Page 232 - Pressure Swing Adsorption

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208 PRESSURE SWING ADSORPTION DYNAMIC MODELING OF A PSA SYSTEM 209

a small throughout ratw, as m the air drying experiments (on silica gel) Table 5.10. Additional Equations for Nonisothermal PSA-SimulaUon Usmg LDF
reported by Chihara and Suzuki.' These authors were the first to mvest1gate Approximation
the effect of nomsothermality in a trace component PSA system. 4 Later,
9 12 15
Yang and co-workers • • showed that heat effects are even more detnmen- The set of equations tn Table 5.2 together with the followmg equations constitute the model
tal to the performance of equilibrium-controlled bulk seoarat1on orocesses. equatmns for nomsothermal PSA simulation. The subscnpts have the same meamngs as in Table
5.2.
Nomsothennai studies have further revealed, as may be mtuitiveiy deduced, Fluid phase heat baJancea·
that the adia_batic condition, whicn is approached m a large commercial
ooeration, generally results in the worst seoarat1on. Whereas for many
equilibrium-controlled separations, the isothermal approximation may mean
a major departure from physical reality, this 1s usually a good approximation (1)
for separations based on kinetic selectivity smce mass transfer rates are
generally much slower m such systems. Temperature dependency of Langmuir constant:
The LDF model discussed m Section 5.2 is extended here to allow for
nomsothermaJ PSA operation. The additional assumptions are summanzed (2)
and the heat balance equations are given in Table 5.10.
Boundary conditions: pressunzation, high-pressure adsorPtion, and:purge
1. The equilibrmm constants are the most sensitive temperature-dependent KL ilz z _ = - d:r .. oPgCp 8 (Tl~-o- - Tl:r-o): (3)
•T1
terms, and tt 1s assumed that the Langmmr constants show the normal 0
exponential temperature cteoendence (b = b e-AHJRT)_ (4)
0
2. The temperature dependence of the gas and solid properlles and the Equation 4 defines inlet gas temperature of the bed undergomg :purge in tenns of raffinate
transoort parameters 1s assumed negligible. product temperature from the high-pressure bed. This as not applicable when the beds are not
coupled through a purge stream. Slowdown:
3. Effective thermal conductivities of the commercrnl adsorbent particles are
relatively high, and therefore mtraparticle temperature gradients can be arl -o (5)
-
neglected. Thermal eauilibrmm 1s assumed between the fluid and the i}z. z-L -
actsorbent particles, which is also a very common assumot10n m adsorber Initial condition (same for both dean and saturated bed conditions)
calculattons~ 60 T(z,O)~T 0 (6)
4: Bulk flow of heat and conduction in the axial direction are considered in
When the small laboratory columns are msuJated from ou1side the fluid phase heat balance Eq. J i.~
the heat balance eouation, For heat conduction we consider the contribu- modified as follows to account for the heat capacity of and conduction through the column wall:
tion from axial dispersion only. The contribution from the solid phase KAc•+KstcdA')i1 T (OT Tav)
2
becomes important at low Reynolds number, which ts, seldom, if ever, - ( 1 -A -.-A Oz'+ l!Jz+-;;,
approached m a PSA operation. An overall heat transfer coefficient is
used to account for heat loss from the system. The temperature of the
coiumn wall is taken to be eoual to that of the feed. Farooo and
Ruthven, 61 62 in their studies on heat effects m adsorption column dynam-
•
ics, have shown that the maJor resistance to heat transfer m an adsorption
colllmn is at the column wall, and a simple one-dimensional model with all
heat transfer resistance concentrated at the column wall orovides a good
representation of the experimentally obseived behav10r. The advantage of effective axial thermal conductIVlty of the fluid also follows from the
using the one-dimenstonal modeJ is that the system behavior at the assumed similanty between mechanisms of fluid phase mass and heat
isothermal and adiabatic limits may be very easily investigated by assignmg transfer.
a large value and zero, respectively, to the beat transfer coefficient. The 6. Weighted average values for gas density and heat capacity based on feed
isothermal condition 1s also approached if the simulation is carried out composition are used in a multicomponent system.
with AH= 0.
5. The boundary conditions for the heat balance eouation are wntten assum- The numerical solution of the set of coupled nonlinear equations 1-J I m
mg the heat-mass transfer anaiogy for a dispersed plug flow system. The Table 5.2 and 1-6 in Table 5.10 gives gas- and solid-phase concentration and
the bed temoerature at several locauons m the coiumn for vanous values of