Figure 3.4 Effect of pH on the maximal activity of Nitrosomonas. The listed references are cited in 98. (From A. V. Quinlan, Prediction of the optimum pH for ammonia-N oxidation by Nitrosomonas curopaea in well-aerated natural and domestic-waste waters. Water Research 18:561-566, 1984. Copyright © Elsevier Science Ltd.; reprinted with permission.)

noted that this equation only predicts the decline in rate at low pH and does not predict the observed drop-off at pH above 8.5. This is not generally a problem, however, because the release of hydrogen ions during nitrification acts to depress the pH so that values in excess of 8.5 are seldom encountered. There is less agreement concerning the effects of pH on Nitrobacter. For example, Boon and Laudelot" have suggested that their maximum specific growth rate is independent of pH over the range between 6.5 and 9, whereas others"5 have shown a strong pH dependence. Because of this, and because the growth of Nitrosomonas is generally thought to be rate controlling, most investigators do not model the effect of pH on Nitrobacter.

The necessity for employing equations like 3.50 is due in part to the way in which the Monod equation is normally written for nitrifying bacteria. Although, ammonia and nitrite are both ionizable species, the Monod equation is normally written in terms of the total ammonia or nitrite concentration, without regard for the ionization state. However, the nonionized form of ammonia (free ammonia) is thought to be the actual substrate for Nitrosomonas,"* and it is possible that undis-sociated nitrous acid is the substrate for Nitrobacter. For a given total ammonia concentration, the concentration of the nonionized form will change as the pH is changed, thereby making (1 as normally defined an apparent function of pH. A more direct approach would be to write the kinetic expression directly in terms of the true substrate and this has been done for NitrosomonasHowever, because this approach is more complex than combining Eq. 3.36 with Eq. 3.50 to reflect the effect of pH, the latter is more commonly used at nitrogen concentrations normally found in domestic wastewaters.

Free ammonia and undissociated nitrous acid become more of a problem at high nitrogen concentrations because they both act as inhibitory substrates as their concentrations are increased.1 J M Furthermore, free ammonia can also inhibit nitrite oxidation to nitrate.1 This suggests that there are complex relationships between the total ammonia and nitrite concentrations, the pH, and the activity of both groups of nitrifying bacteria. Although these relationships become very important when wastewaters containing high concentrations of nitrogen are being treated, no kinetic relationships are available to depict all of the effects, although some are available for ammonia oxidation.** Nevertheless, it is important to recognize that the simple Monod equation is not adequate to depict the kinetics of nitrification when the concentration of ammonia exceeds that normally found in domestic wastewater (around 30 to 40 mg/L as N) and that alternative expressions should be sought.

Because of the autotrophic nature of nitrifying bacteria the concept developed that organic compounds display a general toxicity toward them. That this concept is fallacious has been demonstrated in pure1"" and mixed""''" cultures. Nitrification can proceed at rapid rates in the presence of organic matter, provided that other environmental factors, such as pH and dissolved oxygen concentration, are adequate. In fact, under some circumstances, the presence of biogenic organic matter can even enhance the rate of nitrification."" There are some organic compounds that are inhibitory, however, and act to decrease the specific growth rate of nitrifying bacteria. The most potent specific inhibitors of nitrification are compounds that chelate metals"" and contain amine groups,"'' some of which are capable of decreasing the nitrification rate by 50% at concentrations of less than 1.0 mg/L. Furthermore, it appears that Nitrosomonas is the weak link in the nitrification chain, being more susceptible than Nitrobacter to organic inhibitors/" Many inhibitors have been shown to act in a noncompetitive manner against nitrifiers," allowing an equation like Eq. 3.48 to be used to depict their effect:

where SNH is the ammonia-N concentration, KNH is the half-saturation coefficient for ammonia-N, S, is the concentration of the inhibitor, and K, is the inhibition coefficient. As might be expected, K, is very small for some compounds, '2 denoting extreme inhibition. Although many inhibitors of Nitrosomonus act in a noncompetitive manner, methane and ethylene act as competitive inhibitors."" This is because they are similar in size to ammonia and compete directly with it for the active site on the enzyme that initiates ammonia oxidation. Halogenated hydrocarbons act in a noncompetitive manner, but many are also reactive with the enzyme and can lead to products,.that damage the cell, thereby making their effects worse than simple inhibition.

There have also been suggestions in the literature that the presence of Heterotrophic bacteria is deleterious to the activity of nitrifying bacteria, but this has been shown to be false.Any effect of heterotrophs is indirect, such as a decrease in dissolved oxygen concentration or an alteration of pH. Because of the sensitivity of autotrophs to these factors, care must be given to the design of facilities in which autotrophs and heterotrophs share the same space.

Anaerobic Cultures. As discussed in Section 2.3.2 and seen in Figure 2.3, in anaerobic operations three groups of bacteria are involved in acidogenesis and two in methanogenesis. Fermentative bacteria convert amino acids and simple sugars to acetic acid, volatile acids, and a minor amount of H:. Bacteria performing anaerobic oxidation convert long chain fatty acids and volatile acids to acetic acid and major amounts of H:. Finally H2-oxidizing acetogens form acetic acid from carbon dioxide and H:, but they are considered to be of minor importance in anaerobic wastewater treatment operations and will not be considered here. The two groups of methanogens are aceticlastic methanogens, which split acetic acid into methane and carbon dioxide, and H:-oxidizing methanogens, which reduce carbon dioxide.

To have a complete picture of the kinetics of microbial growth and substrate utilization in anaerobic systems, the kinetic parameters for all groups should be characterized. Unfortunately, because of the role of H: in regulating microbial activity and the close association between H:-producing and H;-consuming bacteria, this is not an easy task. For this reason and because the complex interactions among the microbial groups have only recently been recognized, most kinetic studies of anaerobic treatment processes have measured rates associated with entire communities rather than individual groups. That literature is too extensive to include here, but reviews"11,4 provide good summaries and the reader is encouraged to consult them for overall kinetic information.

As our understanding of the interactions in anaerobic processes has increased, engineers have sought to model anaerobic systems on a more fundamental level by including reaction steps for each important microbial group."4" Although those efforts represent first attempts at expressing the kinetics of these complex systems, they provide information that is helpful in developing an appreciation of the kinetic characteristics of anaerobic bacteria. Because a temperature of 35°C is commonly

used for anaerobic operations, the following parameter values are for that temperature range. Fermentative bacteria (group 2 in Figure 2.3) grow relatively rapidly on amino acids and simple sugars, and their kinetics can be represented by the Monod equation (Eq. 3.36) with a jl value on the order of 0.25 hr ' and a Ks value around 20 to 25 mg/L as COD. Review of available data suggests that this reaction does not limit system performance.4" The bacteria which oxidize long chain fatty acids (group 3 in Figure 2.3) grow more slowly than the fermentative bacteria and are subject to inhibition by H,. The values of p. and Ks depend on the degree of saturation of the fatty acid serving as growth substrate, with saturated acids having lower (1 and Ks values than unsaturated ones.4^ Nevertheless, Bryers14 has adopted a (i value of 0.01 hr 1 and a Ks value of 500 mg/L as COD as being representative of the entire group. Reaction 4 in Figure 2.3 represents the bacteria that degrade short chain fatty acids, such as propionic and butyric acids. Butyric acid appears to be degraded in a manner similar to that of the long chain fatty acids and bacteria growing on it have kinetic parameters similar to those in group 3. Propionic acid, on the other hand, is degraded by more specialized bacteria which grow more slowly. Gujer and Zehnder4" reported fx and Ks values of 0.0065 hr ' and 250 mg/L as COD, respectively, whereas Bryers14 chose values of 0.0033 hr 1 and 800 mg/L as COD based on other studies. Although the two sets of values differ somewhat in magnitude, they both suggest that growth on propionic acid is much slower than growth on other fatty acids. Aceticlastic methanogenesis (reaction 6 in Figure 2.3) is a very important reaction in anaerobic operations because it produces about 70% of the methane. Two major types of aceticlastic methanogenic bacteria can be present in anaerobic systems, but the one which predominates will depend on the bioreactor conditions imposed because their growth kinetics are quite different. Methanosarcina can grow rapidly, but do not have a high affinity for acetic acid. Representative parameter values for them are 0.014 hr 1 for |i and 300 mg/L as COD of acetic acid for Ks.""' Methunosaeta (formerly Methanothrix), on the other hand, grow more slowly, but have a higher affinity for acetic acid, as shown by a jl value of 0.003 hr ' and a Ks value of 30 to 40 mg/L as COD of acetic acid."1" Finally, the H:-oxidizing methanogens produce methane from H;, thereby keeping the H: concentration low and allowing the H:-producing reaction to proceed as discussed in Section 2.3.2. The kinetic parameters for their growth have been reported to be (1 = 0.06 hr 1 and Ks = 0.6 mg/L as COD of dissolved although others have reported Ks to be in the range of 0.03-0.21 mg/L as COD of dissolved H

The pH of an anaerobic system has a strong impact on |i, with an optimum around pH 7. Just as with nitrifying bacteria, this is probably because the nonionized form of the substrate (fatty acids in this case) serves as the actual substrate for growth and the amount of nonionized form will depend on the pH. As a consequence, relationships between (i and pH are needed for the major groups of bacteria On the other hand, some " have modeled acetic acid utilization with the Andrews equation using nonionized acetic acid as the substrate, but it is unclear whether that equation should be used if (1 is made an explicit function of pH. In addition, the role of in regulating the utilization of propionic and butyric acids and the activity of the H_,-producing bacteria is very important, but is not reflected in the parameter values reported above, which are all for low H2 levels. Bryers14 has argued that the H: effect is based on thermodynamics, and as such, does not translate directly into kinetic expressions. Labib et al.,'1" on the other hand, have demonstrated inhibition of butyric acid utilization by H: separate from the thermodynamic effects. Thus, even though information on the kinetic impacts of is very limited, it appears to be important, suggesting that additional studies are needed to allow development of appropriate rate expressions. In spite of these limitations, however, the kinetic parameters above provide a good sense of the relative capabilities of the microorganisms involved in anaerobic operations.


As discussed in Section 2.4.2, a number of complex events interact to make the observed yield in biochemical operations less than the true growth yield and to cause only a fraction of the suspended solids to be active biomass. Even if our knowledge of all of those events was sufficient to allow mechanistically accurate kinetic models to be written, it is doubtful that they would be used in engineering practice because of their complexity. Consequently, as is common in engineering, simplified models have been adopted because of their utility and adequacy, and two will be reviewed in this section. The traditional approach has been in use for many years and has found many applications. " ,| '4"1'"1 Its main attributes are its simplicity and familiarity. Its main weakness, however, is its inability to easily handle situations in which the nature of the terminal electron acceptor is changing. The second model addresses that situation.' ' It is called the lysis:regrowth approach. "

3.3.1 The Traditional Approach

In the traditional approach, all of the events-leading to the reduction in yield and viability are expressed by the following stoichiometry:

Biomass + electron acceptor —* CO. + reduced acceptor

+ nutrients + biomass debris (3.52)

The important concepts incorporated into this expression are that active biomass is destroyed as a result of "decay" and that the electrons removed as a result of the oxidation of the carbon to carbon dioxide pass to the electron acceptor. Furthermore, not all of the biomass is totally oxidized and a portion is left as biomass debris."' Although the debris is ultimately biodegradable,'""" its rate of biodégradation is so low that for all practical purposes it is inert to further biological attack in most biochemical operations, causing it to accumulate, reducing the fraction of active biomass in the suspended solids. Finally, nitrogen is released as ammonia-N, although some remains in the biomass debris. Figure 3.5 illustrates how these events are related to microbial growth in an aerobic environment. If Eq. 3.52 is rewritten as a COD balance the result is:

Biomass COD + [ — (1 — fnjO-. equivalents of electron acceptor —»

where f„ is the fraction of the active biomass contributing to biomass debris, X,,. For the type of biomass normally found in biochemical operations for wastewater


What Happens When Biomass Decays
Figure 3.5 Schematic representation of the traditional approach to modeling biomass decay and loss of viability.

treatment it has a value of around O.2.25 7K NI Equation 3.53 shows that the utilization of oxygen or nitrate due to decay must equal the loss of active biomass COD minus the production of biomass debris COD.

Another important concept inherent in Eq. 3.52 is that nitrogen is released as ammonia as biomass is destroyed. If Eq. 3.52 were reformulated as a nitrogen based stoichiometric equation it would read:

Since we have used biomass COD as the basic measurement of biomass, it would be convenient to write the nitrogen based stoichiometric equation in a way which linked it to biomass COD. This can be done by introducing two conversion factors, iN XH and iN xi), which are respectively, the mass of nitrogen per mass of COD in active biomass and the mass of nitrogen per mass of COD in biomass debris. Their use leads to:

iNX1(-Biomass COD —» NH,-N + iNXi>' biomass debris COD (3.55)

Because the destruction of a unit mass of biomass COD leads to the generation of f,> units of biomass debris COD (Eq. 3.53), Eq. 3.55 tells us that the amount of ammonia-N released from the destruction of a unit mass of biomass COD is (iN Xli — ¡sxi>fi>)- If C<H70;N is representative of biomass, then iNXB has a value of 0.087 mg N/mg biomass COD. The nature of biomass debris is less well characterized than active biomass and thus there is no generally accepted empirical formula from which iN XI> can be calculated. However, because many nitrogenous compounds serve as energy reserves that are destroyed during endogenous metabolism, it is likely that the nitrogen content of biomass debris is less than that of biomass. As a result, a value of 0.06 mg N/mg COD has been recommended for iN xd-^4'55

The rate expression for decay of biomass is first order with respect to the biomass concentration:

where b is the decay coefficient, with units of hr '. Employing the concept in Eq. 3.10, the rate of production of biomass debris can be seen to be:

and the rate of oxygen (electron acceptor) utilization associated with biomass decay is:

rso = (1 - f,>)b-X„ (COD units) = -(1 - f„)b-XH (0: units) (3.58)

The same equation would hold for utilization of nitrate expressed as oxygen equivalents, although the numerical value of the decay coefficient may well be different with alternative electron acceptors. Finally, the rate of ammonia-N release is:

As might be expected from the discussion of parameter values in Section 3.2.10, the value of b is very dependent on both the species of organism involved and the substrate on which it is grown. The latter effect is probably due to the nature of the energy reserves synthesized during growth. Because Eq. 3.56 is an approximation describing very complex events, the value of b also depends to some extent on the rate at which the biomass is grown. Dold and Marais25 have reviewed the literature concerning b and have concluded that in aerobic and anoxic wastewater treatment systems a typical value for heterotrophic biomass is 0.01 hr '. Others'" have reported values as low as 0.002 hr 1 as being common in similar systems. Thus, it can be seen that quite a large range can exist. A large range of b values has also been reported for autotrophic nitrifying bacteria,22 with values ranging from 0.0002 to 0.007 hr '. A value of 0.003 hr 1 is considered typical at 20°C/5

Decay also occurs in anaerobic systems, but the b values for such systems are lower than those for aerobic systems because the bacteria have much lower (1 values, and the two parameters appear to be correlated. For example, Bryers14 has reported b values around 0.0004 hr ' for bacteria carrying out anaerobic oxidations and mcth-anogenesis and values around 0.001 hr ' for fermentative bacteria.

3.3.2 The Lysis:Regrowth Approach

The most complete model depicting the loss of viability and biomass in biochemical operations was devised by Mason et al.71 after an extensive review of the literature. 4 In that model, viable biomass can either die or be inactivated, leading to dead and nonviable biomass, respectively. Furthermore, all biomass can undergo lysis, although at different rates for different types, leading to soluble and particulate organic matter. The particulate organic matter is hydrolyzed to soluble organic matter, and the soluble organic matter from either source can be used by the viable biomass for new growth. Loss of viability is accounted for because the presence of dead biomass and particulate organic matter reduces the number of viable bacteria per unit mass of particulate material. Loss of biomass, i.e., decay, results from the fact that yield values are less than one so that the amount of biomass grown from the soluble substrate released is always less than the amount destroyed by lysis, as discussed in Section 2.4.1.

A conceptually similar, but less complex, model was developed by Dold et al.'" for use in modeling wastewater treatment systems containing both aerobic and anoxic zones. Only one type of biomass is considered to be present: active, viable biomass. However, it is viewed as continually undergoing death and lysis, yielding particulate substrate and biomass debris. As in the model of Mason et al., 1 particulate substrate is hydrolyzed to soluble substrate, and the soluble substrate is used by the viable biomass for growth, yielding new cell material. However, as above, because biomass yield values are always less than one, the amount of new biomass formed is always less than the amount destroyed by death and lysis, resulting in a net loss of biomass from the system (i.e., decay). A loss of viability results from the accumulation of biomass debris and particulate substrate.

The model of Dold et al."1' is simpler than that of Mason et al., 1 yet appears to be adequate for modeling many important wastewater treatment systems. s Furthermore, it can account for differences in decay observed as bacteria are cycled through aerobic, anoxic, and anaerobic conditions, whereas those differences cannot be accounted for by the traditional decay approach.1 ' Finally, it has been adopted for use in a general model of single-sludge processes"'that has been shown to adequately represent the dynamic performance of full-scale systems.* Thus, it will be used herein as an alternative to the traditional approach. The events in it are depicted in Figure 3.6.

The COD-based stoichiometry of the lysis:regrowth approach of Dold et al."'"

Biomass COD —» (1 - f,',) particulate substrate COD

where f,', is the fraction of active biomass contributing to biomass debris. No COD is lost during death and lysis. Rather active biomass COD is simply converted into an equivalent amount of COD due to biomass debris and particulate substrate. As a



Figure 3.6 Schematic representation of decay and loss of viability.

the lysis:regrowth approach to modeling biomass

Figure 3.6 Schematic representation of decay and loss of viability.

the lysis:regrowth approach to modeling biomass consequence, no use of electron acceptor is directly associated with the loss of biomass, i.e., decay. Electron acceptor utilization occurs as soluble substrate, which arises from hydrolysis of particulate substrate, is used by active biomass for growth. As with the traditional approach, cell debris is assumed to be resistant to microbial attack within the time constraints of biochemical operations.

The nitrogen in the biomass is divided between biomass debris and particulate substrate, with the latter being called particulate biodegradable organic nitrogen. The nitrogen based stoichiometric equation depicting this is:

Biomass N —* particulate biodegradable organic N + biomass debris N

Giving the same meanings to iN x„ and iN XI) as given above, Eq. 3.61 can be rewritten in terms of biomass COD and biomass debris COD:

iNX„-Biomass COD —» particulate biodegradable organic N

Thus, each unit of biomass COD lost to decay yields (iN Mi — ¡Nxi>'fi>) units of particulate biodegradable organic nitrogen. This differs from the traditional approach which leads directly to soluble ammonia nitrogen.

As in the traditional approach, the rate of loss of biomass COD to death and lysis is considered to be first order with respect to the active biomass concentration:

where b, has units of hr ', just as b does. In a manner similar to the traditional approach, the rate of production of biomass debris COD is:

And the rate of production of particulate substrate COD (Xs) is:

Note the similarity of this equation to Eq. 3.58, the equation for oxygen consumption in the traditional approach. This similarity arises from the retention in the particulate substrate of all electrons lost from active biomass, rather than their transfer to oxygen. Finally, the rate of production of particulate, biodegradable organic nitrogen (XNS) is:

It is important to realize that b, is conceptually and numerically different from b and that f,', is numerically different from f„. This follows from the cycling of COD that occurs in the lysis:regrowth approach. Biomass COD is lost, releasing particulate substrate COD, which is hydrolyzed to soluble substrate COD, which is degraded by active biomass yielding new biomass, which is lost by death and lysis giving particulate substrate COD, etc. The net effect of the two approaches is the same because a given amount of biomass will be lost from a bioreactor regardless of how we conceptualize the actual events occurring. Since it is necessary for carbon to cycle around the system several times in the lysis:regrowth conceptualization to achieve the same loss of biomass that the traditional approach achieves in one pass, b, must be numerically larger than b. Likewise, since the same amount of biomass debris is ultimately formed from the loss of a given amount of biomass by decay, f,', must be numerically smaller than f„. In fact, the values of the four parameters are related:"


It was stated above that f,, has a value around 0.2. Given the Y values associated with the biomass for which f,> was estimated, Eq. 3.68 suggests that the value of f,', is around 0.08.~s The values of f,, and fi, are not likely to vary greatly, and thus those values will be adopted herein. It should be noted, however, that the relationship between b, and b also depends on Y:~s b b, =-— (3.69)

Although it is common during parameter evaluation studies to measure both Y and b, neither fn nor f,', is commonly measured. Since Y can influence the relationship between b, and b, it is recommended that Eq. 3.69 be used instead of Eq. 3.67 to convert measured b values to bL values."

An important assumption implicit in the lysis:regrowth approach is that within a given culture, cell lysis occurs all of the time with the same value of the rate coefficient b, , regardless of the rate at which the bacteria are growing. The validity of this assumption has been confirmed by measuring the release of nucleic acids as direct evidence of cell lysis.

For autotrophic growth, the relationship between b, and b is different.1" This is because autotrophic organisms do not use organic matter for growth. Thus, death and lysis will not lead to additional autotrophic biomass growth. (The amount of autotrophic biomass that will grow from the nitrogen released is negligible.) Rather, heterotrophic biomass will grow on the organic matter released. As a consequence, the lysis:regrowth and traditional approaches are the same for autotrophic biomass; the result is that the two parameter values are equal.

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