For an absorption in a packed bed column at 1 atm and 300 K, entering gas stream has a molar flow rate of 30 kmol/hr on solute free basis and solvent having 75 kmol/hr. Solution fo... For an absorption in a packed bed column at 1 atm and 300 K, entering gas stream has a molar flow rate of 30 kmol/hr on solute free basis and solvent having 75 kmol/hr. Solution follows Henry law with henry constant as 253.3 kPa. Solvent is free from solute and solute in inlet gas stream is 9% and 95% absorption is required then NTU is?
Understand the Problem
The question is asking for the Number of Transfer Units (NTU) in a packed bed column scenario involving gas absorption. It provides specific flow rates, the condition of solute and solvent, and the requirements for absorption, suggesting that relevant calculations must be carried out.
Answer
The NTU is 1.
Answer for screen readers
The Number of Transfer Units (NTU) is $1$.
Steps to Solve
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Identify Given Data
- Gas stream inlet flow rate, ( G = 30 \text{ kmol/hr} )
- Solvent flow rate, ( S = 75 \text{ kmol/hr} )
- Inlet solute concentration, ( y_1 = 0.09 ) (9%)
- Required absorption, ( y_2 = 0.05 ) (95% absorption = 5% remaining)
- Henry's constant, ( H = 253.3 \text{ kPa} )
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Calculate the Gas Outlet Concentration
The concentration of the solute in the gas stream after absorption can be calculated as: [ y_2 = y_1 \cdot (1 - \text{Absorption Efficiency}) ] Given ( y_1 = 0.09 ) and knowing that ( y_2 = 0.05 ) for 95% absorption, verify:
( y_2 ) confirms correctly as provided.
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Determine the Overall Mass Transfer Coefficient
Using Henry's law, the partial pressure of the solute in the gas phase can be calculated: [ p_{y2} = H \cdot y_2 = 253.3 \text{ kPa} \cdot 0.05 ] Calculate ( p_{y2} ).
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Calculate NTU using the Transfer Unit Concept
The NTU can be found using the relation: [ NTU = \frac{\Delta Y}{Y_1 - Y_2} ] where ( \Delta Y = y_1 - y_2 ). Substitute values:
- ( \Delta Y = 0.09 - 0.05 = 0.04 )
- Therefore: [ NTU = \frac{0.04}{0.09 - 0.05} = \frac{0.04}{0.04} ]
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Final Calculation
Carry out the calculation: [ NTU = 1 ]
The Number of Transfer Units (NTU) is $1$.
More Information
The NTU is a crucial parameter in mass transfer operations and indicates the efficiency of the gas absorption process. An NTU of 1 suggests a single transfer unit effectiveness, which may simplify design considerations for packed bed columns.
Tips
- Misinterpreting absorption percentages; ensure to derive ( y_2 ) from correct absorption calculation.
- Neglecting to calculate pressure contributions and units consistently.
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