CA1283559C - Methods for metering two-phase flow - Google Patents
Methods for metering two-phase flowInfo
- Publication number
- CA1283559C CA1283559C CA000512155A CA512155A CA1283559C CA 1283559 C CA1283559 C CA 1283559C CA 000512155 A CA000512155 A CA 000512155A CA 512155 A CA512155 A CA 512155A CA 1283559 C CA1283559 C CA 1283559C
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- orifice
- phase
- orifice plate
- pressure drop
- equations
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Abstract
ABSTRACT OF THE DISCLOSURE
A method for metering two phase flow wherein the successive accelerational pressure drops across two ori-fice plates installed in series are correlated to obtain one or more flowrate parameters.
A method for metering two phase flow wherein the successive accelerational pressure drops across two ori-fice plates installed in series are correlated to obtain one or more flowrate parameters.
Description
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 obtainà ble 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:
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 obtainà ble 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 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.
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 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.
Claims (3)
1. A method for metering two-phase flow in a pipe-line comprising the steps of:
installing an orifice plate in the pipeline;
installing a second orifice plate in series with the first orifice plate in the pipeline;
introducing two-phase flow into the pipeline;
measuring the pressure drop across the first orifice plate;
measuring the pressure drop across the second orifice plate; and correlating the two-phase pressure drop across the second orifice plate with the two-phase pressure drop across the first orifice plate to obtain one or more two-phase flow rate parameters.
installing an orifice plate in the pipeline;
installing a second orifice plate in series with the first orifice plate in the pipeline;
introducing two-phase flow into the pipeline;
measuring the pressure drop across the first orifice plate;
measuring the pressure drop across the second orifice plate; and correlating the two-phase pressure drop across the second orifice plate with the two-phase pressure drop across the first orifice plate to obtain one or more two-phase flow rate parameters.
2. The method as recited according to Claim 1 wherein a first set of equations, applied to said first orifice, and a second set of equations, applied to said second orifice, are used to predict the flow conditions of quality and flow rate and wherein said first set of equations comprises:
, , and , and wherein said second set of equations comprises:
, Fp = axb, and W = where:
1/X = Martinelli's parameter, x = steam quality, P? = the density of a liquid phase (water), Pg = the density of a gaseous phase (steam), .DELTA.P? = liquid pseudo-pressure drop, .DELTA.P = the measured pressure drop across the device to which the equation is applied, C = a correlation coefficient based upon calibration data, W = the two-phase mass flow rate, K = an orifice coefficient for the orifice plate, Fp = a flow parameter, D = the diameter of the orifice, a = a first constant determined from calibration data, and b = a second constant based on calibration data.
, , and , and wherein said second set of equations comprises:
, Fp = axb, and W = where:
1/X = Martinelli's parameter, x = steam quality, P? = the density of a liquid phase (water), Pg = the density of a gaseous phase (steam), .DELTA.P? = liquid pseudo-pressure drop, .DELTA.P = the measured pressure drop across the device to which the equation is applied, C = a correlation coefficient based upon calibration data, W = the two-phase mass flow rate, K = an orifice coefficient for the orifice plate, Fp = a flow parameter, D = the diameter of the orifice, a = a first constant determined from calibration data, and b = a second constant based on calibration data.
3. The method as recited according to Claim 1 wherein a first set of equations, applied to said first orifice, and a second set of equations, applied to said second orifice, are used to predict the flow conditions of quality and flow rate and wherein said first set of equations comprises:
Fp = D2 , Fp = axb, and W = and wherein said second set of equations comprises:
, , and , where:
1/X = Martinelli's parameter, x = steam quality, p? = the density of a liquid phase (water), pg = the density of a gaseous phase (steam), .DELTA.p = the measured pressure drop across the device to which the equation is applied, C = a correlation coefficient based upon cali-bration data, W = the mass-flow rate of the two-phase mixture, K = an orifice coefficient for the orifice plate Fp = a flow parameter, D = the diameter of the orifice, a = a first constant determined from calibra-tion data, and b = a second constant based on calibration data.
Fp = D2 , Fp = axb, and W = and wherein said second set of equations comprises:
, , and , where:
1/X = Martinelli's parameter, x = steam quality, p? = the density of a liquid phase (water), pg = the density of a gaseous phase (steam), .DELTA.p = the measured pressure drop across the device to which the equation is applied, C = a correlation coefficient based upon cali-bration data, W = the mass-flow rate of the two-phase mixture, K = an orifice coefficient for the orifice plate Fp = a flow parameter, D = the diameter of the orifice, a = a first constant determined from calibra-tion data, and b = a second constant based on calibration data.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US06/763,378 US4662219A (en) | 1984-05-17 | 1985-08-06 | Methods for metering two-phase flow |
| US763,378 | 1985-08-06 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1283559C true CA1283559C (en) | 1991-04-30 |
Family
ID=25067682
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000512155A Expired - Fee Related CA1283559C (en) | 1985-08-06 | 1986-06-23 | Methods for metering two-phase flow |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA1283559C (en) |
-
1986
- 1986-06-23 CA CA000512155A patent/CA1283559C/en not_active Expired - Fee Related
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