Time Dependence—The Transient Approach to Steady-State and Saturation Kinetics

3 Time Dependence—The Transient Approach to Steady-State and Saturation Kinetics 

Although thesteady-stateCSTRissimpletooperateand analyzeand even thoughit offers 

Once B isformed,ittooundergoesadsorptionanddesorption.Thedesorptioncarries B from the surface and into the bulk fluid phase. In this case we will assume that the reaction is 

The surface concentration is dif ficult to measure thus we need to reexpress it in terms of thebulkphaseconcentration of species A. To do this we take advantage of the factthatthe 

Recallthatthesolidcatalystoccupiesafraction 1 — e ofthereactorvolumeleavingafraction e forthe fluidphasevolume.Wewritethebalancesintermsofthe fluidphase.Thekinetics havebeen written also intermsof the fluidphaseconcentration,buttheyarewrittenfora 

Although the steady-state CSTR is simple to operate and analyze and even though it offers real advantages to the kineticist, it is also true that these systems must go through a start-up. They do not start up and necessarily achieve steady state instantaneously. The time period in which the system moves toward a steady-state condition is called the transient, meaning that the system is in transition from one that is time-dependent to one that is time-independent. 

We have no way of knowing how long it will take a given reaction or set of reactions to achieve a steady state in the CSTR before we either do an experiment or solve the time-dependent model equations. If we choose to do experiments as a means to assessing this, then we need to be prepared to do many of them. But if we already know the kinetics, then we do the analysis and the math instead. If we do it correctly, then it is fast and it provides us with insights that complement the experiments and in many cases provides interpretations that a purely experimental approach cannot yield. Therefore, in this problem we will consider just such a case with a more complex set of kinetics. 

As we saw in Chapter 6, when we analyze a reaction of this kind we find that at least two steps are involved—adsorption and surface reaction. The adsorption equilibrium steps take place by the interaction of the molecule in the bulk phase with a so-called adsorption site on the solid surface. The adsorption site is the locus of points on the surface that interact directly with the molecule  

Once B is formed, it too undergoes adsorption and desorption. The desorption carries B from the surface and into the bulk fluid phase. In this case we will assume that the reaction is irreversible and that the rate of this reaction is first order in the surface concentration of A. It also is first order in the concentration of surface sites. Thus the kinetics follow a simple surface 

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