## Extensions Of Basic Model

The simple model developed in Section 5.1 was for a system receiving only soluble substrate. However, most wastewaters contain soluble organic matter that is nonbiodegradable. Furthermore, all domestic and many industrial wastewaters contain suspended matter that escapes removal by sedimentation prior to entrance of the wastewater into the biochemical operation, and the impacts of those solids must be accounted for in any models depicting fully the operation of CSTRs.

Suspended material may be classified in many ways, and one of the most commonly used methods is to split it into organic and inorganic, which have traditionally been measured as volatile and nonvolatile suspended solids, respectively. Unfortunately, this division is not the best for describing biochemical operations, in part because around 40% of the volatile suspended solids in domestic wastewater are nonbiodegradable, and therefore inert to biological attack.8 A more appropriate division would be inert, biodegradable, and biomass, because each influences biochemical operations in a different way. By definition, biodegradable suspended mat ter and biomass are both organic. Inert suspended matter may be either organic or inorganic. We will consider only inert organic particulate matter herein, although it should be recognized that inorganic material will behave in the same manner. In keeping with the convention adopted earlier, the concentrations of all organic particulate constituents will be reported in COD units. It should be noted, however, that the conversion factor from COD to mass units will depend on the nature of the suspended matter and may well be different for each. Even though a conversion factor of 1.20 g COD per g of dry solids has been adopted herein for biomass and microbial debris, it is impossible to generalize about the value of the conversion factor for other constituents and they must be determined on a case by case basis.

5.2.1 Soluble, Nonbiodegradable Organic Matter in Influent

Soluble, nonbiodegradable organic matter will not be acted on by the biomass in a biochemical operation, although its concentration can be influenced by physical/ chemical phenomena such as adsorption and volatilization. If the material is not adsorbed into biomass and if it is not volatilized, then its concentration in the effluent from a bioreactor, S,, will be the same as its concentration in the influent, Slo:

If the material is volatile and/or adsorbable, appropriate reaction terms must be inserted into the mass balance equation, yielding an equation for the effluent concentration. Such expressions are discussed in Chapter 22 where the fate of synthetic organic chemicals will be considered. The total concentration of soluble organic matter (SOM) will be the sum of S[ and Ss, plus any soluble microbial products, as discussed earlier. Except in special cases, the presence of soluble, nonbiodegradable organic matter will be ignored in this book since it has no impact on the systems to be discussed.

### 5.2.2 Inert Organic Solids in Influent

Like soluble, nonbiodegradable organic matter, inert organic solids undergo no reaction in a biological reactor. Consequently, the mass leaving the bioreactor must equal the mass entering it if steady-state is to be achieved. Unlike soluble, nonbiodegradable organic matter, however, the concentration of inert organic solids in the bioreactor depends on the magnitude of the SRT relative to the HRT, as can be seen by performing a mass balance across the bioreactor. This follows from the fact that the solids only leave the bioreactor through the wastage stream. Reference to Figure 5.1 and construction of the mass balance in which X, represents the concentration of inert organic solids yields:

Division of both F and by V and invocation of the definitions of HRT and SRT reveals:

The concentration of inert organic solids in the bioreactor is greater than the concentration in the influent, with the concentration factor being (")l/t. If no effluent is removed through the biomass separator so that all leaves through the wastage flow, then the SRT and HRT are the same and the concentration of inert organic solids in the bioreactor is the same as the concentration in the influent.

Although derived for inert organic solids, Eq. 5.45 holds for all inert solids, regardless of whether they are organic or inorganic, but the concentration of inorganic solids must be expressed in mass units rather than as COD. Generally it is best to consider each type separately because that will allow easy determination of how the fraction of volatile solids in a sludge will change during treatment. Because consideration of inert inorganic solids is simply a bookkeeping exercise, we will consider only organic solids herein. Nevertheless, the impact of inorganic solids should be kept in mind because they contribute to the total concentration of suspended material that must be handled in a treatment system.

If a treatment system receives inert solids, the suspended solids in the bioreactor will include them in addition to active biomass and biomass debris. This combination of suspended solids is called mixed liquor suspended solids (MLSS) and will be given the symbol XM. The concentration of MLSS is the sum of X,, as given by Eq. 5.45, and X,, as given by Eq. 5.24:

Looking at the bracketed term it can be seen that the contribution of biomass related solids (right term) decreases as the SRT is increased, whereas the contribution of inert solids (left term) does not. As a consequence, the percentage of active biomass and biomass debris in the MLSS decreases as the SRT is increased.

The active fraction of the MLSS is the active biomass concentration divided by the MLSS concentration. Use of the appropriate equations in this delinition gives:

This reduces to Eq. 5.26 when XIO is zero. As one might expect, it tells us that the active fraction will be smaller when X,(l is larger, relative to Ss(). It also tells us that the active fraction is not affected by the SRT to HRT ratio, even though the MLSS concentration is. Thus, maintenance of a high active fraction requires minimization of the amount of inert suspended solids entering a biological reactor.

In Section 5.1.5, it was seen that the process loading factor is less convenient than the SRT as a design and control parameter for CSTRs at steady-state because of the necessity of knowing the active fraction of biomass in the MLSS before determining the microbial specific growth rate. This is particularly true when a wastewater contains inert solids because of the impact of those solids on the active fraction, as defined in Eq. 5.47.

As discussed in Section 5.1.3, the observed yield is defined as the mass of biomass formed per unit mass of substrate removed. As such, the presence of inert solids has no impact on it and it is still given by Eq. 5.28.

The mass rate at which solids must be disposed of will be increased by the presence of inert solids. Since nothing happens in the biochemical operation to reduce the amount of inert solids present, the mass rate of solids disposal will just be increased by the rate at which inert solids enter the system. Letting W \i represent the wastage rate of MLSS, often referred to as the solids wastage rate, gives:

Since nothing happens to inert solids in the bioreactor, they will have no impact on the oxygen requirement. Thus, it is still given by Eqs. 5.33-5.36.

Example 5.2.2.1

Continue with the problem begun in Example 5.1.3.1.

a. What will be the MLSS concentration in the bioreactor expressed as COD if the influent contains 25 mg'L as COD of inert organic solids.

From the previous examples, we know that t = 8 hr, (-). = 160 hr, Ss,, = 200 mg/L as COD, and Ss = 0.31 mg/L as COD. Insertion of these into Eq. 5.46 gives:

= /-V5 + M + (0-20)(0.01)(160)1(0.34)(200 - 0.31) j

Comparison of this value to the total biomass concentration in Example 5.1.3.2 shows that the inert solids increased the suspended solids concentration by 500 mg/L as COD. This could also have been seen through application of Eq. 5.45:

b. For the situation in question a, what will be the MLSS concentration as suspended solids if the nature of the inert organic solids is such that they have a COD of 1.0 g COD/g SS?

From Example 5.1.3.2, we know that the total biomass concentration is 575 mg/L as suspended solids. Because the COD of the inert organic solids is 1.0 g COD/g SS, their concentration in the bioreactor is 500 mg/L as suspended solids. Thus, the MLSS concentration, expressed as suspended solids, is:

Note that it was necessary to apply the conversion to each type of solids separately because each has a different value of COD/SS.

c. What fraction of the MLSS is made up of active biomass?

When the MLSS contains inert organic solids that have a unit COD different from that of biomass. the answer to this question depends on the way in which the concentration is measured. If it is measured in COD units, the active biomass concentration is 523 mg/L (from Example 5.1.3.2), and thus the active fraction is:

The same value may be obtained from application of Eq. 5.47. If the concentration is measured and expressed in suspended solids units, the active biomass concentration is 436 mg/L (from Example 5.1.3.2), and the active fraction is:

Equation 5.47 may also be used to obtain this value, but X„, must be expressed in suspended solids units and Y,, must have units of mg biomass suspended solids formed per unit of substrate COD removed.

The dependence of the active fraction on the unit system used to measure the components makes it important to specify that unit system. Regardless of the unit system, however, it is clear that the presence of an apparently-insignificant concentration of inert organic solids in the inlluent to a bioreactor can have a significant impact on the active fraction of the MLSS, in this case decreasing it from 0.76 to 0.44 (when the concentration is expressed as COD), d. What is the solids wastage rate?

Again, the answer to this question depends on the unit system used. Using Eq. 5.48 with W, in COD units as given in Example 5.1.4.1:

Using the same equation with X,<, and W, in suspended solids units:

The same values can be obtained from application of Eq. 5.49 provided X„, and Y„ are expressed in the appropriate units. The significant point, however, is that the addition of 25 mg/hr (as either COD or suspended solids) of inert organic solids to the bioreactor caused an increase of 25 mg/hr in the amount of solids wasted.

### 5.2.3 Biomass in Influent

The effect of the presence of active biomass in the influent to a CSTR can be seen by performing a new mass balance on biomass using Eq. 5.10, and including influent biomass at concentration X|,.n„. Performance of the steps that led to Eq. 5.12 gives:

which reduces to Eq. 5.12 when XI(H() is zero. It is important to recognize that by definition, the SRT is given by Eq. 5.1. The presence of active biomass in the influent to the bioreactor does not change that definition. Rather, Eq. 5.50 shows that the presence of active biomass in the influent reduces the specific growth rate of the biomass in the bioreactor relative to the SRT, and that greater amounts reduce it more. In other words, if biomass is present in the influent, the biomass in the reactor does not have to grow as fast to maintain itself as it does when the influent contains no biomass. This means that if two bioreactors have the same HRT and SRT, but one receives active biomass in the influent, it will produce an effluent with a lower substrate concentration.

The effluent substrate concentration cannot be found by substituting the equation for p.,, into the Monod equation as was done before because the result will contain X,u„ which is unknown. Thus, we must use a different approach. The mass balance on substrate is unchanged, and thus Eq. 5.18 is still valid. Substitution of Eq. 5.50 for p.M into it gives:

Xh.I

Comparison of Eq. 5.51 with Eq. 5.20 reveals that the active biomass concentration will be higher than in a bioreactor receiving no biomass in the influent. Furthermore, it can be seen that the term in the brackets has been divided into two components. The one on the right is the contribution of new growth to the active biomass whereas the term on the left is the contribution of the influent biomass. Note that the latter is less than the input biomass concentration because of decay. Substitution of Eq. 5.51 into Eq. 5.50, with subsequent substitution of the resulting equation into Eq. 3.36 yields a quadratic equation for the substrate concentration:

+ (Ks - SM,)(1/0C + bH)]Ss + Ss„-Ks(l/0c + b„) = 0

The easiest way to use the equations is to calculate the substrate concentration first and then use that result to calculate the biomass concentration.

Any biomass debris in the influent will behave as inert solids, thereby making its concentration in the bioreactor greater than that in the influent by a factor equal to the ratio of the SRT to HRT. In addition, biomass debris will be generated from decay of the active biomass in the influent as well as by decay of the active biomass formed in the bioreactor. Consequently, the total biomass debris concentration will be:

v firbn-Qc-Xp.m) fi> ■ bH - 0, ■ Yii(SS(> - Ss) Alx> + +

where X„0 is the concentration of biomass debris in the influent. The first term in the brackets is the contribution of biomass debris in the influent, the second term represents the debris formed through decay of the active biomass in the influent, and the last term is the formation of biomass debris from growth and decay of new biomass in the bioreactor.

The MLSS concentration is the sum of the active biomass and the debris:

The first term in the brackets is the contribution of influent biomass debris, the second term is the contribution of the active biomass in the influent, and the third is the contribution of new biomass growth on the soluble substrate. Note that Eqs. 5.51, 5.53, and 5.54 all reduce to the equations in Section 5.1.3 when the influent is free of biomass.

One significant impact of having biomass in the influent to a CSTR is to reduce SSmin, the minimum substrate concentration attainable. As was done in Section 5.1.3,

Ss„„„ can be calculated by letting the SRT become very large so that l/C-), approaches zero. If the assumption is made that SSMllIl is negligible with respect to Ss<„ which will generally be the case, then it is possible to show that:

Comparison of Eq. 5.55 to Eq. 5.14 shows clearly that SSlMm will be smaller when the influent contains biomass. Furthermore, if we let ii represent the value of Ss,,,,,, when the influent contains active biomass expressed as a fraction of the value in the absence of active biomass, it can be shown that:

For many situations this can be further simplified by noting that bH/|iH is often much less than one, allowing it to be dropped from the equation:

Equations 5.56 and 5.57 show clearly that the degree of reduction in SSl„„, will depend on the magnitude of the influent biomass concentration relative to the influent substrate concentration, with larger values producing lower SSl„„, values. This suggests that one way to meet a desired Ss„„„ concentration when a normal CSTR cannot is to add active biomass to the influent.

Another impact of having biomass in the influent to a CSTR is the prevention of washout, because if the influent contains active biomass, so will the bioreactor, no matter how small the SRT is made. Thus, a minimum SRT can no longer be defined in the same sense that it was defined for a bioreactor without biomass in the influent. However, the degree of substrate removal that will occur at very small SRTs depends on the influent biomass concentration, as can be seen by examination of Eq. 5.52. Consider the special situation in which the SRT has been selected so that

Under that condition, Eq. 5.52 reduces to

Xn.Hl

Consequently, the larger the influent biomass concentration, the greater the degree of substrate removal, even when the SRT is very small. Equations 5.52 and 5.57 can be used to evaluate the potential impacts of purposeful addition of biomass (bioaugmentation) on process performance.

In Eq. 5.47, we saw how the presence of inert solids in the influent to a CSTR influenced the active fraction of the suspended solids. Thus, it would be instructive to see how the entrance of biomass into a CSTR influences it. Application of the definition of active fraction gives:

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