Interphase mass transfer correlations

Local Interfacial Molar Flux. Results for P(0 and Sc(t) via (11-199) and (11-202), respectively, represent basic information from which interphase mass transfer correlations can be developed. Gas-liquid mass transfer of mobile component A occurs because it is soluble in the liquid phase, and there is a nonzero radial component of the total molar flux of A, evaluated at r = R(t). Even though motion of the interface induces convective mass transfer in the radial direction, there is no relative velocity of the fluid with respect to the interface at r = R t). It should be emphasized that a convective contribution to interphase mass transfer in the radial direction occurs only when motion of the interface differs from Vr of the liquid at r = R. Hence, Pick s first law of diffusion is sufficient to calculate the molar flux of species A normal to the interface at r = R t) when f > 0 ... 

The mass transfer between phases is, of course, the very basis for most of the diffusional operations of chemical engineering. A considerable amount of experimental and empirical work has been done in connection with interphase mass transfer because of its practical importance an excellent and complete survey of this subject may be found in the text book of Sherwood and Pigford (S9, Chap. Ill), where dimensionless correlations for mass transfer coefficients in systems of various shapes are assembled. 

Experimental study of more systems with interphase mass transfer, with the aim of correlating interfacial resistance with other physical properties. 

Several theories have been developed to describe the rate of interphase mass transfer. These include film theory, boundary layer theory, penetration theory, and surface renewal theory. In this chapter we will review the first two, along with an overview of empirical correlations that are used to describe mass transfer. A more thorough overview of mass transfer theories can be found in Bird, Stewart and Lightfoot [48], Clark [49], Logan [50], and Weber and DiGiano [51]. 

I-power dependence of the dimensionless mass transfer coefficient on Re reveals fbat the flow regime is laminar. Turbulent mass transfer across high-shear no-slip interfaces also scales as Shaverage Sc, but the exponent of Re in this correlation is somewhere between 0.8 and 1. AU of these dimensionless scaling laws for interphase mass transfer are summarized in Table 12-1 for solid-liquid and gas-Uquid interfaces. 

Design a two-phase gas-liquid CSTR that operates at 55°C to accomplish the liquid-phase chlorination of benzene. Benzene enters as a liquid, possibly diluted by an inert solvent, and chlorine gas is bubbled through the liquid mixture. It is only necessary to consider the first chlorination reaction because the kinetic rate constant for the second reaction is a factor of 8 smaller than the kinetic rate constant for the first reaction at 55°C. Furthermore, the kinetic rate constant for the third reaction is a factor of 243 smaller than the kinetic rate constant for the first reaction at 55°C. The extents of reaction for the second and third chlorination steps ( 2 and 3) are much smaller than the value of for any simulation (i.e., see Section 1-2.2). Chlorine gas must diffuse across the gas-liquid interface before the reaction can occur. The total gas-phase volume within the CSTR depends directly on the inlet flow rate ratio of gaseous chlorine to hquid benzene, and the impeller speed-gas sparger combination produces gas bubbles that are 2 mm in diameter. Hence, interphase mass transfer must be considered via mass transfer coefficients. The chemical reaction occurs predominantly in the liquid phase. In this respect, it is necessary to introduce a chemical reaction enhancement factor to correct liquid-phase mass transfer coefficients, as given by equation (13-18). This is accomplished via the dimensionless correlation for one-dimensional diffusion and pseudo-first-order irreversible chemical reaction ... 

The interphase mass transfer coefficient of reactant A (i.e., a,mtc), in the gas-phase boundary layer external to porous solid pellets, scales as Sc for flow adjacent to high-shear no-slip interfaces, where the Schmidt number (i.e., Sc) is based on ordinary molecular diffusion. In the creeping flow regime, / a,mtc is calculated from the following Sherwood number correlation for interphase mass transfer around solid spheres (see equation 11-121 and Table 12-1) ... 

Values for the interphase mass transfer coefficient kgA can be calculated from y rcorrelations (see Chapter 3). Specific correlations for fluidized beds can be found in Perry [1984]. 

Interphase Mass Transfer. There are a number of interphase mass transfer steps that must occur in a trickle flow reactor. The mass transfer resistances can be considered as occurring at the more or less stagnant fluid layer interfaces, i.e., on the gas and/or the liquid side of the gas/llquld Interface and on the liquid side of the liquid/solid Interface. The mass transfer correlations (8) indicate that the gas/llquld Interface and the liquid/solid interface mass transfer resistances decrease with higher liquid velocity and smaller particle size. Thus, in the PDU, the use of small inert particles partially offsets the adverse effect of low velocity. These correlations indicate that for this system, external mass transfer limitations are more likely to occur in the PDU than in the commercial reactor because of the lower liquid velocity, but that probably there is no limitation in either. If a mass transfer limitation were present, it would limit conversion in a way similar to that shown for axial dispersion and incomplete catalyst wetting illustrated in Figure 1. Due to the uncertainty in the correlations and in the physical properties of these systems, particularly the molecular diffuslvities, it is of interest to examine if external mass transfer is influencing the PDU results. 

Our discussion of multiphase CFD models has thus far focused on describing the mass and momentum balances for each phase. In applications to chemical reactors, we will frequently need to include chemical species and enthalpy balances. As mentioned previously, the multifluid models do not resolve the interfaces between phases and models based on correlations will be needed to close the interphase mass- and heat-transfer terms. To keep the notation simple, we will consider only a two-phase gas-solid system with ag + as = 1. If we denote the mass fractions of Nsp chemical species in each phase by Yga and Ysa, respectively, we can write the species balance equations as... 

In the rate-based models, the mass and energy balances around each equilibrium stage are each replaced by separate balances for each phase around a stage, which can be a tray, a collection of trays, or a segment of a packed section. Rate-based models use the same m-value and enthalpy correlations as the equilibrium-based models. However, the m-values apply only at the equilibrium interphase between the vapor and liquid phases. The accuracy of enthalpies and, particularly, m-values is crucial to equilibrium-based models. For rate-based models, accurate predictions of heat-transfer rates and, particularly, mass-transfer rates are also required. These rates depend upon transport coefficients, interfacial area, and driving forces. It... 

For interphase limitations (boundary layer effects) the situation seems, at first glance, as simple as that for internal gradients, since most correlations for heat-and mass-transfer eoeffieients show a proportionality to the flow velocity of the surrounding fluid, u", where normally 0.6 < n < 1. At the lower velocities associated in particular with laboratory reactor operation, however, n tends to be closer to 0.6 than to 1, and the transport coefficients become insensitive to flow velocity and changing flow velocity is not an effective diagnostic. 

Lee and Dudukovic [18] described an NEQ model for homogeneous RD in tray columns. The Maxwell-Stefan equations are used to describe interphase transport, with the AIChE correlations used for the binary (Maxwell-Stefan) mass-transfer coefficients. Newton s method and homotopy continuation are used to solve the model equations. Close agreement between the predictions of EQ and NEQ models were found only when the tray efficiency could correctly be predicted for the EQ model. In a subsequent paper Lee and Dudukovic [19] presented a dynamic NEQ model of RD in tray columns. The DAE equations were solved by use of an implicit Euler method combined with homotopy continuation. Murphree efficiencies calculated from the results of an NEQ simulation of the production of ethyl acetate were not constant with time. 

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