16-Civ-B5 Water Supply and Wastewater Treatment · December 2015

Question 7 of 7: The Four Biochemical Stages of Anaerobic Sludge Digestion

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. 98-Civ-B5 Water Supply and Wastewater Engineering — National Examination, December 2015. Three hours; closed book, one aid sheet written on both sides; an approved calculator is permitted. Question 1 is compulsory and the candidate attempts any five of the remaining six, so 100 marks are written out of the 115 printed (Q1 = 25 marks, Q2 to Q7 = 15 marks each; Q2 splits 12 + 3). Every one of the seven questions is solved below, because this set is a study resource rather than an exam script.

Reference texts.

Metcalf & Eddy / AECOM, Wastewater Engineering: Treatment and Resource Recovery, 5th ed. — solids fractionation, nitrogen chemistry, sedimentation theory, anaerobic digestion.
Crittenden, Trussell, Hand, Howe & Tchobanoglous, MWH's Water Treatment: Principles and Design, 3rd ed. — coagulation and flocculation theory, softening, filtration, disinfection.
Davis & Cornwell, Introduction to Environmental Engineering, 5th ed. — treatment-train selection, hardness chemistry, residuals management.
Mihelcic & Zimmerman, Environmental Engineering: Fundamentals, Sustainability, Design, 3rd ed. — mass balances, reaction kinetics, water-quality indicators.
CCME, Canadian Environmental Quality Guidelines (ammonia and receiving-water criteria) and Health Canada, Guidelines for Canadian Drinking Water Quality (treated-water objectives).
APHA/AWWA/WEF, Standard Methods for the Examination of Water and Wastewater — Method 2540 D/E for the solids series.

Check: representative design data. Questions 1, 3, 4 and 7 are discussion questions and print no numbers. Where a number appears in those answers it is a representative Canadian municipal value chosen by the solver to make the argument concrete; it is labelled as such at the point of use, and every one of them. The graded content of those questions is the reasoning, not the arithmetic.

Question 7: The Four Biochemical Stages of Anaerobic Sludge Digestion (15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The anaerobic digestion of municipal sludge, a particulate substrate composed of carbohydrate, protein and lipid. The illustrative digester loading used at the end is a representative Canadian medium-sized plant chosen by the solver.

Find. The names and functions of the four biochemical stages, and which stage limits the overall rate, with the reason.

Figure 7.1 — The four stages in sequence, with the two organism groups that dominate each and the two different answers to the rate-limiting question, according to whether the feed is particulate or soluble.

Stage 1 — Hydrolysis

Sludge arrives as particles: cell walls, fibre, fat globules and protein. No bacterium can transport a polymer across its membrane, so nothing can happen until the polymers are broken into monomers outside the cell. Fermentative bacteria secrete extracellular enzymes — cellulases, amylases, proteases and lipases — which cleave carbohydrates to simple sugars, proteins to amino acids and peptides, and lipids to long-chain fatty acids and glycerol. The step is purely enzymatic and produces no gas and no energy for the organisms that pay for the enzymes. Its rate depends on the accessible surface area of the particles, which is why sludge grinding, thermal hydrolysis and ultrasonic or chemical pre-treatment all target this stage specifically.

Stage 2 — Acidogenesis (fermentation)

The monomers now diffuse into the fermentative bacteria and are fermented to a mixture of short-chain volatile fatty acids — principally propionate, butyrate and valerate — together with acetate, lactate, alcohols, ammonia, hydrogen and carbon dioxide. Amino-acid fermentation also releases the ammonia and hydrogen sulphide that appear in the digester gas and supernatant. These organisms are fast: maximum specific growth rates of the order of 5 d⁻¹, generation times measured in hours, and tolerance of a wide pH range. That speed is exactly why they are dangerous. If anything downstream slows, the acidogens keep producing acid at full rate and the digester sours.

Stage 3 — Acetogenesis

The volatile fatty acids longer than acetate cannot be used directly by methanogens and must first be converted to acetate, carbon dioxide and hydrogen by obligate hydrogen-producing acetogenic bacteria, for example

$$\mathrm{CH_3CH_2COO^-} + 3\,\mathrm{H_2O} \longrightarrow \mathrm{CH_3COO^-} + \mathrm{HCO_3^-} + \mathrm{H^+} + 3\,\mathrm{H_2}$$

This reaction is thermodynamically unfavourable at standard conditions and proceeds only if the hydrogen partial pressure is kept below roughly $10^{-4}$ atm by the hydrogenotrophic methanogens consuming it as fast as it is made. The two groups are therefore obligately coupled — a relationship called syntrophy or interspecies hydrogen transfer — and it is the most fragile link in the whole chain. A parallel group, the homoacetogens, produces acetate from hydrogen and carbon dioxide.

Stage 4 — Methanogenesis

Methanogenic archaea convert the products of stage 3 into methane by two distinct routes. The acetoclastic route splits acetate,

$$\mathrm{CH_3COO^-} + \mathrm{H_2O} \longrightarrow \mathrm{CH_4} + \mathrm{HCO_3^-}$$

and accounts for roughly 70 % of the methane from municipal sludge. The hydrogenotrophic route reduces carbon dioxide,

$$4\,\mathrm{H_2} + \mathrm{CO_2} \longrightarrow \mathrm{CH_4} + 2\,\mathrm{H_2O}$$

and supplies the remaining 30 %, while also performing the essential service of keeping the hydrogen partial pressure low for stage 3. Methanogens are strict anaerobes, grow slowly with maximum specific growth rates near 0.3 d⁻¹, and tolerate only a narrow pH window of about 6.6 to 7.6. Their slow growth is what sets the minimum solids retention time of a digester, conventionally 15 to 20 days at 35 °C with a safety factor over the 10-day washout limit.

Which stage is rate-limiting, and why

For the digestion of municipal sludge the rate-limiting step is hydrolysis. The reason is the physical state of the feed, not the biochemistry: the substrate arrives as particles, enzymatic attack can proceed only at the particle surface, and the rate is therefore proportional to the available surface area rather than to any bulk concentration. Waste activated sludge is the extreme case, because its organic matter is locked inside bacterial cell walls and extracellular polymeric substances that resist enzymatic attack, which is why waste activated sludge typically achieves only 35 to 45 % volatile solids destruction against 55 to 65 % for primary sludge. The decisive operational evidence is that every intervention which accelerates hydrolysis — thermal hydrolysis at 160 to 170 °C, mechanical or ultrasonic disintegration, chemical pre-treatment — increases gas production and shortens the required retention time, while interventions that accelerate methanogenesis do not.

The qualification matters and earns marks. If the feed is soluble and readily fermentable — a food-processing or brewery effluent, for instance — hydrolysis is trivial and methanogenesis becomes limiting, because the methanogens are by an order of magnitude the slowest-growing group present. Methanogenesis is also the limiting and the failing step in any upset, whatever the feed: an organic overload, a temperature swing, a toxic slug or an ammonia inhibition affects the methanogens first, acid accumulates because the fast acidogens upstream do not slow down, the pH falls, and the methanogens are inhibited further. That is the classic souring spiral, and it is diagnosed by a rising volatile-acid to alkalinity ratio — above about 0.4 is a warning, above 0.8 a failure — long before the gas production falls. So the complete answer is that hydrolysis limits the steady-state rate on sludge, while methanogenesis limits stability and is the step that governs the design retention time.

Given. A digester fed 120 m³/d of sludge at 4.5 % total solids of which 75 % is volatile, achieving 55 % volatile solids destruction at 35 °C on a 20-day solids retention time — representative values chosen by the solver.

Find. The methane production and the organic loading rate, to show what the four stages deliver in practice.

Compute the volatile solids fed and destroyed. $$\mathrm{VS_{fed}} = 120\times 0.045\times 0.75\times 1000 = 4050\ \mathrm{kg\ VS/d}, \qquad \mathrm{VS_{destroyed}} = 0.55\times 4050 = 2228\ \mathrm{kg/d}$$
Convert destroyed solids to a COD equivalent and then to methane. Since $\mathrm{CH_4}+2\,\mathrm{O_2}\to\mathrm{CO_2}+2\,\mathrm{H_2O}$, each mole of methane carries 64 g of COD, so at 35 °C the yield is $RT/P$ divided by 64, that is $25.28/64 = 0.395$ m³ per kg COD. Taking 1.42 kg COD per kg of volatile solids, $$V_{\mathrm{CH_4}} = 2228\times 1.42\times 0.395 = \boxed{1249\ \mathrm{m^3\ CH_4/d}}$$ which at a 65 % methane content corresponds to about 1920 m³/d of digester gas, roughly 12 GJ/d of recoverable energy.
Check the loading against the design window. The digester volume is $120\times 20 = 2400$ m³, so the organic loading rate is $4050/2400 = 1.69$ kg VS/(m³·d), inside the conventional mesophilic range of 0.8 to 2.4 and comfortably above the 10-day methanogen washout limit.

Question 7 — the four stages and the rate-limiting answer
Stage	Conversion	Organisms	Speed
1. Hydrolysis	Particulate polymers → soluble monomers	Extracellular enzymes of fermentative bacteria	Slow on particulate feed
2. Acidogenesis	Monomers → volatile fatty acids, alcohols, H₂, CO₂	Fermentative (acidogenic) bacteria	Fast, $\mu_{\max}\approx 5$ d⁻¹
3. Acetogenesis	VFAs → acetate + H₂ + CO₂	Obligate H₂-producing acetogens (syntrophic)	Moderate; requires low H₂ partial pressure
4. Methanogenesis	Acetate → CH₄+CO₂; 4H₂+CO₂ → CH₄+2H₂O	Methanogenic archaea	Slowest, $\mu_{\max}\approx 0.3$ d⁻¹
Rate-limiting: hydrolysis, for particulate sludge feed, because enzymatic attack is confined to the particle surface. Methanogenesis instead limits soluble, readily fermentable feeds, sets the minimum solids retention time, and is the step that fails first in any upset.
Illustrative methane yield	0.395 m³ CH₄ per kg COD stabilised at 35 °C; 1249 m³/d for the example digester
Illustrative organic loading rate	1.69 kg VS/(m³·d) at a 20-day solids retention time

Topic. The four-stage biochemistry of anaerobic digestion, the syntrophic coupling between acetogens and methanogens, and the identification of the rate-limiting step.

Key relations. Propionate oxidation and its hydrogen-partial-pressure constraint; the acetoclastic and hydrogenotrophic methanogenesis routes; 64 g COD per mole of CH₄, giving a yield of 0.35 m³/kg COD at 0 °C and 0.395 m³/kg COD at 35 °C; the volatile-acid to alkalinity ratio as the stability indicator.

Why this works. Anaerobic digestion is a food chain, not a single reaction, and its behaviour follows from the fact that the organisms in that chain differ in growth rate by more than an order of magnitude. Because the slow group sits at the end, the system has no way to buffer an upset: a disturbance that slows the methanogens does not slow the acidogens feeding them, so intermediates accumulate rather than clearing. The thermodynamic coupling at stage 3 sharpens this further, because the acetogenic reaction only releases energy when its own product is continuously removed by the stage that follows. Understanding the chain in these terms is what allows an operator to read a digester: falling gas production with stable pH points at hydrolysis or feed quality, whereas rising volatile acids with falling alkalinity points at the methanogens and calls for feed reduction and alkalinity addition, not for more feed.

Common pitfall. The frequent error is to answer “methanogenesis” flatly because the methanogens are the slowest-growing organisms present. Growth rate and process rate are not the same thing: on a particulate feed the methanogens are rarely substrate-limited, because hydrolysis cannot supply substrate fast enough to saturate them. The complete answer distinguishes the steady-state limitation, which is hydrolysis on sludge, from the stability limitation and the retention-time criterion, which are methanogenic. A second error is to merge acidogenesis and acetogenesis into a single “acid-forming” stage, which loses the syntrophic hydrogen coupling that is the most interesting biochemistry in the process and the usual site of failure.

Source. Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery, 5th ed., Ch. 10 (anaerobic suspended-growth treatment) and Ch. 13 (sludge digestion); Davis & Cornwell, Introduction to Environmental Engineering, 5th ed., Ch. 11.

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