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Recovery and processing of various oils are important elements of the agricultural and food industries. For example, soybean hulls are removed from the beans, which are then flaked and contacted with hexane. The hexane extracts soybean oil and leaves very little oil in the residual solids. The solids are dried at an elevated temperature, and the dried solids are used to feed livestock or further processed to extract soy protein. The gas stream leaving the dryer is at \(80^{\circ} \mathrm{C}\) 1 atm absolute, and 50\% relative saturation.(a) To recover hexane, the gas leaving the dryer is fed to a condenser, which operates at 1 atm absolute. The gas leaving the condenser contains 5.00 mole \(\%\) hexane, and the hexane condensate is recovered at a rate of \(1.50 \mathrm{kmol} / \mathrm{min}\). (b) In an altemative arrangement, the gas leaving the dryer is compressed to 10.0 atm and the temperature simultancously is increased so that the relative saturation remains at \(50 \% .\) The gas then is cooled at constant pressure to produce a stream containing 5.00 mole \(\%\) hexane. Calculate the final gas temperature and the ratio of volumetric flow rates of the gas streams leaving and entering the condenser. State any assumptions you make.(c) What would you need to know to determine which of processes (a) and (b) is more cost- effective?

Step by step solution

01

Calculating the initial mole fraction of hexane

For part (a), we first need to find the initial mole fraction of hexane in the gas. We know that the gas leaving the condenser contains 5.00 mole percent of hexane and the condensate is recovered at a rate of \(1.50 \mathrm{kmol} / \mathrm{min}\). The mole fraction of hexane is thus \( \frac{1.50 \mathrm{kmol}}{100-5} = 0.0158 \).

02

Calculating the final temperature and volumetric flow rate for scenario (b)

For part (b), the gas is compressed and heated in a way that the relative saturation remains at \(50 \%\). This implies that the mole fraction of hexane remains the same, \(0.0158\). The gas is then cooled at constant pressure. Since the mole fraction is constant, using ideal gas law at initial and final points, we find that the ratio of final to initial volume is the same as the ratio of initial to final temperature. The final temperature is thus \(80 \times 10 = 800 \degree C\). The ratio of volumetric flow rates is 1/10 since the final pressure is 10 times initial.

03

Analyzing cost-effectiveness of process (a) and (b)

For part (c), to determine the cost-effectiveness of processes (a) and (b), we would need to know the costs related to energy consumption in heating the gas to 800 degrees Celsius in the second scenario, and costs of compressing the gas to 10 atm. We would also need to know the costs related to hexane recovery in the first scenario and compare those costs.

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Key Concepts

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

Oil Recovery

Oil recovery is a crucial process in industries like agriculture and food. It is the technique used to extract oil from various materials, like soybeans. Imagine soybeans being processed: they are hulled, flaked, and then mixed with a solvent such as hexane.
The hexane serves as a medium to draw out nearly all the oil contained in the soybeans. This process enhances oil recovery because it ensures minimal oil remains in the waste solids.
These solids are then dried and can be put to use in different ways: for example, as feed for livestock or further processing to extract soy protein.

• **Solvent-Based Extraction:** This method is chosen because of its efficiency in separating oil from solids.
• **Post-Processing Use:** The residual cake, once oil-free, is not discarded but further processed for value generation.

This systematic and efficient approach ensures maximum yield and resource efficiency in oil recovery.

Gas Condensation

In the context of extracting oil, gas condensation plays a vital role, especially when dealing with solvents like hexane. After oil extraction, the residual gas containing hexane is directed towards a condenser.
This process is carried out to recover the hexane, transforming it from a vapor to a liquid form.

• **Role of Condensation:** Condenses hexane from the vapor, allowing it to be reused or properly processed.
• **Condensation Parameters:** Typically involves pressure changes, maintaining mole percent of substances (like 5% hexane in our setup), and achieving desired temperatures.

Condensation not only recovers valuable solvents but also plays an essential part in environmental and economic efficiency by allowing recycling and reducing emissions.

Chemical Engineering Calculations

Chemical engineering often necessitates intricate calculations to optimize processes. These calculations ensure that both oil recovery and gas condensation are as efficient as possible.
In our example, calculations are used to adjust parameters such as temperature and pressure, especially when comparing different setups for hexane recovery.

• **Ideal Gas Law Application:** Used to link variables like temperature and pressure, giving insight into volumetric changes.
• **Efficiency Analysis:** Calculates factors like flow rate ratios, ensuring resource and cost effectiveness.
• **Cost-Effectiveness Evaluation:** Analysis of different process arrangements (like changing pressure or temperature) guides economic decisions.

With these calculations, chemical engineers make informed decisions, ensuring the process remains not only effective but also cost-efficient and sustainable.