Basics of Multiphase flow - II

Introducing a second phase in the flow complicates the calculations, the fluids may develop rough interface and mixture properties become difficult to determine. Two-phase flow implies the liquid and gas phases, although liquid phase could already include two immiscible phases (oil and water). Multiphase flow could be either homogeneous or non-homogeneous. Whalley (1987) showed that homogeneous models are limited in oil/gas production, and should only be used as a reference case.

I - Introduction

A) Homogeneous

The simplest form of two-phase flow that assumes the fluid to have uniform structure such that the two phases travel at the same in-situ velocity as if the acting forces on each phase are equal, which results in no accumulation of one phase along the pipe.?Flow configurations could be (uniform dispersion of solid particles in gas/liquid, uniform dispersion of gas in liquid (dispersed bubble flow) or uniform dispersion of liquid in gas/liquid (mist flow)).

Homogeneous two-phase flow is different from stationary two-phase since the combined drag and buoyancy forces overcome gravity forces, such that the higher density phase will disperse into the other phase resulting in equal traveling velocity for both phases, unlike stationary case in which gravity forces overcome shear and buoyancy resulting in segregated phases.

B) Non-Homogeneous

In non-homogeneous flow, slippage occurs due to the difference in viscosity and density resulting in liquid accumulation. The distribution of liquid and gas phases along the pipe follows different structures that are known as flow patterns. ?Unlike homogeneous flow procedure, here we have to identify flow pattern after calculating two-phase basic variables, and then calculate slip mixture properties prior to calculating pressure gradient.

In vertical wells, the two-phase flow is controlled by gravitational and buoyancy forces. Patterns are symmetrical, and high slippage effect happens as phases tend to separate due to density difference and shear forces. In horizontal pipelines, gravity, viscous, surface tension, and inertia/momentum forces govern two-phase flow. If the flow velocity were low, phases would be segregated. An increased viscosity result in lower inertia effect, while an increased gas density (system pressure) resulting in increase of relative gravity effect. Transition between phases could occur due to some condition that might alter the original balance between the existing forces.?

II - Flow Patterns

A) Vertical Wells:

1) Dispersed Bubble Flow: A no-slip homogeneous flow, in which gas bubbles travel at the same velocity of liquid that us carrying them. 2) Bubble Flow: Due to pressure drop, gas bubbles coalesce and gas volumetric flow rate increases for their buoyancy force. Thus, slippage occurs between two-phases. 3) Slug Flow: The increase in gas fraction results in coalescence of larger bubbles forming “Taylor Bubble” shaped liked bullets and separated by liquid slug bodies that transport dispersed gas bubbles. 4) Churn Flow: An unstable oscillatory system, in which neither of the two-phases appear to be continuous as Taylor bubbles grow longer and get distorted and broken up into random shapes. 5) Annular Flow: As gas flow rate increase, shear forces overcome gravity and expelled liquid to walls. A central gas core, carrying entrained liquid particles, is formed and surrounded by a thin annular film of continuous liquid. 6) Mist Flow: At very high gas flow rates, shear forces increase between the film/core interface, forming a homogenous two-phase flow in which liquid droplets are entrained in the gas phase.

B) Horizontal Wells:

1) Dispersed Bubble Flow: it occurs at low gas and high liquid flow rates. 2) Intermittent Flow: it consists of A) Plug Flow: in which the Taylor bubbles are separated by pure liquid, and B) Slug Flow: in which, the volume of gas pockets increase. 3) Stratified Flow: As gas velocity increases and liquid flow rate decreases, Taylor bubbles merge and form a separate phase on top of a continuous liquid phase. It could be either smooth or wavy. 4) Annular Flow: At higher gas flow rates, gas/liquid phase is pushed downward. The liquid film at bottom is thicker than the top thin film. The gas core is entrained with liquid particles due to high shear force. It could be either smooth or wavy. 5) Mist Flow: The continuous phase here is gas.

III) Pressure Gradient Calculations

Empirical correlations and Mechanistic models were used to calculate pressure drop across pipelines. Most of the mechanistic models imply hydrodynamic approach instead of thermodynamic one. On the other hand, empirical correlations are based on experiments and do not usually have physical explanation.

A)???Procedure

1. Phase properties, flow rates and two-phase variables: Characteristics of each single phase should be known prior to working such as (density, viscosity, surface tension, in-situ flow rates, and geometry of the pipe). Those parameters could be obtained from PVT analysis and empirical correlations. ?Superficial velocities are then calculated.
2. Flow-Pattern prediction for non-homogeneous flow: Flow pattern should be identified correctly either for vertical or horizontal pipe using the proper correlations or models.
3. Liquid Holdup and mixture properties calculations: Calculation of mixture properties depend primarily on liquid holdup. A) For Mechanistic model: various liquid holdup correlations are used according to the predicted flow pattern. B) For Empirical correlations: Beggs and Brill (1973) correlations could be used, and interpolation could be implied for transition zones.
4. Pressure Traverse Calculations: A) For Mechanistic model, some changes to the basic pressure gradient equation are listed according to the corresponding flow pattern implying slip mixture characteristics. B) For Empirical correlations, mixture properties are used instead of single phase properties.

B) Mixture Properties Calculations

1. Liquid Holdup: A) Slip Liquid Holdup: The fraction of pipe that is occupied by liquid, which cannot be calculated analytically. B) No-slip Liquid Holdup / liquid content: The fraction of pipe occupied by liquid that would exist if both fluids travel at the same velocity. It is always smaller than actual liquid holdup ?due to liquid accumulation in horizontal and upward flow.
2. Velocity: A) Superficial velocity: Velocity of fluid assuming that it occupies the entire cross-section alone. ?B) Actual velocity: The actual velocity a phase has in-situ, as the flow area is reduced by the presence of gas phase, and it is greater than superficial velocity: C) Mixture velocity: The algebraic sum of phases superficial velocities, and it represents the actual mixture velocity that occupies the entire cross section: D) Slip velocity: Relative actual velocity between two phases: .
3. Two-phase mixture properties: Oil/water mixture and Liquid/gas mixture properties are calculated.

C) Flow Pattern Maps

In 1986, Spisak mentioned 32 maps for upward flow, and 10 maps for downward flow. Most maps were only experimental except the one developed by Taitel et. al. (1980) that has semi-theoretical model. Coordinates of maps could vary depending on the model used. Example is shown below for Beggs and Brill (1973) regime flow pattern map (Top: Flow map from original publication.?Bottom: Updated flow map)

For three-phase multiphase flow, Dziubinski et. al. (2004) conducted experiments and hat solid particles do not have much effect on flow structures as long as solid particle concentration are less than 17.8wt% . They also showed that non-Newtonian liquids exhibit the same multiphase flow structures as with Newtonian fluids.

A detailed discussion of mathematics of multiphase flow pattern identification and advances in machine learning in this field would follow in the next article.

References:

1. H. Dale Beggs (1991). Production Optimization Using NODAL Analysis. OGCI Publications.
2. Al-Safran, E. M., & Brill, J. P. (2017). Applied multiphase flow in pipes and flow assurance: Oil and Gas Production. Society of Petroleum Engineers.
3. Spisak, W., 1986. Two-phase flow of gas-highly viscous liquid. Ph.D. thesis, Wroclaw Technical University, Poland.
4. Dziubinski, M., Fidos, H. and Sosno, M., 2004. The flow pattern map of a two-phase non-Newtonian liquid–gas flow in the vertical pipe.?International journal of multiphase flow,?30(6), pp.551-563.