91Ó°ÊÓ

In an absorption tower (or absorber), a gas is contacted with a liquid under conditions such that one or more species in the gas dissolve in the liquid. A stripping tower (or stripper) also involves a gas contacting a liquid, but under conditions such that one or more components of the feed liquid come out of solution and exit in the gas leaving the tower. A process consisting of an absorption tower and a stripping tower is used to separate the components of a gas containing 30.0 mole \(\%\) carbon dioxide and the balance methane. A stream of this gas is fed to the bottom of the absorber. A liquid containing 0.500 mole\% dissolved \(\mathrm{CO}_{2}\) and the balance methanol is recycled from the bottom of the stripper and fed to the top of the absorber. The product gas leaving the top of the absorber contains 1.00 mole \(\% \mathrm{CO}_{2}\) and essentially all of the methane fed to the unit. The CO_-rich liquid solvent leaving the bottom of the absorber is fed to the top of the stripper and a stream of nitrogen gas is fed to the bottom. Ninety percent of the \(\mathrm{CO}_{2}\) in the liquid feed to the stripper comes out of solution in the column, and the nitrogen/CO_stream leaving the column passes out to the atmosphere through a stack. The liquid stream leaving the stripping tower is the \(0.500 \% \mathrm{CO}_{2}\) solution recycled to the absorber. The absorber operates at temperature \(T_{\mathrm{a}}\) and pressure \(P_{\mathrm{a}}\) and the stripper operates at \(T_{\mathrm{s}}\) and \(P_{\mathrm{s}}\) Methanol may be assumed to be nonvolatile- -that is, none enters the vapor phase in either column and \(\mathrm{N}_{2}\), may be assumed insoluble in methanol. (a) In your own words, explain the overall objective of this two-unit process and the functions of the absorber and stripper in the process. (b) The streams fed to the tops of each tower have something in common, as do the streams fed to the bottoms of each tower. What are these commonalities and what is the probable reason for them? (c) Taking a basis of 100 mol/h of gas fed to the absorber, draw and label a flowchart of the process. For the stripper outlet gas, label the component molar flow rates rather than the total flow rate and mole fractions. Do the degree-of-freedom analysis and write in order the equations you would solve to determine all unknown stream variables except the nitrogen flow rate entering and leaving the stripper. Circle the variable(s) for which you would solve each equation (or set of simultaneous equations), but don't do any of the calculations yet. (d) Calculate the fractional \(\mathrm{CO}_{2}\) removal in the absorber (moles absorbed/mole in gas feed) and the molar flow rate and composition of the liquid feed to the stripping tower. (e) Calculate the molar feed rate of gas to the absorber required to produce an absorber product gas flow rate of \(1000 \mathrm{kg} / \mathrm{h}\). (f) Would you guess that \(T_{\mathrm{s}}\) would be higher or lower than \(T_{\mathrm{a}} ?\) Explain. (Hint: Think about what happens when you heat a carbonated soft drink and what you want to happen in the stripper.) What about the relationship of \(P_{\mathrm{s}}\) to \(P_{\mathrm{a}} ?\) (g) What properties of methanol would you guess make it the solvent of choice for this process? (In more general terms, what would you look for when choosing a solvent for an absorption-stripping process to separate one gas from another?)

Step by step solution

01

Explain the process

The dual process of absorption and stripping is used to separate carbon dioxide from methane. In the absorption tower, gas containing CO2 and methane is fed and CO2 is absorbed in the methanol solvent fed from the top. The unabsorbed gas mainly methane is let out. The CO2 rich methanol solvent is then sent to the stripping tower where nitrogen is introduced to strip out CO2 which is then let out to the atmosphere. Residual methanol solvent is recycled back to the absorption tower.

02

Identify commonalities

The common trait for the streams fed at the top of both absorber and stripper units is that they both contain methanol solvent (CO2 rich for absorber and CO2 lean for stripper). Similarly, the streams fed at the bottom (gas phase for absorber and pure nitrogen for stripper) are both gases. This arrangement promotes counter-current contact for maximum efficiency of mass transfer.

03

Draw and label a flowchart and conduct degree-of-freedom analysis

A labeled flowchart primarily contains two towers namely the absorption tower and the stripping tower. The variables included are the molar flow rates of methane, carbon dioxide, and nitrogen, the molar fractions, and the streams of gases and solvents flowing between the towers.

04

Calculate fractional CO2 removal and molar flow rate

Remove CO2 in the absorber= (Initial CO2 involved - CO2 remaining)/Initial CO2 involved = (30 - 1)/30 =29/30= 0.967 or 96.7%. The molar flow rate and composition of the liquid feed to the stripping tower equal to the total amount of CO2 absorbed i.e., 29% of 100 = 29 mol/h.

05

Molar feed rate of gas to the absorber

The molar feed rate of gas to the absorber equals 1000 kg/h divided by the molar mass of the mixture. The exact quantity can only be calculated if we know the percentage of CO2 and CH4 in the gas feed to the absorber.

06

Predict Ts and Ps with respect to Ta and Pa

TS is expected to be higher than TA since heating usually alleviates the solubility of a gas in a solution. Concerning the pressure, PS is anticipated to be lower, because reducing pressure often drives the gas out of the solution, aiding the stripping process.

07

Properties of methanol as the solvent of choice

Methanol is likely the solvent of choice due to its capacity to dissolve CO2 but not CH4 or N2. It's also stable and doesn't evaporate under conditions of the process. In general, a good solvent for an absorption-stripping process should have high solubility for the target gas, low solubility for other gases, and be stable under process conditions.

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Key Concepts

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

Absorption and Stripping

In a chemical process design, absorption and stripping are essential methods used to separate gases. This dual-unit operation involves two towers: an absorption tower and a stripping tower. In the absorption process, a gas mixture containing undesirable components like carbon dioxide is brought into contact with a liquid solvent, such as methanol, which absorbs specific components from the gas.
- The outcome of this step is a gas phase, predominantly the desired component (methane in this case), and a rich solvent containing the absorbed gas (carbon dioxide).
- The stripped function follows, where the absorbed gas (carbon dioxide) is removed from the solvent.

This is achieved by introducing another gas, like nitrogen, to aid in the removal of carbon dioxide. Through careful pressure and temperature manipulation, the carbon dioxide is driven out of the solution in the stripping tower, allowing the solvent to be recycled back into the system. This repeated cycle ensures efficient separation.

Gas Separation

Gas separation within absorption and stripping processes hinges on physical principles and process conditions. The concept is conducted by exploiting differences in solubility and volatility between gases in the system.
- In the absorber, carbon dioxide is selectively absorbed into the methanol solvent due to its higher solubility compared to methane.
- Reduced solubility of methane allows it to exit the absorber as the primary gas, achieving separation.

During stripping, process conditions are altered to favor the release of carbon dioxide from the methanol solvent. Increasing the temperature or decreasing the pressure typically enhances this release. The stripping gas, such as nitrogen, further assists in carrying the desorbed carbon dioxide away. This separation method is efficient and recyclable, utilizing methanol's properties to achieve repeated cycles of absorption and stripping without significant loss of materials.

Methanol Solvent Properties

Methanol is a solvent of choice in separation processes due to its specific properties. One significant feature is its selective solubility, which is high for carbon dioxide and low for other components like methane.
- Methanol does not vaporize easily in the given process conditions, making it stable and efficient for repeated cycles of use.
- Its low volatility is beneficial as it minimizes solvent loss while maintaining a high capacity to dissolve gases.

In the context of absorption and stripping, a suitable solvent like methanol must quickly absorb the target gas (carbon dioxide) and release it under altered conditions, ensuring the process's continuity and efficiency. Additionally, methanol's low reactivity and compatibility with process materials make it a durable choice for gas separation tasks.

Degree-of-Freedom Analysis

In process design, a degree-of-freedom analysis is a crucial step to confirm if there are enough equations available to solve for all unknowns within a system.
- The process involves listing all balances and constraints applicable, including the mass balance, energy balance, and any specific operational conditions (such as temperature and pressures).
- Each component or stream brings in specific variables like molar flow rates and compositions.

For the absorption-stripping process with methanol, a degree-of-freedom analysis helps determine the feasibility of solving for all unknown variables, ensuring the system is neither over-specified nor under-specified. By addressing degrees of freedom, the design can confidently proceed with practical calculations, such as determining the accurate flow rates and compositions needed for effective operation.