Fixed fundamental balance equations

Various laws restrict the values of the process quantities. These laws may represent either fundamental, empirical physicochemical relationships or experimentally identified equations (from statistical modelling or from dimensional analysis particularizations). In contrast to statistical or dimensional analysis based models [1.14], which are used to fix the behaviour of signal transformers, the models of transport phenomena are used to represent generalized phases and elementary phase connections. Here, the model equations reveal all the characterizing attributes given in the description of a structure. They include balance equations, constitutive equations and constraints. 

Nonconstant density. In the general case, we can consider the following variables to fully determine the state of the reactor T, P, n/, IT. We assume throughout that the feed conditions, Q/,Cj/, are specified. In the nonconstant density case, we switch to rij from Cj because the material balance is fundamentally a balance on total moles in the reactor, not molar concentrations. If we know the Uj and Vr, then the values of the Cj are known, as required in the reaction rate expressions and the equation of state. To specify the right-hand sides of the material balances, Equation 4.47, we also require the value of Q. Because T,P are regarded as known, fixed constants in this chapter, the set of unknowns is rij, Vr, Q. We therefore have tis + 2 unknowns to determine and require Us+ 2 equations. We have the n, equations from the component mole balances, Equations 4.47. The equation of state, Equation 4.53, provides one additional equation. The final equation is provided by... 

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