Correlation of mass transfer

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

TABLE 23-12 Correlations of Mass-Transfer Coefficients in Stirred Tanks... 

The above correlation is valid for a bioreactor size of less than 3000 litres and a gassed power per unit volume of 0.5-10 kW. For non-coalescing (non-sticky) air-electrolyte dispersion, the exponent of the gassed power per unit volume in the correlation of mass transfer coefficient changes slightly. The empirical correlation with defined coefficients may come from the experimental data with a well-defined bioreactor with a working volume of less than 5000 litres and a gassed power per unit volume of 0.5-10 kW. The defined correlation is ... 

The mass transfer coefficient can be found along with other constants from appropriate rate data, or it can be evaluated from an independent known correlation of mass transfer data, of which several are available. In most of... 

Numerous investigations have been conducted of mass transfer coefficients in vessels with a variety of kinds of packings. Many of the mote acceptable results are cited in recent books on mass transfer, for instance, those of Sherwood et al. (Mass Transfer, McGraw-Hill, New York, 1975), Cussler (Diffusion, Cambridge, 1984), and Hines and Maddox (1985). A convenient correlation of mass transfer coefficients in granular beds covering both liquid and vapor films is that of Dwivedi and Upadhyay [Ind. Eng. Chem. Process Des. Dev. 16, 157 (1977)], namely,... 

TABLE II Useful Correlations of Mass Transfer Coefficients for Fluid-Fluid Interfaces... 

Schuette and McCreery [34] demonstrated that with decreasing wire diameter there was a significant increase in current enhancement and modulation depth. This approached 100% modulation for a wire of diameter, d = 25 pm vibrated at 160 Hz. They showed that in these circumstances, for low Re numbers, the limiting current strictly followed the wire velocity and used [6] an empirical power-law correlation of mass-transfer coefficient to flow velocity /lim = /min(l + A/ cos(ft>.f)f) with s 0.7. They also noted that the frequency and amplitude dependence of the mean current, and the modulation depth, was linked to whether the flow was strictly laminar or not. Flow modelling indicated that for Re > 5 where Re = u dlv, there was separation of the boundary layer at the wire surface, when aid 1. For Re > 40 the flow pattern became very irregular. Under these circumstances, a direct relation between velocity and current should be lost, and they indeed showed that the modulation depth decreased steeply with increase of wire diameter, down to 10% for 0.8 mm diameter wire. 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

Let us now turn to the more difficult problem of explaining why the limits -> 0, N2 0 appear in Eq. 7.1.3. During the actual mass transfer process itself the composition (and velocity) profiles are distorted by the flow (diffusion) of 1 and 2 across the interface. The mass transfer coefficient defined in Eq. 7.1.3 corresponds to conditions of vanishingly small mass transfer rates, when such distortions are not present. These low-flux or zero-flux coefficients are the ones that are usually available from correlations of mass transfer data. These correlations usually are obtained under conditions where the mass transfer rates are low. For the actual situation under conditions of finite transfer rates, we may write... 

Onda s Correlations for Randomly Packed Columns Onda et al. (1968) developed correlations of mass transfer coefficients for gas absorption, desorption, and vaporization in randomly packed columns. The vapor-phase mass transfer coefficient is obtained from... 

This type of plot has been used widely to correlate experimental mass-transfer data. De Acetis and Thodos have summarized the data available up to 1960 in a single rve of vs Reynolds number, as shown in Fig. 10-2. For spherical pellets /)sis the diameter for other shapes dp can be taken as the diameter of a sphere with the same external area. Other investigations and correlations of mass-transfer datg include those of Carberry, Yeh, Bradshaw and Bennett, and Thoenes and Kramers. ... 

J. Mamugozis and A. J, Johnson, A Correlation of Mass Transfer Data of Solid-Liquid Systems... 

Although reliable correlations of mass transfer coefficients for the components of a multicomponent mixture remain to be developed, a development of the equations required to describe simultaneous mass and heat transfer in a packed column follows. 

The various forms of the penetration theory can be classified as surface-renewal models, implying either formation of new surfaee at frequent intervals or replacement of fluid elements at the surface with fresh fluid from the bulk. The time or its reciprocal, the average rate of renewal, are functions of the fluid velocity, the fluid properties, the the geometry of the system and can be accurately predicted in only a few special cases. However, even if tj must be determined empirically, the surface-renewal models give a sound basis for correlation of mass-transfer data in many situations, particularly for transfer to drops and bubbles. The similarity between Eqs. (21.44) and (15,20) is an example of the close analogy between heat and mass transfer. It is often reasonable to assume that tj-is the same for both processes and thus to estimate rates of heat transfer from measured mass-transfer rates or vice versa. 

Figure 8.12 Correlation of mass transfer to a single sphere in a liquid for low relative velocities. [After C.N. Satterfield, Mass Transfer in Heterogeneous Catalysis, with permission of MIT Press, Cambridge, MA, (1970).]...

However, the correlation of mass transfer with heat fiansfer is relevant only to the heat transferred directly to the evaporating surface. That other modes of energy delivery can be highly useful and have to be considered separately is well appreciated in the literature. 

Diffusion is the mass transfer caused by molecular movement, while convection is the mass transfer caused by bulk movement of mass. Large diffusion rates often cause convection. Because mass transfer can become intricate, at least five different analysis techniques have been developed to analyze it. Since they all look at the same phenomena, their ultimate predictions of the mass-transfer rates and the concentration profiles should be similar. However, each of the five has its place they are useful in different situations and for different purposes. We start in Section 15.1 with a nonmathematical molecular picture of mass transfer (the first model) that is useful to understand the basic concepts, and a more detailed model based on the kinetic theory of gases is presented in Section 15.7.1. For robust correlation of mass-transfer rates with different materials, we need a parameter, the diffusivity that is a fundamental measure of the ability of solutes to transfer in different fluids or solids. To define and measure this parameter, we need a model for mass transfer. In Section 15.2. we discuss the second model, the Fickian model, which is the most common diffusion model. This is the diffusivity model usually discussed in chemical engineering courses. Typical values and correlations for the Fickian diffusivity are discussed in Section 15.3. Fickian diffusivity is convenient for binary mass transfer but has limitations for nonideal systems and for multicomponent mass transfer. 

The following relationship is suggested as a basis for the correlation of mass transfer data [9, 17, 23] ... 

---