Statistics for Environmental Engineers

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0 S


Monod model:    fat =    1 * + et


02 +


Tiessier model: /л* = 03( 1 — exp(04Si)) + e{


where fa is the growth rate observed at substrate concentration S;. Each experimental setting of the reactor’s dilution rate (flow rate divided by reactor volume) produces a pair of values of growth rate (fafa) and substrate concentration Si.


TABLE 47.1


Bacterial Growth Rate Data of Schulze and Lipe (1964)


a=


0.059


0.091


0.124


0.177


0.241


0.302


0.358


0.425


S =


5.1


8.3


13.3


20.3


30.4


37.0


43.1


58.0


a=


0.485


0.546


0.61


0.662


0.725


0.792


0.852


S =


74.5


96.5


112


161


195


266


386

Note: a = growth rate (1/h) and S = substrate concentration (mg/L).


The parameter в2 controls the shape of the hyperbolic Monod model, and в4 has this function in the exponential Tiessier model. The parameters 61 and в3 have units of 1/h. They are asymptotic (i.e., maximum) growth rates that are approached when the system is operated at high substrate concentration and high dilution rate. Unfortunately, direct observation of 61 and в3 is impossible because the system tends to become unstable and fail at high dilution rates because bacteria are “washed out” of the reactor faster than they can grow.


The Monod and Tiessier models were fitted to the n = 15 observations of Schulze and Lipe (1964), given in Table 47.1, who pushed the experimental conditions toward the asymptotic limits. We might then expect these data to “stress the models” and be advantageous for discriminating between them.

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