ABSTRACT
Resumen La descripción del comportamiento de un flujo bifásico, a través de lechos porosos, por medio de modelos, basados en las ecuaciones de fenómenos de transporte, se dificulta debido a la irregularidad geométrica de los canales que se forman entre las partículas sólidas que constituyen el lecho. Los modelos deterministas desarrollados para flujos monofásicos requieren del ajuste de constantes empíricas y no pueden extrapolarse a flujos bifásicos, donde el patrón de flujo generado en el sistema influye significativamente sobre el comportamiento del flujo total y las pérdidas de presión por fricción. Por lo anterior, en este trabajo se presenta un modelo para describir el comportamiento del flujo bifásico en función del patrón de flujo y de la morfología, las dimensiones y las condiciones de operación del lecho poroso, cuya obtención se basó en un formalismo, empleando conjuntamente las ecuaciones de conservación de la cantidad de movimiento, la geometría fractal y el cálculo diferencial fraccional. El modelo predice que, para una misma composición del flujo bifásico, el patrón de flujo influye significativamente sobre las pérdidas de presión por fricción, habiendo un incremento cuando una de las fases se encuentra dispersa en el seno de la otra. Por otro lado, el incremento de la dimensión fractal de los poros causa a su vez un incremento de las pérdidas de presión por fricción. El modelo presenta limitaciones asociadas a las consideraciones establecidas durante su obtención, de tal manera que sólo es válido cuando los efectos de la tensión superficial son más significativos que los gravitatorios, despreciándose los efectos de esos últimos sobre el patrón de flujo, así como para el estado estacionario.
Abstract The description of the behavior of a biphasic flow through porous beds by means of models based on the equations of transport phenomena is made difficult due to the geometric irregularity of the channels that are formed between the solid particles that make up the bed. Deterministic models developed for single-phase flows require the adjustment of empirical constants and cannot be extrapolated to biphasic flows, where the flow pattern generated in the system significantly influences the behavior of the total flow and the frictional pressure losses. Therefore, in this paper, we present a model to describe the behavior of the biphasic flow in relation to the flow pattern and the morphology, dimensions, and operating conditions of the porous bed, whose obtainment was based on a hierarchy that used the equations for conservation of momentum, fractal geometry and fractional differential calculus jointly. The model predicts that, for the same composition of the biphasic flow, the flow pattern significantly influences friction pressure losses, with an increase when one of the phases is dispersed within the other. On the other hand, the increase in the fractal dimension of the pores, in turn, causes an increase in pressure loss due to friction. The model has limitations associated with the considerations established during its collection, since it is only valid when the effects of surface tension are more significant than the gravitational effects, the effects of the latter being disregarded on the flow pattern, as well as for the stationary state.
ABSTRACT
O tratamento de efluentes com coalescedor de leito consiste em induzir o aumento das gotas de óleo, pela passagem da emulsão por um leito poroso, para que elas possam, posteriormente, flotar por processo de separação gravitacional. O objetivo deste artigo foi apresentar considerações técnicas e experimentais sobre o uso do coalescedor de leito granular, com leito constituído por resinas de trocas catiônicas, visando o pré-tratamento de óleo emulsionado em efluentes líquidos. Os testes ocorreram em uma unidade em escala de bancada alimentada com emulsão óleo em água (O/A) com um teor de óleos e graxas (TOG) entre 200 e 400 mg.L-1 e diâmetro de gotas entre 3 a 8 μm. As velocidades do fluido (v) testadas foram entre 4,4 e 17,4 m.h-1. A altura do leito do coalescedor foi fixada em 5 cm. Os parâmetros usados para avaliar a eficiência dos testes foram eficiência de remoção de óleo (%E), pressão diferencial através do leito (Δp) e permeabilidade do leito (ko). Os resultados mostraram que o processo operou em estado estacionário e que os valores de TOG testados influenciaram no processo, bem como as velocidades do fluido, cuja elevação reduziu a eficiência significativamente. Os valores aproximados de %E obtidos foram 50 e 20-30%, para valores de v de 4,4 e 17,4 m.h-1, respectivamente.
The wastewater treatment with a bed coalescer consists of inducing the increase of oil droplets by passing the emulsion through a porous bed, so they can flote by gravitational separation process. The objective of this paper is to present technical and experimental considerations on the use of a granular bed coalescer, with a bed made of cationic exchange resins, for pre-treatment of emulsified oil from oily wastewater. Tests were conducted on a bench scale unit, which was fed with oil in water emulsion with oil and grease concentration (O & G) between 200 and 400 mg.L-1 and oil droplet diameter between 3 and 8 μm. The fluid velocities (v) tested were between 4.4 and 17.4 m.h-1. The coalescer bed height was fixed at 5 cm. The parameters used for assessing the tests efficiency were oil removal efficiency percentage (%E), differential pressure across the bed and, bed permeability. Results showed that the process operates in a steady-state condition and that the influent O&G affected the process efficiency, as well as the fluid velocities which reduced the efficiency significantly, with its increasing. The %E values obtained were between 50 and 20-30% to v between 4.4 and 17.4 m.h-1, respectively.