Mass transfer multiphase flow

To simulate the effects of reaction kinetics, mass transfer, and flow pattern on homogeneously catalyzed gas-liquid reactions, a bubble column model is described [29, 30], Numerical solutions for the description of mass transfer accompanied by single or parallel reversible chemical reactions are known [31]. Engineering aspects of dispersion, mass transfer, and chemical reaction in multiphase contactors [32], and detailed analyses of the reaction kinetics of some new homogeneously catalyzed reactions have been recently presented, for instance, for polybutadiene functionalization by hydroformylation in the liquid phase [33], car-bonylation of 1,4-butanediol diacetate [34] and hydrogenation of cw-1,4-polybutadiene and acrylonitrile-butadiene copolymers, respectively [10], which can be used to develop design equations for different reactors. 

Hetsroni G, Mosyak A, Pogrebnyak E, Yarin LP (2005c) Heat transfer in micro-channels comparison of experiments with theory and numerical results. Int J Heat Mass Transfer 48 5580-5601 Hetsroni G, Mosyak A, Segal Z, Pogrebnyak E (2003b) Two-phase flow patterns in parallel microchannels. Int J Multiphase Flow 29 341-360... 

Zhao TS, Bi QC (2001b) Pressure drop characteristics of gas-liquid two-phase flow in vertical miniature triangular channels. Int J Heat Mass Transfer 44 2523-2534 Zimmerman R, Gurevich M, Mosyak A, Rozenblit R, Hetsroni G (2006) Heat transfer to air-water annular flow in a horizontal pipe. Int J Multiphase Flow 32 1-19... 

Klein D, Hetsroni G, Mosyak A (2005) Heat transfer characteristics of water and APG surfactant solution in a micro-channel heat sink. Int J Multiphase Flow 31 393 15 Kosar, A, Kuo, CJ, Peles, Y (2005) Boiling heat transfer with reentrant cavities. Int. J. Heat Mass Transfer 48 4867-4886... 

Tran TN, Wambsganss MW, France DM (1996) Small circular and rectangular channel boiling with two refrigerants. Int J Multiphase Flow 22 485-498 Unal HC (1975) Determination of the initial point of net vapor generation in flow boiling system. Int J Heat Mass Transfer 18 1095-1099... 

Yen T-H, Kasagi N, Suzuki Y (2003) Forced convective boiling heat transfer in micro-tubes at low mass and heat fluxes. Int J Multiphase Flow 29 1771-1792 Yu W, France DM, Wambsganss MW, Hull JR (2002) Two-phase pressure drop, boiling heat transfer, and critical heat flux to water in a small-diameter horizontal tube. Int J Multiphase Flow 28 927-941... 

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

The several industrial applications reported in the hterature prove that the energy of supersonic flow can be successfully used as a tool to enhance the interfacial contacting and intensify mass transfer processes in multiphase reactor systems. However, more interest from academia and more generic research activities are needed in this fleld, in order to gain a deeper understanding of the interface creation under the supersonic wave conditions, to create rehable mathematical models of this phenomenon and to develop scale-up methodology for industrial devices. 

Thus, just as for incompressible single-phase flow, the pressure p constrains the velocity fields to ensure (in the case of multiphase flows) that the sum of the phase volume fractions equals unity. In the presence of mass transfer, the right-hand side of Eq. (148) is nonzero nevertheless, the role of the pressure is still the same. Finally, we should note that in gas-solid flows the maximum volume fraction of the solid phase is less than unity due to physical constraints (i.e., when particles are close packed there is still room for the gas phase so that 0solid-pressure term ps that becomes extremely large when ag approaches its minimum value (e.g., oc — 0.4). 

From the discussion above, we should keep in mind that even if no SGS micromixing model is used to describe the multiphase flow, it may often be the case that chemical reactions (and indeed micromixing) will be limited by mass/ heat transfer between the phases. Because the multifluid model (see Eqs. 164 and... 

In many applications, a mean droplet size is a factor of foremost concern. Mean droplet size can be taken as a measure of the quality of an atomization process. It is also convenient to use only mean droplet size in calculations involving discrete droplets such as multiphase flow and mass transfer processes. Various definitions of mean droplet size have been employed in different applications, as summarized in Table 4.1. The concept and notation of mean droplet diameter have been generalized and standardized by Mugele and Evans.[423] The arithmetic, surface, and volume mean droplet diameter (D10, D2o, and D30) are some most common mean droplet diameters ... 

All dimensionless numbers in this chapter are frequently used in chemical engineering, especially in heat and mass transfer and in multiphase flow [35] ... 

In multiphase reactors we frequently exploit the density differences between phases to produce relative motions between phases for better contacting and higher mass transfer rates. As an example, in trickle bed reactors (Chapter 12) liquids flow by gravity down a packed bed filled with catalyst, while gases are pumped up through the reactor in countercurrent flow so that they may react together on the catalyst surface. 

Thus we see that these multiphase reactors can be quite complex because the volumes of each phase can change as reaction proceeds and, more important, the interfacial area between phases can change, depending on conversion, geometry, and flow conditions. Thus it is essential to describe the mass transfer rate and the interfacial area in these reactors in order to describe their performance. 

In connection with multiphase diffusion another poorly understood topic should be mentioned—namely, the diffusion through porous media. This topic is of importance in connection with the drying of solids, the diffusion in catalyst pellets, and the recovery of petroleum. It is quite common to use Fick s laws to describe diffusion through porous media fJ14). However, the mass transfer is possibly taking place partly by gaseous diffusion and partially by liquid-phase diffusion along the surface of the capillary tubes if the pores are sufficiently small, Knudsen gas flow may prevail (W7, Bl). 

Complexity in multiphase processes arises predominantly from the coupling of chemical reaction rates to mass transfer rates. Only in special circumstances does the overall reaction rate bear a simple relationship to the limiting chemical reaction rate. Thus, for studies of the chemical reaction mechanism, for which true chemical rates are required allied to known reactant concentrations at the reaction site, the study technique must properly differentiate the mass transfer and chemical reaction components of the overall rate. The coupling can be influenced by several physical factors, and may differently affect the desired process and undesired competing processes. Process selectivities, which are determined by relative chemical reaction rates (see Chapter 2), can thenbe modulated by the physical characteristics of the reaction system. These physical characteristics can be equilibrium related, in particular to reactant and product solubilities or distribution coefficients, or maybe related to the mass transfer properties imposed on the reaction by the flow properties of the system. 

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