Chapter-I (Multiphase Flow)
The simultaneous flow of two or more phases through a conduit
where the phases interact at the interface is termed multiphase
flow. Although simultaneous flow of as many as four phases
namely, water, crude oil, gas and sand is not uncommon during
oil exploration, flow of two phase mixtures is the most common
occurrence in industry.
The different variations of two phase flow are
Fig. 2.3 Flow regimes in vertical evaporator tubes
flow patterns can also be observed during condensationas shown in Fig. 2.4.
Methods of Analysis
They can be successful for organizing experimental results or predicting
design parameters with minimum computational effort. A few such models
are:
(i) Homogenous model: where the components are assumed to be
intimately mixed with one another such that the two phase mixture can be
treated as a single pseudo fluid with suitable average properties without
bothering about the detailed description of flow pattern. This model gives
accurate results for suspension of droplet in gas, well dispersed gas-liquid
bubbly flow, gas-solid or liquid-solid particulate flow and liquid-liquid
dispersed flows.
(ii) Drift flux model: which modifies the homogeneous model by
incorporating the relative motion between the phases. This is achieved by
introducing the concept of drift flux which shall be discussed in the next
chapter. It has been observed to give good results for the mixed flow
patterns .
(iii) Separated flow model: where the phases are assumed to flow side
by side. Accordingly, separate equations are formulated for each phase and
the interaction between phases is considered separately. This gives accurate
results for annular and stratified flow.
For gas-liquid two phase flow, the composition is expressed either in terms of the
gas voidage α which is a measure of the fractional volume of the flow channel
occupied by the gas phase or as liquid holdup HL which is a measure of the
volumetric content of the liquid in the mixture. For two-phase gas-liquid flow, the
average value of liquid holdup can be expressed mathematically
When the flow is not uniform, often it is not possible to measure <α> over a long
length of pipe. In this case a large number of instantaneous readings over a length
dL gives the time average α at a given location. The average value of α both in
space and time is then
Usually the symbol α is used
loosely to represent an average volumetric concentration without bothering
exactly how the average is to be taken. Therefore one has to take extra care
when periodic phenomena and non uniform concentrations are important.
The average gas voidage <α> is usually not equal to the inlet or outlet
volume composition, <β> even under steady state conditions where <β> is
obtained in terms of phase superficial velocities as
This is because the phases travel at different velocities due to a difference in
their density, interfacial distribution and other properties. This causes the
fluid of lower density to slip past that of higher density and reduces the gas-
liquid ratio in the flow channel over that of the entering or leaving mixture.
Since the existence of holdup arises due to the distribution and properties of
the two phases and does not depend upon the entry conditions only, it
cannot be manipulated according to the convenience of the experimenter or
the designer.
Though the term liquid holdup refers to the volume averaged property by
definition, it is not always possible to measure holdup over a volume
element. The measurements then obtain averaged values with respect to
different space dimensions and with time which are subsequently converted
to the volumetric averaged parameter. This gives rise to the following
definitions of liquid holdup for gas-liquid flow through a conduit.
Volume average holdup: It is obtained as the fraction of the conduit volume
occupied by the liquid phase at any instant of time. In mathematical terms
the definition can be expressed as
This is the
most useful definition of holdup in industrial designs and gives the overall
composition of the flowing mixture.
Area average holdup: It is the fraction of the conduit cross sectional area
occupied by the liquid phase at any instant of time. This average property is
usually determined by impedance method and optical techniques. This is the
volume average value for infinitesimal length of the test section and is equal
to the volumetric average holdup when the holdup does not vary with the
length of the conduit geometry. Mathematically this can be expressed as:
average
holdup: It is defined as the composition of the mixture along a particular
chord of known length. It is obtained when it is difficult to measure the area
or volume average values. It is used particularly in connection with the
radiation attenuation and scattering techniques. It is converted to the area
average values either by mathematical manipulation or by the use of
multiple beams and is mathematically expressed as:
Time average
holdup: This is obtained by measuring the holdup of the mixture at a
particular point in the two phase flow field as a function of time. This is
usually required to obtain the void fraction profile in any system since
knowledge of it adequately describes the structure of the flow field. Any
point in the field can only be occupied by one phase at a time. Therefore, by
definition, the point average holdup of a phase varies from zero to one and
vice versa instantaneously and assumes a square wave form with respect to
time. The point average holdup or local holdup with respect to time is,
therefore, meaningless. The holdup under these situations is defined as the
average fraction of a particular interval of time during which the point is
occupied by the liquid phase. It does not carry the sense of volume or area
and can be mathematically expressed as
Where i = 1,2,…..n and n is the number of periods during which liquid phase
exist at a particular point.
In our discussion, the holdup HL and the gas voidage α refers to the volume
average value unless otherwise mentioned.
In boiling /condensation applications, it is often necessary to have a
measure of the fraction of total mass across a given area which is composed
of each component. This is given by the quality of the mixture which is
defined as
Method of analysis of single and two-phase flow: A comparison
It is interesting to note that two-phase flow occurs when an
additional fluid is introduced in the flow passage, but a
straightforward extension of single-phase momentum equation
does not give us information about two-phase hydrodynamics.
For example single-phase pressure drop for flow of an
incompressible fluid through an inclined pipe can be obtained
from the following equation:
Where, , A, S, G, ρ and v are the wall shear stress, cross
sectional area, interfacial area, mass flux, density and specific
volume of the fluid respectively.
