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One-factor-at-a-time
experimental design Desired region
gives a false optimum of operation

Ferric Chloride (g/L) 1.0
2.0

0.5
0.0 0.1 0.2 0.3 0.4 0.5
Sulfuric Acid (g/L)

FIGURE 22.3 Response surface of residual oil as a function of ferric chloride and sulfuric acid dose, showing a valley-
shaped region of effective conditions. Changing one factor at a time fails to locate the best operating conditions for emulsion
breaking and oil removal.

1st
1.4 400 1000
design
Promising cycle
direction
Ferric Chloride (g/L) 1.2 2400 400 100 300 design

2nd

1.0 4200 50 cycle

0 0.1 0.2 0.3
Sulfuric Acid (g/L)

FIGURE 22.4 Two cycles (a total of eight runs) of two-level, two-factor experimental design efficiently locate an optimal
region for emulsion breaking and oil removal.

low, in general terms), the experiment is a two-level design. The total number of experimental runs
2
2
needed to investigate two levels of two factors is n = 2 = 4. The 2 experimental design for jar tests on
breaking the oil emulsion is:
Acid (g/ L) FeCl 3 (g/ L) Oil (mg/ L)
0 1.2 2400
0 1.4 400
0.2 1.2 100
0.2 1.4 1000

These four experimental runs define a small section of the response surface and it is convenient to arrange
the data in a graphical display like Figure 22.4, where the residual oil concentrations are shown in the
squares. It is immediately clear that the best of the tested conditions is high acid dose and low FeCl 3 dose.
It is also clear that there might be a payoff from doing more tests at even higher acid doses and even lower
iron doses, as indicated by the arrow. The follow-up experiment is shown by the circles in Figure 22.4.
The eight observations used in the two-level, two-factor designs come from the 28 actual observations
made by Pushkarev et al. (1983) that are given in Table 22.3. The factorial design provides information
© 2002 By CRC Press LLC