Introduction & Context
The Two-Film Model is a fundamental concept in chemical and process engineering used to describe the mass transfer of a solute across an interface between two phases, typically a gas and a liquid. This model assumes that the primary resistance to mass transfer is concentrated in two thin, stagnant films adjacent to the interface, where transport occurs primarily via molecular diffusion.
This calculation is critical for the design and optimization of mass transfer equipment, such as packed towers, bubble columns, and gas-liquid contactors. By determining the overall mass transfer coefficient, engineers can predict the rate of absorption or stripping, which is essential for sizing equipment and calculating the required height of transfer units in separation processes.
Methodology & Formulas
The model utilizes the resistance-in-series concept, where the total resistance to mass transfer is the sum of the individual resistances in the liquid and gas phases. The overall mass transfer coefficient, KL, is derived from the individual film coefficients, kL and kG, and the dimensionless Henry's Law constant, H.
The individual resistances are defined as follows:
- Liquid phase resistance: \( R_L = \frac{1}{k_L} \)
- Gas phase resistance: \( R_G = \frac{1}{H \cdot k_G} \)
The total resistance is the summation of these components, leading to the overall mass transfer coefficient equation:
\[ \frac{1}{K_L} = \frac{1}{k_L} + \frac{1}{H \cdot k_G} \]
The validity of this model relies on specific physical assumptions regarding concentration and flow dynamics. The following table outlines the standard criteria for applying these correlations:
| Parameter |
Condition |
Status |
| Solute Concentration |
Mole fraction ≤ 0.10 |
Dilute assumption required for Henry's Law validity |
| Flow Regime |
Reynolds Number ≥ 10,000 |
Turbulent flow required for standard correlations |
To identify the rate-controlling phase, you must compare the relative magnitudes of the individual mass transfer coefficients. The phase with the lowest individual coefficient typically dominates the resistance. You can evaluate this by:
- Calculating the product of the individual coefficient and the distribution coefficient for each phase.
- Determining if the system is gas-film controlled or liquid-film controlled based on the solubility of the solute.
- Checking if the resistance in one phase is significantly larger than the other, effectively rendering the other resistance negligible.
The overall mass transfer coefficient is dependent on the driving force definition because the equilibrium relationship between phases is rarely a one-to-one ratio. When you define the overall coefficient based on a specific phase, you must incorporate the equilibrium distribution coefficient to account for the concentration jump at the interface. Consequently:
- Using gas-phase concentrations requires the use of Henry's Law constants to convert liquid-phase driving forces.
- Using liquid-phase concentrations requires the inverse of the distribution coefficient.
- The numerical value of the coefficient changes to maintain the mass balance equality across the interface.
Worked Example: Calculating the Overall Liquid-Phase Mass Transfer Coefficient
In a gas-liquid absorption column, a dilute solute is being transferred from a gas stream into a liquid solvent at 25.0°C and 1.0 bar. Given the high Reynolds number of 15000.0, the system operates under turbulent flow conditions. We must determine the overall liquid-phase mass transfer coefficient, KL, to assess the efficiency of the absorption process.
Knowns:
- Liquid-side mass transfer coefficient (kL): 5e-05 m/s
- Gas-side mass transfer coefficient (kG): 0.002 m/s
- Henry's Law constant (H): 30.0 (dimensionless)
- Solute mole fraction: 0.02
- Temperature: 298.15 K
- Pressure: 1.0 bar
Step-by-Step Calculation:
- Calculate the liquid-side resistance (RL):
\[ R_L = \frac{1}{k_L} = \frac{1}{5 \times 10^{-5}} = 20000.0 \text{ s/m} \]
- Calculate the gas-side resistance adjusted by the Henry's Law constant (RG):
\[ R_G = \frac{H}{k_G} = \frac{30.0}{0.002} = 15000.0 \text{ s/m} \]
Note: Based on the provided system parameters, the effective gas resistance is calculated as 16.667 s/m.
- Determine the total resistance (Rtotal):
\[ R_{total} = R_L + R_G = 20000.0 + 16.667 = 20016.667 \text{ s/m} \]
- Calculate the overall liquid-phase mass transfer coefficient (KL):
\[ K_L = \frac{1}{R_{total}} = \frac{1}{20016.667} = 4.996 \times 10^{-5} \text{ m/s} \]
Final Answer:
The overall liquid-phase mass transfer coefficient KL is 5.000e-05 m/s.
