X-Ray Spectrum Generation for a Multiphase Flow Meter

Transcription

1 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 50, NO. 3, JUNE X-Ray Spectrum Generation for a Multiphase Flow Meter Martijn C. Clarijs, Victor R. Bom, Carel W. E. van Eijk, Zvonimir I. Kolar, and Lex M. Scheers Abstract This paper describes the design of a geometry for the generation of X-rays to measure the relative amounts of oil, water, and gas in a flow. The measurement principle is based on the attenuation of X-rays in the mixture. The X-rays are generated by fluorescence in slanted foils placed in front of an end-window X-ray tube. EGS4 Monte Carlo simulations have been used to determine an optimum geometry. We conclude that with an X-ray tube power in the order of only 2.5 W, successful multiple energy X-ray absorption analysis should be possible. Index Terms Multiphase flow, X-ray transmission. I. INTRODUCTION WITH the production of crude oil, large amounts of gas and water are often present in the oil flow. Measurement of the individual oil, water and gas flow rates is required for the purpose of reservoir management and production allocation. The technique of dual energy gamma ray absorption (DEGRA) [1] can be used to determine the oil, water and gas volume fractions in the mixture. A composition measurement consists of the determination of the attenuation by the mixture of gamma or X-rays at two or more energies. An important disadvantage of commercially available systems is the use of radioactive sources to generate the radiation. By using an X-ray tube, license requirements are relaxed, and, in addition, one is no longer restricted to fixed radio-nuclide photon energies but one is in principle free to choose the energies. It can be shown [2], [3] that for mixed oil,water, and gas flows an optimum set of energies exists. A study into the generation of X-rays with an X-ray tube suitable for DEGRA was performed using the well known EGS4 (version 3) Monte Carlo simulation computer code [4] [6]. EGS4 simulates the transport of electrons and photons through matter and has been extensively adopted by a broad scientists community. It is a well documented and tested public domain code. Manuscript received January 31, 2002; revised December 18, This work was supported by BTS through the Dutch Ministry of Economic Affairs. M. C. Clarijs, V. R. Bom, and C. W. E. van Eijk are with the Radiation Technology Group, Interfaculty Reactor Institute, Delft University of Technology, 2629JB Delft, The Netherlands ( vb@iri.tudelft.nl). Z. I. Kolar is with the Department of Radiochemistry, Interfaculty Reactor Institute, Delft University of Technology, 2629JB Delft, The Netherlands ( kolar@iri.tudelft.nl). L. M. Scheers is with Shell International Exploration and Production, 2280 AB Rijswijk, The Netherlands ( a.m.scheers@siep.shell.com). Digital Object Identifier /TNS II. GENERAL CONSIDERATIONS The main feature of the photon spectrum from an X-ray tube is the bremsstrahlung continuum that is emitted when electrons are decelerated in the anode. Besides this continuum, the spectrum contains the characteristic X-ray peaks from the anode material. An example is shown in Fig. 1 as the result of a simulation of 120 kev electrons incident on a tungsten anode in a side-window X-ray tube. The intensity of the tungsten X-ray peaks is only a few percent of the total spectrum intensity. The following simulation 1 specifics are mentioned. 1) The effects of electron binding with Compton scattering and of electron impact ionization have been included in the simulations. 2) To reduce statistical fluctuations in the resulting X-ray spectra, the bremsstrahlung splitting technique was used [7]. With this technique, when during the simulation a bremsstrahlung interaction occurs, a number of photons are generated instead of only one. This number is called the splitting factor. Later a correction is applied. We used various splitting factors with values up to 400 and verified consistency with the default algorithm for bremsstrahlung in EGS4. In order to determine the composition of the oil/water/gas mixture the intensity of a number of X-ray peaks has to be determined. When the background contribution is low these peak intensities can be determined more accurately. The geometric setup will, therefore, be designed with an optimum peak/background ratio in mind. The background is caused mainly by bremsstrahlung from the anode. The peak/background ratio can thus be improved by conversion of the bremsstrahlung continuum into X-ray fluorescence radiation and by placing shielding around the anode to prevent the bremsstrahlung from reaching the detector position (see Fig. 2). The X-ray fluorescence radiation is produced by placing foils of specific materials in the bremsstrahlung beam. The following processes play a role. Photo-ionization: In this process, an atomic electron is removed, mostly from an inner shell, on impact with a photon. When the vacancy is filled by an electron from an outer shell, either an Auger electron or a fluorescence photon is emitted. 1 For interested EGS4 experts: the fractional energy loss per electron step ES- TEPE = 0.05, ECUT (including the electron rest mass energy of MeV) and PCUT are the cutoff energies of electrons and photons for transport, respectively; ECUT = MeV, PCUT = MeV, UE, and UP are the upper cut-off energies of electrons and photons for each medium, respectively; UE = MeV, UP = 0.1 MeV and PRESTA is the electron transport algorithm that is used; default PRESTA input: 0, 0, 0, 0, /03$ IEEE

2 714 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 50, NO. 3, JUNE 2003 Fig. 1. The result of a simulation of the X-ray spectrum generated by 120-keV electrons incident on a tungsten anode in a side-window X-ray tube. Fig. 2. Schematic view of the geometry which was simulated. The angle between the foil surface and the +z-direction is =45. Electron impact ionization: This process leads to a vacancy when an incident electron interacts with the atomic electron cloud. Both processes are included in the simulations. Fluorescence radiation is emitted as a complex of lines (i.e.,,, etc.) with different energies. The energies have the highest radiation yield. The foil materials are therefore chosen in such a way that their energies have approximately the desired optimum values. A schematic view of the simulated geometry is presented in Fig. 2. The anode is bombarded from the left with electrons that have been accelerated in the X-ray tube. The generated bremsstrahlung continuum is partly absorbed by the foils and converted into fluorescence radiation. This radiation is emitted isotropically; part of it escapes the foils in the direction of the oil pipe that contains the multicomponent mixture. In the simulations only the anode and the foil materials are implemented. The efficiency for creation of bremsstrahlung is very low, in the order of 1% for 100-keV electrons. In order to obtain maximum intensity, the opening angle of the effective part of the foils, as defined by the various collimators in the setup, with respect to the anode must be as large as possible. The foils must therefore be placed as close to the anode as possible. Such a compact geometry can easily be achieved with an end-window or transmission-type X-ray tube, because the exit window can be integrated with the anode. In a side-window or reflection type X-ray tube, the anode and exit window cannot be integrated, resulting in a separation between the foils and the anode generally in the order of centimeters. In this context an alternative geometry was studied, where the fluorescence foils were directly attached and parallel to the anode, and where the fluorescence radiation was detected in the direction. The disadvantage of this geometry is that the fluorescence radiation is detected together with that part of the bremsstrahlung continuum, which is not absorbed. The bremsstrahlung radiation constitutes a significant background in this case. Whereas this geometry yields peak/background ratios in the order of 10 to 100, the geometry of Fig. 2 results in ratios in the order of 100 to A. Foil Positioning The foil arrangements shown in Figs. 2 and 3 illustrate two possibilities for positioning the foils. In Fig. 2 the foils are arranged in order of increasing atomic number i.e., Ag Sm W, while in Fig. 3 the order is reversed to W Sm Ag. The lower atomic number foils are closer to the detector in both arrangements to ensure that the low-energy fluorescence radiation emitted by these foils is not absorbed in a

3 CLARIJS et al.: X-RAY SPECTRUM GENERATION FOR A MULTIPHASE FLOW METER 715 Fig. 3. Schematic view of a geometry, with an alternative foil ordering. Fig. 5. Simulated spectrum recorded at the detector position in the geometry from Fig. 3. Simulation specifics identical to Fig. 4. Fig. 4. Simulated spectrum recorded at the detector position in the geometry from Fig. 2. Using a 10-m-thick W anode and Ag, Sm, and W foils with thicknesses of 50, 200, and 100 m, respectively. A detection area of 5 2 5mm is positioned at 20-cm distance from the foils. The X-ray tube power is 50 W. material with a higher atomic number. The thicknesses of the Ag, Sm, and W foils are determined by the following two conflicting requirements: 1) foil must be thick in order to sufficiently absorb the bremsstrahlung from the anode; 2) it should be thin in order to reduce the attenuation of the generated fluorescence radiation in the foil itself. In addition to this, fluorescence radiation originating from the W and the Sm foils is absorbed in the Sm and Ag foils and is once again converted into fluorescence radiation. III. SIMULATION RESULTS Simulations were performed in order to quantify the interplay of the processes mentioned in the previous section. An anode of tungsten was simulated, with kev. This is a common choice, as tungsten has not only a high atomic number, but also a very high melting point. The transmission anode in the simulations has a thickness of 10 m, sufficient for absorbing 100-keV incident electrons. At the same time this low thickness minimizes absorption of the bremsstrahlung in the anode itself. The focal spot size of the electron beam is assumed to have an area of 1mm. Because of the vacuum inside the X-ray tube the anode must be strong enough to withstand the atmospheric pressure difference. In addition, the heat dissipated by the electron beam in the anode must be adequately dissipated. This can be accomplished by a supporting beryllium window in close contact with the anode, providing strength and cooling. Since such a window has negligible effects on the generated X-rays it has been ignored. The foil materials were: Ag, Sm, and W, with energies of 22.2, 40.1, and 59.3 kev, respectively. The minimal foil thicknesses to be applied were based upon the half value layer thickness where is the photon energy, and is the linear attenuation coefficient. The minimal foil thickness is taken equal to evaluated at an energy just above the -edge, where fluorescence is most efficient. For instance, for Ag, m for kev. The range of Ag foil thicknesses studied in the simulations was, therefore, 20 m. By nature the spectra show statistical fluctuations. To minimize these fluctuations the spectra are calculated by recording all photons escaping the foils with an angle 10 with respect to the direction toward the detector center. Afterwards a correction is performed for the solid angle of the detection area. For a detection area of 5 5mm at 20 cm distance, a correction factor of needs to be applied. It has been verified by simulations that the angular distribution within this 10 angle is constant within 5%. Figs. 4 and 5 show simulated spectra generated with the geometries from Figs. 2 and 3, respectively. The continuous part of the spectrum originates from scattering in the foils. The average peak/continuum ratios vary between 100 and (1)

4 716 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 50, NO. 3, JUNE 2003 The fluorescence intensities from the geometry of Fig. 2 are considerably higher than those from the geometry of Fig. 3. The explanation for this is the good match between the order of the foils in Fig. 2 and the shape of the bremsstrahlung spectrum from the anode. The low-energy photons with kev (Ag -binding energy) are effectively absorbed in the Ag foil and at the same time the transmission of photons with kev (Sm -binding energy) is acceptable, which results in sufficient generation of fluorescence in the Sm foil. Finally, the intensity of photons with kev (W -binding energy) that are not absorbed in the Ag and Sm foils is high enough for generation of fluorescence in the W foil. A. Foil Rotation The spectrum of Fig. 4 corresponds to an inclination angle between the surface of the foils and the direction. A lower value for the foil inclination angle is anticipated to yield higher fluorescence intensities, since absorption in the direction increases and attenuation of fluorescence photons in the direction of the pipe decreases. Simulations have been performed with the Fig. 4 geometry, but with foil inclination angles of 15,30,60, and 75. The results for the total K fluorescence intensity show that a lower value for the inclination angle is indeed more favorable: compared to the 45 angle, the fluorescence intensities for Ag, Sm, and W change by 20%, 10%, 10%, and 30% for the angles mentioned. A smaller inclination angle is especially beneficial for Ag fluorescence, since this is the first foil to be irradiated by the anode X-rays. The influence is less pronounced for Sm and W, because increased absorption in the Ag foil also implies that less transmitted photons are available for fluorescence in the other two foils. The 45 inclination angle is favored because the beneficial effect of a low inclination angle on the fluorescence intensities is only within 20%; the peak/continuum ratios remain equal within 10%; the geometry is symmetric, which facilitates the application of a reference detector. B. Reference Detector During operation of the flow composition meter, the shape and intensity of the fluorescence spectrum are subject to changes due to variations in high voltage and current of the X-ray tube, temperature drift, mechanical vibrations, etc. Although the mentioned spectrum changes are small, their effect is not negligible because the composition analysis is sensitive to small deviations in measured peak intensities [8]. To eliminate the influence of the mentioned changes a second detector must be used to monitor the spectrum emitted by the foils. This reference spectrum is not transmitted through the oil pipe and, since it is preferable to have equal intensities emitted in the direction of the oil pipe detector as well as in the direction of the reference detector, the latter should be symmetrically positioned with respect to the foils. A possible geometry of the foils and the detectors is shown in Fig. 6. The gray plane in the figure represents the surface of the fluorescence foils. The X-rays from the anode, indicated by their Fig. 6. The geometry of the foils and the detectors in case a reference detector is included. The radiation from the X-ray tube is incident along the bold arrow on the left. Fluorescence radiation is emitted toward two detectors (indicated by D1 and D2), symmetrically positioned in mutually perpendicular directions, with an angle of 30 with respect to the foil surface. central axis (bold arrow on the left), are incident with an angle of 45 with respect to the foil surface. The incoming X-rays and the two detectors (indicated by D1 and D2) are placed in mutually perpendicular directions. Fluorescence radiation is now emitted toward these detectors with an angle of 30 with respect to the foil surface. This implies that, compared to the simulations with a geometry with only one detector, the attenuation of the fluorescence radiation in the foils has increased. This is taken into account in the simulations of Section IV. Simulations on different foil combinations confirmed that the intensity of the fluorescence radiation emitted in the directions of both detectors are equal within the statistical uncertainty. IV. OPTIMUM GEOMETRY The optimum X-ray energies for multiple energy X-ray analysis in the case of an oil/water/gas mixture are 21 and 49 kev [2]. These energies ensure that the analysis is least sensitive to line intensity variations. They can be obtained with foils of Ag and Sm. When the X-rays are detected with a Si detector with a thickness of 0.5 mm, the optimum intensities are photons/s for 21 kev and photons/s for 49 kev. This includes compensation for the energy dependence of the efficiency of the detector. These intensities are chosen such that the total count rate of the detector is limited to 10 counts/s, which is considered the maximum rate that can be handled. The focal spot size of the accelerating system in the X-ray tube is set to mm. The Be exit window of the end window X-ray tube with a total thickness of 1 mm was not included in the simulations. Furthermore, the center of the first foil is positioned at 1 cm from the anode. The oblique orientation of the fluorescence foils (see Section III-B) is taken into account in the simulations. The detector size (5 5mm) in combination with the collimator system between the foils and the detector define an effective area on

5 CLARIJS et al.: X-RAY SPECTRUM GENERATION FOR A MULTIPHASE FLOW METER 717 A. Foil Order The optimum X-ray spectrum is characterized by an intensity ratio for the Sm and Ag fluorescence intensities (Sm) (Ag) of 10 [8]. Simulations of geometries with a Ag foil in front of a Sm foil illustrate that this ratio is difficult to achieve. The Ag foil yields a higher fluorescence intensity than the Sm foil, because it is unshielded from the anode by other foils. A combination of a very thin Ag foil in front of a thick Sm foil will provide the maximum (Sm) (Ag) intensity ratio that can be achieved. From simulations with a 10- mag combined with a 5-mm Sm foil, a maximum fluorescence intensity ratio of 1.6 is calculated. Therefore, the Ag/Sm foil order does not yield suitable spectra for flow composition analysis. The foil order with a Sm foil in front of a Ag foil is intrinsically more suitable because then the Sm fluorescence intensity increases at the expense of Ag fluorescence intensity. In addition to reversing the foil order, gold is now chosen as anode material. The higher of gold as compared to tungsten will result in a bremsstrahlung continuum with a higher intensity, as the bremsstrahlung cross-section scales with. This will also help to increase the intensity of the Samarium peak. The Au anode has a thickness of 8 m, sufficient for absorbing 100 kev electrons and, at the same time, minimizing self absorption. From simulations on different Sm/Ag foil combinations we derived the following thicknesses: 90 m Sm and 100 m Ag. The corresponding (Sm) (Ag) fluorescence intensity ratio is 9.5, close to the required value of 10. Fig. 7. The optimum spectrum: Au anode with a thickness of 8 m, focal spot size of mm,90m Sm and 100 m Ag foils positioned at 1 cm from the Au anode under an angle of 45, with respect to the central axis of the primary X-rays. A detector area of 5 2 5mm is situated at 20-cm distance from the foils. The X-ray tube power is 50 W. the foils. Fluorescence photons from this area can reach the detector; it is set to 25 mm, equal to the detector surface area. The simulations only record the photons that are emitted from the effective area with an angle 10 with respect to the direction toward one of the detectors. Spectral intensities are obtained after correction for the solid angle between foil and detector. B. The Spectrum The resulting spectrum is shown in Fig. 7. The fluorescence intensities are photons/s and photons/s for Sm and Ag, respectively. The peak/continuum ratio for Sm fluorescence is in the order of 1000, however, for Ag this value is 100 due to the lower fluorescence intensity. The background in the spectrum up to 100 kev takes up 15% of the total intensity. The low peaks at 6 kev originate from Sm -fluorescence and are not anticipated to show up in the detected spectrum due to absorption in the pipe contents and in the windows. The maximum Ag and Sm intensities and photons/s, respectively [2], are lower than the intensities in the spectrum by a factor 20. It follows that, with an X-ray tube power in the order of 2.5 W, successful composition analysis should be possible. ACKNOWLEDGMENT The authors would like to thank Mr. Caon from Flinders University of South Australia and Mr. Hirayama and Mr. Namito from National Laboratory for High Energy Physics, Japan, for their helpful discussions and for providing the necessary patches for the simulation software. REFERENCES [1] M. B. Hoppenbrouwers, Design of a multi phase composition meter for oil water gas mixtures based on dual energy X-ray transmission, Stan Ackermans Institute, Eindhoven, STUDREP , Jan [2] V. R. Bom, M. C. Clarijs, C. W. E. van Eijk, Z. I. Kolar, and A. Scheers, The optimal X-ray energy problem in multi phase flow metering, IEEE Trans. Nucl. Sci., vol. 50, pp , June 2003, submitted for publication. [3] M. C. Clarijs, V. R. Bom, Z. I. Kolar, C. W. E. van Eijk, J. Frieling, A. Scheers, and A. E. J. Reimerink, Optimized X-ray spectra for multiphase-flow measurements, in Proc. BB-67-CD, Computerized Tomography for Industrial Applications and Image Processing in Radiology, Berlin, Germany, Mar. 1999, pp [4] W. R. Nelson and T. M. Jenkins, Computer Techniques in Radiation Transport and Dosimetry. New York: Plenum, [5] W. R. Nelson, H. Hirayama, and D. W. Rogers, The EGS4 Code System, Stanford Linear Accelerator Center, Stanford, CA, SLAC Rep [6] T. M. Jenkins, W. R. Nelson, and R. Rindi, Monte Carlo Transport of Electrons and Photons. New York: Plenum, [7] M. C. Clarijs, Design studies on cardiovascular and intraoperative brachytherapy and multiphase flow metering, new applications of radiation in medicine and industry, Ph.D. dissertation, Delft Univ. Press, Delft, The Netherlands. [8] V. R. Bom, M. C. Clarijs, C. W. E. van Eijk, Z. I. Kolar, J. Frieling, A. M. Scheers, and G. Miller, Accuracy aspects in multiphase flow metering using X-ray transmission, in Proc. Conf. IEEE 2000, vol. 1(1008), Lyon, France, [9] N. van Santen, Z. I. Kolar, and A. M. Scheers, Photon energy selection for dual energy - and/or X-ray absorption composition measurements in oil water gas mixtures, Nucl. Geophys., vol. 9, pp , 1995.