91Ó°ÊÓ

A small power plant produces \(500 \mathrm{MW}\) of electricity through combustion of coal that has the following composition on a dry basis: 76.2 wt\% carbon, \(5.6 \%\) hydrogen, \(3.5 \%\) sulfur, \(7.5 \%\) oxygen, and the remainder ash. The coal contains 4.0 wt\% water. The feed rate of coal is 183 tons/h, and it is burned with \(15 \%\) excess air at 1 atm, \(80^{\circ} \mathrm{F}\), and \(30.0 \%\) relative humidity. (a) Estimate the volumetric flow rate (ft \(^{3} / \mathrm{min}\) ) of air drawn into the furnace. (b) Effluent gases are discharged from the furnace at \(625^{\circ} \mathrm{F}\) and 1 atm. Estimate the molar (lb-mole/ min) and volumetric (ft \(^{3} / \mathrm{min}\) ) flow rates of gas leaving the furnace. (c) Injection of dry limestone ( \(\mathrm{CaCO}_{3}\) ) into the furnace is being considered as a means of reducing the \(\mathrm{SO}_{2}\) emitted from the plant. The technology calls for \(\mathrm{SO}_{2}\) to react with limestone: $$\mathrm{CaCO}_{3}+\mathrm{SO}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{CaSO}_{4}+\mathrm{CO}_{2}$$ Unfortunately, the process is expected to remove only \(75 \%\) of the \(\mathrm{SO}_{2}\) in the effluent gases, even though the limestone is fed at a rate 2.5 times the stoichiometric amount. What is the required feed rate of limestone? since some of the \(S O_{2}\) is removed from the furnace efflucnt [in contrast to Part (b)], recalculate the molar flow rate and composition of the effluent from the fumace. (d) The gas leaving the furnace passes through an electrostatic precipitator, where particulates from ash and limestone are removed, and then enters a stack (chimney) for release to the atmosphere. What is the gas velocity at a point in the stack where the stack diameter is \(25 \mathrm{ft}\) and the temperature is \(300^{\circ} \mathrm{F}\) ? Does the gas discharged from the stack meet the new Environmental Protection Agency standard that emissions from such power plants contain less than 75 parts of \(\mathrm{SO}_{2}\) per billion?

Step by step solution

01

Calculation of air flow into the furnace.

The first step in solving this is to find the total weight of dry air entering the furnace. This would require identifying the percentage composition of dry air and multiplying each by the total air inflow. Once the individual components are identified, the molar flows can be calculated by dividing the weight by the molecular weight of each component. Since the air inflow is with 15% excess, the air inflow would be 1.15x the stoichiometric air inflow calculated. Using the ideal gas law, convert the molar flow into volumetric flow using the conditions given.

02

Calculate molar and volumetric flow rates of gas leaving the furnace.

The stoichiometry of combustion should be written down first for carbon, hydrogen and sulfur in the coal to find the flue gas composition. Take into account the 15% excess air which would result in additional N2 and O2 in the flue gas. To find the molar flow of the flue gas, sum all the individual molar flows. This molar flow can be converted to volumetric flow again using the ideal gas law and the furnace exit conditions.

03

Calculate feed rate of limestone and new effluent composition.

From the stoichiometry of the reaction, 1 mol of SO2 reacts with 1 mol of CaCO3. So, calculate the molar flow of SO2 from Step 2. The limestone feed is at 2.5 times this stiochiometric amount but is only 75% effective, so the actual CaCO3 usage can be found. From this, the SO2 removed is found. The SO2 in the effluent can be recalculated subtracting the removed SO2 from the original SO2 flow.

04

Calculate stack velocity and verify emission standards

Using the ideal gas law and the total molar flow from Step 3, convert the molar flow to volumetric flow using the stack conditions. The velocity can then be found from the volumetric flow and stack diameter using the equation for volumetric flow in a pipe. For emission standard verification, calculate the number of parts per billion of SO2 in the effluent based on its molar flow found in Step 3 and see if it is below the limit of 75 ppb.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Combustion Analysis

Combustion analysis involves understanding how fuels, such as coal, burn in the presence of oxygen. This process releases energy, which is captured and utilized for power generation. In a typical combustion reaction for carbon, hydrogen, and sulfur in coal, these elements react with oxygen to produce carbon dioxide, water, and sulfur dioxide. To optimize combustion, it's essential to consider all products, including gases and residual ash.
The key to effective combustion is ensuring there is enough oxygen to completely react with the fuel components. This is where the concept of excess air comes into play. Excess air ensures complete combustion, which minimizes the production of harmful gases such as carbon monoxide. However, too much excess air can lead to energy loss because some of it merely heats the extra air which exits the furnace.
By examining the combustion process in this exercise, we're able to estimate the amount of air needed for the process, and how that influences the composition of exhaust gases. This sets the stage for controlling emissions and improving efficiency.

Air Pollution Control

Air pollution control is a crucial aspect of operating any power generation plant due to the environmental impact. The combustion of coal leads to the production of several pollutants, including sulfur dioxide (SO₂). To mitigate these emissions, technologies such as the injection of limestone into the furnace are utilized. Limestone (CaCO₃) reacts with sulfur dioxide to form calcium sulfate (CaSO₄), thus reducing the amount of SO₂ released into the atmosphere. This chemical reaction effectively reduces harmful emissions, but its effectiveness can vary, as seen in the exercise where only 75% of SO₂ is removed. This inefficiency requires feeding limestone at a rate higher than the stoichiometric requirement to optimize SO₂ capture.
Control strategies must be evaluated against environmental standards, such as those from the Environmental Protection Agency (EPA), to ensure compliance. These ensure emissions are kept below permissible limits, like the 75 parts per billion (ppb) of SOâ‚‚.

Stoichiometry

Stoichiometry is the foundation for understanding chemical reactions in exercises like these. It involves the calculation of reactants and products in chemical reactions, embodying the Law of Conservation of Mass.
In the context of combustion, stoichiometry helps us quantify how much air is required to fully combust the coal. Each element in the coal—carbon, hydrogen, and sulfur—combines with oxygen in specific molar ratios to form their respective oxides and other compounds. Calculating these ratios is crucial to predict how much of each reactant is consumed and product is formed.
For example, the exercise demonstrates using stoichiometry to identify the amount of limestone needed to remove SOâ‚‚. By understanding these ratios and compensating for reaction inefficiencies, engineers can optimize the composition of gases exiting the furnace.

Fluid Dynamics

Fluid dynamics plays a significant role in determining how gases flow through the different parts of the power plant, such as the furnace, precipitator, and stack. By treating gases as fluids, engineers can analyze and control their behavior within confined systems.
Applying fluid dynamics to the stack, we can calculate gas velocity using principles such as the continuity equation and ideal gas law. For example, if the stack's diameter and the volumetric flow rate of the effluent gas are known, the flow velocity can be determined. This is essential for evaluating how efficiently the gases are released into the atmosphere. Understanding fluid dynamics also aids in designing control systems to reduce resistance and optimize flow rates, ensuring that pollutants are effectively captured and removed before gases enter the environment.