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Chapter 8: Problem 26

Propane is to be burned with \(25.0 \%\) excess air. Before entering the furnace, the air is preheated from \(32^{\circ} \mathrm{F}\) to \(575^{\circ} \mathrm{F}\) (a) At what rate (B tu/h) must heat be transferred to the air if the feed rate of propane is \(1.35 \times 10^{5}\) SCFH (ft \(^{3} / \mathrm{h}\) at \(\mathrm{STP}\) )? (b) The stack gas leaves the furnace at \(855^{\circ} \mathrm{F}\). How is the air likely to be preheated?

Short Answer

Expert verified
a) The rate of heat transfer required is approximately 3.94x10^7 Btu/h. b) Preheating the air is likely achieved using a heat exchanger that transfers heat from the stack gas exiting the furnace to the incoming air.

Step by step solution

01

Calculate Air Demand

First, one must determine the amount of air needed for perfect (stoichiometric) combustion of the propane C3H8. The balanced combustion reaction is: C3H8 + 5 O2 -> 3 CO2 + 4 H2O Thus, one mole of C3H8 requires 5 moles of oxygen. Air is approximately 21% oxygen, so instead of 5 moles of pure oxygen, 5/0.21 = 23.81 moles of air is required for perfect combustion. However, we are told that 25% excess air is provided for combustion, hence the air supplied = 1.25 * 23.81 = 29.76 SCF (standard cubic feet).
02

Determine the Heat Capacity of Air

The heat capacity of air, Cp_air, needs to be known to calculate the heat transfer. The Cp_air is approximately 0.24 Btu/lb-F, and the density of air at standard temperature and pressure (STP) is approximately 0.075 lb/ft3.
03

Calculate Heat Transfer

The amount of heat transferred to preheat the air can be calculated using the equation Q = m * Cp * DeltaT, where m is the mass of air, Cp the heat capacity and DeltaT is the temperature change. We are told that the air is preheated from 32掳F to 575掳F, hence DeltaT = 575 - 32 = 543掳F. With the previously calculated demand of air (of 29.76 SCF for perfect combustion) and the feed rate of propane (1.35x10^5 SCF/h), the hourly air volume can be calculated as Vair_hourly = 1.35x10^5 SCF/h * 29.76 SCF/SCF = 4.02x10^6 SCF/h. The mass of the air, mair, is obtained from using the volume and the density of air (from Step 2), which gives mair = 4.02x10^6 ft^3/h * 0.075 lb/ft^3 = 3.02x10^5 lb/h. With these numbers, the heat rate can be calculated as Q = 3.02x10^5 lb/h * 0.24 Btu/lb-掳F * 543 掳F = 3.94x10^7 Btu/h.
04

Address the Preheating

The stack gas leaving the furnace is likely hotter than the preheated air entering the furnace. As such, it probably makes sense to use some type of heat exchanger to transfer heat from the stack gas to the incoming air. This would allow for some level of heat recovery, increasing the overall efficiency of the furnace.

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Key Concepts

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

Stoichiometric Combustion
Understanding stoichiometric combustion is fundamental in the field of chemical engineering education as it directly impacts the design and operation of combustion systems. Stoichiometric combustion refers to the ideal chemical reaction where fuel, such as propane, is burned with the exact amount of oxygen needed, with no excess air. For propane (C3H8), the balanced equation is: C3H8 + 5 O2 -> 3 CO2 + 4 H2O.

When the reaction uses 25% excess air, it ensures complete combustion while avoiding a situation where unreacted fuel would be wasted. However, this excess air must also be heated up, which requires additional energy. This forms a significant consideration for engineers working on improving the efficiency of heating systems. They must account for the mass flow rate of both the fuel and air to optimize the process.

Heat Capacity
A critical component to solving problems in thermo-fluid systems is the heat capacity, defined as the amount of heat required to raise the temperature of a unit mass of a substance by one degree. In the educational example of preheating air for combustion, the heat capacity (Cp) of air plays a pivotal role.

For air, Cp is approximately 0.24 Btu/lb-F, indicating the energy needed to raise the temperature of one pound of air by one degree Fahrenheit. Knowledge of the heat capacity allows engineers to quantitatively assess how much heat (Q) is to be transferred to or from a substance when its temperature changes. This heat transfer is necessary to reach the desired temperature before introducing air into the furnace for efficient combustion.
Heat Transfer
Heat transfer is a fundamental concept in chemical engineering, encompassing the exchange of thermal energy between physical systems. The rate at which heat must be transferred (Q) can be determined by using the equation Q = m * Cp * 螖T, where m represents the mass, Cp the heat capacity, and 螖罢 the temperature difference. In our scenario, preheating the air from 32掳F to 575掳F entails a substantial temperature increase, thereby requiring a significant amount of heat.

Understanding how this heat transfer occurs enables engineers to implement systems such as heat exchangers. These devices can enhance efficiency by recovering heat from exhaust gases (in this case, stack gases) and using it to preheat incoming air, as suggested by the exercise improvement advice. This type of energy recovery is a key strategy in reducing fuel consumption and minimizing waste in industrial processes.

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Most popular questions from this chapter

Propane gas enters a continuous adiabatic heat exchanger \(^{17}\) at \(40^{\circ} \mathrm{C}\) and \(250 \mathrm{kPa}\) and exits at \(240^{\circ} \mathrm{C}\). Superheated steam at \(300^{\circ} \mathrm{C}\) and 5.0 bar enters the exchanger flowing countercurrently to the propane and exits as a saturated liquid at the same pressure. (a) Taking as a basis 100 mol of propane fed to the exchanger, draw and label a process flowchart. Include in your labeling the volume of propane fed \(\left(\mathrm{m}^{3}\right),\) the mass of steam fed \((\mathrm{kg}),\) and the volume of steam fed \(\left(\mathrm{m}^{3}\right)\) (b) Calculate values of the labeled specific enthalpies in the following inlet-outlet enthalpy table for this process. $$\begin{array}{|l|cc|cc|} \hline \text { Species } & n_{\text {in }} & \hat{H}_{\text {in }} & n_{\text {out }} & \hat{H}_{\text {out }} \\ \hline \mathrm{C}_{3} \mathrm{H}_{8} & 100 \mathrm{mol} & \hat{H}_{\mathrm{a}}(\mathrm{kJ} / \mathrm{mol}) & 100 \mathrm{mol} & \hat{H}_{\mathrm{c}}(\mathrm{kJ} / \mathrm{mol}) \\ \mathrm{H}_{2} \mathrm{O} & m_{\mathrm{w}}(\mathrm{kg}) & \hat{H}_{\mathrm{b}}(\mathrm{kJ} / \mathrm{kg}) & m_{\mathrm{w}}(\mathrm{kg}) & \hat{H}_{\mathrm{d}}(\mathrm{kJ} / \mathrm{kg}) \\ \hline \end{array}$$ (c) Use an energy balance to calculate the required mass feed rate of the steam. Then calculate the volumetric feed ratio of the two streams ( \(\mathrm{m}^{3}\) steam fed \(/ \mathrm{m}^{3}\) propane fed). Assume ideal-gas behavior for the propane but not the steam and recall that the exchanger is adiabatic. (d) Calculate the heat transferred from the water to the propane ( \(k J / m^{3}\) propane fed). (Hint: Do an energy balance on either the water or the propane rather than on the entire heat exchanger.) (e) Over a period of time, scale builds up on the heat-transfer surface, resulting in a lower rate of heat transfer between the propane and the steam. What changes in the outlet streams would you expect to see as a result of the decreased heat transfer?

Saturated steam at \(300^{\circ} \mathrm{C}\) is used to heat a countercurrently flowing stream of methanol vapor from \(65^{\circ} \mathrm{C}\) to \(260^{\circ} \mathrm{C}\) in an adiabatic heat exchanger. The flow rate of the methanol is 6500 standard liters per minute, and the steam condenses and leaves the heat exchanger as liquid water at \(90^{\circ} \mathrm{C}.\) (a) Calculate the required flow rate of the entering steam in \(\mathrm{m}^{3} / \mathrm{min}\). (b) Calculate the rate of heat transfer from the water to the methanol ( \(\mathrm{kW}\) ). (c) Suppose the outlet temperature of the methanol is measured and found to be \(240^{\circ} \mathrm{C}\) instead of the specified value of \(260^{\circ} \mathrm{C}\). List five possible realistic explanations for the \(20^{\circ} \mathrm{C}\) difference. 7 An adiabatic heat exchanger is one for which no heat is exchanged with the surroundings. All of the heat lost by the hot stream is transferred to the cold stream.

A mixture of \(n\) -hexane vapor and air leaves a solvent recovery unit and flows through a \(70-\mathrm{cm}\) diameter duct at a velocity of \(3.00 \mathrm{m} / \mathrm{s}\). At a sampling point in the duct the temperature is \(40^{\circ} \mathrm{C}\), the pressure is \(850 \mathrm{mm}\) Hg, and the dew point of the sampled gas is \(25^{\circ} \mathrm{C}\). The gas is fed to a condenser in which it is cooled at constant pressure, condensing \(70 \%\) of the hexane in the feed. (a) Perform a degree-of-freedom analysis to show that enough information is available to calculate the required condenser outlet temperature \(\left(^{\circ} \mathrm{C}\right)\) and cooling rate \((\mathrm{kW})\) (b) Perform the calculations. (c) If the feed duct diameter were \(35 \mathrm{cm}\) for the same molar flow rate of the feed gas, what would be the average gas velocity (volumetric flow rate divided by cross-sectional area)? (d) Suppose you wanted to increase the percentage condensation of hexane for the same feed stream. Which three condenser operating variables might you change, and in which direction?

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.

Estimate the specific enthalpy of steam (kJ/kg) at \(100^{\circ} \mathrm{C}\) and 1 atm relative to steam at \(350^{\circ} \mathrm{C}\) and 100 bar using: (a) The steam tables. (b) Table B.2 or APEx and assuming ideal-gas behavior. What is the physical significance of the difference between the values of \(\hat{H}\) calculated by the two methods?
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