Mass transfer coefficient constant, correlation

The unknown intermediate concentration C, has been mathematically ehminated from the last term. In this case, r can be solved for explicitly, but that is not always possible with surface rate equations of greater complexity. The mass transfer coefficient /ci is usually obtainable from correlations. When the experimental data are of (C, r) the other constants can be found by linear plotting. 

The mass transfer coefficient KLa is constant the general correlation is considered by many as proportional to the power per unit volume with constant exponent, and gas superficial velocity to another constant power as shown below 1,2... 

Mass-transfer coefficients for a single newtonian component in various module types and flow regimes can be correlated by Eq. (20-65) with values for the constants in Table 20-18 ... 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

This simplified description of molecular transfer of hydrogen from the gas phase into the bulk of the liquid phase will be used extensively to describe the coupling of mass transfer with the catalytic reaction. Beside the Henry coefficient (which will be described in Section 45.2.2.2 and is a thermodynamic constant independent of the reactor used), the key parameters governing the mass transfer process are the mass transfer coefficient kL and the specific contact area a. Correlations used for the estimation of these parameters or their product (i.e., the volumetric mass transfer coefficient kLo) will be presented in Section 45.3 on industrial reactors and scale-up issues. Note that the reciprocal of the latter coefficient has a dimension of time and is the characteristic time for the diffusion mass transfer process tdifl-GL=l/kLa (s). 

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... 

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]. 

In what follows, the preceding evaluation procedure is employed in a somewhat different mode, the main objective now being to obtain expressions for the heat or mass transfer coefficient in complex situations on the basis of information available for some simpler asymptotic cases. The order-of-magnitude procedure replaces the convective diffusion equation by an algebraic equation whose coefficients are determined from exact solutions available in simpler limiting cases [13,14]. Various cases involving free convection, forced convection, mixed convection, diffusion with reaction, convective diffusion with reaction, turbulent mass transfer with chemical reaction, and unsteady heat transfer are examined to demonstrate the usefulness of this simple approach. There are, of course, cases, such as the one treated earlier, in which the constants cannot be obtained because exact solutions are not available even for simpler limiting cases. In such cases, the procedure is still useful to correlate experimental data if the constants are determined on the basis of those data. 

Mass transfer coefficients In the mass transfer calculations, we need the Henry constant of oxygen in water at 30 °C, which can be evaluated using the relevant correlations presented in Section 1.3.2, Appendix I, and is equal to 34.03. The next parameter we need is the diffusion coefficient of oxygen in water at 30 °C, which can be also found in Table 1.10, Appendix I. The correction for the temperature has been also presented in eq. (1.28) Appendix I. The evaluated diffusion coefficient is 2.5 X 10-9 m2/s. 

Otos could be computed. All the Hixson and Smith data plot well in this fashion, and the straightness of the lines indicate the utility of the time-of-a-transfer-unit concept. Hixson, Drew, and Knox (H3) showed that a characteristic agitation number may be defined as the product of 0tOE and a velocity term for the agitated system. If then the mass transfer coefficient varies as the first power of the chosen velocity term, the agitation number would be constant for a given ratio of interfacial surface to total number of moles of extract phase. In liquid extraction, speed of agitation influences both terms of the quantity Ke[Pg.307]

In the cases above, a two-parameter model well represents the data. A model with more parameters would be more flexible, but by using a partition constant, K, or a desorption rate constant ka and k, , for the mass-transfer coefficients, the data are well described (see Figs. 3.4-15 and 3.4-13). While K would be a value experimentally determined, kp can be estimated from eqn. (3.4-97) with the external mass-transfer coefficient, km, estimated from the correlation of Stiiber et al. [25] or from that of Tan et al. [27], and the effective diffusivity from the Wakao Smith model [36], Typical values of kp obtained by fitting the data of Tan and Liou are shown in Fig. 3.4-16. As expected, they are below the usual mass-transfer correlations, because internal resistance diminishes the global mass transfer coefficient. These data correspond to the regeneration of spent activated carbon loaded with ethyl acetate, using high-pressure carbon dioxide, published by Tan and Liou [45]. 

We see that, in principle, the overall reaction rate can be expressed in terms of coefficients such as the reaction rate constant and the mass transfer coefficient. To be of any use for design purposes, however, we must have knowledge of these parameters. By measuring the kinetic constant in the absence of mass transfer effects and using correlations to estimate the mass transfer coefficient we are really implying that these estimated parameters are independent of one another. This would only be true if each element of external surface behaved kinetically as all other surface elements. Such conditions are only fulfilled if the surface is uniformly accessible. It is fortuitous, however, that predictions of overall rates based on such assumptions are often within the accuracy of the kinetic information, and for this reason values of k and hD obtained independently are frequently employed for substitution into overall rate expressions. 

For the scale-up of the gas-liquid contactor, the volumetric mass-transfer coefficient kLa can be used as a scale-up criterion. In general, the volumetric mass-transfer coefficient is approximately correlated to the power per volume. Therefore, constant power per volume can mean a constant kLa. 

The substance-specific kinetic constants, kx and k2, and partition coefficient Ksw (see Equations 3.1 and 3.2) can be determined in two ways. In theory, kinetic parameters characterizing the uptake of analytes can be estimated using semiempirical correlations employing mass transfer coefficients, physicochemical properties (mainly diffusivities and permeabilities in various media), and hydro-dynamic parameters.38 39 However, because of the complexity of the flow of water around passive sampling devices (usually nonstreamlined objects) during field exposures, it is difficult to estimate uptake parameters from first principles. In most cases, laboratory experiments are needed for the calibration of both equilibrium and kinetic samplers. 

Some of this theoretical thinking may be utilized in reactor analysis and design. Illustrations of gas-liquid reactors are shown in Fig. 19-26. Unfortunately, some of the parameter values required to undertake a rigorous analysis often are not available. As discussed in Sec. 7, the intrinsic rate constant kc for a liquid-phase reaction without the complications of diffusional resistances may be estimated from properly designed laboratory experiments. Gas- and liquid-phase holdups may be estimated from correlations or measured. The interfacial area per unit reactor volume a may be estimated from correlations or measurements that utilize techniques of transmission or reflection of light, though these are limited to small diameters. The combined volumetric mass-transfer coefficient kLa, can be also directly measured in reactive or nonreactive systems (see, e.g., Char-pentier, Advances in Chemical Engineering, vol. 11, Academic Press, 1981, pp. 2-135). Mass-transfer coefficients, interfacial areas, and liquid holdup typical for various gas-liquid reactors are provided in Tables 19-10 and 19-11. 

If external mass transport limitations strongly dominate, the rate becomes equal to the mass transfer rate, (eq 15). Hence, a first-order dependency is observed and, since the mass transfer coefficient is fairly independent of the temperature the apparent activation energy is negligible. However, due to the existing correlations, the observed rate constant is dependent on the flow rate and particle size. 

The pore diffusivity used in this analysis was determined by the Renkin equation4, the axial dispersion coefficient calculated by assuming a constant Peclet number of 0.2, and the mass transfer coefficient from the bulk to the particle surface calculated by the correlation of Wakao and Kaguei. The product of the heat capacity and density of the solid phase was taken to be the same as that used by Raghavan and Ruthven17. The density of the fluid phase was assumed to be that of pure C02 and was calculated from data provided by the Dionix Corporation in their AI-450 SFC software. Constant pressure heat capacities for the mobile phase were also assumed to be that of pure C02 and were taken from Brunner3. 

It is desired to double the capacity of the existing plant by processing twice the feed of reactant A while maintaining the same fractional conversion of A to B in the reactor. How much larger a reactor, in terms of catalyst weight, would be required if all other operating variables are held constant You may use the Thoenes-Kramers correlation for mass transfer coefficients in a packed bed. Describe the effects of the flow rate, temperature, particle size at conversion. 

The development of mass transfer models require knowledge of three properties the diffusion coefficient of the solute, the viscosity of the SCF, and the density of the SCF phase. These properties can be used to correlate mass transfer coefficients. At 35 C and pressures lower than the critical pressure (72.83 atm for CO2) we use the diffusivity interpolated from literature diffusivity data (2,3). However, a linear relationship between log Dv and p at constant temperature has been presented by several researchers U>5) who correlated diffusivities in supercritical fluids. For pressures higher than the critical, we determined an analytical relationship using the diffusivity data obtained for the C02 naphthalene system by lomtev and Tsekhanskaya (6), at 35 C. 

The advantage of using P is that it is approximately constant over normal ranges of temperature and pressure for any given pair of vapor and gas values. This avoids having to estimate values of heat- and mass-transfer coefficients a and ky from uncertain correlations. For the air-water system, considering convective heat transfer alone, P-l.l. In practice, there is an additional contribution from radiation, and P is very close to 1. As a result, the wet-bulb and adiabatic saturation temperatures differ by less than 1°C for the air-water system at near-ambient conditions (0 to 100°C, Y < 0.1 kg/kg) and can be taken as equal for normal calculation purposes. Indeed, t ically the T b measured by a practical psychrometer or at a wetted solid surface is closer to Tjs than to the pure convective value of T b. 

In the design of extraction equipment with complex flows, mass-transfer coefficients are determined by experiment and then correlated as a function of molecular diffusivity and system properties. The available theories provide an approximate framework for the data. The correlation constants vary depending upon the type of equipment and operating conditions. In most cases, the dominant mass-transfer resistance resides in the feed (raffinate) phase, since... 

You will be solving for Ca ), but you cannot evaluate the rate of reaction in Eq. (8.45) because you do not know Ca.s- You need a mass balance relating the rate of mass transfer to the catalyst to the rate of reaction. One form of that is Eq. (8.46), where is a mass transfer coefficient in units of m/s, determined from correlations derived in fluid mechanics and mass transfer courses, a is the surface area exposed per volume of the reactor (m /m ), and k is a rate of reaction rate constant (here rn /kmol s). Other formulations are possible, too ... 

Early SBCR models were reviewed by Ramachandran and Chaudhari (5) and by Deckwer (9). They require hold-up correlations as an input and do not compute flow patterns. The most complete and useful of these models applied to the Fischer-Tropsch (F-T) conversion of synthesis gas in a SBCR is that of Prakash and Bendale (79). They sized commercial SBCR for DOE. They gave syngas conversion and production as a function of temperature, pressure and space velocity. Input parameters with considerable uncertainty that influenced production rates were the gas hold-up, the mass transfer coefficient and the dispersion coefficient. Krishna s group (77) extended such a model to compute product distribution using a product selectivity model. Air Products working with Dudukovic measured dispersion coefficients needed as an input into such model. The problem with this approach is that the dispersion coefficients are not constant. They are a function of the local hydrodynamics. 

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