Note: Descriptions are shown in the official language in which they were submitted.
3~
METI-IODS FOR METERING TWO-PHASE FLOW
05 ~ACKGROUND OF THE INVENTION
The present invention pertains in general to
methods for metering two-phase flow and in particular to
methods for metering two-phase flow using using two ori-
fice plates in series.
In an oil field in which steam injection is
employed to enhance oil recovery, each of a number of
steam injectors may be fed by a branch of a trunk line
from a common steam generator. Due to flow splitting
phenomena at the branches, a different ratio of steam to
total Elow (steam plus water), also called steam quality,
is likely to be present in each branch.
A knowlec1ge of the ratio of steam to total Elow
being injected in a two-phase flow is critical to any
understanding o the effects of steam injection. Because
it is impractical to predict this ratio from analysis of
the injection apparatus, it is important to be able to
determine flowrate parameters for calculating steam
quality from mea~urements made at each branch.
Many methods for metering single-phase flow,
such as those dependent upon critical choke flow or those
employing single orifice meters, lose their accuracy when
applied to a two~phase flow system. Other methods, such
as steam calorimetry, have inherent sampling problems.
Two-phase flow may be metersd by employing two
or more measurements which are mathematically correlated.
One such approach involves the use of a gamma
ray densitometer to maks void fraction measurements and a
turbine meter or drag disc to obtain a second measurement.
This approach is limited to a small quality range and
requires the use of an expensive and delicate gamma ray
densitometer instrument.
In another such approach, exemplified by
K. Sekoguchi et al, "Two-Phase Flow Measuremen-ts with
Orifice Couple in Horizonta:L Pipe Line", Bulletin of the
~0 JSME, ~ol. 21, No. 162, December, 1978, pp. 1757-64, two
~ 2~33~i5~3
Ol -2-
segmental orifices or baffles are coupled in series. Thepressure ~rop across each orifice or baffle is measured
05 and correlated with the pressure drop across the other
orifice or baffle. The orifices must differ in configura-
tion in order to provide independent measurements for the
purpose of correlation. One drawback of this approach is
that data is not presented in dimensionless form suitable
for predicting performances for different systems.
Yet another such approach involves measurement
of a frictional pressure drop across a twisted tape, mea-
surement of an accelerational pressure drop across a ven-
turi and correlation of the results. A disadvantage of
this approach is that a ver~v sensitive device is required
to measure the pressure drop across the twisted tape.
Measurement of the pressure drops across two
orifices in series may be done simply and at reasonable
cost, as shown in D. Collins et al, "Measurement of Steam
Quality in Two-phase ~pflow with Venturi Meters and Orifice
Plates", Journal of Basic Engineering, Transactions of the
ISME, March 1971. Although concurrent pressure drops were
measured for calibration purposes in Collins et al, pp. 11-
21, the pressure drops across two orifice plates in series
have not previously been correlated for the purpose of
metering two-phase flow prior to the present invention.
SUMMARY OF THE INVENTION
Accordingly, the method of the present invention
involves ~etering two-phase flow in a pipeline including
the following steps. An orifice plate is installed in the
pipeline. A second orifice plate is installed in series
with the first orifice plate in the pipeline and a two-
phase mixture is introduced. The respective accelerational
pressure drops across the orifice plates are measured and
then correlated to obtain one or more two-phase flow
flowrate parameters.
BRIEF DESCRIPTION OF THE DRAWI_GS
FIG. 1 is a view in diagrammatic partial cross-
section of an apparatus for practicing the method accord-
ing to the present invention; and
~L2835~
01 _3_
FIG. 2 is a plot of the steam quality as calcu-
lated according to the method of the present invention
~5 versus measured steam quality.
DESC~IPTION OF THE PREFERRED EMBODIMENT
As illustrated in FIG. 1, apparatus for practic-
ing the method according to the present invention includes
a first, upstream orifice plate 20 having a concentric
orifice 25 within a portion of a steam pipeline 10. A
second, downstream orifice plate 30 is installed in series
with the first orifice plate 20 so that the same two-phase
flow of steam and water passes through both in direction 15.
The orifice plates should be spaced far enough apart so
that there is no disturbance in fluid flow between the
upstream and the downstream orifices.
The accelerational pressure drop across the
first orifice plate 20 is measured by means of pressure
gauge 40 while the accelerational pressure drop across the
second oriEice plate 30 is measured by pressure gauge 50.
Steam pipelines and generators for two-phase
steam flow are well understood by those slcilled in the art
and will not be discussed ~urther. Orifice plates 20 and
30 may be a sharp~edged orifice plate having a concentric
orifice. Gauges 40 and 50 may be piezoelectric strain-
gauges or mercury manometers, for example.
According to a preEerred embodiment of -the pre-
sent invention, two sets of calculations are correlated in
order to obtain steam quality or flow rate. A first set
of three equations is applied to the pressure drop across
one of the orifice plates while a second set of three
equations is applied to the pressure drop across the other
orifice plate. Each set of equations may be used Eor
either orifice.
The first set of equations makes use of
Martinelli's parameter 1/X as defined by
1 IPQ X (1)
X p l-x
g
~;~83~
0l _4_
where:
x = the steam quality;
05 pQ = the density of the liquid phase (water); and
pg = the density of the gas phase (steam).
Martinelli's parameter is used to calculate the
liquid pseudo-pressure drop, ~pQ, which is the pressure
drop which would be recorded if the liquid phase were
flowing as a single-phase fluid, so that
~p
l + C (_) +( 1) 2 (2)
where:
Ap = the measured pressure drop;
C = a correlation coefficient based upon cali-
brat:ion data; and
all other variables are as defined above.
The liquid pseudo-pressure drop is used to cal-
culate the two-phase mass :Elow rate, W, using the equa-
tion:
K ~ Q
W = ~ (3)
1--x
where:
K = the appropriate orifice coefficient; and
all other variables are as defined above.
In the above set of equations, steam and water
densities at given temperature and pressures are readily
available to those skilled in the art in tabular form.
The correla-tion coe~ficient, C, is readily obtainàble for
a given orifice by running calibration tests on the ori-
fice. The constant, K, may be calculated according to the
American Gas Association Method as described in "Orifice
Metering of Natural Gas", American Gas Association Report
No. 3, June, 1979.
~0
~Z83~
~1 -5-
The second set of calculations employs the para-
meter Fp modified from Rhodes et al, U.S. Patent
05 No. ~,312,234, at column 4, as:
2 ~Pg~P
Fp = D ( _ )
where:
D = the diame~er of the orifice, and
all other variables are as defined above.
Fp is correlated as a function of steam quality,
x, in the form:
F = aXb (5)
where a and b are constants obtained by runnillg cali-
bration tests on a particular orifice.
The total mass flow rate is then given by:
a ~Pg~P) x (6)
where all variables are as defined above.
Accordingly, in order to predict quality and
flow rate, equations (1)-(3) may be applied to orifice
plate 20, or example, and equations (4)-(6) may be
applied to orifice plate 30, for example (however, each
set of equations may apply to the other orifice plate).
These two sets o equations are solved for the two-phase
flow rate, W. ~t the correct value for steam quality, x,
the two-phase flow rates given by equations (3) and (6)
should be equal.
EXAMPLE
Data was collected using one orifice plate
having a 2-inch internal diameter orifice and another
orifice plate having a 2.25 inch internal diameter orifice
~,Z~3~sg
01 -6-
in a 3-inch schedule 80-pipe. Two-phase steam was intro-
duced into ~he pipe.
nsEquations (1)-(3) were applied to orifice
plate 20 and equations (4)-(6) were applied to orifice
plate 30.
For orifice plate 20,
10Qp
1 + 6 fX) ~ (X) 2
and
126.72 /p~ Qp~ (8)
1--x
For oriEice plate 30,
Fp = 1.396 x 0.871
and
~ ~ = 81.295 /pgQp x -0.871 (10)
;,~, As illustrated by FIG. ~t, the following results
were obtained for steam quality:
Measured QualityPredicted Quality
0.58 0.63
0.85 0.83
0.75 0.63
0.55 0.53
0.65 0.58
0.82 0.78
0.88 0.88
0.69 0.78
0.64 0.68
0.55 0.58
~335i~9
Ol _7_
One of the advantages of the method according to
the pre.sent invention is that orifice plates are very
05 popular in flow metering and thus are easily obtainable
and well understood. Also, only two parameters are mea-
sured to predict flow rates as opposed to most techniques
which require three parameters to be measured.
While the present invention has been described
in terms of a preferred embodiment, further modifications
and improvements will occur to those slcilled in the art.
For example, although metering of two-phase steam has baen
described above, metering of any two-phase flow may be
obtained by employing the method according to the present
lS invention.
I desire it to be understood, therefore, that
this invention is not limited to the particular form shown
and that I intend in the appealed claims to cover all such
equivalent variations which come within the scope of the
~ invention as claimed.
