TWO PHASE FLOW
                         METHODOLOGY


FLOW REGIME  The type of the flow regime of a gas-liquid
system must be determined to select the correct correlation
for pressure drop.  In a horizontal pipe the following types
of flow can exist, and with the characteristic velocities
shown in Table 1.

                           Table 1

Regime                   Liquid Phase            Vapor Phase
                           ft/s                     ft/s

Dispersed                  near vapor vel           >200

Annular                    < 0.5                    >20

Stratified                 < 0.5                    0.5-10

Slug                       15 <vapor vel            3-50

Plug                       2                        <4

Bubble                     5-15                     0.5-2


DISPERSED flow occurs at very high gas velocities with the
liquid phase dispersed as droplets.  The liquid phase
velocity approaches the gas-phase velocity.

ANNULAR flow occurs at lower gas velocities.  The liquid
phase forms an annulus around the circumference of the pipe
with the gas flowing through the central core.

STRATIFIED flow only occurs in horizontal pipes when the gas-
phase velocity is insufficient to maintain the annulus of
liquid around the circumference of the pipe.

WAVE flow is a form of stratified flow where there are waves
formed on the surface of the liquid.  This occurs near the
transition point where stratified flow may be transformed
into slug flow.

SLUG flow is an intermittent pattern of alternating liquid
phases and gas phases along the length of the line.  The
entire pipe cross-sectional area is occupied by a slug of
either liquid or vapor.

PLUG flow occurs when the liquid  forms a nearly continuous
phase with large elongated bubbles or plugs of gas in them.


BUBBLE or FROTH flow is predominately liquid, but the liwuid
phase in bubble flow is at a higher velocity then in plug
flow.  The gas phase is dispersed into small bubbles within
the liquid.  Higher gas phase flow are considered to be froth
and lower gas rates are bubble.

BAKER CHART  The Baker plot is most commonly used to
determine the flow regime, and is the method used in this
program.  The horizontal axis of the graph is defined as:

            X = [ Wl / Wg ] * Lamba * Beta

     Wl = Liquid mass flow rate, Lb/H
     Wg = Gas mass flow rate, Lb/H
     Lamba = 0.463 * SQRT[ Rho[l] * Rho[g] ]
     Rho = density Lb/Ft^3
     Surf-Tension = dyne/cm
     Visc[l] = Lb/(Ft-H)
     Beta = [1147/Surf-Tension]*[(Visc(l)/Rho[l]^2)]^0.333

The Y axis of the Baker chart is defined as:

            Y = G / Lamba

     Where G = Wg / A , A = Cross-sectional area of pipe Ft2

Once the values of X, and Y are determined and plotted on the
Baker chart, their intersection determines the expected two-
phase flow regime.  Although the Baker chart is based on
horizontal flow it can be used in estimating vertical flow
regimes with the observation that stratified and wavy flow
cannot exist.  Stratified flow will be transformed to slug
flow in vertical pipe.


                 PRESSURE DROP CORRELATIONS


There are two common methods for prediction the pressure drop
in two phase flow.  If the gas and liquid phases are expected
to be well mixed and homogeneous the pressure drop can be
approximated by using the single phase program with weight
averaged physical properties.
A more accurate method is used in this program based upon the
use of different correlations for each flow reqime as were
developed by Lockhart and Martinelli.








This method calculates the Martinelli two-phase flow modulus
defined as:

     Xmod^2 = [ P,100,liq / P,100,gas ]

     Where P,100,liq = friction pressure drop for 100 ft of
pipe for the liquid phase as if it were flowing as a single
phase in the pipe with no gas present.
     The value of Xmod is used then used to calculate the two
phase flow modulus Omega from a relationship taking the
general form

     Omega = a * Xmod^n

where a and n are emperical constants for the specific fow
regime.

After the Omega value has been calculated the two phase
frictional pressure drop is calculated by the relationship

     P,100,TP = P,100,gas * Omega^2


The exact equations used in the program for each flow regime
are as follows.

ANNULAR FLOW

     Omega = a * Xmod^n

where a = 4.8 - 0.315*d
      n = 0.343 - 0.021*d
      d = inside pipe diameter in inches, if d>10 then d = 10

BUBBLE FLOW

     Omega = 14.2*Xmod^0.75 / [Wl/A]^0.1

STRATIFIED FLOW

     Omega = 15400 * Xmod / [Wl/A]^0.8

SLUG FLOW

     Omega = 1190 * Xmod^0.815 / [Wl/A]^0.5

PLUG FLOW

     Omega = 27.315 * Xmod^0.855 / [Wl/A]^0.17





DISPERSED FLOW

The value of Omega as a function of Xmod is determined by a
curve fit of the data taken by Lockhart and Martinelli as
give in the following Table 2.  Omega,T,T is generally used
and it denoted turbulent flow in both the liquid and gas
phases.  If the flow of the liquid phase is laminar on a
single flow basis then Omega,V,T is used.

                           Table 2

     Xmod               Omega,T,T                Omega,V,T

     0.01                  1.28                     1.20
     0.02                  1.37                     1.28
     0.04                  1.54                     1.36
     0.07                  1.71                     1.45
     0.10                  1.85                     1.52
     0.20                  2.23                     1.78
     0.40                  2.28                     2.25
     0.70                  3.53                     2.85
     1.0                   4.20                     3.48
     2.0                   6.2                      5.25
     4.0                   9.5                      8.20
     7.0                  13.7                     12.0
    10.0                  17.5                     15.9
    20.0                  29.5                     28.0
    40.0                  51.5                     50.0
    70.0                  82.0                     82.0
   100.0                 111.0                    111.0


WAVE FLOW

The pressure drop is calculated using the Huntington
correlation.  The Huntington correlation calculates a two
phase friction factor by the following relationship.

    Ftp = 0.0044 * [ (Wl*Visl)/(Wg*Visg) ]^0.216

where viscosity is in centipoise.

The two phase friction factor is used to calculate the
pressure drop by the equation.

    P,100,tp = 3.33E-9 * (Ftp*G^2) / (D*Rhog)

Where D = pipe diameter in feet.






                      HYDROSTATIC HEAD

For homogeneous flow regimes (disperse or Bubble) the effect
of the static head can be estimated by using the average
mixture density.  Disperse flow has a minor static head since
the density is nearly gas.  Bubble flow has a high static
head since the flow is mainly liquid.

    P = ( Rho(mix) * Z ) / 144  where Z = ft

For other flow regimes the effect of static head is complex
and requires an estimate of the relative slip between the two
phases.  Baker proposed a relationship

    P = ( Rho(l) * Z * E / 144

where
    E = 1.61*(Velocity gas)^ -0.7
    Velocity in Ft/Sec


Govier and Aziz and DeGance and Atherton's papers present
relationships for vertical two phase flow that are beyond the
scope of this program.

When calculating static head pressure losses for two phase
flow, do NOT subtract the head resulting from possible
downward flow.  Only considerer the sum of the vertical
rises.


                    DESIGN CONSIDERATIONS

Slug flow should be avoided if possible by reducing the
diameter of the piping to achieve annular, dispersed or
bubble flow.  Slug flow results in water hammer that can
damage piping and equipment.  It can also upset distillation
equipment by introducting cyclic feed conditions.

Dispersed flow may sometimes be undesirable since it can be
difficult to separate in flash drums ect. You may need to use
centrifugal separators ie tangential inlets to separate the
phases.

Erosion should be checked with two phase systems.  Coulson
proposed a relationship based upon the mixture density and
mixture average velocity as follows:

    Rho(mix)*(Velocity mix)^2 < 10,000  to avoid erosion.

    Velocity mix = Vel gas + Vel liq
    Rho(m) =  [ Wl + Wg ] / [Wl/Rhol + Wg/Rhog ]


                         REFERENCES

G.W.Grover and K. Aziz, The Flow of Complex Mixtures in Pipes
Van Nostrand Reinhold Co, New York, 1972

Baker, Simultaneous Flow of Oil and Gas, Oil and Gas Journal
Vol 53, 1954 pp 185-190

A.E. DeGance and R.W. Atherton, Chemical Engineering Aspects
of Two Phase Flow, Part 4 , Chemical Engineering, Apr 20,
1970, pp 96,97 also Oct 5, 1970 pp 87-94

J.M Coulson, Chemical Engineering, Vol 1, 3rd Ed,, Pergamon
Press, New York, 1978, pp 91,92