Physical Consistency of Generalized Linear Driving Force Models for Adsorption in a Particle

Physical Consistency of Generalized Linear Driving Force Models for Adsorption in a Particle

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Physical Consistency of Generalized Linear Driving Force Models for Adsorption in a Particle Jose ´ A Ä lvarez-Ramı ´ rez,* Guillermo Ferna ´ ndez-Anaya, ² Francisco J. Valde ´ s-Parada, and J. Alberto Ochoa-Tapia Departamento de Ingenierı ´ a de Procesos e Hidra ´ ulica, Universidad Auto ´ noma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F., P.C. 09340 Mexico The so-called (first-order) linear driving force (LDF) model for gas adsorption kinetics is frequently and successfully used for analysis and design of adsorptive processes because it is simple, analytical, and physically consistent. Yet, for certain operating conditions, such as cyclic adsorption and desorption, significant differences between the LDF model and the rigorous Fickian diffusion (FD) model can be found. In principle, increasing the order of the approximate LDF model can yield predictions closer to the FD model. As in the classical first-order LDF model, generalized LDF must be consistent with the physics of the FD model. This paper provides a minimal set of properties that generalized LDF models should meet in order to be physically consistent. This is done by showing that the FD model describes positive real dynamics, which are closely related to the thermodynamics of the adsorption - diffusion process. In this form, a generalized LDF model should inherit this property in order to guarantee that the main thermodynamic characteristics of the adsorption - diffusion dynamics will be retained to some extent. 1. Introduction Consider diffusion and adsorption dynamics in a uniformly porous spherical particle. The mass balance equation describing the concentration profile c ( r p , t ) inside the particle is where r is the radial particle coordinate, ± p is the porosity in the particle, and D p is the effective pore diffusivity based on the total area. A linear adsorption equilibrium on the pore walls with equilibrium constant K was assumed. Equivalently, the above equation can be written in dimensionless form as where q ) ( ± p + K ) c / c * is a dimensionless concentration per unit volume in the particle, c * is a characteristic concentration, and Œ ) r / R p is the dimensionless radial variable. A diffusion time constant can be defined as By introducing the dimensionless time variable τ ) t / τ D , one obtains the standard formulation referred to as the pore diffusion model: The boundary conditions, for all τ g 0, are and the initial condition, for all Œ [0,1], is often taken as Equations 1 - 3 will be referred to as the Fickian diffusion (FD) model. Sometimes, for different values of the “design parameter” f ( τ ), repeated solutions of eqs 1 - 3 have to be obtained for optimization-based designs or simply for simulation purposes. An important ex- ample is the cyclic operation of adsorption systems where the solution of the diffusion model must be repeated over many cycles of operation in order to establish the final cyclic steady-state separation per- formance of the overall process. 1 Although the solution of the problem (eqs 1 -
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/10/2011 for the course CBI 101 taught by Professor O.tapia during the Spring '11 term at UNAM MX.

Page1 / 8

Physical Consistency of Generalized Linear Driving Force Models for Adsorption in a Particle

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online