Lecture 3 2011

# Lecture 3 2011 - MATHEMATICAL MODELING PRINCIPLES...

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MATHEMATICAL MODELING PRINCIPLES Objectives : 1. Formulate dynamic models based on fundamental balances 2. Solve simple first-order linear dynamic models 3. Determine how key aspects of dynamics depend on process design and operation Outline : 1. Reasons why we need dynamic modeling 2. Many examples: mixing tank, CSTR, CSTRs in series, draining tank, etc. 3. General conclusions about models Why we need dynamic models : Example I: Do the bus and bicycle have different dynamics? Which can make a U-turn in 1.5 meters? Which responds better when it hits a bump? Dynamic performance depends more on the vehicle than on the driver. The process dynamics are more important than the computer control. Example II: Feed material is delivered periodically, but the process requires a continuous feed flow. How large should the tank volume be? We must provide process flexibility for good dynamic performance!

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Example III: The cooling water pumps have failed. How long do we have until the exothermic reactor runs away? Process dynamics are important for safety! Why we develop mathematical models : How does the process influence the response? How far? How fast? What “shape”? Mathematical models help answer these questions. Six-Step Modeling Procedure : 1. Define Goals a. What decision? b. What variable? c. Location d. Examples of variable selection: i. Liquid level total mass in liquid ii. Pressure total moles in vapor iii. Temperature energy balance model iv. Concentration component mass
2. Prepare information: a. Sketch process b. Collect data c. State assumptions d. Define system 3. Formulate the model: Conservation balances a. Overall material: Accumulation of mass = mass in – mass out

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Lecture 3 2011 - MATHEMATICAL MODELING PRINCIPLES...

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