A Mathematical Model for Batch-Recirculation Reactor Systems and Its Numerical Calculation Method

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  • Fukinbara Satoru
    Department of Biochemical Engineering and Sicence, Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology
  • Shiraishi Fumihide
    Department of Biochemical Engineering and Sicence, Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology
  • Nagasue Hiroyuki
    Department of Chemical and Biochemical Engineering, Sasebo College of Technology

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Other Title
  • 回分循環式反応器システムに対する数学モデルとその数値計算法
  • カイブン ジュンカンシキ ハンノウキ システム ニ タイスル スウガク モデル ト ソノ スウチ ケイサンホウ

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Description

A mathematical model is set up for the batch recirculation reactor system (consisting of a perfectly-mixed flow room, plug-flow reactor, and plug-flow pipes situated in upstream and downstream regions of the reactor), which may be constructed to treat harmful substances in a CELSS, and the performances of two numerical calculation methods (Method 1; a combination of Runge-Kutta and modified Runge-Kutta methods, Method 2; a combination of Runge-Kutta and Euler methods) are investigated. First, these methods are applied to a simplified batch recirculation reactor system with first-order reaction kinetics and negligible reactor volume and the numerical solutions are compared with the analytical solutions. As a result, it is found that the accuracies of the numerical solutions by Method 1 and 2 consistently increase with the increase of step number and Method 1 gives numerical solutions whose significant figures are always larger by at least two-digits than those of Method 2. Method 1 is further applied to a practical reactor system with first-order or Langmuir-Hinshelwood type reaction kinetics and finite reactor volume to elucidate the effects of initial conditions and systemic parameters on the characteristics of the practical batch recirculation reactor system. The results of the present work clearly show that Method 1 promises highly stable and reliable numerical calculation because of the introduction of modified Runge-Kutta method and the devised calculation algorithm.

Journal

  • Eco-Engineering

    Eco-Engineering 12 (2), 9-18, 2000

    The Society of Eco-Engineering

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