91Ó°ÊÓ

In the preliminary design of a furnace for industrial boiler, methane at \(25^{\circ} \mathrm{C}\) is burned completely with \(20 \%\) excess air, also at \(25^{\circ} \mathrm{C} .\) The feed rate of methane is \(450 \mathrm{kmol} / \mathrm{h}\). The hot combustion gases leave the furnace at \(300^{\circ} \mathrm{C}\) and are discharged to the atmosphere. The heat transferred from the furnace \((\dot{Q})\) is used to convert boiler feedwater at \(25^{\circ} \mathrm{C}\) into superheated steam at 17 bar and \(250^{\circ} \mathrm{C}\). (a) Draw and label a flowchart of this process [the chart should look like the one shown in Part (b) without the preheater] and calculate the composition of the gas leaving the furnace. Then, calculate \(\dot{Q}(\mathrm{kJ} / \mathrm{h})\) and the rate of steam production in the boiler \((\mathrm{kg} / \mathrm{h})\). (b) In the actual boiler design, the air feed at \(25^{\circ} \mathrm{C}\) and the combustion gas leaving the furnace at \(300^{\circ} \mathrm{C}\) pass through a heat exchanger (the air preheater). The combustion (flue) gas is cooled to \(150^{\circ} \mathrm{C}\) in the preheater and is then discharged to the atmosphere, and the heated air is fed to the furnace. Calculate the temperature of the air entering the furnace (a computer solution is required) and the rate of steam production (kg/h). (c) Explain why preheating the air increases the rate of steam production. (Suggestion: Use the energy balance on the furnace in your explanation.) Why does it make sense economically to use the combustion gas as the heating medium?

Step by step solution

01

Determine the composition of the gas leaving the furnace

Methane (\(CH_4\)) is burned completely with 20% excess air. This means there is 1.2 times of the theoretical air required for the complete combustion of methane. The balanced chemical reaction of the combustion of methane with air (which is composed by 79% Nitrogen (\(N_2\)) and 21% Oxygen (\(O_2\))), would be:\(CH_4 + 2O_2 + 7.52N_2 \rightarrow CO_2 +2H_2O + 7.52N_2\)We have assumed that the combustion of methane only produces \(CO_2\) and \(H_2O\), but it can also produce other compounds like \(CO\), \(NO_x\) or \(SO_x\), depending on several factors.Now, with 20% excess air, the reaction is\(CH_4 + 1.2(2O_2 + 7.52N_2) \rightarrow CO_2 +2H_2O + 1.2 * 7.52N_2\)Calculate the quantity of \(CO_2,H_2O\) and \(N_2\) to define the composition of the gas leaving the furnace.

02

Determine the heat transferred from the furnace and the rate of steam production

The heat balance for the boiler is given by\(\dot{Q}=m_{CH4}HHV = m_{w}(\Delta h_{w})\)Where:\(\dot{Q}\) is the heat transferred from the furnace (\(kJ/h\))\(m_{CH4}\) is the mass flow rate of methane (\(kg/h\))\(HHV\) is the higher heating value of methane, which represents the heat released when a certain mass of fuel is burned completely with oxygen.\(m_{w}\) is the mass flow rate of the water (\(kg/h\))\(\Delta h_{w}\) is the change in the enthalpy of the water (which becomes steam) (\(kJ/kg\))The water is at \(25^{\circ}\) C, and it becomes steam at \(17bar\) and \(250^{\circ}\) C. Given that the heat is transferred completely from the furnace to the water, we can say that the rate of heat transferred equals the capacity of heat absorbed by the water. This allows us to calculate \(m_{w}\) and \(\dot{Q}\), once we have defined the values for \(HHV\) and \(\Delta h_{w}\).

03

Determine the effect of preheating and calculate the new rate of steam production

In the second part of the exercise we're asked to calculate the temperature of the air entering the furnace and the new rate of steam production when the input air goes through a heat exchanger. This puts an additional layer of complexity which can be determined by setting up a temperature-enthalpy (T-H) diagram and calculating he areas between the curves of the two fluids in the heat exchanger.In the heat exchanger the heat is transferred from the combustion gas, which cools from \(300^{\circ}\) C to \(150^{\circ}\) C, to the air, which temperature we need to calculate.We can assume that the heat transferred is directly proportional to the variation in temperature and the air and gas flow rates: \(\Delta T_{gas} * m_{gas} = \Delta T_{air} * m_{air}\)That allows us to calculate the air temperature exiting the heat exchanger and gets fed to the furnace.Finally, we can calculate the new rate of steam production \(m'_{w}\) using the previous balance with the new value for the air temperature in the furnace. The new heat transferred to the water becomes higher since the furnace is now hotter.

04

Explain the benefits of preheating

Preheating the air increases the rate of steam production because it increases the efficiency of the combustion process in the furnace. Essentially, preheating the air reduces the amount of heat the furnace needs to generate in order to reach the combustion temperature, thus more of the generated heat can be used to convert boiler feedwater into steam resulting in an increased steam production rate. Economical sense is due to the fact that we're using a 'waste' product from the combustion (the exhaust flue gas) to preheat the air, thus saving fuel that we would use otherwise to heat this air. This improves the overall efficiency of the process and thus makes it more cost-effective.

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Key Concepts

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

Chemical Process Engineering

Chemical process engineering is essential in designing systems that transform raw materials into valuable products. It involves understanding and applying principles of chemistry, physics, and engineering with an aim to achieve optimal plant operations. For instance, in our exercise involving the design of a furnace for an industrial boiler, chemical process engineering would guide the preparation of a flowchart, which details all the process steps and the interconnections between different equipment pieces such as the furnace, boiler, and heat exchanger. It would also involve the analysis of the combustion reaction, crucial for determining the furnace's efficiency and environmental impact, and deciding on parameters like air feed rate and temperature. Designing a reliable and efficient setup requires deep knowledge of thermochemical properties, reaction kinetics, heat transfer, and fluid dynamics—all essential components of chemical process engineering.

Moreover, by combining this information with practical constraints such as safety regulations, cost considerations, and equipment availability, engineers can devise a system that not only performs well but also adheres to environmental standards and meets economic objectives. Clearly, industrial boiler design is a multifaceted challenge that benefits greatly from the insights provided by chemical process engineering.

Combustion Reaction

Combustion reactions are chemical processes where a fuel reacts with an oxidizer to release energy in the form of heat. In the context of our exercise, the fuel is methane (CH_4), which burns completely with oxygen from the air to produce carbon dioxide (CO_2) and water (H_2O), releasing a significant amount of heat. An understanding of combustion is crucial as it determines the fuel efficiency and emission rates of the furnace.

When methane is burned with a 20% excess air supply, it ensures that there is enough oxygen for the methane to combust completely, avoiding the production of unwanted substances like carbon monoxide (CO). Complete combustion is more efficient and environmentally friendly, as it maximizes energy output while minimizing pollutants. To analyze a combustion reaction in an industrial context, one must account for the stoichiometric balance, which involves calculating the precise amounts of reactants needed to ensure complete combustion without leaving an excess of either fuel or oxygen.

Energy Balance

Energy balance is a fundamental concept in evaluating the efficiency of chemical processes. It entails equating the energy entering a system to the energy exiting the system, taking into account any energy losses. For practical purposes, the first law of thermodynamics, which states that energy cannot be created or destroyed, guides this balance.

When we look at the given industrial boiler furnace design, the heat (\f\(\f\backslash dot{Q}\f\))) transfer process needs meticulous calculation. Heat is transferred from the furnace to convert boiler feedwater into superheated steam. The energy balance would involve equating the heat released by burning methane to the heat required to convert the water to steam at specified pressure and temperature. Preheating the air through a heat exchanger introduces another layer to this balance, as it makes the combustion process more energy-efficient. The heat that would have been lost with the exhaust gases is now used to increase the inlet air temperature, which in turn leads to a more efficient heat transfer to the boiler feedwater.

This improved process efficiency is evident in the increased rate of steam production. By calculating the enthalpy change of the feedwater, and using the higher heating value (HHV) of methane, we can determine the actual heat transfer rate and the degree to which the preheater impacts the system—clearly demonstrating energy conservation principles in practice.

Heat Exchanger Efficiency

Heat exchanger efficiency is a critical consideration in process engineering as it directly impacts the overall efficiency of thermal systems. Heat exchangers are designed to transfer heat from one fluid to another without them coming into direct contact. In the context of our exercise, the heat exchanger preheats the air before it enters the furnace, improving the furnace's thermal efficiency.

The effectiveness of a heat exchanger is judged by how well it can bring the temperature of the process fluid (in our case, the air) close to the initial temperature of the hot fluid (combustion gases). This process conserves energy by utilizing the thermal energy of the exhaust gases, otherwise released to the atmosphere, and reduces the fuel needed to reach the desired combustion temperature inside the furnace. Such a system contributes to reduced operational costs and enhanced energy savings.

It's important to note that the performance of heat exchangers can be affected by factors such as fouling, which is the accumulation of deposits on the heat transfer surfaces, and the thermal properties of the fluids involved. Regular maintenance and the use of appropriate design criteria can help maintain the high efficiency necessary for the system to function economically and sustainably.