9.3 Biological Treatment Kinetics & Microbiology

9.3 Biological Treatment Kinetics & Microbiology

[!NOTE] Biological Foundations of Advanced Reclamation: Under ADEQ water quality rules (A.A.C. Title 18, Chapter 11), facilities generating reclaimed water for unrestricted urban irrigation or direct groundwater recharge must meet rigorous standards—including complete nitrification ($NH_3$-N < 1.0 mg/L), total nitrogen reduction ($TN < 10\text{ mg/L}$ to protect groundwater aquifers under the Aquifer Protection Permit program), and near-zero effluent turbidity. Certified operators must understand biological kinetics, environmental classifications, and process microbiology to maintain stable biological ecosystems.

While preliminary and primary treatments physically remove discrete debris and settleable solids, the bulk of dissolved, finely dispersed, and colloidal organic contaminants passes directly into the secondary treatment stage. Biological wastewater treatment is the engineered process that utilizes mixed consortia of microorganisms to convert dissolved organic matter into settleable biological flocs and harmless end products ($CO_2$, $H_2O$, $N_2$).

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Principles of Biological Organic Conversion

Biological treatment relies on living microorganisms (primarily bacteria) suspended in liquid (activated sludge) or attached to fixed media (trickling filters, moving bed biofilm reactors). The microbial consortium metabolizes carbonaceous organic waste through two simultaneous metabolic pathways:

                               Dissolved Organic Matter
                                    (BOD5 / COD)
                                         │
                  ┌──────────────────────┴──────────────────────┐
                  ▼                                             ▼
       CATABOLISM (Oxidation)                         ANABOLISM (Synthesis)
      Energy-Generating Pathway                      Cell-Building Pathway
                  │                                             │
  Organics + O2 ──┼──► CO2 + H2O + NH3 + Energy        Organics + Nutrients + Energy ──► New Biomass
                  │                                                            (C5H7O2N)
                  ▼                                             │
           Waste Products                                       ▼
          (Released to air/water)                         Settleable Flocs
                                                      (Removed in Secondary Clarifier)

1. Catabolism (Respiration / Dissimilation): Microorganisms oxidize organic molecules to generate the biochemical energy (adenosine triphosphate, ATP) required for cellular maintenance and synthesis:

$\text{Organic Matter } (C_xH_yO_z) + O_2 \longrightarrow CO_2 + H_2O + NH_3 + \text{Energy (ATP)}$

1. Anabolism (Biomass Synthesis / Assimilation): Microorganisms utilize a portion of the organic carbon, essential nutrients (nitrogen and phosphorus in an approximate $BOD_5:N:P$ ratio of 100:5:1), and ATP energy to synthesize new bacterial cellular protoplasm (empirically represented as $C_5H_7O_2N$):

$\text{Organic Matter} + NH_3 + O_2 + \text{Energy} \longrightarrow C_5H_7O_2N \text{ (New Cells)} + CO_2 + H_2O$

Because these synthesized bacterial cells naturally aggregate into heavy flocs through bio-flocculation, they can be separated by gravity in downstream secondary clarifiers, effectively removing dissolved organic pollution from the liquid water stream.

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Environmental Classifications: Aerobic, Anoxic & Anaerobic Regimes

Biological systems are engineered around specific electron acceptors used by microorganisms for respiration:

1. Aerobic Environment

Requires maintaining a continuous molecular dissolved oxygen concentration of 1.5 to 2.0 mg/L (supplied via mechanical surface aerators or fine-pore ceramic/membrane diffusers). Aerobic heterotrophs rapidly consume carbonaceous $BOD_5$, while obligate aerobic autotrophs oxidize ammonia into nitrate.

2. Anoxic Environment (Denitrification)

Characterized by the total absence of free molecular dissolved oxygen ($DO = 0.0\text{ mg/L}$) but the presence of chemically bound oxygen in the form of nitrate ($NO_3^-$) or nitrite ($NO_2^-$). In anoxic selector zones, facultative heterotrophic bacteria substitute nitrate for molecular oxygen as their terminal electron acceptor, converting nitrate into harmless inert nitrogen gas ($N_2$) that vents harmlessly to the atmosphere:

$2NO_3^- + 10e^- + 12H^+ \longrightarrow N_2\uparrow + 6H_2O$

Denitrification strips nitrate from the wastewater, preventing eutrophication and protecting drinking water aquifers from exceeding the 10 mg/L nitrate Maximum Contaminant Level (MCL).

3. Anaerobic Environment

Strictly devoid of both free molecular dissolved oxygen and chemically combined nitrate/nitrite oxygen. Under anaerobic conditions, specialized obligate and facultative anaerobes break down complex organic compounds in two sequential phases:

• Acidogenesis & Acetogenesis: Acid-forming bacteria hydrolyze complex organics into volatile fatty acids (VFAs, primarily acetic and propionic acids), $CO_2$, and hydrogen gas.
• Methanogenesis: Strict anaerobic methanogenic archaea (Methanothrix, Methanosarcina) convert acetic acid and hydrogen into methane gas ($CH_4$, 65%–70%) and carbon dioxide ($CO_2$, 30%–35%).

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Heterotrophic vs. Autotrophic Microorganisms & Nitrification Kinetics

Microorganisms in wastewater are fundamentally distinguished by their carbon and energy sources:

+-----------------------------------------------------------------------------------+
|                    Heterotrophs vs. Autotrophs in Wastewater                      |
+-----------------------------------------------------------------------------------+
| Characteristic        | Heterotrophic Bacteria       | Autotrophic Nitrifiers     |
|-----------------------+------------------------------+----------------------------|
| Carbon Source         | Organic Carbon (BOD / Sugars)| Inorganic Carbon (HCO3-/CO2|
| Energy Source         | Oxidation of Organic Matter  | Oxidation of Ammonia / NO2-|
| Growth Rate           | Rapid (Doubling: 30-60 min)  | Very Slow (Doubling: 12-24h|
| Biomass Yield (Y)     | High (0.4 - 0.6 lb VSS/lb BOD| Low (0.10-0.15 lb VSS/lb N)|
| Oxygen Demand         | ~1.0 - 1.2 lb O2/lb BOD      | 4.57 lb O2/lb NH4+-N       |
| Alkalinity Impact     | Neutral / Slightly Produces  | Consumes 7.14 lb CaCO3/lb N|
+-----------------------------------------------------------------------------------+

Nitrification Stoichiometry & Environmental Constraints

Nitrification is a two-step autotrophic aerobic process performed by two specialized bacterial genera:

1. Step 1: Ammonia Oxidation to Nitrite by Ammonia-Oxidizing Bacteria (AOB, primarily Nitrosomonas):

$2NH_4^+ + 3O_2 \longrightarrow 2NO_2^- + 4H^+ + 2H_2O + \text{Energy}$

1. Step 2: Nitrite Oxidation to Nitrate by Nitrite-Oxidizing Bacteria (NOB, primarily Nitrobacter and Nitrospira):

$2NO_2^- + O_2 \longrightarrow 2NO_3^- + \text{Energy}$

Overall Combined Nitrification Reaction:

$NH_4^+ + 2O_2 \longrightarrow NO_3^- + 2H^+ + H_2O + \text{Energy}$

Critical Operating Rules for Nitrification:

1. Massive Oxygen Consumption: Complete oxidation of ammonia requires 4.57 pounds of dissolved oxygen ($O_2$) per pound of $NH_4^+$-N oxidized (3.43 lbs for AOB step + 1.14 lbs for NOB step). If aeration basin DO falls below 2.0 mg/L, nitrification slows drastically.
2. Alkalinity Destruction & Acidification: The nitrification reaction releases two hydrogen ions ($H^+$) for every mole of ammonia oxidized, destroying natural bicarbonate alkalinity:

$\text{Alkalinity Consumed} = 7.14\text{ lbs of Alkalinity (as } CaCO_3\text{) per lb of } NH_4^+\text{-N oxidized}$

If wastewater lacks sufficient natural alkalinity (common in softened or acidic waters), basin pH will collapse below 6.8, severely inhibiting or completely halting nitrification. Utilities must feed supplemental alkalinity (caustic soda, lime, or magnesium hydroxide) to maintain pH between 7.2 and 7.8. 3. Temperature Sensitivity: Nitrifiers are sensitive to temperature. In winter, nitrification rates drop significantly, requiring operators to increase Mean Cell Residence Time (MCRT) to retain slow-growing nitrifiers.

Microscopic Bio-Indicators & Mixed Liquor Ecology

Daily microscopic examination of fresh Mixed Liquor Suspended Solids (MLSS) at 100x and 400x magnification provides operators with an immediate, real-time diagnostic window into activated sludge health, sludge age, and settling characteristics.

                               Ecological Succession Ladder

  Relative Microorganism Population
   ▲
   │  Amoebas / Flagellates
   │      ┌──────┐
   │     ┌┘      └┐      Free-Swimming Ciliates
   │    ┌┘        └┐          ┌──────┐            Stalked Ciliates / Rotifers
   │   ┌┘          └┐        ┌┘      └┐                    ┌──────────┐
   │  ┌┘            └┐      ┌┘        └┐                  ┌┘          └┐    Nematodes / Tardigrades
   │ ┌┘              └┐    ┌┘          └┐                ┌┘            └┐          ┌──────┐
   │┌┘                └───┼┘            └───────────────┼┘              └─────────┼┘      └┐
   └──────────────────────┴─────────────────────────────┴─────────────────────────┴────────┴──► Sludge Age (MCRT)
       Young Sludge (F/M > 0.6)       Optimal Sludge (F/M 0.2 - 0.4)       Old Sludge (F/M < 0.1)

1. Amoebas (Amoeba proteus, Arcella)

• Morphology: Single-celled protozoa that move via slow cytoplasmic extensions (pseudopodia).
• Diagnostic Meaning: Signifies very young sludge (MCRT < 2 to 3 days), excessively high Food-to-Microorganism ratio (F/M > 0.6 to 1.0 day⁻¹), organic overloading, or recovery from a toxic shock. Bacteria are dispersed and un-flocculated, providing abundant food for amoebas. Effluent is turbid with elevated $BOD_5$.

2. Flagellates (Bodo, Monas, Peranema)

• Morphology: Small, rapidly moving protozoa propelled by one or two whiplike flagella.
• Diagnostic Meaning: Co-exist with amoebas in young sludge age and high organic loading environments where soluble food concentrations remain elevated.

3. Free-Swimming Ciliates (Paramecium, Colpidium, Euplotes)

• Morphology: Oval or elongated protozoa covered with short, hair-like cilia used for locomotion and filter-feeding.
• Diagnostic Meaning: Indicate an intermediate sludge age (MCRT 3 to 5 days, moderate F/M). They swim actively through the bulk liquid, ingesting dispersed un-flocculated bacteria and clearing the water column.

4. Stalked Ciliates (Vorticella, Opercularia, Epistylis, Carchesium)

• Morphology: Bell-shaped bodies anchored to floc particles by contractile or non-contractile stalks. Rapidly beating oral cilia create a localized vortex that draws free-swimming bacteria into their cytostomes.
• Diagnostic Meaning: The prime indicator of mature, stable, healthy activated sludge (MCRT 5 to 12 days, optimal F/M 0.2 to 0.4 day⁻¹). Signifies strong bio-flocculation, excellent settleability, crystal-clear effluent, high $BOD_5$ removal (>90%–95%), and active autotrophic nitrification.

5. Rotifers (Philodina, Rotaria)

• Morphology: Complex, multicellular metazoans possessing a rotating ciliated head corona and a specialized grinding pharynx (mastax).
• Diagnostic Meaning: Found in mature to older sludge (moderate to high MCRT). Rotifers feed on larger organic fragments, flocs, and bacteria, acting as final effluent polishers.

6. Nematodes (Roundworms) & Water Bears (Tardigrades)

• Morphology: Microscopic multicellular worms and segmented micro-animals with clawed appendages.
• Diagnostic Meaning: Indicate very old sludge age (MCRT > 15 to 25+ days, very low F/M < 0.1 day⁻¹). Common in extended aeration facilities, oxidation ditches, and aerobic digesters. Sludge flocs begin breaking down into small, dense pinpoint flocs that settle rapidly but leave a cloudy, fine-particulate effluent ("straggler floc" or "ashing").

7. Filamentous Bacteria (Nocardia, Microthrix parvicella, Type 021N, Sphaerotilus natans)

• Morphology: Thread-like filaments that form the structural backbone of activated sludge flocs in moderate quantities.
• Operational Hazard (Bulking & Foaming): When filamentous organisms grow excessively, they bridge between flocs, preventing compact gravity settling in secondary clarifiers (sludge bulking, characterized by a Sludge Volume Index SVI > 150 mL/g). Nocardia and Microthrix synthesize hydrophobic waxy mycolic acids that trap air bubbles, producing thick, greasy chocolate-brown surface foam mats across aeration basins and clarifiers.

The Bacterial Growth Curve in Wastewater Treatment

When bacteria are introduced into a batch environment containing organic food, or as wastewater flows along a plug-flow aeration basin, biomass growth progresses through four sequential physiological phases:

  Log Biomass Concentration (X)
   ▲
   │                               Declining Growth Phase
   │                             ┌─────────────────────────┐
   │        Log-Growth Phase     │ (Optimal Conventional   │
   │      ┌──────────────────┐   │  Activated Sludge Zone) │
   │     ┌┘                  └───┼─────────────────────────┼───┐
   │    ┌┘ Substrate Excess      │ Substrate Rate-Limiting │   └───┐ Endogenous Respiration
   │   ┌┘  (µ = µmax)            │ Microbes produce EPS    │       └───┐ (Self-Oxidation,
   │  ┌┘   High F/M              │ Strong Bio-Flocculation │           └───► Extended Aeration)
   │  │    Dispersed Cells       └─────────────────────────┘
   │ ┌┘
   │ ├── Lag Phase (Acclimation)
   └─┴─────────────────────────────────────────────────────────────────► Time / Basin Length

1. Lag Phase: Initial period during which bacteria acclimate to the wastewater characteristics, temperature, and pH. Microorganisms synthesize adaptive metabolic transport enzymes; cell numbers do not increase, but metabolic readiness ramps up.
2. Log-Growth (Exponential Growth) Phase: Food (substrate, $S$) is present in massive excess ($S \gg K_s$). Microorganisms reproduce at their maximum theoretical specific growth rate ($\mu = \mu_{\max}$). Biomass doubles exponentially. Because bacteria have excess food, they do not produce adhesive surface biopolymers; cells remain dispersed and non-settleable. Operating a treatment plant in this phase results in turbid, non-settling effluent.
3. Declining Growth Phase: The food supply becomes rate-limiting ($S \approx K_s$). Reproduction slows as substrate is depleted. In response to nutritional stress, bacteria begin synthesizing Extracellular Polymeric Substances (EPS)—sticky biopolymers consisting of polysaccharides, mucopolysaccharides, and proteins. These biopolymers coat cell walls, enabling colliding bacteria to stick together and agglutinate into heavy, dense, settleable flocs (bio-flocculation). This is the ideal operational zone for conventional activated sludge systems.
4. Endogenous Respiration Phase: The external food supply is exhausted ($S \ll K_s$). Microorganisms must oxidize their own internal cellular protoplasm and dead cellular debris to obtain maintenance energy:

$C_5H_7O_2N \text{ (Cells)} + 5O_2 \longrightarrow 5CO_2 + 2H_2O + NH_3 + \text{Energy}$

Operating in endogenous respiration produces well-stabilized, low-yield sludge, which is the foundational design principle of extended aeration plants, oxidation ditches, and aerobic digesters.

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Monod Kinetics, Substrate Utilization & Biomass Yield

Microbial growth and substrate removal kinetics are mathematically modeled through the Monod equation:

$\mu = \mu_{\max} \frac{S}{K_s + S}$

• $\mu$ = Specific growth rate of biomass ($\text{day}^{-1}$)
• $\mu_{\max}$ = Maximum theoretical specific growth rate under unlimited food ($\text{day}^{-1}$)
• $S$ = Soluble substrate concentration ($BOD_5$ or COD, mg/L)
• $K_s$ = Half-velocity constant (substrate concentration at which $\mu = 0.5 \mu_{\max}$, mg/L)

Substrate Utilization Rate

The rate at which dissolved organic matter is removed from solution is directly proportional to biomass concentration ($X$, mg/L MLVSS):

$r_{su} = -\frac{k \cdot S \cdot X}{K_s + S}$

(where $k = \frac{\mu_{\max}}{Y}$ is the maximum rate of substrate utilization per unit biomass).

True Yield ($Y$) vs. Net Observed Yield ($Y_{obs}$)

• True Biomass Yield ($Y$): The incremental mass of bacterial cells synthesized per unit mass of organic substrate metabolized:

$Y = \frac{\text{Mass of Cells Formed (lbs VSS)}}{\text{Mass of Substrate Consumed (lbs } BOD_5\text{)}}$

For aerobic heterotrophs treating municipal sewage, $Y$ typically ranges from 0.40 to 0.60 lb VSS produced per lb $BOD_5$ removed.

• Net (Observed) Biomass Yield ($Y_{obs}$): In practical operating systems, a significant fraction of newly grown biomass is consumed through endogenous decay ($k_d$, typically 0.04 to 0.08 day⁻¹). The observed yield accounts for sludge age (Mean Cell Residence Time, $\theta_c$ or MCRT):

$Y_{obs} = \frac{Y}{1 + k_d \cdot \theta_c}$

Operational Significance: As operators increase sludge age ($\theta_c$), the term $(1 + k_d \cdot \theta_c)$ increases in the denominator, driving down $Y_{obs}$. In an extended aeration plant operating at a 25-day MCRT, $Y_{obs}$ drops to ~0.20–0.25 lb VSS/lb $BOD_5$, resulting in substantially less Waste Activated Sludge (WAS) mass that requires thickening, dewatering, and disposal.