Statistics for Environmental Engineers

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Time (days)


0


2


4


6


8


10


12


14


16


18


20


Ca (mg/L)


5.5


3.12


1.88


0.97


0.57


0.16


1.05


0.55


0.45


0.05


0.18


Cb (mg/L)


0.24


2.17


1.89


2.37


1.21


1.99


1.35


0.16


0.74


0.76


0.53

(a) Fit the model for CB to estimate 01 and 02. Plot the 95% joint confidence region for the parameters. (b) Fit the models for CA and CB simultaneously to estimate 01 and 62. Plot the 95% joint confidence region for the parameters. (c) Comment on the improvements gained by fitting the two models simultaneously.


46.2    Bacterial Growth. Formulate the Box-Draper determinant criterion for the case study using S = в4 + [62D/(e1 D)] as the model for substrate degradation. Estimate the four parameters in the models.


46.3    Biokinetics. A solution with substrate concentration S0 = 100 mg/L was fed to a batch reactor and the following data were obtained. The proposed model is St = S0 exp(— 01t) and Xt = 6(S0 — S), where X is microorganism concentration. Estimate 61 and 62.


Time (min)


10


30


50


60


100


120


130


140


S (mg/L)


78.7


54.7


33.2


32.6


13


8.5


9.5


3.5


X (mg/L)

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