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Chemical Engineering Hand Written_Notes_Part_5

Chemical Engineering Hand Written_Notes_Part_5 - 12 1...

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Unformatted text preview: 12 1. MATHEMATICAL MODELING AND SIMULATION LT TT LC FT FC Hot Water Flow Cold Water Flow Steam Flow CV-1 CV-2 CV-3 Level Setpoint Flow Setpoint Valve Position Figure 6. Stitted Tank Heater (STH) System Now, f ow out due to the gravity is also a function of height F = k √ h Thus, (2.34) A dh dt + k √ h = F i Total energy of liquid in the tank is given by E = U + k + P However, since tank does not move dk dt = dP dt = 0 ; dE dt = dU dt For liquid systems (2.35) dU dt ≈ dH dt where H is total enthalpy of the liquid in the tank. (2.36) H = ρV C p ( T − T ref ) = ρAhC p ( T − T ref ) T ref represents reference temperature where the speci F c enthalpy of the liquid is assumed to be zero. Now, using the energy conservation principle (2.37) d ( ρAhC p ( T − T ref )) dt = ρF i C p ( T i − T ref ) − ρF C p ( T − T ref ) + Q 2. MECHANISTIC MODELS AND ABSTRACT EQUATION FORMS 13 where Q is the amount of heat supplied by the steam per unit time. Assuming T ref = 0 , we have (2.38)(2....
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