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              Adsorption (Chemical Engineering)                                                           265

              allow detailed mathematical modelingalongthe lines indi-  no information on the regeneration conditions needed. In
              cated in the previous sections, one can in principle predict  practice, in most two-bed purification processes the de-
              the dynamic capacity for any defined feed and regenera-  sorption step in fact controls the cycle, either directly or
              tion conditions. An a priori design of the bed is therefore  through the heat balance. Initial design of the regeneration
              feasible. Such an approach has been adopted only rather  cycle is commonly based on the assumption that during
              infrequently, however, probably because the capability of  desorption the column approaches equilibrium. However,
              solving the governing equations for the more complex  at the low concentrations prevailing during the later steps
              systems typical of industrial operations has been achieved  of desorption, kinetic effects may be important, so a more
              only recently. A more common approach is to base the de-  detailed analysis is desirable.
              sign on experimental measurements of dynamic capacity  Another factor that is particularly important in the re-
              using the LUB concept. A breakthrough curve is measured  generation of molecular sieve driers is the rate at which
              using the same adsorbent under the same hydrodynamic  the temperature is raised during regeneration. If this is too
              conditions but in a laboratory-scale column. The LUB,  rapid relative to the rate of moisture removal, one may get
              which is essentially a measure of the width of the mass  rapid desorption of moisture from the initial section of the
              transfer zone, is given by                        bed, which is in contact with the hot desorbent gas, fol-
                                                                lowedbycondensationofliquidwaterinthecoolerregions


                      LUB = (1 − ¯ q /q 0 )L = (1 − t /¯ t)L  (25)
                                                                some distance from the inlet, with serious consequences
              where q 0 is the adsorbed-phase concentration in equilib-  for adsorbent life.

              rium with the feed, t the break time, and ¯ t the mean in-  To avoid the possibility of fluidizing the bed the system
              tention time. These quantities can be calculated directly  is normally operated in the downflow mode with upflow
              by integration from an experimental breakthrough curve  desorption since the gas velocity during desorption is nor-
              (Fig. 9),                                         mally lower than that during adsorption. The maximum
                                                                upflow velocity is normally limited to 80% of the mini-
                                 ∝

                                  (1 − c/c 0 ) dt               mum fluidization velocity, while velocities as high as 1.8
                            ¯ t =
                                0                               times minimum fluidization can be tolerated in downflow.
                                         (striped area in Fig. 9)
                                  t

                                                                B. Pressure Swing Processes
                            t =    (c − c/c 0 ) dt
                                 0                              The general features of a simple two-bed pressure swing
                                         (hatched area in Fig. 9)  adsorption (PSA) system are shown in Fig. 10, and de-
                                                                tails of two simple cycles are shown in Fig. 11. One of
              where c 0 is the feed concentration of sorbate. The effective
                                                                the important features of such processes is that the less
              capacity of a column length L will be the equilibrium ca-
                                                                strongly adsorbed species (the raffinate product) can be


              pacity of a column of length L , where L = L − LUB, and
                                                                recovered at high purity but at relatively low fractional
              on this basis the size of a column required for a given duty
                                                                recovery, while the more strongly adsorbed species (the
              can be readily estimated. It is important that the experi-
                                                                extract product) is always recovered in impure form dur-
              mental LUB be measured under conditions that are pre-
                                                                ing the blowdown and purge steps. This type of process, is
              cisely analogous to the large-scale process. For example,
                                                                therefore especially suitable for gaseous separations when
              if the small laboratory column operates isothermally while
                                                                the feed is inexpensive and the less strongly adsorbed
              the full-scale unit is adiabatic, the LUB may be seriously
                                                                species is the required product. All three major indus-
              underestimated, leading to an inadequate design. Further-
                                                                trial applications of PSA (air drying, air separation, and
              more, the method is valid only for a constant-pattern sys-
                                                                hydrogen purification) fulfill these requirements.
              tem (adsorption with a favorable isotherm) and provides
                                                                  PSA systems are well suited to rapid cycling, making it
                                                                possible to obtain relatively large througput with relatively
                                                                small adsorbent beds. However, the energy efficiency of
                                                                such processes is not high, and since mechanical energy
                                                                is generally more expensive than heat, PSA systems are
                                                                generally not economic for large-scale operations. Their
                                                                advantage lies in their compactness and simplicity, mak-
                                                                ing them ideal for applicatins such as the production of
                                                                medical oxygen in the home or in hospitals in remote ar-
              FIGURE 9 Sketch of a typical breakthrough curve showing rela-  eas. However, with recent improvements in process effi-
                                                     --

              tionship between break time t and mean retention time t.  ciency PSA processes are economically competitive with
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