PSet_03_solution

# PSet_03_solution - Spring 2003 10.450 Process Dynamics...

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T o Q Spring 2003 10.450 Process Dynamics, Operations, and Control Problem Sets - 3 1. You are responsible for a reactor in which an exothermic liquid-phase reaction occurs. The feed must be preheated to the threshold activation temperature of the catalyst, but the product stream must be cooled. To reduce utility costs, you are considering installing a heat recovery system in which the product preheats the feed. Of course you will design and select the heat exchanger to handle the desired steady-state heat duty, but you would also like to consider the control system as part of the design. That means you want to understand the system dynamics - how variations in the inlet temperature and reactor heat load affect the outlet temperature. You therefore represent the system as a collection of first-order lags. Here the heat exchanger is represented as two stirred tanks connected by heat transfer area A. Each tank will have its own volume. The heat of reaction is represented by a heating coil that delivers power Q. T i T o T i T 1 T 2 feed prod A 2 a. Model the system: begin with M&E balances and obtain standard-form differential equations. Classify your variables as input, intermediate, and output. (You have 3 tanks - how many equations do you expect?) Three equations, of course - we must write an energy balance on each tank. For example, on the tank representing the feed side of the heat exchanger, d ( V 1 r C p ( T 1 - T r ) ) = F r C p ( T i - T r ) - F r C p ( T 1 - T r ) + UA ( T o - T 1 ) T 1 (0) = T 1 s dt T r is a reference temperature for defining enthalpy of the flowing liquid. In our simplified

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