## Simple Soluble Substrate Model With Traditional Decay As Presented In Chapter

This model should be applied only to wastewaters without significant quantities of particulate organic matter for which the primary focus is on carbon oxidation. It can also be applied to situations in which nitrification is an objective. The focus here will be on carbon oxidation, but the reader can extend the principles presented to nitrification, in which case the substrate would be ammonia-N rather than soluble, biodegradable organic matter. Generally, particulate organic matter is operationally defined as the material that will be retained on a 0.45 p.m pore-size filter. Many colloidal sized particles will pass such a filter, and therefore, in a strict sense, "soluble" organic matter may not all be truly soluble. Nevertheless, for purposes of parameter estimation it is generally acceptable to apply the model of Chapter 5 to any wastewater in which the organic matter will all pass such a filter.

### 8.2.1 Data to Be Collected

For this application the test bioreactors should be simple CSTRs with biomass recycle. They should be operated at a number of SRTs and the following data should be collected during the steady-state period following stabilization:

Slo = Soluble chemical oxygen demand (COD) in the influent (mg/L) Sc = Soluble COD in the bioreactor (mg/L) XT = Total biomass COD in the bioreactor (mg/L)

XTw = Total biomass COD in the waste solids (mg/L) (This will be the same as

XT if the Garrett flow scheme is used.) XTl = Total biomass COD in the final effluent (mg/L) fA = Active fraction of biomass V = Reactor volume under aeration (L) F = Influent flow rate (L/h) Fw = Waste solids flow rate (L/h)

Several points should be noted about the data to be collected. To be consistent with the models in Chapters 5-7, the biomass concentrations are expressed in COD units. They can also be measured in mass units, either as total suspended solids (TSS) or as volatile, i.e., organic, suspended solids (VSS). If that is done, the yield, Yh, will have units of TSS or VSS formed per unit of substrate COD removed. In such a situation, in order to have consistent units, the yield must be multiplied by a conversion factor, i, when it is used in the computation of the oxygen requirement,

RO, by Eq. 5.33. The value of the conversion factor will depend upon the method of measuring the biomass concentration, as discussed in Sections 2.4.1 and 5.1.3. When biomass is measured as TSS, i is denoted as i,,xiu and is generally considered to have a value of 1.20 g COD/g TSS (as shown in Table 3.1) unless data are collected that suggest otherwise. Similarly, when biomass is measured as VSS, i is denoted as i(>XBA and is considered to have a value of 1.42 g COD/g VSS, as shown in Table 3.1. The active fraction of the biomass, fA, is the most difficult data to collect during treatability studies. As a consequence, most studies do not try to measure it. In Section 8.3 we examine how to estimate parameters in the absence of such data. A number of techniques have been proposed for measuring the active fraction, but all are tedious and subject to error. Consequently, they are used mostly in a research setting. The most direct method is the slide culture technique of Post-gate,1" which involves plating bacteria on microscope slides and observing the fraction that divide. This works well with soluble substrates but becomes more difficult when particulate materials are present. An indirect method involves quantifying the amount of adenosine triphosphate (ATP) present per unit of biomass. It has been used successfully because the amount of ATP per viable cell is relatively independent of SRT and ATP is quickly lost from nonviable ce]ls.,1", Another indirect method involves measurement of the amount of deoxyribonucleic acid (DNA) present per unit of biomass. Like ATP, it is relatively independent of the SRT"" and is quickly degraded when cells die and lyse."

The data collected during the treatability study will be used to estimate the values of |i, Ks, YH, bM, and fn. In the process of doing this we will also have to estimate the soluble inert COD, S,. Because many of the equations describing the performance of a CSTR can be reduced to linear form, graphical procedures have commonly been used to estimate the parameters. Linear transformations usually change the structure of the error in a data set, and nonlinear parameter estimation techniques are preferable whenever possible. However, because an explanation of such techniques is beyond the scope of this book, the linear techniques will be described. Because some of the parameters appear in more than one equation it is necessary to determine them in a sequential manner when the linear techniques are employed. Regardless of the estimation technique employed, however, it is important to recognize that all parameters estimated from a data set are interrelated. Consequently, an error in the estimation of one will influence the estimated values of the others. This means that more emphasis should be placed on the parameter set as a whole than on any individual values within it.

### 8.2.2 Determination of YH and bH

The first parameters to be estimated are the biomass yield, Y,„ and the traditional decay coefficient, bH. As presented in Chapter 5, Y,t has units of mg biomass COD formed per mg of substrate COD used whereas bH has units of hr '. Both can be obtained from a rearranged form of Eq. 5.20:

Examination of Eq. 5.20 reveals that the units on Yn must be consistent with the units of Xlul, i.e., XHmust be measured in COD units to give a YH value in COD

units. As discussed in the preceding section, it is often desirable to measure the biomass concentration in TSS or VSS units. In that case, Y,, will have similar units. It makes no difference which unit system is used provided that it is used consistently and that the appropriate COD conversion factor, il)Xi>.i or i(1.N|1A, is used when COD balances are performed. During the experimental studies, measurements were made of the total biomass concentration, XT, not the active biomass, X,i H. Thus, use must be made of the active fraction to get X1U,:

Measurements were also made of the soluble COD in the feed, S0„ and in the bioreactor, S<, not the biodegradable COD, which is the substrate. The concentrations of biodegradable COD can be obtained from the measured soluble COD values by subtracting the inert soluble COD, S„ which passes through the bioreactor:

However, for use in Eq. 5.20, knowledge of the inert soluble COD is not required because it cancels out:

Substitution of Eqs. 8.2 and 8.5 in Eq. 5.20 yields:

Data are collected on the effect of SRT (©J on fA, XT, and Sr, with t and S( (l as controlled input values. Consequently, sufficient information is available for estimation of YH and bM. The most suitable method for doing this depends on the structure of the errors in the data.2 If the errors have constant variance, then a nonlinear least squares technique applied directly to Eq. 8.6 without transformation is the most appropriate method.2 Such techniques are available in commercially available statistical software, such as SAS,,J as well as in many spreadsheet and graphics programs. If nonlinear least squares estimation is inappropriate or if the analyst does not have access to appropriate software, then a linear least squares technique must be used. Linear least squares procedures are available on most engineering calculators as well as in almost all spreadsheet and graphics programs. Equation 8.6 can be linearized to give:

A plot of (Sec, — S( )/(fA • XT • t) vs. 1/(m)l will give a straight line with a slope of 1/YH and an ordinate intercept of bn/Yn- This is illustrated in Figure 8.1.

If the study is conducted in CSTRs without biomass separators, then (H\ and t will be the same, and Eq. 5.21 must be used:

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