91Ó°ÊÓ

The concentration of oxygen in a 5000 -liter tank containing air at 1 atm is to be reduced by pressure purging prior to charging a fuel into the tank. The tank is charged with nitrogen up to a high pressure and then vented back down to atmospheric pressure. The process is repeated as many times as required to bring the oxygen concentration below 10 ppm (i.c., to bring the mole fraction of \(\mathrm{O}_{2}\) below \(10.0 \times 10^{-6}\) ). Assume that the temperature is \(25^{\circ} \mathrm{C}\) at the beginning and end of each charging cycle. When doing \(P V T\) calculations in Parts (b) and (c), use the generalized compressibility chart if possible for the fully charged tank and assume that the tank contains pure nitrogen. (a) Speculate on why the tank is being purged. (b) Estimate the gauge pressure (atm) to which the tank must be charged if the purge is to be done in one charge-vent cycle. Then estimate the mass of nitrogen (kg) used in the process. (For this part, if you can't find the tank condition on the compressibility chart, assume ideal-gas behavior and state whether the resulting estimate of the pressure is too high or too low.) (c) Suppose nitrogen at 700 kPa gauge is used for the charging. Calculate the number of charge-vent cycles required and the total mass of nitrogen used. (d) Use your results to explain why multiple cycles at a lower gas pressure are preferable to a single cycle. What is a probable disadvantage of multiple cycles?

Step by step solution

01

Reason for Purging

Considering that a fuel is to be charged into the tank, the purging is required to avoid the possibility of any explosive reaction with oxygen and to maintain the chemical stability of the fuel.

02

Estimate Pressure and Mass for Purging

Purging in one cycle means removal of all oxygen. Since we are starting with air at 1 atm which contains 21% oxygen, we want to reduce it to 10 ppm, which is like reducing it to 0.0001 %. Apply the ideal gas law to calculate the new pressure after purging by the formula \(P' = P \times (1 - X)\), where P' is the new pressure, P is the initial pressure (1 atm) and X is the fraction of oxygen (0.21 as 21%). To calculate the amount of nitrogen required, we need to calculate the moles of nitrogen needed to replace the oxygen. Each mole of oxygen replaced by nitrogen reduces its mole fraction by its initial value. So, moles of nitrogen = initial moles of air × initial mole fraction of oxygen × reduction factor. Mass of nitrogen can then be calculated using the molar mass of nitrogen.

03

Number of Cycles Required and Total Nitrogen Used

Given that nitrogen is charged at 700 kPa (approximately 6.9 atm), we need to calculate how much oxygen is left after one purge. Apply the same formula as in Step 2 for the reduction in oxygen fraction after one purge. Then, find out how many cycles required to reach 10 ppm. Recall from formula, number of cycles \(n\) can be derived from \(X = X_0(1 - X_N)^n \) where \(X_0\) is initial oxygen concentration and \(X_N\) is desired oxygen concentration. Total mass of nitrogen used is then the mass per cycle times the number of cycles

04

Purging Cycles Analysis

Based on results from previous steps, state why multiple cycles at lower gas pressure are preferable to a single cycle (since less nitrogen is needed and the pressure is safer), however also note that multiple cycles would take more time, which could be a disadvantage.

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Key Concepts

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

Ideal Gas Law Applications

The Ideal Gas Law, represented by the equation PV=nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin, is a fundamental equation in the study of gases. In chemical engineering, it is especially useful for calculating the behavior of gases under varying conditions of pressure, volume, and temperature.

When applying this law to real-life scenarios such as pressure purging in a chemical process, we assume that the gases involved behave ideally, meaning their particles are non-attracting and occupy no volume. This assumption simplifies the calculation, but it's important to note when real gases might deviate from this behavior, taking into consideration the conditions at which the gas is being manipulated. In the given exercise, it is used to estimate the pressure and mass of nitrogen required to purge a tank of oxygen to a safe level for the introduction of fuel.

During the purging process, it's crucial to account for the initial and final gas concentrations, ensuring the safety and efficacy of the procedure. As oxygen is removed and replaced by nitrogen, the application of the Ideal Gas Law helps us estimate the new pressure necessary for a complete purge in one cycle or multiple cycles, as well as the mass of nitrogen needed - both critical factors for the success of the operation.

Compressibility Chart Usage

Compressibility charts are valuable tools used to determine the deviation of real gas behavior from ideal gas laws under various pressures and temperatures. These charts provide the compressibility factor Z, which corrects the ideal gas law for real gas behavior. The compressibility factor is defined as Z=PV/(nRT), where a Z value of 1 indicates ideal behavior.

Chemical engineers use these charts to improve the accuracy of their PV calculations when dealing with high pressures or low temperatures where gases may not act ideally. In the exercise, the compressibility chart is referenced to calculate the properties of nitrogen in the fully charged tank to account for deviations from the Ideal Gas Law which assumes a Z value of 1. If the state of nitrogen is outside the range of the chart, or the chart is not readily accessible, the exercise improvement advice suggests assuming ideal-gas behavior while noting whether the estimate is too high or low. While this is a practical approach, it is essential to understand its limitations and the potential for error in the absence of compressibility data.

Chemical Engineering Safety

Safety is paramount in chemical engineering processes, especially when handling flammable or explosive substances, such as in the pressure purging process described in the problem. Purging is a crucial step to prevent any explosive reactions by removing oxygen that could otherwise react with the fuel being loaded into the tank.

Engineers must design safe procedures that lower the concentration of oxygen to non-flammable levels, adhering to strict safety regulations and guidelines. This is due to the potential risk that any residual oxygen presents when it comes in contact with highly reactive substances. The approach to use multiple charge-vent cycles at a lower gas pressure, rather than a single high-pressure purge, is an application of these safety practices. It minimizes risks associated with handling high-pressure gases and the potential for accidents. In the realm of safety, time is also a trade-off, as multiple cycles might require more time and might potentially increase exposure to risk. Nevertheless, this methodical approach generally aligns with the industry's best practices for safety.

Mole Fraction Calculations

Mole fraction is a way of expressing the concentration of a component in a mixture and is calculated as the moles of the component divided by the total moles of all components in the mixture. It's a dimensionless number that plays a key role in processes like purging because it helps in setting and achieving concentration targets. For example, reaching a mole fraction of oxygen below 10^-6 is critical for safety in the given exercise.

The exercise involves calculating the number of purging cycles required to dilute the oxygen concentration to a safe level. By using repeated calculations of the mole fraction after each cycle, engineers can determine how many cycles are needed to eventually reach the desired oxygen concentration. This process of calculation not only ensures the safety and effectiveness of the purging process but also allows for optimization of resource usage, in this case, the nitrogen used for purging.

Understanding mole fraction calculations is essential for engineers to accurately design and control chemical processes, preventing safety hazards and ensuring the proper functioning of equipment.