be converted between the two units systems by using the coefficients i()xn.t and ioxis.v defined in Section 8.2.1 and quantified in Table 3.1. To assist in the interconversions for particulate constituents, the following conventions will be adopted throughout the remainder of this book. All symbols for particulate constituents defined in the simplified model of Chapter 5 and in ASM No. 1 will be assumed to be in COD units. When particulate constituents are expressed in TSS units, a subscripted T will be attached and when they are expressed in VSS units, a subscripted V will be used. For example, the concentration of active heterotrophic biomass will be denoted as X,( M when expressed in COD units and as X,,.„.,■ when expressed in TSS units. Therefore,
Similar conversions apply for autotrophic biomass, biomass debris, etc.
Throughout the remainder of this book, biomass and MLSS concentrations will be expressed in either COD or TSS units, with the use of TSS units being indicated by a subscripted T, as indicated above. Although VSS units are frequently used by practitioners, we have adopted only those two to reduce the number of interconversions required and to make the examples easier to follow. If a reader has need to use VSS units, the interconversion is a straightforward one.
Yield values express the amount of biomass formed per unit of substrate used. Consequently, if there are three possible measures of biomass (COD, TSS, and VSS) and three possible measures of substrate (COD, BOD„, and BOD^), then there are nine possible yield values to describe the same situation. This is one reason we have limited biomass measurements to two techniques (COD and TSS) and substrate measurements to one (COD). In that way the reader will only have to routinely deal with two types of yield values, and the interconversion of one to the other is straightforward. If we employ a subscripted T to indicate that the biomass concentration is expressed in TSS units, then the relationship between a COD/COD yield and a TSS/ COD yield is given by:
Although they will not commonly be used herein, conversion factors are presented below for the other types of heterotrophic yield one is likely to encounter, thereby assisting the reader in converting historical yield values into the forms used herein. They were derived by applying the substrate and biomass relationships of Section 8.6. The additional subscripts UB and 5B will be used to represent ultimate and 5-day BOD, respectively, as the measure of substrate. For yields in which biomass is measured as VSS and substrate is measured as COD, the relationship is simple:
Yields measured in TSS and ultimate BOD units can be converted to the yields used herein with:
For yields measured in VSS and ultimate BOD units, the conversion can be done with:
When the substrate is measured as BOD, and the biomass is expressed as TSS, the expression is:
Finally, when biomass is expressed as VSS and substrate as BODs, conversion may be done with:
For domestic wastewater, the term (1 — 10 often has a value of 0.67, as indicated by Eq. 8.30, allowing simplification of Eqs. 8.46 and 8.47.
Translation of autotrophic yields requires only conversion of the biomass concentration because the substrate is expressed as nitrogen in all situations. Thus,
It should be noted that it is common for designers to use days as the unit of time in kinetic parameters, reflecting the fact that SRTs are normally longer than one day. Conversion between hours and days as the units of time is a trivial exercise, but it is important to recognize that it may be necessary.
The parameter values in Table 6.3 represent typical ones for use in ASM No. 1 for domestic wastewater at neutral pH and a temperature of 20°C. You wish to use the simple model of Chapter 5 to make rough calculations about the size of a bioreactor system before conducting detailed simulations using ASM No. 1. Convert the parameters into a form that will allow this to be done. Express the parameters in both COD/COD and COD/TSS units, with days as the measure of time.
The results of the conversion are shown in Table E8.5. First compare the column in COD/COD units to Table 6.3. The differences between the two tables in |i|,, jlA, and bA (which is equal to b, A) are only in the change from hr : to day '. The conversion from b, M to b|, requires application of Eq. 3.69 and the change of time units from hr 1 to day ', whereas the conversion of f,', to f,, requires application of Eq. 3.68 as discussed in Section 3.3.2.
Conversion of the parameters of the simple model from COD/COD to COD/TSS units requires changes in Yn, and Ya. Conversion of Y,, to Y,u- requires use of Eq. 8.42:
Table E8.5 Stoichiometric and Kinetic Parameters from Table 6.3 After Conversion for Use in the Simple Model from Chapter 5
Parameters in COD/COD Units
Parameters in COD/TSS Units
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