Question

A coal-burning steam power plant produces a net power of \(300 \mathrm{MW}\) with an overall thermal efficiency of 32 percent. The actual gravimetric air- fuel ratio in the furnace is calculated to be \(12 \mathrm{kg}\) air/kg fuel. The heating value of the coal is \(28,000 \mathrm{kJ} / \mathrm{kg} .\) Determine \((a)\) the amount of coal consumed during a 24 -hour period and \((b)\) the rate of air flowing through the furnace.

Short answer

a) The amount of coal consumed during a 24-hour period is approximately 293,665 kg. b) The rate of air flowing through the furnace is approximately 40.68 kg/s.

Step-by-step solution

Calculate the rate of coal consumption

To find the rate of coal consumption, we will use the following formula: Rate of coal consumption = \(\frac{\text{Net Power}}{(\text{Overall Thermal Efficiency} * \text{Heating Value of Coal})}\) Substituting the given values, we have: Rate of coal consumption = \(\frac{300\times10^6\,\text{W}}{0.32 * 28,000\,\text{kJ/kg}}\)

Convert the units of power and heating value

Before we perform the division, we need to ensure the units are consistent. Currently, the net power is in watts and the heating value of coal is in kJ/kg. We will convert the net power from watts to kJ/s: 1 W = 1 J/s = 0.001 kJ/s Therefore, Rate of coal consumption = \(\frac{300\times10^6 \times 0.001\,\text{kJ/s}}{0.32 * 28,000\,\text{kJ/kg}}\)

Solve for the rate of coal consumption

Now, we can perform the division to obtain the rate of coal consumption: Rate of coal consumption = \(\frac{300\times10^3}{0.32 * 28,000}\,\text{kg/s}\approx 3.39\,\text{kg/s}\)

Calculate the amount of coal consumed in 24 hours

In order to find the amount of coal consumed in 24 hours, we will multiply the rate of coal consumption by the duration of 24 hours: Amount of coal consumed = Rate of coal consumption \(\times\) Duration Amount of coal consumed = \(3.39\,\text{kg/s} \times 24\,\text{hours} \times 3600\,\text{s/hour} \approx 293,665\,\text{kg} \) Therefore, the amount of coal consumed during a 24-hour period is approximately 293,665 kg.

Calculate the rate of air flowing through the furnace

To find the rate of air flowing through the furnace, we will use the given air-fuel ratio and the rate of coal consumption: Rate of air flow = Air-fuel ratio \(\times\) Rate of coal consumption Rate of air flow = \(12\,\text{kg air/kg fuel} \times 3.39\,\text{kg/s}\) Rate of air flow \(\approx 40.68\,\text{kg/s}\) Hence, the rate of air flowing through the furnace is approximately 40.68 kg/s.

Key concepts

Gravimetric Air-Fuel Ratio

Understanding the gravimetric air-fuel ratio is crucial when considering combustion processes and engine operation. Simply put, it is the ratio of the mass of air to the mass of fuel in the combustion mixture. This ratio is significant as it affects the efficiency of the combustion and therefore the overall thermal efficiency of an engine or furnace.

For a coal-burning steam power plant, a correct air-fuel ratio is essential to ensure complete combustion of the coal, thus maximizing the energy obtained from the fuel, while minimizing pollutants. In the case of our exercise, the actual gravimetric air-fuel ratio is calculated to be 12 kg air/kg fuel, meaning that for every kilogram of coal, 12 kilograms of air is used in the combustion process. If this ratio is too high or too low, it can lead to incomplete combustion and inefficient plant operation.

Heating Value of Fuel

The heating value of fuel, often referred to as the caloric value, is a measure of the energy content in a fuel. It is defined as the amount of heat released when a certain quantity of the fuel is completely burned. Typically reported in units like joules per kilogram (J/kg) or kilojoules per kilogram (kJ/kg), this value is pivotal for calculating the rate of fuel consumption and energy production in power plants.

For the given problem, the heating value of the coal is 28,000 kJ/kg. This represents the energy that can be extracted from each kilogram of coal during combustion. A higher heating value means more energy can be extracted, implying less fuel consumption for the same amount of energy produced, which is a critical factor in assessing the plant's operational cost and environmental impact.

Rate of Coal Consumption

The rate of coal consumption is a measure of how much coal is used over a certain period. It is an important indicator of a power plant's performance and economic efficiency. In the context of our exercise, determining the rate of coal consumption involves using the thermal efficiency of the plant and the heating value of the coal.

The step-by-step solution calculates the rate of coal consumption to be approximately 3.39 kg/s, which is then used to find out how much coal is consumed over a 24-hour period. Understanding and optimizing the rate of coal consumption is essential for the financial running and environmental impact of the power plant. By reducing coal consumption, not only are running costs lowered, but emissions of pollutants are also decreased, contributing to a cleaner environment.