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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.

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 — 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.