Closed-form solution to the problem of reaction with fixed bed adsorption using delay-differential equations

Shu Xia, Nichole Y. Hodge, Theodore F. Wiesner

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Delay-differential equations (DDEs) can describe many chemical engineering models. However, the formalism of DDEs appears to be underutilized in chemical engineering. We have recast the canonical chemical engineering problem of batch reaction with fixed bed sorption into the form of a delay-differential equation, obtaining a more intuitive model and a simpler closed form solution than those previously reported. Considerable model reduction is possible through the use of DDE formalism when one considers that chemical processes can be partially represented by networks of transportation and state delays. Analytical and numerical methods for solution, as well as controllability and stability theory for systems of DDEs, are nearly as rich and developed as those for ordinary differential equations. Significant progress thus may be possible in areas such as the modeling, synthesis, and control of chemical processes, if the governing equations can be expressed in the form of delay-differential equations.

Original languageEnglish
Pages (from-to)2057-2066
Number of pages10
JournalChemical Engineering Science
Volume64
Issue number9
DOIs
StatePublished - May 1 2009

Keywords

  • Chemical reactors
  • Delay-differential equations
  • Dynamic simulation
  • Mathematical modeling
  • Organic acids
  • Packed bed

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