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Chapter 9: Problem 66

A gaseous fuel containing methane and ethane is burned with excess air. The fuel enters the furnace at \(25^{\circ} \mathrm{C}\) and 1 atm, and the air enters at \(200^{\circ} \mathrm{C}\) and 1 atm. The stack gas leaves the furnace at \(800^{\circ} \mathrm{C}\) and 1 atm and contains 5.32 mole\% \(\mathrm{CO}_{2}, 1.60 \%\) CO, \(7.32 \%\) O \(_{2}, 12.24 \% \mathrm{H}_{2} \mathrm{O}\), and the balance \(\mathrm{N}_{2}\). (a) Calculate the molar percentages of methane and ethane in the fuel gas and the percentage excess air fed to the reactor. (b) Calculate the heat (kJ) transferred from the reactor per cubic meter of fuel gas fed. (c) A proposal has been made to lower the feed rate of air to the furnace. State advantages and a drawback of doing so.

Short Answer

Expert verified
For task (a), the molar percentages of methane and ethane in the fuel gas and the percentage excess air fed to the reactor are computed based on stoichiometric relations and given stack gas composition. Task (b)'s answer is expressed in kJ, reflecting the heat balance for the reaction process. For task (c), describing the potential benefits and drawbacks of reducing the air feed requires understanding of the principles of combustion and furnace operation possibilities.

Step by step solution

01

Balance the combustion reaction

Write the chemical equations for combustion of methane (CH4) and ethane (C2H6), separately. Each fuel reacts with oxygen (O2) to form carbon dioxide (CO2) and water (H2O). Input these balanced equations here.
02

Back-calculate the molar percentages of methane and ethane in the fuel gas

Use the given stack gas composition and the balanced equations from Step 1 to back-calculate the amounts of reactants (CH4 and C2H6). Mathematics based on mole percentages will be required here.
03

Calculate the percentage excess air fed to the reactor

After finding the composition of the fuel gas in Step 2, calculate the stoichiometric amount of air needed for complete combustion. Compare this with the amount of air actually fed (we know it's excess because it's stated in the problem) to get the percentage excess air.
04

Calculate the heat transferred from the reactor per cubic meter of fuel gas fed

Use the known compositions, temperatures and heat capacities of the reactants and products to find the heat transferred per cubic meter of fuel gas. This step requires application of thermodynamics principles including the specific heat formula Q = mc螖T (where Q is heat, m is mass, c is specific heat and 螖T is the temperature difference).
05

Discuss the advantages and a drawback of lowering the air feed rate

Analyze the advantages and disadvantages of reducing the air feed rate under typical furnace operation. Based on principles of combustion and furnace operation, lower air feed rate may lead to improvement in overall combustion efficiency but could also cause incomplete combustion resulting in formation of harmful emissions and lowered heat output.

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Key Concepts

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

Chemical Engineering Education
Chemical engineering education lays the foundation for understanding complex processes like combustion reactions. It's crucial for students to grasp fundamental concepts such as balancing chemical equations, which is the first step in solving combustion problems. A strong grasp of thermodynamics is required as well, especially when calculating the heat transfer in reactors.

Students learn to apply these principles in real-world scenarios, such as analyzing furnace operations and reactor efficiency. In this context, knowing how to determine the composition of a fuel and calculate excess air are essential skills. The exercise in question challenges learners to use these concepts to analyze a gaseous fuel mixture burned with excess air, encouraging an application of theoretical knowledge to practical situations.
Stoichiometric Combustion Analysis
Stoichiometric combustion analysis is the process of quantifying the reactants and products in a combustion reaction to ensure the precise amount of oxygen is available for the complete burning of the fuel. This is vital for maintaining efficiency and minimizing harmful emissions in industrial processes.

An understanding of stoichiometry allows engineers to calculate the ideal ratios of fuel to oxygen. They use balanced chemical equations, as in the provided exercise where the combustion of methane and ethane is analyzed. By back-calculating the molar percentages of the fuel components, one can determine the precise fuel composition. This information is pivotal for optimizing reactions and ensuring complete combustion, which in turn maximizes energy output and minimizes pollutants such as carbon monoxide.
Heat Transfer in Reactors
Heat transfer in reactors is a fundamental aspect of chemical reactor design and operation. Reactors must be able to effectively manage the energy produced or consumed during reactions. In combustion reactions, such as the burning of methane and ethane in the given exercise, the heat transfer analysis determines how much heat is transferred from the reactor per unit of fuel gas fed.

Engineers use the specific heat formula \( Q = mc\Delta T \) to calculate the heat transfer, where \( Q \) is the heat transferred, \( m \) is the mass, \( c \) is the specific heat capacity of the substances involved, and \( \Delta T \) is the temperature change. This is critical for designing reactors that operate safely and efficiently. Additionally, the temperatures of the inlet and outlet streams are considered to accurately calculate the overall energy balance of the system.
Excess Air Calculation
Excess air calculation is used to determine the amount of air supplied to a reaction beyond the stoichiometric requirement. Providing excess air is common practice to ensure complete combustion, but it must be optimized to prevent energy loss and increase the efficiency of the combustion process.

In the exercise, the percentage of excess air fed to the reactor is calculated by comparing the stoichiometrically-required air to the actual air used. Ensuring the right amount of excess air is critical; too little can lead to incomplete combustion and higher emissions of pollutants, while too much can lower the combustion temperature and increase heat loss with the stack gases, thus reducing the reactor's thermal efficiency. Mastery of this calculation impacts the operational decisions in furnace management and is an excellent example of the application of chemical engineering principles.

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Most popular questions from this chapter

You are checking the performance of a reactor in which acetylene is produced from methane in the reaction $$2 \mathrm{CH}_{4}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g})$$ An undesired side reaction is the decomposition of acetylene: $$\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{g})$$ Methane is fed to the reactor at \(1500^{\circ} \mathrm{C}\) at a rate of \(10.0 \mathrm{mol} \mathrm{CH}_{4} / \mathrm{s}\). Heat is transferred to the reactor at a rate of \(975 \mathrm{kW}\). The product temperature is \(1500^{\circ} \mathrm{C}\) and the fractional conversion of methane is 0.600 . A flowchart of the process and an enthalpy table are shown below. (a) Using the heat capacitics given below for enthalpy calculations, write and solve material balances and an energy balance to determine the product component flow rates and the yield of acctylene (mol \(\mathbf{C}_{2} \mathbf{H}_{2}\) produced/mol \(\mathbf{C H}_{4}\) consumed). $$\begin{aligned}\mathrm{CH}_{4}(\mathrm{g}): & C_{p} \approx 0.079 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\ \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g}): & C_{p} \approx 0.052 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\ \mathrm{H}_{2}(\mathrm{g}): & C_{p} \approx 0.031 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\ \mathrm{C}(\mathrm{s}): & C_{p} \approx 0.022 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\end{aligned}$$ For example, the specific enthalpy of methane at \(1500^{\circ} \mathrm{C}\) relative to methane at \(25^{\circ} \mathrm{C}\) is \(\left[0.079 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]\left(1500^{\circ} \mathrm{C}-25^{\circ} \mathrm{C}\right)=116.5 \mathrm{kJ} / \mathrm{mol}\) (b) The reactor efficiency may be defined as the ratio (actual acetylene yield/acetylene yield with no side reaction). What is the reactor efficiency for this process? (c) The mean residence time in the reactor \([\tau(\mathrm{s})]\) is the average time gas molecules spend in the reactor in going from inlet to outlet. The more \(\tau\) increases, the greater the extent of reaction for every reaction occurring in the process. For a given feed rate, \(\tau\) is proportional to the reactor volume and inversely proportional to the feed stream flow rate. (i) If the mean residence time increases to infinity, what would you expect to find in the product stream? Explain. (ii) Someone proposes running the process with a much greater feed rate than the one used in Part (a), separating the products from the unconsumed reactants, and recycling the reactants. Why would you expect that process design to increase the reactor efficiency? What else would you need to know to determine whether the new design would be cost-effective?

In the production of many microelectronic devices, continuous chemical vapor deposition (CVD) processes are used to deposit thin and exceptionally uniform silicon dioxide films on silicon wafers. One CVD process involves the reaction between silane and oxygen at a very low pressure. $$\mathrm{SiH}_{4}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{SiO}_{2}(\mathrm{s})+2 \mathrm{H}_{2}(\mathrm{g})$$ The feed gas, which contains oxygen and silane in a ratio \(8.00 \mathrm{mol} \mathrm{O}_{2} / \mathrm{mol} \mathrm{SiH}_{4},\) enters the reactor at 298 \(\mathrm{K}\) and 3.00 torr absolute. The reaction products emerge at \(1375 \mathrm{K}\) and 3.00 torr absolute. Essentially all of the silane in the feed is consumed. (a) Taking a basis of \(1 \mathrm{m}^{3}\) of feed gas, calculate the moles of each component of the feed and product mixtures and the extent of reaction, \(\xi\) (b) Calculate the standard heat of the silane oxidation reaction (kJ). Then, taking the feed and product species at \(298 \mathrm{K}\left(25^{\circ} \mathrm{C}\right)\) as references, prepare an inlet-outlet enthalpy table and calculate and fill in the component amounts (mol) and specific enthalpies (kJ/mol). (See Example 9.5-1.) Data $$\left(\Delta \hat{H}_{\mathrm{f}}\right)_{\mathrm{SiH}_{4}(\mathrm{g})}=-61.9 \mathrm{kJ} / \mathrm{mol}, \quad\left(\Delta \hat{H}_{\mathrm{f}}^{\mathrm{o}}\right)_{\mathrm{SiO}_{2}(\mathrm{s})}=-851 \mathrm{kJ} / \mathrm{mol}$$ $$\left(C_{p}\right)_{\mathrm{SiH}_{4}(g)}[\mathrm{k} \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})]=0.01118+12.2 \times 10^{-5} T-5.548 \times 10^{-8} T^{2}+6.84 \times 10^{-12} T^{3}$$ $$\left(C_{p}\right)_{\mathrm{SiO}_{2}(\mathrm{s})}[\mathrm{kJ} /(\mathrm{mol} \cdot \mathrm{K})]=0.04548+3.646 \times 10^{-5} T-1.009 \times 10^{3} / T^{2}$$ The temperatures in the formulas for \(C_{p}\) are in kelvins. (c) Calculate the heat ( \(k\) J) that must be transferred to or from the reactor (state which it is). Then determine the required heat transfer rate ( \(\mathrm{kW}\) ) required for a reactor feed of \(27.5 \mathrm{m}^{3} / \mathrm{h}\).

Synthetically produced ethanol is an important industrial commodity used for various purposes, including as a solvent (especially for substances intended for human contact or consumption); in coatings, inks, and personal-care products; for sterilization; and as a fuel. Industrial cthanol is a petrochemical synthesized by the hydrolysis of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{v})$$ Some of the product is converted to diethyl ether in the undesired side reaction $$2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{v}) \rightleftharpoons\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}(\mathrm{v})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) $$The combined feed to the reactor contains 53.7 mole \(\% \mathrm{C}_{2} \mathrm{H}_{4}, 36.7 \% \mathrm{H}_{2} \mathrm{O}\) and the balance nitrogen, and enters the reactor at \(310^{\circ} \mathrm{C}\). The reactor operates isothermally at \(310^{\circ} \mathrm{C}\). An ethylene conversion of \(5 \%\) is achieved, and the yield of ethanol (moles cthanol produced/mole cthylene consumed) is 0.900 . Data for Diethyl Ether $$\begin{aligned}&\Delta \hat{H}_{f}^{\circ}=-271.2 \mathrm{kJ} / \mathrm{mol} \text { for the liquid }\\\ &\left.\Delta \hat{H}_{v}=26.05 \mathrm{kJ} / \mathrm{mol} \quad \text { (assume independent of } T\right)\end{aligned}$$ $$C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]=0.08945+40.33 \times 10^{-5} T\left(^{\circ} \mathrm{C}\right)-2.244 \times 10^{-7} T^{2}$$ (a) Calculate the reactor heating or cooling requirement in \(\mathrm{kJ} / \mathrm{mol}\) feed. (b) Why would the reactor be designed to yield such a low conversion of ethylene? What processing step (or steps) would probably follow the reactor in a commercial implementation of this process?

The standard heat of combustion \(\left(\Delta \hat{H}_{c}\right)\) of liquid 2,3,3 -trimethylpentane \(\left[\mathrm{C}_{8} \mathrm{H}_{18}\right]\) is reported in a table of physical properties to be \(-4850 \mathrm{kJ} / \mathrm{mol} .\) A footnote indicates that the reference temperature for the reported value is \(25^{\circ} \mathrm{C}\) and the presumed combustion products are \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\). (a) In your own words, briefly explain what all that means. (b) There is some question about the accuracy of the reported value, and you have been asked to determine the heat of combustion experimentally. You burn 2.010 grams of the hydrocarbon with pure oxygen in a constant-volume calorimeter and find that the net heat released when the reactants and products \(\left[\mathrm{CO}_{2}(\mathrm{g}) \text { and } \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\right]\) are all at \(25^{\circ} \mathrm{C}\) is sufficient to raise the temperature of \(1.00 \mathrm{kg}\) of liquid water by \(21.34^{\circ} \mathrm{C}\). Write an energy balance to show that the heat released in the calorimeter equals \(n_{\mathrm{C}_{3} \mathrm{H}_{18}} \Delta \hat{U}_{\mathrm{c}}^{\mathrm{S}},\) and calculate \(\Delta \tilde{U}_{\mathrm{c}}^{\mathrm{o}}(\mathrm{kJ} / \mathrm{mol}) .\) Then calculate \(\Delta \hat{H}_{c}^{c}\) (See Example 9.1-2.) By what percentage of the measured value does the tabulated value differ from the measured one? (c) Use the result of Part (b) to estimate \(\Delta \hat{H}_{f}\) for 2,3,3 -trimethylpentane. Why would the heat of formation of 2,3,3 -trimethylpentane probably be determined this way rather than directly from the formation reaction?

The production of most of the steel manufactured in the United States begins with the reduction of hematite ore (mostly ferric oxide) with coke (carbon) in a blast furnace to obtain pig iron. The basic reaction is $$\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}\left(77^{\circ} \mathrm{F}\right)=2.111 \times 10^{5} \mathrm{Btu}$$ Suppose that stoichiometric amounts of ferric oxide and carbon are fed at \(77^{\circ} \mathrm{F}\), the reaction is complete, the iron emerges as a liquid at \(2800^{\circ} \mathrm{F}\), and \(\mathrm{CO}\) emerges at \(570^{\circ} \mathrm{F}\). Perform the following calculations for a basis of 1 ton of iron produced. (a) Draw and label a flowchart and perform all the material balance calculations needed to determine the amounts (lb-mole) of each feed and product stream component. (b) Taking the reactant and product species in their normal states at \(77^{\circ} \mathrm{F}\) as references, prepare an inlet-outlet enthalpy table and calculate and fill in all unknown component specific enthalpies (Btu/lb- mole). Use the following physical property data for iron: \(\mathrm{Fe}(\mathrm{s}): \quad C_{p}\left[\mathrm{B} \operatorname{tu} /\left(\mathrm{lb}-\mathrm{mole} \cdot^{\circ} \mathrm{F}\right)\right]=5.90+1.50 \times 10^{-3} T\left(^{\circ} \mathrm{F}\right)\) \(T_{\mathrm{m}}=2794^{\circ} \mathrm{F}, \quad \Delta \hat{H}_{\mathrm{m}}\left(T_{\mathrm{m}}\right)=6496 \mathrm{Btu} / \mathrm{lb}-\mathrm{mole}\) \(\mathrm{Fe}(\mathrm{l}): \quad C_{p}\left[\mathrm{Btu} /\left(\mathrm{lb}-\mathrm{mole} \cdot^{\circ} \mathrm{F}\right)\right]=8.15\) (c) Estimate the furnace heat requirement (Btu/ton Fe produced). (d) List the assumptions that make the value calculated in Part (c) only an approximate estimate of the furnace heat requirement. (One of the assumptions has something to do with the reactor pressure.)
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