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Chapter 6: Problem 24

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?

Short Answer

Expert verified
For part (a), the initial mole fraction of hexane in the gas is 0.0158. For part (b), the final gas temperature is 800掳C and the volumetric flow rates ratio is 1/10. For part (c), a cost analysis including energy consumption for process (b) and hexane recovery cost for process (a) is needed.

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.

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Most popular questions from this chapter

The vapor pressure of ethylene glycol at several temperatures is given below:$$\begin{array}{|l|r|r|r|r|r|r|}\hline T\left(^{\circ} \mathrm{C}\right) & 79.7 & 105.8 & 120.0 & 141.8 & 178.5 & 197.3 \\\\\hline p^{*}(\mathrm{mm} \mathrm{Hg}) & 5.0 & 20.0 & 40.0 & 100.0 & 400.0 & 760.0 \\\\\hline\end{array}$$ a semilog plot e vapor-pressure data and determine a linear expression for \(\ln p^{*}\) function of \(1 / T(\mathrm{K}) .\) Use the results to estimate the heat of vaporization \((\mathrm{kJ} / \mathrm{mol})\) of ethylene glycol, and then use that value in the Clausius-Clapeyron equation to estimate the vapor pressures at each of the temperatures given in the table.(b) Repeat Part (a) using the Slope and Intercept functions of APEx to obtain the expression for \(\ln p^{*}\) vs. \(1 / T(\mathrm{K})\).(c) Use the results from Part (b) to estimate vapor pressures of ethylene glycol at \(50^{\circ} \mathrm{C}, 80^{\circ} \mathrm{C},\) and \(110^{\circ} \mathrm{C} .\) Also estimate the boiling point of this substance at system pressures of \(760 \mathrm{mm} \mathrm{Hg}\) and 2000 mm Hg. Compare all five results with those obtained directly using APEx functions. In which of the estimates at the given temperatures and pressures would you have the least confidence? Explain your reasoning.

A stage of a separation process is defined as an operation in which components of one or more feed streams divide themselves between two phases, and the phases are taken off separately. In an ideal stage or equilibrium stage, the effluent (exit) streams are in equilibrium with each other.Distillation columns often consist of a series of vertically distributed stages. Vapor flows upward and liquid flows downward between adjacent stages; some of the liquid fed to each stage vaporizes,and some of the vapor fed to each stage condenses. A representation of a section of a distillation column is shown below. (See Problem 4.42 for a more realistic representation.) Consider a distillation column operating at 0.4 atm absolute in which benzene and styrene are being separated. A vapor stream containing 65 mole\% benzene and 35 mole\% styrene enters stage 1 at a rate of \(200 \mathrm{mol} / \mathrm{h}\), and liquid containing 55 mole\% benzene and 45 mole\% styrene leaves this stage at a rate of 150 mol/h. You may assume (1) the stages are ideal, (2) Raoult's law can be used to relate the compositions of the streams leaving each stage, and (3) the total vapor and liquid molar flow rates do not change by a significant amount from one stage to the next.(a) How would you expect the mole fraction of benzene in the liquid to vary from one stage to another, beginning with stage 1 and moving up the column? In light of your answer and considering that the pressure remains essentially constant from one stage to another, how would you then expect the temperature to vary at progressively higher stages? Briefly explain. (b) Estimate the temperature at stage 1 and the compositions of the vapor stream leaving this stage and the liquid stream entering it. Then repeat these calculations for stage 2 . (c) Describe how you would calculate the number of ideal stages required to reduce the styrene content of the vapor to less than 5 mole\%.

The vapor leaving the top of a distillation column goes to a condenser in which either total or partial condensation takes place. If a total condenser is used, a portion of the condensate is returned to the top of the column as \(r e f l u x\) and the remaining liquid is taken off as the overhead product (or distillate). (See Problem 6.63.) If a partial condenser is used, the liquid condensate is returned as reflux and the uncondensed vapor is taken off as the overhead product.The overhead product from an \(n\) -butane- \(n\) -pentane distillation column is 96 mole \(\%\) butane. The temperature of the cooling fluid limits the condenser temperature to \(40^{\circ} \mathrm{C}\) or higher.(a) Using Raoult's law, estimate the minimum pressure at which the condenser can operate as a partial condenser (i.e., at which it can produce liquid for reflux) and the minimum pressure at which it can operate as a total condenser. In terms of dew point and bubble point, what do each of these pressures represent for the given temperature?(b) Suppose the condenser operates as a total condenser at \(40^{\circ} \mathrm{C}\), the production rate of overhead product is \(75 \mathrm{kmol} / \mathrm{h}\), and the mole ratio of reflux to overhead product is \(1.5: 1 .\) Calculate the molar flow rates and compositions of the reflux stream and the vapor feed to the condenser.(c) Suppose now that a partial condenser is used, with the reflux and overhead product in equilibrium at \(40^{\circ} \mathrm{C}\) and the overhead product flow rate and reflux-to-overhead product ratio having the values given in Part (b). Calculate the operating pressure of the condenser and the compositions of the reflux and vapor feed to the condenser.

Penicillin is produced by fermentation and recovered from the resulting aqueous broth by extraction with butyl acetate. The penicillin distribution coefficient \(K\) (mass fraction of penicillin in the butyl acetate phase/mass fraction of penicillin in the water phase) depends strongly on the pH in the aqueous phase:$$\begin{array}{|r|c|c|c|}\hline \mathrm{pH} & 2.1 & 4.4 & 5.8 \\\\\hline K & 25.0 & 1.38 & 0.10 \\\\\hline\end{array}$$,This dependence provides the basis for the process to be described. Water and butyl acetate may be considered immiscible. The extraction is performed in the following three-unit process:\(\bullet\) After filtration, broth from a fermentor containing dissolved penicillin, other soluble impurities, and water is acidified in a mixing tank. The acidified broth, which contains 1.5 wt\% penicillin, is contacted with liquid butyl acetate in an extraction unit consisting of a mixer, in which the aqueous and organic phases are brought into intimate contact with each other, followed by a settling tank, in which the two phases separate under the influence of gravity. The pH of the aqueous phase in the extraction unit equals \(2.1 .\) In the mixer \(90 \%\) of the penicillin in the feed broth transfers from the aqueous phase to the organic phase.\(\bullet\) The two streams leaving the settler are in equilibrium with each other- -that is, the ratio of the penicillin mass fractions in the two phases equals the value of \(K\) corresponding to the pH of the aqueous phase \((=2.1 \text { in Unit } 1\) ). The impurities in the feed broth remain in the aqueous phase. The raffinate (by definition, the product stream containing the feed-solution solvent) leaving Extraction Unit 1 is sent elsewhere for further processing, and the organic extract (the product stream containing the extracting solvent) is sent to a second mixer-settler unit.\(\bullet\) In the second unit, the organic solution fed to the mixing stage is contacted with an alkaline aqueous solution that adjusts the pH of the aqueous phase in the unit to \(5.8 .\) In the mixer, \(90 \%\) of the penicillin entering in the organic feed solution transfers to the aqueous phase. Once again, the two streams emerging from the settler are in equilibrium. The aqueous extract is the process product.(a) Taking a basis of \(100 \mathrm{kg}\) of acidified broth fed to the first extraction unit, draw and completely label a flowchart of this process and carry out the degree-of-freedom analysis to show that all labeled variables can be determined. (Suggestion: Consider the combination of water, impurities, and acid as a single species and the alkaline solution as a second single species, since the components of these "pseudospecies" always stay together in the process.)(b) Calculate the ratios (kg butyl acetate required/kg acidified broth) and (kg alkaline solution required/kg acidified broth) and the mass fraction of penicillin in the product solution.(c) Briefly explain the following:(i) What is the likely reason for transferring most of the penicillin from an aqueous phase to an organic phase and then transferring most of it back to an aqueous phase, when each transfer leads to a loss of some of the drug? (ii) What is the purpose of acidifying the broth prior to the first extraction stage, and why is the extracting solution added to the second unit a base? (iii) Why are the two "raffinates" in the process the aqueous phase leaving the first unit and the organic phase leaving the second unit, and vice versa for the "extracts"? (Look again at the definitions of these terms.)(d) An alternative process for recovering the penicillin from the fermentation broth might involve evaporation to dryness. In that case, all the water simply is evaporated. Give two possible reasons for rejection of this alternative.

Nitric acid is a chemical intermediate primarily used in the synthesis of ammonium nitrate, which is used in the manufacture of fertilizers. The acid also is important in the production of other nitrates and in the separation of metals from ores. Nitric acid may be produced by oxidizing ammonia to nitric oxide over a platinum-rhodium catalyst, then oxidizing the nitric oxide to nitrogen dioxide in a separate unit where it is absorbed in water to form an aqueous solution of nitric acid.The reaction sequence is as follows:$$\begin{aligned} 4 \mathrm{NH}_{3}+5 \mathrm{O}_{2} & \rightarrow 4 \mathrm{NO}+6 \mathrm{H}_{2} \mathrm{O} \\\4 \mathrm{NO}+2 \mathrm{O}_{2} & \rightarrow 4 \mathrm{NO}_{2} \\\4 \mathrm{NO}_{2}+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{O}_{2} & \rightarrow 4 \mathrm{HNO}_{3}(\mathrm{aq}) \end{aligned}$$.Ammonia vapor produced by vaporizing pure liquid ammonia at 820 kPa absolute is mixed with air, and the combined stream enters the ammonia oxidation unit. Air at \(30^{\circ} \mathrm{C}, 1\) atm absolute, and \(50 \%\) relative humidity is compressed and fed to the process. A fraction of the air is sent to the cooling and hydration units, while the remainder is passed through a heat exchanger and mixed with the ammonia. The total oxygen fed to the process is the amount stoichiometrically required to convert all of the ammonia to HNO \(_{3},\) while the fraction sent to the ammonia oxidizer corresponds to the stoichiometric amount required to convert ammonia to NO.The ammonia reacts completely in the oxidizer, with \(97 \%\) forming NO and the rest forming \(\mathrm{N}_{2}\). Only a negligible amount of \(\mathrm{NO}_{2}\) is formed in the oxidizer. However, the gas leaving the oxidizer is subjected to a series of cooling and hydration steps in which the NO is completely oxidized to \(\mathrm{NO}_{2}\) which in turn combines with water (some of which is present in the gas from the oxidizer and the rest is added) to form a 55 wt\% aqueous solution of nitric acid. The product gas from the process may be taken to contain only \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\). (a) Taking a basis of \(100 \mathrm{kmol}\) of ammonia fed to the process, calculate (i) the volumes \(\left(\mathrm{m}^{3}\right)\) of the ammonia vapor and air fed to the process using the compressibility-factor equation of state; (ii) the amount (kmol) and composition (in mole fractions) of the gas leaving the oxidation unit; (iii) the required volume of liquid water \(\left(\mathrm{m}^{3}\right)\) that must be fed to the cooling and hydration units; and (iv) the fraction of the air fed to the ammonia oxidizer. (b) Scale the results from Part (a) to a new basis of 100 metric tons per hour of 55\% nitric acid solution.(c) Nitrogen oxides (collectively referred to as \(\mathrm{NO}_{x}\) ) are a category of pollutants that are formed in many ways, including processes like that described in this problem. List the annual emission rates of the three largest sources of \(\mathrm{NO}_{x}\) emissions in your home region. What are the effects of exposure to excessive concentrations of \(\mathrm{NO}_{x} ?\) (d) A platinum-rhodium catalyst is used in ammonia oxidation. Fxplain the function of the catalyst, describe its structure, and explain the relationship of the structure to the function.
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