Single-pore model, mass transfer

We first give a rather general mass-transfer model, which is useful for most processes of porous-solid extraction with dense gases. Two cases are possible [43] for a single particle loaded with solute. In (a), the solute is adsorbed over the internal surface of the particle, and is desorbed from the sites and diffuses out to the external surface, (b) The solute fills in the pore-cavities completely, and is dissolved from an inner core that moves progressively to the centre of the particle. 

Depending on the distribution chosen, as few as three fitting parameters may be required to define a distribution of diffusion rates. In some cases, a single distribution was used to describe both fast and slow rates of sorption and desorption, and in other cases fast and slow mass transfer were captured with separate distributions of diffusion rates. For example, Werth et al. [42] used the pore diffusion model with nonlinear sorption to predict fast desorption, and a gamma distribution of diffusion rate constants to describe slow desorption. 

Kaczmarski et al. used a similar model for the calculation of the band profiles of the enantiomers of 1-indanol on a chiral phase in HPLC [29,57]. These authors ignored the external mass transfer and assumed that local equilibrium takes place for each component between the pore surface and the stagnant fluid phase in the macropores (infinite fast kinetics of adsorption-desorption). They also assumed that surface diffusion contribution is much faster than pore diffusion and neglected pore diffusion entirely. Instead of the single file Maxwell-Stefan diffusion, these authors used the generalized Maxwell-Stefan diffusion (see Chapter 5).The calculation (see below) requires first the selection of equations to calculate the surface molecular flux [29,57,58],... 

Figures 16.23a to d compare experimental profiles of mixtures of the enantiomers of 1-indanol on cellulose tribenzoate with those calculated with the GMS-GRM model of these authors [57]. For the numerical calculations, they assmned that surface diffusion plays the dominant role in mass transfer across the particles and neglected the contribution of pore diffusion to the fluxes. Unfortunately, it was impossible independently to measure or even estimate the surface diffusion parameters. So, the numerical values of the surface diffusion coefficients needed for the calculation were estimated by minimizing the discrepancies between the measured and the calculated band profiles i.e., by parameter adjustment). Yet, it is impressive that, using a unique set of diffusion coefficients, it was possible to calculate band profiles of single components of binary mixtures in the whole range of relative composition, for loading factors between 0 and 10%.

Note that Eq. (18z56a) is very similar to Eq. (18=48b) except that c replaces the concentration of the pore fluid Cp j-e and the lunped parameter mass transfer coefficient l, replaces the film coefficient kf. As expected, the lunped parameter expressions using the single-porosity model are sirtpler. 

To understand and to model coke burn-off within a single particle the intrinsic kinetics (without any resistance by diffusion), mass transfer by pore diffusion and external diffusion, and structural parameters of the catalyst have to be taken into account. 

A quantitative answer to above questions may be given through the theoretical modeling of non-isobaric, non-isothermal single component gas phase adsorption. External heat and mass transfer, intrapai ticle mass transport through Knudsen diffusion, Fickian diffusion, sorbed phase diffusion and viscous flow as well as intraparticle heat conduction are accounted for. Fig. 1 presents the underlying assumption on the combination of the different mass transport mechanisms in the pore system. It is shown elsewhere that the assumption of instantaneous... 

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