# Development of Decay in Biofilms under Starvation Conditions—Rethinking of the Biomass Model

^{*}

## Abstract

**:**

^{−1}, that allows the biocenosis to withstand long periods of starvation. In activated sludge modeling, biomass decay is regarded as first order kinetics with a 10 times higher constant decay rate (0.17–0.24 d

^{−1}, depending on the model used). In lab-scale OUR measurements, the degradation of biofilm layers led to wavy sequence of biomass activity. After long starvation, the initial decay rate (comparable to activated sludge model (ASM) approaches) dropped by a factor of 10. This much lower decay rate is supported by experiments comparing the maximum OUR in pilot-scale biofilm systems before and after longer starvation periods. These findings require rethinking of the approach of single-stage decay rate approach usually used in conventional activated sludge modelling, at least for the investigated conditions: the actual decay rate is apparently much lower than assumed, but is overshadowed by degradation of either cell-internal substrate and/or the ability to tap “ultra-slow” degradable chemical oxygen demand (COD) fractions. For the intended stormwater treatment, this allows the application of technical biofilm systems, even for long term dynamics of wastewater generation.

## 1. Introduction

_{H}), expressed as chemical oxygen demand (COD).

_{U}) remains as endogenous residue X

_{E}.

_{E}and a biodegradable COD fraction X

_{S}during decay, which is then consumed by an organism, justifying oxygen consumption under starvation conditions (Figure 2). As a by-product of these decayed bacteria and, therefore, released bioavailable X

_{S}fraction, new growth is obtained, which is called regeneration. With this approach, increasing respiration rate after anaerobic periods can firstly be explained with the substrate release as a consequence of decay. If decay is an independent process, it would not stop under anaerobic conditions and, therefore, the substrate would accumulate, which then can be oxidized under aerobic conditions.

_{H}must become larger than in the endogenous respiration approach to compensate for regeneration. The decay rate from the respiration model b’ can be converted to the death-regeneration model with Equation (1): for this, an endogenous residue factor f

_{U}of 0.08 was assumed [13].

_{H}is the heterotrophic biomass yield, b and b’ is the decay rate within the death-regeneration and endogenous respiration approach, respectively. Applying the proposed biological constants of ASM [12], the corresponding decay rate for domestic wastewater is b = 0.62 d

^{−1}and b’ = 0.24 d

^{−1}.

_{H}is measuring the respiration rate, expressed as biological oxygen uptake rate (OUR). With slight variations, the same method is commonly used for various research questions [16,17,18,19]. In the state of the art, OUR is measured with respirometers under strictly controlled conditions to avoid side-effects. The magnificent advantage of this method is highly time resolved and low-cost measuring of kinetic parameters and COD fractions as it is just based on measuring dissolved oxygen. Figure 3 shows in a schematic way the conversion of COD fraction in the raw water (left) and into biomass (right) during the biological process. The influent COD

_{h,in}can either be degraded, which can be measured with the oxygen respiration rate for degradation OUR

_{deg}or incorporated into biomass as excess sludge X

_{ES}.

_{E}and yield coefficient for heterotrophic organism Y

_{H}is regarded to be constant for a particular substrate in the ASM. These are rather mechanistic assumptions and only valid for systems with rather low load variations. Current research in activated sludge systems proved that both the X

_{E}fraction [22] and the decay rate b

_{H}[23] are a function of sludge retention time SRT (i.e., function of substrate supply). Due to this observation at extreme conditions of low COD, the question arises if organisms can adapt their decay rate and the assumption of a constant decay rate has to be reconsidered or if the existing ASM has to be extended with an additional very slowly degradable COD fraction (consisting of “hard” external COD and/or cell-internal reserves) and according degradation process. Consequently, this would mean that the actual decay leading to cell death would occur at a lower rate than previously calculated. This is important for the activity and sludge production of all systems running with permanent or periodically occurring starvation conditions.

- The quantification of cell-decay rate under starvation conditions;
- To identify and quantify degradation of a “new” COD fraction, made accessible under those conditions;
- To quantify the recovery of the biofilm after starvation.

## 2. Material and Methods

#### 2.1. Design of Wastewater Treatment Plant

^{2}·m

^{–3}. During the starvation period, no stormwater was added and the SBR-TFS was only operated with the same treated wastewater.

#### 2.2. Analytical Procedure

^{−3}. OUR was calculated for each switch-off phase by a linear regression of the declining DO. During the starvation period, the reactor filled with biofilm carriers was aerated without substrate supply. From the resulting respirogramm during starvation, the endogenous respiration rate OUR

_{e}was calculated according to [20], (see “mathematical model” below, Section 2.3).

_{max}was calculated from the respirogramm in the same way as OUR

_{e}. Assuming a typical value for f

_{U}and a substrate specific yield coefficient, the growth rate can be calculated from the endogenous and maximum OUR according to the mathematical model, described below.

#### 2.3. Mathematical Model

_{H}, reduced by an endogenous residue factor f

_{U}:

_{H}is the difference of growth and decay. Both growth and decay can be described as first order kinetics of actual biomass concentration. Additionally, there is a substrate dependency for the growth, usually expressed by a Monod kinetics (Equation (3)).

_{H}is the decay rate of heterotrophic organism, $\mathsf{\mu}$ is the bacteria growth rate, S is the substrate concentration, and K

_{S}is the substrate saturation coefficient.

_{max}at time t(0) can be determined with Equation (5):

_{H}in Equation (5) by the rearranged Equation (2) results in:

_{H}of silage effluent was separately determined with 0.87 [20]. This rather high yield is attributable to its sugar-like ingredients as glucose have a yield coefficient of 0.90–0.91 [30]. The decay rate b

_{H}was calculated from the respirogramm and for f

_{U}, a typical value of 0.2 for heterotrophic biomass was assumed [12].

## 3. Results

#### 3.1. Decay Rate During Starvation

^{−1}as widely applied and proved in activated sludge modelling (ASM1) [21]. Considering both parts of the wavy respirogramm, the decreasing and increasing OUR, a net decay rate b

_{H+stor}of 0.17 d

^{−1}in accordance with ASM3 would fit best for a certain time period, here 6–7 days. To express this switch of decay rate, the apparent OUR under endogenous condition is divided into OUR obtained by degradation of an additional fraction X

_{US}(gray dot pointed line, Figure 7) and OUR obtained by base decay rate b

_{H}of active biomass (black dot pointed line, Figure 7). The total OUR is therefore the sum of both (gray dotted line). After this time period, the modelled net decay rate changes significantly to a lower value of 0.025 d

^{−1}, nearly a tenth of the conventionally applied decay rates. From this time on, all storage fractions are consumed and the sole decay rate is obtained (black dot pointed line).

_{US}applies, the net decay rate after substrate feed as sum parameter of decay and X

_{US}degradation should be the same as in the beginning of the experiment (0.17 d

^{−1}) and then fall back to the base decay rate b

_{H}as soon as this additional storage fraction is consumed (0.025 d

^{−1}). To answer this, substrate was fed in excess to ensure an accumulation of X

_{US}after 18 days of starvation. As Figure 8 shows, the brutto decay rate b

_{H+stor}increased again from 0.025 (before day 18) to 0.17 d

^{−1}after substrate feed. After complete consumption of X

_{US}, the decay rate during OUR decreased to 0.025 d

^{−1}once more (=b

_{H}). Precisely, degradation of an addition fraction extended the base decay rate b

_{H}by this storage fraction, which can be expressed again with the degradation rate b

_{H+stor}. Hence, the best model fit for modelling the overall process for the base decay rate is 0.025 d

^{−1}in addition with a consumption rate (=b

_{H+stor}) for X

_{US}of 0.17−0.025 d

^{−1}. This shows that the alternation is only temporary and therefore can be related with an additional degradation process of the new fraction X

_{US}.

#### 3.2. Verification of the Low Decay Rate in Pilot Scale

_{US}fraction and (2) a base decay rate in “real” starvation conditions—should be provable under operational conditions of the pilot plant. The proof can be performed with two experimental concepts: (i) decline of the “operational” OUR under starvation conditions and (ii) measuring maximum biomass activity after starvation. The latter experiment assumes that the identified base decay rate should preserve the biomass activity on a much higher level than calculated with the commonly proposed decay rate.

^{−1}, including degradation of “ultra-slow” degradable COD fraction X

_{US}(gray dotted line) and pure decay (black dotted line). At this point, X

_{US}is consumed and the decay rate decreases to the base decay rate of 0.022 d

^{−1}. Separating both processes would yield a decay rate for the storage products of 0.14 d

^{−1}(−0.022 d

^{−1}). In conclusion, the results show that the findings of a low decay rate are indeed representative under real operational conditions for treating stormwater-runoff from silo facilities.

_{max}represents (according to Equation (5)) directly the reduction of active biomass X

_{H}. Knowing the initial OUR

_{max}(0) and decay rate b

_{H}, OUR

_{max}at certain times of starvation can be calculated with Equation (8):

_{max}according to Equation (8) are nearly the same even after 13 days of continuous starvation. Therefore, it can be inferred that the decay rate of about 0.025 d

^{−1}is true and is suitable for an adequate prediction of biomass decrease under long starvation periods. The respirogramm for the case of 13 days of continuous starvation is shown in Figure 10 on the right. Based on the measurements of OUR

_{e}and OUR

_{max}and considering Equation (7), a growth rate ${\mu}_{max}$ of 7.9 d

^{−1}results at a constant Y

_{H}and f

_{U}at a temperature of 25 °C. However, with respect to typical growth rates of 6 d

^{−1}at 20 °C, a growth rate of approximately 8.5 d

^{−1}would be expected. Therefore, the estimated rate is within the expected range.

## 4. Discussion

_{US}, which is not “tapped” under normal conditions. The identity of X

_{US}is not clear yet. It can be thought as (i) cell internal reserve substrate or (ii) hardly accessible external substrate or a mix of both. From a modelling perspective, taking it as external substrate is the simplest approach, since X

_{US}formation is in this case decoupled from bacterial growth. This conceptual idea could also explain the wavy decline of decay, especially if combined with the death-regeneration approach. Transformation processes within the rather thick biofilm used in our experiments were probably diffusion controlled and oxygen limited in deeper layers. The diffusion limitation and oxygen penetration into the biofilm are presented in the Supplementary Materials. However, in the death-regeneration approach, decay is defined to be independent from oxygen supply. Therefore, independent from the aerobic state, biodegradable fractions are released by decay of organism but not used due to oxygen limitation. The biodegradable fractions are preserved in the inward layer of the biofilm carrier. The preserved COD fractions in the lower layers would lead to an increased respiration rate as soon as the upper layer is fully decayed. This short-term regrowth is followed by aerobic decay of the newly formed biomass, leading to the wave-like behavior of the observed respiration rates. This layering effect causing diffusion limitations is often associated with a simultaneous nitrification and denitrification in biofilm systems [27,33]. In contrast to the biofilm experiments in this study, experiments with activated sludge will probably not allow such a clear distinction between decay of X

_{US}and actual decay of biomass due to the stochastic distribution of both fractions. Accordingly, respirometry measurement would show a more continuous adaptation of the decay rate.

_{US}fraction as an external substrate is illustrated in Figure 11. It can be made available via hydrolyzation to a slow degradable fraction (1 − f

_{E}) and is then consumed as S

_{S}. A small ratio f

_{E}remains as endogenous residue X

_{E}. The hydrolyzation itself is poorly understood, yet, due to the variety of substrates and apart from this, the experiments in the literature are mainly accomplished with pure substrates [34]. Most model concepts (for instance ASM1, ASM2d, ASM3) are based on a one step hydrolyzation. In the approach proposed here, the X

_{US}fraction is firstly hydrolyzed into X

_{S}and further hydrolyzed into S

_{S}. However, X

_{US}hydrolyzation is inhibited by the concentration of the better accessible X

_{S}and will only be degraded under real starvation conditions when X

_{S}is fully degraded. Once X

_{US}is consumed, only the base decay rate is obtained. Mathematically, this can be considered with an inversed Monod kinetic (Equation (10)). The key idea behind this is that the term for X

_{US}is “inactive” as long as X

_{S}is still available (Equation (9) is above zero). With decreasing X

_{S}, the term becomes more and more “active” and is most active when X

_{S}drops to zero. Now, X

_{US}becomes the limiting step measured in respirometry. As soon as X

_{US}is degraded also, the term reaches zero and only the base decay rate is active (see Equation (7)).

_{US}fraction. In this approach, the fast-degraded substrate during endogenous conditions (illustrated with a bold line) internal storage fraction X

_{US}is directly degraded into the endogenous residue X

_{E,}without prior hydrolysis. Both base decay and X

_{US}consumption are running parallel. The degradation rate of X

_{US}can be expressed as the sum decay rate of storage product and base decay rate b

_{H+stor}discussed above minus the base decay rate (b

_{H+stor}− b

_{H}). The irreversible decay of active biomass is running in parallel with the observed much lower decay rate b

_{H}(illustrated with a thin line). Summarizing, as long as X

_{US}is still available as substrate, the brutto degradation rate b

_{H+stor}is suitable as best model fit for describing the OUR decrease with time. As soon as X

_{US}is fully degraded, the sole decay rate b

_{H}is obtained.

_{US}as a cell internal COD fraction or as an external fraction which can be made available to heterotrophic organism by a multi-step hydrolyzation depends on the model approach taken and can both be easily integrated. Compared to the complex adaptation of microorganisms to varying nutritional and environmental conditions, both approaches are still rather conceptual but would sufficiently describe the observed change of decay rate.

## 5. Conclusions

- Starvation of biofilm carrier was characterized by wavy increase and decrease of endogenous respiration, ending at a surprisingly low base decay rate. Justifying this effect with either the existing death-regeneration model or the endogenous respiratory model is not a straightforward task;
- A possible explanation approach is the layering and the associated oxygen diffusion limitations, which preserves the lower layers from real degradation of COD but not from decay;
- However, even taking these biofilm specific conditions apart: the base decay rate is considerably lower than the recommended value in existing ASM;
- This lower decay rates allow a conservation of biological activity over long starvation periods as shown by reactivation experiments at the pilot SBR trickling filter;
- To explain these findings, the common one step decay model needs be divided into at least two processes: (i) a fast degradation of cell internal reserves and/or hardly degradable external COD, named here as “ultra-slow” degradable COD X
_{US}and (ii) the net decay of active biomass; - Based on recent publications, it can be assumed that these findings are transferrable to activated sludge systems;
- The findings have practical consequences for aerobic biologic reactors suffering from long starvation conditions: (i) they should survive those conditions better than commonly presumed, (ii) biomass production is larger and aeration demand is lower than commonly presumed.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Nomenclature | |

A | surface area |

ASM | activated sludge model |

ASS | activated sludge system |

b | decay rate |

BF | biofilm |

COD | chemical oxygen demand |

D | diffusion coefficient |

DO | dissolved oxygen |

EBPR | enhanced biological phosphorus removal |

f | residue factor |

k | rate constant |

L | characteristic length |

n | number of |

N | oxygen demand for nitrification |

OUR | oxygen uptake rate |

r | rate expression |

S | dissolved fraction |

SBR | sequence batch reactor |

SBR-TFS | SBR-trickling filter system |

SRT | sludge retention time |

ß | oxygen penetration factor |

t | time |

X | particulate fraction |

Y | yield coefficient |

Indices | |

0 | initial |

deg | degraded |

E | endogenous residue |

e | endogenous |

eff | effluent |

eli | elimination |

ES | excess sludge |

f | filtrated |

F | fluid |

H | heterotrophic organism |

H+stor | degradation of heterotrophic organism and storage fraction |

h | homogeneous |

i | inert |

i,BM | inert biomass residue |

in | influent |

N | nitrification |

S | substrate |

sp | specific |

tot | total |

U | unbiodegradable |

US | ultra slow |

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**Figure 3.**Chemical oxygen demand (COD) fractions during biological treatment [20].

**Figure 4.**Principle schema of the trickling filter system [27].

**Figure 5.**Steps of one SBR cycle [27].

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**MDPI and ACS Style**

Cramer, M.; Tränckner, J.
Development of Decay in Biofilms under Starvation Conditions—Rethinking of the Biomass Model. *Water* **2020**, *12*, 1249.
https://doi.org/10.3390/w12051249

**AMA Style**

Cramer M, Tränckner J.
Development of Decay in Biofilms under Starvation Conditions—Rethinking of the Biomass Model. *Water*. 2020; 12(5):1249.
https://doi.org/10.3390/w12051249

**Chicago/Turabian Style**

Cramer, Michael, and Jens Tränckner.
2020. "Development of Decay in Biofilms under Starvation Conditions—Rethinking of the Biomass Model" *Water* 12, no. 5: 1249.
https://doi.org/10.3390/w12051249