KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Simulation)-Chapter_2

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Simulation)-Chapter_2

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1 Chapter 2 Development of Dynamic Models Illustrative Example: A Blending Process An unsteady-state mass balance for the blending system: rate of accumulation rate of rate of (2-1) of mass in the tank mass in mass out = -
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2 Chapter 2 The unsteady-state component balance is: ( 29 1 1 2 2 ρ (2-3) d V x w x w x wx dt = + - The corresponding steady-state model was derived in Ch. 1 (cf. Eqs. 1-1 and 1-2). 1 2 1 1 2 2 0 (2-4) 0 (2-5) w w w w x w x wx = + - = + - or where w 1 , w 2 , and w are mass flow rates. ( 29 1 2 ρ (2-2) d V w w w dt = + -
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3 Chapter 2 General Modeling Principles The model equations are at best an approximation to the real process. Adage : “All models are wrong, but some are useful.” Modeling inherently involves a compromise between model accuracy and complexity on one hand, and the cost and effort required to develop the model, on the other hand. Process modeling is both an art and a science. Creativity is required to make simplifying assumptions that result in an appropriate model. Dynamic models of chemical processes consist of ordinary differential equations (ODE) and/or partial differential equations (PDE), plus related algebraic equations.
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4 Chapter 2 Table 2.1. A Systematic Approach for Developing Dynamic Models 1. State the modeling objectives and the end use of the model. They determine the required levels of model detail and model accuracy. 2. Draw a schematic diagram of the process and label all process variables. 3. List all of the assumptions that are involved in developing the model. Try for parsimony; the model should be no more complicated than necessary to meet the modeling objectives. 4. Determine whether spatial variations of process variables are important. If so, a partial differential equation model will be required. 5. Write appropriate conservation equations (mass, component, energy, and so forth).
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5 Chapter 2 1. Introduce equilibrium relations and other algebraic equations (from thermodynamics, transport phenomena, chemical kinetics, equipment geometry, etc.). 2. Perform a degrees of freedom analysis (Section 2.3) to
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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Simulation)-Chapter_2

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