yn — ynþ1 yn—1 yn

Clearly, the variation in the value of HETPn  can be greatly

Gðyn — ynþ1Þ¼ ðKOyamÞjn HETPn     ð

Þ—ð — Þ

lnhyn —ynþ1 i A

affected  by kn

as one  moves  from stage to stage。   Therefore,

yn—1 —yn

(2)

k has a great impact on the economics of any separation。

To calculate the packed depth required to accomplish a given level of separation, one must perform the sum shown below

KOyam|n  is the product of the overall mass-transfer    coefficient

based  on  the  vapor  phase  with  the  area  involved  in  mass

N N 1

。 ln kn  。

transfer  per  unit  volume  on  stage  ‘‘n,’’  and  HETPn   is   the

Z ¼ X HETPn ¼ G X     

(7)

packed depth corresponding to theoretical plate ‘‘n。’’ This expression can be rearranged  to

n¼1

n¼1 ðKOyamÞjn

ðkn — 1Þ

0 1

1

yn —ynþ1

The simple appearance of this formula is deceptive。 A sig- nificant amount of computational effort is required for each

G ¼ ðKOyamÞjn HETPn@  h ð

A (3)

It can be shown  that

 yn  — ynþ1

ln  yn —ynþ1 i

yn—1 —yn

L

(4)

stage。 In practice, this calculation is seldom, if ever,    done。

The average HETP

The usual experimental method for measuring the effi- ciency of a packed section involves the  calculation  of  a rather   different   HETP:   the   packed   section,   or   average,

yn—1 — yn ¼ mnG

HETP。 This is defined  as

Reconciling the HETP definitions

The above description of the two different HETP defini- tions in use shows that the   sum

N lnðknÞ

(12)

N n¼1  ðKOyamÞjmn ðkn  — 1Þ

must be performed to apply the point HETP definition to average HETP data usually reported。 This is a challenging task。 To illustrate the experimental and computational complexity implied in this sum, let us consider rectification at total reflux (i。e。, kn ¼ mn) of a binary pair, where the relative volatility, a, over the entire composition spectrum is constant。 First, the total number of stages needs to be determined from the experimental composition data recorded at the bottom and the top of the packed section。 The number of stages can be calculated with the Fenske equation:15

Figure 2。 Factor relating the HETP to the HTU, ln(k)/(k

2 1), as a function of k。

ln。xtð1—xb Þ。