KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec18

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec18

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1 Chapter 6 Time Delays Time delays occur due to: 1. Fluid flow in a pipe 2. Transport of solid material (e.g., conveyor belt) 3. Chemical analysis - Sampling line delay - Time required to do the analysis (e.g., on-line gas chromatograph) Mathematical description: A time delay, , between an input u and an output y results in the following expression: θ ( 29 ( 29 0 forθ (6-27) θ forθ t y t u t t < = -
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2 Chapter 6 Example: Turbulent flow in a pipe Let, fluid property (e.g., temperature or composition) at point 1 fluid property at point 2 u @ y @ Assume that the velocity profile is “flat”, that is, the velocity is uniform over the cross-sectional area. This situation is analyzed in Example 6.5 and Fig. 6.6. Fluid In Fluid Out Figure 6.5 Point 1 Point 2
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3 Chapter 6
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4 Chapter 6 Example 6.5 (a) relating the mass flow rate of liquid at 2, w 2 , to the mass flow rate of liquid at 1, w t , (b) relating the concentration of a chemical species at 2 to the concentration at 1. Assume that the liquid is incompressible. Solution (a) First we make an overall material balance on the pipe segment in question. Since there can be no accumulation (incompressible fluid), material in = material out ( 29 ( 29 1 2 w t w t = For the pipe section illustrated in Fig. 6.5, find the transfer functions:
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Chapter 6 (b) Observing a very small cell of material passing point 1 at time t , we note that in contains Vc 1 ( t ) units of the chemical species of interest where V is the total volume of material in the cell. If, at time t + , the cell passes point 2, it contains units of the species. If the material moves in plug flow, not mixing at all with adjacent material, then the amount of species in the cell is constant: Putting (6-30) in deviation form and taking Laplace transforms yields the transfer function,
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This note was uploaded on 09/22/2009 for the course CHEMICAL CHE 401 taught by Professor Dr.muhammadal-arfaj during the Spring '09 term at King Fahd University of Petroleum & Minerals.

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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec18

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