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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?

Step by step solution

01

Balancing The Reaction Equation For Complete Combustion

By the stoichiometry of the complete combustion reaction of methane with air (primarily oxygen), we know \(CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O\). As per the problem, there's 25% excess air, which means the total air required is 125% of the stoichiometric air, so the overall reaction becomes \(CH_4 + 2.5O_2 \rightarrow CO_2 + 2H_2O + 0.5O_2\).

02

Calculation of Molar Flow Rates

Methane is entering at a rate of 550 L/s at 1.10 atm and 25°C. Using the ideal gas law we can convert this flow rate to a molar flow rate. \(PV = nRT\), where P is pressure (1.10 atm), V is volume (550 L/s), R is the ideal gas constant (0.0821 L.atm/(K.mol)) and T is temperature (25°C = 298 K). Solving for n (the number of moles), we have \(n = PV/RT\).

03

Calculating The Combustion Temperature

Determining the exit temperature of the combustion requires the application of an energy balance around the reactor and the use of heat capacity data for the various species present. Since the reactor is adiabatic, there is no heat exchange with the surroundings, so all the heat generated by combustion is retained in the products. The temperature rise of the products is found by equating the heat generated from the combustion reaction (which can be determined from standard heat of combustion data and the molar flow rate of methane) with the increase in the enthalpy of the products (which is determined by integrating the heat capacities of the product species over the temperature range).

04

Calculate The Degree Of Superheat

The degree of superheat can be calculated by subtracting the saturation temperature at the pressure given from the temperature calculated in Step 3. The saturation temperature can be found from steam tables for the given pressure of the reactor effluent.

05

Discuss The Effects Of Reducing Excess Air

Reducing the amount of excess air would cause the exit temperature to increase, because there would be less nitrogen present to absorb some of the heat of the reaction. The degree of superheat would also increase for the same reason. One risk involved in lowering the percent excess air is incomplete combustion, which might lead to the formation of hazardous products like carbon monoxide (CO), or even unburnt methane (which is a significant greenhouse gas).

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Key Concepts

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

Combustion Reaction

A combustion reaction, often seen in chemical and mechanical engineering applications, involves the burning of a fuel in the presence of oxygen, releasing energy in the form of heat and light. Methane, a common fuel, reacts with oxygen in a 1:2 ratio for complete combustion, producing carbon dioxide and water vapor. The excess air ensures that there is more than enough oxygen to completely react with the fuel. Understanding the combustion reaction is crucial for optimizing the use of fuels and managing energy outputs efficiently.

In the given exercise, complete combustion of methane is assumed, which is an ideal scenario in practical applications. Industrial combustion systems aim for complete combustion to maximize energy generation while minimizing harmful emissions.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. In an engineering context, it is used to calculate the amounts of inputs and outputs from a chemical process. For methane combustion, stoichiometry dictates the exact ratio of methane to oxygen required for complete combustion.

However, in real-life applications, excess air is introduced to ensure complete combustion, as seen in our problem statement which uses 25% excess air. Stoichiometry becomes more complex with excess reactants and must account for the additional volume and mass flow rates, affecting overall reactor calculations.

Adiabatic Reactor

An adiabatic reactor is a system where no heat exchange occurs with its surroundings. This condition is essential for certain chemical processes where maintaining a specific temperature range is crucial for reaction efficiency and safety. In adiabatic conditions, all the heat generated from the combustion reaction stays within the system, raising the temperature of the products.

The calculation of temperature within an adiabatic reactor is critical and requires an understanding of energy conservation. Engineers must design such reactors to withstand high temperatures without releasing heat, ensuring efficiency and preventing energy loss.

Ideal Gas Law

The ideal gas law is an equation of state for a hypothetical ideal gas. It is a good approximation for behavior of real gases under many conditions, and it relates the pressure (P), volume (V), temperature (T), and the amount in moles (n) of the gas, with the universal gas constant (R). Expressed as the formula: \(PV = nRT\).

For the solution provided, the ideal gas law allows us to convert the volumetric flow rate of methane and air into a molar flow rate, which is a necessary step in calculating the energy balance and determining the final temperature and composition of products.

Energy Balance

Energy balance is a fundamental concept in engineering, stating that energy cannot be created or destroyed, only transformed or transferred. In the context of a reactor, this means that the energy input, in the form of fuel, must equal the energy output, which comes out as heat and work alongside the chemical products. The adiabatic reactor used in the exercise is an excellent example where all heat generated from the combustion is used to increase the enthalpy of the products, as there is no heat loss to the environment.

To calculate the temperature of the effluent, engineers use the energy balance, alongside specific heat capacity data, to determine how much energy is retained in the system and raises the temperature.

Degree of Superheat

The degree of superheat refers to how much a vapor, such as steam, is heated above its saturation temperature at a particular pressure. It is a critical parameter for efficiency in power generation and refrigeration. A higher degree of superheat indicates a higher temperature and thus more thermal energy in the vapor phase.

In our exercise scenario, calculating the degree of superheat involves determining the saturation temperature from steam tables for water vapor at the given pressure and subtracting it from the calculated effluent temperature. Understanding the degree of superheat helps engineers assess the performance and safety of heat transfer systems.