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Chapter 8: Problem 31

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?

Short Answer

Expert verified
For propane, \(\hat{H}_{a}\) and \(\hat{H}_{c}\) can be found from thermodynamic tables at the given temperatures. The same applies for \(\hat{H}_{b}\) and \(\hat{H}_{d}\) for steam. Mass feed rate and heat transferred can be calculated from energy balance equations. Volumetric feed rate can be found using ideal gas law for propane and steam properties for steam. Scale affects heat transfer causing less heat exchange between propane and steam.

Step by step solution

01

Sketch the Flowchart

For part (a), sketch a flowchart with propane and steam coming into the adiabatic heat exchanger and exiting as heated propane and saturated water respectively. Importantly, mark the quantities asked in the exercise.
02

Calculate the Specific Enthalpies

In part (b), determine the specific enthalpies (\(\hat{H}_{in}\) and \(\hat{H}_{out}\)) for propane and steam using thermodynamic properties data tables, where you need to reference the state (temperature, pressure, and phase) of each substance.
03

Energy Balance and Mass Feed Rate

In part (c), apply the energy balance equation. As there are no other forms of energy involved and it's an adiabatic system (no heat is lost to surroundings), energy going in will equal to energy coming out. From this, calculate the mass feed rate of steam.
04

Volumetric Feed Ratio

Next, use the ideal gas law for the propane and steam volume from steam tables to derive the volumetric feed ratios of propane and steam.
05

Heat Transfer Calculation

In part (d), use the principle of energy conservation to calculate the heat transferred. It can be calculated from the change in enthalpy of propane and the feed rate.
06

Predict the Effect of Scale Build-up

Lastly, part (e) involves a qualitative analysis. As the heat transfer decreases because of scale build up, one would expect less heat to be transferred from steam to the propane, which would likely result in a lower exit temperature for the propane and a less condensed steam.

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Key Concepts

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

Heat Exchanger
A heat exchanger is a device that allows energy exchange between two fluids at different temperatures. In this exercise, propane gas and steam are flown through a continuous adiabatic heat exchanger. The goal is simple: transfer heat from one fluid to another without mixing them. By using metal walls and countercurrent flow, heat can be transferred effectively from the hotter steam to the cooler propane. This process is essential in many industrial applications, enabling processes like heating, cooling, or maintaining specific temperatures.

In a heat exchanger, the main objective is usually to achieve an energy balance, where the heat lost by the hot stream equals the heat gained by the cold stream. During operation, both streams can either increase or decrease in temperature, achieving the required outlet conditions. Awareness of process parameters like inlet and outlet temperatures, pressure conditions, and phase changes is important. It ensures design efficiency and operational stability of the heat exchanger unit.
Enthalpy Calculation
Enthalpy represents the total heat content of a fluid or a system, with both internal energy and the work done by the system to change its volume factored in. For calculations in processes involving heat exchange, like in this exercise, specific enthalpy in kilojoules per mole (kJ/mol for gases) or kilojoules per kilogram (kJ/kg for liquids) can be crucial.

To determine the heat transfer in our gas exchange, knowing the specific enthalpy helps us to calculate how much energy is being moved into or out of the stream. In the context of this problem, it's important to find the specific enthalpies of propane and steam at both the inlet and outlet. For this, one uses data from thermodynamic tables or charts that relate enthalpy to temperature, pressure, and, if applicable, phase changes during the process.
  • Inlet and outlet temperatures and pressures are key variables needed for accurate enthalpy evaluation.
  • Thermodynamic properties help understand phase changes, essential in determining specific enthalpy adjustments.
Understanding these enthalpy changes is key for any energy balance problem.
Ideal-Gas Behavior
Ideal-gas behavior is an assumption applied to gases that behave according to the ideal gas law, expressed as \(PV = nRT\). Here, \(P\) represents pressure, \(V\) is the volume, \(n\) is the amount of substance in moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin. Assuming ideal-gas behavior simplifies calculations of volumetric flow and energy changes in processes.

In our exercise, propane is assumed to behave like an ideal gas. This makes it easier to calculate the volume of propane using the gas law, given the pressure and temperature conditions. The assumption is typically valid under high temperature and low pressure conditions, where intermolecular forces and volumes are negligible.
  • Predicts how gases expand, contract, and transfer heat when heated or cooled.
  • Assumptions are simplified but accurate enough for a first approximation in engineering calculations.
This concept is crucial because it allows engineers to predict process behaviors without complex calculations involving real gas behaviors.
Adiabatic Process
An adiabatic process refers to a thermodynamic process where no heat enters or leaves the system. This means that the system is thermally isolated, with all energy transfers being in the form of work or changes in internal energy. No energy is lost or gained as heat through its boundaries with the surroundings.

In the context of our heat exchanger scenario, being adiabatic implies that the exchange of energy between the propane and steam occurs solely between them without it being gained or lost to the surroundings. This condition is crucial for energy balance calculations, where the energy entering and leaving must be equal.
  • Ensures all energy in such a system is managed and conserved within the system.
  • Crucial for ensuring accuracy in energy and enthalpy calculations in systems designed with thermal isolation.
Adiabatic processes are common in engineering systems designed for efficiency and conservation of energy.

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Most popular questions from this chapter

A gas stream containing \(n\) -hexane in nitrogen with a relative saturation of \(90 \%\) is fed to a condenser at \(75^{\circ} \mathrm{C}\) and 3.0 atm absolute. The product gas emerges at \(0^{\circ} \mathrm{C}\) and 3.0 atm at a rate of \(746.7 \mathrm{m}^{3} / \mathrm{h}\). (a) Calculate the percentage condensation of hexane (moles condensed/mole fed) and the rate \((\mathrm{kW})\) at which heat must be transferred from the condenser. (b) Suppose the feed stream flow rate and composition and the heat transfer from the condenser are the same as in Part (a), but the condenser and outlet stream pressure is only 2.5 atm instead of 3.0 atm. How would the outlet stream temperatures and flow rates and the percentage condensations of hexane calculated in Parts (a) and (b) change (increase, decrease, no change, no way to tell)? Don't do any calculations, but explain your reasoning.

Polyvinylpyrrolidone (PVP) is a polymer product used as a binding agent in pharmaceutical applications as well as in personal-care items such as hairspray. In the manufacture of \(\mathrm{PVP}\), a spray-drying process is used to collect solid PVP from an aqueous suspension, as shown in the flowchart on the next page. A liquid solution containing 65 wt\% \(\mathrm{PVP}\) and the balance water at \(25^{\circ} \mathrm{C}\) is pumped through an atomizing nozzle at a rate of \(1500 \mathrm{kg} / \mathrm{h}\) into a stream of preheated air flowing at a rate of \(1.57 \times 10^{4}\) SCMH. The water evaporates into the stream of hot air and the solid PVP particles are suspended in the humidified air. Downstream, the particles are separated from the air with a filter and collected. The process is designed so that the exiting solid product and humid air are in thermal equilibrium with each other at \(110^{\circ} \mathrm{C}\). For convenience, the spray-drying and solid- separation processes are shown as one unit that may be considered adiabatic. (a) Draw and completely label the process flow diagram and perform a degree- of-freedom analysis. (b) Calculate the required temperature of the inlet air, \(T_{0}\), and the volumetric flow rate \(\left(\mathrm{m}^{3} / \mathrm{h}\right)\) and relative humidity of the exiting air. Assume that the polymer has a heat capacity per unit mass one third that of liquid water, and only use the first two terms of the polynomial heat-capacity formula for air in Table B.2. (c) Why do you think the polymer solution is put through an atomizing nozzle, which converts it to a mist of tiny droplets, rather than being sprayed through a much less costly nozzle of the type commonly found in showers? (d) Due to a design flaw, the polymer solution does not remain in the dryer long enough for all the water to evaporate, so the solid product emerging from the separator is a wet powder. How will this change the values of the outlet temperatures of the emerging gas and powder and the volumetric flow rate and relative humidity of the emerging gas (increase, decrease, can't tell without doing the calculations)? Explain your answers.

A sheet of cellulose acetate film containing 5.00 wt\% liquid acetone enters an adiabatic dryer where \(90 \%\) of the acetone evaporates into a stream of dry air flowing over the film. The film enters the dryer at \(T_{\mathrm{f} 1}=35^{\circ} \mathrm{C}\) and leaves at \(T_{\mathrm{f} 2}\left(^{\circ} \mathrm{C}\right) .\) The air enters the dryer at \(T_{\mathrm{al}}\left(^{\circ} \mathrm{C}\right)\) and 1.01 atm and exits the dryer at \(T_{\mathrm{a} 2}=49^{\circ} \mathrm{C}\) and 1 atm with a relative saturation of \(40 \% . C_{p}\) may be taken to be \(1.33 \mathrm{kJ} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right)\) for dry film and \(0.129 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\) for liquid acetone. Make a reasonable assumption regarding the heat capacity of dry air. The heat of vaporization of acetone may be considered independent of temperature. Take a basis of \(100 \mathrm{kg}\) film fed to the dryer for the requested calculations. (a) Estimate the feed ratio [liters dry air (STP)/kg dry film]. (b) Derive an expression for \(T_{\mathrm{al}}\) in terms of the film temperature change, \(\left(T_{\mathrm{f} 2}-35\right),\) and use it to answer Parts (c) and (d). (c) Calculate the film temperature change if the inlet air temperature is \(120^{\circ} \mathrm{C}\). (d) Calculate the required value of \(T_{\mathrm{al}}\) if the film temperature falls to \(34^{\circ} \mathrm{C},\) and the value if it rises to \(36^{\circ} \mathrm{C}.\) (e) If you solved Parts (c) and (d) correctly, you found that even though the air temperature is consistently higher than the film temperature in the dryer, so that heat is always transferred from the air to the film, the film temperature can drop from the inlet to the outlet. How is this possible?

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.

Estimate the heat of vaporization of diethyl ether at its normal boiling point using Trouton's rule and Chen's rule and compare the results with a tabulated value of this quantity. Calculate the percentage error that results from using each estimation. Then estimate \(\Delta \hat{H}_{\mathrm{v}}\) at \(100^{\circ} \mathrm{C}\) using Watson's correlation.
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