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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

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.

The specific internal energy of formaldehyde (HCHO) vapor at 1 atm and moderate temperatures is given by the formula $$\hat{U}(\mathrm{J} / \mathrm{mol})=25.96 T+0.02134 T^{2}$$ where \(T\) is in \(^{\circ} \mathrm{C}\) (a) Calculate the specific internal energies of formaldehyde vapor at \(0^{\circ} \mathrm{C}\) and \(200^{\circ} \mathrm{C}\). What reference temperature was used to generate the given expression for \(\hat{U} ?\) (b) The value of \(\hat{U}\) calculated for \(200^{\circ} \mathrm{C}\) is not the true value of the specific internal energy of formaldehyde vapor at this condition. Why not? (Hint: Refer back to Section 7.5a.) Briefly state the physical significance of the calculated quantity. (c) Use the closed system energy balance to calculate the heat (J) required to raise the temperature of 3.0 mol HCHO at constant volume from 0^0 C to 200^'C. List all of your assumptions. (d) From the definition of heat capacity at constant volume, derive a formula for \(C_{v}(T)\left[\mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]\) Then use this formula and Equation \(8.3-6\) to calculate the heat \((\) J) required to raise the temperature of 3.0 mol of HCHO(v) at constant volume from 0^ C to 200^'C. [You should get the same result you got in Part (c).]

A fuel gas containing 95 mole\% methane and the balance ethane is burned completely with 25\% excess air. The stack gas leaves the furnace at \(900^{\circ} \mathrm{C}\) and is cooled to \(450^{\circ} \mathrm{C}\) in a waste- heat boiler, a heat exchanger in which heat lost by cooling gases is used to produce steam from liquid water for heating, power generation, or process applications. (a) Taking as a basis of calculation 100 mol of the fuel gas fed to the fumace, calculate the amount of heat (kJ) that must be transferred from the gas in the waste heat boiler to accomplish the indicated cooling. (b) How much saturated steam at 50 bar can be produced from boiler feedwater at \(40^{\circ} \mathrm{C}\) for the same basis of calculation? (Assume all the heat transferred from the gas goes into the steam production.) (c) At what rate ( \(k\) mol/s) must fuel gas be burned to produce 1280 kg steam per hour (an amount required elsewhere in the plant) in the waste heat boiler? What is the volumetric flow rate \(\left(\mathrm{m}^{3} / \mathrm{s}\right)\) of the gas leaving the boiler? (d) Briefly explain how the waste-heat boiler contributes to the plant profitability. (Think about what would be required in its absence.)

The heat required to raise the temperature of \(m\) (kg) of a liquid from \(T_{1}\) to \(T_{2}\) at constant pressure is $$ Q=\Delta H=m \int_{T_{1}}^{T_{2}} C_{p}(T) d T $$ In high school and in first-year college physics courses, the formula is usually given as $$ Q=m C_{p} \Delta T=m C_{p}\left(T_{2}-T_{1}\right) $$ (a) What assumption about \(C_{p}\) is required to go from Equation 1 to Equation \(2 ?\) (b) The heat capacity \(\left(C_{p}\right)\) of liquid \(n\) -hexane is measured in a bomb calorimeter. A small reaction flask (the bomb) is placed in a well- insulated vessel containing \(2.00 \mathrm{L}\) of liquid \(n-\mathrm{C}_{6} \mathrm{H}_{14}\) at \(T=300 \mathrm{K} .\) A combustion reaction known to release \(16.73 \mathrm{kJ}\) of heat takes place in the bomb, and the subsequent temperature rise of the system contents is measured and found to be \(3.10 \mathrm{K}\). In a separate experiment, it is found that \(6.14 \mathrm{kJ}\) of heat is required to raise the temperature of everything in the system except the hexane by \(3.10 \mathrm{K}\). Use these data to estimate \(C_{p}[\mathrm{kJ} /(\mathrm{mol} \cdot \mathrm{K})]\) for liquid \(n\) -hexane at \(T \approx 300 \mathrm{K},\) assuming that the condition required for the validity of Equation 2 is satisfied. Compare your result with a tabulated value.

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?
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