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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 (COâ‚‚) for carbon, water (Hâ‚‚O) for hydrogen, and sulfur dioxide (SOâ‚‚) for sulfur.

However, the reality of combustion is more complex. For instance, not all carbon in the fuel may form COâ‚‚; 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

When a liquid or a gas occupies a volume, it may be assumed to fill the volume completely. On the other hand, when solid particles occupy a volume, there are always spaces (voids) among the particles. The porosity or void fraction of a bed of particles is the ratio (void volume)/(total bed volume). The bulk density of the solids is the ratio (mass of solids)/(total bed volume), and the absolute density of the solids has the usual definition (mass of solids)/(volume of solids). Suppose \(600.0 \mathrm{g}\) of a crushed ore is placed in a graduated cylinder, filling it to the \(184 \mathrm{cm}^{3}\) level. One hundred \(\mathrm{cm}^{3}\) of water is then added to the cylinder, whereupon the water level is observed to be at the \(233.5 \mathrm{cm}^{3}\) mark. Calculate the porosity of the dry particle bed, the bulk density of the ore in this bed, and the absolute density of the ore.

A process stream flowing at \(35 \mathrm{kmol} / \mathrm{h}\) contains 15 mole \(\%\) hydrogen and the remainder 1 -butene. The stream pressure is 10.0 atm absolute, the temperature is \(50^{\circ} \mathrm{C}\), and the velocity is \(150 \mathrm{m} / \mathrm{min}\). Determine the diameter (in \(\mathrm{cm}\) ) of the pipe transporting this stream, using Kay's rule in your calculations.

A stream of oxygen enters a compressor at \(298 \mathrm{K}\) and 1.00 atm at a rate of \(127 \mathrm{m}^{3} / \mathrm{h}\) and is compressed to \(358 \mathrm{K}\) and 1000 atm. Estimate the volumetric flow rate of compressed \(\mathrm{O}_{2},\) using the compressibility-factor equation of state.

A fuel gas containing \(86 \%\) methane, \(8 \%\) ethane, and \(6 \%\) propane by volume flows to a furnace at a rate of \(1450 \mathrm{m}^{3} / \mathrm{h}\) at \(15^{\circ} \mathrm{C}\) and \(150 \mathrm{kPa}\) (gauge), where it is burned with \(8 \%\) excess air. Calculate the required flow rate of air in SCMH (standard cubic meters per hour).

The label has come off a cylinder of gas in your laboratory. You know only that one species of gas is contained in the cylinder, but you do not know whether it is hydrogen, oxygen, or nitrogen. To find out, you evacuate a 5 -liter flask, seal it and weigh it, then let gas from the cylinder flow into it until the gauge pressure equals 1.00 atm. The flask is reweighed, and the mass of the added gas is found to be 13.0g. Room temperature is \(27^{\circ} \mathrm{C}\), and barometric pressure is 1.00 atm. What is the gas?

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