💧Multiphase Flow Modeling Unit 4 – Flow Regimes and Pattern Transitions

Key Concepts and Definitions

• Multiphase flow involves the simultaneous flow of two or more phases (gas, liquid, or solid) in a system
• Flow regimes describe the spatial distribution of the phases in a multiphase flow system
• Superficial velocity is the velocity of a phase assuming it occupies the entire cross-sectional area of the pipe
• Void fraction represents the fraction of the pipe cross-sectional area occupied by the gas phase
  • Determined by the ratio of the gas superficial velocity to the total superficial velocity
• Slip velocity refers to the relative velocity between the phases in a multiphase flow
• Flow pattern transitions occur when the flow regime changes due to variations in flow conditions (superficial velocities, pipe geometry, or fluid properties)
• Pressure gradient is the change in pressure per unit length along the pipe and is influenced by the flow regime

Flow Regime Classifications

• Bubble flow consists of discrete gas bubbles dispersed in a continuous liquid phase
  • Occurs at low gas superficial velocities and high liquid superficial velocities
• Slug flow is characterized by large gas bubbles (Taylor bubbles) separated by liquid slugs
  • Forms at intermediate gas and liquid superficial velocities
• Churn flow is a chaotic flow regime with oscillating gas and liquid phases
  • Develops at higher gas superficial velocities compared to slug flow
• Annular flow features a continuous gas core with liquid flowing along the pipe wall as a film
  • Prevails at high gas superficial velocities and low to moderate liquid superficial velocities
• Stratified flow occurs when the gas and liquid phases flow separately, with the liquid at the bottom and gas at the top of the pipe
  • Observed at low gas and liquid superficial velocities in horizontal pipes
• Dispersed bubble flow has small gas bubbles uniformly distributed in a continuous liquid phase
  • Encountered at very high liquid superficial velocities and low gas superficial velocities
• Mist flow consists of liquid droplets entrained in a continuous gas phase
  • Dominates at extremely high gas superficial velocities

Factors Influencing Flow Patterns

• Superficial velocities of the gas and liquid phases determine the flow regime
  • Increasing gas superficial velocity tends to transition from bubble to slug, churn, and annular flow
  • Higher liquid superficial velocities promote bubble and dispersed bubble flow
• Pipe orientation (horizontal, vertical, or inclined) affects the flow regime due to gravity effects
  • Stratified flow is unique to horizontal and slightly inclined pipes
• Pipe diameter influences the flow regime boundaries and transition mechanisms
  • Smaller diameters favor intermittent flow regimes (slug and churn flow)
• Fluid properties, such as density, viscosity, and surface tension, impact the flow regime
  • Higher liquid viscosity stabilizes bubble flow and delays the transition to slug flow
• Operating pressure and temperature alter the fluid properties and, consequently, the flow regime
• Pipe roughness and geometry (e.g., bends, valves) can induce local flow pattern changes
• Inlet conditions and mixing devices affect the initial distribution of phases and the resulting flow regime

Mathematical Models for Flow Regimes

• Empirical flow regime maps (e.g., Baker plot, Mandhane map) predict flow regimes based on superficial velocities and fluid properties
  • Limited to the specific conditions and fluids used in their development
• Mechanistic models consider the physical mechanisms governing flow regime transitions
  • Drift-flux model relates the gas velocity to the mixture velocity and drift velocity
    • Suitable for bubble, slug, and churn flow regimes
  • Two-fluid model treats the phases as separate fluids with their own conservation equations
    • Captures the physics of stratified, annular, and mist flow regimes
• Computational Fluid Dynamics (CFD) models solve the governing equations for multiphase flow
  • Eulerian-Eulerian approach treats the phases as interpenetrating continua
  • Eulerian-Lagrangian approach tracks individual particles or droplets in a continuous phase
• Dimensionless numbers (e.g., Reynolds number, Weber number) characterize the relative importance of forces and aid in flow regime prediction
• Stability analysis examines the stability of flow regimes and the conditions leading to transitions
  • Kelvin-Helmholtz instability describes the interfacial waves in stratified and annular flow
  • Rayleigh-Taylor instability explains the formation of Taylor bubbles in slug flow

Experimental Techniques and Observations

• Visual observations through transparent pipe sections provide qualitative information on flow regimes
• High-speed imaging captures the dynamics of flow regime transitions and interfacial phenomena
• Electrical conductance probes measure the local void fraction and identify flow regimes
  • Based on the difference in electrical conductivity between the gas and liquid phases
• Capacitance sensors detect changes in the dielectric constant caused by the presence of different phases
• Gamma-ray densitometry determines the average void fraction along a radiation path
• Particle Image Velocimetry (PIV) measures the velocity fields in multiphase flows
  • Requires seeding the flow with tracer particles and illuminating them with a laser sheet
• Wire-mesh sensors provide high-resolution spatial and temporal information on phase distribution
• Pressure drop measurements reflect the flow regime and its influence on the pressure gradient
• Tomographic techniques (e.g., Electrical Resistance Tomography, X-ray tomography) reconstruct the phase distribution in a cross-section

Pattern Transition Mechanisms

• Stratified to slug flow transition occurs due to the growth of interfacial waves
  • Kelvin-Helmholtz instability leads to wave formation and eventual bridging of the pipe cross-section
• Slug to churn flow transition happens when the Taylor bubbles become unstable and break up
  • Caused by the increase in gas velocity and the entrainment of liquid in the gas core
• Churn to annular flow transition takes place when the gas velocity is sufficient to suspend the liquid film on the pipe wall
  • Entrainment of liquid droplets in the gas core becomes significant
• Bubble to slug flow transition is driven by bubble coalescence and the formation of larger gas structures
  • Influenced by the bubble rise velocity and the turbulence in the liquid phase
• Annular to mist flow transition occurs when the liquid film is completely entrained in the gas core
  • Results from the high shear forces exerted by the gas phase on the liquid film
• Slug to dispersed bubble flow transition happens when the turbulence in the liquid phase is strong enough to break up the Taylor bubbles
• Stratified to annular flow transition is possible in horizontal pipes at high gas velocities
  • Occurs when the interfacial shear stress overcomes the gravitational force acting on the liquid phase

Applications in Industry

• Oil and gas production involves multiphase flow of oil, gas, and water in wells and pipelines
  • Flow regime prediction is crucial for optimizing production and preventing flow assurance issues (slugging, hydrate formation)
• Chemical processing industries encounter multiphase flow in reactors, separators, and heat exchangers
  • Understanding flow regimes is essential for designing efficient and safe process equipment
• Nuclear power plants rely on multiphase flow for heat removal and steam generation
  • Flow regime transitions can affect the heat transfer and hydrodynamics in nuclear reactor cores
• Geothermal systems exploit multiphase flow of steam and water for power generation
  • Predicting flow regimes is necessary for optimizing the performance of geothermal wells and surface facilities
• Refrigeration and air-conditioning systems involve multiphase flow of refrigerants in evaporators and condensers
  • Flow regime analysis helps in designing efficient and compact heat exchangers
• Fuel cells utilize multiphase flow of reactants (hydrogen, oxygen) and products (water) in the porous electrodes
  • Understanding flow regimes is critical for optimizing mass transport and minimizing flooding in fuel cells
• Spray drying processes in the food and pharmaceutical industries rely on multiphase flow of atomized droplets and drying air
  • Controlling the flow regime is essential for achieving the desired particle size and morphology

Challenges and Future Research

• Developing unified models that accurately predict flow regimes across a wide range of conditions and fluids
• Incorporating the effects of complex geometries, such as bends, contractions, and expansions, on flow regime transitions
• Advancing experimental techniques for non-intrusive and real-time monitoring of flow regimes in opaque systems
• Investigating the influence of surface wettability and roughness on flow regime transitions and hysteresis effects
• Exploring the dynamics of flow regime transitions and the associated pressure fluctuations and instabilities
• Extending flow regime studies to more complex fluids, such as non-Newtonian liquids, emulsions, and foams
• Integrating machine learning and data-driven approaches for flow regime classification and prediction
• Studying the impact of phase change phenomena (evaporation, condensation) on flow regimes and transitions
• Developing multiscale models that bridge the gap between microscopic interfacial phenomena and macroscopic flow behavior
• Investigating the influence of external fields (electric, magnetic) on flow regimes and their potential for flow control