Transient CSTR

Note that this is exactly the transient CSTR equation we derived previously, and elimination of the flow terms yields the batch reactor. Keeping aU these terms and allowing Uq, v, V, and Cao to vary with time yields the semibatch reactor. 

While this equation is correct for the steady-state CSTR with variable density, it does not give a correct description of the transient CSTR for variable density because Na (meaning the number of moles of species A in the reactor) is not given by the preceding expression unless the density is constant. 

These are two coupled algebraic equations, which must be solved simultaneously to determine the solutions Cj(x) and T(t). For multiple reactions the + 1 equations are easily written down, as are the differential equations for the transient situation. However, for these situations the solutions are considerably more difficult to find We will in fact consider theaolutions of the transient CSTR equations in Chapter 6 to describe phase-plane trajectories and the stability of solutions in the nonisothermal CSTR. 

The food and water processing reactor system has a semibatch feed, continuous chemical reactors, and a semibatch elimination system. Food is chewed in the mouth to small pieces of solid and enters the stomach every 8 hours or so. In the stomach food is further mixed with water, acidified, and mixed with enzymes, which begin reacting it into small particles and molecules. The food mixes in the stomach (volume 0.5 Hter), but its feed is semibatch so we describe it as a transient CSTR. 

For a CSTR we solve the transient CSTR mass-balance equation because we want the time dependence of a pulse injection without reactiou The transient CSTR equation on a species of concentration C is... 

Note that this is simply the transient CSTR equation with the reaction term omitted, which implies either no reaction (r = 0) or that the species in question is an inert in a reacting system so that its stoichiometric coefficient is zero. 

If the fluid is mixed, the transient CSTR equation becomes dC ... 

Another reactor equation useful in reaction kinetics analyses represents the transient CSTR. This situation is encountered in temperature-programmed desorption and isotope tracer experiments. The material balance for the transient CSTR operating at constant total pressure for an ideal gas is... 

Abraham (1) used Z-transforms with numerical evaluation to handle the transient behavior of a CSTR for this mechanism. Smith and Sather (45) had earlier attempted analytical and numerical solution of this transient CSTR. The large number of equations and storage limitations of even large computers limited them to degrees of polymerization of less than 75. 

Transient CSTR, Batch, and Semibatch Reactors with Heat Exchanger—Ambient Temperature Not Spatially Uniform... 

Figure 8.14. Transient CSTR, Le = 0.1, integration to r = 100, elapsed time = 5.67 s.

Problem 8.10 is considered as a transient CSTR. The equations governing it are... 

Energy balance on a transient CSTR or sernibatch reactor. 

For the non-transient CSTR model the design equation reduces to... 

Figure 2. N2TPD from an iron-based catalyst. Comparison of the modeling results using either the transient CSTR model (solid line B) or the PFR model (dashed line C). TTie inset shows the experimental trace (solid line A) obtained by Muhler et al.[10]...

We have seen how the kinetics fit into a reactor equation as a constitutive relationship. Elow and reaction come together in these systems to affect the rate of accumulation. Hence when we refer to the "rate" we must be careful to be specific about the reactor—if it is a constant volume batch reactor, then rate means the chemical rate. If the reactor is a transient CSTR or PER, then the rate of change of the concentration at the exit of the reactor is not the chemical rate alone. Mixing effects are important and we have seen how to begin to account for the fluid mechanics in a reactor through the empirical measure of the r.t.d. The r.t.d. does affect the outcome from the reactor, but the sensitivity to the r.t.d. depends upon the kinetics and their fimctional form. 

Figure 4.1 Variation of concentration in a transient CSTR reactor...

Insertion of these rate laws in mass balances of ideal reactors (batch/plug flow or transient CSTR) leads to systems of semi-linear, first-order, partial differential equations, with a single family of characteristics [Eq. (139)]. 

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