CHAPTER5Flow of Multiphase Mixtures5.1. INTRODUCTIONThe flow problems considered in previous chapters are concerned with homogeneousfluids, either single phases or suspensions of fine particles whose settling velocities aresufficiently low for the solids to be completely suspended in the fluid. Consideration isnow given to the far more complex problem of the flow of multiphase systems in whichthe composition of the mixture may vary over the cross-section of the pipe or channel;furthermore, the components may be moving at different velocities to give rise to thephenomenon of "slip" between the phases.Multiphase flow is important in many areas of chemical and process engineering and thebehaviour of the material will depend on the properties of the components, the flowratesand the geometry of the system. In general, the complexity of the flow is so great thatdesign methods depend very much on an analysis of the behaviour of such systemsin practice and, only to a limited extent, on theoretical predictions. Some of the moreimportant systems to be considered are:Mixtures of liquids with gas or vapour.Liquids mixed with solid particles ("hydraulic transport").Gases carrying solid particles wholly or partly in suspension ("pneumatic transport").Multiphase systems containing solids, liquids and gases.Mixed materials may be transported horizontally, vertically, or at an inclination to thehorizontal in pipes and, in the case of liquid-solid mixtures, in open channels. Althoughthere is some degree of common behaviour between the various systems, the range ofphysical properties is so great that each different type of system must be consideredseparately. Liquids may have densities up to three orders of magnitude greater than gasesbut they do not exhibit any significant compressibility. Liquids themselves can rangefrom simple Newtonian liquids such as water, to non-Newtonian fluids with very highapparent viscosities. These very large variations in density and viscosity are responsiblefor the large differences in behaviour of solid-gas and solid-liquid mixtures which must,in practice, be considered separately. For, all multiphase flow systems, however, it isimportant to understand the nature of the interactions between the phases and how theseinfluence the flow patterns — the ways in which the phases are distributed over the crosssection of the pipe or duct. In design it is necessary to be able to predict pressure dropwhich, usually, depends not only on the flow pattern, but also on the relative velocity ofthe phases; this slip velocity will influence the hold-up, the fraction of the pipe volumewhich is occupied by a particular phase. It is important to note that, in the flow of a181
182CHEMICAL ENGINEERINGtwo-component mixture, the hold-up (or in situ concentration) of a component will differfrom that in the mixture discharged at the end of the pipe because, as a result of slip ofthe phases relative to one another, their residence times in the pipeline will not be thesame. Special attention is therefore focused on three aspects of the flow of these complexmixtures.(1) The flow patterns.(2) The hold-up of the individual phases and their relative velocities.(3) The relationship between pressure gradient in a pipe and the flowrates and physicalproperties of the phases.The difference in density between the phases is important in determining flow pattern.In gas-solid and gas-liquid mixtures, the gas will always be the lighter phase, and inliquid-solid systems it will be usual for the liquid to be less dense than the solid. Invertical upward flow, therefore, there will be a tendency for the lighter phase to rise morequickly than the denser phase giving rise to a slip velocity. For a liquid-solid or gas-solidsystem this slip velocity will be close to the terminal falling velocity of the particles. In aliquid-gas system, the slip velocity will depend on the flow pattern in a complex way. Inall cases, there will be a net upwards force resulting in a transference of energy from thefaster to the slower moving phase, and a vertically downwards gravitational force will bebalanced by a vertically upwards drag force. There will be axial symmetry of flow.In horizontal flow, the flow pattern will inevitably be more complex because the gravitational force will act perpendicular to the pipe axis, the direction of flow, and will causethe denser component to flow preferentially nearer the bottom of the pipe. Energy transferbetween the phases will again occur as a result of the difference in velocity, but the netforce will be horizontal and the suspension mechanism of the particles, or the dispersionof the fluid will be a more complex process. In this case, the flow will not be symmetricalabout the pipe axis.In practice, many other considerations will affect the design of an installation. Forexample, wherever solid particles are present, there is the possibility of blockage of thepipe and it is therefore important to operate under conditions where the probability of thisoccurring is minimised. Solids may be abrasive and cause undue wear if the velocitiesare too high or changes in direction of flow are too sudden. Choice of suitable materialsof construction and operating conditions is therefore important. In pneumatic transport,electrostatic charging may take place and cause considerable increase in pressure gradient.5.2. TWO-PHASE GAS (VAPOUR)-UQUiD FLOW5.2.1. IntroductionSome of the important features of the flow of two-phase mixtures composed of a liquidtogether with a gas or vapour are discussed in this section. There are many applicationsin the chemical and process industries, ranging from the flow of mixtures of oil and gasfrom well heads to flow of vapour-liquid mixtures in boilers and evaporators.Because of the presence of the two phases, there are considerable complications indescribing and quantifying the nature of the flow compared with conditions with a singlephase. The lack of knowledge of the velocities at a point in the individual phases makesit impossible to give any real picture of the velocity distribution. In most cases the gas
FLOW OF MULTIPHASE MIXTURES183phase, which may be flowing with a much greater velocity than the liquid, continuouslyaccelerates the liquid thus involving a transfer of energy. Either phase may be in streamlineor in turbulent flow, though the most important case is that in which both phases areturbulent. The criterion for streamline or turbulent flow of a phase is whether the Reynoldsnumber for its flow at the same rate on its own is less or greater than 1000-2000. Thisdistinction is to some extent arbitrary in that injection of a gas into a liquid initially instreamline flow may result in turbulence developing.If there is no heat transfer to the flowing mixture, the mass rate of flow of each phasewill remain substantially constant, though the volumetric flowrates (and velocities) willincrease progressively as the gas expands with falling pressure. In a boiler or evaporator,there will be a progressive vaporisation of the liquid leading to a decreased mass flowrateof liquid and corresponding increase for the vapour, with the total mass rate of flowremaining constant. The volumetric flowrate will increase very rapidly as a result of thecombined effects of falling pressure and increasing vapour/liquid ratio.A gas-liquid mixture will have a lower density than the liquid alone. Therefore, if in aU-tube one limb contains liquid and the other a liquid-gas mixture, the equilibrium heightin the second limb will be higher than in the first. If two-phase mixture is dischargedat a height less than the equilibrium height, a continuous flow of liquid will take placefrom the first to the second limb, provided that a continuous feed of liquid and gas ismaintained. This principle is used in the design of the air lift pump described in Chapter 8.Consideration will now be given to the various flow regimes which may exist and howthey may be represented on a "Flow Pattern Map"; to the calculation and prediction ofhold-up of the two phases during flow; and to the calculation of pressure gradients forgas-liquid flow in pipes. In addition, when gas-liquid mixtures flow at high velocitiesserious erosion problems can arise and it is necessary for the designer to restrict flowvelocities to avoid serious damage to equipment.A more detailed treatment of the subject is given by GoviER and AziZ (l) , byCHISHOLM (2) and by HEwnr(3).5.2.2. Flow regimes and flow patternsHorizontal flowThe flow pattern is complex and is influenced by the diameter of the pipe, the physicalproperties of the fluids and their flowrates. In general, as the velocities are increased andas the gas-liquid ratio increases, changes will take place from "bubble flow" through to"mist flow" as shown in Figure 5.1 (1 7) ; the principal characteristics are described inTable 5.1. At high liquid-gas ratios, the liquid forms the continuous phase and at lowvalues it forms the disperse phase. In the intervening region, there is generally someinstability; and sometimes several flow regimes are lumped together. In plug flow andslug flow, the gas is flowing faster than the liquid and liquid from a slug tends to becomedetached, to move as a relatively slow moving film along the surface of the pipe andthen to be reaccelerated when the next liquid slug catches it up. This process can accountfor a significant proportion of the total energy losses. Particularly in short pipelines, theflow develops an oscillating pattern arising largely from discontinuities associated withthe expulsion of successive liquid slugs.
184CHEMICAL ENGINEERINGBubble flowPlug flowStratified - wavy flowSlug flowAnnular flowUpward vertical flowMist flowHorizontal flowFigure 5.1.Table 5.1.Flow patterns in two-phase flowFlow regimes in horizontal two-phase flowTypical velocities (m/s)RegimeDescriptionLiquidVapour1.5-50.6 O.I50.3-3 1 ,00.6-35. Slug flow(a)Bubbles of gas dispersed throughout the liquidPlugs of gas in liquid phaseLayer of liquid with a layer of gas aboveAs stratified but with a wavy interface due tohigher velocitiesSlug of gas in liquid phase6. Annular flow(h)7. Mist flow (h)Liquid film on inside walls with gas in centreLiquid droplets dispersed in gas126.96.36.199.(alBubble flowPlug flow(a)Stratified flowWavy flow 0.3 5Occurs over a widerange of velocities 6 60uo Frequently grouped together as intermittent flowSometimes grouped as annular/mist flowl!l)The regions over which the different types of flow can occur are conveniently shownon a "Flow Pattern Map" in which a function of the gas flowrate is plotted against afunction of the liquid flowrate and boundary lines are drawn to delineate the variousregions. It should be borne in mind that the distinction between any two flow patternsis not clear-cut and that these divisions are only approximate as each flow regime tendsto merge in with its neighbours; in any case, the whole classification is based on highlysubjective observations. Several workers have produced their own maps 4 8\Most of the data used for compiling such maps have been obtained for the flow ofwater and air at near atmospheric temperature and pressure, and scaling factors have beenintroduced to extend their applicability to other systems. However, bearing in mind thediffuse nature of the boundaries between the regimes and the relatively minor effect of
135FLOW OF MULTIPHASE MIXTURESchanges in physical properties, such a refinement does not appear to be justified, Theflow pattern map for horizontal flow illustrated in Figure 5,2 which has been preparedby CHHABRA and RiCHARDSON(9) is based on those previously presented by MANDHANEet fl/.(8) and WEISMAN et a/. (7) The axes of this diagram are superficial liquid velocity «./,and superficial gas velocity UG (in each case the volumetric flowrate of the phase dividedby the total cross-sectional area of the pipe).Bubble flowMistIntermittent flow0.50.20,10.050.020.01Stratified flow0.0050.002IIII0.001J0.01 0.02 0.05 0.1 0.2 0.5 125 10Superficial gas velocity LIG (m/s)Figure 5.2.L2050100Flow pattern mapSlug flow should be avoided when it is necessary to obviate unsteady conditions, and itis desirable to design so that annular flow still persists at loadings down to 50 per cent ofthe normal flow rates. Even though in many applications both phases should be turbulent,excessive gas velocity will lead to a high pressure drop, particularly in small pipes.Although most of the data relate to flow in pipes of small diameters ( 42 mm), resultsof experiments carried out in a 205 mm pipe fit well on the diagram. The flow patternmap, shown in Figure 5.2, also gives a good representation of results obtained for theflow of mixtures of gas and shear-thinning non-Newtonian liquids, including very highlyshear-thinning suspensions (power law index n 0.1) and viscoelastic polymer solutions.In vertical flow, axial symmetry exists and flow patterns tend to be somewhat more stable.However, with slug flow in particular, oscillations in the flow can occur as a result ofsudden changes in pressure as liquid slugs are discharged from the end of the pipe.The principal flow patterns are shown in Figure 5.1, In general, the flow pattern map(Figure 5.2) is also applicable to vertical flow. Further reference to flow of gas-liquidmixtures in vertical pipes is made in Section 8.4.1 with reference to the operation of theair-lift purnp.
186CHEMICAL ENGINEERING5.2.3. Hold-upBecause the gas always flows at a velocity greater than that of the liquid, the in situvolumetric fraction of liquid at any point in a pipeline will be greater than the inputvolume fraction of liquid; furthermore it will progressively change along the length ofthe pipe as a result of expansion of the gas.There have been several experimental studies of two-phase flow in which the holdup has been measured, either directly or indirectly. The direct method of measurementinvolves suddenly isolating a section of the