Multiphase Reaction-Equilibrium Calculations

With the initial guesses for the mole numbers N,- given in Table 11.7 and a value of the stability control parameter = 1, the algorithm converges in 17 iterations to the mole numbers in Table 11.7. Final values for the affinities were KilKT = -2.0(10 ), llRT = 1.6(10 ), and 7I3/KT = 2.1(10 ). Note that the elemental balances AN = b are satisfied by the initial guesses and by the final values of the mole numbers  

Also note that although this problem involves three independent reactions, we need not identify explicitly any three reactions. Particular reactions and their stoichiometric 

We now briefly introduce the problem of reaction equilibria in multiphase systems. In such problems, the difficulties that arise are more computational than thermodynamic, and since this is a book on thermodynamics, we do not delve deeply into the computational issues. The overriding theme here is that multiphase reaction problems combine the salient features of phase equilibria and reaction equilibria, and therefore such problems adhere to the general patterns established earlier in this chapter. We first consider computational difficulties that can be posed by indifferent situations ( 11.3.1), then we present and illustrate one elementary algorithm ( 11.3.2). 

In discussing states of multiphase, nonreacting systems in 9.1, we presented two ways for identifying an intensive state T and T specifications. That discussion was extended to reacting systems in 10.3.1. For both reacting and nonreacting systems we found that the difference between T and T is the number of internal constraints in an T -specification we implicitly rely on internal constraints to complete an identification of state, but in an F -specification we explicitly include the consequences of internal constraints. In multiphase reacting systems, the difference is 

Indifferent situations can create problems in the trial-and-error procedures routinely used in calculations for phase and reaction equilibrium. In such calculations, we may start with an T or T spedfication that properly doses the problem, but during the course of the trial-and-error search, the algorithm may enter an indifferent situation that couples properties that are otherwise independent. This may occur not only when azeotropes and critical points are encountered, but also when algorithms enter metastable and unstable regions of phase diagrams [20]. 

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We will need values of conceptuals for two classes of problems (a) calculation of thermodynamic properties for one-phase systems and (b) calculation of multiphase and chemical reaction equilibria. For both kinds of problems, we use the same basic strategy (i) Compare raw or modeled experimental data with computed properties of an ideal substance to obtain measures for deviations from the ideality, then (ii) exploit the deviation measures to obtain expressions for the required conceptuals in terms of measurables. Calculations of one-phase properties are typically based on differences, while phase and reaction equilibrium calculations typically use ratios. In 6.2.1 and... 

Coupled phase-reaction equilibrium problems not only raise no new thermodynamic issues, but they also raise few new computational issues. By building on the phase and reaction-equilibrium algorithms presented earlier in this chapter, we can devise an elementary algorithm. Reaction-equilibrium problems typically start with known values for T, P, and initial mole numbers N° in a phase-equilibrium context, these variables identify an T problem, such as an isothermal flash calculation. Therefore we can combine the Rachford-Rice method with the reaction-equilibrium calculation given in 11.2 an example is provided in Figure 11.8 for a vapor-liquid situation. This is a traditional way for attacking multiphase-multireaction problems [21, 22] ... 

Bertucco et al. investigated the effect of SCCO2 on the hydrogenation of unsaturated ketones catalyzed by a supported Pd catalyst, by using a modified intemal-recycle Berty-type reactor [63]. A kinetic model was developed to interpret the experimental results. To apply this model to the multiphase reaction system, the calculation of high-pressure phase equilibria was required. A Peng-Robinson equation of state with mixture parameters tuned by experimental binary data provided a satisfactory interpretation of all binary and ternary vapor-liquid equilibrium data available and was extended to multicomponent... 

The heterogeneities of most concern to us are those that involve the presence of more than one phase. The analysis of multiphase systems can be important to the design and operation of many industrial processes, especially those in which multiple phases influence chemical reactions, heat transfer, or mixing. For example, phase-equilibrium calculations form the bases for many separation processes, including stagewise operations, such as distillation, solvent extraction, crystallization, and supercritical extraction, and rate-limited operations, such as membrane separations. 

For non-ideal multicomponent mixtures the multiphase flow calculation can be combined with a more rigorous thermodynamic equilibrium calculation to determine the mixture properties at the interface as discussed by [60, 70, 98]. However, describing the chemical reactor performance under industrial operation conditions the heat balance is normally dominated by the heat of reaction term, the transport terms and the external heating/cooling boundary conditions, hence for chemical processes in which the phase change rates are relatively small the latent heat term is often neglected. 

The multiphase method provides a practical screening tool for industrial process research and development, even though under many circumstances the nonequilibrium effects such as supersaturation of solutions, retarded mass transfer or reaction kinetics and inhomogeneity of suspensions limit the applicability of the thermodynamic calculations. When the thermodynamic multiphase models are developed towards process simulation tools, one should incorporate such methods that include the effects of these non-equilibrium factors. They must be based on... 

In a typical problem, multiple reactions are taking place in a multiphase system at fixed T and P, and we are to compute the equilibrium compositions of all phases. At this point, such calculations raise no new thermodynamic issues for example, for (R independent reactions occmrring among C species distributed between phases a and P, the problem is to solve the phase-equilibrium criteria... 

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