Statistics for Environmental Engineers

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2.0


1.0


0.5

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 valleyshaped region of effective conditions. Changing one factor at a time fails to locate the best operating conditions for emulsion breaking and oil removal.


1.4


1.2


1.0


400 1000


1st


design


Promising ! direction [


4


cycle


о


о


…….<ь


1


о


о


-(300)


2nd


design


cycle


4200

i11


0    0.1    0.2    0.3


О


£


О


О


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)


FeCl3 (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 FeCl3 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.

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