Quasi-steady state reactor operation

It can be shown by simulation that a quasi-steady state can be reached for a fed-batch fermenter, where dX /dt=0 and //= l /V (Dunn and Mor, 1975). Since V increases, // must therefore decrease, and thus the reactor moves through a series of changing steady states for which //= I), during which Sj and ft decrease, and X remains constant. A detailed analysis of fed batch operation has been made by Keller and Dunn (1978). 

There is a number of points in relation to the proposed algorithm that should be mentioned in passing. (1) Maintenance requirements were not considered in the previous equation but can be included easily once the appropriate information is available. (2) Eq. (1) is valid at steady state only however, it can be employed for biochemical reactors operating in transient because the gases are essentially at quasi-steady state with respect to the culture. 

Figure 1.4. Flow chart sheet of the strategy of bioprocess kinetic analysis for different process situations stationary/instationary, homogeneous/heterogeneous, differential/ integral, and true dynamic/balanced (frozen) reactor operation, rds, rate-determining step qss, quasi-steady-state, (From Moser, A. 1983.)...

Transient reactor operation plays an increasingly important role in bioprocessing and has to some extent already been considered (classification, see Fig. 3.31 fed-batch culture, see Fig. 3.37 situation, see Fig. 4.4 guidelines to solution, see Sect. 4.2 and Fig. 4.5 structured cell model concept, see Fig. 4.7 application, see Chap. 6). Both balanced and frozen conditions have also been considered in Fig. 3.34. A biosystem is in balanced condition when the mechanism is fully adapted, as in a quasi-steady-state (if x ). All different equations can be reduced to algebraic equations. A biosystem is in frozen condition of the initial state (if x x ) and the mechanism may be neglected due to the fact that the slowest step is rate determining ( rds concept ). By this procedure, equations are reduced to parameters so that the number of equations is reduced (e.g., the case of dropwise addition of substrate). This is the case of steady state CSTR. 

In view of their own power requirements tokamak reactors have to be operated quasi-steady state with long burn times. Otherwise the mean energy gain would be too small and the circulating power of the system... 

Substitute t = z/u into the ODEs of Example 12.5. They then apply to a steady-state PER that is fed with freely suspended, pristine enzyme. There is an initial distance down the reactor before the quasi-steady equilibrium is achieved between S in solution and S that is adsorbed on the enzyme. Under normal operating conditions, this distance will be short. Except for the loss of catalyst at the end of the reactor, the PER will behave identically to the confined enzyme case of Example 12.4. Unusual behavior will occur if / / is small or if the substrate is very dilute so Ein. Then, the full equations in Example 12.5 should be (numerically) integrated. 

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