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Chapter 9: Problem 63

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

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.

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?

Methane is burned completely with 40\% excess air. The methane enters the combustion chamber at \(25^{\circ} \mathrm{C},\) the combustion air enters at \(150^{\circ} \mathrm{C},\) and the stack gas \(\left[\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{O}(\mathrm{v}), \mathrm{O}_{2}, \mathrm{N}_{2}\right]\) exits at \(450^{\circ} \mathrm{C} .\) The chamber functions as a preheater for an air stream flowing in a pipe through the chamber to a spray dryer. The air enters the chamber at \(25^{\circ} \mathrm{C}\) at a rate of \(1.57 \times 10^{4} \mathrm{m}^{3}(\mathrm{STP}) / \mathrm{h}\) and is heated to \(181^{\circ} \mathrm{C}\). All of the heat generated by combustion is used to heat the combustion products and the air going to the spray dryer (i.e., the combustion chamber may be considered adiabatic). (a) Draw and completely label the process flow diagram and perform a degree- of-freedom analysis. (b) Calculate the required molar flow rates of methane and combustion air (kmol/h) and the volumetric flow rates \(\left(\mathrm{m}^{3} / \mathrm{h}\right)\) of the two effluent streams. State all assumptions you make. (c) When the system goes on line for the first time, environmental monitoring of the stack gas reveals a considerable quantity of CO, suggesting a problem with either the design or the operation of the combustion chamber. What changes from your calculated values would you expect to see in the temperatures and volumetric flow rates of the effluent streams [increase, decrease, cannot tell without doing the calculations]?

A 2.00 mole \(\%\) sulfuric acid solution is neutralized with a 5.00 mole\% sodium hydroxide solution in a continuous reactor. All reactants enter at \(25^{\circ} \mathrm{C}\). The standard heat of solution of sodium sulfate is \(-1.17 \mathrm{kJ} / \mathrm{mol} \mathrm{Na}_{2} \mathrm{SO}_{4},\) and the heat capacities of all solutions may be taken to be that of pure liquid water [4.184 kJ/(kg.'C)]. (a) How much heat (kJ/kg acid solution fed) must be transferred to or from the reactor contents (state which it is) if the product solution emerges at \(40^{\circ} \mathrm{C} ?\) (b) Estimate the product solution temperature if the reactor is adiabatic, neglecting heat transferred between the reactor contents and the reactor wall.

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.
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