Class 14 - Mathematical Modeling Of Chemical System

System Modeling Coursework Class 14: Modeling of Chemical systems – Example of Batch reactor P.R. VENKATESWARAN Faculty, Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal Karnataka 576 104 INDIA Ph: 0820 2925154, 2925152 Fax: 0820 2571071 Email: [email protected], [email protected] Web address: http://www.esnips.com/web/SystemModelingClassNotes

WARNING! • I claim no originality in all these notes. These are the compilation from various sources for the purpose of delivering lectures. I humbly acknowledge the wonderful help provided by the original sources in this compilation. • For best results, it is always suggested you read the source material. • Of late, this has becoming supplement to what is taught in the class. So BEWARE! You are on two tracks!

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Contents • Description of a Batch reactor system • Model of the batch reactor

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Introduction • Although the progress of the chemical industry has been toward continuous processes, some reactions will inevitably be conducted batch wise. • The bulk of commercial batch reactions are polymerizations involved in the production of rubber and many types of plastics. • Distribution of molecular weight is an important parameter in polymer manufacture, and it seems to be the most easily controlled batch wise. Another consideration is the great change in viscosity frequently encountered between the reactants and products. July – December 2008

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Steps in a chemical process • Charge the reactor with reactants and catalyst. • Heat to operating temperature. • Allow the reaction to proceed to completion, normally several hours. • Heat or cool to cure temperatures. • Cool and empty the reactor. • Production reactors are stirred, jacketed vessels of several thousand gallons capacity. Here, a stirred tank reactor is considered as an example of a chemical system. July – December 2008

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A stirred tank reactor

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Assumptions for the system • • •

Fluid in the tank is perfectly mixed so that it is at uniform temperature The tank is insulated to eliminate heat loss to the surrounding air. There is no heat storage in the insulation.

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Derivation of the transfer function

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Derivation of the transfer function

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Can you derive the transfer function for this system?

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… and this?

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T.F of multiple input system

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T.F of multiple input system

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T.F of multiple input system

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References 1. Advanced Control Systems Engineering, Ronald Burns 2. Modern Control Engineering, Ogata 3. Chemical Process Control and Chemical Modeling - Stephanopoulous …amongst others

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And, before we break… • When the great scorekeeper comes, he counts not whether you won or lost but how you played the game.

Thanks for listening… July – December 2008

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