Glossary

5.2 Equilibrium and mass transfer in absorption/stripping

3 min read•july 24, 2024

is crucial for understanding absorption and stripping processes. , , and help predict how components distribute between phases. Absorption and stripping factors quantify the ease of separating components in these operations.

Mass transfer in gas-liquid systems involves and film resistances. The models interface behavior, while overall mass transfer coefficients combine individual resistances. Understanding these concepts is essential for designing efficient absorption and stripping columns.

Vapor-Liquid Equilibrium and Mass Transfer in Absorption/Stripping

Vapor-liquid equilibrium in absorption

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  • Henry's law for dilute solutions describes solute concentration in vapor phase proportional to liquid phase
    • Expression: y=Hxy = Hx relates mole fractions in vapor (y) and liquid (x) phases
    • HH: Henry's constant varies with temperature, pressure (atm⋅L/mol)
  • Raoult's law for ideal solutions predicts vapor pressure of components in liquid mixture
    • Expression: yi=xiPi∗/Py_i = x_i P_i^*/P calculates vapor composition from liquid composition
    • Pi∗P_i^*: vapor pressure of pure component ii at system temperature (kPa)
    • PP: total system pressure (kPa)
  • K-values (vapor-liquid distribution ratios) measure tendency of component to vaporize
    • Ki=yi/xiK_i = y_i/x_i represents ratio of mole fractions in vapor and liquid phases
    • Related to equilibrium constant, indicates relative volatility of components
  • Absorption factor quantifies ease of absorption process
    • A=L/(mG)A = L/(mG) compares liquid flow rate to product of gas flow rate and equilibrium line slope
    • LL: liquid flow rate (mol/h), GG: gas flow rate (mol/h), mm: slope of equilibrium line
  • measures difficulty of removing solute from liquid phase
    • S=mG/L=1/AS = mG/L = 1/A inverse of absorption factor
    • Higher stripping factor indicates easier removal of solute from liquid

Mass transfer in gas-liquid systems

  • Two-film theory models mass transfer resistance at gas-liquid interface
    • Gas film resistance limits transfer of sparingly soluble gases (O₂ in water)
    • Liquid film resistance controls transfer of highly soluble gases (NH₃ in water)
  • combines individual film resistances
    • 1/KG=1/kG+m/kL1/K_G = 1/k_G + m/k_L relates overall coefficient to gas and liquid film coefficients
    • KGK_G: overall gas-phase coefficient, kGk_G: gas-phase coefficient, kLk_L: liquid-phase coefficient
  • Concentration gradients drive mass transfer between phases
    • Steeper gradients lead to faster mass transfer rates
  • Diffusion in gas and liquid phases follows
    • Flux proportional to concentration gradient and diffusion coefficient
  • affects absorption/stripping efficiency
    • Larger area increases mass transfer rate (packed columns, spray towers)

Mass transfer coefficients for columns

  • (kGk_G) estimated using dimensionless correlations
    • Sherwood number relates mass transfer to fluid flow and diffusion (Re, Sc)
  • (kLk_L) predicted by theoretical models
    • Penetration theory assumes unsteady-state diffusion into liquid elements
    • Surface renewal theory considers continuous replacement of liquid surface
  • Overall mass transfer coefficient (KGK_G or KLK_L) combines individual resistances
    • KGK_G used for gas-phase controlled systems, KLK_L for liquid-phase controlled
  • (aa) measures available surface for mass transfer
    • Defined as surface area per unit volume of column (m²/m³)
  • (KGaK_Ga or KLaK_La) crucial for column design
    • Combines mass transfer coefficient and interfacial area
  • estimate coefficients for different packing types
    • Random packing (Raschig rings, Pall rings) and structured packing (corrugated sheets)

Theoretical stages for separation

  • graphically determines number of equilibrium stages
    • represents material balance between phases
    • shows composition relationship at equilibrium
    • Step-wise construction between operating line and equilibrium curve
  • for absorbers calculates theoretical stages analytically
    • N=log⁡[(A−1)(y1/yN+1−1/A)+1]log⁡AN = \frac{\log[(A-1)(y_1/y_{N+1} - 1/A) + 1]}{\log A}
    • NN: number of theoretical stages, y1y_1: inlet gas composition, yN+1y_{N+1}: outlet gas composition
  • Kremser equation for strippers determines stages for liquid purification
    • N=log⁡[(S−1)(xN/x0−1/S)+1]log⁡SN = \frac{\log[(S-1)(x_N/x_0 - 1/S) + 1]}{\log S}
    • xNx_N: inlet liquid composition, x0x_0: outlet liquid composition
  • relates packed height to stages
    • HETP = total packed height / number of theoretical stages (m)
  • and alternative approach
    • HTU represents height of column in which concentration change equals driving force
    • NTU measures difficulty of separation, analogous to number of stages

Key Terms to Review (22)

Concentration Gradients: Concentration gradients refer to the difference in concentration of a substance across a space, often resulting in the movement of that substance from an area of higher concentration to an area of lower concentration. This movement is a fundamental principle in processes like absorption and stripping, where the driving force for mass transfer relies heavily on the presence of these gradients, leading to the eventual equilibrium between phases.
Empirical correlations: Empirical correlations are mathematical relationships derived from observed data, typically used to predict or describe the behavior of a system under certain conditions. These correlations are essential in fields like absorption and stripping processes, as they help engineers estimate mass transfer rates and equilibrium states based on experimental results without needing complex theoretical models.
Equilibrium Curve: The equilibrium curve is a graphical representation that illustrates the relationship between the concentration of a solute in two phases at equilibrium, typically plotted with one phase on the x-axis and the other on the y-axis. It serves as a critical tool in understanding how mass transfer occurs during processes like absorption and stripping, as well as extraction techniques, revealing how much solute can be transferred between phases under varying conditions.
Fick's Law: Fick's Law describes the process of diffusion, stating that the rate of mass transfer of a substance across a unit area is proportional to the concentration gradient. This law is fundamental in understanding how substances move from areas of high concentration to areas of low concentration, and it plays a crucial role in various mass transfer operations, including the design and optimization of separation processes.
Gas-phase mass transfer coefficient: The gas-phase mass transfer coefficient is a measure of the rate at which a substance moves from the gas phase to another phase, such as a liquid, during processes like absorption or stripping. This coefficient is crucial because it affects how efficiently substances are transferred between phases, influencing the overall effectiveness of separation processes. Understanding this coefficient helps in optimizing equipment design and operational conditions to achieve desired separation outcomes.
Height equivalent to a theoretical plate (HETP): Height equivalent to a theoretical plate (HETP) is a measure used to evaluate the efficiency of a separation process, indicating how tall a column would need to be for one theoretical plate. This concept is important in understanding how well mass transfer occurs during processes like absorption and stripping, where multiple equilibrium stages are involved in separating components from a mixture.
Height of a transfer unit (HTU): The height of a transfer unit (HTU) is a measure used in mass transfer operations that represents the height of a column required to achieve one equilibrium stage in a separation process, such as absorption or stripping. It indicates the efficiency of mass transfer and relates to both the driving force for the transfer and the overall system design. A lower HTU signifies a more efficient process, allowing for fewer stages to reach the desired separation.
Henry's Law: Henry's Law states that at a constant temperature, the amount of a gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid. This principle is essential in understanding how gases interact with liquids in various separation processes, particularly in absorption and stripping operations, as well as in the analysis of vapor-liquid and liquid-liquid equilibria.
Interfacial Area: Interfacial area refers to the surface area that exists between two immiscible phases, such as liquid-liquid or gas-liquid interfaces, which plays a crucial role in mass transfer processes. The size and characteristics of the interfacial area influence how effectively mass can be transferred between these phases, impacting the overall efficiency of separation processes. A larger interfacial area usually promotes enhanced mass transfer rates, while the nature of the interface can also affect phenomena like diffusion and turbulence.
K-values: K-values, or equilibrium constants, represent the ratio of concentrations of a solute in two phases at equilibrium. They are essential for understanding the distribution of components in separation processes like distillation and absorption. K-values help to determine how well a mixture can be separated based on the volatility or solubility of its components, making them crucial for designing efficient separation systems.
Kremser Equation: The Kremser Equation is a mathematical expression used to describe the mass transfer processes in absorption and stripping operations, focusing on the relationship between the concentration of solute in both the liquid and gas phases. It provides a way to analyze how effective a separation process is, linking equilibrium conditions to the number of transfer units and the overall efficiency of the operation.
Liquid-phase mass transfer coefficient: The liquid-phase mass transfer coefficient is a crucial parameter that quantifies the rate at which a solute moves from the gas phase into the liquid phase during processes like absorption and stripping. This coefficient reflects the efficiency of mass transfer between phases, indicating how easily a substance can diffuse through a liquid. In absorption and stripping operations, understanding this coefficient helps engineers optimize designs to enhance the transfer of materials, ensuring effective separation of components.
McCabe-Thiele Method: The McCabe-Thiele Method is a graphical technique used for designing and analyzing distillation processes, specifically for binary mixtures. It helps in visualizing the number of theoretical stages required for separation based on vapor-liquid equilibrium data, allowing engineers to optimize the distillation column’s efficiency and performance.
Number of transfer units (ntu): The number of transfer units (ntu) is a dimensionless measure that quantifies the efficiency of mass transfer in processes such as absorption and stripping. It represents the number of theoretical stages needed for a given separation to occur, linking the actual mass transfer performance with equilibrium conditions. A higher ntu value indicates better mass transfer performance, helping engineers design and optimize separation processes effectively.
Operating Line: The operating line is a graphical representation that describes the relationship between the concentrations of two components in a separation process, often in the context of mass transfer operations. It serves as a crucial tool for analyzing and designing processes such as absorption, stripping, and extraction, by illustrating how the concentration of one component changes in relation to another as it passes through different stages of the operation.
Overall Mass Transfer Coefficient: The overall mass transfer coefficient is a crucial parameter that quantifies the efficiency of mass transfer between two phases in a separation process. It incorporates the resistance to mass transfer in both phases, allowing for a comprehensive understanding of how effectively substances move from one phase to another. This coefficient is essential for designing and analyzing processes like distillation and absorption, where phase interactions are key to achieving desired separations.
Raoult's Law: Raoult's Law states that the partial vapor pressure of a component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution. This law is fundamental in understanding how mixtures behave during processes like distillation and absorption, providing insight into vapor-liquid equilibrium and helping in the design of separation processes.
Specific Interfacial Area: Specific interfacial area refers to the surface area of a phase interface per unit volume of the contacting phases in a separation process. This term is crucial in understanding mass transfer, particularly in processes like absorption and stripping, where the effectiveness of mass transfer relies heavily on the availability of surface area for contact between phases, such as gas and liquid.
Stripping Factor: The stripping factor is a dimensionless number that quantifies the efficiency of the stripping process in separating a solute from a liquid phase by using a gas or vapor. It is defined as the ratio of the concentration of the solute in the liquid phase before stripping to that after stripping, reflecting how effectively the solute has been removed. This factor is crucial for understanding and optimizing mass transfer operations, as it directly relates to the equilibrium and performance of both absorption and stripping processes.
Two-film theory: Two-film theory is a model used to describe mass transfer processes, where the mass transfer occurs through two stagnant films: one on the gas side and one on the liquid side. This theory helps to simplify the understanding of how substances dissolve in liquids or gases by proposing that the resistance to mass transfer occurs primarily in these boundary layers, rather than in the bulk phases. The concept is essential for analyzing equilibrium and mass transfer in absorption and stripping operations.
Vapor-Liquid Equilibrium: Vapor-liquid equilibrium (VLE) is a state where the rates of evaporation and condensation of a liquid are equal, resulting in a stable balance between its vapor and liquid phases. This concept is essential in various separation processes, as it helps to understand how mixtures behave and how components can be separated based on their volatilities.
Volumetric Mass Transfer Coefficient: The volumetric mass transfer coefficient is a crucial parameter that quantifies the rate at which a solute is transferred from one phase to another during processes like absorption and stripping. This coefficient takes into account the mass transfer area and fluid dynamics, linking the concentration gradient of the solute across phases to the mass transfer rate. Understanding this coefficient is essential for designing efficient separation processes in chemical engineering, especially in systems where gas-liquid interactions are prominent.
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