Page 203 - Pressure Swing Adsorption

PRESSURE SWING ADSORPTION DYNAMIC MODELING OF A PSA SYSTEM 181

equations are implicit and an iterative subroutine is therefore needed to In the LDF model the mass transfer rate equation is represented as:
determine the composit10n of the euuilibnum adsorbed ollase. This increases
the bulk of the comoutat1on so the simpler explicit equations are generally i1q; * -
at~ k;(q; - q;) ( 5 .15)
preferred, except m unusual situations.
12
Yang and co-workers have reported that for the adsorption of various ' where
binary and ternary mIXtures of CH , CO, CO , H , and H S on PCB
2
2
2
4
activated carbon, the !AS and LRC methods give very similar results. It 1s j
also of interest to note that for these systems the exponent values used in the macrooore control
LRC model are close to unity. In a more recent study Yang and co-workers 34
have further shown that IAS and Langrnmr models give very similar predic- I
tions for multicomponent adsorption of vanous mixtures of H , CH , CO, m1crooore control (5.16)
2 4 i
and CO 2 on SA zeolite. The extended Langmuir model has also been
successfully used to simulate the bulk PSA separation of methane-carbon I In Eq. 5.15 a* IS the equilibnurn value of the solid-ohase concentration
dioxide 21 and nitrogen-methane 24 on carbon moiecular sieve and j corresoonding to fluid-phase concentration, c.
oxygen-nitrogen on both SA zeolite 22 and carhon molecular sieve. 13 18 26 Nakao and Suzuki 35 have shown by solvmg the ·diffu:sion and LDF models
• •
One may conclude that for most practical systems there 1s little to be gained mcteoendently for a single sohericai particle subjected to alternate adsorp-
from usmg a more complex isotherm model. tion/desorotion steps that, for cyclic orocesses, the va·1ue of fl for macrop•
ore and rnicrooore diffusion 1s not 15 (as suggested by Glueckauf and
l Coates 36 ) but 1s in fact dependent on the frequency of the adsorption and
5. 1.3 Mass Transfer Models desorption steps. They oresent a correlation from which the LDF constant, n
may be esttmatect for any specified cycle time. Raghavan, Hassan, and
The cl101ce of an appropriate model to account for the resistance to mass Ruthven 14 in thelf study solved the pore diffusion model for a PSA system
transfer between the fluid and porous adsorbent particles is essential for any I and by companng the solutions denved from the s1mbler LDF model con-
dynamic PSA simuiation. The adsorbate gas must cross the external fluid film firmed that fl 1s mdeed deoendent on cycle time. The proposed correlation
and penetrate into .the porous structure dunng adsorption, and travel the based on the full PSA simulation 1s, however, somewhat different from that
same path 111 the reverse direction dunng desorption. The mtraparticle proposed by Nakao and Suzuki based on a s1ngie-oart1cle study, as may· be
transport by diffusion generally offers the controlling mass transfer resis- seen from Figure 5.2. Farooa anct Ruthven 26 ran a limited test to examme
tance. The various mechanisms by which pore diffuston may occur have been the validity of these correlations (based on a smgle-component study) for a
discussed in Chapter 2. In an equilibrium~controlled PSA process macrooore binary system by comoaring with constant-diffus1v1ty oore moctei predictions.
diffusion 1s often the ma1or resistance to mass transfer. However, in the The results, shown m Figure 5.3, suggest that the LDF model with either
macrooore control regime there is no significant kinetic select1v1ty. In a correiation predicts the correct aualitat1ve trends.
kinetically controlled process 1t 1s therefore desirable to operate under Al pay and Scott 37 addressed the same issue by a more fundamentai
1
conditions such that all external mass transfer resistances are minimized, and approach usmg penetratmn theory. They assume that the dimensions of the
the relative importance of the kinetically seiective mternal (micropore) diffu- adsorbent part1cle are sufficiently iarge that the concentration at the center is
sion process is mamtained as large as possible. not significantly affected by the boundary condition at the particle surface
Full simulations of PSA systems using oore diffusion models have been and is therefore constant, even when the particle 1s subjected to a periodic
16
presented by Ruthven et al. 14 and by Shin and Knaebel. The former study change m surface concentration. Comoanson of the :LOF rate expression
deals with macrooore diffusion in a nonlinear trace system while the latter with the expression derived from the diffusion equation then yields O = 5.14/
deals with mtcropore diffusion, with constant diffusivities, in a linear equilib- /ii;, which, over the range 10- < Oc < 10- 1s very c!Ose to the correlat1on
3
1
rmm system. Although the pore diffus10n models are more realistic, the of Nakao and Suzuki.
associated computations are very bulky. The linear driving force (LDF) Detailed studies of diffusmn in microoorous adsorbents reveal that, for
model has therefore been widely used with varying degrees of success, both zeolites 38 39 and carbon molecular sieves, 40 41 the- rnicrooore diffus1v1ty
•
•
regardless of the actual nature of the mass transfer resistance, smce this varies strongly with sorbate concentration. The concen~ration depen0ence of
approach offers a s1moler and computat10nally faster alternative. microoore diffusivity is even more oronounced m a binary system since,