D The total energy balance from Sec. 5 is given by 36 1 Basic Concepts In this case the number of components, S=4 and the number of reactions, R=2. The reaction enthalpies at standard temperature, Tst, are then All heats of formation, AHFi, are at standard temperature.
Dimensionless variables can be defined as The equations become where z is the residence time (=V/F). The number of parameters is reduced, and the equations are in dimensionless form. An equivalency can be demonstrated between the concept of time constant ratios and the new dimensionless parameters as they appear in the model equations. The concept of time constants is discussed in Sec. 2. Thus the variables in this example can be interpreted as follows 1 - Transfer time constant -- Convection rate KLa 1' : Residence time constant Transfer rate and kc,, KLa = Transfer time constant Reaction time constant - Reaction rate Transfer rate Further examples of the use of dimensionless terms in dynamic modelling applications are given in Sec.
Component balancing for species i. 2 Formulation of Dynamic Models In the case of chemical reaction, the balance equation is represented by Rate of accumulation of mass of component i in the system Mass flow of Mass flow of Rate of the system the system by reaction Expressed in terms of volume, volumetric flow rate and concentration, this is equivalent to d(VCi) = (Fo Cio)-(Fl Cil)+(ri V) dt with dimensions of masdtime In the case of an input of component i to the system by interfacial mass transfer, the balance equation now becomes i Rate of accumulation of mass of component in the system Mass flow of Mass flow of Rate of interfacial the system the system of component i into the system d(VCi) - (Fo Cio) dt - (F1 Cil) + Qi where Qi, the rate of mass transfer is given by Qi = Ki AACi 1 .