9.3 Overall mass transfer coefficients

Mass transfer coefficients are crucial in understanding how substances move between phases. They help quantify the rate of transfer, accounting for resistances in bulk phases and at interfaces. This knowledge is key for designing and optimizing separation processes in various industries.

Overall mass transfer coefficients combine individual phase resistances, simplifying complex transfer phenomena. By using these coefficients, engineers can predict transfer rates, design equipment, and improve process efficiency in applications like absorption, extraction, and membrane separations.

Overall Mass Transfer Coefficients

Definition and Interpretation

Top images from around the web for Definition and Interpretation

• 

  Gas–liquid phase equilibrium of a model Langmuir monolayer captured by a multiscale approach ... View original

  Is this image relevant?

• 

  Site and bond-specific dynamics of reactions at the gas–liquid interface - Physical Chemistry ... View original

  Is this image relevant?

• 

  Gas–liquid phase equilibrium of a model Langmuir monolayer captured by a multiscale approach ... View original

  Is this image relevant?

• 

  Site and bond-specific dynamics of reactions at the gas–liquid interface - Physical Chemistry ... View original

  Is this image relevant?

1 of 2

Top images from around the web for Definition and Interpretation

• 

  Gas–liquid phase equilibrium of a model Langmuir monolayer captured by a multiscale approach ... View original

  Is this image relevant?

• 

  Site and bond-specific dynamics of reactions at the gas–liquid interface - Physical Chemistry ... View original

  Is this image relevant?

• 

  Gas–liquid phase equilibrium of a model Langmuir monolayer captured by a multiscale approach ... View original

  Is this image relevant?

• 

  Site and bond-specific dynamics of reactions at the gas–liquid interface - Physical Chemistry ... View original

  Is this image relevant?

1 of 2

• Overall mass transfer coefficients represent the combined resistance to mass transfer across multiple phases or layers (gas-liquid or liquid-liquid interfaces)
• Account for the individual mass transfer resistances in series, including the resistances in the bulk phases and the interface
• Expressed in units of mass flux per unit driving force (mol/(m²·s) or kg/(m²·s))
• Depend on the specific system and operating conditions
• Driving force for mass transfer typically expressed as a concentration difference or partial pressure difference between the bulk phases

Application and Significance

• Used to quantify the rate of interphase mass transfer
• Essential for the design and analysis of mass transfer equipment (absorption columns, extraction columns, membrane contactors)
• Determine the required interfacial area or contact time to achieve a desired separation or purification performance
• Calculated from experimental data (inlet and outlet concentrations, flow rates) to assess the performance and identify potential improvements
• Used in the scale-up and optimization of mass transfer processes, investigating the effects of process variables (temperature, pressure, flow rates) on the overall mass transfer rate

Deriving Overall Mass Transfer Coefficients

Resistance-in-Series Model

• Overall mass transfer coefficient derived by considering the individual mass transfer resistances in series, similar to electrical resistances in series
• For a two-phase system (gas-liquid or liquid-liquid), the overall mass transfer coefficient is related to the individual phase mass transfer coefficients by: $1/K = 1/k₁ + 1/k₂$
  • $K$ is the overall mass transfer coefficient
  • $k₁$ and $k₂$ are the individual phase mass transfer coefficients
• Individual phase mass transfer coefficients ($k₁$ and $k₂$) estimated using appropriate correlations or models (film theory, penetration theory, surface renewal theory)
• When one phase resistance is significantly larger than the other, the overall mass transfer coefficient is primarily determined by the limiting phase resistance, and the expression can be simplified accordingly

Equilibrium Relationships

• Derivation of the overall mass transfer coefficient requires knowledge of the equilibrium relationship between the phases
• Gas-liquid systems: Henry's law
• Liquid-liquid systems: partition coefficients
• Equilibrium relationships are essential for determining the driving force for mass transfer and relating the concentrations in different phases

Calculating Overall Mass Transfer Coefficients

Gas-Liquid Systems

• Individual gas-side and liquid-side mass transfer coefficients ($k_g$ and $k_l$) determined using appropriate correlations or experimental data
• Overall mass transfer coefficient expressed in terms of the gas-side or liquid-side concentrations, depending on the controlling resistance and the equilibrium relationship (Henry's law)
• Example: Absorption of a solute from a gas phase into a liquid phase, where the liquid-side resistance is controlling and Henry's law applies

Liquid-Liquid Systems

• Individual liquid-phase mass transfer coefficients ($k₁$ and $k₂$) and the partition coefficient ($m$) between the two liquid phases are used
• Partition coefficient ($m$) represents the equilibrium distribution of the solute between the two liquid phases and is determined by the solute's solubility in each phase
• Example: Extraction of a solute from an aqueous phase into an organic solvent phase, where the partition coefficient determines the equilibrium distribution of the solute

Unit Consistency and Driving Force

• Calculation of overall mass transfer coefficients requires consistent units for the individual phase mass transfer coefficients, concentrations, and partition coefficients
• Appropriate driving force expression must be used, depending on the system and the equilibrium relationship
• Driving force can be expressed as a concentration difference or partial pressure difference between the bulk phases

Applying Overall Mass Transfer Coefficients

Equipment Design

• Overall mass transfer coefficients are essential for the design of various mass transfer equipment (absorption columns, extraction columns, membrane contactors)
• Used to determine the required interfacial area or contact time to achieve a desired separation or purification performance
• Overall mass transfer coefficient, along with the driving force and interfacial area, determines the rate of mass transfer and the overall efficiency of the mass transfer process
• Design requires knowledge of the system geometry, flow patterns, and operating conditions, as well as the appropriate mass transfer correlations and models

Process Analysis and Optimization

• Overall mass transfer coefficient can be calculated from experimental data (inlet and outlet concentrations, flow rates) to assess the performance of existing mass transfer equipment and identify potential improvements
• Used in the scale-up and optimization of mass transfer processes
• Effects of process variables (temperature, pressure, flow rates) on the overall mass transfer rate are investigated and optimized
• Example: Optimizing the operating conditions of an absorption column to maximize the removal efficiency of a pollutant from a gas stream, considering the effects of temperature, pressure, and liquid-to-gas ratio on the overall mass transfer coefficient and the driving force