Historical review of multiphase flow in a pipeline
- 1. CHAPTER II Historical Review of Multiphase Fluid Flow in Pipelines
- 2. Introduction • Gas, oil, and water phases exists • Multiphase flow phenomena by using classical momentum and mass balances. • One-dimensional models. • Mechanical energy balance equation, which relates pressure drop to its various components. • Understanding the mechanics of multi-phase flow is to understand first the single-phase flow phenomen.
- 3. Single Phase Flow Calculation of the pressure drop: Assumption • Steady state conditions. • Pressure remains the same at any point in the cross sectional plane. Key concept • The sum of the different forces acting on fluid element equals the change of momentum of the fluid. • the total pressure gradient is the sum of three terms, frictional gradient, hydrostatic gradient, and acceleration gradient.
- 4. Continued Static gradient • Static gradient requires density and inclination angle. • In gas-phase flow, the gas density depends on the current pressure. • In liquid-phase flow, this variation depends on temperature and dissolved gas. Acceleration gradient • Incompressible fluid: Change in fluid velocity with the axial distance is negligible. • Compressible fluid: Kinetic pressure loss can be a significant portion of the total pressure loss and must be calculated properly.
- 5. Continued Frictional pressure gradient • It depends on fluid velocity, density, viscosity, pipe roughness and diameter. • Friction Factor (f): Function of Reynolds number (Re), and roughness factor (ε/d) • The friction factor can be obtained for example from the well known Moody chart
- 7. Background of Multiphase Flow Calculations • Different results are drived based on specific laboratory test or collected data, pilot plant or full scale systems using a limited number of fluids, flow rates and pipe sizes. • Transportation flow pipelines can be horizontal, vertical or inclined. • The analysis of multi-phase flow closely follows the well-established previous method for single-phase flow equation
- 8. Continued Two different methods are used to express frictional, accelerational and potential pressure gradient: Generalized Approach: • Develops methods for pressure drop and liquid holdup. • Types of flow models: Homogeneous. Separated Flow Models. Flow-pattern based: • Models developed based on observed physical phenomena. • Accuracy in correlations for different flow regimes.
- 9. Continued Homogeneous Flow Model: • Assumes phases behave as a single fluid. • No slip condition: all phases move with the same velocity. Separated Flow Model: • Recognizes phase segregation and differing velocities. • Requires knowledge of slip and empirical correlations.
- 10. Continued Classification of Analysis Approaches: Empirical Correlations: • Simplified relationships validated by experimental data. • Limited to conditions of experiments. Mechanistic Models: • Focus on important processes, neglecting less significant effects. Numerical Models: • Utilize Navier-Stokes equations for detailed insights into flow dynamics.
- 11. Empirical Methods for Multiphase Flow Introduction to Flow Behavior • Investigators often analyze flow behavior under ideal horizontal conditions. • Corrections are made for inclined flows. • Multiple flow regimes exist within a given pipeline length due to varying forces, elevations, and gas-liquid ratios. • Critical Factors in Horizontal Flow: 1. Flow rates of gas and liquid. 2. Gas-liquid ratio. 3. Physical properties of both phases. 4. Pipeline diameter. 5. Interfacial energies and shear forces at the phase interface.
- 12. Continued Lockhart-Martinelli Correlation (1949) • A widely-used empirical model for horizontal flow without significant acceleration. • Assumes equal pressure drop for both phases and total pipe volume equals the sum of gas and liquid volumes. Limitations: • Data obtained from small pipes (≤ 25 mm). • Ignores liquid build-up and inclined flow effects. • Assumes constant liquid holdup, neglecting flow regime variations.
- 13. Continued Bertuzzi & Poettmann Approach (1956) • Determines pressure drop using a two-phase friction factor. • Incorporates gas-flow mass ratio and Reynolds numbers. • Graphical form aids computation; still treats flow as homogeneous. Baker Correlation (1958) • Introduced different flow regimes. • Provided corrections for inclined flow in small diameter pipes (1-4 in). • Developed a flow map using dimensionless groups. Flanigan’s Correlation (1958) • Similar to Baker but uses Panhandle-A equation. • Different efficiency term calculation reduces data spread. • Effective for low gas velocities but limited at higher rates.
- 14. Continued Duns and Ros (1963) Contributions • Developed empirical correlations for horizontal mist flow and vertical flow. • Focused on flow pattern-based models with distinct regimes. Dukler’s Statistical Study (1964) • Analyzed 20,000 data points, reduced to 2,600 for consistency. • Best results from Lockhart-Martinelli correlation, but deviations noted. • New correlations for slip effects and constant phase velocity ratios. Brown’s Research • Correlation Development: • Based on field test data from pipes 2-4 in diameter. • Iterative calculations for pressure differences.
- 15. Continued Knowles and Flow Regime Maps (1966) • Developed new flow regime maps using modified Reynolds and Weber numbers. Beggs and Brill (1973) • Extended correlations for horizontal and vertical flow. • Included consideration of inclination angles (0° to 90°) Mandhane et al. (1977) Proposal • Comparison of 16 previous correlations. • Proposed a two-step prediction method for friction pressure losses. Brookbank and Fagiano Review (1975) Reviewed available theory and practice. Emphasized liquid segregation’s impact on flow characteristics.
- 16. Continued Prudhoe Bay (1980) • Conducted tests on 12- and 16-inch pipelines. • Analyzed slug and froth flow conditions, adjusting for inclination. Mukherjee & Brill (1983) Contributions • Presented a new empirical approach considering inclination effects. • Claimed general applicability across flow angles. Goyon et al. (1988) • Developed a method for calculating pressure drop and temperature profiles. • Utilized direct flash calculations for each pressure and temperature condition. Coulter and Bardon Equation: • Commonly used for pipeline temperature prediction. • Originally derived for gas flow; applicable to single and two-phase flows.
- 17. Continued Alves et al. (1992) • Proposed a general equation for temperature prediction. • Applicable to various inclinations from horizontal to vertical in single or two- phase flow. Kang-Jepson Study (2002) • Pipe dimensions: 10.16 cm diameter, 36 m long. • Investigated flow regimes at inclinations of ±2°, ±5°, and ±30°. • Superficial oil velocities: 0.2 to 2 m/s; gas velocities: 1 to 14 m/s. Kang-Jepson • Dominant regime: slug flow for upward inclinations. • As liquid velocity increases, gas velocity required for transition from plug to slug also increases.
- 18. Continued Oddie et al. (2003) • Investigated two- and three-phase flows in a large inclined pipe (11 m long, 15 cm diameter). • Varied pipe inclination from 0 to 92 degrees. • Water-gas flow: Qg ranged from 5-100 m³/h. • Oil-water and oil-water-gas flow: Qo ranged from 2-40 m³/h. • Bubble, churn, elongated bubble, slug, and stratified flows observed for water- gas and oil-water-gas. • Dispersed flows noted in oil-water scenarios. Asante’s Research • Investigated the effect of small increases in liquid phase on pressure drop. • Notable findings: pressure drop can double relative to dry gas values with minimal liquid increase.
- 19. Physical Description of the Flow Patterns Flow regimes depend on operating conditions, fluid properties, flow rates, and pipe geometry. Identifying flow patterns is complex, especially in horizontal pipes. Flow Pattern Classifications:- Dispersed Flow (Bubble flow, mist flow and froth flow): • Uniform distribution of one phase. Separated Flow (Stratified flow and annular flow) • Non-continuous phase in radial direction. • Continuous phase in axial direction. Intermittent Flow (Slug flow, plug flow and elongated bubble flow) • Non-continuous phases in both directions. • Exhibits unsteady behavior.
- 20. Continued Taitel and Dukler Model (1976) • Model for predicting flow regime transitions in two-phase gas-liquid flow. • Effect of roughness initially negligible in horizontal pipes. Six Distinct Flow Regimes:- 1. Stratified Smooth Flow (SSF): Low flow rates; liquid at bottom, gas at top. 2. Stratified Wavy Flow (SWF): High gas flow rates; liquid at bottom, gas at top. 3. Plug Flow (PF): Low gas and high liquid rate; liquid fills pipe as plugs. 4. Slug Flow (SF): Large bubbles, violent liquid slugs. 5. Annular Flow (AF): Gas in center, liquid as annulus along walls. 6. Dispersed Bubbly Flow (DBF): Gas as small bubbles in continuous
- 21. Continued
- 22. Flow Pattern Identifications and Transitions Models Flow pattern map by Petalas and Aziz shows Flow regimes vary based on changes in following velocities: Vsl: Superficial liquid velocity. Vsg: Superficial gas velocity. Flow Regimes depends on: • Gas and Liquid Velocities. • Pipe inclination. • Fluid properties. • Operating pressure.
- 23. Continued Flow Pattern Prediction Steps 1. Assume Initial Flow Pattern: Start with a specific regime. 2. Examine Stability Criteria: Assess whether the regime is stable. 3. Reassess if Unstable: If instability is detected, assume a new flow pattern. 4. Repeat as Necessary: Continue until a stable regime is identified. Types of Flow Regimes: • Stratified Flow • Intermittent Flow • Dispersed Flow • Annular Flow
- 24. • Predicting the stability of the stratified flow regime needs the calculation of the liquid height. • Momentum balance equations, steady state, two fluids model approachis used and changes of phase velocity or liquid level is neglected. • Xiao et al. and Gomez et al. suggested following equation for estimating pressure gradient: Stratified Flow Model
- 25. Continued If interfacial tension and liquid phase hydrostatic pressure gradient are neglected, the pressure gradients in both phases are the same. Combining both equation becomes: Liquid Holdup
- 26. Continued Petalas and Aziz Model • Assumes Flat gas-liquid interface profile. • Simplifies calculations but may not reflect actual conditions. Real Interface Dynamics • Variations in interface shape affect contact area between fluids and pipe walls. • Influences pressure drop and overall transport phenomena. • Brauner et al. developed solutions for interface shapes in immiscible fluids. • Arirachakaran et al. correlation shows that frictional pressure drop depends on mixture velocity, water fraction, oil viscosity, continuous phase. • Vlachos et al. improved interfacial friction factor calculations using exponential expressions.
- 27. Transition between Smooth Stratified to Stratified Wavy Flow Examining wave stability predicts transition from stratified to non-stratified flow. Waves exist on the gas-liquid interface in equilibrium stratified flow. Kelvin-Helmholtz Instability • Result of Bernoulli effect: pressure drop over wave crest due to velocity acceleration. • Opposes gravitational forces. Transition Criteria from Taitel and Duklerw: When suction force > gravity, stratified flow cannot be maintained.
- 28. Wave Growth and Slugging: • Ansari (1998) performed numerical analysis on steam-water transitions in horizontal pipes. • Used Taitel-Dukler criteria for low inclination but noted limitations at -90° inclination. • For negative inclination, stratified flow can transition to annular flow at low gas rates. • Liquid film development influenced by droplet shear and velocity. • Stratified-annular transition liquid velocity can be controlled by: Continued
- 29. • Intermittent flow is characterized by the alternate movement of liquid and gas. • Includes slugs and plugs where liquid fills the entire pipe cross- section, separated by gas pockets. • Some dispersed gas bubbles may exist at the front of the slug. • A fast-moving liquid slug overrides a slower-moving liquid film ahead. Intermittent Flow Modeling
- 30. • A uniform liquid level in the film zone is sufficient for model calculations. • Momentum energy equation is represented by: • Solving the momentum energy equation provides the equilibrium liquid level (E_f). • For calculating frictional gradient during slug flow: • Formula to compute the liquid holdup: Continued
- 31. Transition of Intermittent to Annular Flow Regime Slug flow stability relies on maintaining adequate liquid levels. Small fluctuations in fluid conditions can lead to significant transitions. • Stratified Flow: Low flow rates. • Annular Flow: High gas flow rates. • Dispersed Flow: Increased liquid flow at the expense of gas. Slug Flow to Annular Studies by Taitel and Dukler (1976) and Barnea (1998). Conditions Influencing Transition: 1. Insufficient Liquid Supply Critical equilibrium liquid level: 2. Spontaneous Blockage Condition for transition to intermittent flow:
- 32. Transition of Intermittent to Dispersed Flow Regime • Dispersed bubble flow occurs when gas bubbles break up and distribute uniformly within a liquid phase. • Breaking up bubbles prevents coalescence, promoting uniform dispersion. • Barnea & Shemer proposed a unified model for this transition for inclined pipelines. • Xiao et al modified the Taitel-Dukler model for low inclination angles (<15°). • Turbulent force is high enough to overcome buoyant force.
- 33. Annular Flow Modeling Annular flow is a type of separated flow characterized by: • A thin liquid film on the internal pipe wall. • A gas phase containing liquid droplets entrained in the core. The equations of momentum conservation for liquid film and gas core:
- 34. Annular Flow Transition to Intermittent Flow Barnea and Petalas and Aziz (1998) suggested two mechanisms:- Interfacial Shear Stress: • Minimum shear stress linked to the velocity profile change in the film. • A negative velocity profile leads to instability, resulting in a transition to intermittent flow, particularly in uphill flows. Liquid Supply and Bridging: • Sufficient liquid in the film can block the gas core by forming a liquid bridge. • Occurs when liquid volume exceeds half of the maximum packing density of uniformly sized gas bubbles.
- 35. Dispersed Flow Modeling • Gas phase is dispersed throughout the liquid phase, filling the entire pipeline. • Bubble size and distribution can vary based on boundary conditions and fluid properties. • Occurs at very high liquid flow rates with strong turbulence. • Under strong turbulence, a homogeneous model is applicable. • Liquid Holdup: • Transitional bubble velocity: • Pressure gradient:
- 36. Transition of Bubble Flow to Intermittent Flow • At high liquid flow rates and low gas flow rates, turbulent fluctuations disperse the gas phase in the liquid. • Decreasing liquid velocity allows buoyant forces to push gas bubbles upward, leading to agglomeration and potential transition to slug or plug flow. • Transition criteria for intermittent to bubby flow:
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