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 (e.g. flow of water and water vapor), or several different chemical components (e.g. flow of oil and water). A phase is classified as continuous if it occupies a continually connected region of space (as opposed to disperse if the phase occupies disconnected regions 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.

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 (e.g. flow of water and water vapor), or several different chemical components (e.g. flow of oil and water). A phase is classified as continuous if it occupies a continually connected region of space (as opposed to disperse if the phase occupies disconnected regions 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. G = \dot{m} = \lim\limits_{\Delta t \rightarrow 0}\frac{\Delta m}{ \Delta t}= \frac{{\rm d}m}{{\rm d}t} Where \ G = mass flow rate of a single phase, Δ = change in quantity, m = Mass of that phase t = time and the dot above m being a time derivative. The volumetric flow rate can be described using the below equation: Q = \dot V = \lim\limits_{\Delta t \rightarrow 0}\frac{\Delta V}{\Delta t}= \frac{\mathrm d V}{\mathrm d t} Where Q = volumetric flow rate of a single phase, V = Volume. The variables stated above can be input into the below parameters that are important in the description of multiphase flow. In wellbore multiphase flow the mass flow rate, volumetric fraction and velocity of each phase are important parameters. 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. If these conditions are variable with time then the flow is known as transient. The gas phase most commonly flows at a higher velocity than the liquid phase, this is due to the lower density and viscosity. 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 pressure force acts on an area or surface elements and accelerates the fluid in the downwards direction of the pressure gradient. The pressure difference between the beginning and the end of the pressure gradient is known as the pressure drop. The Darcy-Weisbach equation can be utilised to calculate pressure drop in a channel. The viscous force acts on a surface or area element and tends to make the flow uniform by diminishing velocity differences between phases, effectively opposes flow and lessens flow rate. This is evident in comparisons between high viscosity oil mixtures in comparison with low viscosity mixtures, where the higher viscosity oil moves slower. The inertia force is a volume force, which retains the direction and the magnitude of the motion. It is equivalent to the magnitude of the mass of the element multiplied by its acceleration. Acceleration is defined in this case as U^2L^{-1} , due to the linear dimension L being proportional to time. Higher inertia forces lead to turbulence, whereas lower inertia results in laminar flow. The buoyancy force represents the net action of gravity whilst the density is non-uniform. The surface-tension force acts on a line or curve element and minimizes the surface area of the interface - this force is specific to gas-liquid or liquid-liquid flows. \mathrm{Re} = \frac{F_I}{F_V} = \frac{f_I}{f_V}=\frac{\rho\ LU}{\mu} At low Reynolds numbers, flow tends towards laminar flow, whereas at high numbers turbulence results from differences in fluid speed. In general, laminar flow occurs when Re 4000. In the interval, both laminar and turbulent flows are possible and these are called transition flows. This number is dependent on geometry of the flow. For a mixture of oil and water flowing at high velocity it is most common to form a dispersed bubble type flow. Turbulent flow consists of eddies of different size range. Eddies that have larger size than droplets, transport these droplets through the flow field. Eddies, which are smaller or equal to the size of the droplets, cause droplet deformation and break-up. It can be viewed as eddies collide with droplets and break them if they have sufficient energy to overcome the droplets internal forces. At the same time, turbulent flow induces droplet-droplet interaction, which is important for the coalescence mechanism. When two droplets collide, this may lead to coalescence, resulting in a bigger droplet size. The Euler number describes the relationship between the pressure and inertial forces. \mathrm{Eu} = \frac{F_P}{F_I} = \frac{f_P}{f_I}=\frac{\Delta\ p}{\ \rho U^2} It is used to characterise energy losses in the flow. A completely friction-less flow is represented by an Euler number of 1. This number is important when the pressure force is dominant. Examples include, flow through pipes, flow over submerged bodies and flow of water through orifices. The Froude number is the ratio of inertia against gravity. \mathrm{Fr} = \frac{F_I}{F_G} = \frac{f_I}{f_G}=\frac{U^2}{gL} When Fr 1 they will be carried downstream and when Fr = 0 the velocity is equal to the surface waves. This number is relevant when gravitational force is predominant in the fluid motion. For example, open channel flow, wave motion in the ocean, forces on bridge piers and offshore structures. The Eötvös number defines the ratio of buoyancy compared with surface tension forces. \mathrm{Eo} = \frac{F_B}{F_S} = \frac{f_B}{f_S}= \frac{\Delta\rho gL^2}{\sigma} A high value for this number indicates that the system is relatively unaffected by surface tension effects. A low value indicates that surface tension dominates. The Weber number determines the relationship between the inertial force and surface tension. \mathrm{We} = \frac{F_I}{F_S} = \frac{f_I}{f_S}= \frac{\rho LU^2}{\sigma} It also determines the droplet size of the disperse phase. This number is used extensively in flow regime maps. The influence of pipe diameter is well understood through the Weber number. Three different regimes in assuming that gravity is negligible, or within microgravity can be identified: Surface tension dominated regime with bubble and slug flow. (We 20) Transitional regime with a frothy slug-annular flow. The transition from frothy slug-annular flow to fully developed annular flow occurs at We = 20. The Capillary number can be defined using the Weber number and the Reynolds number. It is the relative importance of viscous forces relative to surface forces. \mathrm{Ca} = \frac{F_V}{F_S} = \frac{f_V}{f_S}=\frac{\mu U}{\sigma}=\frac{We}{Re} In microchannel flows, the capillary number plays a critical role as both surface tension and viscous forces are important. In enhanced oil recovery operations, capillary number is an important number to consider. Whilst capillary number is higher, viscous forces dominate and the effect of interface tension between fluids in rock pores are reduced thereby augmenting recovery. In typical reservoir conditions, capillary number varies from 10 −8 to 10 −2 .

Text derived from https://en.wikipedia.org/w/index.php?oldid=1374063962 under CC BY-SA 4.0; modifications have been made.