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Chapter 9: Problem 75

In a surface-coating operation, a polymer (plastic) dissolved in liquid acetone is sprayed on a solid surface and a stream of hot air is then blown over the surface, vaporizing the acetone and leaving a residual polymer film of uniform thickness. Because environmental standards do not allow discharging acetone into the atmosphere, a proposal to incinerate the stream is to be evaluated. The proposed process uses two parallel columns containing beds of solid particles. The air-acetone stream, which contains acetone and oxygen in stoichiometric proportion, enters one of the beds at \(1500 \mathrm{mm} \mathrm{Hg}\) absolute at a rate of 1410 standard cubic meters per minute. The particles in the bed have been preheated and transfer heat to the gas. The mixture ignites when its temperature reaches \(562^{\circ} \mathrm{C}\), and combustion takes place rapidly and adiabatically. The combustion products then pass through and heat the particles in the second bed, cooling down to \(350^{\circ} \mathrm{C}\) in the process. Periodically the flow is switched so that the heated outlet bed becomes the feed gas preheater/combustion reactor and vice versa. Use the following average values for \(C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]\) in solving the problems to be given: 0.126 for \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}, 0.033\) for \(\mathrm{O}_{2}, 0.032\) for \(\mathrm{N}_{2}, 0.052\) for \(\mathrm{CO}_{2},\) and 0.040 for \(\mathrm{H}_{2} \mathrm{O}(\mathrm{v})\) (a) If the relative saturation of acetone in the feed stream is \(12.2 \%,\) what is the stream temperature? (b) Determine the composition of the gas after combustion, assuming that all of the acetone is converted to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O},\) and estimate the temperature of this stream. (c) Estimate the rates ( \(\mathrm{kW}\) ) at which heat is transferred from the inlet bed particles to the feed gas prior to combustion and from the combustion gases to the outlet bed particles. Suggest an alternative to the two-bed feed switching arrangement that would achieve the same purpose.

Short Answer

Expert verified
The initial stream temperature is calculated from the vapor pressure curve for acetone, given a specified relative saturation. After complete combustion, the gas composition consists of carbon dioxide and water, and its temperature can be calculated from energy conservation. Finally, heat transfer rates can be estimated based on changes in gas enthalpy before and after combustion. An alternative to the two-bed system could be a rotating heat exchanger.

Step by step solution

01

Calculate the initial temperature

Given a relative saturation of 12.2%, we are to find the stream temperature. The saturation pressure of acetone at \(1500 mmHg\) is proportional to the vapor pressure at its boiling point, as given by Clausius鈥揅lapeyron equation. Use the relation \( P = P_0 * x \), where \( P \) is the partial pressure, \( P_0 \) is the saturation pressure, and \( x \) is the mole fraction. Solving for the mole fraction will give us the initial temperature of the stream based on the vapor pressure curve for acetone.
02

Determine the composition of the gas after combustion

Assuming complete combustion of acetone, it will convert to carbon dioxide and water with stoichiometric proportions. From the combustion reaction equation, \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O} + 4O_2 \rightarrow 3CO_2 + 3H_2O\), we can count the number of moles and calculate the composition as mole fractions of each component in the gas.
03

Calculate the post-combustion temperature

Use the principle of energy conservation. The heat gained by the gases is equal to the heat lost by the combustion reaction with respect to the heat capacity, \( C_p \), of each component. Solve the energy balance equation, \( Q = \Delta H = \Sigma n_i * C_{p,i} * ( T_f - T_0 ) \), where \( T_f \) is the final temperature, \( T_0 \) is the initial temperature, and \( n_i \) is the number of moles of each component. Again, we assume adiabatic conditions, implying no heat is lost to the surroundings.
04

Estimate the heat transfer rates

The heat transferred from the inlet bed particles to the feed gas is equal to the increase in enthalpy of the gas before combustion, calculated using \( Q = m * C_p * \Delta T \). Similarly, the heat transferred from the combustion gases to the outlet bed is equal to the decrease in enthalpy of the gas, calculated in the same manner. Note: the rate of heat transfer will be in kilowatts, as heat transfer rate is power.
05

Suggest an alternative

An alternative solution to the two-bed feed switching arrangement could be a continuously rotating heat exchanger system, where one half of the exchanger is heated while the other half cools, rotating to allow for continuous operation.

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Key Concepts

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

Understanding the Combustion Process
The combustion process in chemical engineering is a cornerstone reaction where a fuel, like acetone in our exercise, reacts with an oxidant, such as oxygen, to produce heat and new chemical species.

Combustion is an exothermic reaction meaning it releases energy, which is particularly vital in energy generation and industrial processes. The key is the stoichiometric balance that ensures the oxidant reacts completely with the fuel, which can be represented by the balanced equation \( \text{C}_3 \text{H}_6 \text{O} + 4\text{O}_2 \rightarrow 3\text{CO}_2 + 3\text{H}_2\text{O} \). In the exercise, ensuring that the acetone and oxygen are in the correct proportions is critical to prevent both the wastage of reactants and the emission of harmful by-products.

For educational purposes, it's useful to note that combustion can be complete or incomplete, with complete combustion yielding only carbon dioxide and water as products, while incomplete combustion can result in carbon monoxide and other hydrocarbons as well鈥攑otentially dangerous outcomes. The conditions found within the given columns facilitate an environment for complete combustion, characterized by a high temperature of \(562^\circ C\) for ignition and a rapid reaction.
Navigating Energy Balance in Combustion Systems
Energy balance in chemical processes maintains the law of conservation of energy, stating that the energy entering a system must equal the energy exiting the system plus any changes in the energy within the system.

For students, understanding energy balance involves tracking how energy is transformed during chemical reactions and how it's transferred between the system and its surroundings. In our exercise, the temperature rise and the heat transfer are manifestations of the energy balance principle. Since the reaction is adiabatic (no heat loss to the surroundings), the energy released during combustion must equal the increase in enthalpy of the reaction products.

The energy balance equation, \( Q = \Sigma n_i * C_{p,i} * ( T_f - T_0 ) \), where \(C_p\) is the heat capacity at constant pressure, \(n_i\) is the number of moles, \(T_f\) the final temperature, and \(T_0\) the initial temperature, encapsulates this concept. Students should grasp that the heat capacities are crucial for calculating the energy balance, as they dictate how much heat is required to raise the temperature of each component within the reaction mixture.
Heat Transfer in Chemical Engineering Operations
Heat transfer is a fundamental concept thrown into sharp relief in our exercise involving two beds of solid particles and a hot gas stream. This process occurs in three primary forms: conduction, convection, and radiation. In engineering applications, such as the one described, convection is the mode of energy transmission we discuss, where heat is carried away by the movement of fluids鈥攊n this case, the hot air-acetone mixture and the combustion gases.

The rate of heat transfer is directly linked to the temperature difference between the hot and cold zones, the area through which heat is transferred, and the properties of the fluids and materials involved. As the preheated particles transfer heat to the gas stream, and the gas stream subsequently heats the second bed of particles after combustion, determining these rates involves using formulas such as \( Q = m * C_p * \Delta T \).

Exploring alternatives to the two-bed system, such as a rotating heat exchanger mentioned in the exercise solution, provides a practical perspective for students on how process efficiency can be improved in real-world scenarios. This system could potentially provide continuous operation and improved energy conservation compared to the periodic switching of beds, a vital consideration in process design.

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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.

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.

A culture of the fungus aspergillus niger is used industrially in the manufacture of citric acid and other organic species. Cells of the fungus have an ultimate analysis of \(\mathrm{CH}_{1,79} \mathrm{N}_{0.2} \mathrm{O}_{0.5}\), and the heat of formation of this species is necessary to approximate the heat duty for the bioreactor in which citric acid is to be produced. You collect a dried sample of the fungus and determine its heat of combustion to be \(-550 \mathrm{kJ} / \mathrm{mol} .\) Estimate the heat of formation \((\mathrm{kJ} / \mathrm{mol})\) of the dried fungus cells.

Sulfur dioxide is oxidized to sulfur trioxide in a small pilot-plant reactor. SO \(_{2}\) and \(100 \%\) excess air are fed to the reactor at \(450^{\circ} \mathrm{C}\). The reaction proceeds to a \(65 \% \mathrm{SO}_{2}\) conversion, and the products emerge from the reactor at \(550^{\circ} \mathrm{C}\). The production rate of \(\mathrm{SO}_{3}\) is \(1.00 \times 10^{2} \mathrm{kg} / \mathrm{min}\). The reactor is surrounded by a water jacket into which water at \(25^{\circ} \mathrm{C}\) is fed. (a) Calculate the feed rates (standard cubic meters per second) of the \(\mathrm{SO}_{2}\) and air feed streams and the extent of reaction, \(\xi\) (b) Calculate the standard heat of the SO_ oxidation reaction, \(\Delta H_{\mathrm{t}}^{\mathrm{r}}(\mathrm{kJ}) .\) Then, taking molecular species at \(25^{\circ} \mathrm{C}\) as references, prepare and fill in an inlet-outlet enthalpy table and write an energy balance to calculate the necessary rate of heat transfer ( \(\mathrm{kW}\) ) from the reactor to the cooling water. (c) Calculate the minimum flow rate of the cooling water if its temperature rise is to be kept below \(15^{\circ} \mathrm{C}\) (d) Briefly state what would have been different in your calculations and results if you had taken elemental species as references in Part (b).

Coke can be converted into \(\mathrm{CO}-\mathrm{a}\) fuel gas- -in the reaction $$\mathrm{CO}_{2}(\mathrm{g})+\mathrm{C}(\mathrm{s}) \rightarrow 2 \mathrm{CO}(\mathrm{g})$$ A coke that contains \(84 \%\) carbon by mass and the balance noncombustible ash is fed to a reactor with a stoichiometric amount of \(\mathrm{CO}_{2}\). The coke is fed at \(77^{\circ} \mathrm{F}\), and the \(\mathrm{CO}_{2}\) enters at \(400^{\circ} \mathrm{F}\). Heat is transferred to the reactor in the amount of \(5859 \mathrm{Btu} / \mathrm{lb}_{\mathrm{m}}\) coke fed. The gascous products and the solid reactor effluent (the ash and unburned carbon) leave the reactor at \(1830^{\circ} \mathrm{F}\). The heat capacity of the solid is \(0.24 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right)\) (a) Calculate the percentage conversion of the carbon in the coke. (b) The carbon monoxide produced in this manner can be used as a fuel for residential home heating, as can the coke. Speculate on the advantages and disadvantages of using the gas. (There are several of each.)
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