---
title: "Sludge treatment aims; digester volume (94%)"
subject: "Sanitary Engineering"
chapter: 8
key: "semester_6/sanitary_engineering:sludge-aims-digestion-volume-94"
source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sludge-aims-digestion-volume-94
site: BCT Engineering
---

# Sludge treatment aims; digester volume (94%)

Sanitary Engineering · Chapter 8: Sludge Treatment and Disposal

- Asked in: 2081 Chaitra, 2+6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sludge-aims-digestion-volume-94
- Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-8

## Question

Write down the aims of sludge treatment. A sewage treatment plant produces sludge having a moisture content of 94% with a dry solid of 500 kg/d in which 70% solids are volatile. The specific gravity of volatile and fixed solids are 1.02 and 2.65. Assuming parabolic digestion of 30 days and 12 days of monsoon storage, calculate the volume of conventional rate digester required to produce digested sludge with a moisture content of 90%.

## Short answer

Aims: reduce volume, stabilize organics, destroy pathogens, improve dewatering, recover biogas and manure, protect environment. For 94% moisture, 500 kg/d dry solids (70% volatile), 50% VS destruction, 30-day digestion, 12-day storage: raw sludge volume V1=8.233 m3/d, digested sludge V2=3.153 m3/d. Using parabolic formula V=[V1-2/3(V1-V2)]td+V2ts, digester volume = 183.2 m3.

## Answer

#### Aims of sludge treatment
1. To reduce the volume (water content) so handling, transport and disposal become cheaper.
2. To stabilise the organic matter so that it does not putrefy and cause odour.
3. To destroy pathogens and make the sludge safe to handle and reuse.
4. To make the sludge easy to dewater and dry.
5. To recover resources: biogas (methane) for energy and the dried sludge as manure/soil conditioner.
6. To protect the environment and public health from nuisance, flies and water pollution.

#### Digester volume

For a conventional-rate digester the capacity with parabolic variation of sludge volume is

$$
V=\left[V_1-\frac{2}{3}(V_1-V_2)\right]t_d+V_2\,t_s
$$

where $V_1$ = raw sludge volume per day, $V_2$ = digested sludge volume per day, $t_d$ = digestion period, $t_s$ = storage period.

**Assumption:** 50% of the volatile solids are destroyed in the digester (usual 40-60% for conventional rate).

**Raw sludge** (500 kg dry solids/day, 70% volatile, moisture 94% i.e. 6% solids):

$$
\begin{aligned}
VS &= 350\ \text{kg},\quad FS=150\ \text{kg}\\
\text{Mass of wet sludge} &= \frac{500}{0.06}=8333\ \text{kg},\ \text{water}=7833\ \text{kg}=7.833\ \text{m}^3\\
\text{Volume of solids} &= \frac{350}{1.02\times1000}+\frac{150}{2.65\times1000}=0.3997\ \text{m}^3\\
V_1 &= 7.833+0.3997=8.233\ \text{m}^3/\text{day}
\end{aligned}
$$

**Digested sludge** (VS destroyed $=0.5\times350=175$ kg; remaining VS $=175$ kg, FS $=150$ kg; total solids $=325$ kg at 10% solids):

$$
\begin{aligned}
\text{Mass of wet sludge} &= \frac{325}{0.10}=3250\ \text{kg},\ \text{water}=2.925\ \text{m}^3\\
\text{Volume of solids} &= \frac{175}{1020}+\frac{150}{2650}=0.2282\ \text{m}^3\\
V_2 &= 2.925+0.2282=3.153\ \text{m}^3/\text{day}
\end{aligned}
$$

**Volume of digester** ($t_d=30$ days, $t_s=12$ days):

$$
V=\left[8.233-\frac{2}{3}(8.233-3.153)\right]\times30+3.153\times12=183.2\ \text{m}^3
$$

**Answer: digester volume $\approx 183.2$ m³ (say 183 m³).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which is NOT an aim of sludge treatment?
   A. Increase the putrescibility of sludge
   B. Stabilise organic matter
   C. Destroy pathogens
   D. Reduce volume and recover biogas
   Answer: A. Treatment aims to reduce putrescibility, not increase it. (Key point: Aims of sludge treatment)

2. The parabolic digester capacity formula is
   A. V = (V1 + V2) t_d
   B. V = [V1 - (2/3)(V1 - V2)] t_d + V2 t_s
   C. V = V1 t_s + V2 t_d
   D. V = V1 x V2 / (t_d + t_s)
   Answer: B. V1 is raw sludge per day, V2 digested sludge per day, t_d digestion and t_s storage period. (Key point: Formula)

3. For 500 kg/day dry solids at 94% moisture, the raw sludge volume V1 is about
   A. 8.23 m3/day
   B. 5.75 m3/day
   C. 0.40 m3/day
   D. 83 m3/day
   Answer: A. Wet mass = 500/0.06 = 8333 kg, water 7.833 m3 plus solids 0.3997 m3 = 8.233 m3/day. (Key point: Raw sludge volume)

4. Digested sludge at 10% solids has solids of 325 kg/day. This is because
   A. all volatile solids remain
   B. all volatile solids are destroyed
   C. 50% of the 350 kg volatile solids (175 kg) are destroyed, leaving 175 + 150 kg
   D. fixed solids are destroyed
   Answer: C. Assumed 50% VS destruction leaves V2 = 3.153 m3/day, giving V = 183.2 m3. (Key point: Digested sludge)

## Close variants set in other exams

- [Digester volume for sludge, moisture 92%](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-digester-volume-92) — Sanitary Engineering, chapter 8, asked 2×

## Related in Sanitary Engineering

- [Volume-moisture relation; specific gravity](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-specific-gravity-95) — Sanitary Engineering, chapter 8
- [Sludge volume and digester, 4 MLD](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-volume-4mld-digester) — Sanitary Engineering, chapter 8
- [Digester diameter from 500 m³ sed. tank](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-digester-diameter-500m3) — Sanitary Engineering, chapter 8
- [Sludge volume before and after digestion](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-volume-before-after-600kg) — Sanitary Engineering, chapter 8
- [Sludge volume from sedimentation tank, 10 MLD](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-volume-10mld-250) — Sanitary Engineering, chapter 8
- [Sludge treatment need; digester sketch](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-necessity-digester-sketch) — Sanitary Engineering, chapter 8

## Related in other subjects

- [Quality, moisture content, specific volume of mixture](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aquality-moisture-specific-volume) — Fundamental of Thermodynamics & Heat Transfer, chapter 3