Models of reactive settling for wastewater treatment.
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Date
2023
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Universidad de Concepción.
Abstract
En esta tesis, se pone especial énfasis en el proceso de lodo activado en la sedimentación reactiva, en tanques de sedimentación secundarios (SSTs, por sus siglas en inglés) y reactores por lotes secuenciales (SBRs, por sus siglas en inglés). Entre los temas tratados se encuentran el desarrollo de un modelo matemático unidimensional moderno y la implementación de esquemas numéricos para simular la sedimentación reactiva en los SBRs. El modelo gobernante consiste en un sistema acoplado de ecuaciones de leyes de conservación parabólicas de convección-difusión-reacción fuertemente degeneradas, siendo las incógnitas las concentraciones de los componentes sólidas (bacterias; lodos activados) y líquidos (substratos) en función de la altura y el tiempo. También es de interés desarrollar el ajuste de datos experimentales obtenidos de un SST piloto con área de sección transversal variable al modelo de sedimentación reactiva. La tesis tiene los siguientes objetivos: Primero, formular un modelo físico-matemático basado en ecuaciones de conservación de masa para modelar el proceso de sedimentación reactiva de los SBRs donde la superficie superior es una frontera móvil. Segundo, desarrollar un esquema numérico confiable (consistente y estable) para las ecuaciones gobernantes derivadas del primer objetivo, considerando una discretización espacial con un número fijo de celdas a través de las cuales se mueve la superficie, y demostrar que el esquema numérico es monótono y satisface una propiedad de región invariante (en particular, preserva la positividad) cuando se ejecuta en una formulación de división simple. Tercero, ajustar un modelo de sedimentación reactiva a datos experimentales de una planta piloto que tiene un área de sección transversal variable, donde las ecuaciones del modelo se extienden, incluyendo términos adicionales para la dispersión hidrodinámica y la mezcla heurística. Cuarto, realizar una transformación espacial adecuada de las ecuaciones gobernantes del primer objetivo a un dominio fijo y discretizarlas utilizando un esquema explícito monótono y una variante semi-implícita, formulaciones que, entre otras ventajas, son más fáciles de implementar en comparación con el enfoque del segundo objetivo.
In this thesis, special emphasis is placed on the activated sludge process in reactive settling, in secondary settling tanks (SSTs) and sequencing batch reactors (SBRs). Among the topics covered are the development of a modern one-dimensional mathematical model and the implementation of numerical schemes to simulate reactive settling in the SBRs. The governing model consists of a coupled system of strongly degenerate parabolic convection-diusion-reaction conservation law equations, with unknowns being the concentrations of solid (bacteria; activated sludge) and liquid (substrates) components as functions of height and time. It is also of interest to develop the fitting of experimental data obtained from a pilot SST with variable cross-sectional area to the model of reactive settling. The thesis has the following objectives: First, to formulate a physical-mathematical model based on mass conservation equations to model the reactive settling process of the SBRs where the upper surface is a moving boundary. Second, to develop a reliable numerical scheme (consistent and stable) for the governing equations derived from the first objective, considering a space discretization with a fixed number of cells across which the surface moves, and to demonstrate that the numerical scheme is monotone and satisfies an invariant region property (in particular, it preserves positivity) when executed in a simple splitting formulation. Third, to fit a reactive settling model to experimental data from a pilot plant which has a variable cross-sectional area, where the model equations are extended, including additional terms for hydrodynamic dispersion and heuristic mixing. Fourth, to perform an appropriate spatial transformation of the governing equations from the first objective to a fixed domain and discretize them using a monotone explicit scheme and a semi-implicit variant, formulations which among other advantages are easier to implement compared to the approach of the second objective.
In this thesis, special emphasis is placed on the activated sludge process in reactive settling, in secondary settling tanks (SSTs) and sequencing batch reactors (SBRs). Among the topics covered are the development of a modern one-dimensional mathematical model and the implementation of numerical schemes to simulate reactive settling in the SBRs. The governing model consists of a coupled system of strongly degenerate parabolic convection-diusion-reaction conservation law equations, with unknowns being the concentrations of solid (bacteria; activated sludge) and liquid (substrates) components as functions of height and time. It is also of interest to develop the fitting of experimental data obtained from a pilot SST with variable cross-sectional area to the model of reactive settling. The thesis has the following objectives: First, to formulate a physical-mathematical model based on mass conservation equations to model the reactive settling process of the SBRs where the upper surface is a moving boundary. Second, to develop a reliable numerical scheme (consistent and stable) for the governing equations derived from the first objective, considering a space discretization with a fixed number of cells across which the surface moves, and to demonstrate that the numerical scheme is monotone and satisfies an invariant region property (in particular, it preserves positivity) when executed in a simple splitting formulation. Third, to fit a reactive settling model to experimental data from a pilot plant which has a variable cross-sectional area, where the model equations are extended, including additional terms for hydrodynamic dispersion and heuristic mixing. Fourth, to perform an appropriate spatial transformation of the governing equations from the first objective to a fixed domain and discretize them using a monotone explicit scheme and a semi-implicit variant, formulations which among other advantages are easier to implement compared to the approach of the second objective.
Description
Tesis para optar al grado de Doctor en Ciencias Aplicadas con mención en Ingeniería Matemática