Statistics for Environmental Engineers

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Case Study: Bacterial Growth Model

The data in Table 46.1 were collected on a continuous-flow completely mixed biological reactor with no recycle (Ramanathan and Gaudy, 1969). At steady-state operating conditions, the effluent substrate and biomass concentrations will be:

material balance on substrate

X _ 03(50 — 0Ь)_ 03(S0S)

These equations define the material balance on a well-mixed continuous-flow reactor with constant liquid volume V and constant liquid feed rate Q. The reactor dilution rate D _ Q/V.

The reactor contents and effluent have substrate concentration S and biomass concentration X. The rate of biomass production as substrate is destroyed is described by the Monod model ji _ 0j S/(02 + S) where 0j and 02 are parameters. Each gram of substrate destroyed produces 03 grams of biomass. The liquid detention time in the reactor is V/Q. The feed substrate concentration is S0 = 3000 mg/L.

Experiments are performed at varied settings of D to obtain measurements of X and S in order to estimate 0b 02, and 03. One approach would be to fit the model for X to the biomass data and to independently fit the model for S to the substrate data. The disadvantage is that 01 and 02 appear in both equations and two estimates for each would be obtained. These estimates might differ substantially. The alternative is to fit both equations simultaneously to data on both X and S and obtain one estimate of each parameter. This makes better use of the data and will yield more precise parameter estimates.

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