Transient diffusion in solids with a bipore distribution

Abstract

Transient diffusion of n-butane, iso-butane, and 1-butene in synthetic CaX(Na) spherical pellets is studied in a constant volume, well-stirred and T. Y. LEE system. The intracrystalline diffusion coefficients are in the order of 10-14 cm2/s, and the activation energy is about 7.0 Kcal/g-mole. Experimental data agree well with a mathematical model developed to describe Department of Chemical Engineering transient diffusion. SCOPEThe diffusion in porous pellets formed from zeolite crystals usually involves two main mechanisms: diffusion through the micropore structure within the crystals (intracrystalline diffusion) and diffusion through macropore structure between crystals (intercrystalline diffusion). The determination of each individual diffusion coefficient can be of importance in data interpretation and improving engineering design in operations such as purification, separation, and catalytic conversions.Previous work on the study of diffusion in zeolites concentrated mostly in micropore diffusion with powder forms. Recent studies on the diffusion in solids with a bipore distribution include the fheoretical and experimental investigation of diffusion in ion exchanged resins by Ruckenstein et al. (1971), the experimental study of diffusion of carbon dioxide in commercial 5A pellets by Sargent and Whitford (1971), and mathematical and experimental investigation of diffusion in Linde 13X by Ma and Ho (1974). All the above-mentioned studies were performed under constant pressure conditions. The present work employed a constant volume technique to examine quantitatively the diffusion of C4-hydrocarbons in micropores. Diffusion coefficients were evaluated based on a mathematical model taking into account intercrystalline and intracrystalline diffusion and adsorption under constant volume conditions. Rates of sorption of n-butane, iso-butane, and 1-butene in synthetic CaX(Na) were measured at three temperatures, and the activation energies for diffusion were determined from an Arrhenius plot. CONCLUSIONS AND SIGNIFICANCEMicropore diffusion coefficients were determined by assuming that the transport processes in macropores and micropores obey Fick's equation. The activation energy for diffusion was found to be about 6 to 8 Kcal/g-mole for the C4-hydrocarbons used in the study. The relatively low activation energy may, in part, be due to the large openings of the zeolite X.A mathematical model was developed to describe the diffusion in a solid with a bipore distribution. The present model differs from previous studies in that it deals with a well-stirred system where the total quantity of the diffusing species is finite. Agreement between experimental data and theoretical results was good. It should be noted that the present model can be reduced to those developed January 1976

Adsorption Kinetics

“…Under these conditions, for intracrystalline control the relevant diffusion equation for a set of uniform spherical particles is: (15) with the relevant initial and boundary conditions for a step change in sorbate concentration at t = 0:…”

Hindered Diffusion of Asphaltenes at Elevated Temperature and Pressure

“…A more detailed treatment with the time dependent bath concentration being considered has been made by Ma and Lee (1976) and Lee (1978).…”

Importance of finite adsorption rate in the evaluation of adsorption and diffusion parameters in porous catalysts

“…Chromatography (Hashimoto and Smith, 1974) Diffusion Cell (Dogu and Smith, 1975) Batch reservoir (Ma and Lee, 1976) Flow-through reservoir (Frost, 1981) Infinite reservoir (Ruthven and Derrah, 1973) The methods usually involve applying a step or pulse of adsorbing tracer to the catalyst pellet and evaluating the diffusion and Figure 1 compares for many cases the important parameters in the diffusion and adsorption process at low and high temperatures. Since many diffusion parameters are measured at low temperatures (-25-1 OOOC) for extrapolation to much higher values, it is extremely important that the pore diffusivity (the tortuosity is extracted only from the pore diffusivity) be evaluated without a contribution from the surface diffusion and adsorption.…”