Mass transfer coefficients average values

The ratio of l> j /hbio represents an effective mass transfer coefficient, Thoms [5] report 38 measiuements in freshwater systems for which this ratio can be calculated. The average value is 130 cm/year and about 60% of the measurements exceed 1 cm/year and 90% exceed 0.1 cm/year. In shallow waters such as would be observed nearshore, Boudreau [7] provided correlations between biotiubation and depth that suggest a 2.54 and 29.5 cm/year effective particle mass transfer coefficient. A value of 1 cm/year appears to be a reasonably conservative estimate of the effective particle bioturbation mass transfer coefficient in a clean shallow system, such as the top of a nearshore sediment cap. A coefficient of the order of 1 cm/year or more has also been observed by Thibodeaux [8]. 

The value of the saturation concentration,, is the spatial average of the value determined from a clean water performance test and is not corrected for gas-side oxygen depletion therefore K ji is an apparent value because it is determined on the basis of an uncorrected. A tme volumetric mass transfer coefficient can be evaluated by correcting for the gas-side oxygen depletion. However, for design purposes, can be estimated from the surface saturation concentration and effective saturation depth by... 

Oxygen transfer rate (OTR) The product of volumetric oxygen transfer rate kj a and the oxygen concentration driving force (C - Cl), (ML T ), where Tl is the mass transfer coefficient based on liquid phase resistance to mass transfer (LT ), a is the air bubble surface area per unit volume (L ), and C and Cl are oxygen solubility and dissolved oxygen concentration, respectively. All the terms of OTR refer to the time average values of a dynamic situation. 

Table 3.1 shows the kinetic parameters for cell growth, rate models with or without inhibition and mass transfer coefficient calculation at various acetate concentrations in the culture media. The Monod constant value, KM, in the liquid phase depends on some parameters such as temperature, initial concentration of the carbon source, presence of trace metals, vitamin B solution, light intensity and agitation speeds. The initial acetate concentrations in the liquid phase reflected the value of the Monod constants, Kp and Kp. The average value for maximum specific growth rate (/xm) was 0.01 h. The value... 

Mass transfer rates from drops are obtained by measuring the concentration change in either or both of the phases after passage of one or more drops through a reservoir of the continuous phase. This method yields the average transfer rate over the time of drop rise or fall, but not instantaneous values. For measurements of the resistance external to the drop this is no drawback, because this resistance is nearly constant, but the resistance within the drop frequently varies with time. The fractional approach to equilibrium, F, is calculated from the compositions and is then related to the product of the overall mass transfer coefficient and the surface area ... 

The mass transfer coefficient given here is the value averaged over the length. 

Experimentally one often measures the average value of the mass transfer coefficient, which is defined as... 

The exponent of the Schmidt number in Eq. (259) coincides with the experimental one, while the coefficient 0.0067 is somewhat low. However, one must not take very seriously the value of 243 for the coefficient in Eq. (254a). Accounting for the statistical distribution of the pathlength xc and the associated average value of the mass transfer coefficient with respect to this distribution, one might avoid the slight discrepancy. 

Average values calculated from the mass transfer coefficient kt. 

C] represents the concentration of species Ain the liquid and x represents the mole fraction of the diffusing species in the liquid. Note that we have introduced kL, the liquid phase mass transfer coefficient. The cap ( ) indicates average value. 

So far we have approximated the external heat and mass transfer coefficients by virtue of an average value however, precise measurements have indicated that the local value may substantially change along the catalyst surface. Moreover, for a highly exothermic reaction a very strong gas phase concentration and temperature gradients may occur so that the pellet is bathed by a nonuniform external field (13, 14). 

The rate parameters of importance in the multicomponent rate model are the mass transfer coefficients and surface diffusion coefficients for each solute species. For accurate description of the multicomponent rate kinetics, it is necessary that accurate values are used for these parameters. It was shown by Mathews and Weber (14), that a deviation of 20% in mass transfer coefficients can have significant effects on the predicted adsorption rate profiles. Several mass transfer correlation studies were examined for estimating the mass transfer coefficients (15, jL6,17,18,19). The correlation of Calderbank and Moo-Young (16) based on Kolmogaroff s theory of local isotropic turbulence has a standard deviation of 66%. The slip velocity method of Harriott (17) provides correlation with an average deviation of 39%. Brian and Hales (15) could not obtain super-imposable curves from heat and mass transfer studies, and the mass transfer data was not in agreement with that of Harriott for high Schmidt number values. 

Due to the complexity of mass transfer between gas-liquid-solid phases, it is difficult to evaluate the average value of mass transfer coefficient ki from the literature. A realistic way to evaluate ki is to use the algebraic expression of solution and by regression to obtain the experimental data rather than by regression with solving the set of non-linear differential equations. 

Numerically evaluated average mass transfer coefficients, k, based on the average of 200 different realizations of the log-normal hydraulic conductivity, as a function of C,JC,X for several variances of Y=lnK (a =0.1,0.2,0.3,0.4, and 0.5) for a hydraulic gradient of dhldx=0.01 and mean log-transformed hydraulic conductivity of 7=0.8 are shown in Fig. 7a. The results indicate that for increasing C,JC,X there is a significant increase in k. Low values of the anisotropy... 

Fig. 7a, b Average mass transfer coefficient as a function of a aquifer anisotropy ratio for several variances of the log-transformed hydraulic conductivity distribution b variance of the log-transformed hydraulic conductivity distribution where open circles represent numerically generated data and solid lines represent linear fits. All model parameter values are identical with those used in Fig. 6... 

Fig. 12a, b Fitted time invariant overall mass transfer coefficients as a function of Ux evaluated from the averaged two sets of concentration measurements with error bars representing the 95% confidence intervals, b Comparison between experimentally determined Sh values (solid circles) and the experimental overall mass transfer correlation (solid curve) as a function of Ux... 

To implement these simulation approaches, the value of the liquid film mass transfer coefficient Kf is required, which for nonporous and porous HPLC particles, can be calculated from literature correlations derived for bath357,400,408 or column models.407,408 For the case with porous particles, the apparent pore liquid mass transfer coefficient Kp can be expressed as an effective pore diffusivity over an average effective diffusion path length, such that... 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

Liquid toluene (C iHsCHj) was stored at6.4°C in an open top 20-cm-diameter cylindrical container. Tile vapor pressure of toluene at 6.4°C is 10 nun Hg. A gentle stream of fresh air at 6.4"C and 101.3 kPa was allowed to flow over the open end of the container. The rale of evaporation of toluene into air was measured to be 60 g/day. E.stimaie the concentration of toluene (in g/m ) at exactly 10 nun above the liquid surface. The diffusion coefficient of toluene at 2S° C is D.,a = 0.084 X 10-"inVs. 14-141 In an experiment, a sphere of crystalline sodium. chloride (NaCI) was suspended in a. stirred tank filled with water at 20°C. It-s initial mass was 100 g. In 10 minutes, the mass Of sphere was found to have decreased by 10 percent. The density of NaCl is 2160 kg/ra Its solubility in water at 20°C is 320 kg/m, Use these results to obalin an average value for the mass transfer coefficient. 

The mass transfer coefficient used in this equation should be the average value over the total external particle surface area Ap, including the flat ends of each particle. Hqwever,... 

Mass-transfer coefficients calculated from average absorption efficiency. More than 10 measurements were averaged for each coefficient value. 

Then a and By were optimized to minimize the percent absolute average relative deviation (% AARD) between the calculated solubility and the experimental solubilty measured here, and the experimental solubilities at 35 C reported by Tsekhanskaya et al. (11) and by McHugh and Paulaitis (12), The equilibrium solubilities of naphthalene in CO2 used to calculate the mass transfer coefficients are given in Table IL The optimized values of ay, By, and %AARD are 0.0402, 6.5384 and 9.23 respectively. Prediction of the solubility with these two optimized parameters is given in Figure 2 with data of Tsekhanskaya et al. (Ij, McHugh and Paulaitis (12) and our experimental solubility data (below the critical pressure). 

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