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two “pure” products. The McCabe-Thiele construction is illustrated in Figures 12.5(c)  and 12.5(d).  In
                    this illustration, increasing the system pressure lowers the azeotropic composition of A. The McCabe-
                    Thiele construction in Figure 12.5(d) is at a higher pressure than that in Figure 12.5(c). Therefore, for the
                    case illustrated, the feed is distilled in one column to produce “pure” B and a near-azeotropic distillate
                    (D ). This distillate is then pumped to a higher pressure, which lowers the azeotropic composition. At a
                       1
                    suitable pressure, the distillate from the first column is now above the azeotropic composition, and a
                    second column is then used to purify A. “Pure” A is the bottoms product of the second column because of
                    the reversal in volatilities caused by the azeotrope. The near-azeotropic distillate (D ) is recycled to the
                                                                                                                      2
                    first column.


                    A related method for pressure-sensitive azeotropes is to run only one column at vacuum conditions. If the
                    equilibrium  behavior  is  favorable,  the  azeotrope  will  be  at  a  mole  fraction  of A  approaching  unity.
                    Depending on the desired purity of component A, the maximum possible distillate composition may be
                    sufficient.


                    It  is  important  to  remember  that  pressure-swing  methods  are  applicable  only  when  the  azeotropic
                    composition is highly pressure sensitive. Although there are examples of this behavior, it is actually quite
                    rare.


                    Azeotropes in Ternary Systems.   In binary systems, the McCabe-Thiele method provides a conceptual
                    representation of the distillation process. In ternary systems, there is a method that provides a similar
                    conceptual representation. It is called the boundary value design method (BVDM), and it is particularly
                    useful  for  conceptualizing  azeotropic  distillation  in  ternary  systems.  This  method  is  introduced  here;
                    however,  the  reader  seeking  a  more  in-depth  treatment  of  this  method  and  all  aspects  of  azeotropic

                    distillation should consult the definitive reference in the field [17].

                    In the BVDM, ternary distillation is represented on a right-triangular diagram just as binary distillation is

                    represented  on  a  rectangular  plot  in  the  McCabe-Thiele  method.  Each  point  on  the  right-triangular
                    diagram represents the mole fraction of each of the three components on a tray. For example, in Figure
                    12.6(b), the vertex labeled B is the origin of a rectangular coordinate system. At that point, the mole
                    fractions of A and C are zero, and the mole fraction of B is obtained by subtraction from 1. Hence, the
                    mole fraction of B at the origin is 1. Consider any other point on the diagram, point p, as illustrated. The
                    mole fractions of C and A are obtained using the horizontal and vertical coordinates, respectively, based
                    on B as the origin. The mole fraction of B is obtained by subtraction of the mole fractions of A and C from
                    1.


                    Figure  12.6  Comparison  of  McCabe-Thiele  for  Binary  Distillation  (a)  and  Triangular  Diagram  for
                    Ternary Distillation (b)
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