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Chapter 9: Problem 64

Methane at \(25^{\circ} \mathrm{C}\) is burned in a boiler furnace with \(10.0 \%\) excess air preheated to \(100^{\circ} \mathrm{C}\). Ninety percent of the methane fed is consumed, the product gas contains \(10.0 \mathrm{mol} \mathrm{CO}_{2} / \mathrm{mol} \mathrm{CO},\) and the combustion products leave the furnace at \(400^{\circ} \mathrm{C}\). (a) Calculate the heat transferred from the furnace, \(-\dot{Q}(\mathrm{kW}),\) for a basis of \(100 \mathrm{mol} \mathrm{CH}_{4}\) fed/s. (The greater the value of \(-\dot{Q}\), the more steam is produced in the boiler.) (b) Would the following changes increase or decrease the rate of steam production? (Assume the fuel feed rate and fractional conversion of methane remain constant.) Briefly explain your answers. (i) Increasing the temperature of the inlet air; (ii) increasing the percent excess air for a given stack gas temperature; (iii) increasing the selcctivity of \(\mathrm{CO}_{2}\) to \(\mathrm{CO}\) formation in the furnace; and (iv) increasing the stack gas temperature.

Short Answer

Expert verified
The heat transferred from the furnace can be calculated based on the change in enthalpy during the combustion of methane. Increasing the temperature of the inlet air, increasing the percent excess air, and increasing the selectivity of CO2 to CO formation in the furnace will increase the rate of steam production, while increasing the stack gas temperature will decrease the rate of steam production.

Step by step solution

01

Establish the Combustion Reaction

First, the combustion reaction of methane (CH4) in excess oxygen is set up. As we know, the complete combustion of methane forms carbon dioxide (CO2) and water (H2O) as follows: \(CH4 + 2O2 -> CO2 + 2H2O\). In our problem, only 90% of methane is consumed, and the product gas contains 10 mol CO2 per mol CO. Thus, the actual combustion reaction in the furnace is: \(0.9 CH4 + 2*1.1 O2 -> 0.1 CO + 0.9 CO2 + 1.8 H2O\).
02

Calculate the Heat of the Reaction

Second, we employ the table of standard enthalpies of formation to calculate the heat of reaction. The heat of reaction (\(\Delta H\)) can be calculated using the equation: \(-\dot{Q} = -\Delta H * \dot{n}_{CH4}\), where \(\Delta H\) is the heat of reaction and \(\dot{n}_{CH4}\) is the mol/s flow of methane. The 'minus' sign indicates that the reaction is exothermic, i.e., heat is released during the combustion.
03

Analyze the Changes on Steam Production

(i) If the temperature of the inlet air is increased, the combustion would become more vigorous, leading to a higher \(\Delta H\), thus more heat transferred. So, steam production will increase. (ii) More excess air for a given stack gas temperature means more oxygen for combustion, hence more heat transferred and more steam produced. (iii) Increasing the selectivity of CO2 to CO in the furnace means more complete combustion, which will also result in more heat transferred and more steam produced. (iv) Increasing the stack gas temperature will reduce the furnace heat transfer (since heat transfer is proportional to the temperature difference between the furnace and the stack gas). Hence, steam production will decrease.

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Key Concepts

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

Enthalpy of Combustion
The enthalpy of combustion is a fundamental concept in understanding how chemical reactions release or absorb energy. It refers to the amount of heat released when a substance undergoes complete combustion with oxygen under standard conditions. For any hydrocarbon, like methane in our exercise, the reaction typically produces carbon dioxide and water, releasing heat in the process.

In the context of the exercise, the heat of combustion can be calculated from the reaction enthalpy, taking into account the stoichiometry and the percentages provided. For instance, since only 90% of methane reacts and there are 10.0% excess air, the calculation must include these variations. The enthalpy change, \( \Delta H \), is a crucial factor in determining the efficacy of combustion processes, such as those in boilers to produce steam.

Since heat release is an exothermic process, in our problem's terms, the larger the negative value of \( -\dot{Q} \) (heat transfer rate), the more energy is available for steam production. This, in turn, can be used to generate electricity or provide heating in industrial applications.
Excess Air in Combustion
Excess air in combustion plays a vital role in ensuring the complete burning of fuel, thus maximizing the efficiency of the combustion process. It is defined as the amount of air in excess of what is theoretically required for the complete oxidation of the fuel. This concept is especially significant in boilers where maintaining an ideal combustion environment is critical for energy efficiency and reducing emissions of uncombusted gases.

In the exercise, we are given that the combustion occurs with 10.0% excess air. While excess air is important to ensure complete combustion and thus maximizing the heat release, too much of it can lead to heat losses because the excess air needs to be heated as well. The balance between sufficient excess air for complete combustion and the energy loss due to heating the additional air is delicate and requires precise control.

As the solution indicates, increasing the excess air, given a constant stack gas temperature, increases the rate of steam production because it ensures more complete combustion. However, it's also crucial to optimize the amount of excess air to avoid unnecessary energy consumption in heating the extra air.
Steam Production in Boilers
Boilers are essential components in many industrial processes, serving to generate steam by applying heat energy to water. The efficiency of steam production in boilers is heavily dependent on the combustion process where fuel, such as methane, is burned to heat the water. The more effective the combustion, the more heat is available to convert water into steam, which can then be used for heating, powering turbines, or other industrial processes.

The enthalpy of combustion, as covered earlier, directly influences the \( -\dot{Q} \) value representing the heat transfer from the furnace. If \( -\dot{Q} \) is higher, more energy is transferred to the water in the boiler, resulting in higher steam production. The step-by-step solution provided outlines several factors that can increase or decrease the rate of steam production, such as the inlet air temperature and stack gas temperature. These factors affect the overall heat transfer efficiency within the boiler.
Chemical Reaction Stoichiometry
Chemical reaction stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. It ensures that the conservation of mass is maintained by accounting for the molar ratios of the substances involved. Stoichiometry is the foundation for reaction calculations, balancing chemical equations, and determining the yield from reactions.

In our methane combustion example, the stoichiometry becomes complex as the reaction does not proceed to complete conversion鈥攐nly 90% of methane reacts. Additionally, the presence of 10.0% excess air changes the proportions of reactants. Stoichiometry allows us to calculate the actual amounts of reactants and products based on these percentages, as showcased in the solution. For example, the formation of CO and CO2 in the reaction must align with the stoichiometric coefficients and the quantities provided, such as 10 mol CO2 per mol CO, to accurately determine the enthalpy of the reaction and therefore the heat transferred for steam production.

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Most popular questions from this chapter

Biodiesel fuel - a sustainable alternative to petroleum diesel as a transportation fuel- -is produced via the transesterification of triglyceride molecules derived from vegetable oils or animal fats. For every \(9 \mathrm{kg}\) of biodiesel produced in this process, \(1 \mathrm{kg}\) of glycerol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3},\) is produced as a byproduct. Finding a market for the glycerol is important for biodiesel manufacturing to be economically viable. A process for converting glycerol to the industrially important specialty chemical intermediates acrolein, \(C_{3} \mathrm{H}_{4} \mathrm{O},\) and hydroxyacetone (acetol), \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2},\) has been proposed. $$\begin{array}{l}\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}+2 \mathrm{H}_{2} \mathrm{O} \\ \mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \end{array}$$ The reactions take place in the vapor phase at \(325^{\circ} \mathrm{C}\) in a fixed bed reactor over an acid catalyst. The feed to the reactor is a vapor stream at \(325^{\circ} \mathrm{C}\) containing 25 mol\% glycerol, \(25 \%\) water, and the balance nitrogen. All of the glycerol is consumed in the reactor, and the product stream contains acrolein and hydroxyacctone in a 9: 1 mole ratio. Data for the process species are shown below. $$\begin{array}{|l|c|c|}\hline \text { Species } & \Delta \hat{H}_{\mathrm{f}}(\mathrm{kJ} / \mathrm{mol}) & C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right] \\ \hline \text { glycerol(v) } & -620 & 0.1745 \\ \hline \text { acrolein(v) } & -65 & 0.0762 \\\\\hline \text { hydroxyacetone(v) } & -372 & 0.1096 \\ \hline \text { water(v) } & -242 & 0.0340 \\\\\hline \text { nitrogen(g) } & 0 & 0.0291 \\ \hline\end{array}$$ (a) Assume a basis of 100 mol fed to the reactor, and draw and completely label a flowchart. Carry out a degree-of-freedom analysis assuming that you will use extents of reaction for the material balances. Then calculate the molar amounts of all product species. (b) Calculate the total heat added or removed from the reactor (state which it is), using the constant heat capacities given in the above table. (c) Assuming this process is implemented along with biodiesel production, how would you determine whether the biodiesel is an cconomically viable alternative to petroleum diesel? (d) If you do a degree-of-freedom analysis based on atomic species balances, you are likely to count one more equation than you have unknowns, and yet you know the system has zero degrees of freedom. Guess what the problem is, and then prove it.

Lime (calcium oxide) is widely used in the production of cement, steel, medicines, insecticides, plant and animal food, soap, rubber, and many other familiar materials. It is usually produced by heating and decomposing limestone (CaCO \(_{3}\) ), a cheap and abundant mineral, in a calcination process: $$\mathrm{CaCO}_{3}(\mathrm{s}) \stackrel{\text { heat }}{\longrightarrow} \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$ (a) Limestone at \(25^{\circ} \mathrm{C}\) is fed to a continuous calcination reactor. The calcination is complete, and the products leave at \(900^{\circ} \mathrm{C}\). Taking 1 metric ton \((1000 \mathrm{kg})\) of limestone as a basis and clemental species \(\left[\mathrm{Ca}(\mathrm{s}), \mathrm{C}(\mathrm{s}), \mathrm{O}_{2}(\mathrm{g})\right]\) at \(25^{\circ} \mathrm{C}\) as references for enthalpy calculations, prepare and fill in an inlet-outlet enthalpy table and prove that the required heat transfer to the reactor is \(2.7 \times 10^{6} \mathrm{kJ}\) (b) In a common variation of this process, hot combustion gases containing oxygen and carbon monoxide (among other components) are fed into the calcination reactor along with the limestone. The carbon monoxide is oxidized in the reaction $$\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})$$ Suppose the combustion gas fed to a calcination reactor contains 75 mole \(\% \mathrm{N}_{2}, 2.0 \% \mathrm{O}_{2}, 9.0 \% \mathrm{CO},\) and \(14 \% \mathrm{CO}_{2}\) the gas enters the reactor at \(900^{\circ} \mathrm{C}\) in a feed ratio of \(20 \mathrm{kmol}\) gas/kmol limestone; the calcination is complete; all of the oxygen in the gas feed is consumed in the CO oxidation reaction; the reactor effluents are at \(900^{\circ} \mathrm{C}\) Again taking a basis of 1 metric ton of limestone calcined, prepare and fill in an inlet-outlet enthalpy table for this process [don't recalculate enthalpies already calculated in Part (a)] and calculate the required heat transfer to the reactor. (c) You should have found that the heat that must be transferred to the reactor is significantly lower with the combustion gas in the feed than it is without the gas. By what percentage is the heat requirement reduced? Give two reasons for the reduction. State another benefit of feeding the combustion gas, besides the reduction of the heating requirement.

Cumene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{C}_{3} \mathrm{H}_{7}\right)\) is produced by reacting benzene with propylene \(\left[\Delta H_{\mathrm{r}}\left(77^{\circ} \mathrm{F}\right)=-39,520 \mathrm{Btu}\right]\) A liquid feed containing 75 mole \(\%\) propylene and \(25 \%\) n-butane and a second liquid stream containing essentially pure benzene are fed to the reactor. Fresh benzene and recycled benzene, both at \(77^{\circ} \mathrm{F},\) are mixed in a 1: 3 ratio \((1 \text { mole fresh feed } / 3\) moles recycle) and passed through a heat exchanger, where they are heated by the reactor effluent before being fed to the reactor. The reactor effluent enters the exchanger at \(400^{\circ} \mathrm{F}\) and leaves at \(200^{\circ} \mathrm{F}\). The pressure in the reactor is sufficient to maintain the effluent stream as a liquid. After being cooled in the heat exchanger, the reactor effluent is fed to a distillation column (T1). All of the butane and unreacted propylene are removed as overhead product from the column, and the cumene and unreacted benzene are removed as bottoms product and fed to a second distillation column (T2) where they are scparated. The benzenc leaving the top of the sccond column is the recycle that is mixed with the fresh benzene feed. Of the propylene fed to the process, \(20 \%\) does not react and leaves in the overhead product from the first distillation column. The production rate of cumene is \(1200 \mathrm{lb}_{\mathrm{m}} / \mathrm{h}\). (a) Calculate the mass flow rates of the streams fed to the reactor, the molar flow rate and composition of the reactor effluent, and the molar flow rate and composition of the overhead product from the first distillation column, T1. (b) Calculate the temperature of the benzene stream fed to the reactor and the required rate of heat addition to or removal from the reactor. Use the following approximate heat capacities in your calculations: \(C_{p}\left[\operatorname{Btu} /\left(\operatorname{lb}_{m} \cdot F\right)\right]=0.57\) for propylene, 0.55 for butane, 0.45 for benzene, and 0.40 for cumene. (c) Most people unfamiliar with the chemical process industry imagine that chemical engineers are people who deal mainly with chemical reactions carried out on a large scale. In fact, in most industrial processes, a visitor to the plant would have trouble finding the reactor in a maze of towers and tanks and pipes that were added to the process design to improve the profitability of the process. Briefly explain how the heat exchanger, the two distillation columns, and the recycle stream in the cumene process serve that function.

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 and \(30 \%\) excess air are to be fed to a combustion reactor. An inexperienced technician mistakes his instructions and charges the gases together in the required proportion into an evacuated closed tank. (The gases were supposed to be fed directly into the reactor.) The contents of the charged tank are at \(25^{\circ} \mathrm{C}\) and 4.00 atm absolute. (a) Calculate the standard internal energy of combustion of the methane combustion reaction. \(\Delta \hat{U}_{c}^{\circ}(\mathrm{kJ} / \mathrm{mol}),\) taking \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{v})\) as the presumed products. Then prove that if the constant-pressure heat capacity of an ideal-gas species is independent of temperature, the specific internal energy of that species at temperature \(T\left(^{\circ} \mathrm{C}\right)\) relative to the same species at \(25^{\circ} \mathrm{C}\) is given by the expression $$\hat{U}=\left(C_{p}-R\right)\left(T-25^{\circ} \mathrm{C}\right)$$ where \(R\) is the gas constant. Use this formula in the next part of the problem. (b) You wish to calculate the maximum temperature, \(T_{\max }\left(^{\circ} \mathrm{C}\right),\) and corresponding pressure, \(P_{\max }(\text { atm }),\) that the tank would have to withstand if the mixture it contains were to be accidentally ignited. Taking molecular species at \(25^{\circ} \mathrm{C}\) as references and treating all species as ideal gases, prepare an inlet-outlet internal energy table for the closed system combustion process. In deriving expressions for each \(\dot{U}_{i}\) at the final reactor condition \(\left(T_{\max }, P_{\max }\right),\) use the following approximate values for \(C_{p_{i}}\left[\mathrm{k} J /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]: 0.033 \mathrm{for} \mathrm{O}_{2}, 0.032\) for \(\mathrm{N}_{2}, 0.052 \mathrm{for} \mathrm{CO}_{2},\) and \(0.040 \mathrm{for} \mathrm{H}_{2} \mathrm{O}(\mathrm{v}) .\) Then use an energy balance and the ideal-gas equation of state to perform the required calculations. (c) Why would the actual temperature and pressure attained in a real tank be less than the values calculated in Part (a)? (State several reasons.) (d) Think of ways that the tank contents might be accidentally ignited. The list should suggest why accepted plant safety regulations prohibit the storage of combustible vapor mixtures.
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