Algorithms mole balances

Write out the general algorithm and derive an expression for conversion as a function of time, the reactor parameters, and the catalyst parameters. Fill in the following algorithm Mole balance Rate law Decay law Stoichiometry ... 

Closure. The goal of this text is to weave the fundamentals of chemical reaction engineering into a structure or algorithm that is easy to use and apply to a variety of problems. We have just finished the first building block of this algorithm mole balances... 

Analysis In this example we used our CRE algorithm (mole balance —> rate law — sioichiomeiry... 

There are a number of instances when it is much more convenient to work in terms of the number of moles (iV, N-g) or molar flow rates (Fj, Fg, etc.) rather than conversion. Membrane reactors and multiple reactions taking place in the gas phase are two such cases where molar flow rates rather than conversion are preferred. In Section 3.4 we de.scribed how we can express concentrations in terms of the molar flow rates of the reacting species rather than conversion, We will develop our algorithm using concentrations (liquids) and molar flow rates (gas) as our dependent variables. The main difference is that when conversion is used as our variable to relate one species concentration to that of another species concentration, we needed to write a mole balance on only one species, our basis of calculation. When molar flow rates and concentrations are used as our variables, we must write a mole balance on each species and then relate the mole balances to one another through the relative rates of reaction for... 

We now will apply this algorithm to a specific situation. The first step is to derive or apply the mole balance equation for the system at hand. Suppose that we have, as shown in Figure 4-2, mole balances for three reactors, three... 

Sec. 6.3 Algorithm tor Solution to Complex Reactions (2) Mole balance on NHj ... 

It is acceptable (and usual) for the value of n calculated from Equation (14-12) to be a noninteger in Equation (4-11) to calculate the conversion. For reactions other than first-order, an integer number of reactors must be used and sequential mole balances on each reactor must be carried out. For example, if x /a =2.8 then one would round up to three tanks. The conversion and effluence concentrations would be solved sequentially using the algorithm developed in Chapter 4. That is, after solving for the effluent from the first tank, it would be used and the input to the second tank and so on. 

Fijture 4-11 Isulbermul reaction design algorithm for mole balances. 

In this chapter, we discuss reactor selection and general mole balances for multiple reactions. First, we describe the four baste types of multiple reactions series, parallel, independent, and complex. Next, we define the selectivity parameter and discuss how it can be used to minimize unwanted side reactions by proper choice of operating conditions and reactor selection. We then develop the algorithm that can be used to solve reaction engineering problems when multiple reactions are involved. Finally, a number of examples are given that show how the algorithm is applied to a number of real reactions. 

The algorithm for solving complex reactions is applied to a gas-pha.se reaction in Figure 6-5. This algorithm is very similar to the one given in Chapter 4 for w riling the mole balances in terms of molar flow rates and concentrations (i.e.. 

Figure 4-11). After numbering each reaction, we write a mole balance on eac species similar to those in Figure 4-11. The major difference between the iw algorithms is in rate law step. Here we have four steps ( , , . and ) t find the net rate of reaction for each species in terms of the concentration c the reacting species in order to combine them with their respective mole ba ances. The remaining steps are analogous to those in Figure 4-8.

Examples on How to Ese Table 8-1. Wc now couple the energy balance equations in Table 8-1 with the appropriate reactor mole balance, rate law. stoichiometry algorithm to solve reaction engineering problems with heat effects. For example, recall rate law for a first-order reaction. Equation (E8-1.5) in Example 8-1. 

The first step in our CRE algorithm is the mole balance, which we now need to extend to include the molar fiux, and diffusional effects. The molar flow rate of A in a given direction, such as the z direction down the length of a tubular reactor, is just the product of the flux. (mol/m s), and the cross-sectional area. Ac (nt ), that is. 

To find the volume neccessary we can then use the algorithm starting with the mole balance ... 

Overview. In Chapters 5 and 6 we have shown that once the rate law is known, it can be substituted into the appropriate mole balance, and then through the use of the appropriate stoichiometric relationships, we can apply the CRE algorithm to analyze any isothermal reaction system. In this chapter we focus on ways of obtaining and analyzing reaction rate data to obtain the rate law for a specific reaction. 

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. 

In the case of the flash calculations, different algorithms and schemes can be adopted the case of an isothermal, or PT flash will be considered. This term normally refers to any calculation of the amounts and compositions of the vapour and the liquid phase (V, L, y,-, xh respectively) making up a two-phase system in equilibrium at known T, P, and overall composition. In this case, one needs to satisfy relation for the equality of fugacities (eq. 2.3-1) and also the mass balance equations (based on 1 mole feed with N components of mole fraction z,) ... 

In many systems, slow reactions occur to an appreciable extent in the presence of fast, reversible reactions. Given extents of reaction measured experimentally, or computed by integration of a kinetic model, it is desired to compute compositions of a system. This has been accomplished using EQUILK (19) given specifications for extents or temperature approaches for less than R reactions, or the moles of some species in the product. The RAND Method has been extended to permit these specifications, as well (38). In principle, these specifications are easily added to the mass balances for any nonlinear programming algorithm. 

---