Multiple reactions energy balance

Energy balance— multiple reactions— reactors in series... 

The various energy transfer constraints enter into the analysis primarily as boundary conditions on the difference equations, and we now turn to the generation of the differential equations on which the difference equations are based. Since the equations for the one-dimensional model are readily obtained by omitting or modifying terms in the expressions for the two-dimensional model, we begin by deriving the material balance equations for the latter. For purposes of simplification, it is assumed that only one independent reaction occurs within the system of interest. In cases where multiple reactions are present, one merely adds an appropriate term for each additional independent reaction. 

If feed at a specified rate and T0 enters a CSTR, the steady-state values of the operating temperature T and the fractional conversion fA (for A —> products) are not known a priori. In such a case, the material and energy balances must be solved simultaneously for T and fA. This can give rise to multiple stationary states for an exothermic reaction, but not for an endothermic reaction. 

For an endothermic reaction, whether the operation is adiabatic or nonadiabatic, there is no possibility of multiple stationary-states because of the negative slope of the /A versus T relation in the energy balance (see equation 14.3-11). This is illustrated schematically in Figure 14.8. 

Figure 14.8 Illustration of solution of material and energy balances for an endothermic reaction in a CSTR (no multiple stationary-states possible)...

In this chapter and in Chapter 6 we will usually solve these equations assuming a single first-order irreversible reaction, r = k T)C/. Other orders and multiple reactions could of course be considered, but the equations are much more difficult to solve mathematically, and the solutions are qualitatively the same. We will see that the solutions with these simple kinetics are sufficiently complicated that we do not want to consider more complicated kinetics and energy balances at the same time. 

The performance of propints is a unique function of the temp of the hot reaction products, their compn and their pressure. The pro-pint bums at constant pressure and forms a set of products which are in thermal and chemical equilibrium with each other. The multiplicity of the reaction products requires that the combustion chamber conditions be calcd from the solution of simultaneous equations of pressure and energy balances. This calcn is best performed by computer, although the manual scheme has been described well by Sutton (Ref 14) and Barr re et al (Ref 10). The chamber conditions determine the condition in the nozzle which in turn characterizes the rocket engine performance in terms of specific impulse and characteristic exhaust velocity... 

These forms of the energy balance will be applied to multiple reactions... 

In this section we give the energy balance for multiple reactions that are in parallel and/or in series. The energy balance for a single reaction taking place in a PFR was given by Equation (8-60)... 

For q multiple reactions and m species, the CSTR energy balance becomes... 

For multiple reactions occurring in either a semibatch or batch reactor, Equation (9-18) can be generalized in the same manner as the steady-state energy balance, to give... 

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. 

Below, we describe tbe design formulation of isothermal batch reactors with multiple reactions for various types of chemical reactions (reversible, series, parallel, etc.). In most cases, we solve the equations numerically by applying a numerical technique such as the Runge-Kutta method, but, in some simple cases, analytical solutions are obtained. Note that, for isothermal operations, we do not have to consider the effect of temperature variation, and we use the energy balance equation to determine tbe dimensionless heat-transfer number, HTN, required to maintain the reactor isothermal. 

In the remainder of the chapter, we discuss how to apply the design equations and the energy balance equations to determine various quantities related to the operations of CSTRs. In Section 8.2 we examine isothermal operations with single reactions to illustrate how the rate expressions are incorporated into the design equation and how rate expressions are determined. In Section 8.3, we expand the analysis to isothermal operations with multiple reactions. In Section... 

When more than one chemical reaction takes place in the reactor, we have to determine how many independent reactions there are (and how many design equations are needed) and select a set of independent reactions. Next, we have to identify all the reactions that actually take place (including dependent reactions) and express their rates. We write Eq. 8.1.1 for each independent chemical reaction. To solve the design equations (obtain relationships between Z s and t), we express the rates of the individual chemical reactions in terms of the Zm Js and t. Since the temperature is constant, the energy balance equation is used to determine the heating load. The procedure for designing isothermal CSTRs with multiple reactions goes as follows ... 

The design formulation of nonisothermal CSTRs with multiple reactions follows the same procedure outlined in the previous section—we write the design equation, Eq. 8.1.1, for each independent reaction. However, since the reactor temperature, out> is not known, we should solve the design equations simultaneously with the energy balance equation (Eq. 8.1.14). 

We will use this form of the energy balance for membrane reactors and also extend this form to multiple reactions. 

Energy Balance for Multiple Reactions in Plug-Flow React ... 

Closure. After completing this chapter, the reader should be able to appi the unsteady-state energy balance to CSTRs, semibatch and batch reactor The reader should be able to discuss reactor safety using two examples on a case study of an explosion and the other the use of the ARSST to hel prevent explosions. Included in the reader s discussion should be how t start up a reactor so as not to exceed the practical stability liniit. After reac ing these examples, the reader should be able to describe how to operat reactors in a safe maimer for both single and multiple reactions. 

---