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Chapter 5: Problem 51

A gas turbine power plant receives a shipment of hydrocarbon fuel whose composition is uncertain but may be represented by the expression \(\mathrm{C}_{x} \mathrm{H}_{y}\). The fuel is burned with excess air. An analysis of the product gas gives the following results on a moisture-free basis: \(10.5 \%(\mathrm{v} / \mathrm{v}) \mathrm{CO}_{2}, 5.3 \% \mathrm{O}_{2},\) and \(84.2 \% \mathrm{N}_{2}\) (a) Determine the molar ratio of hydrogen to carbon in the fuel ( \(r\) ), where \(r=y / x\), and the percentage excess air used in the combustion. (b) What is the air-to-fuel ratio ( \(m^{3}\) air/kg of fuel) if the air is fed to the power plant at \(30^{\circ} \mathrm{C}\) and \(98 \mathrm{kPa} ?\) (c) The specific gravity of the fuel (a petroleum product) is \(0.85 .\) Estimate the ratio standard cubic feet of gas fed to the turbine per barrel of fuel. (d) What are the issues associated with using oil as a fuel as opposed to natural gas? Consider two factors: (i) the complete composition of typical fuel oils and their resulting emissions, and (ii) the availability and global distribution of the two fuel sources.

Short Answer

Expert verified
a) The molar ratio \(r = 0.1205\), and the percentage excess air is 17.58%. b) The air-to-fuel ratio is \(15.66 [m^3/kg]\). c) The ratio of standard cubic feet of gas fed to the turbine per barrel of fuel is \(2114 [scf/barrel]\). d) Using oil as fuel poses issues like emission of harmful compounds and availability compared to natural gas.

Step by step solution

01

Molar Ratio Calculation

To find 'r', the molar ratio \(r = \frac{y}{x}\), the balance equation for nitrogen is used, considering the air consists of 79% Nitrogen: \(0.79*(1+r+\alpha) = 0.842\), where \(\alpha\) is the excess air fraction. Solving for 'r' we get \(r=0.1205\).
02

Excess Air Calculation

The percentage of excess air used in the combustion (excess O2 / total O2 x 100%) can be calculated by using: \(%_{\text{excess}} = \frac{5.3}{(1+0.1205)*0.21}*100 = 17.58\% \)
03

Air-to-Fuel Ratio Calculation

The air-to-fuel ratio can be computed by using the ideal gas law and the molecular weights: \( \frac{(1+\alpha)\times 29}{12+1.205\times1.8} \times \frac{22.414}{0.85} = 15.66 m^3/kg \)
04

Conversion of Fuel to Gas Volume

Using the relation 1 barrel = 159 L, the volume ratio is given by \( 15.66 [m^3/kg] \times 0.85 [kg/L] \times 159 [L/barrel] = 2114 scf/barrel \)
05

Issues with Using Oil as a Fuel

(i) Fuel oils are more complex in composition compared to natural gas, and might result in the emission of sulfur and nitrogen compounds which can have harmful environmental effects. (ii) Natural gas reserves are more evenly distributed across the world compared to oil, and it is also more available.

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Key Concepts

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

Molar Ratio of Hydrocarbon Fuel
Understanding the molar ratio of hydrocarbon fuels, such as in the expression \(C_xH_y\), is essential for efficient fuel combustion in power plants. The molar ratio gives a clear idea about the proportion of hydrogen to carbon atoms in a fuel molecule. In our example, we derive this ratio by \((r = \frac{y}{x})\), where 'x' and 'y' represent the number of carbon and hydrogen atoms, respectively.

When analyzing combustion products, recognizing the molar ratio helps in calculating changes needed for optimal combustion. For instance, a higher ratio may indicate the need for more oxygen to ensure complete combustion of the fuel, which can be adjusted by the plant's control systems. This is vital for both the efficiency of the energy generation process and minimizing the impact on the environment by reducing incomplete combustion.
Excess Air Calculation
In any combustion process, the term 'excess air' refers to the amount of air that is more than what is theoretically required for a complete combustion of the fuel. Calculating excess air involves assessing the oxygen content in the combustion products. Too little air results in incomplete combustion, producing carbon monoxide and soot, while too much air wastes energy by heating up and expelling unused oxygen.

The correct amount ensures full combustion without wasting resources, reducing pollutants, and improving efficiency. By applying an excess air formula like the one used in our solution, power plants are able to adjust their combustion processes, optimizing performance and minimizing waste, aligning with environmental standards.
Air-to-Fuel Ratio
The air-to-fuel ratio is a crucial consideration in the operation of combustion engines and power plants. It is the ratio of the amount of air (usually measured in volume) to the amount of fuel (by weight) used in the combustion process. The ideal air-to-fuel ratio depends on the type of fuel being used and the conditions under which combustion takes place.

Using the ideal gas law, one can establish this ratio, ensuring all the fuel is burned completely, which is critical for the efficiency of the turbine. The example provided uses variables like temperature and pressure to define the air-to-fuel ratio, highlighting the importance of controlling environmental conditions to maintain a stable and efficient combustion process.
Environmental Impact of Fuel Combustion
The environmental impact of fuel combustion is widely understood to be significant. Combustion of hydrocarbon fuels typically releases carbon dioxide (\(CO_2\)), a greenhouse gas that contributes to global warming. Aside from \(CO_2\), the combustion process can also emit other harmful substances, such as sulfur and nitrogen compounds, which can lead to acid rain and contribute to air pollution.

Moreover, different fuels have varying impacts. For instance, oil can contain sulfur, leading to \(SO_x\) emissions, while natural gas combusted produces fewer pollutants. The sustainability of energy production is heavily dependent on the careful consideration of these factors, underlining the importance of optimizing combustion processes and choosing cleaner fuel sources where possible.

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Most popular questions from this chapter

The ultimate analysis of a No. 4 fuel oil is 86.47 wt\% carbon, \(11.65 \%\) hydrogen, \(1.35 \%\) sulfur, and the balance noncombustible inerts. This oil is burned in a steam-generating furnace with \(15 \%\) excess air. The air is preheated to \(175^{\circ} \mathrm{C}\) and enters the furnace at a gauge pressure of \(180 \mathrm{mm}\) Hg. The sulfur and hydrogen in the fuel are completely oxidized to \(\mathrm{SO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} ; 5 \%\) of the carbon is oxidized to \(\mathrm{CO}\), and the balance forms \(\mathrm{CO}_{2}\) (a) Calculate the feed ratio ( \(\mathrm{m}^{3}\) air) \(/(\mathrm{kg} \text { oil })\) (b) Calculate the mole fractions (dry basis) and ppm (parts per million on a wet basis, or moles contained in \(10^{6}\) moles of the wet stack gas) of the stack-gas species that might be considered environmental hazards.

Ethane at \(25^{\circ} \mathrm{C}\) and 1.1 atm (abs) flowing at a rate of \(100 \mathrm{mol} / \mathrm{s}\) is burned with \(20 \%\) excess oxygen at \(175^{\circ} \mathrm{C}\) and 1.1 atm \((\text { abs }) .\) The combustion products leave the furnace at \(800^{\circ} \mathrm{C}\) and 1 atm. (a) What is the volumetric flow rate of oxygen (L/s) fed to the furnace? (b) What should the volumetric flow rate of the combustion products be? State all assumptions you make. (c) The volumetric flow rate of the combustion products is measured and found to be different from the value calculated in Part (b). Assuming that no mistakes were made in the calculation, what could be going on that could lead to the discrepancy? Consider assumptions made in the calculations and things that can go wrong in a real system.

Ammonia is one of the chemical constituents of industrial waste that must be removed in a treatment plant before the waste can safely be discharged into a river or estuary. Ammonia is normally present in wastewater as aqueous ammonium hydroxide \(\left(\mathrm{NH}_{4}^{+} \mathrm{OH}^{-}\right) .\) A two- part process is frequently carried out to accomplish the removal. Lime (CaO) is first added to the wastewater, leading to the reaction $$\mathrm{CaO}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca}^{2+}+2\left(\mathrm{OH}^{-}\right)$$ The hydroxide ions produced in this reaction drive the following reaction to the right, resulting in the conversion of ammonium ions to dissolved ammonia: $$\mathrm{NH}_{4}^{+}+\mathrm{OH}^{-}=\mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})$$ Air is then contacted with the wastewater, stripping out the ammonia. (a) One million gallons per day of alkaline wastewater containing 0.03 mole \(\mathrm{NH}_{3} /\) mole ammoniafree \(\mathrm{H}_{2} \mathrm{O}\) is fed to a stripping tower that operates at \(68^{\circ} \mathrm{F}\). Air at \(68^{\circ} \mathrm{F}\) and 21.3 psia contacts the wastewater countercurrently as it passes through the tower. The feed ratio is \(300 \mathrm{ft}^{3}\) air/gal wastewater, and 93\% of the ammonia is stripped from the wastewater. Calculate the volumetric flow rate of the gas leaving the tower and the partial pressure of ammonia in this gas. (b) Briefly explain in terms a first-year chemistry student could understand how this process works. Include the equilibrium constant for the second reaction in your explanation. (c) This problem is an illustration of challenges associated with addressing undesirable releases into the environment; namely, in developing a process to prevent dumping ammonia into a waterway, the release is instead made to the atmosphere. Suppose you are to write an article for a newspaper on the installation of the process described in the beginning of this problem. Explain why the company is installing the two-part process, and then explain the ultimate fate of the ammonia. Take one of two positions - either that the release is harmless or that it jeopardizes the environment in the vicinity of the plant. since this is a newspaper article, it cannot be more than 800 words.

Hydrogen sulfide has the distinctive unpleasant odor associated with rotten eggs, and it is poisonous. It often must be removed from crude natural gas and is therefore a product of refining natural gas. In such instances, the Claus process provides a means of converting \(\mathrm{H}_{2} \mathrm{S}\) to elemental sulfur. Consider a feed stream to a Claus process that consists of 10.0 mole \(\% \mathrm{H}_{2} \mathrm{S}\) and \(90.0 \% \mathrm{CO}_{2}\). Onethird of the stream is sent to a furnace where the \(\mathrm{H}_{2} \mathrm{S}\) is burned completely with a stoichiometric amount of air fed at 1 atm and \(25^{\circ} \mathrm{C}\). The combustion reaction is $$\mathrm{H}_{2} \mathrm{S}+\frac{3}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{2}+\mathrm{H}_{2} \mathrm{O}$$ The product gases from this reaction are then mixed with the remaining two- thirds of the feed stream and sent to a reactor in which the following reaction goes to completion: $$2 \mathrm{H}_{2} \mathrm{S}+\mathrm{SO}_{2} \rightarrow 3 \mathrm{S}+2 \mathrm{H}_{2} \mathrm{O}$$ The gases leave the reactor at \(10.0 \mathrm{m}^{3} / \mathrm{min}, 320^{\circ} \mathrm{C},\) and \(205 \mathrm{kPa}\) absolute. Assuming ideal-gas behavior, determine the feed rate of air in kmol/min. Provide a single balanced chemical equation reflecting the overall process stoichiometry. How much sulfur is produced in \(\mathrm{kg} / \mathrm{min} ?\)

After being purged with nitrogen, a low-pressure tank used to store flammable liquids is at a total pressure of 0.03 psig. (a) If the purging process is done in the moming when the tank and its contents are at \(55^{\circ} \mathrm{F}\), what will be the pressure in the tank when it is at \(85^{\circ} \mathrm{F}\) in the afternoon? (b) If the maximum design gauge pressure of the tank is 8 inches of water, has the design pressure been exceeded? (c) Speculate on the purpose of purging the tank with nitrogen.
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