/*! 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 63 Methanol vapor is burned with ex... [FREE SOLUTION] | 91Ó°ÊÓ

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Methanol vapor is burned with excess air in a catalytic combustion chamber. Liquid methanol initially at \(25^{\circ} \mathrm{C}\) is vaporized at 1.1 atm and heated to \(100^{\circ} \mathrm{C}\); the vapor is mixed with air that has been preheated to \(100^{\circ} \mathrm{C},\) and the combined stream is fed to the reactor at \(100^{\circ} \mathrm{C}\) and 1 atm. The reactor effluent emerges at \(300^{\circ} \mathrm{C}\) and 1 atm. Analysis of the product gas yields a dry-basis composition of \(4.8 \% \mathrm{CO}_{2}\) \(14.3 \% \mathrm{O}_{2},\) and \(80.9 \% \mathrm{N}_{2}\) (a) Calculate the percentage excess air supplied and the dew point of the product gas. (b) Taking a basis of 1 g-mole of methanol burned, calculate the heat ( \(k\) J) needed to vaporize and heat the methanol feed, and the heat (kJ) that must be transferred from the reactor. (c) Suggest how the energy economy of this process could be improved. Then suggest why the company might choose not to implement your redesign.

Short Answer

Expert verified
Please refer to the step by step guide provided for specific calculations and results. In general, excess air could be reduced, heat recovered from the product gas could be used to preheat the feed, optimization of conditions could be done for better efficiency. However, costs, safety considerations and practicality could prevent these changes from being implemented.

Step by step solution

01

Stoichiometry calculations

We start by analysing the stoichiometry of the reaction. The balanced reaction of combustion of methanol (CH3OH) is CH3OH(g) + 3/2 O2(g) = CO2(g) + 2H2O(g). Analyze the product gas composition and find the amount of air used.
02

Calculate Excess air and dew point

The amount of O2 in air is approx 21%, therefore we can calculate the amount of excess air used in the combustion. The dew point of the product gas can be calculated knowing the vapour pressure of water at different temperatures and using the humidity ratios.
03

Calculate heat needed to vaporize and heat methanol

Use the enthalpy of vaporization of methanol and specific heat capacities to calculate the heat absorbed by the methanol feed in vaporization and heating up to the reactor temperature.
04

Calculate heat transferred from the reactor

The heat transferred from reactor can be calculated using the difference in enthalpy of products and reactants and considering the reaction stoichiometry.
05

Suggest improvements and analyze potential reasons for non-implementation

Suggest ways to make the process more energy efficient, such as heat integration or optimizing the operation conditions. Then discuss why these improvements might not be implemented considering factors such as cost, practicality and safety.

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Key Concepts

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

Stoichiometry Calculations
The chemical combustion process of methanol combustion starts with a balanced chemical reaction, which is crucial for stoichiometry calculations. In this case, methanol (\(\text{CH}_3\text{OH}\)) reacts with oxygen (\(\text{O}_2\)) to produce carbon dioxide (\(\text{CO}_2\)) and water vapor (\(\text{H}_2\text{O}\)). The stoichiometric equation is expressed as:\[\text{CH}_3\text{OH (g)} + \frac{3}{2}\text{O}_2 (g) \rightarrow \text{CO}_2 (g) + 2\text{H}_2\text{O (g)}\]Stoichiometry helps us find the proportions in which reactants combine and products form. It allows us to determine the amount of oxygen needed for the complete combustion of methanol. From the problem, we learn about the product gases, including the quantity of carbon dioxide, and using these observations, we can also estimate the air used in the reaction. Knowing the stoichiometry, you can compare the actual moles of oxygen with those expected in perfect reaction conditions to further your analysis.
Excess Air Calculation
The concept of excess air is important in chemical combustion, as it impacts efficiency and safety. To determine the percentage of excess air supplied, one needs to calculate the excess oxygen beyond what is required for complete combustion. Given that air is about 21% oxygen, the excess air percentage (\(\text{EA}\%\)) can be calculated by the formula:\[\text{EA}\% = \left( \frac{\text{Actual } \text{O}_2 - \text{Theoretical } \text{O}_2}{\text{Theoretical } \text{O}_2} \right) \times 100\]In the provided exercise, with \(14.3\%\) of oxygen in the dry product gases, we identify how much oxygen exceeds the stoichiometric need. This excess is crucial for ensuring complete combustion, preventing pollutants, and affecting system energy efficiency. Additionally, you can determine the dew point of the exhaust gases by examining the equilibrium vapor pressures and humidity.
Heat Transfer Analysis
In order to understand energy flow in the combustion process, heat transfer analysis becomes key. Firstly, methanol must be vaporized before entering the reactor. This requires calculating the enthalpy change, which includes the enthalpy of vaporization and the specific heat capacity of methanol. The energy required can be broken down into:
  • Energy required to vaporize methanol.
  • Energy needed to raise the methanol's temperature.
Heat absorbed amounts can be calculated with:\[Q = m \times c \times \Delta T\]where\(m\) is the mass of methanol,\(c\) is the specific heat capacity, and\(\Delta T\) is the change in temperature. Post-reaction, the outlet effluent emits energy due to temperature differences and reaction energetics. Recognizing these energy changes is crucial in optimizing thermal management within an industrial process.
Energy Efficiency in Chemical Processes
Improving energy efficiency in a combustion process involves multiple approaches, aiming to reduce waste and enhance performance. Processes can be enhanced by using
  • Heat integration techniques, which utilize waste heat to preheat reactants.
  • Optimizing operation parameters like temperature and pressure.
Such modifications aim to cut down the heat needed for vaporization and decrease overall energy demand. However, companies might avoid implementing improvements due to following reasons:
  • High initial costs associated with new technologies.
  • Complexity and risk in operational changes.
  • Need to comply with ongoing regulations and safety standards.
Understanding these trade-offs enables balancing between ideal efficiency and practical feasibility, ensuring profitable and reliable chemical operations.

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Most popular questions from this chapter

Ethylene oxide is produced by the catalytic oxidation of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(\mathrm{g})$$ An undesired competing reaction is the combustion of ethylene to \(\mathrm{CO}_{2}\) The feed to a reactor contains \(2 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{4} / \mathrm{mol} \mathrm{O}_{2} .\) The conversion and yield in the reactor are respectively \(25 \%\) and \(0.70 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) produced/mol \(\mathrm{C}_{2} \mathrm{H}_{4}\) consumed. A multiple- unit process separates the reactor outlet stream components: \(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{O}_{2}\) are recycled to the reactor, \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) is sold, and \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) are discarded. The reactor inlet and outlet streams are each at \(450^{\circ} \mathrm{C}\), and the fresh feed and all species leaving the separation process are at \(25^{\circ} \mathrm{C}\). The combined fresh feedrecycle stream is preheated to \(450^{\circ} \mathrm{C}\). (a) Taking a basis of 2 mol of ethylene entering the reactor, draw and label a flowchart of the complete process (show the separation process as a single unit) and calculate the molar amounts and compositions of all process streams. (b) Calculate the heat requirement ( \(k J\) ) for the entire process and that for the reactor alone. Data for gaseous ethylene oxide $$\begin{aligned}\Delta \hat{H}_{\mathrm{f}}^{\prime} &=-51.00 \mathrm{kJ} / \mathrm{mol} \\ C_{p}[\mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})] &=-4.69+0.2061 T-9.995 \times 10^{-5} T^{2} \end{aligned}$$ where \(T\) is in kelvins. (c) Calculate the flow rate \((\mathrm{kg} / \mathrm{h})\) and composition of the fresh feed, the overall conversion of ethylene, and the overall process and reactor heat requirements (kW) for a production rate of \(1500 \mathrm{kg} \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O} /\) day. Briefly explain the reasons for separating and recycling the ethylene-oxygen stream. (d) One of the attributes of this process defined in the problem statement is extremely unrealistic. What is it?

Formaldehyde is produced by decomposing methanol over a silver catalyst: $$\mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{HCHO}+\mathrm{H}_{2}$$ To provide heat for this endothermic reaction, some oxygen is included in the feed to the reactor, leading to the partial combustion of the hydrogen produced in the methanol decomposition. The feed to an adiabatic formaldehyde production reactor is obtained by bubbling a stream of air at 1 atm through liquid methanol. The air leaves the vaporizer saturated with methanol and contains \(42 \%\)methanol by volume. The stream then passes through a heater in which its temperature is raised to \(145^{\circ} \mathrm{C} .\) To avoid deactivating the catalyst, the maximum temperature attained in the reactor must be limited to \(600^{\circ} \mathrm{C}\). For this purpose, saturated steam at \(145^{\circ} \mathrm{C}\) is metered into the air-methanol stream, and the combined stream cnters the reactor. A fractional methanol conversion of \(70.0 \%\) is achicved in the reactor, and the product gas contains 5.00 mole\% hydrogen. The product gas is cooled to \(145^{\circ} \mathrm{C}\) in a waste heat boiler in which saturated steam at 3.1 bar is generated from liquid water at \(30^{\circ} \mathrm{C}\). Several absorption and distillation units follow the waste heat boiler, and formaldehyde is ultimately recovered in an aqueous solution containing 37.0 wt\% HCHO. The plant is designed to produce 36 metric kilotons of this solution per year, operating 350 days/yr. (a) Draw the process flowchart and label it completely. Show the absorption/distillation train as a single unit with the reactor product gas and additional water entering and the formaldehyde solution and a gas stream containing methanol, oxygen, nitrogen, and hydrogen leaving. (b) Calculate the operating temperature of the methanol vaporizer. (c) Calculate the required feed rate of steam to the reactor \((\mathrm{kg} / \mathrm{h})\) and the molar flow rate and composition of the product gas. (d) Calculate the rate ( \(\mathrm{kg} / \mathrm{h}\) ) at which steam is generated in the waste heat boiler. (e) Enough saturated steam was added to the feed to the reactor to keep the reactor outlet temperature at \(600^{\circ} \mathrm{C}\). Explain in your own words (i) why adding steam lowers the outlet temperature, and (ii) the cconomic drawbacks of higher and lower outlet temperatures.

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.

Various uses for nitric acid are given in Problem \(6.43,\) along with information about how this important chemical is synthesized industrially. The key reactions are oxidations of ammonia to nitric oxide and of nitric oxide to nitrogen dioxide, followed by dissolution of \(\mathrm{NO}_{2}\) in water: $$\begin{aligned} 4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) & \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \\ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) & \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \\ 3 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(1) & \rightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g}) \end{aligned}$$ Nitric oxide generated on dissolution of \(\mathrm{NO}_{2}\) in water is oxidized to produce additional \(\mathrm{NO}_{2},\) which is then combined with water to form more \(\mathrm{HNO}_{3}\). In this problem we neglect side reactions that would lower the product yield. Ammonia vapor at \(275^{\circ} \mathrm{C}\) and 8 atm is mixed with air, also at \(275^{\circ} \mathrm{C}\) and 8 atm, and the combined stream is fed to a converter. Fresh air entering the system at \(30^{\circ} \mathrm{C}\) and 1 atm with a relative humidity of \(50 \%\) is compressed to \(100^{\circ} \mathrm{C}\) and 8 atm, and the compressed air then exchanges heat with the product gas leaving the converter. The quantity of oxygen in the feed to the converter is \(20 \%\) in excess of the amount theoretically required to convert all of the ammonia to \(\mathrm{HNO}_{3}\). The entire process after the compressor may be taken to operate at a constant pressure of 8 atm. In the converter, the ammonia is completely oxidized, with a negligible amount of \(\mathrm{NO}_{2}\) formed. The product gas leaves the converter at \(850^{\circ} \mathrm{C}\), and, as described in the preceding paragraph, exchanges heat with the air entering the system. The product gas then is fed to a waste-heat boiler that produces superheated steam at \(200^{\circ} \mathrm{C}\) and 10 bar from liquid water at \(35^{\circ} \mathrm{C}\). The product gas leaving the wasteheat boiler is cooled further to \(35^{\circ} \mathrm{C}\) and fed to an absorption column in which the NO is completely oxidized to \(\mathrm{NO}_{2},\) which in turn combines with water (some of which is present in the product gas). Water is fed to the absorber at \(25^{\circ} \mathrm{C},\) at a rate sufficient to form a 55 wt\% aqueous nitric acid solution. The NO formed in the reaction of \(\mathrm{NO}_{2}\) to produce \(\mathrm{HNO}_{3}\) is oxidized, and the NO \(_{2}\) produced is hydrated to form still more \(\mathrm{HNO}_{3}\). The off-gas from the process may be taken to contain only \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) (a) Construct a flowchart showing all process streams, including input and output from the process and the following equipment: converter, air compressor, exchanger recovering heat from the converter product, waste-heat boiler producing superheated steam, exchanger cooling the product gas before it is fed to the absorber, and absorber. (b) Taking a basis of \(100 \mathrm{kmol}\) of ammonia fed to the process, develop spreadsheets (preferably incorporating the use of APEx) to determine the following: (i) Molar amounts (kmol) of oxygen, nitrogen, and water vapor in the air fed to the process, cubic meters of air fed to the process, and kmol of water fed to the absorber. (ii) Molar amounts, molar composition, and volume of the off-gas leaving the absorber. (iii) Mass (kg) of product nitric acid solution. (iv) Molar amounts and composition of the gas leaving the converter. (v) Heat removed from or added to (state which) the converter. (vi) Temperature of the product gas after it has exchanged heat with the air, assuming no heat is transferred between the heat exchanger and the surroundings. (vii) Production rate of superheated steam if the gas temperature leaving the boiler is \(205^{\circ} \mathrm{C}\). Before performing this calculation, determine if condensation of water occurs when the gas is cooled to \(205^{\circ} \mathrm{C}\). Since the superheated steam temperature is \(200^{\circ} \mathrm{C}\), explain why the selected temperature of the product gas is reasonable. (viii) Heat removed from the product gas before it is fed to the absorber (Hint: Check the condition of the gas at \(35^{\circ} \mathrm{C}\) ) and mass of cooling water required to remove that heat if the water temperature can only be increased by \(5^{\circ} \mathrm{C}\). Assume no heat is transferred between the heat exchanger and the surroundings. (ix) Heat removed from or added to the absorber. Assume the heat capacity of the nitric acid solution is approximately the same as that of liquid water and the outlet temperatures of the off-gas and product streams are \(25^{\circ} \mathrm{C}\) and \(35^{\circ} \mathrm{C}\), respectively. (c) Scale up the results calculated in Part (b) to determine all stream flow rates and heat transfer rates for a production rate of \(5.0 \times 10^{3} \mathrm{kg} / \mathrm{h}\) of the product solution.

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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