Consider A 400 MW, 32% Efficient Coal-Fired Power Plant

Consider A 400 Mw 32 Percent Efficient Coal Fired Power Plant That

Analyze a 400-MW coal-fired power plant operating at 32% efficiency that uses cooling water withdrawn from a nearby river (with an upstream flow of 10 m³/s and temperature 20 °C). The coal used has a heat content of 8,000 Btu/lb, a carbon content of 60% by mass, and a sulfur content of 2% by mass. The assignment involves calculating electricity production, coal consumption, emissions, effects of cooling water heating, and pollution control measures, as well as analyzing an air pollution model involving vehicle emissions and local atmospheric conditions.

Paper For Above instruction

Introduction

Coal remains one of the most abundant and utilized fossil fuels worldwide, providing substantial electricity generation capacity. However, environmental considerations such as greenhouse gas emissions, air pollutants, and thermal impacts on aquatic ecosystems necessitate careful examination of coal-fired power plant operations. This paper evaluates the environmental and operational aspects of a hypothetical 400-MW coal-fired power plant, integrating thermodynamic calculations, emission estimations, and air quality modeling to assess sustainability and pollution control strategies.

Electricity Generation and Coal Consumption

The power plant's electrical output is given as 400 megawatts (MW), operating at 32% efficiency. To determine annual energy production, first convert the plant's capacity into annual energy output. The total hours in a non-leap year are 8,760. The total energy produced is calculated as:

Electrical energy per year = Power × Hours per year = 400 MW × 8,760 hours = 3,504,000 MWh.

Expressed in kilowatt-hours (kWh), this equals 3,504,000,000 kWh/year.

The plant's thermal energy input can be derived as:

Thermal input = Electrical output / Efficiency = 3,504,000,000 kWh / 0.32 ≈ 10,950,000,000 kWh.

Converting thermal energy to Btu (since 1 kWh = 3,412 Btu):

Total Btu input = 10,950,000,000 kWh × 3,412 Btu/kWh ≈ 37,382,000,000,000 Btu.

The amount of coal burned annually is then:

Coal energy content per pound = 8,000 Btu/lb, so:

Coal burned annually (lb) = Total Btu / Btu per pound = 37,382,000,000,000 Btu / 8,000 Btu/lb ≈ 4,672,750,000 lb.

Converting to pounds per hour:

~4.67 billion pounds per year / 8,760 hours ≈ 533,420 pounds/hour.

Estimated Carbon Emissions

Carbon content per pound of coal is 60%, so carbon burned annually is:

Mass of carbon = total coal × carbon fraction = 4,672,750,000 lb × 0.60 ≈ 2,803,650,000 lb.

Converting pounds to metric tons (1 metric ton = 2,204.62 lb):

Carbon in metric tons = 2,803,650,000 lb / 2,204.62 ≈ 1,272,200 metric tons of C per year.

Carbon Emissions per Energy Unit and Comparison

The total energy produced annually in joules is:

Energy in Joules = 3,504,000,000 kWh × 3.6×10^6 J/kWh ≈ 1.262×10^16 J.

Thus, the emissions per gigajoule (GJ = 10^9 J):

Emissions = 1,272,200 metric tons C / (1.262×10^16 J / 10^9) ≈ 0.101 g C per kJ.

Compared to petroleum combustion (about 0.056 g C/kJ) and methane (approximately 0.025 g C/kJ), coal's higher carbon emissions per energy unit underscore its status as a "dirty" fossil fuel, associated with greater greenhouse gas emissions, acid rain precursors, and health hazards.

Cooling Water Temperature Rise and Flow Rate

If the cooling water's temperature rise is limited to 10 °C, the heat rejected is:

Q = mass flow rate × specific heat capacity × ΔT.

Specific heat capacity of water ≈ 4.186 J/g·°C, and 1 m³ of water weighs 1,000 kg.

Heat rejected annually (from thermal energy input) ≈ 10.95×10^9 kWh × 3.6×10^6 J/kWh ≈ 3.94×10^16 J.

Flow rate (m³/s) to maintain 10 °C temperature increase:

Flow rate = Q / (specific heat × ΔT × total seconds in a year).

Flow rate ≈ 3.94×10^16 J / (4,186 J/kg·°C × 10°C × 31,536,000 s) ≈ 2,396 m³/s.

This flow rate exceeds the current river flow of 10 m³/s, indicating unsustainability. Therefore, alternative cooling strategies or limiting plant capacity is advisable.

River Temperature Increase and Environmental Impact

Assuming all waste heat is transferred to the river, the temperature rise is simply:

ΔT_river = Q / (mass flow rate of river × specific heat capacity of water).

Mass flow rate of river per second = 10 m³/s × 1000 kg/m³ = 10,000 kg/s.

ΔT_river = 3.94×10^16 J / (10,000 kg/s × 4,186 J/kg·°C × 31,536,000 s) ≈ 30°C.

A 30°C rise would significantly impact aquatic ecosystems, potentially leading to hypoxia, loss of biodiversity, and altered river chemistry, emphasizing the need for heat dissipation measures.

Sulfur Dioxide and Particulate Emissions

The total sulfur in coal burned annually is 2% by mass:

Sulfur mass = 4,672,750,000 lb × 0.02 = 93,455,000 lb.

Assuming complete oxidation to SO₂, the moles of sulfur (sulfur atomic weight ≈ 32 g/mol):

Convert sulfur mass to grams: 93,455,000 lb × 453.592 g/lb ≈ 42,396,000,000 g.

Moles of sulfur = 42,396,000,000 g / 32 g/mol ≈ 1.324×10^9 mol.

Mass of SO₂ produced = moles × molar mass of SO₂ (64 g/mol):

≈ 1.324×10^9 mol × 64 g/mol ≈ 8.47×10^10 g = 84,700,000 kg/year.

Hourly SO₂ emissions = 84,700,000 kg / (365×24 hours) ≈ 9,680 kg/h.

Environmental and Regulatory Concerns of SO₂

Releasing SO₂ into the atmosphere can lead to acid rain, respiratory problems, and environmental degradation. It is a regulated pollutant, with the U.S. National Ambient Air Quality Standards (NAAQS) setting limits on SO₂ concentrations at 75 ppb (parts per billion) averaged over 1 hour. This emphasizes the importance of SO₂ control technologies such as flue gas desulfurization (FGD) scrubbers.

Control Measures for Sulfur Dioxide and Particulates

To mitigate SO₂ emissions, power plants employ scrubbers—most commonly wet FGD systems—that can remove over 90% of sulfur dioxide, achieving substantial reductions to meet regulatory standards. Particulate matter is controlled using electrostatic precipitators or fabric filters, reducing particulate emissions to below specified limits (e.g., 0.03 lb per 10^6 Btu). These controls not only protect air quality but also reduce health hazards related to airborne toxins.

Emission Standards and Characteristics

If the plant is limited to a SO₂ emission of 0.6 lb per million Btu, the required removal efficiency of the scrubber can be calculated based on the total heat input. Similarly, particulate emissions constraints inform the design and operation of pollution control devices, emphasizing the ongoing need for regulation-compliant technologies in reducing the environmental footprint of coal-based power generation.

Air Quality Modeling of Vehicle Emissions

In the second scenario, a box model assesses CO pollution from 300,000 vehicles traveling 50 km each, emitting 4 g CO/km. Total CO emitted per hour is:

Total CO emission = 300,000 vehicles × 50 km × 4 g/km = 60,000,000 g = 60,000 kg over the period.

The steady state concentration in the atmospheric box, considering the odor and oxidation, can be estimated via mass balance—factoring in the atmospheric half-life of three hours—and wind speed. The faster wind speed disperses CO more quickly, lowering concentrations, which demonstrates how meteorological conditions directly influence air quality and compliance with NAAQS.

Conclusion

The analysis illustrates that coal-fired power plants have significant environmental impacts, including greenhouse gas emissions, acid rain precursors, and thermal pollution. Implementing pollution control mechanisms is essential to reduce emissions and meet regulatory standards. Additionally, sustainability considerations, particularly regarding water resource use and thermal impacts, indicate a need for alternative cooling strategies, cleaner energy sources, and integrated environmental management to ensure long-term operational viability while protecting ecosystems and public health.

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