N ¼ lnðaÞ —

1 (13)

Note   that  reboilers  are  usually  treated  as  ideal    stages;

Z X hence, one equilibrium stage is usually subtracted from the

hHETPi ¼ N ¼ N

n¼1

HETPn

N

stage count for the entire column so that the number of   stages

relates only to those generated by the column internals。 Next, we must enumerate the compositions at every stage。    Starting

 G X

1 。 ln kn    。 8

at the top of the packed section, we next calculate the   compo-

¼ N

n¼1

ðKOyamÞjn

ðkn — 1Þ ð Þ

sition at stage 1 (numbering stages from the top  down)

The average HETP—hHETPi—has the advantage of being easy to calculate from experimental data。 However, it  is clearly not the same as the point  HETP。 The  two are  related in that the packed-section HETP is the average value of the

ln。xtð1—x1 Þ。

1 x1 ð1—xt Þ

¼ lnðaÞ

(14)

inpidual-point HETPs。

Usually, it  is  the  average  HETP  for  a  packed  section that is reported。 The variation of these average HETPs with

We proceed down the column until we reach the bottom composition

vapor and liquid loadings, system physical properties, pack- ing topology, and packed  depth  is  then  usually  modeled with  the  equations  developed  for  the  point  HETP。  To  use

ln。x1 ð1—x2 Þ。

1 x2 ð1—x1 Þ

¼ lnðaÞ ¼

ln。 x2 ð1—x3 Þ。

  x3 ð1—x2 Þ

lnðaÞ

¼ · · · ¼

ln。 xN—1 ð1—xN Þ。

  xN ð1—xN—1 Þ

lnðaÞ

(15)

the point HETP equation and  apply  it  to  average  HETP data, one must calculate the sum in Eq。 8。 This calculation is  almost  never  performed。  Rather,  the  average  HETP     is

The vapor mole fractions in equilibrium with the set of liquid mole fractions just enumerated can be found    from

taken  to be

G 。 ln k¯ 。

  ax

ym ¼

þ ð   — Þ

(16)

hHETPi ¼

Oy   m

k¯ — 1