Process Dynamics Lecture 1 ChE 479 Fall 2000 Pr. Alexander Couzis

Process Dynamics Dynamics Implies that the process behavior/performance is not at steady state, i.e. the process variables change with time. The process still obeys the same laws (mass and energy conservation). The time derivative component, is not zero.

Example: Well Mixed Tank Gather all relevant information: –The tank is well mixed; –Input flow rate is m 3 /min; –Tank Volume is V=2.1m 3 ; –C Ainit = mole/m 3 ; –  C A0 = mole/m 3 ; –The system is initially at steady state Assumptions: –Density of liquid constant

Example: Well Mixed Tank Conservation Balance: Accumulation = Input- Output+Generation Overal Material Balance Accumulation = Input- Output Component Material Balance (Accumulation of Component i) = (Input of i)- (Output of i)+(Generation of Component i) Energy Balance Accumulation of E+PE+KE=(E+KE+PE in)-(E+KE+PE out)+Q-W

Example: Well Mixed Tank Constitutive Equations –Heat Transfer Q=hA  T –Chemical Reaction Rate: r A =k 0 e -(E/RT) C A –Fluid Flow: F=C v (  P/  ) 1/2 –Equation of State: PV=nRT –Equilibrium: y i =k i x i Degrees of Freedom (DOF) DOF = NV -NE DOF = 0 exactly specified; DOF 0 underspecified

Material Balance on Well Mixed Tank (Overal Mass Balance) Consitutive Equation

Material Balance on Well Mixed Tank (Overal Mass Balance) Variables are C A, and F 1 ===>DOF = = 0  is the time constant of the system, in this case it describes the residence time of the tank