Local mass-transfer coefficients

The mass and heat transfer performance of the SDR is indeed impressive. Aoune and Ramshaw [91] found local heat transfer coefficients ranging from about 10 000 to about 30 000 W m K and local mass transfer coefficients between about 4E-04... 

Symbols used include the following p is the fluid density v is the kinematic viscosity D is the diffusion coefficient of the material being transferred and k is the local mass transfer coefficient. Other symbols are defined for the specific situation. 

Introducing the local mass transfer coefficient kx and the local Sherwood number by the expressions... 

Using the computer programs discussed above, it is possible to extract from these breakthrough curves the effective local mass transfer coefficients as a function of CO2 concentration within the stable portion of the wave. These mass transfer coefficients are shown in Figure 15, along with the predicted values with and without the inclusion of the surface diffusion model. It is seen that without the surface diffusion model, very little change in the local mass transfer coefficient is predicted, whereas with surface diffusion effects included, a more than six-fold increase in diffusion rates is predicted over the concentrations measured and the predictions correspond very closely to those actually encountered in the breakthrough runs. Further, the experimentally derived results indicate that, for these runs, the assumption that micropore (intracrystalline) resistances are small relative to overall mass transfer resistance is justified, since the effective mass transfer coefficients for the two (1/8" and 1/4" pellets) runs scale approximately to the inverse of the square of the particle diameter, as would be expected when diffusive resistances in the particle macropores predominate. 

As can be seen from Figure 8, if Fo < 0.02, the concentration changes within the film are confined largely to the surface layer and the local mass transfer coefficient is given by the Higbie penetration theory (9) as... 

Predictions for Ribbons. The simplest situation to consider is that when the catalyst is a flat ribbon orientated parallel to the direction of flow of gas. Then at a distance x downstream from the leading edge the local mass transfer coefficient, h, is given by ... 

In view of Eq. (1), the time and space dependent local mass transfer coefficient is given by... 

At the relatively rare case where steady-state physicochemical and hydrodynamic conditions exist, the local mass transfer coefficient is independent of time,... 

It should be noted that the local mass transfer coefficient can only be obtained experimentally and is case specific. An analytical relationship for the local mass transfer rate coefficient can be obtained if a mathematical expression describing the gradient of the dissolved concentration at the NAPL-water interface is known. Unfortunately, the local mass transfer coefficient usually is not an easy parameter to determine with precision. Thus, in mathematical modeling of contaminant transport originating from NAPL pool dissolution, k(t, x,y) is often replaced by the average mass transfer coefficient, k(t), applicable to the entire pool, expressed as [41]... 

Given that the presence of humics enhance the solute solubility, the local mass transfer coefficient, k, defined in Eq. (3) should be modified accordingly. In view of Eq. (42), the appropriate expression for the effective local mass transfer coefficient, ke(t, x), is given by [57]... 

In the absence of dissolved humic substances, the preceding equation reduces to the local mass transfer coefficient defined in Eq. (3). Furthermore, the corresponding average effective mass transfer coefficient, ke(t), applicable to the entire pool, can be expressed as... 

Chrysikopoulos and Kim [70] developed time invariant, local mass transfer correlations for NAPL pool dissolution in saturated media based on numerically determined local mass transfer coefficients evaluated for interstitial fluid velocities of 0.1,0.5,0.7,0.85, and 1.0 m/day. It should be noted that solubility concentrations may occur at a NAPL-water interface when interstitial fluid velocities are less than 1.0 m/day [8]. Over 200 different rectangular pools with dimensions xx y in the range from 0.2 mx0.2 m to 10.0 mxlO.O m and approximately the same number of elliptic/circular pools with semiaxes axb in the range 0.1 mxO.l m to 5.0 mx5.0 m were examined. 

For a single component elliptic/circular NAPL pool the fundamental parameters that affect the local mass transfer coefficient are the same as those listed for the case of a rectangular pool. Therefore, the time invariant local mass transfer coefficient for a single component elliptic NAPL pool can be represented by the... 

In a binary flow system with interfacial fluid composition xao and bulk fluid composition x b, the local mass-transfer coefficient k corrected for the interfacial total molar flux cvq + Nbo] satisfies... 

The mass flux of a solute can be related to a mass transfer coefficient which gathers both mass transport properties and hydrodynamic conditions of the system (fluid flow and hydrodynamic characteristics of the membrane module). The total amount transferred of a given solute from the feed to the receiving phase can be assumed to be proportional to the concentration difference between both phases and to the interfacial area, defining the proportionality ratio by a mass transfer coefficient. Several types of mass transfer coefficients can be distinguished as a function of the definition of the concentration differences involved. When local concentration differences at a particular position of the membrane module are considered the local mass transfer coefficient is obtained, in contrast to the average mass transfer coefficient [37]. 

The different values ofkifl depending on the type of mass-transfer process (vaporization, chemical, or physical absorption) are due not only to variations of the liquid areas involved in mass transfer operation (JIO, P16), but also to variations in the local mass-transfer coefficients within these zones (B2, B3, P13), for example, those due to the effect of interfacial turbulence which may accompany chemical absorption (L15). 

Axial Distribution of Local Mass-Transfer Coefficient and Directly Contacting Catalyst... 

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