The venturimeter used as gas fraction meter
Erling Hammer
The combination of a venturi differential pressure flowmeter and a density gauge also
provides the mass flow rate of liquids in two-phase (liquid/ gas) pipe flow (See Figure
14.2.5). The venturimeter is a differential pressure meter and if d/D < 0.6
approximately 75 % of the differential pressure Δp will be recovered. A gamma-ray
densitometer is positioned to measure the gas volume fraction (α) across the
venturimeter throat where the flow is more turbulent and thus more homogeneously
mixed.
P1
P2
v1
v2
v1
A1
1
E1
Z1
v2
A2
2
E1
Z1
Figure 1. The principle of a venturimeter
It can then be shown that for gas pressures less than about 100 bar, where the density
of the gas is negligible compared to the liquid density, the mass flow rate of the liquid
component is given as (Hammer and Nordtvedt 1991):
M  2CEA2M 2  mix P  qmix   mix
1
E
 D
1 d
A2M 
d 2
4
4
(1)
where
C is the discharge coefficient of the venturimeter
ε is the expansibility coefficient of the fluid
E is the velocity of approach factor
A2M is the throat cross section area
 mix  gass  liq  gass  (1   )  liq  (1   )  liq
since  gas   liq
This gives
CEA2M 2(1   )  liqP  (1   )  liqqmix   liqqliq
where qliq is volume flow rate of the liquid phase
and  is the gas fraction in the venturi throat
and hence:
q  CEAM
liq
2
2(1 )
liq P
(2)
The discharge coefficient C and the expansibility coefficient  can for all practical
reasons in multi flow measurements be set to 1.
In multi phase flowmeters a density gauge will always be installed to measure the gas
fraction . Thus the gas fraction  will be monitored and the liquid flow rate can be
measured according to equation 2.The accuracy of the measurement will increase with
increasing velocity and decrease with increasing gas fraction. To obtain better mixing
the venturimeter must be installed in vertical pipes with upward flow.
An interesting feature using a venturimeter is that if the velocity of the liquid (vliq) is
measured, by using the cross correlation of signals from two sets of capacitance
electrodes in the venturimeter throat, the gas fraction  can be found from equation 2.
The capacitance electrodes should be naked and mounted inside the throat wall. They
should also have short axial lengt so the small bobbles can be measured to determine
the liquid velocity:
  1
2 2 C 2 E 2 P
2C 2 E 2 P

1

v22liq  liq
v22liq  liq
(3)
Using the fact that qliq  A2M (1   )v2liq
where v2liq is the liquid flow velocity in venturi throat
Thus the gas fraction in the venturi throat can be found without any radioactive
gauges. That is important for delivering multi-phase meters to foreign countries.