shaped adsorbent (intracrystalline micropores and intercrystalline meso/
macropores), the internal mass transfer resistances were described by a double
Linear Driving Force model.
The choice of the isotherm model to represent the adsorption equilibrium appears
as a prerequisite for the modeling of adsorption processes since it affects the
multicomponent behavior of the overall process and, consequently, inadequate
representation of the system. As already explained above, SSL and DSL were the
leading models considered to fit the adsorption equilibrium data. Consequently, the
ExSSL and ExDSL models were, respectively, introduced to describe the
multicomponent adsorption equilibrium.
In the momentum balance, only the axial velocity gradient was considered, while
the radial gradient was neglected. The Ergun equation described well the relation
between gas velocity and pressure drop along the length of the packed bed. This
equation also represents the pressure drop dependency with the packing size, length
of the bed, fluid viscosity, and fluid density.
In all the cases mentioned, the authors assumed that the temperature of the gas
and the solid varies, and so the energy balance to both was considered. That is the
energy balance to the fluid phase and the energy balance to the adsorbent particle.
Both equations allow the determination of the respective gas and solid temperatures.
Finally, a third energy balance associated with the wall is usually taken into
consideration, aiming at accounting for possible heat transfers between the wall
and the environment. The temperature was considered uniform throughout the solid,
and the heat transfer is usually assumed to be linear between the different phases.
This energy balance has been established by conducting various approximations
such as not taking into account the thermal conduction through the solid and
neglecting the heat transfer between the solid phase and the wall. The column wall
only interchanges energy with the gas phase and the surroundings. Additionally, no
radial heat gradient was considered.
The procedure used to calculate the transport parameters and general properties of
the gases and their mixtures is well described by Da Silva et al. [103]. Briefly, the
transport parameters such as molecular diffusivity and macropore diffusivity can be
estimated by the Chapman-Enskog and Bosanquet equations, respectively
[104]. The Wakao and Funazkri correlation can be used to determine the axial
mass and heat dispersion coefficients [104]. The film heat transfer coefficient
between the gas and the column wall can be estimated with the Wasch and Froment
correlation [104]. The viscosity of pure components can be obtained by the method
of Chung et al., and the viscosity of the gas mixtures can be calculated from the
method of Wilke [105]. The thermal conductivity of the pure gases and gas mixture
can be determined by the use of Eucken and Wassiljewa equations, respectively
[104, 105].
Information extracted from single- and multicomponent dynamic studies is used
to validate the adopted mathematical model and allows the evaluation of many
different process schemes (VPSA or SMB) and different operating conditions for
the separation by adsorption-based technologies. As an example, we will show some
single- and multicomponent breakthrough experiments performed by Narin et al.
Perspectives of Scaling Up the Use of Zeolites for Selective Separations from. . .
169
macropores), the internal mass transfer resistances were described by a double
Linear Driving Force model.
The choice of the isotherm model to represent the adsorption equilibrium appears
as a prerequisite for the modeling of adsorption processes since it affects the
multicomponent behavior of the overall process and, consequently, inadequate
representation of the system. As already explained above, SSL and DSL were the
leading models considered to fit the adsorption equilibrium data. Consequently, the
ExSSL and ExDSL models were, respectively, introduced to describe the
multicomponent adsorption equilibrium.
In the momentum balance, only the axial velocity gradient was considered, while
the radial gradient was neglected. The Ergun equation described well the relation
between gas velocity and pressure drop along the length of the packed bed. This
equation also represents the pressure drop dependency with the packing size, length
of the bed, fluid viscosity, and fluid density.
In all the cases mentioned, the authors assumed that the temperature of the gas
and the solid varies, and so the energy balance to both was considered. That is the
energy balance to the fluid phase and the energy balance to the adsorbent particle.
Both equations allow the determination of the respective gas and solid temperatures.
Finally, a third energy balance associated with the wall is usually taken into
consideration, aiming at accounting for possible heat transfers between the wall
and the environment. The temperature was considered uniform throughout the solid,
and the heat transfer is usually assumed to be linear between the different phases.
This energy balance has been established by conducting various approximations
such as not taking into account the thermal conduction through the solid and
neglecting the heat transfer between the solid phase and the wall. The column wall
only interchanges energy with the gas phase and the surroundings. Additionally, no
radial heat gradient was considered.
The procedure used to calculate the transport parameters and general properties of
the gases and their mixtures is well described by Da Silva et al. [103]. Briefly, the
transport parameters such as molecular diffusivity and macropore diffusivity can be
estimated by the Chapman-Enskog and Bosanquet equations, respectively
[104]. The Wakao and Funazkri correlation can be used to determine the axial
mass and heat dispersion coefficients [104]. The film heat transfer coefficient
between the gas and the column wall can be estimated with the Wasch and Froment
correlation [104]. The viscosity of pure components can be obtained by the method
of Chung et al., and the viscosity of the gas mixtures can be calculated from the
method of Wilke [105]. The thermal conductivity of the pure gases and gas mixture
can be determined by the use of Eucken and Wassiljewa equations, respectively
[104, 105].
Information extracted from single- and multicomponent dynamic studies is used
to validate the adopted mathematical model and allows the evaluation of many
different process schemes (VPSA or SMB) and different operating conditions for
the separation by adsorption-based technologies. As an example, we will show some
single- and multicomponent breakthrough experiments performed by Narin et al.
Perspectives of Scaling Up the Use of Zeolites for Selective Separations from. . .
169