Gas-liquid reactor modelling

Figure 8.12 Gas-liquid reactor model (Yagi, 19H6) where...

Romanainen, J.J. and Salmi, T., Numerical strategies in solving gas-liquid reactor models—1. Stagnant films and a steady state CSTR, Comput. Chem. Eng., 15,767-781,1991. 

A survey of the mathematical models for typical chemical reactors and reactions shows that several hydrodynamic and transfer coefficients (model parameters) must be known to simulate reactor behaviour. These model parameters are listed in Table 5.4-6 (see also Table 5.4-1 in Section 5.4.1). Regions of interfacial surface area for various gas-liquid reactors are shown in Fig. 5.4-15. Many correlations for transfer coefficients have been published in the literature (see the list of books and review papers at the beginning of this section). The coefficients can be evaluated from those correlations within an average accuracy of about 25%. This is usually sufficient for modelling of chemical reactors. Mathematical models of reactors arc often more sensitive to kinetic parameters. Experimental methods and procedures for parameters estimation are discussed in the subsequent section. 

Lo, S., Application of population balance to CFD modelling of gas-liquid reactors . Conference on Trends in Numerical and Physical Modelling for Industrial Multiphase Flows , Cargese, Corse 27-29 September (2000). 

The two extreme hypotheses on mixing produce lumped models for the fluid dynamic behavior, whereas real reactors show complex mixing patterns and thus gradients of composition and temperature. It is worthwhile to stress that the fluid dynamic behavior of real reactors strongly depends on their physical dimensions. Moreover, in ideal reactors the chemical reactions are supposed to occur in a single phase (gaseous or liquid), whereas real reactors are often multiphase systems. Two simple examples are the gas-liquid reactors, used to oxidize a reactant dissolved in a liquid solvent and the fermenters, where reactions take place within a solid biomass dispersed in a liquid phase. Real batch reactors are briefly discussed in Chap. 7, in the context of suggestions for future research work. 

Cyclohexene hydrogenation is a well-studied process that serves as model reaction to evaluate performance of gas-liquid reactors because it is a fast process causing mass transfer limitations for many reactors [277,278]. Processing at room temperature and atmospheric pressure reduces the technical expenditure for experiments so that the cyclohexene hydrogenation is accepted as a simple and general method for mass transfer evaluation. Flow-pattern maps and kinetics were determined for conventional fixed-bed reactors as well as overall mass transfer coefficients and energy dissipation. In this way, mass transfer can be analyzed quantitatively for new reactor concepts and processing conditions. Besides mass transfer, heat transfer is an issue, as the reaction is exothermic. Hot spot formation should be suppressed as these would decrease selectivity and catalytic activity [277]. 

As is shown in Figure 2, in the two-phase model the fluid bed reactor is assumed to be divided into two phases with mass transfer across the phase boundary. The mass transfer between the two phases and the subsequent reaction in the suspension phase are described in analogy to gas/liquid reactors, i.e. as an absorption of the reactants from the bubble phase with pseudo-homogeneous reaction in the suspension phase. Mass transfer from the bubble surface into the bulk of the suspension phase is described by the film theory with 6 being the thickness of the film. D is the diffusion coefficient of the gas and a denotes the mass transfer coefficient based on unit of transfer area between the two phases. 6 is given by 6 = D/a. 

It is important to recognize that results of this study are based on models which involve several assumptions. The validity of some of these assumptions may be questionable under certain circumstances. However, gas-liquid reaction systems involve complex interacting events, which are difficult to describe precisely. There is also a paucity of experimental data on the behavior of gas-liquid reactors. In view of all this, we believe that studies of this type can be valuable qualitatively for the purpose of model discrimination. 

MODELS FOR THE PACKED-BUBBLE-COLUMN GAS-LIQUID REACTOR... 

Development of a mathematical model for a nonisothermal gas-liquid reactor in which the absorption is accompanied by the generation of a large amount of heat. The rate of absorption could, therefore, be affected by the heat release. Several practical examples where this type of analysis would be useful are noted in Sec. 2-6. 

Thus the oxidation of aqueous Na2S03 solutions with C0SO4 as a catalyst proves to be a convenient model reaction for determining interfacial area in gas-liquid reactors. The kinetics of the reaction is not simple many variables influence the reaction rate but, provided the range of cobalt and sulfite concentrations, pH values, and temperatures previously indicated is satisfied, the reaction is zero-order in sulfite, first-order in cobalt, and second-order in O2. The specific rate of absorption is... 

Rigby et al. (1997) also applied a CFD-based model to understand bubble break-up from ventilated cavities in gas-liquid reactors. Ranade etal. (2001d) used a volume of fluid (VOF) approach to understand cavity formation behind blades. Observations and insight gained through such studies may be used to develop appropriate sub-models, which can then be incorporated in a detailed reactor-engineering model. 

Lo S (2000) Application of population balance to CFD modeling of gas-liquid reactors. Proc of Trends in numerical and physical modelling for industrial multiphase flows. Corse, 27-29 September... 

PEiTm, M., MARcrasio, D. L., Vanni, M. et al. 2009 Effect of drag modeling on the prediction of critical regime transitions in agitated gas-liquid reactors with bubble size distribution modeling. Multiphase Science and Technology 21, 95-106. 

The dynamics of bubble formation and growth and of solids movement within the bubbling fluidized beds have been analyzed in great detail, and elaborate computer simulations have been developed for all regimes of flnidization. The reader is referred to the specialized literatnre for details on snch models. Here we describe a fairly simple model that is applicable to the bnbbling regime and that treats a catalytic fluidized bed much like a gas-liquid reactor. 

An often used gas-liquid reactor is the bubble column. The gas is usually fed from the bottom through a sparger and the liquid flows either cocurrently or counter-currently. Counter-current operation is more efficient than co-current, but for certain types of parallel reactions, cocurrent operation can give better selectivity. Bubble columns are often operated in semi-batch mode the gas bubbles through the liquid. This mode of operation is attractive in the production of fine chemicals which are produced in small quantities - especially in the case of slow reactions. The flow patterns can vary a lot in a bubble column. Generally, as a rule of thumb, the liquid phase is more back-mixed than the gas phase. The plug flow model is suitable for the gas phase whereas the liquid phase can be modelled with the backmixed, dispersion, or plug flow model. 

The mathematical models for different kinds of gas-liquid reactors are based on the mass balances of the components in the gas and liquid phases. The bulk gas and liquid phases are divided by thin films where chemical reactions and molecular diffusion occur. The flux of component i from the gas bulk to the gas film is, and the flux from the liquid film to the liquid bulk is, Vf(. The fluxes are given with respect to the interfacial contact area (A)... 

Figure 8.17 A two-phase mass transfer model for gas-liquid reactors.

From the correlations given above it is also evident that the liquid composition has an important effect on the interfacial area. All other conditions being equal, the area may be a factor 10 larger in electrolytes than in pure liquids. Evidently, the design and scaling up of stirred gas-liquid reactors still relies on model experiments involving the liquids actually used in the reaction. 

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