Unsteady reactors

The general material balance of Section 1.1 contains an accumulation term that enables its use for unsteady-state reactors. This term is used to solve steady-state design problems by the method of false transients. We turn now to solving real transients. The great majority of chemical reactors are designed for steady-state operation. However, even steady-state reactors must occasionally start up and shut down. Also, an understanding of process dynamics is necessary to design the control systems needed to handle upsets and to enable operation at steady states that would otherwise be unstable. 

Unsteady mass and energy balances consider three kinds of accumulation  

These accumulation terms are added to the appropriate steady-state balances to convert them to unsteady balances. The circumflexes indicate averages over the volume of the system, e.g.. 

The three accumulation terms represent the change in the total mass inventory, the molar inventory of component A, and the heat content of the system. The circumflexes can be dropped for a stirred tank, and this is the most useful application of the theory. 

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Equations (1.1) to (1.3) are diflerent ways of expressing the overall mass balance for a flow system with variable inventory. In steady-state flow, the derivatives vanish, the total mass in the system is constant, and the overall mass balance simply states that input equals output. In batch systems, the flow terms are zero, the time derivative is zero, and the total mass in the system remains constant. We will return to the general form of Equation (1.3) when unsteady reactors are treated in Chapter 14. Until then, the overall mass balance merely serves as a consistency check on more detailed component balances that apply to individual substances. 

State. The washout function for an unsteady reactor is dehned as... 

Although percolation reactors have been in use extensively over several decades, it was not until 1983 that the first theoretical model of this type of reactor was introduced [5]. The model was developed for sequential first-order reactions in order to assess the performance in hydrolysis of hemicellulose. As an unsteady reactor, the model involves a partial differential equation with the following parameters kinetic parameter a = k2/kj operational parameter (3 = kiL/u, T = ut/L, where L is the bed length and u is the liquid flow velocity. 

The da/dt term in Equation 8.18 corresponds to unsteady operation. It will be used in Chapter 16 where the method of false transients is introduced as a solution technique for PDEs. It is also used to smdy unsteady reactors in Chapter 14. There are two... 

The RTD is normally considered a steady-state property of a flow system, but material leaving a reactor at some time 0 will have a distribution of residence times regardless of whether the reactor is at steady state. The washout function for an unsteady reactor is defined as... 

On the other hand, a step decrease in feed hydrogen resulted in a relatively very rapid and monotonic decline to the final steady-state ethylene concentration. It should be noted that the sum of all hydraulic and mixing lags for this system is of the order of 75 s and the diffusional relaxation time (R /Dg) is much smaller than one second. Hence, the extremely slow response observed in the step-up experiment and its asymmetry compared to the step-down result suggest that non-linear dynamics of the gas phase-catalyst surface interaction play a major role in unsteady reactor behavior. 

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