Multiphase flow

In fluid mechanics, multiphase flow is the simultaneous flow of materials with two or more thermodynamic phases. Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve some form of multiphase flow. It is also prevalent in many natural phenomena.
These phases may consist of one chemical component, or several different chemical components. A phase is classified as continuous if it occupies a continually connected region of space. The continuous phase may be either gaseous or a liquid. The disperse phase can consist of a solid, liquid or gas.
Two general topologies can be identified: disperse flows and separated flows. The former consists of finite particles, drops or bubbles distributed within a continuous phase, whereas the latter consists of two or more continuous streams of fluids separated by interfaces.

History

The study of multiphase flow is strongly linked to the development of fluid mechanics and thermodynamics. A key early discovery was made by Archimedes of Syracuse who postulated the laws of buoyancy, which became known as the Archimedes' principle – which is used in modelling multiphase flow.
In the mid-20th century, advances in nucleate boiling were developed and the first two-phase pressure-drop models were formed, primarily for the chemical and process industries. In particular, Lockhart and Martinelli presented a model for frictional pressure drop in horizontal, separated two-phase flow, introducing a parameter that is still utilised today. Between 1950 and 1960, intensive work in the aerospace and nuclear sectors triggered further studies into two-phase flow. In 1958 one of the earliest systematic studies of two-phase flow was undertaken by Soviet scientist Teletov. Baker conducted studies into vertical flow regimes.
From the 1970s onwards, multiphase flow especially in the context of the oil industry has been studied extensively due to the increasing dependence of petroleum by the world economy.
The 1980s saw further modelling of multiphase flow by modelling flow patterns to different pipe inclinations and diameters and different pressures and flows. Advancements in computing power in the 1990s allowed for increasingly complex modelling techniques to modelling multiphase flow, flows that were previously limited to one-dimensional problems could be pushed to three-dimensional models.
Projects to develop multiphase flow metering technology, used to measure the rate of individual phase flow appeared in the 1990s. The impetus behind this technology was a forecasted decline of production from the major North Sea oil fields. Oil companies that created early prototypes included BP and Texaco, MFMS have now become ubiquitous and are now the primary metering solution for new-field developments.

Examples and applications

Multiphase flow occurs regularly in many natural phenomena, and also is well documented and crucial within various industries.

In nature

Sediment transport in rivers is subject to multiphase flow, in which the suspended particles are treated as a disperse second phase which interacts with the continuous fluid phase.
An example of multiphase flow on a smaller scale would be within porous structures. Pore-structure modelling enables the use of Darcy's law to calculate the volumetric flow rate through porous media such as groundwater flow through rock. Further examples occur within the bodies of living organisms, such as blood flow (with plasma being the liquid phase and red blood cells constituting the solid phase. Also flow within the intestinal tract of the human body, with solid food particles and water flowing simultaneously.

In industry

The large majority of processing technology involves multiphase flow. A common example of multiphase flow in industry is a fluidized bed. This device combines a solid-liquid mixture and causes it to move like a fluid. Further examples include water electrolysis, bubbly flow in nuclear reactors, gas-particle flow in combustion reactors and fiber suspension flows within the pulp and paper industry.
In oil and gas industries, multiphase flow often implies to simultaneous flow of oil, water and gas. The term is also applicable to the properties of a flow in some field where there is a chemical injection or various types of inhibitors. In petroleum engineering, drilling fluid consists of a gas-solid phase. Furthermore, crude oil during flow through pipelines is a gas-oil-water three phase flow.

Types

The most common class of multiphase flows are two-phase flows, and these include Gas-Liquid Flow, Gas-Solid Flow, Liquid-Liquid Flow and Liquid-Solid Flow. These flows are the most studied, and are of most interest in the context of industry. Different patterns of multiphase flow are known as flow regimes.

Two-phase liquid-gas pipeline flow

Flow patterns in pipes are governed by the diameter of the pipe, the physical properties of the fluids and their flow rates. As velocity and gas-liquid ratio is increased, "bubble flow" transitions into "mist flow". At high liquid-gas ratios, liquid forms the continuous phase and at low values it forms the disperse phase. In plug and slug flow, gas flows faster than the liquid and the liquid forms a 'slug' which becomes detached and velocity decreases until the next liquid slug catches up.

Regime	Description
Bubble/Dispersed bubble flow	Occurs at large liquid flow rates with little gas flow. Bubbles of gas dispersed or suspended throughout the liquid continuous phase. Typical features of this flow are moving and deformed interfaces of bubbles in time and space domains and complex interactions between the interfaces. This flow can be categorised further into Ideally Separated, Interacting Bubble, Churn Turbulent and Clustered. Due to the buoyancy force, bubbles tend to drift in the upper portion of the pipe.
Plug flow	Develops as the flow rate is increased whilst vapor flow is maintained at a low amount. Plugs of gas in liquid phase where the velocity is assumed to be constant whilst 'plugs', essentially 'bullet shaped' bubbles of gas that cover the cross section of the pipe flow intermittently through the pipe in the upper portion of the pipe due to buoyancy forces.
Stratified flow	Gas and liquid flow where there is separation by an interface. This occurs when the gravity force dominates which causes stratification of the liquid at the bottom of the pipe. Most common in horizontal or slightly inclined pipelines. At low velocities, smooth interfaces occur whereas at greater velocities waves appear.
Wavy flow	Characterised by a gas-liquid flows in parallel streams, the interface between them is flat at low gas velocities, waves appear due to perturbations when velocity is increased. An example would be waves on the sea.
Slug flow	Defined by the intermittent sequence of liquid 'slugs' containing disperse gas bubbles alternating with longer bubbles with greater width. Unsteady flow regime even when velocities are kept constant.
Annular flow	Occurs when a liquid film in gas-liquid flow covers the channel wall in an annulus shape with gas flowing in the core. The core can also contain liquid droplets, this case is known as annular-dispersed flow.
Mist/Dispersed mist flow	Occurs at very high gas flow rates. Characterised by a disperse phase being suspended in a continuous phase. In the case of gas-liquid flow, it occurs when liquid particles are suspended in a continuous gas phase.

In Vertical flow axial symmetry exists and flow patterns are more stable. However, in regards to slug flow oscillations in this regime can occur. Horizontal flow regimes can be applied here, however, we see a more even distribution of particles due to the buoyancy force acting in the direction of the pipe.
Churn flow occurs when slug flow breaks down, leading to an unstable regime in which there is an oscillatory motion of the liquid.
Wispy annular flow is characterised by the liquid 'wisps' that exist in the annular flow regime. Presumably due to the coalescence of the large concentration of contained droplets in the liquid film covering the pipe. This regime occurs at high mass fluxes.

Liquid-solid flow

consists of flows in which solid particles are dispersed in a continuous liquid phase. They are often referred to as slurry flows. Applications include the transport of coals and ores to the flow of mud.
Suspensions are classified into the following groups; fine suspensions in which the particles are uniformly distributed within the liquid and coarse suspensions where particles ted to travel predominantly in the bottom half of a horizontal pipe at a lower velocity than the liquid and a significantly lower velocity than the liquid in a vertical pipe.

Gas-solid pipeline flow

Gas–solid two-phase flow widely exists in chemical engineering, power engineering, and metallurgical engineering. In order to reduce atmospheric pollution and pipe erosion, improve product quality, and process efficiency, flow parameter measurement of two-phase flow by pneumatic conveying is becoming increasingly widespread.

Regime	Description
Uniform Suspended flow	Particles are evenly distributed over the cross-section over the whole length of the pipe.
Non-Uniform suspended flow	The flow is similar to the above description, but a tendency for particles to flow preferentially in the lower portion of the pipe, this occurs especially with larger particles.
Slug flow	As the particles enter the conveying line, they tend to settle out before they are fully accelerated. They form dunes which are then swept downstream creating an uneven longitudinal distribution of particles along the pipeline.
Dune flow	As the particles settle into dunes as stated above, the dunes remain stationary with particles being conveyed above the dunes and being swept from one dune to the next.
Moving bed	Particles settle near the feed point and form a continuous bed at the bottom of the pipe. The bed develops gradually throughout the length of the pipe and moves slowly forward. There is a velocity gradient in the vertical direction in the bed and conveying continues in suspended form above the bed.
Stationary bed	Similar to a moving bed, however, there is little to no movement of particles on the bed. The bed builds up until the pipe is blocked if velocity is low enough.
Plug flow	Following slug flow, the particles instead of forming stationary dunes gradually build up over the cross-section until they cause a blockage; this is less common than dune flow however.