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Chapter 9: Problem 67

A coal contains \(73.0 \mathrm{wt} \% \mathrm{C}, 4.7 \% \mathrm{H}\) (not including the hydrogen in the coal moisture), \(3.7 \% \mathrm{S}, 6.8 \% \mathrm{H}_{2} \mathrm{O}\) and \(11.8 \%\) ash. The coal is burned at a rate of \(50,000 \mathrm{lb}_{\mathrm{m}} / \mathrm{h}\) in a power-plant boiler with air \(50 \%\) in excess of that needed to oxidize all the carbon in the coal to \(\mathrm{CO}_{2}\). The air and coal are both fedat \(77^{\circ} \mathrm{F}\) and 1 atm. The solid residue from the furnace is analyzed and is found to contain \(28.7 \mathrm{wt} \% \mathrm{C}, 1.6 \% \mathrm{S},\) and the balance ash. The sulfur oxidized in the furnace is converted to \(\mathrm{SO}_{2}(\mathrm{g}) .\) Of the ash in the coal, \(30 \%\) emerges in the solid residue and the balance is emitted with the stack gases as fly ash. The stack gas and solid residue emerge from the furnace at \(600^{\circ} \mathrm{F}\). The higher heating value of the coal is \(18,000 \mathrm{Btu} / \mathrm{b}_{\mathrm{m}}\). (a) Calculate the mass flow rates of all components in the stack gas and the volumetric flow rate of this gas. (Tgnore the contribution of the fly ash in the latter calculation, and assume that the stack gas contains a negligible amount of CO.) (b) Assume that the heat capacity of the solid furnace residuc is \(0.22 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right),\) that of the stack gas is the heat capacity per unit mass of nitrogen, and \(35 \%\) of the heat generated in the furnace is used to produce electricity. At what rate in \(\mathrm{MW}\) is electricity produced? (c) Calculate the ratio (heat transferred from the furnace)/(heating value of the fuel). Why is this ratio less than one? (d) Suppose the air fed to the furnace were preheated rather than being fed at ambient temperature, but that everything else (feed rates, outlet temperatures, and fractional coal conversion) were the same. What effect would this change have on the ratio calculated in Part (c)? Explain. Suggest an economical way in which this preheating might be accomplished. Exploratory Exercises - Research and Discover (e) At least three components of the stack gas from the power plant raise significant environmental concerns. Identify the components, explain why they are considered problems, and describe how the problems can be addressed in a modern coal-fired power plant. (f) Several minor constituents of coal were not mentioned in the problem statement, and yet they may be part of the stack gas. Identify one such species and, as in Part (e), explain why it is a problem and how the problem cither is or could be addressed in a modern coal-fired power plant.

Short Answer

Expert verified
The exact numerical answers will depend on the calculations performed in the steps above, but the main conclusions include: the amount of electricity produced is determined by the heating value of the coal and the efficiency of its combustion; the heat transferred from the furnace is less than the heating value of the coal because of energy losses; preheating the air would increase the efficiency; environmentally problematic components include SO2, CO, NOx and minor constituents such as arsenic.

Step by step solution

01

Calculate the mass flow rates of all components in the stack gas

In order to find this, one needs to define all the appropriate reactions and make sure that all inputs and outputs are covered. Then, Stoichiometry is used to calculate the outputs given the inputs and the percentage of reactions. This will involve setting up several equations based on the reactions and solving for each of the required output rates.
02

Calculate rate of electricity production

The rate of electricity production is calculated by taking 35 % of the heat generated and converting from btu/h to MW by using appropriate conversion factors. The heat generated is calculated by the higher heating value multiplied by the rate the coal is burned.
03

Calculate heat transfer ratio

The ratio (heat transferred from the furnace)/(heating value of the fuel) is less than one because not all of the energy from the fuel can be transferred. There are losses like energy used in the combustion process and heat lost to the environment.
04

Analyze the effect of preheating the air to the furnace

Preheating the air would increase the ratio calculated in Part (c) as less energy would be required for the combustion process. This would reduce the heat lost in bringing the air to the combustion temperature. An efficient way to preheat the air would be using the outgoing waste heat from the combustion.
05

Identify and discuss environmental concerns

Three concerning components could include sulfur dioxide, carbon monoxide, and nitrogen oxides. These are problems due to their contribution to air pollution and the human health problems caused by it. The problems can be alleviated with technologies such as scrubbers, efficient burners, and selective catalytic reduction.
06

Discuss minor constituents of coal and their impact

One such minor component could be arsenic. It poses a significant risk to human health and the environment. It can be reduced in the stack gas by use of scrubbers and filters.

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Key Concepts

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

Stoichiometry
Stoichiometry serves as a fundamental concept in chemical process analysis, particularly when examining reactions, such as the combustion of coal in a power-plant boiler. It involves quantitatively studying the ratios of reactants and products in chemical reactions. In the context of our exercise, understanding stoichiometry is crucial for calculating the mass flow rates of the various components in the stack gas.

For the given exercise, stoichiometry helped identify the required reactions, such as the combustion of carbon (C) to form carbon dioxide (CO2), hydrogen (H) to water (H2O), and sulfur (S) to sulfur dioxide (SO2). With an excess of 50% air, we can determine the amount of oxygen (O2) involved and subsequently the volume of nitrogen (N2), which remains largely unreacted but affects the stack gas composition. We can apply the law of conservation of mass to set up equations that reflect the balance of mass in these reactions and solve for the mass flow rates based on the known input quantities and compound stoichiometries.
Furnace Heat Transfer
Furnace heat transfer is an integral part of thermal engineering and is particularly relevant when analyzing combustion processes in industrial furnaces. In our exercise, the furnace converts the chemical energy stored in coal to thermal energy, a portion of which is then transformed into electricity. The efficiency of this transfer is quantified in part 'c' of the exercise, where we calculate the ratio of the heat transferred from the furnace relative to the fuel's heating value.

Why isn't this ratio equal to one? Simply put, it is due to the second law of thermodynamics: not all the heat can be converted into work, and some is inevitably lost to the surroundings or used up in the process itself, for instance, in preheating the combustion air or overcoming the heat capacity of the incoming fuel and air. The heat capacity of the solid furnace residue and the stack gas, as well as the temperature at which the stack gas and solid residue are discharged, are pivotal in understanding these heat losses and, thus, the furnace's overall efficiency.
Environmental Impact of Combustion
The environmental impact of combustion, especially in coal-fired power plants, raises significant concerns that cannot be overlooked. Part 'e' of the exercise prompts us to consider components of the stack gas that affect the environment: sulfur dioxide (SO2), carbon monoxide (CO), and nitrogen oxides (NOx).

Sulfur dioxide contributes to acid rain and respiratory issues, carbon monoxide binds to hemoglobin and impairs oxygen transport in the bloodstream, and nitrogen oxides are involved in the formation of ozone and smog. Modern power plants mitigate these issues through a variety of methods:
  • Scrubbers can remove SO2 from flue gases.
  • Efficient combustion technologies lower CO production.
  • Selective catalytic reduction (SCR) systems can reduce NOx emissions.
Moreover, proper handling of minor constituents like arsenic is essential to prevent environmental contamination and health hazards. This might involve additional advanced filtration technologies to capture such harmful species before they are released into the atmosphere.

In summary, while coal combustion is a significant source of energy, it is vital to implement technologies and practices that minimize its environmental footprint, ensuring compliance with regulatory standards and protecting public health.

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Most popular questions from this chapter

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.

The synthesis of cthyl chloride is accomplished by reacting ethylene with hydrogen chloride in the presence of an aluminum chloride catalyst: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{HCl}(\mathrm{g}) \stackrel{\text { catallyst }}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{g}) ; \quad \Delta H_{\mathrm{r}}\left(0^{\circ} \mathrm{C}\right)=-64.5 \mathrm{kJ}$$ Process data and a simplified schematic flowchart are given here. Data Reactor: adiabatic, outlet temperature \(=50^{\circ} \mathrm{C}\) Feed A: \(100 \% \mathrm{HCl}(\mathrm{g}), 0^{\circ} \mathrm{C}\) Feed \(\mathrm{B}: 93\) mole \(\% \mathrm{C}_{2} \mathrm{H}_{4}, 7 \% \mathrm{C}_{2} \mathrm{H}_{6}, 0^{\circ} \mathrm{C}\) Reactor: adiabatic, outlet temperature \(=50^{\circ} \mathrm{C}\) Feed A: 100\% HCl(g), 0"C Feed B: 93 mole\% C_H_4, 7\% C_H_0, 0"C Product C: Consists of 1.5\% of the HCl, 1.5\% of the C_2 \(\mathrm{H}_{4}\), and all of the \(\mathrm{C}_{2} \mathrm{H}_{6}\) that enter the reactor Product D: \(1600 \mathrm{kg} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{l}) / \mathrm{h}, 0^{\circ} \mathrm{C}\) Recycle to reactor: \(\mathbf{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{l}), 0^{\circ} \mathrm{C}\) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}: \Delta \hat{H}_{\mathrm{y}}=24.7 \mathrm{kJ} / \mathrm{mol}\) (assume independent of \(T\) ) \(\left(C_{p}\right)_{C_{2} H_{3} C(v)}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]=0.052+8.7 \times 10^{-5} T\left(^{\circ} \mathrm{C}\right)\) The reaction is exothermic, and if the heat of reaction is not removed in some way, the reactor temperature could increase to an undesirably high level. To avoid this occurrence, the reaction is carried out with the catalyst suspended in liquid cthyl chloride. As the reaction proceeds, most of the heat liberated goes to vaporize the liquid, making it possible to keep the reaction temperature at or below 50^'C. The stream leaving the reactor contains cthyl chloride formed by reaction and that vaporized in the reactor. This stream passes through a heat exchanger where it is cooled to \(0^{\circ} \mathrm{C},\) condensing essentially all of the cthyl chloride and leaving only unreacted \(\mathrm{C}_{2} \mathrm{H}_{4}, \mathrm{HCl}\), and \(\mathrm{C}_{2} \mathrm{H}_{6}\) in the gas phase. A portion of the liquid condensate is recycled to the reactor at a rate equal to the rate at which ethyl chloride is vaporized, and the rest is taken off as product. At the process conditions, heats of mixing and the influence of pressure on enthalpy may be neglected. (a) At what rates (kmol/h) do the two feed streams enter the process? (b) Calculate the composition (component mole fractions) and molar flow rate of product stream \(\mathrm{C}\). (c) Write an energy balance around the reactor and use it to determine the rate at which ethyl chloride must be recycled. (d) A number of simplifying assumptions were made in the process description and the analysis of this process system, so the results obtained using a more realistic simulation would differ considerably from those you should have obtained in Parts (a)-(c). List as many of these assumptions as you can think of.

Methane is bumed with \(25 \%\) excess air in a continuous adiabatic reactor. The methane enters the reactor at \(25^{\circ} \mathrm{C}\) and 1.10 atm at a rate of \(550 \mathrm{L} / \mathrm{s}\), and the entering air is at \(150^{\circ} \mathrm{C}\) and 1.1 atm. Combustion in the reactor is complete, and the reactor effluent gas emerges at 1.05 atm. (a) Calculate the temperature and the degrees of superheat of the reactor effluent. (Consider water to be the only condensable species in the effluent.) (b) Suppose only 15\% excess air is supplied. Without doing any additional calculations, state how the temperature and degrees of superheat of the reactor effluent would be affected lincrease, decrease, remain the same, cannot tell without more information] and explain your reasoning. What risk is involved in lowering the percent excess air?

Carbon disulfide, a key component in the manufacture of rayon fibers, is produced in the reaction between methane and sulfur vapor over a metal oxide catalyst: $$\begin{array}{c}\mathrm{CH}_{4}(\mathrm{g})+4 \mathrm{S}(\mathrm{v}) \rightarrow \mathrm{CS}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) \\ \Delta H_{\mathrm{r}}\left(700^{\circ} \mathrm{C}\right)=-274 \mathrm{kJ} \end{array}$$ Methane and molten sulfur, each at \(150^{\circ} \mathrm{C}\), are fed to a heat exchanger in stoichiometric proportion. Heat is exchanged between the reactor feed and product streams, and the sulfur in the feed is vaporized. The gascous methane and sulfur leave the exchanger and pass through a second preheater in which they are heated to \(700^{\circ} \mathrm{C}\), the temperature at which they enter the reactor. Heat is transferred from the reactor at a rate of \(41.0 \mathrm{kJ} / \mathrm{mol}\) of feed. The reaction products emerge from the reactor at \(800^{\circ} \mathrm{C}\), pass through the heat exchanger, and emerge at \(200^{\circ} \mathrm{C}\) with sulfur as a liquid. Use the following heat capacity data to perform the requested calculations: \(C_{p}\left[J /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right] \approx 29.4\) for \(\mathrm{S}(1), 36.4\) for \(\mathrm{S}(\mathrm{v}), 71.4\) for \(\mathrm{CH}_{4}(\mathrm{g}), 31.8\) for \(\mathrm{CS}_{2}(\mathrm{v}),\) and 44.8 for \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) (a) Estimate the fractional conversion achieved in the reactor. In enthalpy calculations, take the feed and product species at \(700^{\circ} \mathrm{C}\) as references. (b) Suppose the heat of reaction at \(700^{\circ} \mathrm{C}\) had not been given. What would be different in your solution to Part (a)? (Be thorough in your explanation.) Sketch the process paths from the feed to the products built into both the calculation of Part (a) and your alternative calculation. Explain why the result would be the same regardless of which method you used. (c) Suggest a method to improve the energy economy of the process.

The standard heat of the combustion reaction of liquid \(n\) -hexane to form \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l}),\) with all reactants and products at \(77^{\circ} \mathrm{F}\) and 1 atm, is \(\Delta H_{\mathrm{r}}^{\prime}=-1.791 \times 10^{6} \mathrm{Btu} .\) The heat of vaporization of hexane at \(77^{\circ} \mathrm{F}\) is \(13,550 \mathrm{Btu} / \mathrm{b}\) -mole and that of water is \(18.934 \mathrm{Btu} / \mathrm{h}\) -mole. (a) Is the reaction exothermic or endothermic at \(77^{\circ} \mathrm{F}\) ? Would you have to heat or cool the reactor to keep the temperature constant? What would the temperature do if the reactor ran adiabatically? What can you infer about the energy required to break the molecular bonds of the reactants and that released when the product bonds form? (b) Use the given data to calculate \(\Delta H_{\mathrm{r}}^{\mathrm{r}}\) (Btu) for the combustion of \(n\) -hexane vapor to form \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\overline{\mathrm{H}}_{2} \mathrm{O}(\mathrm{g})\) (c) If \(\dot{Q}=\Delta \dot{H},\) at what rate in \(\mathrm{B}_{\text {tu } / \mathrm{s}}\) is heat absorbed or released (state which) if \(120 \mathrm{lb}_{\mathrm{n}} / \mathrm{s}\) of \(\mathrm{O}_{2}\) is consumed in the combustion of hexane vapor, water vapor is the product, and the reactants and products are all at \(77^{\circ} \mathrm{F} ?\) (d) If the reaction were carried out in a real reactor, the actual value of \(\dot{Q}\) would be greater (less negative) than the value calculated in Part (c). Explain why.
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