Estimation of volume fractions and flow regime identification in multiphase flow based on gamma measurements and multivariate calibration

Flow Measurement and Instrumentation 23 (2012) 56–65

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Estimation of volume fractions and flow regime identification in multiphase flow based on gamma measurements and multivariate calibration Benjamin Kaku Arvoh a,∗ , Rainer Hoffmann b , Maths Halstensen a a

Telemark University College, P.O Box 203, N-3901 Porsgrunn, Norway

b

Statoil ASA, Research Centre Porsgrunn, 3908 Porsgrunn, Norway

article

info

Article history: Received 12 April 2011 Received in revised form 19 October 2011 Accepted 8 November 2011 Keywords: Gamma-ray Volume fraction Multiphase Chemometrics Flow regime identification

abstract Gamma measurements combined with multivariate calibration were applied to estimate volume fractions and identify flow regimes in multiphase flow. Multiphase flow experiments were carried out with formation water, crude oil and gas from different North Sea gas fields in an industrial scale multiphase flow test facility in Porsgrunn, Norway. The experiments were carried out with a temperature of 80◦ C and 100 bar pressure which is comparable to field conditions. Different multiphase flow regimes (stratifiedwavy, slug, dispersed and annular) and different volume fractions of oil, water and gas were investigated. A traversable dual energy gamma densitometer instrument consisting of a 30 mCi Ba133 source and a CnZnTd detector with a sampling frequency of 7 Hz was used. 111 partial least square prediction models were calibrated based on single-phase experimental data. These models were used to predict all the volume fractions and also to identify the different flow regimes involved. The results from the flow regime identification were promising but the first results for the predictions of volume fractions were not acceptable. Principal component analysis was then applied to the calibration data and some of the calibration and test data in combination. The results from the PCA showed that there were differences between the calibration and test data. An average linear scaling technique was developed to improve the models volume fraction prediction performance. This technique was developed from half of the three-phase data sets and tested on the other half. The root mean square error of prediction (RMSEP) for the test data for gas, oil and water was 37.4%, 39.2% and 6.3% respectively before this technique was applied and 6.5%, 8.9% and 4.4% respectively after this technique was applied. Average linear scaling also improved the flow regime identification plots. Average scaling was then applied to predict the volume fractions and to identify the flow regimes of both the Gas/Oil and Gas/Water two-phase data sets. The RMSEP for gas, oil and water for Gas/Oil test data was 4.8%, 6.0% and 6.8% respectively. In the case of Gas/Water, the RMSEP for gas, oil and water were 6.2%, 9.2% and 5.8% respectively. Likewise their respective flow regimes were also easier to identify after this technique was applied. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction Multiphase flow metering has been and continues to be one of the major areas of interest in oil and gas industries operating both onshore and offshore. Liquids and gases are the main components of oil and gas reservoirs and these components are transported through pipelines. Quantitative estimates of the individual components are necessary in determining whether or not it is beneficial to continue drilling. With adequate information on the volume fractions of the individual components, the separating process can be optimized. There is the need to identify

∗

Corresponding author. Tel.: +47 35 57 51 34; fax: +47 35 57 50 01. E-mail address: [email protected] (B.K. Arvoh).

0955-5986/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2011.11.002

the type of flow regime in the transportation process and also the volume fractions of the individual components. This is due to the fact that the flow regime directly affects the efficiency of the separating process whilst the volume fractions of the individual components provide indication as to whether the drilling process should be continued or stopped (i.e. directly related to the economics of the process). The cost of production in the oil industry is relatively high and thus an efficient drilling and separating process greatly determines the profit margins. Recently, there has been a higher interest in development and research in the area of non-invasive measurement principles due to the fact that it is possible to apply these techniques without any need to modify the existing process. In most production pipelines some of the properties of the fluid that are of great interest include temperature, pressure, flow pattern, flow rate, volume fractions of oil, water and gas,

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pressure drop and density of the fluids to mention but a few. The industries exploration for oil and gas in deeper depths below sea level and other remote areas has added up to the complexities in both quantitative and qualitative characterization of multiphase flow. There are continual exploration and development of marginal oil and gas reserves due to the increasing demand and rapid surges in prices of petroleum and its allied products. This thus necessitates the development and optimization of techniques for monitoring multiphase flow. Today, the capital cost of Multi Phase Flow Meters (MPFM) is within the range of US$ 100,000–US$ 1,000,000 nevertheless, most of these MPFM’s do not provide any information about the phase distribution in the pipe, hence the need to develop more advanced instruments. According to Blaney and Yeung [1], Abouelwafa and Kendall [2] were the first to propose and apply a dual-energy gamma attenuation system for static volume fractions in three phase mixtures in horizontal pipes. From their results [2], they concluded that gamma ray attenuation may be successfully used to measure component ratios for three and even n component mixtures. Sætre et al. [3] also applied high speed gamma ray tomography for flow regime identification. They concluded that their sampling frequency (1/5 Hz) was not sufficiently high to analyse the gas ratio in the flow. In [4] their aim for conducting experiments with a multibeam instrument was to acquire flow regime measurements and reduce dependency of gas volume fraction on the flow regime. They concluded that the accuracy of the gas volume fraction measurements was improved as compared to one-beam geometry. Flow regime identification was also demonstrated both theoretically and experimentally by using a multibeam gamma-ray densitometer on liquid/gas flows based on nine-beam geometry [5]. Statoil ASA has designed and commissioned an industrial scale multiphase flow loop capable of withstanding realistic oil and gas producing conditions (i.e. high temperature and high pressure). The description of the test facility has been documented by Robøle et al. [6]. Frøystein et al. [7] applied dual energy gamma tomography in this test facility to determine the local phase distribution in three phase mixtures. They could not draw conclusions as to the quality of the tomogram for different flow configurations with respect to linear and angular positions. Hoffmann and Johnson [8] also performed experiments with this test facility using a traversable dual energy gamma densitometer for flow regime identification. This gamma instrument had the capability of acquiring data at a frequency of 7 Hz. Hoffmann and Johnson [8] carried out multiphase flow experiments with formation water, crude oil and a blend of produced gas from the North Sea. The experiments were conducted at a pressure of 100 bar and temperature of 80 °C which were considered realistic field conditions. Hoffmann and Johnson [8] concluded that it was possible to use the dual energy gamma densitometer to determine the flow regimes for all experiments performed. Midttveit et al. [9], used a capacitance transducer and multivariate calibration for multiphase flow metering. From their feasibility study, they concluded that signal processing coupled with multivariate calibration may be used in advanced measurement techniques and control systems. In this study, chemometric modelling and prediction techniques were applied to the data obtained by Hoffmann and Johnson [8]. The data can be grouped into three categories. 1. Calibration data sets (single phase). 2. Two-phase data sets (gas/water and gas/oil). 3. Three-phase data sets (gas/oil/water). Four different flow regimes were investigated combined with varying volume fractions of the individual components. There were no references available for different flow regimes and different volume fractions for calibration due to the fact that it was

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impossible to measure accurately volume fractions through the entire cross section of the pipe under different flow regimes and varying volume fractions. Thus, the calibration data were based on single phase flow experiments. Even though the calibration data were based only on single phase flow data, the models from the calibration data were used in predicting volume fractions for both two and three phase data carried out under different flow regimes and also to identify their respective flow regimes. The objective of applying chemometric techniques on the data was to study the potential to: 1. Quantitatively estimate volume fraction of oil, water and gas mixtures. 2. Identify flow regimes for each experiment which was also the main objective for Hoffmann and Johnson [8]. 2. Experimental 2.1. Flow loop The Multi Phase Flow Loop (MPFL) at Statoil research centre in Porsgrunn is a recirculation experimental test facility capable of withstanding realistic oil, water and gas production conditions. The 200 m long and 77.9 mm (3 in.) pipe diameter flow loop consists of one three phase separator and three recirculation pumps, one for each phase and heat exchangers to control the temperature of the fluids in the pipeline. The process piping and process units of the MPFL are not only well insulated but also equipped with temperature controlled heat tracing. The main parameters of the MPFL are listed in Table 1 and the fluid properties at 100 bar and 80 °C can be found in Table 2. In this study only horizontal flows were considered. Fig. 1 shows a schematic drawing of the elongated U-shaped flow loop. In order for the flow to be fully developed before instrumentation, the test section of the loop is strategically positioned. To reduce the inlet fluid flow velocity to the separator, the separator is provided with a splash plate. The liquid flows through a pal packed plate, before the gas, oil and water mixture flow through a perforated plate. Downstream from the perforated plate, there is a Vessel Internal Electrostatic Coalescer (VIEC) element, Eowa and Ghadiri [10], in order to improve the separation. The gas leaves the separator from the top, a weir plate separates both liquid (oil and water) and the total volume of the separator is 2.2 m3 . 2.2. Traversable dual-energy gamma densitometer There are a significant number of research and development of new non-intrusive/non-invasive measurement techniques from literature [11]. This has thus resulted in an increase in the application of gamma and X-ray measurement techniques in measuring and estimating oil, water and gas volume fractions, wax deposition and flow identification in a multiphase flow pipe line. Gamma rays are based on electromagnetic radiation. A dual energy gamma ray densitometer has been installed on the test facility. The instrument is equipped with a 133 Ba source of 30 mCi activity and a CdZnTe detector. Single energy gamma densitometry is employed in estimating two phase flow hold up whilst the dual-energy is used in three phase hold up calculations. For each experiment, the dual energy gamma densitometer was traversed after the density measurements from a single energy gamma densitometer were considered to have reached stability. The source and detectors are traversed linearly implying that measurements were obtained at a series of vertical positions in the pipe (Fig. 2). 37 different positions were marked on the cross section of the pipe starting from position −36 mm on top

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Table 1 Multiphase flow loop capacity and ranges [8]. Number of phases Water capacity Gas capacity Oil capacity Maximum pressure Temperature range Inner tube diameter

3 (oil, water and gas) 40 m3 /h 205 m3 /h 40 m3 /h 110 bar 4 °C to 140 °C 77.9 mm (3 in.)

Flow loop length Tilt Material Water phase Oil phase Max, oil viscosity Gas phase

200 m −6° to +10° Duplex steel Formation water Crude oil 200 cP Hydrocarbon

Fig. 1. Multiphase flow loop. Table 2 Fluid properties [8]. Fluid Gas Oil Water

Density

Dynamic viscosity

Surface tension (with gas)

65 785 1028

1 · 10−3 Pa s 1.74 · 10−3 Pa s 5.1 · 10−4 Pa s

– 10 · 10−3 N/m 47 · 10−3 N/m

(kg/m3 )

Fig. 3. Gas position 0 mm, before transformation.

Fig. 2. Traversable two-energy gamma densitometer.

to position +36 mm at the bottom. The distance between each measurement position was 2 mm whilst the measurement time was 20 s for the test experiment and 60 s for the calibration experiments. The detector records the full spectrum with a sampling rate of 7 spectra per second. The spectrum at each position at a particular time is the sum of all the spectra from time t0 to tn . The intensity I at position x measured for a pipe filled homogeneously with a single medium is defined as −µm dpipe (x)

Im (x) = I0 e

(1)

where µm is the attenuation coefficient of the medium and dpipe (x) the distance between the inner pipe wall and position x. To obtain the intensity of each spectrum the (n − 1)th spectrum was subtracted from the nth spectrum and the resulting spectrum divided by the time difference between spectrum n and spectrum (n − 1). Each spectrum consisted of photon energies within the range of 0 and 1024 keV. The set up used in this experiment does not allow measurements at different vertical positions simultaneously, thus there is the need to choose a measurement interval long enough for a representative flow behaviour to be recorded. The transient flow patterns that were investigated in these experiments were stratified-wavy, slug, annular and dispersed flows. The inlet flow conditions were kept at a steady state.

Fig. 4. Gas position 0 mm, after transformation.

Fig. 3 shows one spectrum for gas. Here the 133 Ba source spectrum shows two clear peaks and these peaks represent the two photon energy levels of the gamma instrument. Photon energy levels (variables) outside the range of 30–180 keV were close to zero or zero. Thus variables 30–180 were considered as variables with information and hence all other variables were set to zero. From Eq. (1), intensity is an exponential function and thus a natural logarithmic transformation was computed for all the spectra in the calibration data for the purpose of de-trending the data. Since some of the variables were zero, one was added to all the variables before the transformation to remove all numeric problems that will arise from taking the ln(0) (i.e., for spectra = X , X = LN (X + 1)). Fig. 4 shows the spectrum for the same position after this transformation.

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The loading matrix, P, can be calculated as [17]

2.3. Multivariate calibration 2.3.1. Principal component analysis (PCA) The basis of multivariate data analysis is PCA. PCA is essentially a data compression technique, were the data matrix, X, is decomposed into an ‘‘information’’ part and a ‘‘noise’’ part. It is important to state here that in multivariate data analysis, the X data matrix must contain the information of interest. The matrix, X, consists of N samples and K variables. In traditional models, N is usually lager than K where K may be measurements from sensors (e.g. temperature, flow, pressure, pH, etc.). However in modern applications of PCA, it is common to include spectral data (γ -ray, X-ray, sound signal, NIR, IR, UV. . . ) and chromatographic data (HPLC, GC, TLC, etc.) [12]. Thus in modern use, K may be greater or less than N. It is common to pre-process the data, typical pre-processing techniques that can be applied are:

• Removing the mean from each column. • Scale each column e.g. by dividing by the standard deviation. PCA is mostly applied in cases where there is collinearity between the variables in the X data matrix [13]. The term collinearity means that in the matrix X, there exists some dominating type of variability that carries most of the available information. The main information in the variables X = {xk , k = 1, 2, . . . , K } is compressed into T = {t1 , . . . , tA } (A < K ), which is called the principal components score of X. The eigenvalues show the intensity of variability removed by each factor from X. The columns of the score vectors, T, are orthogonal to each other and in addition, the columns of the loading vectors, P, are also orthogonal to each other. Thus, the data matrix X can be split into X = TPT + E

(2)

T

where TP constitute the information part and E is the X-residuals matrix (noise). When A = K all the eigenvectors (T) can be extracted, hence X = TPT . The most commonly used algorithm is the NIPALS algorithm and it can be found in [13, p. 111] and a detailed description of the theory, application and practical examples can be found in [12–15]. 2.3.2. Partial least square regression (PLS-R) Partial least square regression (PLS-R) is a statistical data modelling technique which aims at finding an empirical parametric model that relates two matrices (X and Y) which can be either linear or nonlinear. The significance of PLS-R has gradually increased in many fields including analytical chemistry, physical, clinical chemistry and industrial process control [16] In PLS-R, the variable Y is used actively during the decomposition of X and thus balances the information in both X and Y resulting in reduction of the impact of large but irrelevant variation in X in the calibration model [13]. A simplified version of the NIPALS algorithm for PLS-R with y as the response vector is presented below [17]: Step 1: Let X0 = X. For a = 1, 2, . . . , Aperform steps 2–6. Step 2: Compute wa = XTa−1 y/ XTa−1 y (with length 1). Step 3: Compute ta = Xa−1 wa .



−1 .  T  −1

Step 4: Compute qa = yT ta tTa ta

. Step 5: Compute pa = XTa−1 ta ta ta Step 6: Compute the residuals Xa = Xa−1 − ta pTa . From the re-interpretation of the NIPALS algorithm by Ergon [17] the resulting PLS1 model can be written as: X = Tw PT WWT + E

(3)

y = Tw qw + f

(4)

where the score matrix Tw = [t1 t2 · · · tA ] is orthogonal, loadings matrix P = [p1 p2 · · · pA ], qw = [q1 q2 · · · qA ] and the loading weight matrix W = [w1 w2 · · · wA ].

P = XT T(TT T)−1 .

(5)

The prediction vector for y = Xb + f corresponds to: ⌢

b = W(WT XT XW)−1 WT XT y.

(6) ⌢

⌢

⌢

The response vector is calculated from y = X b alternatively y can also be calculated as: ⌢

y = T(TT T)−1 TT y.

(7) ⌢

The response vector y is contained in the column space of T. The residual matrix E is contained in the orthogonal complement of the column space of W. The NIPALS algorithm with detailed explanation for PLS-R can be found in [13,14,17]. The theory, principles and application of PLS-R can also be found elsewhere [12–14,16,18,19]. 2.4. Experimental matrix After a decision has been made on the inlet conditions based on the type of fluid flow to be investigated, the inlet conditions were kept constant throughout that particular experimental process. First of all, single phase experiments were conducted in order to obtain the calibration data and then we proceeded with two-phase experiments. In this report a total of 60 data sets of which 30 were obtained by performing experiments under three-phase flow and the remaining two-phase will be presented. In the two-phase data sets, half of it is gas/oil whilst the other half is gas/water. Seven superficial velocities were investigated for the gas/oil mixtures. These seven superficial velocities were in the range of 0.5–5 m/s for the gas whilst that for oil was from 0.42 to 1.68 m/s. The superficial velocities used in the gas/water experiments were 1–5 m/s for gas and 0.5–1.68 m/s for water. In the three-phase data sets, seven superficial gas velocities as in the case of the gas/oil mixtures whereas four superficial water velocities (0.5, 0.84, 1.5 and 1.68 m/s) were applied. The data sets were divided into two categories in relation to the superficial oil velocities. The first category was oil dominated whilst the second was water dominated with the oil/water ratio of 2 and 0.4 respectively. Fig. 5 shows a schematic diagram of all four flow regimes investigated in this study. Fig. 6(A) shows the experimental flow regime map for three-phase experiments whilst with respect to two-phase, the experimental flow regime map for gas/oil is shown (Fig. 6(B)). 3. Results and discussion 3.1. Partial least square regression (PLS-R) Single phase calibration. Each calibration data set was obtained by running experiments with only water, gas and oil (single phase) through the test facility. The reason for using the single phase calibration data for modelling and prediction of two and three-phase data was the fact that it was impossible to have accurate references for different volume fractions of the individual components at each position and throughout the entire cross section of the pipe (−36 mm to +36 mm). Also the aim was to develop a model that could predict both volume fractions and identify different flow regimes independent of the fractions of the individual components in the pipe. For the gas calibration data set, a value of 100% was assigned to the gas variables whilst 0% to both the water and oil variables. The same methodology was repeated for both the oil and water calibration data sets. The three independent single phase data sets were put together as one calibration data set. Here, the X contains

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Fig. 5. Multiphase flow regimes [20].

the residuals on the y-axis and principal components on the x-axis. The residuals decrease with increasing number of principal components. A point is reached where the difference in residuals between principal component n and principal component n + 1 can be considered as negligible. The principal components beyond this point will only describe noise, hence n is the optimum number of principal component. One component was required for separating the gas from the liquid whilst the other component separated the liquids (oil and water). The models were then exported as R . All predictions and subsequent volume a vector to MATLAB⃝ fraction calculations and phase distribution plots were carried out R . in MATLAB⃝ Test data. The same pre-processing technique was applied to both the two-phase and three-phase test data sets. A total of 60 independent data sets were used, of which half was three-phase and the other half two-phase. The independent test data sets were used to investigate the performance of the models in predicting both their volume fraction and identify flow regime for both two-phase and three-phase flow experiments. There might be outliers and other nonlinearities in the test data sets, this will thus reduce the predictive performance of the models and hence aids in investigating the ability of the models to handle such situations. The two-phase data sets contained information on Water/Gas and Oil/Gas experiments.

Fig. 6. Experimental flow regime maps. A: Three-phase B: Two-phase (Gas/Oil).

spectra from the gamma instrument and the Y is the response that is the percentage of oil, water and gas. The commercial software R Unscrambler⃝ was used in modelling the calibration data based on PLS1 regression. In total there were 37 different positions (−36 mm to +36 mm), for each position three PLS1 models were calibrated for oil, water and gas resulting in a total of 111 models. The calibration data was centred but normalization of the variables was not necessary. In all two principal components was optimum for modelling the data. The principal component is a line that best fit a set of data points by minimizing the sum of squares of the residuals. In linear modelling, the number of principal components required to describe the model is equal to the model dimensionality. The optimum number of principal component to use is an important property of the PLS-R model [16]. The residual variance plot is a plot with

3.1.1. Three-phase The experiments for three phase flow were conducted under stratified-wavy, slug and dispersed flow regimes. Some of the prediction values were less than 0% whilst others were greater than 100%. All predictions less than 0% for oil, water and gas were forced to 0% because predictions of oil, water or gas less than zero means there was no such component in that particular position. After those negative values have been removed, the volume fractions for the respective positions were calculated based on the average values in that particular position. In order to estimate the volume fraction in the entire pipe cross section, the volume fraction was estimated based on the ratio of the average value of a component to the sum of all three average values. A stacked bar plot is used to stack all prediction results for all positions to show the distribution of individual components (gas, oil and water) in the entire pipe cross section. From Table 3, the predicted and reference volume fractions for three of the test data are shown. The values for volume fractions used as reference were based on calculations documented in [8]. The oil volume fractions were overestimated whilst those of gas and water were underestimated (Table 3). This trend was consistent throughout all the independent test data. The Root Mean Square Error of Prediction (RMSEP) is given by:

RMSEP =

  2  n   yˆ − yi,ref  i=1 i n

(8)

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Table 3 Volume fraction predictions for three-phase test set. A-1

Predicted Reference

A-3

A-4

Oil

Water

Gas

Oil

Water

Gas

Oil

Water

Gas

0.606 0.37

0.257 0.27

0.137 0.36

0.734 0.39

0.184 0.27

0.082 0.34

0.647 0.12

0.075 0.09

0.278 0.78

where yˆ the predicted volume fraction and n is the number of samples. Taking a closer look at the RMSEP for oil, gas and water from the calibration models, the average RMSEP value for gas, oil and water were about 6%, 18% and 9% respectively for all positions modelled. These values show that the prediction models for oil was not as good as those for water and gas. The colour code for oil, water and gas as shown in Fig. 7 are brown, blue and green respectively. Having in mind that A1 (Fig. 7) was performed under stratified wavy flow conditions, one expected the model to predict gas on top, water beneath and oil in-between, but that was not exactly the case. The model predicted a considerable amount of oil throughout the entire pipe cross section with water and gas at expected positions. The predictions for positions −36 mm and +36 mm were not acceptable (Fig. 7), which is due to the fact that at these positions the gamma ray is very close to the wall of the pipe, resulting in poor signal quality from the traversable gamma densitometer as compared to the other positions. But since our intention was to use the model to predict volume fractions for the entire cross section of the pipe these positions were included. The prediction error for dispersed flow was higher than that of slug flow. Comparing slug and stratified-wavy flow, the prediction error decreased from slug to stratified-wavy. This is due to the fact that the number of inter-phases increases from stratified-wavy to dispersed flow and results in a lower sensitivity of the gamma instruments. Åbro and Johansen [21] determined void fractions for different flow regimes by means of multibeam gamma-ray attenuation measurements. They found a similar trend and concluded that the sensitivity of the densitometer was dependent upon the flow regime and the beam. From the same figure, without any insight into the type of flow regimes for the four different data sets and visually observing the phase distribution plots, it can be seen that two of the data sets were identical whilst the other two were different. Now comparing Fig. 7 (A1-4) to Fig. 5, it is possible to visually identify the three different flow regimes. A1 and A2 were conducted under stratifiedwavy flow whilst A3 and A4 were slug and dispersed flow regimes respectively. Comparing slug and stratified-wavy flow, one could see that there was a considerable amount of liquid in the gas section for slug flow as compared to stratified-wavy. The higher quantities of liquid moving through the gas section of the pipe in time represent the slugs. Likewise in the dispersed flow the liquid and gas quantities are dispersed throughout the cross section. All these flow regimes can be visually identified from the phase distribution plot for all the data sets under investigation. The conclusion that can be drawn here is that the model could identify the flow regime from the phase distribution plots but the volume fraction predictions were not accurate enough. At this point, there was the need to also take a closer look at both the calibration and test data set by principal component analysis. 3.2. Principal component analysis (PCA) PCA was applied to both the calibration and test data to investigate the possible reasons for the relatively high prediction errors. The test data was randomly selected and the first step was to analyse the calibration data. The calibration data was expected to show three clear clusters. In Fig. 8, C1 shows the results for

the calibration data, this figure shows three clusters as expected. The first principal component (PC1) separates the gas from the liquid whilst the second principal component (PC2) separates the liquids, implying that only two principal components were needed in modelling the calibration data which was exactly the case during PLS-R modelling. Also it was expected that when PCA was carried out on both the calibration and test data, there would be three clusters and the individual components in both the test and calibration data would be clustered around the same point. From the same figure, C2 show the PCA analysis of the calibration data combined with test data for Gas/Oil, whilst C3-4 show results for two Gas/Oil/Water data sets. In C2, the position for the oil cluster is the same for both the calibration and test data but there are differences between that for the gas. The gas in the test data was below that of the calibration data and closer to the oil in both the calibration and test data thus gas quantities in the test data would be seen by the model as oil and result in higher prediction values as already seen from Table 3. In C3, again the gas for the calibration and test data are separated and the gas in the test data was closer to the oil in the calibration data than the gas in the calibration data. Finally, C4 also showed a similar trend with the water and oil for both the calibration and test data clustered as in C2 and C3. The gas in C2 and C3 lay in the same principal component direction as the oil. In C4 even though the gas in the test data was a little bit closer to the calibration data, it is clear that the gas in the test data, lay in the same principal component direction as that of the oil. The closer the individual clusters of the test and the calibration data were, the better the volume fraction prediction and the further apart these clusters were the worse the prediction values. This gives the possible reason for the inaccurate volume fraction predictions. After this was realised, the process data for both the calibration and test data were examined to find a possible reason for the differences between the test and calibration data. The process data did not give any information that could possibly be attributed to the differences between the calibration and test data. 3.3. Average linear scaling 3.3.1. Three-phase flow One central question is ‘‘how can one improve the models’ volume fraction prediction performance without compromising its flow regime identification properties?’’ With this in mind, one technique that can be applied is average linear scaling. There were 30 independent three-phase test data, of which the data were divided into two categories bearing in mind that each category must span all the three different flow regimes. One part of the data was used for determining the average scaling factors whilst the other part was used for prediction. The first step in this technique is to predict the volume fractions for one half of the three-phase test data. For each test data, the volume fractions for oil, water and gas were predicted. After which the scaling factor for each component was calculated based on the ratio of the reference to predict values. For each data, when their respective scaling factors were multiplied by the predicted volume fractions, the resulting value was equal to the reference. Finally, the linear average scaling factors were calculated from the average of each component in all the 15 data sets. These average scaling

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Fig. 7. Phase distribution plots. The A panel shows data sets before applying average linear scaling whilst the B panel shows the same data sets as A after applying average linear scaling.

values were then multiplied by the predicted values for each of the other 15 independent tests set to verify whether or not the objective for applying this technique would be achieved. Fig. 9 shows a plot of the predicted and reference volume fractions for the 15 independent three-phase tests set. The water, oil and gas

predictions were plotted in black, white and grey respectively. The same colour code would be applied to the prediction for the two phase test sets. The RMSEP for the 15 independent data sets before application of average scaling technique for gas, oil and water was 37.4%, 39.2%

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Fig. 8. PCA, C1 calibration data, C2 calibration and Gas/Oil, C3 and C4 calibration and Gas/Oil/Water.

Fig. 9. Predicted and reference after average linear scaling for three-phase flow.

and 6.3% respectively. For the same 15 independent data sets the RMSEP for gas, oil and water was 6.5%, 8.9% and 4.4% respectively after this technique was applied. Thus all that this average scaling technique does is to reduce the magnitude of the predictions for oil and increase those for water and gas implying that the prediction error followed a particular trend. Even though the volume fraction prediction performance has been improved, there was the need to verify whether this technique had any effect on the flow regime identification which was possible even before the application of this technique. Here the same four test data sets presented in Fig. 7 (A1-4) are shown in (B1-4) of the same figure after application of

this average scaling technique for comparison. A comparison of the results from the phase distribution plots showed considerable improvement in the flow regime identification properties of the model. 3.3.2. Two-phase flow Both gas/oil and gas/water two-phase flow experiments were conducted, in total 15 of each of the gas/oil and gas/water results are presented and discussed. In two-phase flow, four different flow regimes were studied. They were stratified-wavy, slug, dispersed and annular flow. Our goal was to develop a global model that

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Fig. 10. Predicted and reference for two-phase gas/oil and gas/water.

could predict both the volume fraction and identify flow regime for oil, water and gas in pipe lines without considering whether or not it was single-, two- or three-phase flow mixtures. The model from the single-phase calibration data coupled with the average scaling factor technique developed from three-phase flow would be used to predict the volume fraction and identify the different flow regimes. The first step was to predict the volume fractions for all independent two-phase data set and analyse the degree of accuracy by plotting the predicted and reference values. It must be noted here that even though one of the three components in the mixture must be zero, the reference predicted small percentages of the third component. It was also expected that the model would predict the third component but the magnitude of the value to be predicted could not be forecast at this point. Fig. 10 compares the predicted volume fractions for oil, water and gas to that of the reference. From the oil/gas results, it can be seen that the model predicted slightly higher fractions of water than that of the reference. The increase in water fractions can partly be attributed to the scaling technique applied. In this scaling technique, the water average scaling factor as found from the three phase model was about 106%. Thus volume fraction of water predicted by the model for gas/oil mixtures would be increased by 6%. Comparing the predicted and reference results for both the gas/oil and gas/water data sets (Fig. 10) it was interesting to see the degree of accuracy with which the model predicted the volume fractions even though the average scaling technique was developed from three phase flow mixtures. In the gas/oil test data, the RMSEP for gas, oil and water was 4.8%, 6.0% and 6.8% respectively whilst that of the gas/water test data was 6.2%, 9.2% and 5.8% respectively. The quantities of the third component which in fact should have been zero were not too far from it. Even in the

case where one, based on prior knowledge that the experiments were carried out under two-phase flow and decides to compare the liquid and gas fractions, the results were improved and seem promising. Another objective in this study was to investigate whether or not the model could also identify the flow regimes for the twophase data sets bearing in mind the relatively good predictions in terms of the volume fraction estimation. Here, the gas/oil data sets will be used to demonstrate the flow regime identification ability of the model. In gas/oil experiments, besides the flow regimes studied in three-phase, an additional flow regime was also investigated. Hence, the question was ‘‘can the model be able to identify all the four flow regimes?’’ Fig. 11 illustrates the phase distribution for the four different flow regimes. Clearly, the model again was able to identify all the three flow regimes as in the case of the three phase flow. In annular flow, the heavier fluid (in this case oil) forms a thin layer of film in the inner pipe wall. Since the layer is very thin, the traversable dual energy gamma densitometer cannot capture these areas, thus the phase distribution plots show higher gas fractions with small droplets of liquid which is well predicted by the model. The difference between dispersed and annular flow in Fig. 11 is clear enough to distinguish between them (i.e. there are higher quantities of oil in the pipe for dispersed flow as compared to that of annular flow). 4. Conclusion Multivariate data analysis was applied to data obtained from a dual energy gamma densitometer instrument for volume fraction estimation and flow regime identification in multiphase flow. The first results from volume fraction estimation for three-phase flow

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Fig. 11. Phase distribution plot for gas/oil. D1 stratified-wavy flow, D2 slug flow, D3 dispersed flow and D4 annular flow.

mixtures showed a clear difficulty for the model to accurately predict the component volume fractions, but it was possible for the model to identify the different flow regimes investigated. PCA on the calibration data and on a combination of the calibration and test data showed that there were clear differences between the two data sets. From the PCA it was clear that the test and calibration data exhibited a particular trend. An average linear scaling technique was developed from half of the three-phase test data and tested on the other half with the aim of improving the models volume fraction prediction properties. The RMSEP for the 15 test data for gas, oil and water was 37.4%, 39.2% and 6.3% respectively. After application of average linear scaling, the RMSEP for gas, oil and water was 6.5%, 8.9% and 4.4% respectively. The flow regime identification properties for the model were also considerably improved after this technique was applied. This technique was subsequently applied to estimate the different volume fractions and identify the different flow regimes for twophase flow data sets. In the gas/oil test data, the RMSEP for gas, oil and water was 4.8%, 6.0% and 6.8% respectively whilst that of the gas/water test data was 6.2%, 9.2% and 5.8% respectively. The model was also able to identify all the two-phase flow regimes investigated. Further work on developing this methodology and subsequent potential application is required. References [1] Blaney S, Yeung H. Investigation of the exploitation of a fast-sampling gamma densitometer and pattern recognition to solve the superficial phase velocities and liquid phase water cut of vertically upward multiphase flows. Flow Meas Instrum 2008;19:57–66. [2] Abouelwafa MSA, Kendall EJM. The measurement of component ratios in multiphase systems using γ -ray attenuation. J Phys E Sci Instrum 1980;13: 341–5. [3] Sætre C, Johansen GA, Tjugum SA. Salinity and flow independent multiphase flow measurements. Flow Meas Instrum 2010;21:454–61.

[4] Tjugum S, Frieling J, Johansen GA. A compact low energy multibeam gammaray densitometer for pipe-flow measurements. Nucl Instrum Methods B 2002; 197:301–9. [5] Tjugum SA, Hjertaker BT, Johansen GA. Multiphase flow regime identification by multibeam gamma-ray densitometry. Meas Sci Technol 2002;13:1319–26. [6] Robøle B, Kvandal HK, Schüller RB. The Norsk hydro multi phase flow loop. A high pressure flow loop for real three-phase hydrocarbon systems. Flow Meas Instrum 2006;17:163–70. [7] Frøystein T, Kvandal H, Aakre H. Dual energy gamma tomography systems for high pressure multiphase flow. Flow Meas Instrum 2005;16:99–112. [8] Hoffmann R, Johnson GW. Measuring phase distribution in high pressure three-phase flow using gamma densitometry. Flow Meas Instrum 2011;22: 351–9. [9] Midttveit, Berge V, Dykesteen E. Multiphase flow metering using capacitance transducer and multivariate calibration. Model Identif Control 1992;13:65–76. [10] Eowa JS, Ghadiri M. Electrostatic enhancement of coalescence of water droplets in oil: a review of the technology. Chem Eng J 2002;85:357–68. [11] Salgado CM, Pereira MNA, Schirru R, Brandão LEB. Flow regime identification and volume fraction prediction in multiphase flows by means of gammaray attenuation and artificial neural networks. Prog Nucl Energy 2010;52: 555–562. [12] Eriksson L, Johansson E, Kettaneh-Wold N, Trygg J, Wikström C, Wold S. Multiand megavariate data analysis, part 1 basic principles and applications. Umeå: Umetrics; 2006. pp. 39–52. [13] Martens H, Næs T. Multivariate calibration. Chichester: Wiley; 1989. pp. 73–163. [14] Esbensen KH. Multivariate data analysis—in practice. 5th ed. An introduction to multivariate data analysis and experimental design, Oslo: CAMO; 2006. [15] Wold S, Esbensen K, Geladi P. Principal component analysis. Chemometr Intell Lab Syst 1987;2:37–52. [16] Geladi P, Kowalski BR. Partial least square regression: a tutorial. Anal Chim Acta 1986;185:1–17. [17] Ergon R. Re-interpretation of NIPALS results solves PLSR inconsistency problems. J Chemom 2009;23:72–5. [18] Martens H, Martens M. Multivariate analysis of quality: an introduction. Chichester: Wiley; 2000. [19] Höskuldsson A. Prediction methods in science and technology, vol. 1. Warsaw: Thor; 1996. [20] Mokhatab S, Poe WA, Speight JG. Handbook of natural gas transmission and processing. Gulf Professional Publishing; 2006. p. 88. [21] Åbro E, Johansen GA. Improved void fraction determination by means of multibeam gamma-ray attenuation measurements. Flow Meas Instrum 1999; 10:99–108.