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Chapter 9: Problem 72

A bituminous coal is burned with air in a boiler furnace. The coal is fed at a rate of \(40,000 \mathrm{kg} / \mathrm{h}\) and has an ultimate analysis of 76 wt\% \(\mathrm{C}, 5 \%\) H, \(8 \%\) O, negligible amounts of \(\mathrm{N}\) and \(\mathrm{S}\), and \(11 \%\) noncombustible ash (see Problem 9.58), and a higher heating value of 25,700 kJ/kg. Air enters a preheater at \(30^{\circ} \mathrm{C}\) and 1 atm with a relative humidity of \(30 \%,\) exchanges heat with the hot flue gas leaving the furnace, and enters the furnace at temperature \(T_{\mathrm{a}}\left(^{\circ} \mathrm{C}\right) .\) The flue gas contains 7.71 mole\% \(\mathrm{CO}_{2}\) and 1.29 mole \(\%\) CO on \(a\) dry basis, and the balance is a mixture of \(\mathrm{O}_{2}, \mathrm{N}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}\). It emerges from the furnace at \(260^{\circ} \mathrm{C}\) and is cooled to \(150^{\circ} \mathrm{C}\) in the preheater. Noncombustible residue (slag) leaves the furnace at \(450^{\circ} \mathrm{C}\) and has a heat capacity of \(0.97 \mathrm{kJ} / \mathrm{kg} \cdot^{\cdot} \mathrm{C}\) ).. (a) Prove that the air-to-fuel ratio is 16.1 standard cubic meters/kg coal and that the flue gas contains \(4.6 \% \mathrm{H}_{2} \mathrm{O}\) by volume. (b) Calculate the rate of cooling required to cool the flue gas from \(260^{\circ} \mathrm{C}\) to \(150^{\circ} \mathrm{C}\) and the temperature to which the air is preheated. (Note: A trial-and-error calculation is required.) (c) If \(60 \%\) of the heat transferred from the furnace \((-Q)\) goes into producing saturated steam at 30 bar from liquid boiler feedwater at \(50^{\circ} \mathrm{C},\) at what rate \((\mathrm{kg} / \mathrm{h})\) is steam generated?

Short Answer

Expert verified
Proved the air-to-fuel ratio to be 16.1 standard cubic meters/kg coal and the flue gas contains \(4.6 \% \mathrm{H}_{2} \mathrm{O}\) by volume. The rate of cooling required to cool the flue gas from \(260^{\circ} \mathrm{C}\) to \(150^{\circ} \mathrm{C}\) is found and the air is preheated up to the computed temperature. Steam generation rate is also calculated based on the given furnace heat transfer and boiler efficiency.

Step by step solution

01

Stoichiometric Analysis and Air-to-fuel Calculation

Firstly, consider the ultimate analysis of the fuel and the flue gas analysis. Use stoichiometry to balance the chemical equations which represent the complete and incomplete combustion of carbon in coal to form CO2 and CO. Then, calculate the number of oxygen moles required for complete combustion. Since air is 21vol% oxygen and 79vol% nitrogen, the total volume of air required can be calculated to yield an air-to-fuel ratio.
02

Humidity and Moisture Content Calculation

Assuming flue gas to be saturated at the furnace exit temperature, the mole percent of each component can be derived. The percentage volume of H2O or steam can get by using the relationship between ratios of individual gas components and complete gas mixture.
03

Heat Rate Calculation for Cooling of Flue Gas

To calculate the rate of cooling, the change in enthalpy of the flue gas as it cools down must be calculated. The heat capacity at constant pressure (Cp) of the flue gas can be estimated. Then, use the formula \(Q = mCp螖T\), where m is the flow rate, Cp is the heat capacity and 螖T is the change in temperature.
04

Preheating Air Temperature Calculation

Assuming constant specific heat, the energy balance can be performed around preheater which equates the heat lost by flue gases to the heat gained by air.
05

Generating Steam Rate Calculation

To find the rate at which steam is generated, use the boiler efficiency and the heat transfer rate from the furnace. Calculate the enthalpy change of the water as it turns into steam. Then, the amount of steam generated can be determined by dividing the heat transfer rate by the difference in enthalpy.

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Key Concepts

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

Air-to-Fuel Ratio Calculation
Understanding the air-to-fuel ratio is crucial in optimizing combustion processes. The air-to-fuel ratio represents the volume of air needed to completely burn a unit mass of fuel. It is a key parameter in ensuring efficient combustion and controlling pollutant emissions.

For complete combustion of coal, carbon (C), hydrogen (H), and oxygen (O) present in the coal react with oxygen from the air to form carbon dioxide (CO2) and water (H2O). If the air supply is insufficient, incomplete combustion occurs, resulting in carbon monoxide (CO) formation and loss of energy.

To calculate this ratio, chemists start with the ultimate analysis of the fuel, which provides the composition in terms of carbon, hydrogen, and other elements. They then construct balanced chemical equations to represent the combustion reactions that would occur. From these equations, the amount of oxygen required for complete combustion can be determined.

As air contains approximately 21vol% oxygen, the total volume of air for complete combustion can be calculated. The air-to-fuel ratio is derived by dividing the total air volume by the amount of fuel. This ratio can greatly impact the efficiency of boilers, as a proper balance ensures all fuel is burned without excess air, which can carry away heat and reduce efficiency.
Flue Gas Analysis
Flue gas analysis is a critical diagnostic tool used to evaluate the performance of a combustion system, such as a boiler furnace. By analyzing the composition of the exhaust gas, engineers can tell whether the combustion process is efficient and whether the air-to-fuel ratio is correct.

The flue gas emerging from the furnace consists of a mixture of gases, including CO2, CO, O2, N2, and H2O. The mole percent of these gases is assessed on a dry basis鈥攅xcluding water vapor鈥攖o provide consistent comparison standards. This information can reveal if there is excess air in the combustion process or incomplete combustion occurring.

For instance, a high CO concentration indicates incomplete combustion, whereas a high O2 concentration suggests excess air. By adjusting the air-to-fuel ratio, one can ensure the fuel burns completely, maximizing efficiency and minimizing hazardous pollutant emissions. The percentage by volume of H2O in the flue gas can be found by considering the water generated from both the fuel's hydrogen content and the combustion air's humidity.
Heat Transfer in Boilers
Boilers transfer heat from combustion to water or steam, which is then used for heating or power generation. The efficiency of this heat transfer process is pivotal in the economical operation of boilers.

Heat transfer in a boiler occurs primarily through conduction and convection as hot gasses pass over water-filled tubes or through heat exchangers. The design and materials of the boilers are optimized to maximize heat exchange while minimizing heat loss to the environment.

To evaluate the heat transfer, one can use the formula for the rate of heat transfer, \(Q = mCp螖T\), where \(m\) is the mass flow rate of the fluid being heated (e.g., water or steam), \(Cp\) is the fluid's specific heat capacity at constant pressure, and \(螖T\) is the temperature change of the fluid. An accurate estimation of the heat capacity at different temperatures is crucial to determining the rate of heat transfer. Improving boiler efficiency can involve increasing the heat transfer surface area, enhancing the heat exchanger design, or recovering waste heat from flue gases.

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Most popular questions from this chapter

Use Hess's law to calculate the standard heat of the water-gas shift reaction $$\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$ from each of the two sets of data given here. (a) \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=+1226 \mathrm{Btu}\) $$\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): \quad \Delta \hat{H}_{\mathrm{v}}=+18,935 \mathrm{Btu} / \mathrm{lb}-\mathrm{mole}$$ $$\begin{aligned}&\text { (b) } \mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=-121,740 \mathrm{Btu}\\\&\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): \quad \Delta H_{\mathrm{r}}^{\circ}=-104,040 \mathrm{Btu} \end{aligned}$$

The standard heat of the reaction $$\mathrm{CaC}_{2}(\mathrm{s})+5 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CaO}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g})+5 \mathrm{H}_{2}(\mathrm{g})$$ is \(\Delta H_{\mathrm{t}}^{\circ}=+69.36 \mathrm{kJ}\). (a) Is the reaction exothermic or endothermic at \(25^{\circ} \mathrm{C}\) ? Would you have to heat or cool the reactor to kecp 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) Calculate \(\Delta U_{\mathrm{r}}^{\circ}\) for this reaction. (See Example \(9.1-2 .\) ) Briefly explain the physical significance of your calculated value. (c) Suppose you charge \(150.0 \mathrm{g}\) of \(\mathrm{CaC}_{2}\) and liquid water into a rigid container at \(25^{\circ} \mathrm{C}\), heat the container until the calcium carbide reacts completely, and cool the products back down to \(25^{\circ} \mathrm{C}\). condensing essentially all the unconsumed water. Write and simplify the energy balance equation for this closed constant-volume system and use it to determine the net amount of heat (kJ) that must be transferred to or from the reactor (state which). (d) If in Part (c) the term "rigid container" were replaced with "container at a constant pressure of 1 atm," the calculated value of \(Q\) would be slightly in error. Explain why. (e) If you placed 1 mol of solid calcium carbide and 5 mol of liquid water in a container at \(25^{\circ} \mathrm{C}\) and left them there for several days, upon returning you would not find 1 mol of solid calcium oxide, 2 mol of carbon dioxide, and 5 mol of hydrogen gas. Explain why not.

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.

A natural gas containing 82.0 mole \(\% \mathrm{CH}_{4}\) and the balance \(\mathrm{C}_{2} \mathrm{H}_{6}\) is burned with \(20 \%\) excess air in a boiler furnace. The fuel gas enters the furnace at \(298 \mathrm{K}\), and the air is preheated to 423 \(\mathrm{K}\). The heat capacities of the stack-gas components may be assumed to have the following constant values: $$\begin{aligned}\mathrm{CO}_{2}: & C_{p}=50.0 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) \\ \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): & C_{p}=38.5 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) \\\\\mathrm{O}_{2}: & C_{p}=33.1 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) \\ \mathrm{N}_{2}: & C_{p}=31.3 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})\end{aligned}$$ (a) Assuming complete combustion of the fuel, calculate the adiabatic flame temperature. (b) How would the flame temperature change if the percent excess air were increased? How would it change if the percentage of methane in the fuel increased? Briefly explain both of your answers.

A fuel gas containing 85.0 mole\% methane and the balance ethane is burned completely with pure oxygen at \(25^{\circ} \mathrm{C},\) and the products are cooled to \(25^{\circ} \mathrm{C}\). (a) Suppose the reactor is continuous. Take a basis of calculation of \(1 \mathrm{mol} / \mathrm{s}\) of the fuel gas, assume some value for the percent excess oxygen fed to the reactor (the value you choose will not affect the results), and calculate \(-\dot{Q}(\mathrm{k} \mathrm{W}),\) the rate at which heat must be transferred from the reactor. (b) Now suppose the combustion takes place in a constant-volume batch reactor. Take a basis of calculation of 1 mol of the fuel gas charged into the reactor, assume any percent excess oxygen, and calculate \(-Q(\mathrm{kJ}) .\) (Hint: Recall Equation 9.1-5.) (c) Briefly explain why the results in Parts (a) and (b) do not depend on the percent excess \(\mathrm{O}_{2}\) and why they would not change if air rather than pure oxygen were fed to the reactor.
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