Chemical Engineering January 2019 - 57

8.50
8.25
8.00
7.75
7.50
7.25
7.00
6.75
6.50
6.50
pH of 78 CCD mixtures predicted
with the DSD model (R2 = 0,980)
TABLE 5. COMPARISON OF MODELS OBTAINED WITH THE CCD
(BASED ON 90 RUNS) AND THE DSD (BASED ON 13 RUNS)
CCD
(90 runs)
MODEL
pH of 13 DSD mixtures predicted
with the CCD model (R2 = 0,997)
pH=
7,198
-0.199
+0,391
-0.286
+0.021
-0,024
+0.042
-0.099
+0.016
+0.028
+0.051
6.75
7.00
7.25
7.50
Measure pH
FIGURE 3. Predicted pH values of 78 mixtures (from the CCD experiments)
using the DSD model, and the predicted pH values of 13 mixtures (from the
DSD experiments) using the CCD model, to validate both models.
without center values for any factor
and are referred to as " vertex
runs " by the DSD-inventors [8].
Likewise, to increase the power of
any DSD, one may choose initially
a design with a larger number of
factors than necessary (for example,
in total N+k factors), and then
drop the extra k columns [7-9].
For the sake of visualization, a 3-D
representation for a DSD with three
factors is shown at the right side of
Figure 2, although a DSD with only
three factors is not recommended
[9]. For this visualization, we took the
Hot Topics
in the
Chemical
Processing
Industry
Valves
Selection, Operation and Troubleshooting
Optimal Pump
Management
CHEMICAL
ENGINEERING
CHEMICAL
ENGINEERING
Valves Selection:
Operation and
Troubleshooting
Optimal Pump
Management
Managing Vapor
and Particulate
Emissions
Find these and other related CPI titles in the store.chemengonline.com
CHEMICAL ENGINEERING WWW.CHEMENGONLINE.COM
JANUARY 2019
57
7.75
8.00
8.25
8.50
R²
R²adj
R² pred
0.996
0.995
0.992
DSD design for N = 4 from Table 1
and then dropped the last column.
One can clearly see the so-called
DSD edge runs and vertex runs
(which comes down to cube points),
together with the single DSD center
run at the right side of Figure 2.
The advantages of a DSD are as
follows (For more, see [7-9]):
1. Each factor is analyzed at three
levels, which makes it possible
to analyze quadratic effects, and,
thus, to model curvature with a
very limited amount of runs, rendering
DSDs a relatively inexpenR²
R²adj
R²
pred
0.991
0.985
0.977
sive technique for users in the field
2. Advantages are specifically found
with regard to confounding variables
(note: The term confounding,
used in statistics, indicates
that the effects of model terms
cannot be calculated separately):
* The main effects are completely
independent of each other, completely
independent of two-factor
interactions, and completely independent
of quadratic effects (thus,
there is no confounding at all)
* The two-factor interactions are not
completely confounded with other
× A
× B
× C
× F
× AB
× AC
× BC
× A²
× B²
× C²
pH =
7,328
-0.204
-0.289
-0,058
-0.117
DSD
(13 runs)
× A
+0.425 × B
× C
× AB
× BC
MODEL SUMMARY
Managing Vapor and
Particulate Emissions
Guidebook
Predicted pH
http://store.chemengonline.com http://WWW.CHEMENGONLINE.COM
Chemical Engineering January 2019

Table of Contents for the Digital Edition of Chemical Engineering January 2019
