109 Project Assignment

# 109 Project Assignment - CBE 109 Numerical and Mathematical...

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CBE 109 - Numerical and Mathematical Methods in Chemical and Biomolecular Engineering Fall 2011 PROJECT Steady-state and transient analysis of a diﬀusion-reaction process Assigned: Monday, November 7. Due: Friday, December 9. Process description and modeling The objective of this project is to study the steady-state and transient characteristics of the following reaction scheme: A + 2 B -→ D A -→ P B -→ U U -→ B which takes place in the membrane reactor shown below: The reactants A and B enter the reaction Film BF Reaction Zone 0 L C AF C Figure 1: Schematic of membrane reactor. zone through the left membrane. The concentrations of the species A and B outside of the ﬁlm which is located in the left side of the reaction zone are kept at the ﬁxed values C AF and C BF . In the right side of the reaction zone, all the species deposit with diﬀerent deposition rates. The boundaries in the reaction zone are at r = 0 and r = L . Under the assumptions that the molecular diﬀusion inside the reaction zone is one-dimensional and follows Fick’s law, and that the diﬀusion coeﬃcients D A , D B and D U , of the species A , B and 1

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U , respectively are constant and equal (i.e. D A = D B = D U = ¯ D ), the following equations can be derived, describing the change in C A , C B , C U with position and time: ∂C A ∂t = ¯ D 2 C A ∂r 2 - k 1 C A C 2 B - k 2 C A ∂C
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109 Project Assignment - CBE 109 Numerical and Mathematical...

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