Mass transfer molecular diffusion coefficients

The overall process can be affected by pore diffusion and external mass transfer. Molecular diffusion coefficients DPB may be calculated by Aspen Plus. Effective pore diffusion may be estimated by the relation DP = Dpb( j,/tp) = 0.1 DPE, in which ep is the particle porosity and rp the tortuosity. Furthermore, the Thiele modulus and internal effectiveness can be calculated as ... 

Each of the mass transfer coefficients klA and k2A can be interpreted as a molecular diffusion coefficient, D, divided by a film thickness, z, for the gas phase and the water phase, respectively, i.e., k=D/z. However, this interpretation has no meaning in practice because of the lack of knowledge on the thickness of the two films. 

A number of approaches have been suggested for the determination of the molecular diffusion coefficient, D, of a component in water (Othmer and Thakar, 1953 Scheibel, 1954 Wilke and Chang, 1955 Hayduk andLaudie, 1974 Thibodeaux, 1996). Based on these five references, the diffusion coefficient ratio />/Jl2s / Dlq2 was found to vary within the interval 0.78-0.86 with an arithmetic mean value equal to 0.84. This value can be inserted in Equation (4.22) as a first estimate to determine Km. Equation (4.22) and the empirical expressions for KLC>2 outlined in Table 4.7 are the basis for the determination of the mass transfer coefficient for H2S, KL i S, and thereby, the emission of H2S from the wastewater into the sewer atmosphere. Further details relevant in this respect are dealt with in Section 4.4. 

The low molecular diffusion coefficients of proteins and other biopolymers reduces the efficiency of mass transfer and compromises efficiency as flow rate is increased. Therefore, high-performance SEC columns are usually operated at modest flow rates, e.g., 1 ml/min or less. However, operation at very low flow rates is undesirable due to excessive analysis times, loss of efficiency due to axial analyte diffusion, and the risk of poor recovery due to analyte adsorption. 

The theories vary in the assumptions and boundary conditions used to integrate Fick s law, but all predict the film mass transfer coefficient is proportional to some power of the molecular diffusion coefficient D", with n varying from 0.5 to 1. In the film theory, the concentration gradient is assumed to be at steady state and linear, (Figure 3-2) (Nernst, 1904 Lewis and Whitman, 1924). However, the time of exposure of a fluid to mass transfer may be so short that the steady state gradient of the film theory does not have time to develop. The penetration theory was proposed to account for a limited, but constant time that fluid elements are exposed to mass transfer at the surface (Higbie, 1935). The surface renewal theory brings in a modification to allow the time of exposure to vary (Danckwerts, 1951). 

The data available on the molecular diffusion coefficient of organic vapors in air are meager, but they indicate (in accordance with approximate theory) an inverse proportionality to the square root of molecular weight. The rate of mass transfer by molecular diffusion will be proportional to the diffusion coefficient and to the SVC, itself proportional to vapor pressure times molecular weight (M). We should expect, therefore, under standard conditions of ventilation, that the rate of loss will be proportional to vapor pressure X The ratio of observed rate to... 

Here dp is a relevant length measure of the catalyst particle, such as its diameter, a and kg are the heat and the mass transfer coefficients to the particle, u is the average, characteristic velocity of the reaction medium with respect to the particle, and A, v, p and cp are the heat conductivity, kinematic viscosity, density and heat capacity of the reaction medium surrounding a particle, either a gas or a liquid. D is the molecular diffusion coefficient of the component transferred to the catalyst particle in the reaction medium. 

The mass transfer coefficient,, for a sphere can be determined from the Sherwood number, Sh (= K JD g, where is the molecular diffusion coefficient of the solvent. A, in drying gas, B typical values are 10 -10 cm /sec) and the following engineering correlation [15]... 

In this model the parameters controlling the gas exchange rate are characterized by the replacement time, 0, rather than a boundary layer thickness. Comparing this equation with Eq. (10.1) we see that the mass transfer coefficient is proportional to the square root of the molecular diffusion coefficient. 

Molecular diffusion coefficient mVs cmVs kd Dispeised-phase mass-transfer m/s or cm/s ft/h... 

As shown earlier, the mass transfer coefficient is inversely proportional to the channel diameter and increases with the molecular diffusion coefficient. Accordingly, the influence of mass transfer on the observed reaction rate can be estimated by varying the diameter [84], This method was applied in experiments by Fichtner et al. [91], who varied the hydraulic channel diameter between 125 and 85 pm. The authors investigated the partial oxidation of methane to synthesis gas, a fast reaction, in a MSR made of rhodium. Another method to vary the external mass transfer resistance consists of varying the molecular diffusion coefficient. The... 

The dependence of the molecular diffusion coefficient on the temperature and the total pressure can also be used to unravel the influence of external mass transfer. However, the temperature influences both the diffusivity and the intrinsic kinetics, whereas a variation of the total pressure at constant partial pressures of the reactants affects only the diffusivity. Kolbl et al. [93] applied this method in their investigation of steam reforming in microchannel reactors. 

In this expression, the volumetric mass transfer coefficient is in reciprocal seconds, the molecular diffusion coefficient in m2/s, and the liquid holdup h L in meters. The term F refers to fractional approach to flooding. 

The binary molecular diffusion coefficient, ab> has units of length /time and characterizes the microscopic motion of species A in solvent B, for example. Hab is also the molecular transport property that appears in the linear law that relates diffusional fluxes and concentration gradients. In this respect, the same quantity, Bab. represents a molecular transport property for mass transfer and a diffusion coefficient. This is not the case for the other two transport processes. 

The kinetic theory of dilute gases accounts for collisions between spherical molecules in the presence of an intermolecular potential. Ordinary molecular diffusion coefficients depend linearly on the average kinetic speed of the molecules and the mean free path of the gas. The mean free path is a measure of the average distance traveled by gas molecules between collisions. When the pore diameter is much larger than the mean free path, collisions with other gas molecules are most probable and ordinary molecular diffusion provides the dominant resistance to mass transfer. Within this context, ordinary molecular diffusion coefficients for binary gas mixtures are predicted, with units of cm /s, via the Chapman-Enskog equation (see Bird et al., 2002, p. 526) ... 

The following strategy should be used to calculate the interpellet axial dispersion coefficient and the mass transfer Peclet number in packed catalytic tubular reactors (see Dullien, 1992, Chap. 6). Initially, one should calculate a simplified mass transfer Peclet number (i.e., Pesimpie) based on the equivalent diameter of the catalytic pellets, equivalent, the average interstitial fluid velocity through the packed bed, (Uj>intetstitiai, and the ordinary molecular diffusion coefficient of reactant A, a, ordinary-... 

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