/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 99 A fuel oil is fed to a furnace a... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 99

A fuel oil is fed to a furnace and burned with \(25 \%\) excess air. The oil contains \(87.0 \mathrm{wt} \% \mathrm{C}, 10.0 \% \mathrm{H},\) and 3.0\% S. Analysis of the furnace exhaust gas shows only \(\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{CO}_{2}, \mathrm{SO}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}\). The sulfur dioxide emission rate is to be controlled by passing the exhaust gas through a scrubber, in which most of the \(\mathrm{SO}_{2}\) is absorbed in an alkaline solution. The gases leaving the scrubber (all of the \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{CO}_{2}\), and some of the \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{SO}_{2}\) entering the unit) pass out to a stack. The scrubber has a limited capacity, however, so that a fraction of the furnace exhaust gas must be bypassed directly to the stack. At one point during the operation of the process, the scrubber removes \(90 \%\) of the \(\mathrm{SO}_{2}\) in the gas fed to it, and the combined stack gas contains 612.5 ppm (parts per million) \(\mathrm{SO}_{2}\) on a dry basis; that is, every million moles of dry stack gas contains 612.5 moles of \(\mathrm{SO}_{2}\). Calculate the fraction of the exhaust bypassing the scrubber at this moment.

Short Answer

Expert verified
After solving the final equation derived from the SO鈧� balance in the stack gas, the value of \(\alpha\), which represents the fraction of the exhaust bypassing the scrubber, is obtained.

Step by step solution

01

- Calculate the moles of SO鈧� produced

The first step is to determine how much SO鈧� is produced by burning the fuel oil. Given that the fuel oil is composed of 87% Carbon (C), 10% Hydrogen (H) and 3% Sulphur (S) by weight, the moles of S in 1 kg of fuel oil can be found using the formula \(\frac{weight \% of S}{molar mass of S}\), which equals \(\frac{3 \%}{32 g/mol} = 0.09375 mol\). Each mole of S produces a mole of SO鈧� when burned, so the moles of SO鈧� produced equals 0.09375 mol/kg.
02

- Calculate the SO鈧� released from scrubber

In this step, we determine the amount of SO鈧� released by the scrubber. The scrubber absorbs 90% of the incoming SO鈧�, which means 10% of the SO鈧� is released. The amount of the released SO鈧� equals to \(10 \%\) of the incoming SO鈧�, which is \(0.09375 mol/kg * 10 \% = 0.009375 mol/kg\).
03

- Determine the moles of dry stack gases

The dry stack gases were described as having 612.5 ppm of SO鈧�. This means that for every million (1e6) moles of dry stack gas, there are 612.5 moles of SO鈧�. Hence, 1 mol of dry stack gas is associated with \( \frac{612.5 mol of \, SO_{2}}{1e6 mol of \, stack \, gas} = 6.125e-4 mol of \, SO_{2}\).
04

- Calculate the fraction that bypasses the scrubber

In the final step, we can determine the fraction of exhaust that bypasses the scrubber. The total SO鈧� in stack gases is a sum of the SO鈧� from the bypassed gas and the SO鈧� released by the scrubber. If \(\alpha\) is the fraction of exhaust gas that bypasses the scrubber, the moles of SO鈧� in bypassed gas will be \(0.09375 \alpha mol/kg\). The complete balance of SO鈧� in the stack gas gives us the equation \(0.09375 \alpha + 0.009375 = 6.125e-4 \times (1 + \alpha)\). Solving this equation gives the value of \(\alpha\).

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Key Concepts

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

Furnace Emissions
Understanding furnace emissions is crucial, especially due to their environmental impact. When fuel oil is burned in a furnace, it emits various gases. Among these emissions are nitrogen (\( \mathrm{N}_2 \)), oxygen (\( \mathrm{O}_2 \)), carbon dioxide (\( \mathrm{CO}_2 \)), sulfur dioxide (\( \mathrm{SO}_2 \)), and water vapor (\( \mathrm{H}_2\mathrm{O} \)). The composition of the fuel directly affects the emission profile.
The excessive air introduced into the system, in this case, 25% more than needed for complete combustion, ensures that complete combustion of the carbon and hydrogen occurs. However, it also amplifies the production of nitrogen oxides and, notably, \( \mathrm{SO}_2 \) from sulfur in the fuel oil. \( \mathrm{SO}_2 \) is a major pollutant, contributing to acid rain formation and respiratory problems in humans and animals. This highlights the need for effective emission control strategies, such as scrubbers, to limit the release of these hazardous components into the atmosphere.
Scrubber Systems
Scrubber systems are a vital component in reducing harmful emissions from industrial exhausts. They work by cleaning or 'scrubbing' flue gases of undesirable pollutants, absorbing substances like \( \mathrm{SO}_2 \) in an alkaline solution. The interaction with the solution neutralizes the acidic nature of \( \mathrm{SO}_2 \), typically converting it to a salt. In the described exercise, the scrubber removes up to 90% of entering \( \mathrm{SO}_2 \). This is significant because it limits the environmental damage the emissions can cause.
However, scrubbers are not 100% efficient and have operational limits. Some gases bypass the system entirely, as seen in the problem where a portion of exhaust gases are not scrubbed. This bypass ensures that the system doesn鈥檛 exceed its capacity, but emphasizes the importance of optimizing scrubber operation to balance emissions reduction with functional constraints.
Sulfur Dioxide Control
Controlling sulfur dioxide emissions is key to reducing air pollution and its adverse effects on health and the environment. \( \mathrm{SO}_2 \) is a byproduct of burning sulfur-containing fuels, such as oil or coal. Without intervention, these emissions can lead to acid rain, harm aquatic life, damage forests, and affect air quality.
One approach in sulfur dioxide control is through chemical reactions in scrubber systems, where the \( \mathrm{SO}_2 \) is captured and neutralized. By calculating the fraction of exhaust bypassing a scrubber, operators can better manage and predict emission levels, further regulating \( \mathrm{SO}_2 \) release. It is essential to continually monitor and adapt these systems to maintain compliance with environmental standards and reduce ecological impact.

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Most popular questions from this chapter

A garment to protect the wearer from toxic agents may be made of a fabric that contains an adsorbent, such as activated carbon. In a test of such a fabric, a gas stream containing \(7.76 \mathrm{mg} / \mathrm{L}\) of carbon tetrachloride (CCl_) was passed through a 7.71-g sample of the fabric at a rate of 1.0 L/min, and the concentration of \(\mathrm{CCl}_{4}\) in the gas leaving the fabric was monitored. The run was continued for \(15.5 \mathrm{min}\) with no \(\mathrm{CCl}_{4}\) being detected, after which the \(\mathrm{CCl}_{4}\) concentration began to rise. (a) How much CCl_ was fed to the system during the first 15.5 min of the run? How much was adsorbed? Using this information as a guide, sketch the expected concentration of \(\mathrm{CCl}_{4}\) in the exit gas as a function of time, showing the curve from \(t=0\) to \(t \gg 15.5\) min. (b) Assuming a linear relationship between amount of \(\mathrm{CCl}_{4}\) adsorbed and mass of fabric, what fabric mass would be required if the feed concentration is \(5 \mathrm{mg} / \mathrm{L},\) the feed rate \(1.4 \mathrm{L} / \mathrm{min},\) and it is desired that no \(\mathrm{CCl}_{4}\) leave the fabric earlier than 30 min?

Under the FutureGen 2.0 project (http:///www.futuregenalliance.org/) sponsored by the U.S. Department of Energy, a novel process is used to convert coal into electricity with minimal greenhouse gas \(\left(\mathrm{CO}_{2}\right)\) emissions to the atmosphere. In the process, coal is combusted in a boiler with pure \(\mathrm{O}_{2}\); the heat released produces steam, which is then used for heating and to drive turbines that generate electricity. An excess of \(\mathrm{O}_{2}\) is supplied to the boiler to convert all the coal into a flue gas consisting of carbon dioxide, steam, and any unreacted oxygen. The mass flow rate of coal to the boiler is \(50 \mathrm{kg} / \mathrm{s}\), and \(\mathrm{O}_{2}\) is fed in \(8.33 \%\) excess. For the purposes of this analysis, the chemical formula of coal can be approximated as \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O}_{2}\) (a) Draw and label the flowchart and carry out the degree-of-freedom analysis using balances on atomic species. (b) Determine the molar flow of oxygen supplied to the boiler. (c) Solve for the remaining unknown flow rates and mole fractions. Determine the molar composition of the flue gas on a dry basis. (d) A feature that makes the FutureGen power plant unique is the intent to capture the \(\mathrm{CO}_{2}\) generated, compress it, and pump it into deep geological formations in which it will be permanently stored. List at least two safety or environmental issues that should be considered in the construction and operation of this plant. (e) List at least two pros and two cons of using pure \(O_{2}\) versus air.

\- An equimolar liquid mixture of benzene and toluene is separated into two product streams by distillation. A process flowchart and a somewhat oversimplified description of what happens in the process follow: Inside the column a liquid stream flows downward and a vapor stream rises. At each point in the column some of the liquid vaporizes and some of the vapor condenses. The vapor leaving the top of the column, which contains 97 mole\% benzene, is completely condensed and split into two equal fractions: one is taken off as the overhead product stream, and the other (the reflux) is recycled to the top of the column. The overhead product stream contains \(89.2 \%\) of the benzene fed to the column. The liquid leaving the bottom of the column is fed to a partial reboiler in which \(45 \%\) of it is vaporized. The vapor generated in the reboiler (the boilup) is recycled to become the rising vapor stream in the column, and the residual reboiler liquid is taken off as the bottom product stream. The compositions of the streams leaving the reboiler are governed by the relation $$\frac{y_{\mathrm{B}} /\left(1-y_{\mathrm{B}}\right)}{x_{\mathrm{B}} /\left(1-x_{\mathrm{B}}\right)}=2.25$$ where \(y_{\mathrm{B}}\) and \(x_{\mathrm{B}}\) are the mole fractions of benzene in the vapor and liquid streams, respectively. (a) Take a basis of 100 mol fed to the column. Draw and completely label a flowchart, and for each of four systems (overall process, column, condenser, and reboiler), do the degree-of-freedom analysis and identify a system with which the process analysis might appropriately begin (one with zero degrees of freedom). (b) Write in order the equations you would solve to determine all unknown variables on the flowchart, circling the variable for which you would solve in each equation. Do not do the calculations in this part. (c) Calculate the molar amounts of the overhead and bottoms products, the mole fraction of benzene in the bottoms product, and the percentage recovery of toluene in the bottoms product \((100 \times\) moles toluene in bottoms/mole toluene in feed).

The reaction between ethylene and hydrogen bromide to form ethyl bromide is carried out in a continuous reactor. The product stream is analyzed and found to contain 51.7 mole \(\% \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}\) and 17.3\% HBr. The feed to the reactor contains only ethylene and hydrogen bromide. Calculate the fractional conversion of the limiting reactant and the percentage by which the other reactant is in excess. If the molar flow rate of the feed stream is \(165 \mathrm{mol} / \mathrm{s}\), what is the extent of reaction?

Eggs are sorted into two sizes (large and extra large) at the Cheerful Chicken Coop. Recently, the economic downturn has not allowed Cheerful Chicken to repair the egg-sorting machine bought in 2000. Instead, the company has Chick Poulet, one of the firm's sharper-eyed employees, stamp the big eggs with a "Large" rubber stamp in her right hand and the really big eggs with an "X-large" stamp in her left as the eggs go by on a conveyor belt. Down the line, another employee puts the eggs into one of two hoppers, each egg according to its stamp. On average Chick breaks \(8 \%\) of the 120 eggs that pass by her each minute. At the same time, a check of the "X-large" stream reveals a flow rate of 70 eggs/min, of which 8 eggs/min are broken. (a) Draw and label a flowchart for this process. (b) Write and solve balances about the egg sorter on total eggs and broken eggs. (c) How many "large" eggs leave the plant each minute, and what fraction of them are broken? (d) Is Chick right- or left-handed?
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