A Relaxation Method for Solving Reaction Problem in an Isothermal Tubular Reactor with One-Dimensional Eddy Diffusion.

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  • Yamada Ikuho
    Department of Applied Chemistry, Nagoya Institute of Technology
  • Mori Hideki
    Department of Applied Chemistry, Nagoya Institute of Technology
  • Oda Akiyoshi
    Department of Applied Chemistry, Nagoya Institute of Technology
  • Kato Katsuhiro
    Department of Applied Chemistry, Nagoya Institute of Technology

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  • 一次元混合拡散を伴う等温管型反応器問題対する緩和法による解法
  • 1ジゲン コンゴウ カクサン オ トモナウ トウオンカンガタ ハンノウキ モン

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Abstract

A numerical method is proposed for solving an isothermal equimolar vapor phase parallel reaction problem in a tubular reactor with one dimensional eddy diffusion under the boundary conditions given by Danckwerts.<BR>This problem is described by simultaneous second order ordinary differential equations, and is transformed to a set of nonlinear simultaneous algebraic equations by expansion using the central finite difference operator. The Newton-Raphson method has been frequently used to solve these equations in spite of the difficulties of complicated derivation of Jacobian matrix and selecting adequate initial values.<BR>The proposed method is based on the relaxation method and consists of two calculation loops i) to correct the compositions of segmentation points of a reactor using a θ method with component material balances and ii) to repeat the point-by-point calculation in the sequence shown by Mori et al. in the solution of multistage, multi-component distillation problems. The method provides stable solution with a brief algorithm regardless of the number and rate equation of reactions, and is less sensitive in selecting initial values. The usefulness of the method is demonstrated by some numerical examples.

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