Chemical Engineering Commons^™

Comparison Of Theory And Experiments For Dispersion In Homogeneous Porous Media, Mark Porter, Francisco Valdes-Parada, Brian Wood

Francisco J. Valdes-Parada

Modeling dispersion in homogeneous porous media with the convection–dispersion equation commonly requires computing effective transport coefficients. In this work, we investigate longitudinal and transverse dispersion coefficients arising from the method of volume averaging, for a variety of periodic, homogeneous porous media over a range of particle Péclet (Pep) numbers. Our objective is to validate the upscaled transverse dispersion coefficients and concentration profiles by comparison to experimental data reported in the literature, and to compare the upscaling approach to the more common approach of inverse modeling, which relies on fitting the dispersion coefficients to measured data. This work is unique in …

Bacterial Chemotaxis In Porous Media: Theory Derivation And Comparison With Experiments, Francisco J. Valdes-Parada, Mark L. Porter, Brian D. Wood

Francisco J. Valdes-Parada

Chemotaxis is the movement of organisms toward or away from the concentration gradient of a chemical species. Microbial chemotaxis has been shown to significantly increase contaminant degradation in subsurface environments with respect to traditional methods such as pump-and-treat. This type of transport phenomena often involves diffusion and convection along several scales. In this work we use the method of volume averaging to upscale the governing equations for in situ bioremediation by bacterial chemotaxis. The results are effective medium mass balance equations for both the bacteria and the chemical attractant. These equations are expressed in terms of average transport coefficients, which …

Interpretation Of Closure Variables In Upscaling, Francisco J. Valdes-Parada, Mark L. Porter, Brian D. Wood

Francisco J. Valdes-Parada

In many engineering applications, it is common to nd systems that involve transport at several scales. Despite the increasing computational capabilities, it is still not feasible to model a complete macroscopic system by direct numerical simulations at the microscale. Actually, it is more convenient to derive models at an intermediate level of scale between the microscale and the macroscale; this is the average scale. The derivation of models at this scale can be carried out by means of the method of volume averaging. The results from this method are averaged transport equations expressed in terms of eective medium coecients that …

One-Domain Approach For Heat Transfer At The Fluid-Porous Medium Inter-Region, Francisco J. Valdes-Parada, Carlos G. Aguilar-Madera, Benoît Goyeau, J. Alberto Ochoa-Tapia

Francisco J. Valdes-Parada

The modeling of transport phenomena in the zone of rapid changes between a fluid and a porous medium (i.e., the interregion) can be carried out using two distinctive approaches. The first one, generally called the one-domain approach, describes transport phenomena in the whole fluid-porous system using averaged macroscopic conservation equations including spatially dependent effective properties. These coefficients reduce to their respective constant values in the homogeneous fluid and porous regions of the system. As an alternative, the two-domain approach uses the transport equations with constant coefficients in the entire domain of each region, including the zone of drastic changes. To …

Derivation Of Complete Jump Boundary Conditions Between Homogeneous Media, Francisco J. Valdes-Parada, Benoît Goyeau, J. Alberto Ochoa-Tapia

Francisco J. Valdes-Parada

The modeling of transport phenomena between homogeneous regions requires the derivation of jump boundary conditions. These conditions account for the rapid spatial variations of the transport properties taking place near the dividing surface of the media. There has been a long debate in the literature about whether the discontinuity should apply to the fields (e.g., velocity, temperature, concentration) or to their fluxes. In this work, a general methodology giving rise to jump conditions for both the fields and the fluxes is proposed. This method, besides using a microscopic closure, introduces macroscopic deviation fields that lead to closure schemes for both …

Modelo Aproximado Del Coeficiente De Dispersión En Medios Porosos, Francisco J. Valdes-Parada, Helen D, Lugo-Méndez, J. Alberto Ochoa-Tapia

Francisco J. Valdes-Parada

En este trabajo, se utiliza el método del promedio volumétrico para la predicción del coeficiente efectivo de dispersión y la teoría de las funciones de Green para encontrar una solución analítica aproximada. Como simplificación de la celda representativa del medio poroso homogéneo, se usó la celda de Chang, imponiendo la condición de flujo reptante. Para corroborar los resultados se determinó numéricamente el coeficiente efectivo, en celdas unitarias periódicas usando el programa comercial basado en el método de de elemento finito COMSOL Multiphysics. El coeficiente efectivo de dispersión analítico obtenido en este trabajo presenta una tendencia análoga al numérico, además de …

Diseño De Una Parrilla Para La Reducción De Pérdidas De Energía En Estufas Convencionales, Francisco J. Valdes-Parada, Victor Castillo-Jimenez, Alberto Gabino-Zamora, Armando Astudillo-Velázquez

Francisco J. Valdes-Parada

Las estufas de gas convencionales tienen, por lo general, pérdidas considerables de energía alrededor del quemador, lo que disminuye su eficiencia e incrementa el consumo de recursos. Para atender este problema, en este trabajo se propone concentrar la mayor parte del calor hacia una sola región, para poder obtener la mayor cantidad de energía sin tener que suministrar más combustible y de esta manera aumentar la eficiencia de estufas convencionales. Para ello, se construyó un prototipo experimental a partir de cálculos de diseño teóricos. Con el prototipo ahorrador de energía se consiguió un ahorro hasta del 40% del consumo de …

Análisis De La Transferencia De Calor En Azoteas Verdes, Francisco J. Valdes-Parada, Verónica Freyre-Fonseca

Francisco J. Valdes-Parada

El problema de las islas urbanas de calor contribuye a los drásticos cambios climáticos que se sufren en ciudades densamente pobladas. Para atender este problema se tienen diversas alternativas, entre las cuales se contempla incorporar zonas verdes (e.g., paredes y azoteas verdes) en edificaciones que contrarresten los efectos de calentamiento excesivo. En este trabajo se estudia la transferencia de calor en edificaciones típicas de la ciudad de México utilizando diferentes configuraciones de zonas verdes. Los resultados muestran que el utilizar azoteas verdes tiene un efecto estabilizador en los perfiles locales de temperatura; sin embargo a nivel de toda una edificación, …

Escalamiento De Ecuaciones De Transporte De Energía En Un Tanque Agitado, Francisco J. Valdes-Parada, J. Alberto Ochoa-Tapia

Francisco J. Valdes-Parada

El planteamiento de balances para el diseño de equipos de transporte y reacción en Ingeniería Química suele llevarse a cabo mediante la aplicación de balances de coraza macroscópicos. Esta forma de proceder tiene la desventaja que no proporciona las restricciones y suposiciones que sustentan al modelo resultante, lo cual puede tener consecuencias graves en actividades de diseño y control de procesos. Una alternativa a esta metodología consiste en llevar a cabo un proceso de escalamiento de las ecuaciones de transporte válidas en la microescala, identificando sistemáticamente las suposiciones necesarias para la deducción del modelo macroscópico. En este trabajo se analiza …

Modelado De Un Reactor Solar Para El Cracking De Metano, Francisco J. Valdes-Parada, Hernando Romero-Paredes

Francisco J. Valdes-Parada

En este trabajo se realiza el modelado de un reactor solar tubular con una capacidad de hasta 15 kW para la disociación térmica del metano. El reactor está compuesto por un tubo de grafito inmerso en una cavidad también de grafito que juega el papel de receptor del flujo solar concentrado. El objetivo de este trabajo es evaluar los perfiles de velocidad, de concentración y temperatura a lo largo del reactor en función de la concentración y el flujo de gas a la entrada del reactor. Con lo cual ha sido posible evidenciar algunos fenómenos poco discutidos durante la experimentación. …

Sobre La Suposición De Estado Cuasiestacionario En El Transporte De Calor De Una Ventana Doble, Francisco J. Valdes-Parada, Erika K. Flores-Romero, Geovanni Hernandez-Luna, Erick A. Aguilera-Romero

Francisco J. Valdes-Parada

Es sabido que la mayoría de las edificaciones modernas transfieren la mayor parte de la energía acumulada a través de ventanas. Por ello, en la medida en que se tengan modelos confiables para el transporte de calor a través de estos sistemas, se contará con mejores diseños que tienen una relación directa con el confort, ambiente y gasto energético de edificaciones. El modelado de la transferencia de calor en ventanas dobles suele llevarse a cabo considerando únicamente sus cristales y el aire atrapado entre ellos. Sin embargo, la temperatura del interior es, a su vez, una función del tiempo y …

Escalamiento De Dispersión De Contaminantes En La Ciudad De México, Francisco J. Valdes-Parada, J. Ruben Varela-Ham

Francisco J. Valdes-Parada

En días hábiles, la actividad vehicular más intensa en calles y avenidas de la ciudad de México se inicia a las 6:00 hs y se prolonga por aproximadamente 3 ó 4 horas. En ese periodo, la capa de mezclado permanece relativamente quieta y expuesta a recibir una carga importante de contaminantes producto de emisiones vehiculares. En esas condiciones de ausencia de movimientos atmosféricos verticales y horizontales, y de intensa actividad contaminante, adquieren importancia los procesos de dispersión que ocurren en la horizontal y a nivel del suelo.

En este trabajo se lleva a cabo un proceso de promediado de las …

Integral Formulation For The Solution Of Closure Problems In Upscaling Processes, Francisco J. Valdes-Parada

Francisco J. Valdes-Parada

The derivation of transport models at macroscopic scales can be carried out using upscaling techniques such as the method of volume averaging. This upscaling technique consists on averaging the transport equations that describe phenomena at the microscale. The result is the so-called eective medium models, which are expressed in terms of eective coecients that can be computed from the solution of the corresponding closure problems. In this work, we present an integral formulation based on Green's functions to carry out the formal solution of closure problems. This methodology not only provides a physical interpretation of the closure variables, but it …

Should Tortuosity Still Be Used In Upscaling?, Francisco J. Valdes-Parada, Mark L. Porter, Brian D. Wood

Francisco J. Valdes-Parada

The concept of tortuosity is an integral part of models that describe trans- port in multiscale systems. Traditionally, tortuosity is de#12;ned as the ratio of an e#11;ective path length to the shortest path length in a representative sample of the porous medium microstructure. While the latter can be unambiguously speci#12;ed, the same is not true for the e#11;ective path length, since it changes from one type of transport to another. Consequently, it is possible to have di#11;erent tortuosity values for di#11;erent transport processes taking place in the same system. In order to avoid running into unclear interpretations, we pro- pose …

Computation Of Jump Coefficients For Momentum Transfer Between A Porous Medium And A Fluid Using A Closed Generalized Transfer Equation, Francisco J. Valdes-Parada, José Alvarez-Ramirez, Benoît Goyeau, J. Alberto Ochoa-Tapia

Francisco J. Valdes-Parada

The momentum transfer between a homogeneous fluid and a porous medium in a system analogous to the one used by Beavers and Joseph (J Fluid Mech 30:197–207, 1967) is studied using volume averaging techniques. In this article, we present a closed generalized momentum transport equation (GTE) that is valid everywhere and is expressed in terms of position-dependent effective transport coefficients, which are computed from the solution of associated closure problems previously reported. A combination of the velocity profiles from the GTE in the definition of the excess terms that define the jump coefficients allows their computation using numerical techniques. The …

Jump Condition For Diffusive And Convective Mass Transfer Between A Porous Medium And A Fluid Involving Adsorption And Chemical Reaction, Francisco J. Valdes-Parada, Jose Alvarez-Ramirez, Benoît Goyeau, J. Alberto Ochoa-Tapia

Francisco J. Valdes-Parada

In this paper, mass transfer at the fluid–porous medium boundaries is studied.The problem considers both diffusive and convective transport, along with adsorption and reaction effects in the porous medium. The result is a mass flux jump condition that is expressed in terms of effective transport coefficients. Such coefficients (a total dispersion tensor and effective reaction and adsorption coefficients) may be computed from the solution of the corresponding closure problem here stated and solved as a function of the Péclet number (Pe), the porosity and a local Thiele modulus. For the case of negligible convective transport (i.e., Pe << 1), the closure problem reduces to the one recently solved by the authors for diffusion and reaction between a fluid and a microporous medium.

Effective Medium Equations For Chemotaxis In Porous Media, Francisco J. Valdes-Parada, Mark L. Porter, K. Narayanaswamy, Roseanne Ford, Brian D. Wood

Francisco J. Valdes-Parada

Biodegradation is an important mechanism for contaminant reduction in groundwater environments; in fact, in-situ bioremediation and bioaugmentation methods represent alternatives to traditional methods such as pump-and-treat. Chemotaxis has shown to enhance bacterial transport toward or away from concentration gradients of chemical species in laboratory experiments and can signifficantly increase contaminant flux undergoing degradation at the interfaces of lowand high-permeability regions. In this work, the method of volume averaging is used to upscale the microscale description of chemotactic microbial transport in order to obtain the corresponding macroscale equations for bacteria and the attractant. As a first apprach, cellular growth/death and consumption …

Separation Of Time Scales For Transient Dispersion, Mark L. Porter, Francisco J. Valdes-Parada, Brian D. Wood

Francisco J. Valdes-Parada

No abstract provided.

Modelado Matemático En Ingeniería, Francisco J. Valdes-Parada

Francisco J. Valdes-Parada

En esta plática se discute de una manera sencilla la importancia que tiene el modelado matemático en Ingeniería. Para ello, se presenta una visión personal sobre el papel que juegan asignaturas como fenómenos de transporte y termodinámica en la formación de licenciatura y posgrado en Ingeniería. Más aún, con el objetivo de ilustrar la importancia de los cambios de escala que frecuentemente aparecen en Ingeniería, se analiza el caso del flujo de un soluto a través de tubos capilares. De esta manera, se tiene un sistema donde a escala microscópica son relevantes la difusión (radial y axial) y convección (axial) …

Breves Notas Sobre Modelado, Francisco J. Valdes-Parada

Francisco J. Valdes-Parada

No abstract provided.

Analysis Of Mass Transport And Reaction Problems Using Green's Functions, Francisco J. Valdes-Parada

Francisco J. Valdes-Parada

A methodology to solve typical problems of mass transfer and chemical reaction engineering in terms of Green’s functions is presented. The fundamental idea consists on analytically inverting a differential operator by means of the solution of a boundary value problem associated to the original transport and reaction problem. The dependent variable is expressed then as function of the solution of such associated problem, which is the Green’s function. Among the advantages that this methodology presents are the smoothing of round-off errors as well as the exact incorporation of boundary conditions. A mandatory requirement for the application of this methodology is …

Boundary Conditions For The Transport Between Multiphase Media, Francisco J. Valdes-Parada

Francisco J. Valdes-Parada

The corresponding boundary conditions, for momentum, heat or mass transfer, between two regions is an indispensable element in the development of models that describe transport in heterogeneous systems. For this reason, it is common to find in the literature boundary conditions that may be adequate for describing a particular phenomenon, but were obtained on an empirical basis and, frequently, include unknown coefficients.

The above has caught the attention of several authors that, in the last three decades, have presented methodologies that allow obtaining boundary conditions maintaining a close relation to the physics of the studied phenomenon. Among the various reported …

Condiciones De Frontera Para El Transporte Entre Medios Multifásicos, Francisco J. Valdes-Parada

Francisco J. Valdes-Parada

Las condiciones de frontera adecuadas, ya sea de transferencia de cantidad de movimiento, calor o masa, entre dos regiones es un elemento indispensable en el desarrollo de modelos que describan el transporte en sistemas heterogéneos. Por tal razón, es común encontrar en la literatura condiciones de frontera que, si bien pueden ser adecuadas para describir un fenómeno particular, se obtuvieron empíricamente y frecuentemente incluyen coeficientes desconocidos.

Lo anterior ha despertado el interés de varios autores que, en las tres últimas décadas, han presentado metodologías que permiten obtener condiciones de frontera fundamentadas en la física del fenómeno estudiado. Entre las distintas …

Jump Condition At The Boundary Between A Porous Catalyst And A Homogeneous Fluid, Francisco J. Valdes-Parada, J. Alberto Ochoa-Tapia

Francisco J. Valdes-Parada

The method of volume averaging (Whitaker, 1999) is used to derive the jump conditions between a porous catalyst and a homogeneous fluid. To simplify the analysis a first order kinetics is used and the convective transport is neglected. The statement for the derivation is in terms of the spatially smoothed equations obtained by Wood et al. (2000). We have followed a similar procedure to the one used by those authors to derive, besides a jump boundary condition that couples the two media transport, a closure problem to predict the effective reaction rate coefficient at the interregion dividing surface as a …

Darcy's Law For Immiscible Two-Phase Flow: A Theoretical Development, Francisco J. Valdes-Parada, Gilberto Espinoza-Paredes

Francisco J. Valdes-Parada

The aim of this paper is to show how the method of volume averaging can be used to obtain a closed set of averaged equations for bubbling flow. The Navier–Stokes equations are considered as the starting point for the volume-averaging method. The closure was formulated as an associated problem with the deviations around averaged values of the local variables. When the traditional length-scale restrictions are imposed, the volume-averaged momentum equation can be given by &#;vk k – &#;vm m = Kk⋅ (–∇ &#;pk k + ρkgk), which is equivalent to Darcy’s law. The tensor Kk is determined by closure problems …

Dynamics Of Two-Phase Reactors With Approximate Kinetics, Francisco J. Valdes-Parada

Francisco J. Valdes-Parada

Los sistemas de transporte y reacción en más de una fase han ido adquiriendo un interés creciente en la comunidad científica y tecnológica debido a que la gran mayoría de los procesos industriales se llevan a cabo en sistemas no homogéneos. De la misma forma, es notable el interés que se ha dado en las últimas décadas por los sistemas catalizados por enzimas.

Las enzimas como catalizadores son utilizadas actualmente en una gran variedad de procesos, como son la fabricación de etanol, insulina, ácido láctico, cerveza, vacunas, entre muchos otros; de hecho varias procesos clásicos han sido reemplazados por procesos …