Use Of Batch Reactors To Determine Monod Kinetic Parameters For Single Substrates

The values of the Monod kinetic parameters |XH and Ks determined by the techniques discussed in Section 8.2.5 are for general organic matter as measured by COD. Frequently, however, it is desirable to know the kinetic parameters associated with the biodégradation of a single organic compound in a wastewater. Because of the relatively low specific growth rates at which suspended growth bioreactors operate, it is permissible to use parameter values determined during metabolism of the compound as the sole carbon and energy source without regard for metabolism of the other organic compounds present in the wastewater," provided that none of the other compounds have strongly inhibitory effects. Such parameter values may be determined during batch experiments, but care must be exercised in the way in which those experiments are performed. This follows directly from the effect that growth conditions have on the physiological state of the biomass.

8.4.1 Intrinsic Versus Extant Kinetics

The physiological state of a microbial culture is determined by the manner in which it is grown. This follows from the fact that the physiological state is a measure of the macromolecular composition of the cells in the culture. If the culture is grown at a very high rate, the cells' protein synthesizing system will be fully developed for rapid growth and the cells will contain high levels of all enzymes. If the culture is grown at a slow rate, the cells will adjust the level of their protein synthesizing system to conserve resources. This means that they will contain lower enzyme levels. Consideration must be given to the physiological state of a culture and how it may change when batch experiments are designed for measuring kinetic parameter values. This is necessary because the parameter values measured in the experiment will depend upon the physiological state of the biomass.

To assist in considering the effects of physiological state, the following nomenclature system has been proposed.17 Two extreme conditions represent the limits that the physiological state of a culture may attain during a kinetic experiment. At one extreme, if the physiological state is not allowed to change, the resulting kinetic parameter values are reflective of the conditions of the biomass in the bioreactor from which the microorganisms used in the kinetic test were obtained. Because those parameters reflect the conditions currently existing in the parent bioreactor, they have been called "extant." At the other extreme, if the physiological state of the culture is allowed to change during the test to the point that the cells' protein synthesizing system is fully developed and the bacteria have an enzyme system that allows them to grow at the fastest rate possible on the test substrate at the given temperature and pH, the resulting kinetic parameters are said to be "intrinsic." The name follows from the fact that the parameter values are dependent only on the nature of the substrate and the types of bacteria in the culture. They are independent of the history of the culture, i.e., they are intrinsic. Parameter values obtained from experiments that allow the physiological state to be between these two extremes may be either "defined" or "undefined," depending upon the care with which the experiment is run and reported.

It is unclear which type of kinetic parameter set, intrinsic or extant, is of most utility to environmental engineers and scientists. It appears, however, that intrinsic parameters are most useful for comparing the biodegradability of organic compounds whereas extant parameters are most useful for predicting the performance of an operating bioreactor with respect to the removal of a given organic compound."' Consequently, we will briefly examine how to determine each type.

8.4.2 Intrinsic Kinetics

The key to determining intrinsic kinetic parameter values during a batch test is to provide sufficient substrate to allow the bacteria performing the biodégradation to fully develop their protein synthesizing and enzyme systems. This can usually be accomplished when the initial substrate to biomass ratio (Ss<)/X,ull)) is at least 20 when both concentrations are expressed as COD.1 In addition, the initial substrate concentration should be greater than the expected value of Ks. Since intrinsic Ks values for individual substrates tend to be less than 10 mg/L as COD,'" experiments in which Sso is 20 mg/L as COD have proven to be successful.' Consequently, the initial biomass concentration should be on the order of 1 mg/L as COD. It should be noted that the initial biomass concentration applies only to that portion of the biomass that is active in biodégradation of the test compound. This will generally be only a fraction of the total biomass in a suspended growth system like activated sludge.

The substrate and biomass are placed into a batch reactor and the course of biodégradation is followed over time. Three types of data may be collected and used: (1) substrate disappearance, (2) biomass growth, or (3) oxygen consumption. This follows directly from the proportionality of the three rates during balanced growth as depicted in Eq. 3.34. The equivalency of the three data sets has also been shown experimentally." Mass balance equations for substrate and biomass in a batch reactor must be written using the simplified model of Chapter 5 and solved simultaneously by appropriate numerical methods using assumed values for the parameters. If oxygen consumption data are to be used for parameter estimation, the resulting theoretical substrate and biomass curves can be converted into the equivalent oxygen consumption curve using a COD balance as depicted by Eq. 3.32. The theoretical data curve is then compared to the actual data curve and the parameter values are adjusted until the best agreement is achieved between the theoretical and actual curves. The parameter values associated with the best-fit curve arc considered to be the best estimates of them. Because of the nature of the Monod (and Andrews) equation, a robust fitting routine is required to find the true best estimate of the parameters." Details of a test procedure employing the collection of oxygen consumption data may be found in Brown et al.1

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