The requirements for determining extant values of the Monod (or Andrews) kinetic parameters are just the opposite of the requirements for the determination of intrinsic-values. This follows from the fact that extant parameter values reflect the conditions of the biomass in the bioreactor from which they were obtained. Consequently, the test conditions need to be such that few changes occur in the physiological state of the biomass or the composition of the microbial community during the test. This can be achieved by keeping the value of Sso/XliH() small during batch tests, with 0.02 being a typical value. Again, it should be emphasized that Xlu„, should reflect only that portion of the biomass that is capable of degrading the test compound. Because the amount of substrate added is very small relative to the amount of biomass present, biomass growth may be neglected in any given test, allowing use of only the mass balance equation for substrate. This simplifies the computations somewhat but means that data can only be collected on substrate loss or oxygen consumption.
Two respirometrically based procedures are available for determining extant kinetic parameter values. One, developed by Lamb et al." and refined by Chudoba and colleagues,^ relies on substrate injections into a respirometer at a number of concentrations. The net oxygen uptake rate (OUR) in response to an injection is proportional to the substrate utilization rate (see Eq. 3.34), which in turn is proportional to the growth rate, with the yield being the proportionality factor (Eq. 3.44). Dividing the OUR by the concentration of biomass actively involved in the biodégradation of the substrate gives the specific oxygen uptake rate (SOUR), which can be used to calculate the specific growth rate associated with the concentration of substrate supplied by the injection:
Making injections at several substrate concentrations provides a data set showing the effect of substrate concentration on specific growth rate. Consequently, the Monod (or Andrews) equation may be fit to the data set by using the techniques in Section 8.2.5. As discussed in that section, the best procedure for estimating (ln and Ks is by applying nonlinear parameter estimation to the Monod or Andrews equation. If nonlinear parameter estimation is not possible, the best linearization technique in this situation is that of Hanes:
Ss Ks Ss
Thus, a plot should be made of Ss/|xH versus Ss, with |i,< being determined by the slope and Ks by the ordinate intercept. Because of the way the experiment is run, the substrate concentration is assumed to be free of error, i.e., the independent variable, and |xH is assumed to contain error (because SOUR is the measured variable). Thus, linear least squares analysis can be applied for fitting purposes, even though it could not be earlier.
The other extant respirometric technique relies on a single substrate injection with determination of the kinetic parameters by fitting the theoretical oxygen consumption curve to the observed oxygen consumption curve, in a manner similar to that used for determination of the intrinsic parameter values.'" However, as pointed
out in the preceding paragraph, the fitting routine is simpler because only the substrate mass balance equation must be solved. As in the intrinsic test, Ss„ should also be equal to or greater than the expected Ks value. Details regarding both techniques are too involved to provide herein, but the reader is encouraged to consult the cited references.
8.5 COMPLEX SUBSTRATE MODEL WITH LYSIS: REGROWTH APPROACH TO DECAY AS PRESENTED IN CHAPTER 6 (INTERNATIONAL ASSOCIATION ON WATER QUALITY ACTIVATED SLUDGE MODEL NO. 1)
As we saw in Section 6.1, ASM No. 1 is very complex, with many parameters. Luckily, not all of them need to be evaluated for every wastewater. Rather, some parameter values appear to be about the same for all systems, and fixed values can be assumed.1" These are listed in Table 8.1 and the values given in Table 6.3 are satisfactory for most purposes. In this section, we will briefly review the parameters that require evaluation to provide an overview of how to obtain them. We will also review procedures for characterizing the wastewater. Details can be found elsewhere,1""" as can a number of examples.1114 :1 ",1h
Before proceeding, it is important to recognize that our knowledge of activated sludge modeling is still developing. As a result, one should not assume that it is necessary to assess all of the remaining parameters in all cases, or indeed that assessment of those parameters will ensure that extrapolations made with the model will be successful. Rather, one should recognize that many of the parameters are interrelated and that the value obtained for one will affect the value obtained for another. Furthermore, because of that it is likely that the minimum required parameter set may well turn out to be less than we now think. Consequently, the reader should consult the literature in this rapidly developing field.
Because ASM No. 1 contains more elements than the simple soluble substrate model, evaluation of the parameters involved is more complicated. This requires more bio-reactors to be operated.
Yield for autotrophic biomass
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