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The development of a multiphase flow meter without separation based on sloped open channel dynamics
Flow Measurement and Instrumentation 22 (2011) 120–125
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
The development of a multiphase flow meter without separation based on sloped open channel dynamics Meng Lingya a , Li Yuxing a,∗ , Zhang Jian c , Dong Shouping b a
University of Petroleum China, Dongying, 257061, China
b
University of Petroleum China, Beijing, 102200, China
c
Shengli Oil Field Engineering and Design Corporation, 257016, China
article
info
Article history: Received 13 April 2010 Received in revised form 13 December 2010 Accepted 21 December 2010 Keywords: Multiphase flow meter Sloped open channel Metering models Metering equipment
abstract The online continuous measurement of multiphase flow is one of the most key technologies which influences the development of oil industry in future. A new type of multiphase meter system is developed based on the open channel flow. The test pipe of the meter is slightly slopped to make the flow pattern mainly stratified flow. Based on the study of oil and gas flow dynamics in the open channel test pipe, the liquid metering model and gas metering model are deduced to calculate the gas and the liquid flow rate, the water cut is measured online by the principle of differential pressure. This device can work online without the separation of the production fluid. By the lab test and field application test, the results of the metering system show that the liquid flow rate errors are within ±5%, the gas flow rate errors can be within ±5%, and the water cut absolute error is within ±2%, which can meet the demands of the field flow rate measurement. Crown Copyright © 2010 Published by Elsevier Ltd. All rights reserved.
1. Introduction The measurement of multiphase flow is one of the most critical technologies which influences the development of oil industry in future. This technology need not separate each component of the multiphase flow, and can measure the flow rate of each component (oil, water and gas). So this technology can replace the traditional measurement system which is composed of test separator, single phase monitor instrument and manifold, and is very useful for flow process simplification and investment decrement of petroleum exploitation. During the past few years, the development of the international petroleum industry gradually shifted from the land to the desert and the offshore [1,2]. Limited by the area of the offshore platform, cost and the difficulty of construction, the traditional oil well metering has not met the need of the production [3]. Many companies are developing multiphase flow metering in recent years [4,5]. Some oilfields [6–8] are now using the multiphase flow metering equipment which are based on the Nonintrusive Multiphase Flow Meter [9], or the flow meter without radioactive source [10], compact flow meter [11] or Venturi Meters [12,13]. But few can satisfy the demand of metering in the oilfield. The prominent problem in multiphase metering is that
∗
Corresponding author. Tel.: +86 0546 8399022; fax: +86 0546 8391094. E-mail address: [email protected] (Y. Li).
the metering precision is rather high when the multiphase flow changes and the cost of the multiphase flow meter is very high [14]. Many eastern oilfields of China are in the mid-late exploiting period, and the percentage of water can be up to 90%. To fit with the demands of eastern oilfield exploitation, a new kind of multiphase flow meter based on the open channel principle is developed. 2. Development of metering equipment 2.1. Structure of metering equipment The concept of open channel is quoted from the water flow in the atmosphere. For the two phase gas and liquid flow in the pipeline, the flow of liquid at the bottom of the pipe and the gas at the top is similar to the water ‘‘open channel’’ except that the operation pressure is not equal to the atmosphere pressure. For the measurement of gas and liquid flow rates, the main problem that should be solved is to get the occupied liquid height in the pipelines. So if the flow regime is designed in the region of stratified flow which is similar to the open channel and the liquid height can be measured by the differential pressure, then the flow rate can be calculated by the relations deduced in the paper. The construction of Multiphase Flow Meter is shown in Fig. 1. It concludes inlet tank, sloped test pipe, back outlet tank. The structure of the sloped test pipe is also shown in Fig. 1. The function of the sloped pipe is to make the flow pattern stratified and decrease the influence of the slug flow pattern and the sloped
0955-5986/$ – see front matter Crown Copyright © 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2010.12.011
L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
121
Fig. 1. Multiphase flow metering equipment principle diagram, open channel cross A–A Figure.
Fig. 2. Measure model principles.
angel of the test pipe is calculated by using the following equation.
vgtra
hL ρL − ρg gdAg cos θ = 1− [ 2 ]0.5 d ρg 1 − 2 hdl − 1
can be obtained simultaneously and online, which can replace the traditional metering separator and decrease the manual operation.
(1)
where vgtra is the transition gas velocity. hl is the liquid thickness in the pipe, Ag is the gas occupied area of the pipe’s cross section. ρg , ρl are the gas and liquid densities, θ is the inclination angle of the test pipe, d is the diameter of the pipe. Three uniformly spaced differential pressure transducers are installed on the test top and bottom ends of the pipe to measure the liquid film thickness in the open channel according to the liquid density and water cut. A differential pressure transducer is installed between the inlet tank and the outlet tank to measure the gas pressure difference. The inlet tank is designed to measure the water cut according to density difference of water and oil similar to the principle of ‘‘U’’ type flow and the pressure is measure by two differential pressure transducers. The produced mixture enters from the inlet small tank. Then the liquid is at the bottom of the tank, and the top is filled with steady gas. When the mixture flows through the pipe, different flow patterns will appear at different proportions of the liquid and the gas and the main flow pattern is stratified flow because of the slope. The outlet tank is used to stabilize the pressure. Using the designed multiphase flow meter, once installed at the metering station, the flow rates of gas and liquid, water cut
2.2. Metering principle Metering principle is shown in Fig. 2. The pressure drop and the pressure fluctuation in the sloped open channel have direct relationship with the flow rate of the gas, height and fluctuation of the liquid, and the velocity of the flow [15]. The three differential pressure transducers installed in the test pipe are used to measure the height of the liquid and the differential pressure transducers between the inlet and outlet tanks are used to measure the gas flow rate. These sensors can survey the liquid height in the pipe, the pressure drop along the pipe and the pressure fluctuation. These eigenvalues construct eigenvectors that can be recognized by the flow pattern model classifier. Then we can use the illegibility pattern identifying technology to identify the flow patterns [16]. The flow rate of each phase can be calculated by the metering models. Results of model metering are further optimized by the method of polynomial fitting. And then Artificial Neural Networks are used to process the data after modification to increase metering accuracy [17]. 3. Development of metering models Based on hydrodynamics theory, the liquid metering model to calculate the liquid flow rate, gas metering model to calculate the
122
L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
And 1 2g
(2u22 − u21 − u23 ) = d1 + d3 − 2d2 .
(9)
According to the liquid continuous equations: u1 d1 b = u2 d2 b = u3 d3 b = ql
(10)
where b is the width of the channel, ql is the liquid flow rate. Combining Eqs. (9) and (10), the relationship to calculate the liquid flow rate can be obtained:
Fig. 3. Theory of the liquid metering model.
ql = bd1 d2 d3 gas flow rate and the water cut calculation model are deduced based on the pressure difference parameters measured from the metering device.
2g (2d2 − d1 − d3 ) . (d1 d2 )2 + (d2 d3 )2 − 2(d1 d3 )2
Considering the flow rate coefficient Cl , then
2g (2d2 − d1 − d3 ) . (d1 d2 )2 + (d2 d3 )2 − 2(d1 d3 )2
3.1. The liquid metering model
ql = Cl bd1 d2 d3
Assuming that the interface between the gas and the liquid is a line when the gas and liquid flow in the testing section, the liquid height (d′1 , d′2 , d′3 ) along the direction of gravity at three different positions (x1 , x2 , x3 ) can be measured by the differential pressure transducers, as shown in Fig. 3. And d1 , d2 , d3 are the vertical heights of the liquid perpendicular to the pipe at positions x1 , x2 , x3 , respectively. Then the following equations can be obtained:
The coefficient C can be obtained by the experiment.
d1 ≈ d′1 cos θ ,
d2 ≈ d′2 cos θ ,
d3 ≈ d′3 cos θ .
(2)
If the total length of the test section is l, the Bernoulli equations of hydrodynamics can be obtained at positions x1 , x2 , x3 : 1 2 1 2 1 2
u21 + gd1 + u22
+ gd2 +
u23 + gd3 +
p1
p′1
+
ρ
ρ
p0
= gd0 +
p2
ρ p3
ρ
+
p2
+
p′3
ρ ρ
(3)
p0
ρ
x p′x = p′0 . l
(4)
So the pressure drop p′1 , p′2 , p′3 can be obtained by:
1−
2ls
p′2 = p′0
l
1−
ls
p′3 = p′0
l
(5)
where ls = x2 − x1 = x3 − x2 . If the outlet pressure of the test section is pe , then: p′0 = po − pe ,
p′1 = p0 − p1 ,
p′2 = p0 − p2 ,
p′3 = p0 − p3 .
(6)
2ls l
+ pe
p2 = (p0 − pe )
ls l
(7)
Substituting Eq. (5) into (3) obtains the following relations:
2
u21 + gd1 = gd0
1 2
qg A
.
(13)
u22 + gd2 = gd0
(14)
where Cg is the flow rate coefficient: 1
l λ 2gD
.
(15)
And 1p is the gas pressure drop along the pipe. H is the height of the testing channel section, and h is the height of the liquid at the testing position. 3.3. The water cut metering model The water cut is measured based on the density difference between oil and water and is metered using the principle of Upipe to eliminate the measurement error produced by the pressure loss between the fluid and the pipe wall. Firstly, the oil is filled completely into the U-pipe, as shown in Fig. 4, and the indications of the up-flow differential pressure transducers and down-flow differential pressure transducers are equal to po = ρo gh (h is the height of the liquid). Then the U-pipe is filled with water, and the measured differential pressure of these transducers is equal to pw = ρw gh. If the U-pipe is filled with oil/water mixture and the water cut is ω, then:
1 2
(16)
So:
+ pe
p3 = pe .
1
v=
D 2g
pmix = ρw gh − ρmix gh.
And Eq. (4) can be rewritten as: p1 = (p0 − pe )
l v2
1p = λ
Cg =
where p′1 , p′2 , p′3 are the pressure drops from the original point to positions x1 , x2 , x3 ; u1 , u2 , u3 are the velocities; p1 , p2 , p3 are the pressures at positions x1 , x2 , x3 ; ρ is the density of the liquid. If the distribution of pressure drop along the pipe is linear, p′0 is the total pressure drop of the test section, then the pressure drop at a certain point x can be calculated by following equation:
p′1 = p′0
The gas is always at the top of the test pipe, and the flow area can be calculated. The flow rate of the gas has relation with the pressure drop along the test pipe. So the flow rate of the gas can be calculated according to the hydrodynamics. From the equation of the hydrodynamics:
ρ
= gd0 +
3.2. Gas metering model
qg = Cg (H − h)b 1p
p0
= gd0 +
(12)
Then:
ρ
′
(11)
u23 + gd3 = gd0 . (8)
po − pmix po − pw
=
ρmix gh − ρo gh ρmix − ρo = . ρw gh − ρo gh ρw − ρo
(17)
The mixture density can be calculated by:
ρmix = ωρw + (1 − ω)ρo . Deforming Eq. (18) we get ω =
(18) ρmix −ρo . ρw −ρo
L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
123
Fig. 6. Error distribution for liquid flow rate.
Fig. 4. Water cut measuring diagram and the structural schematic diagram of the inside clapboard and the center canister in the front tank.
Substituting to Eq. (17), then the water cut can be calculated by the measured pmix :
ω=
po − pmix
. (19) po − pw The pmix in Eq. (19) is the hydrostatic pressure, but for online flow in the production, the pressure loss for the flow in the pipe should be considered to eliminate the system error. If the indications of the two transducers are pu and pd , respectively, then: pu = pmix − 1hf 1
(20)
pd = pmix + 1hf 2
where 1hf 1 and 1hf 2 are the pressure losses between the fluid and the pipe wall. Assuming that these two values are equal, then the mixture pressure drop can be calculated by the following relation: pmix =
pu + pd 2
.
(21)
4. The measurement performance of the metering device 4.1. Laboratory test results and analysis In order to test the measurement performance of this metering device, a laboratory test loop is constructed as shown in Fig. 5.
The total length of the experimental pipeline is 20 m and the transparent segment is 119 cm. The inner diameter is 2.54 cm. The flow rates of the liquid and gas are measured using the MicroMotion mass flow meters, the pressure and temperature are tested with the Rosemount Pressure Transducers. And the flow rates of the liquid and gas can be changed with a valve. The data are acquired by using the Labview platform. About 360 experimental cases are done in the flow metering equipment. The model’s coefficients are calculated. The testing mediums are lubricating oil, water and air. The liquid flow rate is in the range of 1.0–3.5 m3 /h. The gas flow rate is in the range of 1–90 m3 /h. The metering results and the error distributions of the equipment for liquid, gas and water cut are shown in Figs. 6–8. From the test results, we can then reach the conclusion that the metering errors for the liquid phase are almost in the range of −5% to 5%, and most of the gas metering errors are in the range of −10% to 10%, the water cut absolute errors are in the band of 2.5%. 4.2. Field applications and analysis Field experiment is carried out at 52# metering station of Shengli oilfield in China. The test loop is shown in Fig. 9. The operation pressure of the production field is in the range of 1–1.5 MPa. The liquid temperature is about 35 °C. The liquid flow rate is in the range of 1.0–300 m3 /d. The gas flow rate is in the range of 1.0–500 m3 /d. The oil and gas flow rates are measured using the turbine flow meter. The produced mixed gas and liquid
Fig. 5. Experimental test loop.
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L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
Fig. 10. The error distribution for the liquid flow rate. Fig. 7. Error distribution for gas flow rate.
Fig. 11. The error distribution for the gas flow rate.
Fig. 8. Error distribution of water cut.
Fig. 9. The field test loop. Fig. 12. The error distribution of the water cut.
from the well is measured using the developed meter. Limited by the field test conditions, the flow rate of the liquid and gas cannot be recorded for every second. So the test results are the accumulated flow rate for 2 h. About 120 test cases are acquired. The test results are shown in Figs. 10–12 for liquid, gas and water cut respectively. According to the figures, the metering errors for the liquid flow rate are between −5% and 5% and the maximum error is 14.8%. The metering errors for gas phase are between −5% and 5% and the maximum error is −4.83%. The water cut metering absolute errors is between −2% to 2%. The precisions
of the metering equipment can meet the demands of the field single well flow rate measurement, and this test device has been used in the field for two years. 5. Conclusions For the high water cut production oilfields, a metering device based on the sloped open channel principle is developed. According to the hydrodynamics, the mathematical models to
L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
calculate the liquid flow rate, gas flow rate and water cut are deduced. The metering performance of the device was tested in the lab and the oil production field. The main conclusions include: (1) Based on the study of oil and gas flow in the sloped open channel, a multiphase flow metering system, which combines three phase flows’ rate metering models are established. It can measure the three phase flow rates online, and the production fluids need not be separated in advance. (2) The structure of the metering device is composed of three differential pressure transducers for liquid, one differential pressure transducer for gas and two differential pressure transducers for water cut measurement. The flow pattern in the sloped open channel is designed to be stratified to make the measurement liable. (3) The metering errors for the liquid flow rate are between −5% and 5% and the maximum error is 14.8%. The metering errors for the gas phase are between −5% and 5% and the maximum error is −4.83%. The water cut metering absolute errors are between −2% to 2%. (4) The precisions of the metering equipment can meet the demands of the field single well flow rate measurement, and this test device has been used in the field for two years. Acknowledgements This development was carried out in the Shengli Oilfield Shengli Engineering & Consulting Company Ltd. The authors thank the support of the company, and also thank all the workers related with the experiment. The research works are also funded by the National Educational foundation (NCET-07-0847), the authors also thank them for the permission to publish this paper.
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References [1] Falcone G, Hewitt GF, Alimonti C, Harrison B. Multiphase flow metering: current trends and future developments. In: SPE 74689. [2] Toral Haluk, Cal Shiqian, Akartuna Ersin, Stothard Ken, Jamieson Andy. Field tests of the ESMER multiphase flowmeter. In: 16th north sea flow measurement workshop. 1998. [3] Warren PB, Al-Dusari KH, Zabihi M, Al-Abduljabbar JM. Field-testing a compact multiphase flow meter-offshore Saudi Arabia. In: SPE 81560. [4] Falcone G, Hewitt GF. Multiphase flow metering: current trends and future developments. In: 2001 SPE annual tech. conf. SPE71474. [5] Jamieson AW. Multiphase metering—the challenge of implementation. Measurement and Control 1999;32(1):5–9. [6] Xuewen Cao. Multiphase flow regime measurement and identification techniques. Oil & Gas Science and Technology 2001;20(11):1–4. [7] Hongyan Sun. The application of multiphase flow meter in Mexico gulf for the first time. Foreign Oilfield Engineering 2000;1. [8] OUBAGE. A new look at measurement uncertainty of multiphase flow meters. In: ASME energy sources tech. conf. Houston, 2/224/98. Proc. 1998. PAP NO ETCE9824661. [9] Athkinson DI, Berard M, Segeral G. Qualification of a nonintrusive multiphase flow meter in viscous flows. In: SPE 63118. [10] Fueki M, Urabe S, Yamazaki D, Yamashita M. Development of multiphase flow meter without radioactive source. In: SPE 59421. [11] Kettle RJ, Ross D, Deznan D. The multiphase flow meter, a tool for well performance diagnostics and production optimization. In: SPE 77893. [12] Lindsay I, Stimpson B, Corlett A. Advanced interpretation of venturi meter measurements in multiphase flow. In: SPE 71535. [13] Shippen ME, Scott SL. A neural network model for prediction of liquid holdup in tow-phase horizontal flow. In: SPE 77499. [14] Jamieson AW. High-performance multiphase metering: a personal perspective. Measurement and Control 2000;33(3):73–9. [15] Shouping Dong. The fractal feature of gas–liquid two-phase flow pattern signals based on wavelet transform. Oil & Gas Science and Technology 2001; 20(7):25–7. [16] Fuxian Zhou, Yuxing Li, Shouping Dong. Study on multiphase flow online metering models without separation. In: 6th international symposium on instrumentation and control technology. 2006. p. 10. [17] Huiming Yang, Yuxing Li, Shouping Dong. Application of artificial neural networks in oil and gas multiphase metering. In: 6th international symposium on instrumentation and control technology. 2006. p. 10.
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
The development of a multiphase flow meter without separation based on sloped open channel dynamics Meng Lingya a , Li Yuxing a,∗ , Zhang Jian c , Dong Shouping b a
University of Petroleum China, Dongying, 257061, China
b
University of Petroleum China, Beijing, 102200, China
c
Shengli Oil Field Engineering and Design Corporation, 257016, China
article
info
Article history: Received 13 April 2010 Received in revised form 13 December 2010 Accepted 21 December 2010 Keywords: Multiphase flow meter Sloped open channel Metering models Metering equipment
abstract The online continuous measurement of multiphase flow is one of the most key technologies which influences the development of oil industry in future. A new type of multiphase meter system is developed based on the open channel flow. The test pipe of the meter is slightly slopped to make the flow pattern mainly stratified flow. Based on the study of oil and gas flow dynamics in the open channel test pipe, the liquid metering model and gas metering model are deduced to calculate the gas and the liquid flow rate, the water cut is measured online by the principle of differential pressure. This device can work online without the separation of the production fluid. By the lab test and field application test, the results of the metering system show that the liquid flow rate errors are within ±5%, the gas flow rate errors can be within ±5%, and the water cut absolute error is within ±2%, which can meet the demands of the field flow rate measurement. Crown Copyright © 2010 Published by Elsevier Ltd. All rights reserved.
1. Introduction The measurement of multiphase flow is one of the most critical technologies which influences the development of oil industry in future. This technology need not separate each component of the multiphase flow, and can measure the flow rate of each component (oil, water and gas). So this technology can replace the traditional measurement system which is composed of test separator, single phase monitor instrument and manifold, and is very useful for flow process simplification and investment decrement of petroleum exploitation. During the past few years, the development of the international petroleum industry gradually shifted from the land to the desert and the offshore [1,2]. Limited by the area of the offshore platform, cost and the difficulty of construction, the traditional oil well metering has not met the need of the production [3]. Many companies are developing multiphase flow metering in recent years [4,5]. Some oilfields [6–8] are now using the multiphase flow metering equipment which are based on the Nonintrusive Multiphase Flow Meter [9], or the flow meter without radioactive source [10], compact flow meter [11] or Venturi Meters [12,13]. But few can satisfy the demand of metering in the oilfield. The prominent problem in multiphase metering is that
∗
Corresponding author. Tel.: +86 0546 8399022; fax: +86 0546 8391094. E-mail address: [email protected] (Y. Li).
the metering precision is rather high when the multiphase flow changes and the cost of the multiphase flow meter is very high [14]. Many eastern oilfields of China are in the mid-late exploiting period, and the percentage of water can be up to 90%. To fit with the demands of eastern oilfield exploitation, a new kind of multiphase flow meter based on the open channel principle is developed. 2. Development of metering equipment 2.1. Structure of metering equipment The concept of open channel is quoted from the water flow in the atmosphere. For the two phase gas and liquid flow in the pipeline, the flow of liquid at the bottom of the pipe and the gas at the top is similar to the water ‘‘open channel’’ except that the operation pressure is not equal to the atmosphere pressure. For the measurement of gas and liquid flow rates, the main problem that should be solved is to get the occupied liquid height in the pipelines. So if the flow regime is designed in the region of stratified flow which is similar to the open channel and the liquid height can be measured by the differential pressure, then the flow rate can be calculated by the relations deduced in the paper. The construction of Multiphase Flow Meter is shown in Fig. 1. It concludes inlet tank, sloped test pipe, back outlet tank. The structure of the sloped test pipe is also shown in Fig. 1. The function of the sloped pipe is to make the flow pattern stratified and decrease the influence of the slug flow pattern and the sloped
0955-5986/$ – see front matter Crown Copyright © 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2010.12.011
L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
121
Fig. 1. Multiphase flow metering equipment principle diagram, open channel cross A–A Figure.
Fig. 2. Measure model principles.
angel of the test pipe is calculated by using the following equation.
vgtra
hL ρL − ρg gdAg cos θ = 1− [ 2 ]0.5 d ρg 1 − 2 hdl − 1
can be obtained simultaneously and online, which can replace the traditional metering separator and decrease the manual operation.
(1)
where vgtra is the transition gas velocity. hl is the liquid thickness in the pipe, Ag is the gas occupied area of the pipe’s cross section. ρg , ρl are the gas and liquid densities, θ is the inclination angle of the test pipe, d is the diameter of the pipe. Three uniformly spaced differential pressure transducers are installed on the test top and bottom ends of the pipe to measure the liquid film thickness in the open channel according to the liquid density and water cut. A differential pressure transducer is installed between the inlet tank and the outlet tank to measure the gas pressure difference. The inlet tank is designed to measure the water cut according to density difference of water and oil similar to the principle of ‘‘U’’ type flow and the pressure is measure by two differential pressure transducers. The produced mixture enters from the inlet small tank. Then the liquid is at the bottom of the tank, and the top is filled with steady gas. When the mixture flows through the pipe, different flow patterns will appear at different proportions of the liquid and the gas and the main flow pattern is stratified flow because of the slope. The outlet tank is used to stabilize the pressure. Using the designed multiphase flow meter, once installed at the metering station, the flow rates of gas and liquid, water cut
2.2. Metering principle Metering principle is shown in Fig. 2. The pressure drop and the pressure fluctuation in the sloped open channel have direct relationship with the flow rate of the gas, height and fluctuation of the liquid, and the velocity of the flow [15]. The three differential pressure transducers installed in the test pipe are used to measure the height of the liquid and the differential pressure transducers between the inlet and outlet tanks are used to measure the gas flow rate. These sensors can survey the liquid height in the pipe, the pressure drop along the pipe and the pressure fluctuation. These eigenvalues construct eigenvectors that can be recognized by the flow pattern model classifier. Then we can use the illegibility pattern identifying technology to identify the flow patterns [16]. The flow rate of each phase can be calculated by the metering models. Results of model metering are further optimized by the method of polynomial fitting. And then Artificial Neural Networks are used to process the data after modification to increase metering accuracy [17]. 3. Development of metering models Based on hydrodynamics theory, the liquid metering model to calculate the liquid flow rate, gas metering model to calculate the
122
L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
And 1 2g
(2u22 − u21 − u23 ) = d1 + d3 − 2d2 .
(9)
According to the liquid continuous equations: u1 d1 b = u2 d2 b = u3 d3 b = ql
(10)
where b is the width of the channel, ql is the liquid flow rate. Combining Eqs. (9) and (10), the relationship to calculate the liquid flow rate can be obtained:
Fig. 3. Theory of the liquid metering model.
ql = bd1 d2 d3 gas flow rate and the water cut calculation model are deduced based on the pressure difference parameters measured from the metering device.
2g (2d2 − d1 − d3 ) . (d1 d2 )2 + (d2 d3 )2 − 2(d1 d3 )2
Considering the flow rate coefficient Cl , then
2g (2d2 − d1 − d3 ) . (d1 d2 )2 + (d2 d3 )2 − 2(d1 d3 )2
3.1. The liquid metering model
ql = Cl bd1 d2 d3
Assuming that the interface between the gas and the liquid is a line when the gas and liquid flow in the testing section, the liquid height (d′1 , d′2 , d′3 ) along the direction of gravity at three different positions (x1 , x2 , x3 ) can be measured by the differential pressure transducers, as shown in Fig. 3. And d1 , d2 , d3 are the vertical heights of the liquid perpendicular to the pipe at positions x1 , x2 , x3 , respectively. Then the following equations can be obtained:
The coefficient C can be obtained by the experiment.
d1 ≈ d′1 cos θ ,
d2 ≈ d′2 cos θ ,
d3 ≈ d′3 cos θ .
(2)
If the total length of the test section is l, the Bernoulli equations of hydrodynamics can be obtained at positions x1 , x2 , x3 : 1 2 1 2 1 2
u21 + gd1 + u22
+ gd2 +
u23 + gd3 +
p1
p′1
+
ρ
ρ
p0
= gd0 +
p2
ρ p3
ρ
+
p2
+
p′3
ρ ρ
(3)
p0
ρ
x p′x = p′0 . l
(4)
So the pressure drop p′1 , p′2 , p′3 can be obtained by:
1−
2ls
p′2 = p′0
l
1−
ls
p′3 = p′0
l
(5)
where ls = x2 − x1 = x3 − x2 . If the outlet pressure of the test section is pe , then: p′0 = po − pe ,
p′1 = p0 − p1 ,
p′2 = p0 − p2 ,
p′3 = p0 − p3 .
(6)
2ls l
+ pe
p2 = (p0 − pe )
ls l
(7)
Substituting Eq. (5) into (3) obtains the following relations:
2
u21 + gd1 = gd0
1 2
qg A
.
(13)
u22 + gd2 = gd0
(14)
where Cg is the flow rate coefficient: 1
l λ 2gD
.
(15)
And 1p is the gas pressure drop along the pipe. H is the height of the testing channel section, and h is the height of the liquid at the testing position. 3.3. The water cut metering model The water cut is measured based on the density difference between oil and water and is metered using the principle of Upipe to eliminate the measurement error produced by the pressure loss between the fluid and the pipe wall. Firstly, the oil is filled completely into the U-pipe, as shown in Fig. 4, and the indications of the up-flow differential pressure transducers and down-flow differential pressure transducers are equal to po = ρo gh (h is the height of the liquid). Then the U-pipe is filled with water, and the measured differential pressure of these transducers is equal to pw = ρw gh. If the U-pipe is filled with oil/water mixture and the water cut is ω, then:
1 2
(16)
So:
+ pe
p3 = pe .
1
v=
D 2g
pmix = ρw gh − ρmix gh.
And Eq. (4) can be rewritten as: p1 = (p0 − pe )
l v2
1p = λ
Cg =
where p′1 , p′2 , p′3 are the pressure drops from the original point to positions x1 , x2 , x3 ; u1 , u2 , u3 are the velocities; p1 , p2 , p3 are the pressures at positions x1 , x2 , x3 ; ρ is the density of the liquid. If the distribution of pressure drop along the pipe is linear, p′0 is the total pressure drop of the test section, then the pressure drop at a certain point x can be calculated by following equation:
p′1 = p′0
The gas is always at the top of the test pipe, and the flow area can be calculated. The flow rate of the gas has relation with the pressure drop along the test pipe. So the flow rate of the gas can be calculated according to the hydrodynamics. From the equation of the hydrodynamics:
ρ
= gd0 +
3.2. Gas metering model
qg = Cg (H − h)b 1p
p0
= gd0 +
(12)
Then:
ρ
′
(11)
u23 + gd3 = gd0 . (8)
po − pmix po − pw
=
ρmix gh − ρo gh ρmix − ρo = . ρw gh − ρo gh ρw − ρo
(17)
The mixture density can be calculated by:
ρmix = ωρw + (1 − ω)ρo . Deforming Eq. (18) we get ω =
(18) ρmix −ρo . ρw −ρo
L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
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Fig. 6. Error distribution for liquid flow rate.
Fig. 4. Water cut measuring diagram and the structural schematic diagram of the inside clapboard and the center canister in the front tank.
Substituting to Eq. (17), then the water cut can be calculated by the measured pmix :
ω=
po − pmix
. (19) po − pw The pmix in Eq. (19) is the hydrostatic pressure, but for online flow in the production, the pressure loss for the flow in the pipe should be considered to eliminate the system error. If the indications of the two transducers are pu and pd , respectively, then: pu = pmix − 1hf 1
(20)
pd = pmix + 1hf 2
where 1hf 1 and 1hf 2 are the pressure losses between the fluid and the pipe wall. Assuming that these two values are equal, then the mixture pressure drop can be calculated by the following relation: pmix =
pu + pd 2
.
(21)
4. The measurement performance of the metering device 4.1. Laboratory test results and analysis In order to test the measurement performance of this metering device, a laboratory test loop is constructed as shown in Fig. 5.
The total length of the experimental pipeline is 20 m and the transparent segment is 119 cm. The inner diameter is 2.54 cm. The flow rates of the liquid and gas are measured using the MicroMotion mass flow meters, the pressure and temperature are tested with the Rosemount Pressure Transducers. And the flow rates of the liquid and gas can be changed with a valve. The data are acquired by using the Labview platform. About 360 experimental cases are done in the flow metering equipment. The model’s coefficients are calculated. The testing mediums are lubricating oil, water and air. The liquid flow rate is in the range of 1.0–3.5 m3 /h. The gas flow rate is in the range of 1–90 m3 /h. The metering results and the error distributions of the equipment for liquid, gas and water cut are shown in Figs. 6–8. From the test results, we can then reach the conclusion that the metering errors for the liquid phase are almost in the range of −5% to 5%, and most of the gas metering errors are in the range of −10% to 10%, the water cut absolute errors are in the band of 2.5%. 4.2. Field applications and analysis Field experiment is carried out at 52# metering station of Shengli oilfield in China. The test loop is shown in Fig. 9. The operation pressure of the production field is in the range of 1–1.5 MPa. The liquid temperature is about 35 °C. The liquid flow rate is in the range of 1.0–300 m3 /d. The gas flow rate is in the range of 1.0–500 m3 /d. The oil and gas flow rates are measured using the turbine flow meter. The produced mixed gas and liquid
Fig. 5. Experimental test loop.
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L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
Fig. 10. The error distribution for the liquid flow rate. Fig. 7. Error distribution for gas flow rate.
Fig. 11. The error distribution for the gas flow rate.
Fig. 8. Error distribution of water cut.
Fig. 9. The field test loop. Fig. 12. The error distribution of the water cut.
from the well is measured using the developed meter. Limited by the field test conditions, the flow rate of the liquid and gas cannot be recorded for every second. So the test results are the accumulated flow rate for 2 h. About 120 test cases are acquired. The test results are shown in Figs. 10–12 for liquid, gas and water cut respectively. According to the figures, the metering errors for the liquid flow rate are between −5% and 5% and the maximum error is 14.8%. The metering errors for gas phase are between −5% and 5% and the maximum error is −4.83%. The water cut metering absolute errors is between −2% to 2%. The precisions
of the metering equipment can meet the demands of the field single well flow rate measurement, and this test device has been used in the field for two years. 5. Conclusions For the high water cut production oilfields, a metering device based on the sloped open channel principle is developed. According to the hydrodynamics, the mathematical models to
L. Meng et al. / Flow Measurement and Instrumentation 22 (2011) 120–125
calculate the liquid flow rate, gas flow rate and water cut are deduced. The metering performance of the device was tested in the lab and the oil production field. The main conclusions include: (1) Based on the study of oil and gas flow in the sloped open channel, a multiphase flow metering system, which combines three phase flows’ rate metering models are established. It can measure the three phase flow rates online, and the production fluids need not be separated in advance. (2) The structure of the metering device is composed of three differential pressure transducers for liquid, one differential pressure transducer for gas and two differential pressure transducers for water cut measurement. The flow pattern in the sloped open channel is designed to be stratified to make the measurement liable. (3) The metering errors for the liquid flow rate are between −5% and 5% and the maximum error is 14.8%. The metering errors for the gas phase are between −5% and 5% and the maximum error is −4.83%. The water cut metering absolute errors are between −2% to 2%. (4) The precisions of the metering equipment can meet the demands of the field single well flow rate measurement, and this test device has been used in the field for two years. Acknowledgements This development was carried out in the Shengli Oilfield Shengli Engineering & Consulting Company Ltd. The authors thank the support of the company, and also thank all the workers related with the experiment. The research works are also funded by the National Educational foundation (NCET-07-0847), the authors also thank them for the permission to publish this paper.
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