparatus fo... more Vapor-liquid equilibrium data were measured using an automatic static total pressure apparatus for binary mixtures of 2-methylpropene + methanol, + 1-propanol, + 2-propanol, + 2-butanol, and + 2-methyl-2-propanol at 364.5 K. The measured p, T, z data were fitted against Legendre polynomials and reduced using Barker's method to obtain phase equilibrium data. In addition to Legendre polynomials, binary interaction parameters were also optimized for Wilson, UNIQUAC, and NRTL activity coefficient models. All binary data showed a positive deviation from the Raoult's law. In addition, azeotropic behavior was observed for the 2-methylpropene + methanol binary mixture.
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