Single Reaction Systems

Having considered reactor temperature and pressure, we are now in a position to judge whether the reactor phase will be gas, liquid, or multiphase. Given a free choice between gas- and liquid-phase reactions, operation in the liquid phase is usually preferred. Consider the single reaction system from Eq. (2.19) ... 

We noted earlier that chemical engineers are seldom concerned with single-reaction systems because they can always be optimized simply by heating to increase the rate or by finding a suitable catalyst [You don t need to hire a chemical engineer to solve the problems in Chapter 3]. Essentially aU important processes involve multiple reactions where the problem is not to increase the rate but to create a reactor configuration that will maximize the production of desired products while rninirnizing the production of undesired ones. 

In this chapter we consider the performance of isothermal batch and continuous reactors with multiple reactions. Recall that for a single reaction the single differential equation describing the mass balance for batch or PETR was always separable and the algebraic equation for the CSTR was a simple polynomial. In contrast to single-reaction systems, the mathematics of solving for performance rapidly becomes so complex that analytical solutions are not possible. We will first consider simple multiple-reaction systems where analytical solutions are possible. Then we will discuss more complex systems where we can only obtain numerical solutions. 

In Chapter 2 we sketched the processes by which petroleum is refined and polyester is made from petroleum fractions and natural gas liquids. In Chapter 3 we sketched the history of the major petrochemical companies and looked at several important single-reaction systems. In this chapter we will consider the evolution of feedstocks and intermediates in the petroleum and chemical industries. 

Most industrial processes use catalysts. Homogeneous single reaction systems are fairly rare and unimportant. The most important homogeneous reaction systems in fact involve free radical chains, which are very complex and highly nonlinear. 

To fix the singular points, additional NR conditions are needed. For NR = 1 - that is, a single-reaction system - there is exactly one additional governing equation which is simply Eq. (7) (condenser) or Eq. (8) (reboiler) with i = k, where k is the reference... 

Most textbook discussions of effectiveness factors in porous, heterogeneous catalysts are limited to the reaction A - Products where the effective diffusivity of A is independent of reactant concentration. On the other hand, it is widely recognized by researchers in the field that multicomponent single reaction systems can be handled in a near rigorous fashion with little added complexity, and recently methods have been developed for application to multiple reactions. Accordingly, it is the intent of the present communication to help promote the transfer of these methods from the realm of the chemical engineering scientist to that of the practitioner. This is not, however, intended to be a comprehensive review of the subject. The serious reader will want to consult the works of Jackson, et al. 

Mass and energy balances on the reactor provide the basis for relating the production rate and composition of the products to the chemical-reaction rate. If the operation is not steady, changes with time are also involved. In a single-reaction system one reactant is usually critical because of cost... 

Perhaps the clearest way of explaining these methods of interpreting laboratory data is to carry out specific examples in some detail, pointing out the features of the method which are general and applicable to any reaction. In Example 4-4 the integration and differential methods are applied to a single-reaction system. Example 4-5, which is concerned with the homogeneous reaction of sulfur vapor and methane to produce carbon disulfide, involves multiple reactions. 

In Example 5-3 the temperature and conversion leaving the reactor were obtained by simultaneous solution of the mass and energy balances. The results for each temperature in Table 5-7 represented such a solution and corresponded to a diiferent reactor, i.e., a different reactor volume. However, the numerical trial-and-error solution required for this multiple-reaction system hid important features of reactor behavior. Let us therefore reconsider the performance of a stirred-tank reactor for a simple single-reaction system. 

For chemical reaction equilibrium in a single-phase, single-reaction system, these criteria lead to (see,I>ec. 8.8)... 

For all future chemical equilibrium calculations in single-phase, single-reaction systems, we will start from Eqs. 13.1-12 or 13 as appropriate, rather than starting at Eq. 

Although multiple reactors can be used for single reaction systems, they are potentially not required. For systems involving multiple reactions, reactor stiuctures may be essential— unlocking certain states that would not... 

Thus, one rate of reaction (e.g., it can of course be Rb or Rc or Rq, but only one rate of reaction) defines automatically, together with the stoichiometric numbers, the other rates of reactions as long as it is a single reaction system. 

We have made it very clear earlier that the single reaction system is fully defined (and solvable) in terms of any conversion for one of the reactants or any yield of one of the products. We have also made it very clear that all rates of reaction of the components of a single reaction are fully defined in terms of one rate of reaction. 

Figure 6.2 Mass balance for single-input, single-output, and single reaction system.

The analogy to Equation 3.67, which is valid for single-reaction systems, is elegant. Equation 3.85 allows the possibility of calculating the molar fractions, x, for all components, from the relative conversions, of the key components. 

These systems excel due to their small size and the option to be operated on site rather than in physically separated facilities. A characteristic of lab-on-a-diip applications is that all process steps are conducted in a single reaction system, where all process steps are highly automated. They comprise on a few square inches only the complete set of consecutive steps starting from sample preparation to final detection. Typical applications are qualitative and quantitative analyses on the microscale of DNA, RNA, proteins, and cells. They can even be used for syntheses on the analytical scale [1—4]. 

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