Experiments in Fluids (2005) 39: 667–678 DOI 10.1007/s00348-005-1008-2
R ES E AR C H A RT I C L E
Bin Hu Æ Colin Stewart Æ Colin P. Hale Christopher J. Lawrence Æ Andrew R. W. Hall Holger Zwiens Æ Geoffrey F. Hewitt
Development of an X-ray computed tomography (CT) system with sparse sources: application to three-phase pipe flow visualization Received: 27 January 2005 / Revised: 20 April 2005 / Accepted: 2 May 2005 / Published online: 24 June 2005 Springer-Verlag 2005
Abstract This paper describes the application of a twobeam X-ray computed tomography (CT) system to multiphase (gas–oil–water) flow measurement. Two highvoltage (160 keV) X-ray sources are used to penetrate a 4-in. (101.6 mm ID) pipeline. A rotating filter wheel mechanism is employed to alternately ‘‘harden’’ and ‘‘soften’’ the X-ray spectra to provide discrimination between the three phases. Because this system offers only two projections, conventional back-projection algorithms are ineffective and thus a new reconstruction technique has been developed. A matrix equation is formed, to which additional ‘‘smoothing equations’’ are added to compensate for the lack of projection data. The tomographic result is obtained by computing an inverse matrix. This is a one-off computation and the inverse is stored for repeated use; reconstructed images from synthesized data demonstrate the effectiveness of this technique. Three-phase tomographic images of a horizontal slug flow are presented, which clearly show the mixing of oil and water layers within the slug body. The relevance of this work to the offshore oil and gas industry is summarized. Abbreviations Ai,j Area fraction of the jth beam within the pipe that is occupied by the (i, j)th element, dimensionless D Pipe diameter, m B. Hu Æ C. P. Hale Æ C. J. Lawrence (&) Æ G. F. Hewitt Department of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK E-mail:
[email protected] Tel.: +44-020-75945622 Fax: +44-020-75945629 C. Stewart Frontier Engineering Solutions Ltd, Aberdeen, AB22 8GT, UK A. R. W. Hall BP Exploration and Production, Aberdeen, UK H. Zwiens University of Hannover, Hannover, Germany
E I I0 N Umix x Xi,j X^i;j Xd
X-ray energy, keV X-ray intensity, W Scaling factor in Eq. 1, W m2 Number of elements on each axis of the reconstructed image, dimensionless Mixture velocity, m s1 Path length of material, m Local phase fraction in the (i, j)th element, dimensionless Adjusted local phase fraction in the (i, j)th element, dimensionless Efficiency of the linear array detector, dimensionless
Greeks l Attenuation coefficient r Smoothing factor, dimensionless / Phase fraction, dimensionless ^ / Adjusted phase fraction, dimensionless Subscripts hard Hard spectrum max Maximal value soft Soft spectrum Superscripts g Air (or gas) phase o Oil phase w Water phase
1 Introduction Computed tomography (CT) imaging, or ‘‘CAT’’ (computer assisted tomography), is used to reconstruct an image of the interior of an object after collecting projection data from different directions at its exterior. Computed X-ray tomography originates from the
668
invention of the X-ray tomographic scanner by Cormack and Hounsfield, for which they received a Nobel Prize in 1972. CT systems have been broadly applied to medical research so far. However, with the development of this technique, CT has become widely used in other fields, e.g., subsea reservoir mapping (Mizumura et al. 1994, 2000), nuclear engineering (Bojarsky et al. 1991; Chen et al. 1998; Hori et al. 2000), concentration measurements in mixing vessels (Williams et al. 1993), and multiphase flow measurements (Theofanous et al. 1998; Morton et al. 1999; Soleimani 1999; Odozi 2000; Wang et al. 2000; Yang and Liu 2000). Accurate reconstruction using CAT depends upon the ability of the source to penetrate the subject medium. Depending on the subject and the application, this penetration may be achieved by visible light (Thomas et al. 1995), infrared radiation (Kawazoe and Inagaki 1997), strong magnetic fields (Gladden 1994), electrical currents or charges (Wang et al. 2000; Yang and Liu 2000), ultrasonic pulses (Hoyle 1993), X-ray radiation or gamma-ray radiation (Herman 1980; Harvel et al. 1996; Gondrom et al. 1999; Soleimani et al. 2000; Prasser et al. 2003; Wong et al. 2004). Transparency measurements, or projection data, are then collected by arranging an array of suitable detectors around the periphery. In twophase flowing systems, gamma-ray and electrical tomography are often used because they are relatively inexpensive. Gamma-ray sources also provide a stable monochromatic photon beam, which enables better phase resolution. Gamma-ray systems offer a more objective result than electrical systems since interpretations of the signals from the latter are subject to ambiguities. However, for implementation in many industrial environments gamma-ray systems have a comparatively slow response for reasonable source strength (50 Hz compared to 500–1,000 Hz for each chordal measurement). X-rays have penetrating power comparable to those of gamma-rays, but often have a much greater intensity and, hence, a response which, though not as rapid as for electrical systems, is much faster than typical gamma-ray systems with reasonable beam strength. In the simplest case, a radiation-based image can be obtained by moving a single source and detector around the subject exterior. This arrangement has been used by Manolis (1995), George et al. (2001), Prasser et al. (2003) and Wong et al. (2004) to study two- and three-phase flows. A computer-controlled stepper motor was used to sweep the source and detector across the pipe; the system was then repositioned to obtain measurements of another projection. Single-source systems are prevalent in medical tomography. However, a major limitation is the time required to obtain sufficient data for a reconstruction. This may be acceptable if the subject is stationary or an ‘‘averaged’’ tomograph is required, but it is unsuitable for imaging temporal variations of, say, phase distribution in multiphase flow. To overcome the time limitation, multiple sources and detector arrays can be positioned around the subject exterior. For example, Harvel et al. (1996) developed a
multi-beam X-ray system, which used 18 X-ray sources and 122 detectors, arranged around a test channel. This system was used for studying two-phase air-water flows. Hori et al. (2000) developed a more complex system for studying steam-water tube bundles in nuclear reactors, with 60 X-ray tubes and 584 detectors arranged on separate concentric circles. In both these systems, the Xray sources are activated in quick succession (a process known as multiplexing) to prevent scattering from surrounding beams affecting the measurement. This constrains the overall speed of the data acquisition. Nevertheless, it is possible to generate tomographic images in real-time at frequencies in excess of 100 Hz. In a three-phase system there is an extra difficulty: a distinction needs to be made between the gas and liquid phases, and also between the primary and secondary liquid (or solid) components. To overcome this problem, Morton et al. (1999) proposed a high-speed multiphase flow imaging system with two concentric detector arrays which measure the low and high energy X-rays, so that projection data for each phase can be derived. The system contains 156 X-ray emission points and is envisaged to obtain detailed three-phase images in approximately 20 ms. However, the energy of the X-ray sources is relatively low (22 keV), hence the penetration is limited. This means that the system would only be useful for studying a relatively small pipeline, up to about 2 in. in diameter. In this paper, we describe an X-ray system that has been developed to obtain three-phase images in approximately 200 ms. This system uses high-energy (160 keV) X-rays that can penetrate up to 100 mm of flowing media, and is therefore able to image the flow in industrial-sized multiphase pipelines. A minimal number of X-ray sources and detector arrays have been used in order to minimize the overall cost; this means that special consideration has to be given to the reconstruction technique. The following sections of this paper discuss: – The principle and operation of the X-ray system – The development of an algorithm for converting the projection data into tomographic images – The effectiveness of the reconstruction technique using ‘‘ideal’’ artificial projection data and actual projection data – Reconstructed images for three-phase slug flow in a 4 in. pipeline The reconstructed images clearly highlight the mixing between the oil and water layers that occurs in a threephase slug flow. Potential uses of the results are then discussed, with particular emphasis towards the development of a multiphase slug flow meter and a threephase transient flow model.
2 System description The X-ray tomography system was developed by AEA Technology and (after a period of use at the National
669
Fig. 1 X-ray system
Engineering Laboratory, East Kilbride) was installed within the WASP (water–air–sand–petroleum) multiphase flow facility at Imperial College London. The machine has two channels. Each of these channels comprises an X-ray source, a rotating filter wheel, a linear array detector and control hardware. These components are illustrated schematically in Fig. 1. The two X-ray sources (Comet AG, Switzerland) are fixed in position at the top and left of the enclosure, and provide vertical and horizontal projections through the pipe. The X-ray tubes have tungsten target anodes oriented at 10, and are activated by a high-voltage source. The entire system occupies a volume of approximately 1 m3 and is entirely enclosed within lead safety shields. The X-ray filter wheels rotate at a frequency of 4.6 Hz (275 rpm) and consist of three segments, as illustrated in Fig. 2. The 120 segment of 2 mm thick copper and the 60 segment of air alternately ‘‘harden’’ and ‘‘soften’’ the X-ray spectrum. These spectra allow a distinction to be made between the oil, water and gas components. The remaining 180 segment is comprised of 8 mm thick lead, and completely blocks the X-ray beam. The two filter wheels are positioned 180 out of phase, so that the test section is never exposed to the two sources simultaneously. The acquisition frequency is mainly dependent on the rotation frequency of the filter wheel. In this paper the frequency of tomographic images is 4.6 Hz for each reconstructed view.
Two 240 mm long linear detector arrays (Thomson Tubes Electroniques, France) are located at a distance of 870 mm from the X-ray sources. Each array contains 256 silicon sensors of 0.45 mm length that measure the intensities of the ‘‘hard’’ and ‘‘soft’’ X-rays passing through the pipe; only about 200 elements are used in each measurement. Optical sensors are positioned around the filter wheels, and are used to synchronize the acquisition of data with the rotation of each wheel. The system is accompanied by a software suite developed by AEA Technology Plc, Harwell, which controls the data acquisition process, and also allows calibration of the detector arrays (gain and offset), data display, and storage of results.
3 Measurement principle A steady stream of electrons strikes the tungsten anode material, and is rapidly decelerated so that X-ray photons are emitted at energies up to 160 keV. As the target angle is relatively small in this instance (10) the resultant X-ray spectrum can be approximated by Kramers’ rule (Kramers 1923). Thus, the X-ray intensity (i.e., the energy of photons emitted per unit area in a unit time) in the energy interval dE at energy E is given by E dE dI ¼ I0 1 ð1Þ Emax Emax where I0 is a scaling factor and Emax is the maximum X-ray energy (160 keV in this instance). The effect of X-rays being absorbed in the target and re-emitted, which will result in a sharp intensity peak in the spectrum at an energy around 69 keV, has been neglected in this analysis. The X-ray beam is attenuated as it passes through the filter wheel material, the pipe walls and the pipe contents, such that the X-ray intensity at the detectors is given by R E dE lðEÞ dx dI ¼ I0 1 e ð2Þ Emax Emax where l(E) is the attenuation coefficient for each material at energy E and x is the corresponding path length. Each detector in the linear array then measures an overall intensity I (the energy striking its surface per unit time), given by: R Z ZEmax E dE I ¼ I0 1 dA e lðEÞ dx Xd ð EÞ Emax Emax A
Fig. 2 X-ray filter wheel
ð3Þ
0
where A is the detector area and the factor Xd(E) represents the efficiency of the linear array detector which is less than unity at high energy levels. Two intensity measurements are made, denoted by Isoft and Ihard, as the pipe is exposed to the soft and hard spectra.
670
Fig. 3 Transmission factors for various materials between the Xray source and the detector array, as a function of energy
Figure 3 illustrates typical levels of X-ray attenuation due to the filter wheel, the pipe walls, and different phases inside the pipe. The attenuating characteristics of oil and water are quite distinct at low energies but are rather similar at higher energies. The copper filter blocks low-energy X-rays and thus ‘‘hardens’’ the spectrum. The intensity of the X-ray beam for the original and hardened spectra, Isoft and Ihard, respectively, is recorded for each rotation of the filter wheel. To convert the intensity measurements Isoft and Ihard into phase fraction data, the system software uses a numerical algorithm. Before flowing measurements are obtained, the test section is filled with gas, oil and water in turn to obtain six calibration intensities: Igsoft, Ighard, Iosoft, Iohard, Iwsoft and Iwhard. Typical values for these calibration data have been estimated using Eq. 3 and their ratios are plotted in Fig. 4. The three points form a triangle, which defines all the possible permutations of the oil, water and gas phases. If the original (soft) and hardened beams were monoenergetic (as is the case for gamma beams), then the fractions of the three phases in the beam path through the tube would be given by solution of the following equations (Pan 1996):
Fig. 4 Ratios of soft and hard spectra intensities, for different gas fractions and water cuts (4 in. path length; computed using Eqs. 1, 2 and 3). The three pairs of calibration count rates form the corner points of the triangle
– Statistical uncertainty, due to the low X-ray count rates that are measured when the copper filter is in place. This is a particular problem when trying to distinguish between phases for small amounts of liquid, as can be seen from Fig. 4. To reduce this problem, the copper segment of the filter wheel has been made twice as large as the air segment (see Fig. 2). – Lack of a unique solution for the phase fractions. Unlike a gamma-ray system, the X-ray spectra are polychromatic, which means that lines of constant liquid holdup in Fig. 4 are slightly curved (if Eq. 4 applied then these lines would be straight). This is known as beam hardening. – Drift in the detector array gain and offset values. Regular calibration of the system was performed prior to each day’s experiments to ensure the best measurement accuracy possible. Despite these difficulties, it is possible to obtain measurement of beam-average phase fractions with acceptable accuracy by the process described.
" #," o o # w w w w ln Isoft =Isoft ln Ihard =Ihard ln Isoft =Isoft ln Ihard =Ihard g g g g / ¼ w w w w =Isoft =Isoft ln Isoft ln Ihard =Ihard ln Isoft ln Ihard =Ihard
ð4aÞ
" #," # w g g g g w ln I =I ln I =I ln I =I ln I =I soft hard soft hard soft hard o soft /w ¼ o hard g g g g o o =Isoft =Isoft =Ihard ln Isoft ln Ihard =Ihard ln Isoft ln Ihard
ð4bÞ
o
/g ¼ 1 ð/o þ /w Þ
ð4cÞ
As with all radiation-based systems, the measurement accuracy is affected by a variety of systematic and random errors. The major sources of uncertainty in this system can be summarized as follows:
4 Pre-processing 4.1 Signal filter Figure 6a illustrates typical data for the oil (Shell Tellus 22), water and gas phase fractions obtained by filling a
671
^a ¼ / i
1 0
if /ai > 1 if /ai \0
ð5Þ
where /ia denotes the phase fraction data of the ith beam for each phase (a=g, o, w) in the pipe, and ^a / i denotes the adjusted data. 2. Restore the phase fraction balance. As a result of action (1) above, the oil, water and gas fractions may no longer add up to unity. The oil phase fraction and the water phase fraction are thus proportionately adjusted according to: Fig. 5 Test section geometry used to generate the phase fraction data in Fig. 6. Oil holdup = 0.11 (red); water holdup = 0.63 (blue); air holdup = 0.26 (green)
test section with stratified layers of fluids as shown in Fig. 5. Sodium iodide (5 g l1) was added to the aqueous phase to improve discrimination. The expected data for this arrangement are shown in Fig. 6b. Though there is qualitative agreement, there is a lot of noise and systematic error (particularly near to the bottom of the pipe) due to the problems discussed above. To enable the best possible reconstruction of the phase distribution in the pipe interior, it was found useful to pre-process these data in the following manner: 1. Force the out-of-range values into range. Data values less than 0 and greater than 1 have no physical interpretation. To correct for this problem, which is due to noise and/or drift in the detector arrays, the following action is performed:
^ o ¼ ð1 /g Þ / i i
/oi ; o / i þ /w i
^ w ¼ ð1 /g Þ / i i
/w i o /i þ / w i
ð6Þ
The gas phase data are left unchanged since the gas– liquid discrimination is usually superior to that between the oil and water. 3. Filter the data to reduce the errors due to noise using a simple rolling average algorithm, for each phase: ^ a ¼ 1 ð/a þ /a þ /a Þ / i i iþ1 3 i1
ð7Þ
4. Set the data values for beam passing outside the pipe equal to the last known values inside the pipe. This allows for the best possible reconstruction near the perimeter. These pre-processing steps bring the projection data much closer to the expected values, thus reducing the measurement uncertainty, as shown in Fig. 6c, where
Fig. 6 Experimental and computed phase fraction data from horizontal beams (a–c) and vertical beams (d–f) for the stratified geometry illustrated in Fig. 5: (a), (d) measured phase fraction data; (b), (e) ideal phase fraction data; (c), (f) measured phase fraction data, after processing and filtering. Sodium iodide (5 g l1) is added to the water phase
672
data for a static tubular test cell having layers of water, oil and air are shown. 4.2 Reconstruction algorithm Several methods are commonly used for reconstruction when the number of projection measurements is large: back-projection (Gullberg et al. 1985), iterative approximation (Kak and Slaney 1988), analytical techniques using Fourier transformation (Kay et al. 1974), filtered back projection (Budlinger et al. 1978) and convolution (Shepp and Logan 1974; Kumar and Ramakrishna 2002). However, as the system presented here uses only two projections, there is insufficient information to obtain an accurate reconstruction with these methods. Consequently, a new algorithm that uses matrix inversion has been developed. Figure 7 illustrates the division of the pipe area into a grid of N·Nelements. The edges of these elements are formed by intersection of adjacent X-ray beams (here, a ‘‘beam’’ is defined as that part of the X-ray emission from one of the X-ray sources which ultimately passes to a given detector), and the boundary of the domain is carefully selected in order to lie just outside the pipe wall. For each of the horizontal beams, the following basis equation can be written: A1; i X1; i þ A2; i X2; i þ þ AN ; i XN ; i ¼ / i
ð8aÞ
where Aj,i is the fraction of the ith beam area within the pipe that is occupied by the (j, i)th element, Xj,i is the local phase fraction in the (j, i)th element, and /i is the ith phase fraction measurement as shown in Fig. 7. Similarly, for each of the vertical beams, we have A i; 1 Xi; 1 þ Ai; 2 Xi; 2 þ þ Ai; N Xi; N ¼ / iþN
ð8bÞ
The two sets of basis equations are combined to form the matrix equation [A][X]=[/]:
Fig. 7 N·N grid of elements used in the tomographic reconstruction process (here N=12)
where [A] is a sparse N2·2Nmatrix consisting of area fractions, [X] is the N2tomographic vector containing the image data, and [/] is the (known) vector containing the measured phase fraction information. As the number of columns in [A] is much greater than the number of rows, it is not possible to obtain a unique solution for the inverse [A]1 using Eq. 9. Therefore, additional rows are added to [A] by using an assumption that the phase fractions within adjacent elements of the grid are very similar. Using each group of four neighbouring elements shown in Fig. 7 it is possible to write four ‘‘smoothing equations’’ of the form: r Xi;j Xi;jþ1 ffi 0; r Xi;j Xiþ1;j ffi 0 ð10Þ r Xi;j Xiþ1;jþ1 ffi 0; r Xi;jþ1 Xiþ1;j ffi 0
2 2
A1;1
6 6 6 6 6 6 6 6 A1;1 6 6 6 6 4
A2;1 0
AN ;1 A1;2
0 A2;2
AN ;2 ..
0 0 A2;1
..
0
A1;2
0 0 A2;2
. AN ;1
0
.
A1;N A1;N
AN ;2
..
0
.
A2;N 0 A2;N
0 .. . 0
36 6 6 76 76 76 76 76 6 AN ;N 7 76 76 76 76 76 76 56 6 6 AN ;N 6 4
X1;1 X2;1 .. .
3
7 2 3 7 /1 7 7 6/ 7 7 2 7 XN ;1 7 6 .. 7 7 6 6 X1;2 7 6 . 7 7 7 /N 7 .. 7 6 7 6 ¼ . 7 /N þ1 7 7 6 7 6 XN ;2 7 /N þ2 7 7 6 7 6 .. 7 6 . 7 . 4 . 7 7 . 5 X1;N 7 /2N .. 7 5 . XN ;N
ð9Þ
673
In fact, the algorithm minimizes (in a least square sense) the values in Eq. 10 rather than setting them to zero. The factor r, called the ‘‘smoothing factor’’, determines the relative weight of the smoothing equations compared to the beam equations. Increasing r causes a blurring of the tomographic image, and prevents spurious features appearing in the reconstruction. Typically r is chosen in proportion to N2, to compensate for the greater number of unknowns. By adding the four smoothing equations, an additional 2(2N1)(N1) rows of equations can now be added to [A], such that: 2 6 6 6 6 6 6 6 6 6 6 4
2N beam equations
2ð2N 1ÞðN 1Þsmoothing equations
With around 25 groups (each) of horizontal and vertical beams to be considered, the matrix [A] contains around 4·104 elements. Around 10 min of computer time is then required to build-up the matrix [A] and compute the inverse, using a 500 MHz Pentium III PC. However, once this initial effort was expended, [A]1 was stored in memory and it was possible to achieve realtime computation of the vector [X] from the stored inverse and the real-time measurements of the phase fraction vector [U].
3 2 X1;1 7 6 7 6 7 6 7 6 .. 7 6 . 7 6 7 6 6 7 6 . 7 6 . 7 6 . 5 4 XN ;N
3 /1 7 6 .. 7 7 6 . 7 7 7 6 7 6 / 2N 7 7 7 6 7 6 0 7 7 7 ¼ 6 7 6 0 7 7 7 6 7 7 6 7 6 . 7 5 4 .. 5 0 3
2
ð11Þ
4.3 Inversion of the matrix
4.4 Mass balance and colour function
The matrix [A], after adding smoothing equations, has more rows than columns. This means it is not possible to find a solution for [A]1 using Gaussian elimination or SU decomposition techniques. Therefore, a singular value decomposition algorithm is employed here to generate a least-squares error solution for the pseudo inverse [A]1 (Press et al. 1992). This algorithm is optimal in the sense that the error quantity: d ¼ det ½A1 ½A ½I ð12Þ
Equation 11 is solved three times (using the same [A]1) in order to obtain the vector [X] for the oil, water and gas phases inside the pipe. However, the constraints that each of the elements in [X] should lie within the range of 0–1, and the sum of the oil, water and gas phase fractions at each element should add up to 1 have not yet been imposed. Hence, each of the data values in [X] is post-processed in a similar way to the projection data. The phase fraction in the (i, j)th element for each of the oil, water and gas phases, Xai,j, is forced into the range of 0–1, i.e., a 1 if Xi;j >1 a X^i;j ¼ ð13Þ a 0 if Xi;j \0
is minimized. This algorithm allows a good estimate of the tomographic vector [X] to be made, but it is very expensive in terms of computer effort. The computational time for inversion is found to be proportional to N3, so rapid reconstruction is not possible when N=200. To greatly speed up the inversion time, the beams are firstly bundled into groups to form the basis beam equations and the corresponding measurement data are summed. By writing a single equation for each group of eight beams, the size of the matrix [A] is reduced by a factor of 82, and thus it takes around only 1/256 of the original time to compute the pseudo-inverse [A]1. The number of elements in the pipe cross-section is also reduced by a factor of 64, resulting in a coarser reconstruction, but it was found that there is not a significant impact on the quality of the reconstructed image. Then, the matrix [A]1 can be evaluated once and stored in computer memory to speed up reconstruction when large numbers of tomographs are required.
where Xai,j denotes the adjusted local phase fraction for each phase (a=g, o, w). Furthermore, to ensure that the sum of the oil, water, and gas phases adds up to 1, mass is proportionately restored to the oil and water phase data as follows: n o Xo i;j g o X^i;j ¼ 1 Xi;j o w Xi;j þ Xi;j n o Xw i;j g w ¼ 1 Xi;j ð14Þ X^i;j o w Xi;j þ Xi;j Here, it is again assumed that the gas phase data are generally more accurate than the oil and water data. In order to create images from the tomographic data, it is necessary to select a colour scheme for each of the reconstructed elements. We have developed two such schemes, illustrated in Fig. 8, for plotting single-phase
674
Fig. 8 Colour schemes for a single-phase tomographic images, and b three-phase tomographic images
and three-phase tomographs. The single-phase colour scheme is one-dimensional and passes from green/red/ blue (for pure gas/oil/water) through white (indicating a mixture) to black (component not present). The threephase colour scheme is two-dimensional: green, red and blue are used for individual phases but intermediate colours are used to represent intermediate states at different values of gas fraction and water cut. Lighter colours (yellow and cyan) were used at a gas fraction of 0.5 to enhance the discrimination of the interface between the gas and liquid phases.
5 Results and discussion 5.1 Reconstructed images obtained from ideal and real data ‘‘Ideal’’ projection data have been generated by specifying simple geometries for the three phases and using a simple computer program to calculate phase fractions along each beam. These data allow the performance of the reconstruction algorithm to be evaluated in the absence of beam hardening, noise and other sources of experimental error. Figure 9 shows the images that have been produced using four ‘‘test’’ geometries: stratified layers, stratified layers with a mixture layer, a crude approximation of a dispersed system, and a concentric annular geometry. A 26·26
grid of elements and a smoothing factor r=0.02 were used to produce each result. Bilinear interpolation has been used in order to enhance the quality of the images. From Fig. 9a, b it is concluded that stratified-type flows can be reconstructed with excellent accuracy. The interfaces of the reconstructed tomographs are in good agreement with those in the original data. The concentration of oil (or water) in a mixed layer can be determined quite well. As shown in Fig. 9c, blobs of different fluids in the pipe can also be identified in threephase dispersed flow, though a few differences in individual features such as drop/bubble location and size are observed. However, the images in Fig. 9d for the concentric annuli case are not as well reconstructed as those for stratified and dispersed flows due to the small number of projections. Square regions of water and oil phases are found rather than circular. This is because the interfaces between the oil, water and air regions do not lie parallel to the beam paths. Additional X-ray sources would need to be added to the system to improve the result in this case. However, the main applications of the system are likely to be in stratifying-type and mixed flow (including slug flow) and the limitations regarding annular flow are not of dominant importance. Real data are, of course, subject to noise, beamhardening and other errors, which will worsen the quality of the images obtained. Figure 10 shows the tomographs obtained using data from the static tests shown in Fig. 6c. In this case, despite small spurious features in the oil and water images, the result is generally satisfactory. 5.2 Reconstructed images of three-phase slug flow Slug flow frequently occurs in offshore production pipelines. Descriptions of slug flow have been presented for two-phase flow by Wallis (1969), Dukler and Hubbard (1975), Taitel and Barnea (1990), Fan et al. (1992), Woods and Hanratty (1996), Hale (2000) and Stewart (2002), and for three-phase flow by Acikgoz et al. (1992), Stapelberg and Mewes (1994) and Odozi (2000) amongst others. Each slug unit is divided into the slug zone, where the pipe is bridged and vigorous mixing takes place, and a stratified zone, which has either a stratified or annular geometry depending on the pipe orientation. Slug flow presents a particular challenge to process engineers because it increases the pressure drop in pipelines (thus reducing production) as well as enhancing pipeline erosion and increasing the stresses on pipeline bends. Sample data for horizontal slug flow have been obtained using the multiphase flow test facility at the National Engineering Laboratory (NEL), UK. Figure 11 illustrates a 120 s sample of projection data that were obtained for slug flow at a total superficial velocity of approximately 3 m s1 and a water cut (volume fraction of the input liquid flow which is water) of 50%. The data have been plotted using the three-phase colour scheme
675
Fig. 9 Reconstructed images for the air, water and oil phases using ‘‘ideal’’ projection data for astratified flow, b stratified flow with a layer consisting of a mixture of oil and water at 50% by volume oil, c ‘‘dispersed’’ flow, and d concentric annuli. The original three-
phase image is on the left, the computed distributions of the individual phases (air, oil and water in succession) are in the middle and the three-phase reconstruction is on the right
shown in Fig. 8. In this sample two slugs are clearly evident at approximately 40 and 93 s, as well as two large waves at approximately 7 and 75 s. Figure 12shows reconstructed three-phase images at various times before, during, and after the first recorded slug. From these images we can observe that the gas, oil and water are arranged in well-stratified layers prior to the passage of the slug front. As the slug front passes there is strong mixing between the liquid phases, with occasional pockets of oil (Fig. 12c) and air (Fig. 12e) collecting at the top of the pipe. In addition, gradual separation of the oil and water phases occurs at the back of the slug
(Fig. 12g) and throughout the beginning of the stratified zone (Fig. 12h, i). Despite the small number of X-ray sources, the reconstruction algorithm can clearly distinguish individual phases and mixing regions within the slug interior. Results of similar quality can be obtained for each of the passing wave objects.
6 Conclusions A two-beam X-ray system has been successfully operated, which can produce tomographic images of multi-
Fig. 10 Reconstructed images obtained from data shown in Fig. 6c and f. Sodium iodide (5 g l1) was added to the water phase to enhance the image quality. The order of the images is the same as in Fig. 9
676
Fig. 11 Three-phase slug flow data obtained from the X-ray system during testing at NEL (mixture velocity Umix3 m s1and water–oil ratio of approximately 50%). aVertical projection data. b Horizontal projection data
phase (oil–water–gas) flow at a frequency of approximate 5 Hz. The system comprises two high voltage (160 kV) supplies, two rotating filter wheels, which harden and soften the source spectrum, and two arrays of X-ray sensitive detectors. Intensity measurements have been gathered and have been converted into phase fractions of oil, water and gas by pre-calibrating the system and using an interpolation process. These data were converted into tomographic images by creating and solving a matrix equation using the basis beam equations. Because of the limited number of projections, smoothing equations were added to this matrix such that images could be produced by a pseudo-inverse algorithm. Real-time imaging was possible provided that the inverse matrix was calculated and stored beforehand. Preliminary images have been presented for horizontal slug flow in a 4 in. pipeline, which demonstrate the effectiveness of the technique. Despite the relatively low imaging frequency, the system has a variety of potential applications in the
offshore oil and gas industry. Two applications that are of particular note are: – Development of an advanced multiphase flow meter. The metering of three-phase flow is notoriously difficult, at least in part because of the relatively unsophisticated techniques (e.g., gamma-ray densitometry), which are used to make the bulk holdup measurements. By using an X-ray system in conjunction with accurate velocity sensors, improvement in the metering accuracy of slug flow could be achieved. – Development of transient multiphase flow models, such as OLGA, PLAC and TACITE. The degree of mixing between liquid components is expected to have a significant effect upon the pressure drop, hence the oil transportation, in a multiphase pipeline. There are presently few data to demonstrate how this phenomenon is affected by phase flowrates, pipe inclination or oil composition. The development of large waves into slugs (i.e., slug initiation), which has a significant
Fig. 12 Three-phase tomographs obtained at key moments before, during and after the first slug shown in Fig. 11
677
impact on oil production, is also poorly understood at present. More detailed results are required in order to lead to more efficient design of pipeline systems in the future. Work is currently ongoing at Imperial College London to improve the performance of the system and to investigate these two areas in greater detail. Acknowledgements This work was supported by the EU through grant No. ENK6-CT-2000-00055 and by the EPSRC through grant No. GR/S17765/01. Prof. C.J. Lawrence is grateful to Schlumberger and the Royal Academy of Engineering for their financial support. This work has been undertaken within the Joint Project on Transient Multiphase Flows. The authors wish to acknowledge the contributions made to this project by the Engineering and Physical Sciences Research Council (EPSRC), the Department of Trade and Industry and the following: Advantica, AspenTech, BP Exploration, ChevronTexaco, ConocoPhillips, ENI, FEESA, Granherne, Institutt for Energiteknikk, Institut Franc¸ais du Pe´trole, Norsk Hydro, Scandpower, Shell, SINTEF, Statoil, Total. The authors wish to express their sincere gratitude for this support.
References Acikgoz M, Franca F, Lahey RT (1992) An experimental study of three-phase flow regimes. Int J Multiphas Flow 18(3):327– 336 Bojarsky E, Deckers H, Lehning H, Piel D, Reiser H, Schmidt L (1991) THIBO experiments—thermohydraulically induced fuel pin oscillations in Na-cooled reactors. Nucl Eng Des 130(1):21– 26 Budlinger TF, Greenberg WL, Derenzo SE, Gullberg GT, Huesman RH (1978) Quantitative potential of dynamic emission computed tomography. J Nucl Med 19(3):309–315 Chen X, Luo R, Yuen WW, Theofanous TG (1998) Experimental simulation of microinteractions in large scale explosions. Nucl Eng Des 189(1–3):163–178 Dukler AE, Hubbard MG (1975) A model for gas-liquid slug flow in horizontal and near-horizontal pipes. Ind Eng Chem Fundam 14:337–347 Fan Z, Jepson WP, Hanratty RJ (1992) A model for stationary slugs. Int J Multiphas Flow 18:477–494 George DL, Shollenberger KA, Torczynski JR, O’Hern TJ, Ceccio SL (2001) Three-phase material distribution measurements in a vertical flow using gamma-densitometry tomography and electrical impedance tomography. Int J Multiphas Flow 27:1903– 1930 Gladden LF (1994) Nuclear magnetic resonance in chemical engineering: principles and applications. Chem Eng Sci 49:3339– 3408 Gondrom S, Zhou J, Maisl M, Reiter H, Kro¨ning M, Arnold W (1999) X-ray computed laminography: an approach of computed tomography for applications with limited access. Nucl Eng Des 190(1–2):141–147 Gullberg GT, Huesman RH, Malko JA, Pelc NJ, Budinger TF (1985) An attenuated projector-backprojector for iterative SPECT reconstruction. Phys Med Biol 30(8):799–816 Hale CP (2000) Slug formation, growth and decay in gas–liquid flows. PhD Thesis, University of London, UK Harvel GD, Hori K, Kawanishi K, Chang JS (1996) Real-time cross sectional averaged void fraction measurements in vertical annulus gas–liquid two-phase flow by neutron radiography and X-ray tomography techniques. Nucl Instrum Methods Phys Res A 371:544–552 Herman GT (1980) Image reconstruction from projections: the fundamentals of computerized tomography. Academic, New York
Hori K, Fujimoto T, Kawanishi K, Nishikawa H (2000) Development of an ultra fast X-ray computed tomography scanner system: application for measurement of instantaneous void distribution of gas–liquid two-phase flow. Heat Trans Asian Res 29(3):155–165 Hoyle BS (1993) Real-time ultrasound process tomography in pipelines. IEE Colloquium on ultrasound in the process industry, September 1993, London, vol 4, pp 1–4 Kak AC, Slaney M (1988) Principles of computerized tomographic imaging. IEEE Press, New York Kawazoe H, Inagaki K (1997) Computed tomography measurement of gaseous fuel concentration by laser light absorption. Proc SPIE 3172:576–584 Kay DB, Keyes JW, Simon W (1974) Radionuclide tomographic image reconstruction using Fourier transform techniques. Nucl Med 15:981–1974 Kramers HA (1923) The theory of X-ray absorption and of the continuous X-ray spectrum. Philos Mag 46:836–871 Kumar U, Ramakrishna GS (2002) A mixed approach to artifacts minimization in a continuous-rotate X-ray based tomographic imaging system using linear detector array. Appl Radiat Isot 57(4):543–555 Manolis IG (1995) High pressure gas–liquid slug flow. PhD Thesis, University of London, UK Mizumura K, Nishimoto T, Yamamoto T (1994) Analysis of sand movement on Noto Coast by geochemical method. J Hydraul Eng 2:923–927 Mizumura K, Yamamoto T, Kumagai Y (2000) Study of seabed elevation changes using geochemical elements. Adv Eng Softw 31(1):1–12 Morton EJ, Luggar RD, Key MJ, Kundu A, Tavora LMN, Gilboy WB (1999) Development of a high speed X-ray tomography system for multiphase flow imaging. IEEE Trans Nucl Sci 46(3) 1:380–384 Odozi UA (2000) Three-phase gas–liquid–liquid slug flow. PhD Thesis, University of London, UK Pan L (1996) High pressure three-phase (gas/liquid/liquid) flow. PhD Thesis, University of London, UK Prasser HM, Baldauf D, Fietz J, Hampel U, Hoppe D, Zippe C, Zschau J, Christen M, Will G (2003) Time resolving gammatomography for periodically changing gas fraction fields and its application to an axial pump. Flow Meas Instrum 14:119– 125 Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in Fortran 77, the art of scientific computing, 2nd edn. Cambridge University Press, Cambridge, pp 51–63 Shepp LA, Logan BF (1974) The Fourier reconstruction of a head section. IEEE Trans Nucl Sci 21:21–43 Soleimani A (1999) Phase distribution and associated phenomena in oil–water flows in horizontal tubes. PhD Thesis, University of London, UK Soleimani A, Lawrence CJ, Hewitt GF (2000) Spatial distribution of oil and water in horizontal pipe flow. SPE J 5(4):394– 401 Stapelberg HH, Mewes D (1994) The pressure drop and slug frequency of liquid–liquid–gas slug flow in horizontal pipes. Int J Multiphas Flow 20:285–303 Stewart C (2002) Metering of two-phase slug flow. PhD Thesis. University of Strathclyde, Glasgow, UK Taitel Y, Barnea D (1990) A consistent approach for calculating pressure drop in inclined slug flow. Chem Eng Sci 45:1199– 1206 Theofanous T, Angelini GS, Chen X, Luo R, Yuen WW (1998) Quantitative radiography for transient multidimensional, multiphase flows. Nucl Eng Des 184(2–3):163–181 Thomas PD, Darton RC, Whalley PB (1995) Liquid foam structure analysis by visible light tomography. Chem Eng J 56:187–192 Wallis GB (1969) One-dimensional two-phase flow. McGraw-Hill, New York Wang M, Doward D, Vlaev D, Mann R (2000) Measurement of gas–liquid mixing in a stirred vessel using electrical resistance tomography (ERT). Chem Eng J 77:93–98
678 Williams RA, Mann R, Dickin FJ, Llyas OM, Ying P, Edwards RB, Rushton A (1993) Application of electrical impedance tomography to mixing in a stirred vessel. Part 2. AIChE Symp Ser 89:8–15 Wong W-L, Hale CP, Hewitt GF, Hu B, Lao L, Lawrence CJ, Mayer P, Parsonage D, Ujang PM (2004) Three-phase flows in complex geometries. Fourth North American conference on multiphase technology, Banff, Canada, pp 251–269
Woods BD, Hanratty TJ (1996) Relation of slug stability to shedding rate. Int J Multiphas Flow 22:809–828 Yang WQ, Liu S (2000) Role of tomography in gas/solids flow measurement. Flow Meas Instrum 11:237–244
