Fluid mass transfer

Wakao, N. and Funazkri, T. Chem. Eng. Sci. 33 (1978) 1375. Effect of fluid dispersion coefficients on particle-fluid mass transfer coefficients in packed beds. 

According to their analysis, if c is zero (practically much lower than 1), then the fluid-film diffusion controls the process rate, while if ( is infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the mechanical parameter represents the ratio of the diffusion resistances (solid and fluid-film). This equation can be used irrespective of the constant pattern assumption and only if safe data exist for the solid diffusion and the fluid mass transfer coefficients. In multicomponent solutions, the use of models is extremely difficult as numerous data are required, one of them being the equilibrium isotherms, which is a time-consuming experimental work. The mathematical complexity and/or the need to know multiparameters from separate experiments in all the diffusion models makes them rather inconvenient for practical use (Juang et al, 2003). 

What has been said above also holds for solid-fluid mass transfer. The concentration gradients for mass transfer from a solid phase to a fluid in turbulent flow should be analogous to the temperature gradients, such as shown in Figure 2.5. 

Mathematical models derived from mass-conservation equations under unsteady-state conditions allow the calculation of the extracted mass at different bed locations, as a function of time. Semi-batch operation for the high-pressure gas is usually employed, so a fixed bed of solids is bathed with a flow of fluid. Mass-transfer models allow one to predict the effects of the following variables fluid velocity, pressure, temperature, gravity, particle size, degree of crushing, and bed-length. Therefore, they are extremely useful in simulation and design. 

The shrinking-core model (SCM) is used in some cases to describe the kinetics of solid and semi-solids-extraction with a supercritical fluid [22,49,53] despite the facts that the seed geometry may be quite irregular, and that internal walls may strongly affect the diffusion. As will be seen with the SCM, the extraction depends on a few parameters. For plug-flow, the transport parameters are the solid-to-fluid mass-transfer coefficient and the intra-particle diffusivity. A third parameter appears when disperse-plug-flow is considered [39,53],... 

FIGURE 16 Schematic representation of the origins of zone-broadening behavior and mass transfer effects of a polypeptide or protein due to Brownian motion, eddy diffusion, mobile phase mass transfer, stagnant fluid mass transfer, and stationary-phase interaction transfer as the polypeptide or protein migrated through a column packed with porous particles of an interactive HPLC sorbent. 

Solution of the shrinking core model at zero time (t=0) depends only on two parameters the solubility of solute in SC CO2 and the external particle to fluid mass transfer coefficient Kq. Hence, knowing the solubility, measurements of the initial extraction rates allow to determine the values of K(j. Detailed discussion on the evaluated mass transfer coefficients are given in [7].These authors found that the overall mass transfer from particles to fluid depends upon both free and forced convection mechanism. Figure 2 illustrates a parity plot of die experimental values of Sh number (evaluated by zero-time solution of the shrinking core model) and the calculated Sh number (using an appropriate mass transfer correlation). 

In addition to elucidation of molecular structures, NMR can also extract valuable information about physicochemical parameters. Because of the omnipresence of protonated solvents in CE/CEC, mobile-phase events can be monitored with NMR. Early studies using E-NMR involved the calculation of diffusion coefficients, electrophoretic mobilities, and viscosity [27]. Stagnant mobile-phase mass transfer kinetics and diffusion effects [60] and fluid mass transfer resistance in porous media-related chromatographic stationary phases [61] have been studied with NMR spectroscopy. NMR imaging of the chromatographic process [62] and NMR microscopy of chromatographic columns [63] have also been reported. Several applications of NMR to on-line studies of CE/ and CEC/ NMR are highlighted. 

Solid—Fluid Mass Transfer in a Packed Bed Under Supercritical Conditions... 

The additivity of tba individual resistances is dependant on tbe linearity of the flux expressions and of the equilibrium relationship. For nonlinear equilibrium relationships Eq. (2,4-IOa) and (2,4-lOb) can still ha used provided m is recognized to he a function of the interfacia] composition. Overall coefficients are often employed in the analysis of fluid-fluid mass transfer operations despite their complex dependence on the hydrodynamics, geometry and compositions of the two phases, In some instances the overall coefficients cen bs predicted from correlations for the individual coefficients for each phase provided the conditions in the apparatus are comparable to those for which the correlation was developed. 

Experimental results obtained in the framework of Pasachalk project are used to define parameters. The validation of the constitutive law is achieved thanks to the modelling of water flooding experiment. Comparisons between experimental and numerical results show that our finite element code is able to reproduce the fluid mass transfer and the mechanical water sensitive behaviour of chalk. 

Wakao N., and T. Funazkri, Effect of Fluid Dispersion Coefficients on Particle-to-fluid Mass Transfer Coefficients in Packed Beds, Chem. Engr. Sci., 33,1375 (1978). 

Based on the aforementioned analysis, different investigators assumed that the relative velocity in the neighborhood of a particulate phase depends on the length scale, and Using the velocity term, u, derived from Kolmogorov s theory and the particle diameter as the linear dimension, a power dissipation Reynolds number Re for particle-fluid mass transfer was defined as follows ... 

Hughmark employed this u to derive a correlation for Son and Hanratty (1967) and Hughmark (1971,1974) correlated wall to fluid heat transfer in pipe flow based on the relatively simple and well-established boundary layer theory. In the case of pipe flow, momentum transfer is solely by skin friction because of the geometry involved. Nonetheless, this approach was extended to particle-fluid mass transfer in turbulent flow. The correlation proposed was of the following form ... 

Overall, it may be concluded that the fluid mechanics-based approaches improved the understanding of particle-fluid mass transfer process. However, estimation of the... 

Pipe wall to fluid mass transfer coefficient (m/s) at the just-suspended condition (m/s) at the terminal settling velocity (m/s)... 

Fluid-Fluid Mass Transfer Without Reaction at the Wall... 

Lim, G. B., G. D. Holder, and Y. T. Shah. 1989. Solid-Fluid Mass Transfer in a Packed Bed under Supercritical Conditions. In Supercritical Eluid Science and Technology, 379-395. American Chemical Society. 

Again based on recommendation by Rase (1990), the following correlations for a particle to fluid mass transfer have accuracy to within 25%... 

Schmidt S, Buchs J, Bom C, Biselli M. A new correlation for the wall-to-fluid mass transfer in liquid-solid fluidized beds. Chem Eng Sci 54 829-839, 1999. 

Both particle-to-fluid mass transfer and intraparticle diffusion controlling... 

Fig 5 6 a. Uptake curve, 17/(70 versus r=(0,f/W )(Co/Pp<7o) both particle-to-fluid mass transfer and pore diffusion controlling, for n=I Eq (5-47) (Reproduced with permission by Suzuki, M and Chihara, K, Seisan Kenk u, 34. 150 (1982))... 

Fig S 6b Uptake curve, q/qo versus t—(D,llR )(Cii/Pfqi>) both particle-to-fluid mass transfer and pore diffusion controlling, for n=°°... 

Coefficient of exchange of momentum between neighboring streams of the fluid Mass transfer coefficient

[Pg.349]

This is a dear demonstration of a very significant enhancement of particle-to-fluid mass transfer in the ProCell unit, compared to a similarly operated conventional fluidized bed. 

The individual fluid mass-transfer coefficients ky, F ) and the interfacial area a which make up these overall volumetric coefficients are differently dependent upon fluid properties, flow rates, and type of packing. The overall volumetric coefficients are therefore useful only in the design of towers filled with the same packing and handling the same chemical system at the same flow rates and concentrations as existed during the measurements. For general design purposes, the individual coefficients and the interfacial area are necessary. 

---