Wilke-Chang correlation

The Wilke-Chang correlation is shown graphically in Figure 8.2. This figure can be used to determine the association constant for a solvent from experimental values for Dl in the solvent. 

In order to solve the mathematical model for the emulsion hquid membrane, the model parameters, i. e., external mass transfer coefficient (Km), effective diffu-sivity (D ff), and rate constant of the forward reaction (kj) can be estimated by well known procedures reported in the Hterature [72 - 74]. The external phase mass transfer coefficient can be calculated by the correlation of Calderback and Moo-Young [72] with reasonable accuracy. The value of the solute diffusivity (Da) required in the correlation can be calculated by the well-known Wilke-Chang correlation [73]. The value of the diffusivity of the complex involved in the procedure can also be estimated by Wilke-Chang correlation [73] and the internal phase mass transfer co-efficient (surfactant resistance) by the method developed by Gu et al. [75]. 

The pure compound rate constants were measured with 20-28 mesh catalyst particles and reflect intrinsic rates (—i.e., rates free from diffusion effects). Estimated pore diffusion thresholds are shown for 1/8-inch and 1/16-inch catalyst sizes. These curves show the approximate reaction rate constants above which pore diffusion effects may be observed for these two catalyst sizes. These thresholds were calculated using pore diffusion theory for first-order reactions (18). Effective diffusivities were estimated using the Wilke-Chang correlation (19) and applying a tortuosity of 4.0. The pure compound data were obtained by G. E. Langlois and co-workers in our laboratories. Product yields and suggested reaction mechanisms for hydrocracking many of these compounds have been published elsewhere (20-25). 

Oiffusivity The kinetic theory of liquids is much less advanced than that of gases. Therefore, the correlation for diffusivities in liquids is not as reliable as that for gases. Among several correlations reported, the Wilke-Chang correlation (Wilke and Chang, 1955) is the most widely used for dilute solutions of nonelectrolytes,... 

Estimate DAB via the Wilke-Chang correlation. The Wilke-Chang correlation is as follows ... 

Convert the estimated value to one that corresponds to 40°C. The Wilke-Chang correlation (see step 1) suggests that (D ab/a / T) is constant for a given liquid system. We may use that assumption... 

For predicting the diffusivity of small molecules (with molecular weights less than about 1000 or molar volumes less than about 0.500 m3/kg) in aqueous solution, we may use the Wilke-Chang correlation to estimate the diffusivity in m2/s... 

In the absence of a rigorous theory for diffusion in liquids, a number of empirical relationships have been proposed, one of which we mention briefly. For a binary mixture of solute A in solvent B, the diffusion coefficient D°AB (cm2 s1) of A diffusing in an infinitely diluted solution of A in B can be found with the Wilke-Chang correlation ... 

Thus generally, for liquids D°AB D°BA. Different techniques with which to estimate the infinite dilution diffusion coefficient are described by Reid et al. [31]. Various correlation s (valid for an arbitrary composition of a binary mixture and for electrolytes) are also given. In the Wilke-Chang correlation for D°AB the effect of temperature has been accounted for by assuming D°AB — T. Although this approximation may be valid over small temperature ranges, it is usually preferable to assume that... 

From Wilke-Chang correlation, D°AB=7.4xlO 8(tMB) TAlBVA - , where D°AB/cm l is mutual diffusion coefficient of solute A in solvent B, Mb /g-mok is molecular weight of solvent B, tib /cp is viscosity of solvent B, Va /cm3-mol is molar volume of solute A at its nomial boiling temperature, and is association factor of solvent B. 

Solution Although the liquids are somewhat viscous, fust estimate the infinite-dilution diffusivities using the Wilke-Chang correlation. Eq. (2.3-17). The molar volumes at the boiling point are estimated hy Shroeder s method10 as... 

The diffusion coefficients is then estimated from the following three equations WILKE-CHANG CORRELATION... 

SO that the ratio of is proportional to the ratio of the square roots of D and a. The diffusivity has been estimated from the Wilke-Chang correlation (17) to be 5.73 x 10 and the thermal diffusivity was calculated to be U. 13 x 10. This interpretation has been carried out using the assumption that the absorption is in the fast reaction regime and that the kinetics are pseudo first order. Since M is defined by... 

The estimation of the film thickness is obtained from the average values for the binary mass transfer and diffusion coefficient, estimated by traditional correlation (Onda (1968) correlation for the mass transfer coefficient. Fuller and Wilke Chang correlation for the vapour and liquid diffusion coefficient). 

Figure 14 Diffusivities of n-paraffins in FT wax (, experimental data at T=504 K —, Wilke-Chang correlation at 7=540 K ---correlation bylglesia etal. n, carbon number D , diffusivities of n-paraffins) (Erkey et al., 1990).

Wilke-Chang correlation A semi-empirical correlation used for the estimation of the diffusion coefficient of a substance present in infinite dilution in a solvent. 

The relationship described in Equation 5.24 is not dimensionally consistent therefore accurate estimates of aqueous diffusivity will only be obtained if the values of the parameters used have the specified units. The Wilke-Chang correlation provides estimates with average errors of 10%. 

Because the Stokes Einstein equation is limited to cases in which the solute is larger than the solvent, many investigators have developed correlations for cases in which solute and solvent are similar in size. The impressive aspect of these efforts is their similarly to the Stokes Einstein equation. Almost all show the same temperature and viscosity dependence. All authors claim marginally better accuracy, but for such increased complexity that their results are rarely used. The exception is the Wilke-Chang correlation (1955), which predicts... 

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