Multiphase flow

[1] Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve some form of multiphase flow.

[1][2] The study of multiphase flow is strongly linked to the development of fluid mechanics and thermodynamics.

[5] 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 (1949)[6] 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.

[9] 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 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.

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

[citation needed] An example of multiphase flow on a smaller scale would be within porous structures.

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.

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.

Presumably due to the coalescence of the large concentration of contained droplets in the liquid film covering the pipe.

[9] Hydraulic transport consists of flows in which solid particles are dispersed in a continuous liquid phase.

An example of a four phase flow system would be that of direct-contact freeze crystallization in which, for example, butane liquid is injected into solution from which the crystals are to be formed, and freezing occurs as a result of the evaporation of the liquid butane.

There are several ways to model multiphase flow, including the Euler-Langrange method, where the fluid phase is treated as a continuum by solving the Navier-Stokes equations.

The concept of a volume fraction is introduced for each phase, discussed in the parameter section below.

The most simple method to categorize continuous multiphase flows is to consider treat each phase independently.

[1] The variables stated above can be input into the below parameters that are important in the description of multiphase flow.

The Volumetric flow rate, defined as the volume of fluid passing through a cross sectional area per unit of time: A flow through a conduit of constant cross-sectional area is considered to be under steady-state conditions when its velocity and pressure may vary from point to point but do not change with time.

): Where P = pressure, ρ = mass density, Δ = change in quantity, σ = surface tension, μ = Dynamic viscosity, A = area g = acceleration due to gravity, L = linear dimension, V = volume, U = velocity of continuous phase.

The buoyancy force represents the net action of gravity whilst the density is non-uniform.

[32] From the forces shown in the table above, five independent dimensionless quantities can be derived, these relations provide insight into how the multiphase flow will behave: The Reynolds number.

At the same time, turbulent flow induces droplet-droplet interaction, which is important for the coalescence mechanism.

For example, open channel flow, wave motion in the ocean, forces on bridge piers and offshore structures.

[citation needed] The Eötvös number defines the ratio of buoyancy compared with surface tension forces.

A high value for this number indicates that the system is relatively unaffected by surface tension effects.

In microchannel flows, the capillary number plays a critical role as both surface tension and viscous forces are important.

Whilst capillary number is higher, viscous forces dominate and the effect of interface tension between fluids in rock pores are reduced thereby augmenting recovery.