Material balance expressions CSTRs

As can be seen for infinite recycle ratio where C = Cl, all reactions will occur at a constant C. The resulting expression is simply the basic material balance statement for a CSTR, divided here by the catalyst quantity of W. On the other side, for no recycle at all, the integrated expression reverts to the usual and well known expression of tubular reactors. The two small graphs at the bottom show that the results should be illustrated for the CSTR case differently than for tubular reactor results. In CSTRs, rates are measured directly and this must be plotted against the driving force of... 

The second expression derives from the material balance on a CSTR. 

A first principle mathematical description of a CSTR is based on balance equations expressing the general laws of conservation of mass and energy. Assuming that n components are mixed, the material balance of the i-component, taking into account all forms of supply and discharge in the volume V of the... 

Figure 11-18 shows the notations used in modeling and analysis of the fermentation process. The material balance on the microorganism in a CSTR at constant volume, assuming perfect mixing (i.e., concentrations of the cell and substrate inside and at the exit are the same) is expressed by ... 

Equation (7-54) allows calculation of the residence time required to achieve a given conversion or effluent composition. In the case of a network of reactions, knowing the reaction rates as a function of volumetric concentrations allows solution of the set of often nonlinear algebraic material balance equations using an implicit solver such as the multi variable Newton-Raphson method to determine the CSTR effluent concentration as a function of the residence time. As for batch reactors, for a single reaction all compositions can be expressed in terms of a component conversion or volumetric concentration, and Eq. (7-54) then becomes a single nonlinear algebraic equation solved by the Newton-Raphson method (for more details on this method see the relevant section this handbook). 

In these definitions, Qr and Kr have been used as arbitrary normalizing parameters. They can be readily identified for a constant volume reactor Qr = Qo = Qf = Q< 3nd Vr = y = Vm where represents the maximum volume of the reactor (in other words, the volume at which the reactor would function as a constant volume CSTR). Clearly, in this case f = F/Q = Fq/Qo is the true residence time. However, for the variable volume reactor, Qr and Fr have to be selected carefully on a case by case basis, and the residence time r= Fr/Qr should be regarded as no more than a parameter whose dimension is time or simply as pseudoresidence time. Using these dimensionless parameters (with normalizing variables different from those for an MFR), the general material balance of Equation 10.22 can be expressed as... 

Eq.(l) and (9) can be utilized for modeling a CSTR considering the material and energy balances as well as the expression for the rate flow of heat removed, Q. This heat rate is obtained from the overall heat transfer coefficient U and the transmission area A by the equation Q = UA(T — Tj) [1], [9], [13], [14], [18], [22],... 

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