Biomedical Engineering Reference
In-Depth Information
HETP
g
:
Bed height
HETP
g
¼
V
d
V
c
2
V
max
54
*
5
:
where V
max
¼
the number of column volumes from the transition initiation to the
maximum rate of change, V
d
¼
CV at 1/2 peak max (right), and V
c
¼
CV at 1/2 peak
max (left).
12.8.7 Asymmetry
Asymmetry factor is a measure of skewness at 10%of peak maximum. The equation is as
follows:
A
f
¼
V
b
V
max
V
max
V
a
where V
max
¼
the number of column volumes from the transition initiation to the
maximum rate of change, V
a
¼
CV at 10% peak max (left), and V
b
¼
CV at 10% peak
max (right).
12.8.8 Skewness and Kurtosis
Recently, skewness and kurtosis are also added to transition analysis measures as higher
moments with some level of success. They provide higher sensitivity; however, they
should be used with care and appropriate signal conditioning to avoid false alarms.
Conley and Thommes [70] have reported positive results for using skewness not only to
discern change types in column integrity but also to demonstrate removal of impurities.
.
Skewness: A measure of the asymmetry of the distribution
.
Kurtosis: A measure of the flatness of a distribution
C
i
, normalized solute signal (e.g., conductivity, pH) value at ith volume reading; V
i
,
normalized buffer volume at ith volume reading; V
R
, normalized buffer volume at the
inflection point of V
i
versus C
i
;
s
, sample standard deviation of solute signal; and n,
number measurements based on buffer volume.
For a step increase transition (as shown in Fig. 12.11),
X
n
i¼1
DC
i
¼
X
n
i¼1
V
i
DC
i
;
X
n
i¼1
ðV
i
V
R
Þ
2
2
C
max
¼
1
;
V
R
s
¼
DC
i
2
3
2
3
n
i¼1
ðV
i
V
R
Þ
n
i¼1
ðV
i
V
R
Þ
3
4
DC
i
DC
i
4
5
;
4
5
Skewness
¼
Kurtosis
¼
s
3
s
4
