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Chapter 8: Problem 35

A gas containing water vapor has a dry-basis composition of 7.5 mole \(\%\) CO, \(11.5 \%\) CO \(_{2}, 0.5 \%.\) \(\mathrm{O}_{2},\) and \(80.5 \% \mathrm{N}_{2} .\) The gas leaves a catalyst regeneration unit at \(620^{\circ} \mathrm{C}\) and 1 atm with a dew point of \(57^{\circ} \mathrm{C}\) at a flow rate of \(28.5 \mathrm{SCMH}\left[\mathrm{m}^{3}(\mathrm{STP}) / \mathrm{h}\right] .\) Valuable solid catalyst particles entrained in the gas are to be recovered in an electrostatic precipitator, but the gas must first be cooled to \(425^{\circ} \mathrm{C}\) to prevent damage to the precipitator electrodes. The cooling is accomplished by spraying water at \(20^{\circ} \mathrm{C}\) into the gas. (a) Use simultaneous material and energy balances on the spray cooler to calculate the required water feed rate ( \(\mathrm{kg} / \mathrm{h}\) ). Treat the spray cooler as adiabatic and neglect the heat transferred from the entrained solid particles as they cool. (b) In terms that a high school senior could understand, explain the operation of the spray cooler in this problem. (What happens when the cold water contacts the hot gas?)

Short Answer

Expert verified
The required feed rate of the water can be solved by balancing both the mass and energy in the system, while the mechanism of spray cooling can be explained as a process of heat transfer from the hot gas to the cold water, resulting in a decrease in the gas temperature and the evaporation of the water.

Step by step solution

01

Analyze the composition of the gas

The composition of the gas is given in terms of moles. The number of moles for each are: \(N_{CO} = 7.5\% \), \(N_{CO2} = 11.5\% \), \(N_{O2} = 0.5\% \), and \(N_{N2} = 80.5\% \). The total number of moles of the mixture is 100%.
02

Convert the composition to mass basis

Next, the number of moles needs to be converted to a mass basis. This can be accomplished by multiplying the mole fraction of each component by its respective molar mass. The molar masses of CO, CO_{2}, O_{2}, and N_{2} are approximately 28, 44, 32, and 28 g/mole, respectively.
03

Calculate the mass flow rate of the gas

The mass flow rate of the dry gas can be found by multiplying the volumetric flow rate by the density of the mixture. The volumetric flow rate and density need to be at standard conditions. Using the given volumetric flow rate of 28.5 m^3/h and the density of an ideal gas at standard conditions, we can find the mass flow rate.
04

Define the system and perform the material balance

The gas mixture and water are the inputs to the system, and the cooled gas mixture and water vapor are the outputs. Based on the conservation of mass, the total mass entering the system equals the mass leaving.
05

Conduct the energy balance

Heat added and energy going into the system are equal to the heat removed and energy leaving the system. Use the enthalpy of each component to calculate the total energy entering and leaving the system. The heat capacity of each component will be needed to compute the change in enthalpy.
06

Solve for the water feed rate

The water feed rate can be isolated in the energy balance equation.
07

Explain how the spray cooler works

When cold water is sprayed into the hot gas, it absorbs the heat from the gas and evaporates, cooling the gas in the process.

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Key Concepts

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

Gas Composition
Gas composition is a crucial aspect when working with material and energy balances, especially in systems involving gases. It refers to the specific breakdown of different gases present in a mixture. In our exercise, the gas mixture is composed of carbon monoxide ( N_{CO} ), carbon dioxide ( N_{CO2} ), oxygen ( N_{O2} ), and nitrogen ( N_{N2} ) with respective mole percentages of 7.5%, 11.5%, 0.5%, and 80.5%. Understanding this composition allows us to perform further calculations, such as determining the mass-based composition and performing balances.
  • Molecular materials possess specific properties like molar mass, which can be used to convert mole fractions to mass fractions. For instance, utilizing molar masses like 28 g/mole for CO or 44 g/mole for CO_2 aids in these conversions.
  • Such conversions are necessary when calculating the mass flow rate of a gas mixture, as many chemical engineering processes involve both mass and energy considerations based on weight, not just the number of particles.
Heat Transfer
Heat transfer is a critical element in many processes, including the spray cooler system in this example. It refers to the movement of heat from one substance to another, causing changes in temperature.
In our exercise, the primary goal is to cool a hot gas stream from 620掳C to 425掳C. This involves transferring heat from the gas to the cooling medium (in this case, water), reducing the temperature of the gas.
  • Various modes of heat transfer include conduction, convection, and radiation. The most relevant here is convection, as the movement of water droplets through gas facilitates heat exchange.
  • The temperature change of the gas and water is driven by their respective heat capacities, which indicate how much heat is required to change their temperatures by a certain amount.
  • By understanding the enthalpy changes in both the gas and water, the amount of heat transferred can be calculated, which is essential for determining the water feed rate.
Adiabatic Process
An adiabatic process is one in which no heat is exchanged with the surroundings. This assumption simplifies calculations but requires that any energy changes happen due to work or changes within the system itself, not from external heat exchange.
In the context of the spray cooler, it implies that the system is isolated concerning heat exchange. Therefore, energy leaving the hot gas as it cools must be absorbed internally, such as by the water being evaporated into steam.
  • This condition simplifies the energy balance, as it enables the use of heat capacities and enthalpy changes directly without accounting for external heat loss.
  • It means all the cooling effect is achieved by the water's absorption of energy from the gas, leading to its vaporization.
  • Understanding adiabatic processes is vital for efficient system design, minimizing unnecessary complexity and computational difficulty.
Cooling Systems
Cooling systems like the spray cooler in this exercise play a fundamental role in temperature regulation of gases and vapors in industrial processes. When hot gas encounters the water spray, several events occur.
  • Initially, colder water droplets absorb heat from the hot gas, reducing its temperature.
  • This absorption of heat causes the water to evaporate into steam, a process that effectively removes heat. The latent heat of evaporation is crucial to this conversion and cooling process.
  • For practical applications, it's essential to calculate the required water feed rate to ensure adequate cooling without oversupply, which would be wasteful.
  • Effective cooling systems are key in preventing equipment damage, such as the protection of electrostatic precipitator electrodes in this scenario, avoiding high repair or replacement costs.
Through careful balance of the energy dynamics and water usage, these systems maintain operational efficiency and extend equipment longevity.

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Most popular questions from this chapter

The brakes on an automobile act by forcing brake pads, which have a metal support and a lining, to press against a disk (rotor) attached to the wheel. Friction between the pads and the disk causes the car to slow or stop. Each wheel has an iron brake disk with a mass of \(15 \mathrm{lb}_{\mathrm{m}}\) and two brake pads, each having a mass of \(11 \mathrm{b}_{\mathrm{m}}\). (a) Suppose an automobile is moving at 55 miles per hour when the driver suddenly applies the brakes and brings the car to a rapid halt. Take the heat capacity of the disk and brake pads to be \(0.12 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right)\) and assume that the car stops so rapidly that heat transfer from the disk and pads has been insignificant. Estimate the final temperature of the disk and pads if the car is (i) a Toyota Camry, which has a mass of about \(3200 \mathrm{Ib}_{\mathrm{m}},\) or (ii) a Cadillac Escalade, which has a mass of about \(5.900 \mathrm{lb}_{\mathrm{m}}.\) (b) Why are the linings on brake pads no longer made of asbestos? Your answer should provide information on specific issues or concerns caused by the use of asbestos.

Fish and wildlife managers have determined that a sudden temperature increase greater than \(5^{\circ} \mathrm{C}\) would be harmful to the marine ecosystem of a river. Warmer waters contain less dissolved oxygen and cause organisms in a river to increase their metabolism; if the temperature increase is sudden, the organisms do not have time to adapt to the new environment and likely will die. (Changes in river temperatures of five degrees and more due to seasonal temperature variations are common, but those temperature changes are gradual.) A proposed chemical plant plans to use river water for process cooling. The river flows at a rate of \(15.0 \mathrm{m}^{3} / \mathrm{s}\) at a temperature of \(15^{\circ} \mathrm{C}\), and a fraction of it will be diverted to the plant. Preliminary calculations reveal that the cooling water will remove \(5.00 \times 10^{5} \mathrm{kJ} / \mathrm{s}\) of heat from the plant. A portion of the extracted water will evaporate from the plant into the atmosphere, and the remainder will be returned to the river at a temperature of \(35^{\circ} \mathrm{C}\). (a) Draw and completely label a flowchart of the process and prove that there is enough information available to calculate all of the unknown stream flow rates on the chart. (b) Estimate the fraction of the river flow that must be diverted to the plant and the percentage of the cooling water that evaporates. Assume that water has a constant heat capacity of \(4.19 \mathrm{kJ} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right)\) and a heat of vaporization roughly that of water at the normal boiling point, and also assume that the specific enthalpy of the water vapor relative to liquid water at \(15^{\circ} \mathrm{C}\) equals the heat of vaporization. (c) Write (but don't evaluate) an expression for the enthalpy change neglected by the assumption about the specific enthalpy of the steam.

On a cold winter day the temperature is \(2^{\circ} \mathrm{C}\) and the relative humidity is \(15 \% .\) You inhale air at an average rate of \(5500 \mathrm{mL} / \mathrm{min}\) and exhale a gas saturated with water at body temperature, roughly \(37^{\circ} \mathrm{C} .\) If the mass flow rates of the inhaled and exhaled air (excluding water) are the same, the heat capacities \(\left(C_{p}\right)\) of the water-free gases are each \(1.05 \mathrm{J} /\left(\mathrm{g} \cdot^{\circ} \mathrm{C}\right),\) and water is ingested into the body as a liquid at \(22^{\circ} \mathrm{C},\) at what rate in \(\mathrm{J} /\) day do you lose energy by breathing? Treat breathing as a continuous process (inhaled air and liquid water enter, exhaled breath exits) and neglect work done by the lungs.

A stream of air at \(77^{\circ} \mathrm{F}\) and 1.2 atm absolute flowing at a rate of \(225 \mathrm{ft}^{3} / \mathrm{h}\) is blown through ducts that pass through the interior of a large industrial motor. The air emerges at \(500^{\circ} \mathrm{F}\). Calculate the rate at which the air is removing heat generated by the motor. What assumption have you made about the pressure dependence of the specific enthalpy of air?

Saturated propane vapor at \(2.00 \times 10^{2}\) psia is fed to a well- insulated heat exchanger at a rate of \(3.00 \times 10^{3} \mathrm{SCFH}\) (standard cubic feet per hour). The propane leaves the exchanger as a saturated liquid (i.e., a liquid at its boiling point) at the same pressure. Cooling water enters the exchanger at \(70^{\circ} \mathrm{F},\) flowing cocurrently (in the same direction) with the propane. The temperature difference between the outlet streams (liquid propane and water) is \(15^{\circ} \mathrm{F}\). (a) What is the outlet temperature of the water stream? (Use the Antoine equation.) Is the outlet water temperature less than or greater than the outlet propane temperature? Briefly explain. (b) Estimate the rate (Btu/h) at which heat must be transferred from the propane to the water in the heat exchanger and the required flow rate \(\left(1 \mathrm{b}_{\mathrm{m}} / \mathrm{h}\right)\) of the water. (You will need to write two separate energy balances.) Assume the heat capacity of liquid water is constant at \(1.00 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right)\) and neglect heat losses to the outside and the effects of pressure on the heat of vaporization of propane.
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