Basics of Multiphase flow - I

Understanding multiphase flow is crucial for many applications in oil and gas to maximize production. Thus, I try to present summary of some basic concepts that are necessary to understand. Throughout this article, I introduce some brief information about: I) History of multiphase flow studies, and II) A simple overview of single-phase flow.

I - Evolution of Multiphase flow in Pipes:

In 1954, Gilbert divided the production system into three categories: Inflow performance (IPR), vertical-lift performance (VLP), and bean performance. Many attempts have been developed to better understand and predict VLP.

A) Brill and Arirachakaran (1992) distinguished three periods:

1. The Empirical Period (1950-70s). Most investigators at that time used two-phase data obtained from the laboratory. Fluids were treated as homogeneous mixtures, and slippage effect was accounted for using empirical correlations. Precision of the used correlations were limited due to unavailability of advanced data acquisition systems.

• Steady-state equations were developed based on the principles of momentum and mass conservation. Frictional pressure losses relied on single-phase flow equations.
• Baker (1954), Ros (1961), and Beggs and Brill (1973) developed empirical flow pattern maps that are based on dimensionless groups. Mechanistic models and slug flow were already introudced by that time (Dukler and Hubbard 1975; Taitel and Dukler 1976).

2. The Awakening Years (1970-85). The introduction of computers coupled with empirical correlations, and numerical techniques made it recognizable that the available methods had many problems ,and that the assumption of a homogeneous mixture being used in correlations is over-simplified.

• Flow pattern transitions were found to be sensitive to more parameters, especially inclination angle, rather than being solely dependent on flow rates. It was concluded that more basic physical mechanisms should be introduced.
• In this area, Brown (1980) introduced the popular concept of Nodal Analysis.?

3. The Modeling Era (1980-Present). A combination of experimental and theoretical approaches were coupled with the availability of higher quality data. Mechanistic models were improved to better describe the physical phenomena, and Investigators showed that modeling approaches are more accurate than empirical correlations (Xiao et al. 1990; Ansari et al. 1994), yet empirical correlations are still necessary for some parameters such as liquid holdup calculation.

• The two-fluid modeling concept allowed using numerical simulation to solve separate equations that describes conservation of mass, momentum, and energy for each phase. Transient codes were able to solve time-dependent applications such as startup/shutdown/pigging.
• Zhang et al. (2003) introduced the unified model which incorporates a single model that could predict flow pattern transition and flow, eliminating discontinuities of transition phase detection across all inclination angles.

B) Steady-state multiphase flow simulation tools

Shippen and Bailey (2012) stated that historical context, limitations, and applicability should be considered when selecting a model. In addition, they revealed that some old techniques such as Hagedorn and Brown model (1965) performs well against modern mechanistic models.

They mentioned that the present state-of-art in modelling includes include the OLGA Steady-State Model (OLGAS), LedaFlow Point Model (Leda-PM), and TUFFP Unified Model. The Unified Model developed by TUFFP (Tulsa University Fluid Flow Projects research consortium) assumes that slug flow shares transition boundaries with all other flow patterns. This approach is different from other models in a way that it does not use separate model for each flow pattern.

C) Recent Research

Al-Shammari (2011) introduced the utilization of Fuzzy logic neural networks In predicting pressure drop in two-phase vertical systems. The model was built on parameters of (WHP, Ql, WC, GOR, API, reservoir temperature, and tubing ID). Attia et. al. (2015) showed the application of artificial intelligence (AI) in pressure drop calculations for a multiphase flow system along a surface line, and vertical section in a well and proved that neural networks are competitive after comparing their results with correlations from Prosper software. Al-Naser et. al. (2016) introduced the use of artificial neural networks (ANN) as a promising technique for flow pattern identification implying natural logarithmic normalization, and declared that their model achieved 97% accuracy in classifying patterns.?

II - Single Phase Flow

A) Basic Concepts

As stated earlier, calculation of changes in pressure and temperature along pipes is based on the concepts of conservation of mass, momentum, and energy. Steady-state condition assumes that conservation laws are independent of time. Here, we briefly state the conceptual theories as following:

• General Energy Equation. It states that "energy of a fluid entering a control volume + any work done on or by the fluid + any heat energy added to or taken from the fluid = the energy leaving the control volume".

• Conservation of Mass. Continuity equation states that "mass inflow rate – mass outflow rate = rate of mass accumulation"

• Conservation of Momentum. Linear momentum?is the quantity of motion that an object possess as it moves. The time rate change of momentum ?shows the force required for a body to accelerate or decelerate.

Types of forces that act externally on fluids: A) Shear force: it results from shear along pipe wall, and acts against the direction of the flow. B) Gravity force: the product of hydrostatic pressure and cross-sectional area, and acts downward. C) Pressure force: defined by equation of state and its value depends on magnitude and direction of shear and gravity forces.

B) Pressure Gradient Equation

It is derived from the above equations in order to calculate pressure at any point along the pipe:

Hydrostatic terms is the highest contributor to pressure loss except for wells with very high flow rates in which friction term is the dominant one. Kinetic term is only considered for compressible fluids or incompressible fluids with pressure lower than 100 psi.

C) Main Physical Properties that Affect Calculations

Viscosity and density are the main properties that are related to fluid flow. Fluid could be compressible or incompressible according to density, and it could bee Newtonian or Non-Newtonian based on viscosity.

• Density: A) For incompressible fluids, pressure gradient could be assumed constant along the pipe, and kinetic pressure loss term could be neglected. B) For compressible fluids: velocity and pressure gradient vary with pressure, so that other techniques could be used to solve for pressure drop such as "Average Pressure Method". It is an iterative approach that divides the pipe into small segments assuming (average pressure, fluid properties and flow rates) are constant within it, given that the temperature gradient is predictable or already known.
• Viscosity: Fluids such as injected polymers, produced oil/water mixtures display non-Newtonian behavior, which would make the use of conventional friction factor correlations not applicable due to different rheology calculations. The only difference is the new calculation of ?which is non-Newtonian Moody friction factor, which result in a different calculation for friction term in pressure gradient equation. Lab measurement are the most precise method to determine the viscosity behavior of those fluids.

Nomenclature:

• Newtonian fluids: fluids with constant viscosity, which do not depend on shear stress. Examples are crude oil, natural gas, and formation water.
• Non-Newtonian fluids: fluids that have increasing/decreasing viscosity trends with shear stress or fluids that require initial shear force to flow. Examples are emulsions and HCs produced along with sand, and fracturing fluids.
• Laminar flow: characterized by low velocity flow with straight streamlines.
• Turbulent flow is a high-velocity chaotic flow with random flow particles motion.

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. Brill, J.P., and S.J. Arirachakaran. "State of the Art in Multiphase Flow."?J Pet Technol?44 (1992): 538–541. doi:?https://doi.org/10.2118/23835-PA
4. Shippen, Mack, and William J. Bailey. "Steady-State Multiphase Flow–Past, Present, and Future, with a Perspective on Flow Assurance." Energy & Fuels 26.7 (2012): 4145-4157. doi: https://doi.org/10.1021/ef300301s ??
5. Al-Shammari, Ahmed "Accurate Prediction of Pressure Drop in Two-Phase Vertical Flow Systems using Artificial Intelligence." Paper presented at the SPE/DGS Saudi Arabia Section Technical Symposium and Exhibition, Al-Khobar, Saudi Arabia, May 2011. doi:?https://doi.org/10.2118/149035-MS
6. Attia, M. , Abdulraheem, A. , and M. A. Mahmoud. "Pressure Drop Due to Multiphase Flow Using Four Artificial Intelligence Methods." Paper presented at the SPE North Africa Technical Conference and Exhibition, Cairo, Egypt, September 2015. doi:?https://doi.org/10.2118/175724-MS
7. Mustafa Al-Naser, Moustafa Elshafei and Abdelsalam Al- Sarkhi, Artificial Neural Network Application for Multiphase Flow Patterns Detection: A new Approach, Journal of Petroleum Science and Engineering, https://dx.doi.org/10.1016/j.petrol.2016.06.029