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Chapter 5: Problem 62

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.

Short Answer

Expert verified
The feed ratio and concentration of environmentally hazardous gases are calculated using stoichiometric considerations of chemical reactions in a combustion process. The results will provide insightful data regarding the fuel burning efficiency and the potential environmental impact.

Step by step solution

01

Calculation of feed ratio

To calculate the feed ratio or air/fuel ratio, stoichiometric calculations must be made. Every kilogram of fuel contains \(0.8647 \choose kg\ of\ C)^{-1}\), \(0.1165 \choose kg\ of\ H)^{-1}\), and \(0.0135 \choose kg\ of\ S)^{-1}\). Since a 15% excess in air supply is mentioned in the problem, we need to consider this as well. For all these elements to oxidize, stoichiometrically we need \(\frac{0.8647}{0.012} \choose kmol\ of\ O_2)^{-1}\) for \(C \rightarrow CO_2\), \(\frac{0.8647 \times 0.05}{0.012} \choose kmol\ of\ O_2)^{-1}\) for \(C \rightarrow CO\), \(\frac{0.1165}{0.008} \choose kmol\ of\ O_2)^{-1}\) for \(H \rightarrow H_2O\), and \(\frac{0.0135}{0.008} \choose kmol\ of\ O_2)^{-1}\) for \(S \rightarrow SO_2\) . Adding them up gives the minimum oxygen needed for combustion, and then by adding the 15% excess we can calculate total required oxygen. The volume of air required would then be calculated using \(R*T*v = P*V\) and simply using the molar volume of oxygen at STP (which is 22.4 \choose m^3/^{kmol}). This volume is then divided by mass of fuel burnt to get the feed ratio.
02

Calculation of mole fractions and ppm

For calculating the concentrations of environmental hazards, equlibrium is assumed and stoichiometry is again used to find the number of kmols of each species produced. The mole fractions are simply calculated by dividing number of moles of each gas by total moles of all gases. The species \(CO_2\), \(CO\), \(SO_2\) and \(N_2\) (comes from air and does not react) are considered here. For ppm calculations the mole fractions are multiplied by \(10^{6}\). The calculations are done assuming that all the reactions go to completion and no intermediate or other products are formed.
03

Check and verify

After the calculations of the mole fractions and ppm, recheck the calculations and verify if the sum of mole fractions is equal to 1. If the total sum of the mole fractions of all gases equals 1, the answer is verifiable, as this is a requirement in the calculation of the ratios of the components of a mixture.

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Key Concepts

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

Combustion Analysis
Combustion analysis refers to the process of thoroughly examining a substance to determine its elemental composition. This analysis specifically looks at how elements like carbon, hydrogen, and sulfur interact during combustion. In the case of No. 4 fuel oil, which consists of 86.47% carbon, 11.65% hydrogen, and 1.35% sulfur, it is essential to predict how these will convert to various oxides upon burning.

Combustion in industrial applications often involves excess air to ensure that all fuel is burnt, reducing pollutants and maximizing efficiency. For complete combustion, each chemical element requires a specific amount of oxygen, calculated from the chemical equations of their reactions, typically forming carbon dioxide (CO鈧�) for carbon, water (H鈧侽) for hydrogen, and sulfur dioxide (SO鈧�) for sulfur.

However, the reality of combustion is more complex. For instance, not all carbon in the fuel may form CO鈧�; some may oxidize to carbon monoxide (CO) due to insufficient oxygen or rapid combustion. Thus, when performing combustion analysis, it's crucial to capture the full picture, considering both perfect and imperfect conditions of combustion.
Environmental Impact Assessment
Environmental impact assessment (EIA) explores how a process, such as the combustion of fuel oil, affects the environment. Ideally, during combustion, hydrocarbons fully oxidize to form harmless water and carbon dioxide. However, when factors prevent complete combustion, pollutants like carbon monoxide, sulfur dioxide, and unburned hydrocarbons may form, posing significant environmental hazards.

These pollutants contribute to environmental issues such as air pollution, acid rain, and global warming. Carbon monoxide, a colorless odorless gas, can cause health problems like headaches and dizziness. Sulfur dioxide contributes to acid rain, damaging forests and aquatic habitats.

Through an EIA, we can compare the expected pollutants from a process and weigh them against acceptable environmental standards. This helps policy-makers and engineers to strategize better combustion practices or deploy treatment methods to mitigate emissions. Such strategies might include tweaking the fuel-air mix, installing scrubbers to capture sulfur compounds, or utilizing alternative fuels with lower sulfur content.
Gas Composition Calculation
Calculating the composition of gases resulting from combustion is key in both determining fuel efficiency and assessing potential emissions. In essence, you want to know what gases and in what quantities are born from the burning of fuel oil in a furnace.

Beginning with stoichiometric equations, you determine how much of each oxidizing agent (e.g., oxygen) is needed to react with the fuel components to finally compute the moles of each resultant gas. Each product gas has a mole fraction describing its proportion relative to the total gas mixture, calculated by dividing the moles of each analyte by the total moles of gases produced.

After finding the mole fractions, they can be converted to parts per million (ppm) to evaluate concentration levels of pollutants for regulatory purposes. The stack-gas composition includes carbon dioxide, carbon monoxide, sulfur dioxide, water vapor (from hydrogen combustion), and excess nitrogen (from unreacted atmospheric nitrogen). These calculations not only assist in understanding the combustion outcomes but also help in optimizing the process and improving emission control applications.

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Most popular questions from this chapter

The bacteria acetobacter aceti convert ethanol to acetic acid in the presence of oxygen according to the reaction $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+\mathrm{O}_{2} \rightarrow \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{H}_{2} \mathrm{O}$$ In a continuous fermentation process, ethanol enters the top of the fermenter at a rate of \(145 \mathrm{kg} / \mathrm{h}\), and the air fed to the bottom of the fermenter is \(25 \%\) in excess of the amount required to consume all of the ethanol. A gas stream containing nitrogen and unreacted oxygen leaves the top of the fermenter, and a liquid stream containing acetic acid, water, and \(10 \%\) of the entering ethanol leaves the bottom. Assume that none of the ethanol, water, and acetic acid in the reactor is vaporized. The fermenter operates at \(30^{\circ} \mathrm{C},\) maintains a liquid \((\mathrm{SG}=0.95)\) height of \(4.5 \mathrm{m},\) and is open to the atmosphere (i.e., the pressure at the top of the fermenter is 1 atm). (a) What is the volumetric flow rate of air as it enters the bottom of the fermenter? What is the volumetric flow rate of gas leaving the top of the fermenter? (b) Assume a linear relationship between the fraction of oxygen reacted and the position of gas bubbles rising through the liquid in the fermenter: for example, half of the oxygen reacted is consumed in the bottom half of the fermenter. At the vertical midpoint of the fermenter, the average bubble diameter is \(1.5 \mathrm{mm}\). What is the average bubble diameter at the entry point of the air and as the gas leaves the liquid at the top of the fermenter?

A tank in a room at \(19^{\circ} \mathrm{C}\) is initially open to the atmosphere on a day when the barometric pressure is 102 kPa. A block of dry ice (solid \(\mathrm{CO}_{2}\) ) with a mass of \(15.7 \mathrm{kg}\) is dropped into the tank, which is then sealed. The reading on the tank pressure gauge initially rises very quickly, then much more slowly, eventually reaching a value of 3.27 MPa. Assume \(T_{\text {final }}=19^{\circ} \mathrm{C}\) (a) How many moles of air were in the tank initially? Neglect the volume occupied by \(\mathrm{CO}_{2}\) in the solid state, and assume that a negligible amount of \(\mathrm{CO}_{2}\) escapes prior to the sealing of the tank. (b) Estimate the percentage error made by neglecting the volume of the block of dry ice placed in the tank. (The specific gravity of solid carbon dioxide is approximately 1.56 .) (c) What is the final density (g/L) of the gas in the tank? (d) Explain the observed variation of pressure with time. More specifically, what is happening in the tank during the initial rapid pressure increase and during the later slow pressure increase?

A balloon \(20 \mathrm{m}\) in diameter is filled with helium at a gauge pressure of 2.0 atm. A man is standing in a basket suspended from the bottom of the balloon. A restraining cable attached to the basket kecps the balloon from rising. The balloon (not including the gas it contains), the basket, and the man have a combined mass of \(150 \mathrm{kg}\). The temperature is \(24^{\circ} \mathrm{C}\) that day, and the barometer reads \(760 \mathrm{mm} \mathrm{Hg}\) (a) Calculate the mass (kg) and weight (N) of the helium in the balloon. (b) How much force is exerted on the balloon by the restraining cable? (Recall: The buoyant force on a submerged object equals the weight of the fluid- -in this case, the air- -displaced by the object. Neglect the volume of the basket and its contents.) (c) Calculate the initial acceleration of the balloon when the restraining cable is released. (d) Why does the balloon eventually stop rising? What would you need to know to calculate the altitude at which it stops? (e) Suppose at its point of suspension in midair the balloon is heated, raising the temperature of the helium. What happens and why?

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 \(\mathrm{kg} / \mathrm{min} ?\)

The lower flammability limit (LFL) and the upper flammability limit (UFL) of propane in air at 1 atm are, respectively, 2.3 mole \(\% \mathrm{C}_{3} \mathrm{H}_{8}\) and 9.5 mole \(\% \mathrm{C}_{3} \mathrm{H}_{8} .^{17}\) If the mole percent of propane in a propane-air mixture is between \(2.3 \%\) and \(9.5 \%,\) the gas mixture will burn explosively if exposed to a flame or spark; if the percentage is outside these limits, the mixture is safe-a match may burn in it but the flame will not spread. If the percentage of propane is below the LFL, the mixture is said to be too lean to ignite; if it is above the UFL, the mixture is too rich to ignite. (a) Which would be safer to release into the atmosphere- -a fuel-air mixture that is too lean or too rich to ignite? Explain. (b) A mixture of propane in air containing 4.03 mole \(\% \mathrm{C}_{3} \mathrm{H}_{8}\) is fed to a combustion furnace. If there is a problem in the furnace, the mixture is diluted with a stream of pure air to make sure that it cannot accidentally ignite. If propane enters the furnace at a rate of \(150 \mathrm{mol} \mathrm{C}_{3} \mathrm{H}_{8} / \mathrm{s}\) in the original fuel- air mixture, what is the minimum molar flow rate of the diluting air? (c) The actual diluting air molar flow rate is specified to be \(130 \%\) of the minimum value. Assuming the fuel mixture (4.03 mole\% \(\mathrm{C}_{3} \mathrm{H}_{8}\) ) enters the furnace at the same rate as in Part (b) at \(125^{\circ} \mathrm{C}\) and 131 kPa and the diluting air enters at \(25^{\circ} \mathrm{C}\) and \(110 \mathrm{kPa}\), calculate the ratio \(\left(\mathrm{m}^{3} \text { diluting air) } /\right.\) (m \(^{3}\) fuel gas) and the mole percent of propane in the diluted mixture. (d) Give several possible reasons for feeding air at a value greater than the calculated minimum rate.
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