Residence-time distributions multiple reactions

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

Practical design problems may need to take into account many additional factors, including the recycle of some reactants (such as hydrogen), residence time distribution, inhomogeneity of the packing, multiple reactions, approach to equilibria, and so on. All of these problems have been encountered before, and professional simulator routines for solving them are versatile, effective and as reliable as the data provided to them. At least half a dozen such computer packages are commercially available. 

After studying this chapter the reader will be able to describe the cumulative F(t), external age E(t), and internal age I(t) residence-time distribution functions and to recognize these functions for PFR, CSTR, and laminar flow reactions. The reader will also be able to apply these functions to calculate the conversion and concentrations exiting a reactor using the segregation model and the maximum mixedness model for both single and multiple reactions. 

In Pan 2 we will learn how to use the residence time data and functions to make predictions of conversion and exit concentrations. Because the residence time distribution is not unique for a given reaction system, we must use new models if we want to predict the conversion in our nonideal reactor. We present the five most common models to predict conversion and then close the chapter by applying two of these models, the segregation model and the maximum mixedness model, to single and to multiple reactions. 

The simplest kinetic reactor model is the CSTR (continuous-stirred-tank reactor), in which the contents are assumed to be perfectly mixed. Thus, the composition and the temperature are assumed to be uniform throughout the reactor volume and equal to the composition and temperature of the reactor effluent However, the fluid elements do not all have the same residence time in the reactor. Rather, there is a residence-time distribution. It is not difficult to provide perfect mixing of the fluid contents of a vessel to approximate a CSTR model in a commercial reactor. A perfectly mixed reactor is used often for homogeneous liquid-phase reactions. The CSTR model is adequate for this case, provided that the reaction takes place under adiabatic or isothermal conditions. Although calculations only involve algebraic equations, they may be nonlinear. Accordingly, a possible complication that must be considered is the existence of multiple solutions, two or more of which may be stable, as shown in the next example. 

The simplest cases occur where either the gas is inert (i.e. y=0 in Equation (42) as in limestone calcination) or the gas is present in great excess. In these cases the conversion of gaseous reactants can be ignored, and it is sufficient to consider only the kinetics of the reactions, the residence time distribution of the solids and an overall energy balance. Kunii and Levenspiel (20) and Fane and Wen (13) provide expressions for solids conversions in single or multiple beds for such cases. 

The tubular reactor with static mixers was chosen for the documented capability of static mixers to accomphsh the following important functions for fast multiple reactions in turbulent flow (1) homogeneity down to the molecular level can be achieved in a few tube diameters (2) very short mixing time and narrow residence time distributions are required and (3) high rates of energy dissipation are achievable (average energy dissipation rates can be calculated from pressure drop and local rates can be estimated). 

The autoclave reactor is a single or a multiple stage continuous stirred tank reactor (CSTR), as shown in Figures 4.2 and 4.3, with its characteristic residence time distribution. The different reaction zones can be isolated by means of proper baffles at the agitator itself. The number of zones in a multistage autoclave varies between... 

We will now show how different RTDs with the. same mean residence time can produce different product distributions for multiple reactions. 

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