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Chapter 4: Problem 17

If the percentage of fuel in a fuel-air mixture falls below a certain value called the lower flammability limit (LFL), which sometimes is referred to as the lower explosion limit (LEL), the mixture cannot be ignited. In addition there is an upper flammability limit (UFL), which also is known as the upper explosion limit (UEL). For example, the LFL of propane in air is 2.3 mole \(\% \mathrm{C}_{3} \mathrm{H}_{8}\) and the UFL is \(9.5 \%^{14}\). If the percentage of propane in a propane-air mixture is greater than \(2.3 \%\) and less than \(9.5 \%,\) the gas mixture can ignite if it is exposed to a flame or spark. A mixture of propane in air containing 4.03 mole \(\% \mathrm{C}_{3} \mathrm{H}_{8}\) (fuel gas) is the feed to a combustion furnace. If there is a problem in the furnace, a stream of pure air (dilution air) is added to the fuel mixture prior to the furnace inlet to make sure that ignition is not possible. (a) Draw and label a flowchart of the fuel gas-dilution air mixing unit, presuming that the gas entering the furnace contains propane at the LFL, and do the degree-of-freedom analysis. (b) If propane flows at a rate of \(150 \mathrm{mol} \mathrm{C}_{3} \mathrm{H}_{8} / \mathrm{s}\) in the original fuel-air mixture, what is the minimum molar flow rate of the dilution air? (c) How would the actual dilution air feed rate probably compare with the value calculated in Part (b)? (>, \(<,=\) ) Explain.

Short Answer

Expert verified
The minimum molar flow rate of the dilution air could be calculated using the given LFL and propane flowrate. The actual dilution air feed rate would likely be greater than this calculated value to include a safety margin and account for non-ideal conditions.

Step by step solution

01

Drawing flowchart and Degree-of-Freedom Analysis

The flowchart would show the inflow of propane and air, possibly merging together into a stream entering the furnace. A separate inlet stream of pure air, labeled 'dilution air', should also be directed to this merge point. Lastly, a single outflow from the furnace should be shown. A degree of freedom analysis reveals there are three specifications: the inflow rates of fuel gas and air, and the composition of fuel gas. The number of unknowns are most likely the same. Hence, the degree of freedom is zero and the system should be solvable.
02

Calculating Minimum Molar Flow Rate of Dilution Air

The LFL for propane is given as 2.3 mole%. To ensure the inflow mixture does not exceed this limit, the molar flow rate for dilution air can be calculated using the formula: \( \text{Dilution air flowrate} = \frac{\text{Propane flowrate}}{LFL} - \text{Propane flowrate} \). Substituting given values, calculate the minimum dilution air flowrate.
03

Comparative Analysis of Actual and Calculated Dilution Air Feed Rate

The actual dilution air feed rate to the furnace would likely be greater than the minimum calculated in part (b). This is because, in practice, a safety margin is usually added to ensure the propane concentration does not exceed the LFL even under non-ideal conditions. Other factors affecting this could include variations in the feed rates, measurement errors, or fluctuations in the propane composition. Verification through experimental methods would provide the most accurate comparison.

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Key Concepts

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

Flammability Limits
When dealing with fuel-air mixtures, understanding flammability limits is crucial for safe operation. Essentially, these limits dictate whether a mixture can ignite. The Lower Flammability Limit (LFL) is the minimum concentration of fuel required for combustion to occur, while the Upper Flammability Limit (UFL) is the maximum concentration before the mixture becomes too rich to ignite. For propane, the LFL is at 2.3% and the UFL is at 9.5%. This means, for a propane-air mixture to ignite, the propane concentration must be between these two values.

If the concentration of propane is below the LFL, the mixture lacks sufficient fuel to sustain combustion. Conversely, if it exceeds the UFL, there is not enough oxygen for the fuel to burn. Safety protocols often involve diluting mixtures outside these limits to ensure that accidental ignition does not occur.
Degree-of-Freedom Analysis
Degree-of-freedom analysis is a pivotal tool in process engineering, helping to determine whether a system of equations can be solved with the provided data. In the case of the propane-air system, conducting this analysis involves counting the knowns and unknowns. The knowns typically include the inflow rates of the main components and their concentrations.

For this particular problem, three specifications are involved: the rates of inflow for fuel gas and air, as well as the composition of the fuel gas. Zero degrees of freedom indicates that the system is perfectly specified 鈥� neither under- nor over-constrained. This balance ensures that with the existing information, we can solve for the necessary parameters such as the dilution air flow rate required to maintain safety.
Dilution Air Calculation
In improving combustion safety, calculating the necessary dilution air is vital. This process involves reducing the fuel-air mixture to a point where ignition is impossible. The formula used is:\[ \text{Dilution air flowrate} = \frac{\text{Propane flowrate}}{\text{LFL}} - \text{Propane flowrate} \]By substituting the known propane flow rate and the LFL into this equation, you can find the minimum amount of dilution air needed. This ensures the mixture's propane concentration is below the LFL, rendering it non-flammable.

In practice, more dilution air than this minimum is often added to account for measurement errors and fluctuations, thereby maintaining a margin of safety. Engineers calculate this excess air to encompass all possible operational uncertainties.
Combustion Furnace Safety
Safety in combustion processes is paramount, especially in industrial settings. A combustion furnace relies on controlled reactions to function safely, and controlling the fuel-air ratio is a critical part. By keeping propane concentrations within non-flammable limits using dilution air, the risk of accidental ignition is minimized.

Beyond setting precise air flow rates, the key to safety also involves account for unexpected variations in fuel composition or flow. This often means implementing systems for monitoring and adjusting air flows automatically in real time. Regular maintenance and equipment checks further ensure the furnace operates under safe conditions.

Such measures prevent situations where the mixture might accidentally enter the flammable range, avoiding potential hazards. Understanding and controlling these factors are part of a broader approach to creating a safer working environment in facilities using combustion furnaces.

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Most popular questions from this chapter

Inside a distillation column (see Problem 4.8), a downward-flowing liquid and an upward-flowing vapor maintain contact with each other. For reasons we will discuss in greater detail in Chapter \(6,\) the vapor stream becomes increasingly rich in the more volatile components of the mixture as it moves up the column, and the liquid stream is enriched in the less volatile components as it moves down. The vapor leaving the top of the column goes to a condenser. A portion of the condensate is taken off as a product (the overhead product), and the remainder (the reflux) is returned to the top of the column to begin its downward journey as the liquid stream. The condensation process can be represented as shown below: A distillation column is being used to separate a liquid mixture of ethanol (more volatile) and water (less volatile). A vapor mixture containing 89.0 mole \(\%\) ethanol and the balance water enters the overhead condenser at a rate of \(100 \mathrm{lb}\) -mole/h. The liquid condensate has a density of \(49.01 \mathrm{b}_{\mathrm{m}} / \mathrm{ft}^{3},\) and the reflux ratio is \(3 \mathrm{lb}_{\mathrm{m}}\) reflux/lb \(_{\mathrm{m}}\) overhead product. When the system is operating at steady state, the tank collecting the condensate is half full of liquid and the mean residence time in the tank (volume of liquid/volumetric flow rate of liquid) is 10.0 minutes. Determine the overhead product volumetric flow rate (ft \(^{3}\) /min) and the condenser tank volume (gal).

Methane and oxygen react in the presence of a catalyst to form formaldehyde. In a parallel reaction, methane is oxidized to carbon dioxide and water: $$\begin{aligned} \mathrm{CH}_{4}+\mathrm{O}_{2} & \rightarrow \mathrm{HCHO}+\mathrm{H}_{2} \mathrm{O} \\ \mathrm{CH}_{4}+2 \mathrm{O}_{2} & \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \end{aligned}$$ The feed to the reactor contains equimolar amounts of methane and oxygen. Assume a basis of \(100 \mathrm{mol}\) feed/s. (a) Draw and label a flowchart. Use a degree-of-freedom analysis based on extents of reaction to determine how many process variable values must be specified for the remaining variable values to be calculated. (b) Use Equation 4.6-7 to derive expressions for the product stream component flow rates in terms of the two extents of reaction, \(\xi_{1}\) and \(\xi_{2}\) (c) The fractional conversion of methane is 0.900 and the fractional yield of formaldehyde is 0.855 . Calculate the molar composition of the reactor output stream and the selectivity of formaldehyde production relative to carbon dioxide production. (d) A classmate of yours makes the following observation: "If you add the stoichiometric equations for the two reactions, you get the balanced equation $$2 \mathrm{CH}_{4}+3 \mathrm{O}_{2} \rightarrow \mathrm{HCHO}+\mathrm{CO}_{2}+3 \mathrm{H}_{2} \mathrm{O}$$ The reactor output must therefore contain one mole of \(\mathrm{CO}_{2}\) for every mole of HCHO, so the selectivity of formaldehyde to carbon dioxide must be \(1.0 .\) Doing it the way the book said to do it, \(I\) got a different selectivity. Which way is right, and why is the other way wrong?" What is your response?

The gas-phase reaction between methanol and acetic acid to form methyl acetate and water takes place in a batch reactor. When the reaction mixture comes to equilibrium, the mole fractions of the four reactive species are related by the reaction equilibrium constant $$K_{y}=\frac{y_{C} y_{D}}{y_{A} y_{B}}=4.87$$ (a) Suppose the feed to the reactor consists of \(n_{\mathrm{A} 0}, n_{\mathrm{B} 0}, n_{\mathrm{C} 0}, n_{\mathrm{D} 0},\) and \(n_{10}\) gram-moles of \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D},\) and an inert gas, I, respectively. Let \(\xi\) be the extent of reaction. Write expressions for the gram-moles of each reactive species in the final product, \(n_{\mathrm{A}}(\xi), n_{\mathrm{B}}(\xi), n_{\mathrm{C}}(\xi),\) and \(n_{\mathrm{D}}(\xi) .\) Then use these expressions and the given equilibrium constant to derive an equation for \(\xi_{c}\), the equilibrium extent of reaction, in terms of \(\left.n_{\mathrm{A} 0}, \ldots, n_{10} . \text { (see Example } 4.6-2 .\right)\) (b) If the feed to the reactor contains equimolar quantities of methanol and acetic acid and no other species, calculate the equilibrium fractional conversion. (c) It is desired to produce 70 mol of methyl acetate starting with 75 mol of methanol. If the reaction proceeds to equilibrium, how much acetic acid must be fed? What is the composition of the final product? (d) Suppose it is important to reduce the concentration of methanol by making its conversion at equilibrium as high as possible, say 99\%. Again assuming the feed to the reactor contains only methanol and acetic acid and that it is desired to produce 70 mol of methyl acetate, determine the extent of reaction and quantities of methanol and acetic acid that must be fed to the reactor. (e) If you wanted to carry out the process of Part (b) or (c) commercially, what would you need to know besides the equilibrium composition to determine whether the process would be profitable? (List several things.)

Effluents from metal-finishing plants have the potential of discharging undesirable quantities of metals, such as cadmium, nickel, lead, manganese, and chromium, in forms that are detrimental to water and air quality. A local metal-finishing plant has identified a wastewater stream that contains 5.15 wt\% chromium (Cr) and devised the following approach to lowering risk and recovering the valuable metal. The wastewater stream is fed to a treatment unit that removes \(95 \%\) of the chromium in the feed and recycles it to the plant. The residual liquid stream leaving the treatment unit is sent to a waste lagoon. The treatment unit has a maximum capacity of 4500 kg wastewater/h. If wastewater leaves the finishing plant at a rate higher than the capacity of the treatment unit, the excess (anything above \(4500 \mathrm{kg} / \mathrm{h}\) ) bypasses the unit and combines with the residual liquid leaving the unit, and the combined stream goes to the waste lagoon. (a) Without assuming a basis of calculation, draw and label a flowchart of the process. (b) Wastewater leaves the finishing plant at a rate \(\dot{m}_{1}=6000 \mathrm{kg} / \mathrm{h}\). Calculate the flow rate of liquid to the waste lagoon, \(\dot{m}_{6}(\mathrm{kg} / \mathrm{h}),\) and the mass fraction of \(\mathrm{Cr}\) in this liquid, \(x_{6}(\mathrm{kg} \mathrm{Cr} / \mathrm{kg})\) (c) Calculate the flow rate of liquid to the waste lagoon and the mass fraction of Crin this liquid for \(\dot{m}_{1}\) varying from \(1000 \mathrm{kg} / \mathrm{h}\) to \(10,000 \mathrm{kg} / \mathrm{h}\) in \(1000 \mathrm{kg} / \mathrm{h}\) increments. Generate a plot of \(x_{6}\) versus \(\dot{m}_{1}\). (Suggestion: Use a spreadsheet for these calculations.) (d) The company has hired you as a consultant to help them determine whether or not to add capacity to the treatment unit to increase the recovery of chromium. What would you need to know to make this determination? (e) What concerns might need to be addressed regarding the waste lagoon?

The reaction between ethylene and hydrogen bromide to form ethyl bromide is carried out in a continuous reactor. The product stream is analyzed and found to contain 51.7 mole \(\% \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}\) and 17.3\% HBr. The feed to the reactor contains only ethylene and hydrogen bromide. Calculate the fractional conversion of the limiting reactant and the percentage by which the other reactant is in excess. If the molar flow rate of the feed stream is \(165 \mathrm{mol} / \mathrm{s}\), what is the extent of reaction?
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