Modelo de un lecho fluidizado de flujo descendente bifásico y trifásico
Downflow fluidization is an attractive unit operation because it allows a smooth circulation of the fluid and the solid support material, as well as an uninterrupted and controlled operation of the fluid to be treated. The motivation of this work, is based on the search for mathematical models that...
| Autor: | |
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | México |
| Institución: | Universidad Autónoma Metropolitana |
| Repositorio: | Repositorio Institucional de la UAM Iztapalapa |
| Idioma: | español |
| OAI Identifier: | oai:bindani.izt.uam.mx:g732d907d |
| Acceso en línea: | https://doi.org/10.24275/uami.g732d907d |
| Access Level: | acceso abierto |
| Palabra clave: | info:eu-repo/classification/LEM/Fluidización info:eu-repo/classification/LEM/Aguas residuales -- Purificación -- Modelos matemáticos info:eu-repo/classification/LEM/Fluidization info:eu-repo/classification/LEM/Hydrodynamics -- Mathematical models info:eu-repo/classification/LEM/Sewage -- Purification -- Mathematical models info:eu-repo/classification/LEM/Mathematical physics info:eu-repo/classification/LEM/Hidrodinámica -- Modelos matemáticos info:eu-repo/classification/LEM/Física matemática info:eu-repo/classification/cti/7 |
| Sumario: | Downflow fluidization is an attractive unit operation because it allows a smooth circulation of the fluid and the solid support material, as well as an uninterrupted and controlled operation of the fluid to be treated. The motivation of this work, is based on the search for mathematical models that allow describing this phenomenon and support hydrodynamic description during wastewater treatment. The models presented in this work are based on the operational physics of downflow fluidization. The main feature of these systems is the minimum fluidization velocity curve, which does not have a plateau where the pressure drop is constant, unlike the upward fluidization systems where it does exist. This pressure drop is given as a function of the density of the particles used. In downwflow fluidization systems, the density of the particles is less than the density of the fluid where they are dispersed. Momentum transport in fluidized beds is generally modeled by macroscopic models. These models are expressed in terms of effective transport coefficients that result from analogies of transport in porous media, which in this case are assumed as a fixed bed. In practice, it is desirable to deduce these models and predict the coefficients involved in a reliable manner, by obtaining the physical meaning of these coefficients associated with momentum transport. The fluidized bed to be modeled is a three-phase system that contains solid particles, the gas that is produced by treating wastewater and the liquid where both, particles and gas bubbles are immersed and interacting. Due to the mathematical complexity of directly addressing the threephase system, the development of this work in a phased manner is proposed. This means that the two-phase liquid-solid and liquid-gas interactions are analyzed first, from which the physical characteristics, average regions along with the proposal of equations and associated boundary conditions are obtained. Once these analyses have been carried out and these parameters have been obtained, these simplifications are used in the three-phase system, giving rise to a model that contains the descriptive characteristics of the interaction with all its phases. In the first part of this work a macroscopic model for the hydrodynamics of the downflow fluidization is developed, using the method of volume averaging, obtaining a model with the form of Darcy’s law with a correction in velocity relative of the fluid with respect to the solid. A salient feature of the model is that it allows predicting the apparent permeability coefficient in different geometries and in different transport conditions. In addition, the average model obtained can be used for both types of fluidization (upward or downflow), since it is not restricted by the flow direction. In the second part of the work, for the modeling of the two-phase liquid-gas flow, an effective medium model is developed and used to predict the hydrodynamics of the bubble flow at its terminal velocity by means of an abbreviated version of the method of volume averaging. This modeling is a challenging problem in hydrodynamics due to the complexity to determine the structure of the gas phase movement. In this case, the momentum transport of that phase is studied by direct numerical simulations. The resulting model is applicable to describe the velocity in the two phases, once the bubbles have acquired the terminal velocity. This model consists of two average equations expressed in terms of four effective average coefficients of apparent permeability. These coefficients are determined from the solution of the closure problems associated with a bubble scale level. The model is validated by comparing the velocity fields of the gas phase with the velocity data arising from direct numerical simulations and with experimental results of of bubble systems that measure the terminal velocity. In the third and last part of the work, the physical parameters obtained from the previous models, the averaging regions and the expressions of momentum transport such as the continuity and transport equations associated with each phase and the corresponding boundary conditions are used at each interface. It should be noted that the time dependence is considered in this part of the modeling, which is a variable that is not usually taken into account in two-phase models. The three-phase macroscopic model obtained is written in terms of the associated coefficients of the developed closure problems, which also consider temporal terms. In general, during the development of the biphasic models the apparent permeabilities in each of them are obtained. In the three-phase system, the macroscopic model is expressed in terms of the effective transport coefficients that in the same way as for the two-phase systems are apparent permeabilities. As a prospective analysis, those effective transport coefficients can be used for the determination of the parameters of the pumping systems necessary for experimental implementation and for an adequate minimum fluidization rate. |
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