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A reactant diffuses through a pore within a catalyst particle (size L) and reacts on the catalysts surface. The reactant concentration at the pore opening (x = L) is Co and the gradient of concentration at the pore bottom (x = 0) is zero. The reaction is fourth order (rate = kC*). Perform the following analysis: (1) Apply mass balance and derive a differential equation that governs the concentration distribution of the reactant within the pore: C=f(x). (2) Non-dimensionalize the differential equation and formulate a regular perturbation analysis problem for the dimensionless concentration y=C/Co.

A reactant diffuses through a pore within a catalyst particle (size L) and reacts on the catalysts surface. The reactant concentration at the pore opening (x = L) is Co and the gradient of concentration at the pore bottom (x = 0) is zero. The reaction is fourth order (rate = kC*). Perform the following analysis: (1) Apply mass balance and derive a differential equation that governs the concentration distribution of the reactant within the pore: C=f(x). (2) Non-dimensionalize the differential equation and formulate a regular perturbation analysis problem for the dimensionless concentration y=C/Co.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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A reactant diffuses through a pore within a catalyst particle (size L) and reacts on the catalysts surface. The reactant concentration at the pore opening (x = L) is Co and the gradient of concentration at the pore bottom (x = 0) is zero. The reaction is fourth order (rate = kC*). Perform the following analysis: (1) Apply mass balance and derive a differential equation that governs the concentration distribution of the reactant within the pore: C=f(x). (2) Non-dimensionalize the differential equation and formulate a regular perturbation analysis problem for the dimensionless concentration y=C/Co. (3) Assume y = yo + ɛyi + e?y2+ ... Define ɛ in terms of system parameters (D, L, k, etc.). Applying the perturbation methods, derive analytical expressions for yo, yı and y2. reaction C=Co C=f(x) diffusion C'=0 x = 0 x = L
Transcribed Image Text:A reactant diffuses through a pore within a catalyst particle (size L) and reacts on the catalysts surface. The reactant concentration at the pore opening (x = L) is Co and the gradient of concentration at the pore bottom (x = 0) is zero. The reaction is fourth order (rate = kC*). Perform the following analysis: (1) Apply mass balance and derive a differential equation that governs the concentration distribution of the reactant within the pore: C=f(x). (2) Non-dimensionalize the differential equation and formulate a regular perturbation analysis problem for the dimensionless concentration y=C/Co. (3) Assume y = yo + ɛyi + e?y2+ ... Define ɛ in terms of system parameters (D, L, k, etc.). Applying the perturbation methods, derive analytical expressions for yo, yı and y2. reaction C=Co C=f(x) diffusion C'=0 x = 0 x = L
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