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Chemical Engineering Hand Written_Notes_Part_6

Chemical Engineering Hand Written_Notes_Part_6 - 14 1...

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14 1. MATHEMATICAL MODELING AND SIMULATION Figure 7. System response to step change in T i Figure 8. System reponse for step change in F i solution of the equation (2.39) using the initial as condition T (0) = T , the steady state value of T . F i is decreased by 10% from its steady state value F i : Since F i appears in both the dynamic equations, the temperature and the liquid level will start changing simultaneously and the dynamics will be governed by simultaneous solution of coupled nonlinear di ff erential equations (2.39- 2.40) starting with initial conditions T (0) = T, h (0) = h. Figures 8 show schematic diagrams of the process responses for step change in F i . It is also possible to investigate response of the system for more complex inputs, such as T i ( t ) = T i + T i sin( ωt ) where above function captures daily variation of cooling water inlet tempera- ture. In each case, the transient behavior T ( t ) and h ( t ) is computed by solving the system of ODEs subject to given initial conditions and time variation of independent inputs (i.e. forcing functions).
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2. MECHANISTIC MODELS AND ABSTRACT EQUATION FORMS
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