che446_10_hw4 - Homework #4 ChE 446 Fall 2010 Problem 1....

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Unformatted text preview: Homework #4 ChE 446 Fall 2010 Problem 1. Consider the following dynamic model of a constant volume, isothermal con- tinuous stirred tank reactor, dV C A dt = q ( C A- C A )- V ( k 1 C A + k 3 C 2 A ) = f 1 ( C A ,q,C AO ) dV C B dt =- qC B + V ( k 1 C A- k 2 C B ) = f 2 ( C A ,C B ,q ) where C A and C B are the concentrations of component A and B, respectively, V is the reactor volume, q and C A are the volumetric flow rate and concentration of the inlet stream, respectively, and k 1 , k 2 , and k 3 are reaction constants. Assume both q and C A vary with respect to time. 1. Find the linear deviation model. 2. Find the transfer functions C B ( s ) Q ( s ) and C B ( s ) C AO ( s ) 3. Find C B ( t ) for a unit step change in C AO ( t ). 4. Can C B ( t ) exhibit an inverse response for a change in q ( t )? If so, find the range of C A which lead to an inverse response in terms of the constants V , k 1 , k 2 , k 3 , q , and C AO ....
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che446_10_hw4 - Homework #4 ChE 446 Fall 2010 Problem 1....

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