Mass transfer coefficients individual

Langmuir adsorption coefficient overall mass transfer coefficient individual mass transfer coefficients at G-L interface ibid, at liquid-solid interface homogeneous reaction velocity... 

The relationship of the overall gas-phase mass transfer coefficient to the individual film coefficients maybe found from equations 4 and 5, assuming a straight equiHbrium line ... 

Under equiUbrium or near-equiUbrium conditions, the distribution of volatile species between gas and water phases can be described in terms of Henry s law. The rate of transfer of a compound across the water-gas phase boundary can be characterized by a mass-transfer coefficient and the activity gradient at the air—water interface. In addition, these substance-specific coefficients depend on the turbulence, interfacial area, and other conditions of the aquatic systems. They may be related to the exchange constant of oxygen as a reference substance for a system-independent parameter reaeration coefficients are often known for individual rivers and lakes. 

With complicated geometries, the product of the interfacial area per volume and the mass-transfer coefficient is required. Correlations of kop or of HTU are more accurate than individual correlations of k and since the measurements are simpler to determine the produc t kop or HTU. 

Volumetric Mass-Transfer Coefficients and Kia Experimental determinations of the individual mass-transfer coefficients /cg and /cl and of the effective interfacial area a involve the use of extremely difficult techniques, and therefore such data are not plentiful. More often, column experimental data are reported in terms of overall volumetric coefficients, which normally are defined as follows ... 

It would be desirable to reinterpret existing data for commercial tower packings to extract the individual values of the interfacial area a and the mass-transfer coefficients fcc and /c in order to facilitate a more general usage of methods for scaling up from laboratory experiments. Some progress in this direction has afready been made, as discussed later in this section. In the absence of such data, it is necessary to operate a pilot plant or a commercial absorber to obtain kc, /c , and a as described by Ouwerkerk (op. cit.). 

Note that the transfer rate equation is based on an overall concentration driving force, (X-X ) and overall mass transfer coefficient, Kl. The two-film theory for interfacial mass transfer shows that the overall mass transfer coefficient, Kl, based on the L-phase is related to the individual film coefficients for the L and G-phase films, kL and ko, respectively by the relationship... 

Gas-Liquid Mass Transfer. Gas-liquid mass transfer within the three-phase fluidized bed bioreactor is dependent on the interfacial area available for mass transfer, a the gas-liquid mass transfer coefficient, kx, and the driving force that results from the concentration difference between the bulk liquid and the bulk gas. The latter can be easily controlled by varying the inlet gas concentration. Because estimations of the interfacial area available for mass transfer depends on somewhat challenging measurements of bubble size and bubble size distribution, much of the research on increasing mass transfer rates has concentrated on increasing the overall mass transfer coefficient, kxa, though several studies look at the influence of various process conditions on the individual parameters. Typical values of kxa reported in the literature are listed in Table 19. 

The mass transfer coefficient describes the effect of mass transfer resistance of the reactants flowing from the gas phase to the surface of the individual particles in the bed. The mass transfer coefficient can be obtained from a correlation for the Sherwood number (or dimensionless mass transfer coefficient) given by Eq. (7) ... 

Nonhebel(32) emphasises that values of the individual film mass transfer coefficients obtained from this equation must be used with caution when designing large-scale towers and appropriately large safety factors should be incorporated. 

He Henry s constant Jf Rate of formation of bubbles per unit volume of solution Jd Rate of destruction of bubbles per unit volume of solution Icl Individual liquid phase mass transfer coefficient Kr Product of gas constant and absolute temperature... 

The individual, or phase, mass transfer coefficients (i.e., for the dispersed phase and for the continuous phase) are defined as ... 

Fig. 9.20 Definition of individual and overall mass transfer coefficients.

The values of the mass transfer coefficient will be different on each side of the boundary. For example, when a gas dissolves in a liquid, feg in the gas film will be different from k[ in the liquid film. However, the concentration at the interface is not always known and this leads to the use of overall mass transfer coefficients in conjunction with overall driving forces. The following argument shows how these are related to the individual film coefficients. 

The following one gives the best prediction of the individual liquid-film mass transfer coefficient in water-treatment situations (Chem and Chien, 2002) ... 

The film (individual) coefficients of mass transfer can be defined similarly to the film coefficient of heat transfer. A few different driving potentials are used today to define the film coefficients of mass transfer. Some investigators use the mole fraction or molar ratio, but often the concentration difference AC (kg or kmol m ) is used to define the liquid phase coefficient (m while the partial pressure difference A/i (atm) is used to define the gas film coefficient (kmolh m 2 atm ). However, using and A gp of different dimensions is not very convenient. In this book, except for Chapter 15, we shall use the gas phase coefficient (m h" ) and the liquid phase coefficient ki (m h ), both of which are based on the molar concentration difference AC (kmol m ). With such practice, the mass transfer coefficients for both phases have the same simple dimension (L T" ). Conversion between k and is easy, as can be seen from Example 2.4. 

By applying the effective film thickness concept, we obtain Equation 2.18 for the individual phase mass transfer coefficient k Q (LT ) which is analogous to Equation 2.17 for heat transfer. 

The over-all resistance is then the sum of the individual resistances (see equation 3-8) and the over-all mass transfer coefficient KLa takes all of them into account. In practice, it is often not possible to determine the mass transfer coefficient for a dispersed liquid or solid... 

The above equations may be used for finding the interfacial concentrations corresponding to any set of values of x and y, provided the ratio of the individual mass-transfer coefficients is known. Thus ... 

If it is desired to calculate the rate of mass transfer from the overall concentration-difference based on bulk-liquid compositions (x -x), the appropriate overall coefficient, Ki x, is related to the individual mass-transfer coefficients by the equation ... 

In most types of mass-transfer equipment, the interfacial area, a, that is effective for mass transfer cannot be determined accurately. For this reason, it is customary to report experimentally observed rates of transfer in terms of mass-transfer coefficients based on a unit volume of the apparatus, rather than on a unit of interfacial area. Calculation of the overall coefficients from the individual volumetric coefficients is made practically, for example, by means of the equations ... 

Equations 3.12, 3.13, and the final Equation 3.14 are all forms of the classic engineering expression [Rate = (Driving force)/Resistance] where the driving force is expressed as concentration differences. The overall resistance (1 /K ) can be controlled by a low value of either individual coefficient. The mass transfer coefficient (kd) controls crystallization when the reaction is very rapid relative to diffusion, but the reaction coefficient ( r) controls crystallization when diffusion is much more rapid than reaction. In such cases the overall coefficient K may be approximated by the smaller k value. However, the concentrations in the driving force remain measurable (c) or calculable (ceq) rather than non-measureable (c ). 

Derive the relationship between the overall mass-transfer coefficient for liquid phase Kh and the individual mass-transfer coefficients, kL and kG. How can this relationship be simplified for sparingly soluble gases ... 

Since the oxygen is sparingly soluble gas, the overall mass-transfer coefficient KL is equal to the individual mass-transfer coefficient KL. Our objective in fermenter design is to maximize the oxygen transfer rate with the minimum power consumption necessary to agitate the fluid, and also minimum air flow rate. To maximize the oxygen absorption rate, we have to maximize KL, a, C - CL. However, the concentration difference is quite limited for us to control because the value of C L is limited by its very low maximum solubility. Therefore, the main parameters of interest in design are the mass-transfer coefficient and the mterfacial area. 

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