Page 190 - Pressure Swing Adsorption
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 164   PRESSURE SWING ADSORPTION
                                 CHAPTER
 21.  S.-S.  Suh  and  P.  C.  Wanka1,  "A  New  Pressure  Swmg  Adsorptmn  Process  for  High
 Enrichment and  Recovery,"  Chem.  Eng.  Sci.  44,  567-74 0989).   5
 22.  S.  Sircar,  "Air Fracuonatmn  bv  Adsorption,"  Separ,  Sci.  and  Tech.  24(14 &  15),  2379-96
 (1988).
 23.  K.  P. Kolliopoulos,  M.S.Ch.E. Thesis, Ohio State Umvers1ty,  Columbus, OH,  1987.
 24.  J.  E, 'Mitchell, and  L  H.  Shendalman,  "A  Study  of Heatless  Adsorpuon  in  the  Model   Dynamic Modeling of a
 Svstem CO in  H.  ll,"  A/Ch£ S_vmp.  Ser. 69, 2S  (1973).
 25.  G.  Flores  Fernandez  and  C.  N.  Kenney,  "Modelling  the  Pressure  Swmg  Air  Separation   l   PSA System
 Process,"  Chem.  Ettg.  Sci, 38, 827-34 (1983).
 i
 26.  M.  J.  Matz  and  K.  S.  Knaebel,  "'Temperature  Front  Sensing ,for "Feed  Step· Conirol  m   I
 Pressure Swing Adsorption,"  Ind.  Eng. Chem.  Res.  26(8),  1638 (1987).
 27.  R.  R.  Hill  and K.  S.  Knaebel, "Effects of Combined  Steps  m Pressure  Swmg  Adsorption   I
 Cvcies:  An  Expen!Tlental  and Theoretical  Study,"  Adsorptwn:  Fundam.- and Applic.,  Proc.
 China-Jap.-USA Syn'lp.  on  Adv,  Ads.  Separ. Sci.  and Tech.,  Zheiiang Univ.  Press (1988),
 28.  J. J. Collins. '"Air Separntion by Adsorption," U.S.  Patent  No.  4,026,680 0977).
 I
 29.  D.  R. Garg and C.  M.  Yon, Chem.  E11g.  Prog. 82(2), 54-60 (1986).
 30.  G. W.  Miller, K,  S.  Knaebel, and K.  G. lkels, "Equilibria of Nitrogen, Oxygen, Argon, and
 Air m Molecular Sieve SA," A/Ch£ J.  33,  194-201 (1987).
 31.  I.  Rousar and  P.  Ditl, "Opt1m1zauon  of Pressure  Swing  Adsorption  Equipment:  Part I.,"
 Chem.  Eng.  Commun. 70,  67-91  (1988).
 32.  R.  Kumar, "Adsorption Column  BJowdown:  Adiabatic Equilibrium  Model  for  Bulk Binary   The simplest approach to the modeling of a  PSA separation process involves
 Gas Mixtures,"  Ind.  Em:.  Chem.  Research  28,  1677-83 {1989).
        the  use  of  equilibrium  theory,  which  has  been  discussed  m  the  previous
 33.  z.  P.  LU," J. M.  Loureiro,  M.  D.  LeVan,  and  A.  E.  Rodrigues,  "lutraparticle  Convection   chapter. The advantage of this approach  1s  that tt  allows  analytic solution of
 Effect  on  Pressunzation and Slowdown of Adsorbers," A/ChE J. 38, 857-67 0992).   the  governing  matenai  balance  eQuations  by  the  method  of characteristics.
 34.  z.  p_  Lu,  J.  M.  Loureiro,  M.  D.  uVan,  and  A.  E.  Rodrigues,  "lntraparticle   The  closed-form  eauilibnum  theory  soiutions  provide  orelimmary  design
 Diffusion/ConvectlOn  Models  for  Pressurization  and  Blowdown  of Adsorption  Beds with   guidance and useful insight  mto the  system  behav10r. The auantitat1ve value
 Langmuir Isotherm," Separ.  Sci.  Tech. 21,  1857-74 (1992).   of  this  approach  is,  however,  restncted  to  idealized  systems  in  which  the
 35.  z.  P.  Lu,  J.  M.  Loureiro,  A.  E.  Rodrigues,  and  M.  D.  LeVan,  "Pressurization  and   adsorption selectivity is  based on differences in eauilibnum and there are no
 Blowdown of Adsorption Beds," Chem.  Eng.  Sci. 48,  1699 (1993).   significant dispersive  effects such  as  axial  mixing  or fintte  res1stance  to mass
 J6.  A. E. Rodrigues, J,  M.  Loureiro, nnd M.  D.  Le Van. Gas Sep.  and Purification, S,  I 15 ( 1991 ).   transfer.  Under  these  conditions  a  oerfectly  oure  raffinate  product  is  ob-
        tamed. Eotiilibrium theory does not allow easy extension to the more realistic
 37.  H. Cheng and F.  B.  Hill,  A/Ch£ 1.  31, 95  (1985).
        s1tuat1on where dispersive effects are significant and product purity is  limited.
 38.  D.  M, Scott, Chem,  Er,g.  Sci.  46,  2977 (1991).
        Moreover,  in  real  PSA  systems (eauilibrmrn  controlled) there  are  two  prob-
 39.  J.  Han, M. r. Baltrum, and W. J. Thomas, Gas Sep.  and Pur~ficatwn, 4,  97 (1990).   lems with  this  approach.  In  bulk separations the velocity vanes through  the
 40.  N, Sundaram and P.  C. Wankat, Chem.  Eng. Sci.  43,  123 (1988).   bed,  and,  although an analytic solution  for  the concentration front  may  still
        be  obtamect,  except  in  the  case  of a  linear  isotherm,  fhe  solution  1s  m  the
 41.  S. J, Doong and  R.  T.  Yang,  A/Cl1E Symp.  Ser.  84(284),  145 (1989).
        form  of a cumbersome  mtegral  which  generally  requires  numencai  evalua-
 42.  R.  L.  Pigford, Private communicauon, July 23,  1986.
        tion. i  A  more serious difficulty  arises in  tracking the concentration waves  for
        adsorption  and  desorptJOn  in  oart1ally  ioaded  beds  since,  depending on  the
        initial  profile  and  the  form  of the cauilihnum  relationship, one may observe
        the fonnatmn of combined wave fronts (e.g., parttai shoCk  plus simple waves).
        Under  these  conditions  the  simple  model  1s  no  longer  adequate  and  it  1s
        necessary  to  track  both  waves  and  the  transition  point  s1mu1taneous1v.'
        Durmg pressure changes  the  charactenst,c lines  are  curved  and  the  task  of

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