Molar flow multiple reactions

In a variable-density reactor the residence time depends on the conversion (and on the selectivity in a multiple-reaction system). Also, in ary reactor involving gases, the density is also a function of reactor pressure and temperature, even if there is no change in number of moles in the reaction. Therefore, we frequently base reactor performance on the number of moles or mass of reactants processed per unit time, based on the molar or mass flow rates of the feed into the reactor. These feed variables can be kept constant as reactor parameters such as conversion, T, and P are varied. 

The third way to determine unknown molar flow rates for a reactive process is to write expressions for each product species flow rate (or molar amount) in terms of extents of reaction using Equation 4.6-3 (or Equation 4.6-6 for multiple reactions), substitute known feed and product flow rates, and solve for the extents of reaction and the remaining reactive species flow rates. The degree-of-freedom analysis follows ... 

As we shall see later in the book, there ate some instances in which it is timch more convenient to work in teims of the number of moles (Aa.Ab) or molar flow rates (F, Fg, etc.) rather than conveision. Membrane reactors and gas-phase multiple reactions are two such cases where molar flow rates rather than conversion are preferred. Consequently, the concentrations in the rate laws need to be expressed in terms of (he molar flow rates. We start by recalling and combining Equations (3-40) and (3-41) ... 

Table 8-3 gives the algorithm for the design of PFRs and PBRs with heat exchange for case A conversion as the reaction variable and case S molar flow rates as the reaction variable. The procedure in case B must be used when multiple reactions are present... 

As discussed in Chapter 6, when multiple reactions occur in reacting systems, it is best to work in concentrations, moles, or molar flow rates rather than conversion. 

We see tliiu conversion is not used in this sum. The molar flow rates, Fj, are found by solving the mole balance etjuations. Equation (.1-42) will be u.seci for measures other than ctmversion when we discuss nienibrane reactors (Chapter 4 Part 2) and multiple reactions (Chapter 6). We will use this form of the concentration equation for multiple gas-phase reactions and for membrane reactors. 

We divide the chapter into two parts Part 1 Mote Balances in Terms of Conversion, and Part 2 Mole Balances in Terms of Concentration, C,. and Molar Flow Rates, F,." In Pan 1, we will concentrate on batch reactors, CSTRs, and PFRs where conversion is the preferred measure of a reaction s progress for single reactions. In Part 2. we will analyze membrane reactors, the startup of a CSTR. and semibatch reactors, which are most easily analyzed using concentration and molar How rates as the variables rather than conversion. We will again use mole balances in terms of these variables (Q. f,) for multiple reactors in Chapter 6. 

Chemical Reaction Engineering. There is a greater emphasis on the use of mole balances in terms of concentrations and molar flow rates rather than conversion. It is introduced early in the text so that these forms of the balance equations can be easily applied to membrane reactors and multiple reactions, as well as PFRs. PBRs. and CSTRs. 

For multiple reactions, the set of the stoichiometric independent reactions must be integrated simultaneously. Molar extent of reaction is more convenient as reaction variable, at best by reference to the total mass flow =, / /w. The mass balance equations become ... 

The solution to this problem requires an analysis of multiple gas-phase reactions in a differential plug-flow tubular reactor. Two different solution strategies are described here. In both cases, it is important to write mass balances in terms of molar flow rates and reactor volume. Molar densities and residence time are not appropriate for the convective mass-transfer-rate process because one cannot assume that the total volumetric flow rate is constant in the gas phase, particularly when the total number of moles is not conserved. In each reaction, 2 mol of reactants generates 1 mol of product. Furthermore, an overall mass balance suggests that the volumetric flow rate is constant only when the overall mass density does not change. This is a reasonable assumption for liquid-phase reactors but not for gas-phase problems when the total volume is not restricted. The exception is a constant-volume batch reactor. 

The solution strategy described above is based on writing a differential plug-flow reactor mass balance for each component in the mixture, and five coupled ODEs are solved directly for the five molar flow rates. The solution strategy described below is based on the extent of reaction for independent chemical reactions, and three coupled ODEs are solved for the three extents of reaction. Molar flow rates are calculated from the extents of reaction. The starting point is the same as before. The mass balance is written for component i based on molar flow rate and differential reactor volume in the presence of multiple chemical reactions ... 

Equation (8.3.4) may also be used in the analysis of kinetic data taken in laboratory scale stirred-tank reactors. One may determine the reaction rate directly from a knowledge of the reactor volume, the molar flow rate of the limiting reagent, and stream compositions. The fact that one may determine the rate directly and without integration makes stirred-tank reactors particularly attractive for use in studies of reactions with complex rate expressions (e.g., enzymatic or heterogeneous catalytic reactions) or of systems in which multiple reactions take place. Equation (8.3.4) is... 

Figure 2.18 Molar flow diagram for a multiple-reaction system.

Figure 2.22 Molar flow diagram for multiple-inputs, multiple-outputs, and multiple reactions.

If a reduction in the number of molar balances is desired for the calculations, the stoichiometric relationships developed in the previous section must be utilized. We can thus reduce the number of necessary balance equations from N to S one should keep in mind that the number of chemical reactions is usually much lower than the number of components in a system. The molar flows, /, can be replaced by expressions containing reaction extent, specific reaction extent, and reaction extent with concentration dimension or conversion (, I, I", or tia) in a system containing a single chemical reaction. For systems with multiple chemical reactions, h is replaced by an expression containing or i). ... 

The multiple reaction algorithm can be applied to parallel reactions, series reactions, complex reactions, and independent reactions. The availability of software packages (ODE solvers) makes it much easier to solve problems using moles or molar flow rates Fj rather than conversion. For liquid systems, concentration is usually the preferred variable used in the mole balance equations. 

Equation (12-5) is coupled with llte mole balances on each species [Equation (11 -33)]. Next, we express as a function of either the concentrations for liquid systems or molar flow rates for gas systems, as desenbed in Chapter 4. We will use the molar flow rate form of the energy balance for membrane reactors and also extend this form to multiple reactions. 

Table 12-2 gives the algorilhrn for the design of PFRs and PBRs with heat exchange In Case A Conversion is reaction variable and in Case B Molar Flow Rares are the reaction variables. The procedure in Case B must be used to analyze multiple reactions with heat effects. 

Total change in molar flow rate—multiple reactions in a flow system at steady state... 

The variable that describes composition in Eqn. (3-5) is Nu the total moles of species i . It sometimes is more convenient to work problems in terms of either the extent of reaction or the fractional conversion of a reactant, usually the limiting reactant. Extent of reaction is very convenient for problems where more than one reaction takes place. Fractional conversion is convenient for single-reaction problems, hut can he a source of confusion in problems that involve multiple reactions. The use of all three compositional variables, moles (or molar flow rates), fractional conversion, and extent of reaction, wiU be illustrated in this chapter, and in Chapter 4. 

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