Estimation of volume fraction and flow regime identification in inclined ...

Special Issue Article Received: 31 August 2011,

Revised: 16 February 2012,

Accepted: 24 February 2012,

Published online in Wiley Online Library: 2 April 2012

(wileyonlinelibrary.com) DOI: 10.1002/cem.2437

Estimation of volume fraction and flow regime identification in inclined pipes based on gamma measurements and multivariate calibration Benjamin Kaku Arvoha*, Rainer Hoffmannb, Arne Valleb and Maths Halstensena A combination of gamma measurements and multivariate calibration was applied to estimate multiphase flow mixture density and to identify flow regime. The experiments were conducted using recombined hydrocarbon fluids sampled from an onshore receiving terminal including hydrate thermodynamic inhibitors (monoethylene glycol and methanol (MeOH)). These hydrate inhibitors were added to deionised water at 60% concentration by volume. The experiments were conducted at a temperature of 0 C and a 75-bar pressure, comparable with deep water production on the Norwegian continental shelf. Two angles of inclination (1 and 5 ) and two water cuts (15% and 85%) were investigated. A single-energy gamma densitometer was installed on the test facility for measuring the mixture density, whereas the dual-energy gamma densitometer was traversed linearly from the bottom to the top of the pipe for multivariate calibration and prediction. Seventy partial least square prediction models were calibrated based on single-phase experimental data. These models were used in estimating the mixture density and identifying the flow regime in all the experiments. The estimated mixture densities were accurate as compared with those from the single-energy gamma densitometer with the root mean square error of prediction of 13.6 and 9.7 kg/m3 for 1 angle of inclination and 17 and 26.6 kg/m3 for 5 pipe inclination. The models were also able to identify the flow regimes investigated for both 1 and 5 angles of inclination. Copyright © 2012 John Wiley & Sons, Ltd. Keywords: gamma ray; mixture density; multiphase; chemometrics; flow regime identification

1. INTRODUCTION

J. Chemometrics 2012; 26: 425–434

* Correspondence to: Benjamin Kaku Arvoh, Telemark University College, PO Box 203, N-3901 Porsgrunn, Norway. E-mail: [email protected] a B.K. Arvoh, M. Halstensen Telemark University College, N-3901 Porsgrunn, Norway b R. Hoffmann, A. Valle Statoil ASA, Research Centre Porsgrunn, N-3908 Porsgrunn, Norway

Copyright © 2012 John Wiley & Sons, Ltd.

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Currently, there is increasing request from governments and institutions to develop alternative sources of energy due to the limited availability of oil and gas coupled with the increasing demand of petroleum and its allied products. Hence, there is therefore the need to optimise operations in the oil and gas industries to increase production rates and reduce the loss to meet the demands of the growing population because the world’s oil production has reached its peak [1]. Exploration and drilling of oil and gas in remote and deep water necessitate the transportation of multiphase products through long pipe lines. Typical angles of inclination in these transport lines in the North Sea basin are within the range of 3 to +3 and in extreme cases between -10 and +20 . There is a considerable selection of literature on two-phase flow in pipelines. Most of the earlier experiments reported have been conducted with inert gas and model oils (Exxsol D60 and Exxsol D80) in the case of gas/oil experiments and tap water in the case of gas/water experiments. Kumara et al. conducted their experimental study on twophase oil–water flow to identify flow patterns and also varied the angle of pipe inclination with a single-energy gamma densitometer [2,3]. The only drawback in these types of experiments is that the process fluids and the process conditions do not represent real oil well producing conditions. Comparatively far less experimental work has been reported in the literature on three-phase flow, and experimental data on three-phase flow

performed under realistic oil and gas producing conditions are thus very limited. Pipe inclinations have a great effect on the flow pattern and other characteristics in pipelines and are also not well documented in literature [4]. Blaney and Yeung [5] reported that Abouelwafa and Kendall [6] were the first to propose and apply a dual energy gamma attenuation system for static volume fractions measurements in three-phase mixtures in horizontal pipes. There has been some literature on the application of the dual-energy gamma densitometer for three-phase flow characterisation [7,8,18]. In this experimental study, the experiments were performed in an industrial-scale multiphase flow test facility at Statoil Research Centre in Porsgrunn, Norway. A full description of this facility has been reported by Robøle et al. [7]. A traversable dual energy gamma densitometer is mounted on the multiphase flow loop, a description of which can also be found in Frøystein et al. [8]. Hoffmann and Johnson used this test facility for flow regime

B. K. Arvoh et al. identification for three-phase and two-phase flow mixtures [9], whereas Frøystein et al. studied the local phase distribution in three-phase mixtures [8]. A single-energy gamma densitometer is situated close to the dual-energy gamma densitometer for estimation of the multiphase mixture density. The angles of inclination of the test section in these experiments were +1 and +5 . The experiments were conducted using recombined hydrocarbon system including hydrate thermodynamic inhibitors (monoethylene glycol (MEG) and methanol (MeOH)) at relevant temperature and pressure (75 bar and 0 C) conditions. The theory and application of multivariate data analysis will not be explained in this article. The reader is referred to [10–13] for more information on partial least square (PLS) regression and principal component analysis (PCA) that were applied in this study. Midttveit et al. concluded from their feasibility study that signal processing coupled with multivariate calibration may be used in advanced measurement techniques and control systems in multiphase flow [14]. Åbro and Johansen determined void fractions for different flow regimes by means of multibeam gamma-ray attenuation measurements [15]. They concluded that the sensitivity of the densitometer was dependent upon the flow regime and the beam. In Arvoh et al. [16], the conclusion from applying chemometric modelling and prediction techniques for flow regime identification and volume fraction estimation was that the results were promising. Thorn et al. reviewed developments in three-phase flow measurements [17]. From their review, they stated that the ideal instrument needs to be reasonably accurate (typically 5% rate for each phase). In the oil and gas industry, it is important to have adequate information on the individual component volume fractions in the pipeline, because the economic analysis of the production pipe lines is based on the volume fractions of oil and gas. There are several expensive multiphase flow meters on the market today, but most of these flow meters do not provide any information on the phase distribution in the pipe lines and sometimes the results from the few that provide information on the phase distribution are doubtful. Knowledge of the phase distribution in the production pipeline is vital for optimising the separation process and hence the need to develop more advanced instruments. One of the motivations in this present work was to apply gamma measurements and multivariate calibration to address the need for advanced instruments that can provide both information on the component volume fractions and the phase distribution of the individual components in multiphase flow pipelines. The main difficulty encountered in Arvoh et al. was the differences between the calibration and test data sets [16], thus leading to the development of an average linear scaling technique. All experiments reported in Arvoh et al. were performed in horizontal flow pipe lines [16]; hence, it was important to

From separator

also investigate the application of gamma measurements and multivariate calibration in inclined pipe lines. This article presents the results from comparing the estimated mixture densities from single phase models with that of the single-energy gamma densitometer for both MEG and MeOH hydrate inhibitors at 1 and 5 angles of inclination of the test pipe section. The phase distribution plots for some experiments at 1 and 5 angles of inclination will be shown as an aid for visual flow regime identification purposes. In Arvoh et al. [16], chemometric modelling and prediction techniques were applied to data obtained from a dual-energy gamma densitometer for estimating the component volume fractions and identifying the flow regimes. The first results from the volume fraction estimations were not acceptable, but it was possible to identify the different flow regimes from the phase distribution plots. On the basis of PCA, it was concluded that the calibration and test data were not comparable, thus resulting in the development of a technique to compensate for the differences between the calibration and test data. All the results reported in Arvoh et al. were based on independent data (test set validation) [16].

2. MATERIALS AND METHOD 2.1.

Multiphase flow loop

The multiphase flow loop is a recirculation experimental test facility designed to handle recombined hydrocarbon fluid systems at maximum pressure and temperature of 110 bar and 140 C, respectively. Figure 1 shows a schematic drawing of the elongated U-shaped flow loop. From the three-phase separator, gas, oil and water were individually fed into the 3-in. Duplex steel test section via a double T-junction. The capacities for the liquid and gas phases in the rig were 0.002–40 and 0.3-205 m3/h (absolute), respectively. This represents a superficial gas velocity range of 0.02–11.6 m/s and a superficial liquid velocity range of 0.001– 2.3 m/s. The normal experimental set-up includes cooling of the two heat exchangers with tap water. The temperature of the tap water normally varies between 4 and 10 C. The objective was to perform experiments at real operating conditions, which for cases of deep water production will be in the range of 2 and 0 C. In addition to cooling with tap water, two 200-MW coolers were installed to cool the fluids to the required temperature. From the three-phase mixing point, the multiphase mixture enters the test section that has a total length of 200 m. This comprises of a horizontal pipe of 60 m (770 pipe diameters) followed by an inclined section of 40 m (510 pipe diameters), which represents the main test area. Following the main test area, the pipe returns to the separator through the downward inclined section followed by a 60-m horizontal leg.

Test section

To separator Horizontal section (60m)

Inclined section (40m)

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Figure 1. Multiphase flow loop.

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J. Chemometrics 2012; 26: 425–434

Online multiphase flow characterization 2.2.

Fluid properties

Pipe

The condensate used in these experiments was sampled from an onshore receiving terminal along with the hydrocarbon gas. Water was taken from an in-house deionised water supply. No salt was added as the fluid system should resemble gas-condensate condition with condensing water. The MEG and MeOH were both added at 60% concentration by volume. The physical properties of both MEG and MeOH fluid systems at 75 bar and 0 C are summarised in Tables I and II, respectively.

Source

-ray

Position -38

Detector

0

+38

2.3.

Instrumentation

A significant number of research and developments studies on new non-intrusive/non-invasive measurement techniques can be found in the literature [18]. Currently, neutron, gamma and X-rays are most widely used. Amongst these, gamma ray densitometry is considered the most versatile [19]. Besides the basic instrumentation of the test facility, both dual-energy and single-energy gamma densitometers have been installed on the main test section. 2.3.1.

Figure 2. Traversable dual-energy gamma densitometer.

the bottom of the pipe. The spacing between each measurement position was 2 mm. The spectrum obtained from the traversable dual-energy gamma densitometer consisted of 1024 keV (variables) (Figure 3(a)). The intensity I at position x measured for a pipe filled homogeneously with a single medium is defined as

Traversable dual-energy gamma densitometer

The traversable dual-energy gamma densitometer is equipped with a Ba133 source of 30 mCi activity and a cadmium zinc tellurium (CdZnTe) detector enabling energy levels of 31 and 81 keV. The instrument is mounted on a reinforced carbon fibre pipe section to overcome pipe wall photon absorption. In this study, the source and detectors were traversed linearly with a collimated beam of 5 10 mm, implying that measurements were obtained at a series of vertical positions in the pipe (Figure 2). The set-up used in the experimental work does not allow measurements at different vertical positions in the pipe simultaneously; therefore, the instrument measures at each vertical position sequentially. It is important that the instrument measures for a time interval long enough to represent the flow behaviour in the pipe. The instrument was allowed to stand for 15 s to acquire a representative sample at each defined position. Thirty-nine different positions were marked on the pipe from position 38 mm on top to position +38 mm at

Im ðx Þ ¼ I0 emm dpipe ðxÞ

where mmis the attenuation coefficient of the medium and dpipe (x) the distance between the inner pipe wall and position x. Variables 1–29 and 181–1024 were either zero or very close to zero (Figure 3(a)). Hence, variables 30–180 were considered important and used for modelling. Intensity is an exponential function, and thus a natural logarithmic transformation was applied for all the spectra in the calibration data for the purpose of detrending the data. Averaging by a factor of 4 was then performed in order to reduce noise in the spectra. The total number of samples per position for each of the single-phase data after averaging was 40. Finally, a moving average of rectangular window size 5 keV was applied to smooth the spectra in the variable direction. Figure 3(b) shows the spectrum after logarithmic transformation was computed. 2.3.2.

Table I. Measured properties of MEG Fluid

Gas Condensate Water/MEG

Density (kg/m3)

Viscosity (mPa)

Surface tension (mN/m)

75 712 1092

0.014 0.57 9.60

sGC = 9.2 sGW = 13.4

Interfacial tension (mN/m) sCW = 11.5

Fluid

Viscosity (mPa)

Surface tension (mN/m)

78 692 933

0.014 0.57 3.10

sGC = 8.5

J. Chemometrics 2012; 26: 425–434

sGW = 21.8

Interfacial tension (mN/m) sCW = 5.4

Multiphase flow regimes

Multiphase flow regime identification has been an area of concern in most production sectors and more significantly in the oil and gas drilling and refining sector. For a detailed discussion of the different flow regimes and flow transitions, interested readers are referred to Mokhatab et al. [20]. Only a brief description and explanation on flow regimes will be presented here. Modelling and predicting multiphase flow regimes have been a difficult task even with sophisticated sensors and measurement principles. Application of a dual-energy gamma densitometer along with multivariate data analysis will be used as a tool for identifying the flow regimes in this study. The multiphase flow



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Gas Condensate Water/ MeOH

Density (kg/m3)

Single-energy gamma densitometer

The single-energy gamma densitometer is applied in two-phase flow hold-up calculations, whereas the dual energy gamma densitometer is deployed in three-phase hold-up calculations. The single-energy gamma densitometer uses a 1000-mCi Cs source. The sampling frequency for this high-energy gamma densitometer was 100 Hz. The absolute error in the instrument readings was estimated to be 3 kg/m3. This instrument was used in measuring the mixture density during each experiment. 2.4.

Table II. Measured properties of MeOH

(1)

B. K. Arvoh et al.

A

B

250

6 5

LN(Counts+1)

Counts

200

150

100

50

0

4 3 2 1

0

200

400

600

800

1000

1200

0

0

200

400

Energy [KeV]

600

800

1000

1200

Energy [KeV]

Figure 3. (a) Spectrum from dual energy gamma instrument before logarithmic transformation and (b) same spectrum as in (a) after logarithmic transformation.

regime is dependent on the number of phases in the pipeline. The parameters governing the differences in flow regime are • • • • •

operating conditions fluid properties flow rates orientation of pipe line (angle of inclination) inner pipe line diameter

Figure 4 shows the four different basic flow regimes. Brief descriptions of each of the four basic flow regimes are 2.4.1.

Stratified-wavy flow

In both two-phase and three-phase flows, usually the most viscous fluids flow slowly whereas the gas (lighter fluid) has a high velocity. Gravitational force segregates the fluids due to the differences in densities. Hence, the denser fluid will flow at the bottom whereas the less dense fluids flow on top. The different fluids in the pipe flow with different velocities that result in shear forces at the interphase between the fluids. When the shearing forces become large enough, stratified-wavy flow is observed. The larger the shearing forces, the larger the waves between the denser and less dense fluids. 2.4.2.

Slug flow

Intermittent flow regimes are divided into two categories, plug and elongated bubble flow and slug flow. In slug flow, there is a general gas entrainment in the liquid slug body. The liquid

slugs block the whole area of the pipe. These slugs result in pressure build up behind the blockage. Slug flows are influenced by pressure drop and the slug velocities. When the pressure pulses (slugs) are high, they have an adverse effect on the smooth operation of the separators. Slugs in a separator will reduce both the gas–liquid and oil–water separator efficiency. 2.4.3.

Dispersed flow

The conditions under which the gas will be dispersed in multiphase flow are high liquid flow rate and low gas flow rate. Under these conditions, bubbles form and flow throughout the entire cross-section of the pipe in which it flows. The boundary between the different flow regimes is dependent on the physical property (density and viscosity) of the phases and the angle of inclination of the pipe. In this type of flow, the bubble density is comparatively higher on top of the pipe although there are bubbles throughout the whole cross-section of the pipe. 2.4.4.

Annular flow

In annular flow, the fraction of gas in the pipe is very high as compared with that of the liquid; hence, the liquid flows as a thin film around the cross-section of the pipe. This results in the gas flowing in the central region of the pipe. Some portion of the liquid is also entrained in the gas. In annular flow, the liquid film thickness is higher at the bottom of the pipe than at the top because of gravitational forces acting on the fluid. The only

Stratified-wavy flow

Slug flow

Annular flow

Dispersed flow

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Figure 4. Multiphase flow regimes.



J. Chemometrics 2012; 26: 425–434

Online multiphase flow characterization exception to this is at very low liquid flow rates in which case large waves cover the entire liquid film. 2.5.

Experimental matrix

The main objective was to search for liquid hold-up discontinuities using two different system fluids. The experimental duration for each investigation was long due to the fact that it was important to obtain a steady-state liquid level before the traversable dualenergy gamma densitometer was traversed from the bottom to the top of the pipe. The fact that the experiments had long duration favoured a matrix with limited experimental conditions. Two angles of inclination and two water cuts were chosen, which were considered representative of the steady upwards and undulating topography of the long transport lines in deep water production on the Norwegian continental shelf and also the liquid hold-ups in these transport lines. Table III shows the experimental matrix adopted for these experiments and the superficial gas velocities were varied between 0.5 and 10 m/s. The models were calibrated in the commercial software UnscramblerW (CAMO Software, Oslo, Norway). The prediction coefficients were then exported as a vector to MATLABW (MathWorks, Natick, MA, USA). During model calibration, only mean centring was applied to the data.

3. RESULTS AND DISCUSSION 3.1.

volume fractions and for flow regime identification purposes [16], the first data analysis technique that was applied here was PCA. Because there were two calibration data sets (MEG and MeOH), PCA was applied to both calibration data to investigate the differences between these two calibration sets. The results from the PCA of MEG and MeOH showed three clear groups, each representing gas, oil and water (Figure 5). From this figure, it can be seen that the gas scores were in the opposite direction of the liquids, whereas in the case of the two liquids, the water was above the oil in the principal component space. In the score plot, the oil is sandwiched between the water and gas. This can be attributed to the decrease in density of the fluids from water on the left of the score plot to gas on the right. Having a closer look at both groups for water and oil, it can be seen that the samples from the MeOH shift a little bit away from that of MEG. The distance of separation between the two calibration sets for water (Figure 5) is more significant as compared with that of oil in the same figure. This can also be attributed to the differences in densities between MEG and MeOH for water and oil (Tables I and II). Also, the magnitude of the difference between the densities of water in MEG and MeOH was larger than the difference between the oil in MEG and MeOH. The gas in both MEG and MeOH can be considered similar. From this result, there exists a possibility that a model from MEG calibration data may not accurately predict those with MeOH as hydrate inhibitor. Hence, the need to calibrate separate PLS1 models for the MEG and MeOH hydrate inhibitors.

Principal component analysis

3.1.0.1. Single-phase calibration. The calibration data were obtained by use of three independent single-phase experiments through the test facility. Gas, oil and water were thus transported through the test facility separately. In each of these experiments, the traversable dual-energy gamma densitometer was traversed from position 38 mm to position +38 mm. The number of samples per position was determined and then applied to all the positions in the three single-phase experimental data. In obtaining the calibration data, the gas experimental data were uploaded, after which the oil experimental data were appended followed by that of water.

3.1.2.

The next step was to compare the calibration data with some of the test data to investigate whether there were unexpected differences between the calibration and the test data. Two experimental data sets for MEG and two from MeOH will be reported in this article. The samples were randomly selected to cover the whole experimental matrix. Figure 6(a1) and (a2) shows the results from the PCA for MEG hydrate inhibitor whereas Figure 6(b1) and (b2) shows the results with MeOH as hydrate inhibitor. Figure 6(a1) and (b1) shows the results of the

3.1.0.2. Test data. The same pre-processing technique was applied to all the test data sets. In total, 20 independent data sets of which half were experiments conducted with MEG as hydrate inhibitor and the other half with MeOH will be presented in this article. In each of these groups, half of the experiments were performed at angle of inclination of 5 whereas the other half was at 1 .

1.5

1

0.5

PC 2

3.1.1.

MEG and MeOH calibration data

Guided by previous experience in applying chemometric modelling and data analysis technique in estimating component

Calibration and test data

0 MEG_Gas -0.5

MEG_Oil MEG_Water

Table III. Test matrix for gas–crude oil–water experiments

MeOH_Gas

-1

MeOH_Oil MeOH_Water

Superficial liquid velocity (m/s)

MEG MeOH

0.001 0.001

J. Chemometrics 2012; 26: 425–434

Angle of Water cut (%) inclination ( ) 1 and 5 1 and 5

15 and 85 15 and 85

-1.5 -15

-10

-5

0

5

10

15

PC 1 Figure 5. Principal component (PC1 and PC2) scores for a combination of MEG and MeOH calibration data sets.



429

Fluid system

B. K. Arvoh et al.

A2 1.5

1

1

0.5

0.5

PC 2

PC 2

A1 1.5

0 -0.5

-1.5 -15

-0.5

Cal_Gas Cal_Oil Cal_Water Test_Gas Test_Oil Test_Water

-1

-10

-5

0

5

10

0

Cal_Gas Cal_Oil Cal_Water Test_Gas Test_Oil

-1 -1.5 -15

15

-10

-5

PC 1

0

1.5 1

1

0.5

0.5

0 -0.5 -1

-5

0

15

5

10

0 -0.5

Cal_Gas Cal_Oil Cal_Water Test_Gas Test_Oil Test Water

-10

10

B2 1.5

PC 2

PC 2

B1

-1.5 -15

5

PC 1

Cal_Gas Cal_Oil Cal_Water Test_Gas Tese_Water

-1

15

-1.5 -15

-10

PC 1

-5

0

5

10

15

PC 1

Figure 6. Principal component analysis score. (a1 and b1) Calibration data in combination with a three-phase (gas/oil/water) test data set, (a2) calibration data and two-phase (gas/oil) test data and (b2) calibration data and two-phase (gas/water) test data.

430

calibration data in combination with a three-phase flow test set. In the score plot, it is expected that the individual components in the three-phase data set (test data) will be separated in the PC1 and PC2 scores. It was necessary to compare the calibration data with that of three-phase and two-phase data sets because the predictive ability of the models would be investigated under these flow conditions, and also in Arvoh et al. [16], the error in the first prediction results was associated with the differences between the calibration and test data from the score plot. The score plot for the calibration and three-phase data showed clear similarity between the calibration and the test data. In the score plot for the combination of the two-phase and the calibration data, there were two clear groups with respect to the test data in Figure 6(a2) and (b2) and these groups lay in the same proximity as those in the calibration data. The results from the principal component analysis from the combination of the calibration and the three-phase and twophase data show that the calibration and test data sets can be considered similar, which in actual sense was expected but was not the case in Arvoh et al. [16]. These results also provided an indication of the accuracy with which the models were expected to predict the individual component volume fractions and also to identify the respective flow regimes. Bearing in mind that even though the first volume fraction prediction results in [16] were not acceptable, the models for flow regime identification properties were promising.


3.2. 3.2.1.

Partial least square regression Model calibration

Four additional variables were appended to the data. The first variable represents the position where each spectrum was obtained. The other three variables represented the Y reference for gas, oil and water, respectively. The X contained the spectra from the traversable gamma instrument and the three Y references were the percentage of gas, oil and water. All 39 different positions (from 38 mm to +38 mm with a step of 2 mm) were modelled. For each of these positions, three PLS1 models for gas, oil and water were calibrated against a reference of 0% and 100% resulting in a total of 117 models (39 each for gas, oil and water). A reference value of 100% for gas at a specific position means that there was no other fluid component in that position. A reference of 0% represents the non-existence of gas in that particular position in the pipe. All predictions and subsequent volume fraction calculations, including the phase distribution plots, were carried out in MATLAB. The signal-to-noise ratio at positions close to the upper and lower wall of the pipe was not acceptable. Thus in this article, positions 34 mm to +34 mm will be considered for volume fraction prediction and flow regime identification purposes. This means that 35 positions will be considered for prediction purposes instead of 39, resulting in 70 mm as the internal diameter of the pipe rather than 78 mm. In reality, the volume


J. Chemometrics 2012; 26: 425–434

Online multiphase flow characterization fractions in positions 34 mm to 38 mm are considered to be the same. This is also the case for positions +34 mm to +38 mm. Hence, the predicted volume fraction for position 34 mm was assumed to be the same for position 36 mm and 38 mm. In this case, the investigated diameter will be equal to the true diameter of the pipe. The average root mean square error of prediction (RMSEP) for both the models of water and gas from the calibration data in all positions was approximately 10%, but that for oil was considerably higher. Hence, the models for oil were not considered accurate enough. Because the sum of the predictions for a particular position must be equal to 100%, it was possible to calculate the oil volume fraction with knowledge of the predicted water and gas volume fractions. Thus the predicted oil volume faction can be calculated from Eqn (2) as ^y Oil ¼ 100% ^y Gas ^y Water

3.2.3.

The single-energy gamma densitometer installed on the test facility provided online density measurements of the mixture for all the experiments conducted. The single-energy gamma densitometer instrument provides accurate and reliable measurements of the mixture density but does not provide any information on both the flow regime and the individual component volume fractions. It was important to compare the predictions from the model with a reliable reference; hence instead of presenting the individual component volume fractions, the mixture density would be presented and compared with the density measurements from the single-energy gamma densitometer, which is accurate and reliable. The mixture density was calculated as the mean of the measured density from the beginning to the end of an experiment. The variations in density measurements were dependent on the type of flow through the pipe line and more specifically the size of the waves as in the case of stratified-wavy flow. The mixture density from the model was calculated as Eqn (3):

(2)

where ^y Oil is the calculated oil volume fraction and ^y Gas and ^y Water the predicted gas and water volume fractions, respectively. In this way, the less accurate oil models will have no effect on the estimated component volume fractions because both water and gas models had a better accuracy in comparison. This means that only 70 PLS1 models (35 each for gas and water) were used for estimating the component volume fractions and also for identifying flow regime purposes for each of the hydrate inhibitors investigated in this study. 3.2.2.

rm ¼ ro ao þ rg ag þ rw aw

(3)

where rmis the density of the mixture and roao, rgag and rwaw the product of the density and volume fractions of oil, gas and water, respectively. If the calculated mixture density from the models is approximately equal to the measured density from the single-energy gamma instrument then the volume fractions predicted by the model can be considered to be accurate. Some of the predicted values were slightly negative whereas others were greater than 100%. When the prediction is less than 0%, that particular component does not exist at that position in the pipe during the experiments. Hence, all negative prediction values for gas and water were replaced by 0%. This was applied to all positions in the pipe. The oil fractions were calculated from the predicted gas and water volume fractions. Again, all negative prediction values for oil were set to 0%. In estimating the component volume fraction, the mean of the volume fractions for each position was calculated multiplied by its corresponding scaling factor to account for the differences in volume for each position in the pipe, after which the mean of all positions was calculated. The component volume fraction is then the ratio of the mean of a component to the sum of the means of all components in the pipe. The mixture density was then calculated from Eqn (3).

Volume fraction estimation

In estimating the volume fraction, the volume represented by each position in the cross-section of the pipe was calculated. The volume for the positions increases from the top of the pipe (position 38 mm) to the middle of the pipe (position 0 mm). The volume then decreases from the middle of the pipe (position 0 mm) to the bottom of the pipe (position +38 mm). Figure 7(a) shows the positions and the pipe cross-section as the instrument was traversed from position 38 mm to position +38 mm. This means that the prediction in each position must be scaled to account for the differences in volume from the top to the bottom of the pipe. For each position, the three predictions for gas, oil and water were scaled by their corresponding factor, after which the mean of each component was calculated. Figure 7(b) shows a plot of the scaling factors required for the purposes of this pipe.

Position -38

Mixture density

Pipe

0

+38 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Scaling Factor

J. Chemometrics 2012; 26: 425–434



431

Figure 7. (a) pipe cross section and (b) scaling factors required for each vertical position.

B. K. Arvoh et al. Figure 8 shows the results of the predicted and the measured mixture densities. Figure 8(a1) and (b1) represents experiments conducted under 1 angle of inclination whereas Figure 8(a2) and (b2) represents 5 angle of inclination. Figure 8(a) and (b) represents experiments with MEG and MeOH hydrate inhibitors, respectively. The models from the single-phase calibration were used in predicting all the independent data sets for both 1 and 5 angles of pipe inclination. From Figure 8(a), the predicted densities were relatively similar as compared with that measured by the single-energy gamma densitometer. This was not really a surprise because the individual components in the test and calibration data were in the same principal component space, which was not the case in Arvoh et al. [16]. In the case of MeOH (Figure 8(b)), the same conclusions can be drawn as in MEG. The RMSEP for Figure 8(a1–b2) was 16.3, 16.9, 4.7 and 19.6 kg/m3, respectively. This indicated a relatively high degree of accuracy of the predicted mixture densities from the model as compared with that measured with the single-energy gamma instrument and thus can be concluded that the estimated volume fractions were also very accurate. Both angles of inclination (1 and 5 ) had the same effect on the predictions (i.e. increasing the angle of inclination from 1 to 5 did not result in any significant change in magnitude of the RMSEP). This being only one part of the objective in this task; it was also important to investigate the flow regime identification potential of the models, bearing in mind that it was possible to identify the various flow regimes in the case of [16].

3.2.4.

Flow regime identification

Flow regime identification was of significant importance in this task. Green, brown and blue was used to represent gas, oil and water, respectively, in these phase distribution plots. The phase distribution plots for four of the data sets are shown in Figure 9. In this figure, two of the plots were obtained from MEG whereas the other two were with MeOH as hydrate inhibitor. Figure 9(a1) and (b1) shows results for 1 angle of inclination, whereas Figure 9(a2) and (b2) describes 5 angle of inclination. These plots show the distribution of the individual phases in the pipe during the experimental period. The predictions for each position were averaged and scaled to 100%. A bar plot was first generated for all the predictions in time, after which the two predictions (gas and water) and the calculated oil prediction were scaled to 100%. These 35 separate bar plots (one for each position, 34 mm to +34 mm) were then stacked together as one plot to provide a better view of how the fluids flow through the pipe. A moving average of rectangular window size of 3 keV was then applied to filter the noise in the predictions. Upon applying the moving average, the RMSEP for the same data as in Figure 8 (a1–b2) was 13.6, 17, 9.7 and 26.6 kg/m3, respectively. This filtering technique improved the results for Figure 8(a1) and (b1) but did not have a significant impact on Figure 8(a2) and (b2). The potential for further research into other filtering techniques that can provide better results must be investigated. From Figure 9, the gas–liquid flow pattern was characterised by a relatively smooth interface between the gas and the liquid as

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Figure 8. Predicted versus measured mixture density. (a1 and b1) 1 pipe inclination, (a2 and b2) 5 pipe inclination, (a) MEG and (b) MeOH.



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Online multiphase flow characterization

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Figure 9. Component phase distribution plots observed by visualising the flow through the pipe line. (a1 and a2) MEG and (b1 and b2) MeOH.

in the case of 1 angle of inclination. For high gas rates, the liquid hold-up was too low to generate hold-up measurements. That is, the liquid flows as a thin layer at the bottom of the pipe. Comparing Figure 8(a1) and (b1), it is clear that the flow pattern in both hydrate inhibitors was identical. The flow pattern in Figure 8(a2) and (b2) was characterised by large waves. The waves in 5 angle of inclination had larger amplitude, which can be related to the larger shearing forces at the interface between the gas and the liquid. From all the experiments investigated with low flow rates and high liquid hold-ups, no slug flow pattern was observed but rather only stratified-wavy flow. The fluids in the pipe were separated by gravity with the most viscous fluid flowing slowly at the bottom of the pipe whereas the gas (the lightest) flows at a faster rate on top of the liquids. At the interface between the gas and the water, the oil can be seen as a thin layer flowing between the continuous gas and water zone. From Figure 9, it could be a bit difficult to see pronounce stratified oil–water structure partly because the oil was concentrated in the gas–liquid waves and partly because of noise. Because the flow regime has been identified to be stratified-wavy flow, three layers of gas, water and oil were expected. In the stratified water layer, there were relatively low concentrations of gas and oil. These gas and oil concentrations are due to noise in the predictions. A similar observation can be seen in the continuous gas zone with respect to oil and water concentrations. The flow pattern can be observed from the scan from the dual-energy gamma densitometer. The advantage that this technique possesses over traditional measurement principles is its ability to provide information not only on the component volume fractions but also on the phase distribution of the fluids in time. From the phase distribution plots, it can also be concluded that there were no differences between the MEG-based and MeOH-based fluids investigated with respect to flow regime identification.

4. CONCLUSION

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A single-energy gamma densitometer was used in measuring the mixture density in the multiphase flow pipe line. Multivariate

calibration and prediction techniques were applied to measurement data obtained from a dual-energy gamma densitometer. Two fluids including MEG-based and MeOH-based water were investigated. PCA of a combination of the calibration data and some of the test data for MEG and MeOH showed that the calibration and test data can be considered similar. For each hydrate inhibitor, 70 PLS1 models were used in predicting and estimating the mixture density. The calculated mixture densities were compared with those obtained from the single-energy gamma densitometer. On comparison, the accuracy of the calculated mixture densities was quite high which meant that the estimated component volume fractions were very accurate. The models were then used for flow regime identification. The models were able to identify the gas–liquid flow regimes investigated in this study. For both angles of inclination investigated, stratified-wavy flow patterns were observed. The waves in the experiments performed under 5 angle of inclination were large as compared with those of 1 inclinations. From these results, the potential of applying gamma measurements in combination with multivariate calibration for online estimation of individual component volume fractions and flow regime identification in multiphase flow is bright. This technique can be further developed and implemented to address the difficulties associated with using most of the current multiphase flow meters on the market.

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