2,381 research outputs found
Population balance model and experimental validation for reactive dissolution of particle agglomerates
No full textWe propose a population balance model coupled with a mass transfer model to simulate the simultaneous shrinkage and breakage of particles during the reactive dissolution of particle agglomerates in stirred tank. The high-order moment-conserving method of classes is adopted to solve the population balance model. In the mass transfer model, the driving force is estimated by considering the physical constraints including electroneutrality, water dissociation and dissolution equilibrium. The simulation results, including the concentration and the particle size distribution of the final products, were validated by experiments carried out in a laboratory scale stirred tank. The unknown physical parameters in the particle breakage model were fitted against the experimental data. The results underline the importance of particle breakage in the reactive dissolution modeling under the investigated operating conditions. Several daughter size distributions functions found in literature were tested. Among them, the beta distribution provides the most flexible way to describe breakage of the particle agglomerates
Modeling chlorine dioxide bleaching of chemical pulp
No full textThis doctoral thesis deals with the phenomenon-based modeling of pulp bleaching. Previous bleaching models typically utilize one or two empirical correlations to predict the kinetics in kappa number development. Empirical correlations are simple to develop, but their parameters are often tied to the validation system. A major benefit of physico-chemical phenomenon models is that they are valid regardless of the reaction environment. Furthermore, modeling the bleaching processes at molecular level provides a new way to examine the relative importance of various phenomena, the validity of theories and the bottlenecks of bleaching applications.
The first part of the thesis introduces a model for the pulp suspension environment and describes the physico-chemical models in use (reaction kinetics, mass transfer, thermodynamics). The second part deals with inorganic oxychlorine reactions related to chlorine dioxide bleaching. The reaction kinetics and mechanism are documented for iron- mediated chlorite decomposition, chlorous acid self-decomposition, and for the reaction between hypochlorous acid and chlorous acid. The rate coefficient temperature dependency is reported for the two latter reactions. The reaction kinetic models were utilized in assessing the potential chlorate formation routes encountered in pulp bleaching. It was concluded that chlorous acid self-decomposition is unlikely to contribute to chlorate formation in bleaching applications. The iron-mediated chlorite decomposition and the reaction between hypochlorous acid and chlorous acid are expected to produce chlorate.
The last part introduces a model for chlorine dioxide delignification. Here the pulp suspension model was combined with a broad set of chemical reactions describing the ClO2 bleaching chemistry. The incorporated reactions cover lignin oxidation, lignin chlorination, hexenuronic acid degradation, lignin dissolution, oxidation of extractives and the essential inorganic oxychlorine reactions. The model predictions were compared against experimental delignification results in order to validate the model and obtain the previously unknown reaction rate parameters. The predictions were generally in good agreement with experimental results. Deviations related primarily to hypochlorous acid driven processes: organochlorine formation, hexenuronic acid degrading reactions, chlorite depletion or chlorate formation. The simulation results suggest that organochlorine formation is restricted by the amount of chlorination-susceptible substrates in pulp rather than the availability of chlorine. It was also concluded that, in addition to the fully inorganic reactions, chlorite is also likely to be consumed in reactions with pulp-related compounds, for instance with aldehydes
Calculation of multicomponent mass transfer between dispersed and continuous phases
No full textIn many industrially important unit operations, mass transfer between dispersed and continuous phases takes place. The accurate and fast solution of the mass transfer model equations is essential in order to design these unit operations accurately.
The mass transfer rate between phases is calculated in two parts. The first part is to solve the interphasial mass transfer fluxes. With multicomponent systems, this is best done with the Maxwell-Stefan diffusion model along with a mass transfer model. The other part is to calculate the mass transfer area between the phases. This can be done with population balance models, preferably with a flow model that discriminates various regions of the modeled system. The flow model is needed if the phenomena affecting the development of the mass transfer area are not homogeneous in separate parts of the considered region. The mass transfer rate needed in the material balances is then a product of the mass transfer fluxes and the mass transfer area.
The mass transfer calculations with the Maxwell-Stefan model leads to complicated matrix function calculations. This is very time consuming because these models need to be solved many times during the solution of a unit operation or reactor model. Two simplifications to these complicated functions are presented in this work. The first is a method to calculate general matrix functions related to the multicomponent mass transfer models approximately. It is based on the fact that the diffusion coefficient matrices have larger diagonal than off-diagonal elements. The other approximation is a linearization of the high flux correction. The applicability of these two approximations, along with other modeling aspects, is considered with a distillation tray model. An approximation was also presented in this work for calculating diffusion, and further the mass transfer coefficients, within spherical particles.
A population balance approach is used with a stirred tank flow model to calculate drop size distributions in liquid-liquid dispersions. In order to test the applicability of the flow model with population balances, drop size distributions are measured and the drop breakage and coalescence function parameter values are estimated. The inhomogeneous character of the dispersion in a stirred tank can be used in the parameter estimation process.reviewe
Improved Hydrodynamic Model for Wetting Efficiency, Pressure Drop, and Liquid Holdup in Trickle-Bed Reactors
No full textAn 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
Approximating catalyst effectiveness factors with reaction rate profiles
No full textA novel approximate solution for catalyst effectiveness factors is presented. It is based on carefully selected approximate reaction rate profiles, instead of typical assumption of composition profiles inside the catalyst. This formulation allows analytical solution of the approximate model, leading to a very simple iterative solution for effectiveness factor for general nonlinear reaction stoichiometry and arbitrary catalyst particle shape. The same model can be used with all practical Thiele modulus values, including multicomponent systems with inert compounds. Furthermore, the correct formulation of the underlying physical model equation is discussed. It is shown that an incorrect but often-used model formulation where convective mass transfer has been neglected may lead to much higher errors than the present approximation. Even with a correctly formulated physical model, rigorous discretization of the catalyst particle volume may have unexpectedly high numerical errors, even exceeding those with the present approximate solution. The proposed approximate solution was tested with a number of examples. The first was an equimolar reaction with first order kinetics, for which analytical solutions are available for the standard catalyst particle geometries (slab, long cylinder, and sphere). Then, the method was tested with a second order reaction in three cases: (1) with one pure reactant, (2) with inert present, and (3) with two reactants and non-stoichiometric surface concentrations. Finally, the method was tested with an industrially relevant catalytic toluene hydrogenation including Maxwell-Stefan formulation for the diffusion fluxes. In all the tested systems, the results were practically identical when compared to the analytical solutions or rigorous finite volume solution of the same problem.Peer reviewe
Modeling surfactant and drop size dynamics in polydisperse liquid-liquid systems with population balances
No full textFunding Information: None. Publisher Copyright: © 2021 The AuthorA population balance framework based on high order moment conserving method of classes is extended to capture surfactant dynamics and its effect on drop size distributions. The proposed method is flexible for incorporating various closure models for drop breakage and coalescence, mass transfer, and physical equilibria between dispersed and continuous phase as well as for adsorption to the interface. The method is first schematically explained and derived in a generic form, and then appropriate closure models are discussed. The model is accurate and fast and can be implemented in process models, parameter optimization algorithms, and computational fluid dynamics software due to its high accuracy with limited number of additional variables.Peer reviewe
Improved Hydrodynamic Model for Wetting Efficiency, Pressure Drop, and Liquid Holdup in Trickle-Bed Reactors
No full textAn 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 the fragmentation kinetics of the heterogeneous lignin macromolecule during kraft pulping with stochastic graphs
No full textFunding Information: This work was financially supported and part of the Academy of Finland’s Flagship Program under Projects No. 318890 and 318891 (Competence Center for Materials Bioeconomy, FinnCERES). Publisher Copyright: © 2023 The Author(s)This article presents a novel concept for modelling the kinetics and related phenomena of the kraft pulping process on a macromolecule level with the initial objective to explicitly model and relate the breakage of phenolic and non-phenolic β—O—4 bonds to the observed three-stage delignification profile. The modelling frameworks consist of the building and the fragmentation of the lignin macromolecules. The macromolecules are modelled as stochastic graphs where monolignol object nodes are reassembled in a Monte Carlo approach into internal structures, which aggregate to a lignin macromolecule interconnected through chemical bonds represented by the edges of the graphs. The fractionation follows the splitting of β—O—4 ether bonds with different configurations resulting from functional groups attached to the monolignols, namely the phenolic and non-phenolic β—O—4 bonds with their respective stereochemistry. It is tested against a previously published model based on an extension of the established Purdue kinetic model and experimental data. The results align with the observed delignification trajectory during kraft pulping, and the hypothesis that β—O—4 bonds splitting is mainly responsible for the delignification. However, some discrepancies between the current model, the previous model and experimental data are presented. These differences are discussed in the context of recent experimental findings indicating that β—O—4 bonds splitting might not entirely be responsible for the delignification due to mass transfer/solubility effects limitations.Peer reviewe
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