Statistics for Environmental Engineers

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Phenol Concentration (mg/L)


FIGURE 43.1 Two stages of a response surface optimization. The second stage is a two-level factorial augmented to define quadratic effects.

Case Study: Inhibition of Microbial Growth by Phenol


Wastewater from a coke plant contains phenol, which is known to be biodegradable at low concentrations and inhibitory at high concentrations. Hobson and Mills (1990) used a laboratory-scale treatment system to determine how influent phenol concentration and the flow rate affect the phenol oxidation rate and whether there is an operating condition at which the removal rate is a maximum. This case study is based on their data, which we used to create a response surface by drawing contours. The data given in the following sections were interpolated from this surface, and a small experimental error was added.


To some extent, a treatment process operated at a low dilution rate can tolerate high phenol concentrations better than a process operating at a high dilution rate. We need to define “high” and “low” for a particular wastewater and a particular biological treatment process and find the operating conditions that give the most rapid phenol oxidation rate (R). The experiment is arranged so the rate of biological oxidation of phenol depends on only the concentration of phenol in the reactor and the dilution rate. Dilution rate is defined as the reactor volume divided by the wastewater flow rate through the reactor. Other factors, such as temperature, are constant.


The iterative approach of experimentation, as embodied in response surface methodology, will be illustrated. The steps in each iteration are design, data collection, and data analysis. Here, only design and data analysis are discussed.

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