## 55 Multiphase Reactive Flow Processes

In general, multiphase reactive flow processes are classified into three types according to the location of the reaction zone:

(a) Reactions occur in one of the participating phases (either in the bulk or near the interface). Several gas-liquid, liquid-liquid reactive processes fall into this category.

(b) Reactions occur on the surface of one of the participating phase. Catalytic reactions in gas-solid, liquid-solid and gas-liquid-solid reactive processes fall into this category.

(c) Reactions occur in one phase but products form another immiscible phase. Reactive crystallization, liquid phase reactions generating volatile products or soot formation fall into this category.

For multiphase reactive systems of types (a) and (b), at least one of the reactants has to reach the reaction zone from a different phase. In such systems, generally mass transfer between these two different phases (and its interaction with chemical reactions) is of primary importance and turbulent mixing is often of secondary importance. For such systems, modeling multiphase flows as discussed in Chapter 4 is directly applicable. The only additional complexity is the possibility of interaction between mass transfer and chemical reactions. The typical interphase mass transfer source for component k between phases p and q can be written (for the complete species conservation equation, refer to Chapter 4):

where kMpq is the mass transfer coefficient, apq is an interfacial area per unit volume, npq is an enhancement factor representing interaction of mass transfer and chemical reactions, and ACkpq is the net concentration driving force for mass transfer between phases p and q. For slow (compared to mass transfer rate) reactions, the enhancement factor will be unity. For fast reactions, the enhancement factor will be a function of reaction kinetics and concentrations.

The subject of mass transfer with chemical reactions has been well developed. Several excellent books discuss suitable models to estimate enhancement factors (Doraiswamy and Sharma, 1984; Westerterp et al., 1984) to represent interactions between mass transfer and chemical reactions. Models have been developed to formulate expressions for the enhancement factor for a number of different reacting systems. In many situations, however, it is not possible to derive a closed form expression for the enhancement factor, which is applicable over all temperature ranges and compositions within the reactor. For such cases, it is recommended to use so-called 'look up' tables. A detailed local model for the interaction of mass transfer and chemical reactions can be developed and solved separately, to generate these enhancement factor 'look up' tables at various conditions. Efficient interpolation routines can then supply values of enhancement factor to the multiphase reactive flow model at the desired conditions (compositions and temperature). If an appropriate model is developed to simulate interaction between mass transfer and chemical reactions, such a model may be used within the general modeling framework (VOF, EL or EE) discussed in Chapter 4 to simulate multiphase reactive flow processes.

VOF-based models simulate the small-scale flow processes near the interface. It is possible to calculate the interfacial area from the simulated interface shape and orientation. Thus, VOF simulations may allow a detailed understanding of the interaction of mass transfer and flow processes around the interface. It must, however, be noted that quantitative agreement between VOF predictions and experimental data is not satisfactory for most cases relevant to reactor engineering. Therefore, although VOF simulations may be useful as learning tools, the application of VOF to simulate realistic reactive flow processes is not possible without first getting accurate predictions of flow field and interface shape. In a Eulerian-Lagrangian approach, particle-level phenomena can be modeled rigorously by developing species conservation equations for individual dispersed particles (Eqs (4.21) and (4.22)). The sources appearing in such particle conservation equations will have the form of Eq. (5.32). Interfacial area in such sources is computed from the effective diameter of the concerned dispersed phase particle. Different approaches to handling such systems have been discussed in the previous chapter. To simulate interphase mass transfer and reacting systems, it is necessary to consider two-way coupling between dispersed and continuous phase. The source terms (representing mass or heat transfer) computed from the particle trajectories need to be included in the governing equations of the continuous phase. If there is an interaction between mass transfer and chemical reactions, as discussed above, an appropriate local model needs to be considered when evaluating net sources due to mass transfer. For turbulent reactive multiphase flow processes, several stochastic trajectories must be used to compute an appropriate source term for the continuous phase equation. An instantaneous driving force for concentration (or temperature) will be a function of the instantaneous concentration (or temperature) of the continuous phase. Various ways of estimating the instantaneous velocity of the continuous phase have been discussed in Chapter 4. In principle, similar practices may be applied to estimate instantaneous concentration. However, considering the uncertainties in estimating interphase mass transfer coefficients and other related parameters, often time-averaged concentrations (or temperature) are used to formulate interphase mass transfer and reaction source terms.

In Eulerian-Eulerian (EE) simulations, an effective reaction source term of the form of Eq. (5.32) can be used in species conservation equations for all the participating species. The above comments related to models for local enhancement factors are applicable to the EE approach as well. It must be noted that interfacial area appearing in Eq. (5.32) will be a function of volume fraction of dispersed phase and effective particle diameter. It can be imagined that for turbulent flows, the time-averaged mass transfer source will have additional terms such as correlation of fluctuations in volume fraction of dispersed phase and fluctuations in concentration even in the absence of chemical reactions. If there is an interaction between chemical reaction and mass transfer, time averaging with an enhancement factor will introduce even more additional correlations. In most engineering simulations, however, the time-averaged source term is taken as the source term computed using time-averaged variables. The effort of developing additional closure models is generally not justified in the face of existing uncertainties in estimating mass transfer coefficient and interfacial area. There have been attempts to derive the transport equation for interfacial area rather than computing it from a knowledge of average volume fraction and the size of the dispersed phase particle (Kataoka et al., 1992). Many engineering simulations, however, adopt the approach of calculating the mass transfer/reaction source term based on time-averaged variables and lumping all the effects of turbulence on mass transfer in the value of mass transfer coefficient, kMpq. Additional computational aspects of modeling multiphase reactive flow processes are discussed in Chapter 7. Some examples of CFD-based simulations of multiphase reactive flows are discussed in Parts III and IV.

When reactions occur on a surface, the effective rate of surface reaction may depend on the rates of various intermediate steps including:

• mass transfer of reactants to surface;

• adsorption of reactant species on the surface;

• surface chemical reactions;

• desorption of products from the surface; and

• mass transfer of these products from the surface to the bulk.

It is possible to formulate an expression for effective rate by analyzing relative rates of these different steps. Numerous reaction-engineering textbooks (for example, Levenspiel, 1972; Doraiswami and Sharma, 1984) discuss the formulation of effective rates and, therefore, it will not be discussed here. Such models of effective rate can be incorporated in the CFD framework by suitably modifying the source term (Eq. (5.32)). In many solid catalyzed processes, an effective rate of continuous phase reactions can be defined in terms of catalyst (solid) loading. In such cases, it is not necessary to model the surface reactions rigorously. The reaction sources appearing in the continuous phase can be directly formulated from a knowledge of volume fraction of solid phase. Some of these examples are discussed in Part III and IV.

The interaction of turbulent mixing and chemical reactions is relevant only to multiphase reactive processes of type (c) discussed at the beginning of this section. In this type, reactions take place in one phase. Therefore, if the reactions are fast compared to the mixing rate, turbulent mixing can affect the effective reaction rate, as discussed earlier in this chapter. The reaction part of such systems can be modeled using the methods discussed in Section 5.2. These systems, however, have additional complexity because of the formation of products which are thermodynamically more favorable to exist in a different immiscible phase. For example, in a reactive crystallization, homogeneous liquid phase reaction forms a product, which precipitates. In such a case, two approaches are possible. In the first, simpler approach, interphase mass transfer sources can be modeled as discussed above without any special treatment. Alternatively, in the second approach, the spontaneous nucleation process is represented by employing some empirical models. For example, Magnussen and Hjertager (1976) proposed a nucleation model to simulate soot formation in combustion processes. They developed a conservation equation for nuclei concentration by appropriate formulations of nuclei formation and consumption rates. Similar nucle-ation models can be developed to simulate reactive crystallization (Wei and Garside, 1997). Since most such models rely heavily on empirical information and are rather system-specific, these models are not discussed here. Depending upon the considered objectives of the flow model, the reactor engineer can formulate an appropriate model using the basic methodology discussed in this and the previous three chapters.

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