ch20 - 20-1 CHAPTER 20 SOLUTIONS20.1 Reactor with...

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Unformatted text preview: 20-1 CHAPTER 20 SOLUTIONS20.1 Reactor with Independent Feed Preheating. The degrees-of-freedom analysis is carried out based on the following assumptions: (a) Single reaction A to B; (b) Constant hold-up in both preheater and reactor; (c) Constant fluid densities throughout; (d) Well-mixed fluids in both reactor and heat exchanger hot and cold sides. FTJ0FCA0TFCA0TPFCATTJFFigure 1. Exothermic reactor with independent feed preheating. As shown in Fig. 1, there are nine variables: F, TJ0, TJ, F, CA0,CA, T, TPand T. Of these, three are externally specified, and constitute disturbances: TJ0, CA0andT. Four mass and energy balances relate the system variables: (1) a heat balance for the heat exchangers hot side, (2) a heat balance for the heat exchangers cold side, (3) a heat balance for the reactor, (4) a mass balance on component A for the reactor. Hence, the number of variables to be manipulated independently is NManipulated = NVariables- NExternallyDefined- NEquations= 9 - 3 - 4 = 2. This is also the number of system variables that can be controlled independently. Selection of Controlled Variables: TPshould be selected because of its strong influence on the stability of exothermic reactors. Bearing in mind that Tand CAare highly correlated, it is enough to pick one of these as a control variable. Since Tis easier to measure continuously, it is preferred.Selection of Manipulated Variables:The two obvious candidates are Fand F. An attractive configuration uses Fto control TPand Fto control T. 20-2 Heat-integrated Reactor. The degrees-of-freedom analysis is carried out based on the same assumptions as before. FCA0TFCA0TPFCATTJFCAFigure 2. Heat-integrated exothermic reactor. As shown in Fig. 2, there are nine variables: F, CA0,CA, T, TP, Tand TJ. Of these, two are externally specified, and constitute disturbances: TandCA0. The same four mass and energy balances as before relate the system variables. Hence, the number of variables to be manipulated independently is NManipulated = NVariables- NExternallyDefined- NEquations= 7 - 2 - 4 = 1. This is also the number of system variables that can be controlled independently. Selection of Controlled Variables: TPshould be selected because of its strong influence on the stability of exothermic reactors. It would be desirable to also select T, so that conversion can be controlled, but the degrees-of-freedom do not permit this. Selection of Manipulated Variables:The only free manipulated variable is F. The operability of the heat integrated reactor is significantly improved by installing a bypass on the heat exchanger, as shown in Fig. 3. FCA0TFCA0TPFCATTJFCATxF(1-x)FFigure 3. Heat-integrated exothermic reactor with heat-exchanger bypass. 20-3 This configuration increases the number of variables by two (xand T), and the number of equations by one (a heat balance on the mixing junction). Hence, the degrees-of-freedom increases to two. In the modified configuration, one would select the by-pass fraction,...
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ch20 - 20-1 CHAPTER 20 SOLUTIONS20.1 Reactor with...

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