Page 169 - Pressure Swing Adsorption

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144 PRESSURE SWING ADSORPTION EQUILIBRIUM THEORY 145

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operating at nressures sufficient to meet the product oressure soecification. recovery of 29.1 %. The reoulfed net product, JOO N m /h 1s eoU1valent to
Both cycles emoioy pressurization with product, the first with complete 1.24 mol/s. According to the defimllon of recovery, given by Eo. 4.26, the
ourge, and the second With mm1mal purge. molar feed rate, Q; 0 ,, for the case of comolete purge, 15 19.36 mol/s. This 1s
In reviewmg the steos mentioned pertammg to design of a specific PSA I continuously fed, we will use two oarallel columns to allbw one to go through
system, one might get the impression that, as far as PSA calculations are blowdown, purge, and pressunzat10n while the other column receives feed
concerned, s1mpiy estimating PSA recovery 1s sufficient. It 1s not. An overall I alf.
balance is reumred to determine the amount of adsorbent needed, then to From Eq. 4.22 we find that for a given bed of adsorbent: c/)/tF = 1.21 mol/
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size the bed and to predict the necessary power reqmres stream flow rates s, where</>= eAcsLPL/{3ART = 4.58 X 10- v;.ds and ;v;.ds ts the volume of
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and pressures for mdividual steps. To refine the oerformance estimates I the adsorbent m cm . Accordingly, V,dJt F - 26,442.0 cm" /s. The Reynolds
further (e.g., -to ·see the relationship between bed dimensions, flow rates, number is defined as Re= epvinFdp/µ,, where epv 10 ., = Qin-,;.•MF/Acs, thus
0
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recovery, arid pressure drop), one can use the Reynolds number m the fixed Re - 148000./Acs- Settmg Re - 15, we find that Acs = 9850 cm ; hence
bed. Considermg briefly Figure 4.3, one can see that thete 1s a broad the column diameter is 112 cm. Returning to the ratio Vads/t F, we can
optimum of apparent adsorbent seiectiv1ty versus Reynolds number. In this determme L/tp = 2.685 cm/s. Now, we are free to ch~ose the length of the
exampie, the Reynolds number 1s stipulated to be 15, to be close to the I bed, say, L = 161 cm. The result is that the feect~step duration, ,- ~ = 60 s,
eouilibnum limit. One can see from Figure 4.3, however, that doubling it and the volume of adsorbent (for a two~bed system) 1s Vad~ = 3.17 m:.., which,
would increase the apparent value of 8 = f3 only from about 0.59 to about based on its bulk density of 810 kg/m·\ 1s eou1valent to 2.57 metnc tons of
0.64, which means a loss of recovery of only about 15%. Hence, considering adsorbent.
that iess adsorbent can be used if velocities· are raised, there 1s an econom1- Based on these vaiues and a mechamcal efficiency of 80%, the Teomred
cally oot1mum Reynolds number that is higher than at the apparent eouilib- Power can be estimated. First of all the power for compression. of the feed
rium limit. from I to 4 atm is 109 kW, and that to compress' the subatmosohenc
Once the cycle and adsorbent are set, the vanables that affect the blowctown and purge effluent from 0.25 atm to atmosoheric pressure 1s
optimum pressure ratio are the recovery and the oower requtrement. For the 28.8 kW. Note that the amount of gas evolved dun,ng blowdown at any
sake of s1molic1ty,·we will restrict consideration to adiabatic compression of mtennediate pressure can be determined from Eqs. 4.19 and 4.50, assuming
an ideal gas, that the bed is saturated with feed onor to blowdoWn. Hence the costs
associated with the comoiete ourge case would be: $55,079 oer year for
IP- _Y_ QRT(!P<,-ll1, _ !)
y-J TJ C ( 4.65) power and $12,851 for the adsorbent. Additional costs (for vesseis, compres-
sor, vacuum pump, valves, pIPmg, instrumentat10n, site development, mamte~
where y 1s the rat10 of specific heats at constant pressure and constant nance, and fees) should be orooort1onal to these. These are balanced agamst
voiume, Q 1s the molar flow rate, 7J is the mechanical efficiency, and Pc 1s a oroiectect value of $160,000 per year for the product.
the compression ratio, P cHI P Ci.· For a four-step cycle, 1t ts common to For the case of incomolete ourge, the calcuiations: are somewhat more
operate above atmospheric pressure so that oniy a feed comoressor 1s involved. The minimum extent of purge for the adsorbent properties and
needed, so PL= PcL Sa; 1 atm, and Pc~ P.. It is possible, however, to extend conditions cited and for PL= 1 atm so that P = 4, is X = 41%. This
to subatmosoheric pressure for blowdown and purge. This operating range is corresponds to a recovery of 36.55% (cf. Figure 4.9), ano a requlfed feed flow
often referred to as vacuum swmg adsorrmon (VSA), as if to imply that there rate of Q, • - 15.41 mol/s. Agam, settmg the Reynolds number at 15 leads
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is something inherently different about it from PSA. In that case, PL < 1 to a column diameter of 100 cm. Usmg the same feed duration as before,
atm, and there are Pcs for both a gas compressor and vacuum pump to be t F = 60 s leads to a column length of L - 176 cm. Thus, the volume of
considered, along with eamoment costs and power requirements, though P adsorbent needed to fill two columns 1s Vads = 2. 76 ni 3 Based on the bulk
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(and R 8 ) for the PSA system would be unaffected by the absolute pressure. density of 810 kg/m , this 1s equivalent to 2.24 metnc tons of adsorbent. The
While on the subject of costs, those of the major components are taken to be: necessary power, in this case, is oniy for compression of the feed from 1 to
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$5 per kg of 5A zeolite, $0.05 per kWh, and $0.20 per N m of 95% oxygen at 4 aim. The resuit 1s 88.7 kW (about two-thirds of that reoulfed m !he first
4 bar. case).
For the case of complete purge, recovery can be estimated via Ea. 4.27. It Therefore, the costs associated with the incomplete ,purge case would be:
ts easy to See that if PL = 1 atm and Pu ""' 4 atm so that P = 4, the $34;668 per year for power and $11,197 for the adsorbent. As before,
oredleted recovery is negative. Therefore, rather than considering the gamut addltionai costs (for vessels, etc.) should be oroport1on~1 to these. These are
of possibilities, we can set PL - 0.25 aim, and IP - 16, which 1molies a also balanced against a nroJected value of $160,000 oer year for the product.