7.2 Convective mass transfer

Convective mass transfer is a key process in chemical engineering, involving the transport of mass between surfaces and moving fluids. It's driven by molecular diffusion and bulk fluid motion, playing a crucial role in various applications like heat exchangers and reactors.

Understanding convective mass transfer is vital for designing efficient systems. It's quantified by the mass transfer coefficient, which depends on fluid properties, flow characteristics, and system geometry. This knowledge helps engineers optimize processes and troubleshoot issues in chemical engineering systems.

Convective Mass Transfer

Concept and Importance

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• Convective mass transfer is the transport of mass between a surface and a moving fluid, driven by both molecular diffusion and bulk fluid motion
• Crucial phenomenon in various chemical engineering applications (heat exchangers, reactors, distillation columns, absorption processes)
• Rate of convective mass transfer determines the efficiency and effectiveness of many chemical processes, as it governs the transport of species between phases
• Often coupled with heat transfer and fluid flow, making it a complex and interdependent process
• Convective mass transfer rate is quantified by the mass transfer coefficient, which depends on the fluid properties, flow characteristics, and geometry of the system

Applications and Complexity

• Heat exchangers rely on convective mass transfer to efficiently transfer heat between fluids, ensuring proper temperature control and energy efficiency
• In chemical reactors, convective mass transfer plays a vital role in bringing reactants together and removing products, affecting reaction rates and yields
• Distillation columns and absorption processes heavily depend on convective mass transfer to achieve separation and purification of chemical mixtures
• The coupling of convective mass transfer with heat transfer and fluid flow makes it a complex and interdependent process, requiring careful analysis and design considerations
• Understanding and optimizing convective mass transfer is essential for the proper design, operation, and troubleshooting of various chemical engineering systems

Mass Transfer Coefficients

Flow Regimes and Geometries

• Mass transfer coefficients are determined by the flow regime (laminar, turbulent, transitional) and the geometry of the system (pipes, channels, packed beds)
• In laminar flow, the mass transfer coefficient is primarily dependent on molecular diffusion and can be estimated using the Sherwood number correlation, which relates the mass transfer coefficient to the Reynolds and Schmidt numbers
• Turbulent flow enhances the mass transfer coefficient due to the presence of eddies and fluctuations in the fluid, leading to higher rates of mass transfer compared to laminar flow
• For flow over flat plates, the mass transfer coefficient can be estimated using the Chilton-Colburn analogy, which relates the mass transfer coefficient to the heat transfer coefficient and the Prandtl and Schmidt numbers

Packed Beds and Correlations

• In packed beds, the mass transfer coefficient is influenced by the packing characteristics (particle size, shape, porosity) and can be estimated using correlations like the Wakao and Funazkri correlation
• The choice of the appropriate correlation for estimating mass transfer coefficients depends on the specific flow regime and geometry of the system
• Accurate estimation of mass transfer coefficients is crucial for the design and analysis of mass transfer equipment, such as absorption columns, adsorbers, and catalytic reactors
• Correlations for mass transfer coefficients are often derived from experimental data and dimensional analysis, taking into account the relevant dimensionless numbers and system parameters

Estimating Mass Transfer Rates

Dimensionless Numbers and Correlations

• The mass transfer rate in convective systems can be estimated using correlations that relate the mass transfer coefficient to the relevant dimensionless numbers (Reynolds, Schmidt, Sherwood numbers)
• The Reynolds number (Re) characterizes the flow regime and is defined as the ratio of inertial forces to viscous forces in the fluid
• The Schmidt number (Sc) represents the ratio of momentum diffusivity to mass diffusivity and is a function of the fluid properties
• The Sherwood number (Sh) is a dimensionless number that relates the mass transfer coefficient to the characteristic length and the diffusion coefficient

Specific Correlations for Different Systems

• For flow in pipes, the Dittus-Boelter correlation can be used to estimate the mass transfer coefficient, which is expressed as a function of the Reynolds and Schmidt numbers
• In the case of flow over flat plates, the Chilton-Colburn analogy can be employed to estimate the mass transfer coefficient using the heat transfer coefficient and the Prandtl and Schmidt numbers
• For packed beds, correlations like the Wakao and Funazkri correlation can be used to estimate the mass transfer coefficient based on the particle Reynolds number and the Schmidt number
• The appropriate choice of correlation depends on the specific system geometry, flow conditions, and the availability of reliable experimental data for validation

Factors Affecting Convective Mass Transfer

Fluid Properties and Flow Characteristics

• Convective mass transfer is influenced by various factors, including fluid properties, flow characteristics, and the geometry of the system
• Fluid properties (density, viscosity, diffusivity) play a crucial role in determining the mass transfer rate, as they affect the fluid flow and the molecular diffusion of species
• Flow velocity and the degree of turbulence in the fluid have a significant impact on the mass transfer rate, with higher velocities and turbulence leading to enhanced mass transfer
• The presence of boundary layers (velocity and concentration boundary layers) affects the mass transfer rate by determining the resistance to mass transport between the bulk fluid and the surface

Geometry and Surface Effects

• The geometry of the system (shape and size of the surface) influences the mass transfer rate by affecting the flow patterns and the contact area between the fluid and the surface
• Surface roughness can enhance mass transfer by promoting turbulence and increasing the effective surface area for mass exchange
• In heat transfer systems, temperature gradients can lead to natural convection, which can either enhance or hinder the mass transfer rate, depending on the direction of the temperature gradient relative to the concentration gradient
• Understanding the interplay between fluid properties, flow characteristics, and geometry is essential for optimizing convective mass transfer in chemical engineering applications