Mass transfer coefficients in two phase

Many correlations have been suggested to estimate mass transfer coefficients in two-phase systems for various types of physical scenarios. Oldshue (1983) gives a summary of available correlations for liquid-solid, liquid-liquid, and gas-liquid mass transfer, as well as an estimate of the mass transfer rate of a G-L-S system—namely, the oxidation of sodium sulfite in water. Cussler (1997) gives... 

Sharma.M.M. and P.V.Danckwerts. "Chemical methods of measuring interfacial area and mass transfer coefficients in two-phase systems." Brit.Chem.Eng. 15 (1970) 522-528. 

Table VIII. Mass transfer coefficients in two phase gas-liquid reactors according to van Dierendonck [l08]...

When the two liquid phases are in relative motion, the mass transfer coefficients in eidrer phase must be related to die dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive Uansfer to the Schmidt number. Another complication is that such a boundaty cannot in many circumstances be regarded as a simple planar interface, but eddies of material are U ansported to the interface from the bulk of each liquid which change the concenuation profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most indusuial chcumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass U ansfer model must therefore be replaced by an eddy mass U ansfer which takes account of this surface replenishment. 

The relationships between the overall mass transfer coefficient and the film mass transfer coefficients in both phases are not as simple as in the case of heat transfer, for the following reason. Unlike the temperature distribution curves in heat transfer between two phases, the concentration curves of the diffusing component in the two phases are discontinuous at the interface. The relationship between the interfacial concentrations in the two phases depends on the solubility of the diffusing component. Incidentally, it is known that there exists no resistance to mass transfer at the interface, except when a surface-active substance accumulates at the interface to give additional mass transfer resistance. 

Pangarkar VG, Yawalkar AA, Sharma MM, Beenackers AACM. (2002) Particle—hquid mass transfer coefficient in two-/three-phase stirred tank reactors. Ind. Eng. Chem. Res., 41 4141 167. 

Kielbus-Rapala A, Karcz J, Cudak M. (2011) The effect of the physical properties of the liquid phase on the gas-liquid mass transfer coefficient in two- and three-phase agitated systems. Chem Papers, 65(2) 185-192. 

In this process, the two streams flow countercurrently through the column and undergo a continuous change in composition. At any location are in dynamic rather than thermodynamic equilibium. Such processes are frequently carried out in packed columns, in which the liquid (or one of the two liquids in the case of a liquid-liquid extraction process) wets die surface of the packing, thus increasing the interfacial area available for mass transfer and, in addition, promoting high film mass transfer coefficients within each phase. 

Mass transfer of ozone from the gas phase to the liquid phase strongly depends on the reactor system and the process conditions. Two characteristic factors are in general important the overall mass transfer coefficient between gas phase and water phase, k, and the specific surface area available for mass transfer, Am. 

The design engineer can use the dispersion coefficients determined in this way for the calculation of the real course of concentrations, c, of any component in the dispersed d) and continuous (c) phases along the countercurrent column. If the mass transfer between the two phases, the actual task of an extractor, is included in the balance, the balance equations for an element of height dh of the extractor for stationary conditions is ... 

The coefficient C, related to the resistance to mass transfer between the two phases, becomes important when the flow rate is too high for equilibrium to be obtained. Local turbulence within the mobile phase and concentration gradients slow down the equilibrium process (Cs <=> Cm). The diffusion of solute between the phases is not instantaneous, hence the solute will be in a non-equilibrium process. 

Earlier studies in mass transfer between the gas-liquid phase reported the volumetric mass-transfer coefficient kLa. Since kLa is the combination of two experimental parameters, mass-transfer coefficient and mterfacial area, it is difficult to identify which parameter is responsible for the change of kLa when we change the operating condition of a fermenter. Calderbank and Moo-Young (1961) separated kta by measuring interfacial area and correlated mass-transfer coefficients in gas-liquid dispersions in mixing vessels, and sieve and sintered plate column, as follows ... 

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. 

Liquid-liquid dispersion involves two phases a continuous phase (one with large volume), and a dispersed phase (one with small volume). When the volume fractions of both phases are nearly the same, phase inversion occurs. In this case, which of the two phases becomes a continuous one depends on the starting conditions as well as the physical properties of the system. The range of volume fraction within which either of two immiscible liquids may be continuous is primarily a function of the viscosity ratio it is not strongly dependent upon vessel characteristics or stirring speed (Selker and Sleicher, 1965). Here we briefly evaluate the minimum speed of rotation required to disperse one phase completely into the other, the interfacial area, and the mass-transfer coefficient in liquid-liquid dispersion. 

Any form of convection, of course, increases the value of Ks. In slurry operation with no liquid flow, gas flow induces convection. In an agitated slurry reactor, stirring causes convection. In a pulsating slurry reactor, pulsation of the slurry induces convection and in a three-phase fluidized bed, the movements of both gas and liquid phases cause convection. Any one or more modes of convection will increase the value of the solid-liquid mass-transfer coefficient. In broad terms, the convective liquid-solid mass-transfer coefficient is correlated by-two steady state theories. Here we briefly review and compare them. 

Actually Sato et al. expressed their particle mass-transfer coefficients in terms of an enhancement factor representing the ratio of with two-phase flow to ks at the same liquid flow rate in single-phase flow. For pulsing and dispersed bubble flow this enhancement factor was found to be inversely proportional to liquid holdup j3, which in turn is a function of the two-phase parameter A or A (see Section IV,A,3,a). For comparison, the data for single-phase liquid flow are best represented by an equation of the same form as Eq. (115) but with a constant of 0.8. 

The former corresponds to liquid-phase mass transfer coefficients that are elTectively infinite (no liquid-phase resistance), the latter to zero liquid-phase mass transfer coefficients (infinite liquid-phase resistance). Clearly, the truth lies somewhere between these two limiting cases. There is some evidence to show that if there is a noncondensing component in the vapor phase, then these two limiting cases give essentially identical results (Sections... 

The various concentrations can also be shown graphically, as in Figure 3.4, whose coordinates are those of the equilibrium-distribution curve. Point P represents the two bulk-phase concentrations, and point M those at the interface. For steady-state mass transfer, the rate at which A reaches the interface from the gas must be equal to the rate at which it diffuses to the bulk liquid, so that no accumulation or depletion of A occurs at the interface. We can, therefore, write the flux of A in terms of the mass-transfer coefficients for each phase and the concentration changes appropriate to... 

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