Page 208 - Pressure Swing Adsorption

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184 PRESSURE SWING ADSORPTION DYNAMIC MODELING OF A PSA SYSTEM
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modei. Commonly used techniques for solvmg partial differential equations Farooq, Ruthven. and Boniface, 22 using a sunole two~bed process operated
are finite difference 42 43 and orthogonal collocat1on. 44 46 The deoendent on a Skarstrom cycle (see Figure 3.4). The assumptions for the simulation
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variables in the governmg euuations for a PSA system are functions_ of space model are:
and time. By applying either of the techniques the partial differential equa-
1. The system is assumed to be isothermal.
t10ns (PDEs) are discretized in space, thus reducmg the PDEs mto ordinary
2. Frictional pressure drop through the bed 1s negligible.
differential equaltons (ODEs), which are then integrated in the time domam
using a st:111danJ numerical integration romine. 47 4 3. Mass transfer between the gas and the adsorbed phases is accounted for
· n Algebraic equations (!in~
m all steps. The total pressure m the bed remains constant during the
ear ,and/or nonlinear) may also appear together with the ODEs. _In such
adsorption and the purge steps. During pressunzation and blowdown the
cases Gaussian elimination for linear algebraic eauatlons and Newton's
method for nonlinear algebraic equations (or more sophisticated vanat1ons of total pressure m the bed changes linearly with time.
these methods) are used simultaneously with the numencal mtegratton 4. The fluid velocity in the bed varies aiong the length of the column, as
determined by the overall mass balance.
routine foi solvmg the coupled system of equations. Many standard computer
programs 49 50 5. The flow pattern 1s described by the axial disoersed plug flow model.
• containing a variety of powerful integration routines and alge-
braic equation soivers are available. The software packages referred to here 6. Equilibrium reiattonships' for the components are represented by extended
are those that are mentioned m the various reported studies of PSA simula- I Langmuir 1sotherms.
tion. 7. The mass transfer rates are represented by iinear dnvmg force rate
PDEs may aiso be reduced to OD Es by applying the method of character- exoressions. Molecuiar diffusion controls the transoort of oxygen and
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istics. Whereas the method has been widely used to solve thC equilihnum I mtrogen m SA zeolite. For this oart1cuiar operation, since the pressure
themy modeis, its application m the modeling of kinetic separations 1s quite 1s always greater than atmospheric, any contributmn from Knudsen diffu-
3 24 s10n is neglected and the LDF constants are taken to be pressure cteoen~
limited. •
dent according to the correlation for molecuiar diffusion controi given bv
The mam disadvantage of the fimtc difference method is the large number
Hassan et al. 10 This only affects the choice of mass transfer parameters
of segments needed to approximate the continuous system. This resuils in a
and does not in any way alter the general form of the mass transfer rate
iarge number of equations and therefore an mcreased mtegration load. On
equations.
the other hand, one maJor advantage of orthogonal collocation ts that lt
8. The ideal gas law applies.
reqmres far fewer spatial discrel!zat10n oomts to achieve the specified accu-
9. The presence of argon, which 1s adsorbed with aimbst the same affimtv as
racy. From a comparative study of the two methods m relation to PSA
s1mu1at10n, Raghavan, Hassan, and Ruthven 7 conciuded that orthogonal oxygen and therefore appears with m-..)'gen in the raffinate product. is
ignored. This assumption reduces the mathemattca·1 model to a two-com-
collocation is substantially more efficient m terms of computational CPU
time. ponent system. Theoretically the model can be extended to anv number of
components, but the practicality 1s iimued by the capability of the avail•
able mtegratton routines.
5.2 Details of Numerical Simulations The system of equations describing .the cyclic operation subiect to these
assumptions IS given m Table 5.2. Eouat1ons 1-1 l tn Table 5.2 are rear-
The building blocks which constitute a dynamic simulation modei for a PSA ranged and wntten In dimens1onless form. The dimensionless equations may
system have been .discussed in a general way m the previous section. We now then be solved by the method of orthogonal collocation, to give the solid-phase
discuss the develooment of a complete simulation model. The simpler and concentrations of the two components as a function of the dimens10nless bed
computationally quicker LDF model approach as well as the more rigorous length (z_/L) for various values of time. Details of the collocation form are
vanable diffus1v1ty micropore diffusion model approach are considered m given m Appendix B. Computations are continued until cyclic stead,y state 1s
detail with numencal examples. achieved. In the study of air separation on SA zeolite, depending on the
parameter values, 15-25 cycles were reau1red to approach the cyclic steady
5.2.1 LDF Model state.
The equilibnum and kinetic parameters used to simulate the expenmental
PSA air separation for oxygen production on 5A zeolite 1s considered as an runs are summarized in Table 5.3, together with detail$ of the adsorbent, the
example of the LDF modei approach. Detailed experimental and theoretical bed dimensions, and the cycle. The exoenmentally observed product ounty
studies of this equilibnum-controlled separallon have been presented by and recovery for several operatmg conditions are summanzed m Table 5.4,