Question

A waste-water treatment plant produces sludge containing \(1800 \mathrm{~kg}\) of dry organic solids each day. Assuming the generic formula \(\left[\mathrm{CH}_{2} \mathrm{O}\right]\) for the solids and complete anaerobic digestion by reaction \(16.16\), calculate the fuel value of the generated methane in joules, barrels of oil, and kilowatt hours.

Short answer

The fuel value is 53.4 billion J, approximately 8.73 barrels of oil, or 14,833.33 kWh.

Step-by-step solution

Understanding the Composition

The sludge is composed of dry organic solids, assumed to have the molecular formula \( \mathrm{CH}_{2} \mathrm{O} \). Each molecule of this formula corresponds to 30 g/mol (12 for C, 2 for H, and 16 for O).

Determine Moles of Organic Solids

First, we calculate the number of moles of organic solids in the 1800 kg produced per day:\[\text{Moles of } \mathrm{CH}_2\mathrm{O} = \frac{1800,000 \, \text{g}}{30 \, \text{g/mol}} = 60,000 \, \text{mol}\]

Methane Production from Anaerobic Digestion

Assume the reaction for complete anaerobic digestion that produces methane is:\[\mathrm{CH}_2\mathrm{O} + \text{other reactants} \rightarrow \mathrm{CH}_4 + \text{products}\]Each mole of \( \mathrm{CH}_{2}\mathrm{O} \) can convert to 1 mole of \( \mathrm{CH}_4 \). Therefore, 60,000 moles of methane are produced.

Calculate Energy in Joules

The combustion of methane releases approximately 890 kJ/mol. The energy in joules is:\[E = 60,000 \, \text{mol} \times 890,000 \, \text{J/mol} = 53,400,000,000 \, \text{J}\]

Convert Energy to Barrels of Oil

The energy content of one barrel of oil is about 6.12 \(\times\) 10^9 J. Thus, the equivalent energy in barrels of oil is:\[\frac{53,400,000,000 \, \text{J}}{6.12 \times 10^9 \, \text{J/barrel}} \approx 8.73 \, \text{barrels}\]

Convert Energy to Kilowatt Hours

There are 3.6 million joules in a kilowatt-hour. Therefore, the energy in kilowatt-hours is:\[\frac{53,400,000,000 \, \text{J}}{3,600,000 \, \text{J/kWh}} \approx 14,833.33 \, \text{kWh}\]

Key concepts

Methane Production

Anaerobic digestion plays a vital role in methane production, especially in the context of waste management. It involves breaking down organic matter in the absence of oxygen. This process takes place in several steps, including hydrolysis, acidogenesis, acetogenesis, and methanogenesis.
The final step, methanogenesis, is where most of the methane, or biogas, is generated. This biogas is predominantly composed of methane (CH extsubscript{4}) and some carbon dioxide (CO extsubscript{2}).
Here are important aspects of methane production:

• Sustainability: Methane production from waste reduces the dependence on fossil fuels and minimizes greenhouse gas emissions.
• Efficiency: The anaerobic digestion process can produce a significant amount of methane, as noted in the problem where 60,000 moles are produced daily.
• Resource Utilization: Organic waste materials are converted into energy, making methane production an efficient recycling mechanism.

Energy Conversion

Converting methane into usable energy is a crucial step in the process of energy recovery from waste. Methane is a potent energy carrier because of its high hydrogen content, making it an excellent fuel.
When methane is burned, it releases a considerable amount of energy. Typically, combustion of one mole of methane releases about 890 kJ. This energy can be transformed into other forms, such as electricity or thermal energy, which can then be used in various applications.
For instance, in this exercise:

• The total energy produced from methane combustion is calculated to be approximately 53.4 billion joules.
• This energy can then be converted to barrels of oil equivalent or kilowatt-hours for easier comparison with conventional energy sources.

Waste-Water Treatment

Waste-water treatment facilities are integral in managing and purifying the water we use daily, and anaerobic digestion is a part of this process. These facilities treat sludge—a byproduct composed mainly of organic solids—generated from sewage treatment plants.
By employing anaerobic digestion, we can not only treat these organic solids effectively but also harness their potential energy:

• Organic Solid Processing: Treatment plants process sludge that contains large amounts of organic matter using microbial activity.
• Energy Recovery: Through anaerobic digestion, organic matter from waste-water is transformed into methane, promoting energy efficiency.
• Environmental Impact: Reduces environmental pollution since methane emissions are captured and utilized rather than being released into the atmosphere.

Organic Solids

Organic solids are significant components of waste produced in industrial and residential settings. In the context of waste treatment, they refer to organic materials like food waste, plant matter, and other biodegradable substances.
Anaerobic digestion starts with these organic solids, breaking down their complex molecules into simpler compounds, and eventually converting them into methane. The molecular formula, often simplified as CH extsubscript{2}O for calculation purposes, gives an idea of their basic composition. Notably:

• Compositional Understanding: Each molecule of CH extsubscript{2}O is treated with a molecular weight of 30 g/mol, as shown in the exercise.
• Resource Efficiency: Organic solids serve not only as a waste product but as a starting material for producing renewable energy.

Through careful processing, these solids can be transformed into resources that contribute significantly to energy generation and sustainability.