X-ray Computed Tomography in Mechanical Engineering A Non-intrusive Technique to Characterize Vertical Multiphase Flows

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1 DGZfP Proceedings BB 67-CD Poster 11 Computerized Tomography for Industrial Applications and Image Processing in Radiology March 15-17, 1999, Berlin, Germany X-ray Computed Tomography in Mechanical Engineering A Non-intrusive Technique to Characterize Vertical Multiphase Flows T. Grassler and K.-E. Wirth, Erlangen, Germany Abstract Since years high-loaded riser-reactors have been used successfully for different commercial applications, e.g. for fluid catalytic cracking. The fundamental study of hydrodynamics of such reactors will help to improve the design and operating conditions of existing plants and may lead to higher conversion rates and selectivity. The solids concentration distribution of a riser with an inner diameter of.19 m and 15 m height is investigated with x-ray computed tomography with a minimum spatial resolution of.2 mm and.4 mm thickness. A number of experiments have been carried out with narrowly size distributed glass beads between 5 and 7 µm at superficial gas velocities from 2 to 7 m/s. Even at higher circulation rates obtained radial solids concentration profiles still show a typical core-annulus structure, which gets more uniform at higher elevations. Keywords: Circulating Fluidized Bed; Riser Reactor; X-Ray Computed Tomography Introduction Heterogeneous catalytic reactions are often accompanied by consecutive and side reactions, which lead to a decrease in selectivity and yield of the desired product. Therefore the used gas-solid reactor demands to be characterized by a narrow residence time distribution for the gas and solid phase. Recently an increasing number of heterogeneous catalytic reactions are carried out in riser-reactors, which are a specific design of a circulating fluidized bed (CFB) (Berutti et al., 1995; Zhu and Bi, 1995; Contractor and Chaouki, 199). The characterization of the gas-solids flow inside the reactor, especially the knowledge about the solids distribution in the vertical tube, is the basis for reactor design as well as for finding suitable operating conditions and for modeling multiphase flows. Moreover most of the models concerning heat transfer in circulating fluidized beds require precise information about particle concentration near to the heat transfer surface (Goedicke, 1992). In most of the studies, concerned with characterizing flow patterns in a riser, solids concentration distributions are calculated from vertical pressure gradients or measured with various kinds of intrusive probes (Grace et al., 1997; Issangya et al., 1998; Wei et al., 1995; Schnitzlein and Weinstein, 1988). However, pressure drop profiles only lead to integral values of solids concentration along a certain length of the riser, if acceleration and deceleration effects are neglected. By using probes a disturbance DGZfP Proceedings BB 67-CD 23 Poster 11

2 of the gas-solids flow can never be excluded and often a large-scale calibration is necessary. As a non-intrusive technique with high spatial resolution to determine the local solids distribution in the tube cross-section of the riser an x-ray computed tomography system has been applied. Tomographic measurements have been carried out at three elevations of a cold-running riser in a technical scale, which show the potential and the limits of such a system in process engineering. Principle of X-ray Computed Tomography In order to measure the solids concentration distribution in the cross section of the riser an x-ray computed tomography system has been installed. Computed tomography is a technology, that allows the non-destructive evaluation of the internal structure of objects. Since a lot of years this technique has been used successfully in medicine and material testing to examine local differences in density by generating images of different cutting planes of the object concerned. Recently some efforts have been made to use γ-ray and x-ray computed tomography in multiphase flows (Chaouki et al., 1997; Scott and Williams, 1996). Computed tomography systems consist of two main parts: a physical measuring technique, which yields to integral values of the local density along certain paths, and a mathematical reconstruction algorithm, which calculates the local concentrations from the obtained raw data. In literature a lot of physical sensing methods, available for tomographic measurements, and as well a great number of possible reconstruction techniques can be found (Williams and Xie, 1993). The distributions of local solids concentration in a riser mentioned in this paper are obtained from a physical measuring system, which consists of an x-ray source and an x-ray linear detector to measure the attenuation along a multitude of ray paths through the sample. These data are reconstructed by an Algebraic Reconstruction Technique (ART) (Gordon, 1974; Herman et al., 1973), which is the most common algorithm for industrial applications with limited measurement information. Energy spectrum of x-rays X-rays for technical purposes are normally produced in an x-ray tube. Electrons emitted from a cathode which is heated by a filament are accelerated toward the anode by high voltage between the two electrodes. When the electrons hit the anode, designated as target, they are decelerated which is accompanied by the emission of electromagnetic radiation. The wavelength characteristics of this continuous spectrum are completely independent of the target material and depend only on the voltage V applied to the x-ray tube (Mulligan, 1985). The higher the voltage, the shorter the minimum or cutoff wavelength produced. The cutoff wavelength λ can be calculated by the following empirical equation, where h is the Planck s constant, c the velocity of light and e represents the electronic charge: h c h c 6 λ = with = m V e V e (1) DGZfP Proceedings BB 67-CD 24 Poster 11

3 The spectral intensity distribution I of the electromagnetic radiation as a function of the wavelength λ can be approximately calculated from (Minder and Liechti, 1955): () λ I λ λ = 3 λ λ (2) Figure 1: Schematic emissions spectrum of an x-ray source (Hering, 1992) Equation 2 gives the spectral intensity in any dimensions and represents only the shape of the continuous spectrum. In addition to that continuous spectrum sharp lines occur in the x-ray region of the spectrum. These lines are superimposed on the continuous x-ray spectrum and can be explained on the basis of the simple Bohr theory. In the target electrons can be removed from the atom by electron collision processes. Then electrons from outer shells can fall into the gap which produces characteristic radiation. This process is strongly influenced by the pattern of the electron sheath and therefore by the material of the target. The addition of the continuous spectrum and the characteristic line spectrum to the whole x-ray spectrum is shown in Figure 1 on principle. Interaction of x-rays with material If x-rays pass through an object, the original spectral intensity distribution is influenced, depending on the material and the thickness of the object. The irradiation of an infinitesimal thin layer of material ds with a monoenergetic parallel beam causes a decrease in the intensity di of the radiation, which depends on the linear absorption coefficient of the material µ: di = I µ ds (3) With integrating over the whole thickness L of the object the residual intensity I of an original intensity I can be calculated: DGZfP Proceedings BB 67-CD 25 Poster 11

4 I = I e µ L (4) In practice, the linear absorption coefficient µ is no matter constant, but depends on the spectral intensity distribution of the radiation source, the density ρ of the object and the atomic number Z. The reason for the decrease in intensity by penetrating material are three different effects: photoelectric effect, scattering (coherent, incoherent), pair production (Morneburg, 1995). Photoelectric effect and Auger effect: An x-ray quantum hits an electron of the electronic sheath with enough energy to remove this electron. The atom returns to a state of lower energy by filling the hole with an electron from an outer shell and by simultaneously emitting an electromagnetic quantum. If this quantum hits an electron in an outer shell so that the electron is removed, the process is called Auger effect. Coherent scattering: When a beam of x-rays passes an electron of the electronic sheath, part of it is scattered into a spherical wave diverging from the location of the electron. X-ray quantums are diffracted from their original direction with retention of the energy. Incoherent scattering or Compton effect: When a relatively hard x-ray quantum is scattered by electrons, it partially loses energy to the scattering electron so that the energy leaving the atom is lower. Pair production: If the energy of an quantum is greater then 1.22 MeV, it may be absorbed in the field of an atomic nucleus with the creation or generation of an electron-positron pair. The quantum energy is partly converted into the rest energy of the two created particles, the excess going into their kinetic energy. Attenuation coefficient η [cm 2 /g] Total attenuation Photoelectric absorption Incoherent scattering Coherent scattering Pair production in nuclear field Pair production in electron field Photon Energy E [kev] Figure 2: Attenuation coefficients of glass (Hubbell, 1999) DGZfP Proceedings BB 67-CD 26 Poster 11

5 The linear absorption coefficient µ can be calculated by adding the extinction coefficients of the different processes of attenuation (Figure 2) described above. Tomographic measuring equipment The x-ray computed tomography system mainly consists of a 6 kev x-ray source with an angle of illumination of about 35 and a x-ray linear detector with 124 sensitive elements. Both components are mounted on a stainless steel ring, which can be rotated with the support of a step-by-step motor. The set-up of the measuring system is shown in Figure 3. Step-by-step motor X-ray source RISER X-ray linear detector Figure 3: Set-up of the x-ray computed tomography system The principle of transmission tomography measurements with a radiation source producing a fan beam is pictured in Figure 4. The object, in our case the tube of the riser, is irradiated by fan beams from two different directions in one particular plane. Integral values I of the concentration distribution inside the beam are measured opposite to the radiation source. The whole fan beam can be split up into a number of approximately linear beams, each of them following Beer s Law (Equation 4). So from measured intensities with and without a gas-solids-flow inside the tube, I and I respectively, the average solids concentration 1-ε along one path of the x-ray beam s can be calculated: 1 ε = µ 1 I ln () s ds I (5) DGZfP Proceedings BB 67-CD 27 Poster 11

6 I Computerized Tomography and Image Processing, 1999 I S 1 S 2 Figure 4: Principle of tomographic measurements The attenuation due to the gas can be neglected in comparison to the solids. As shown above, the linear absorption coefficient µ is influenced by a number of different variables and therefore it is a function of the beam coordinate s. To calculate average solids concentration according to Equation 5, a calibration for the whole system is necessary. Figure 5 shows values of the linear detector I for different integral values of solids concentration L(1-ε), which have been measured for glass beads with three different intensity distributions of the x-ray source. The intensity distribution was varied by changing the voltage V applied to the x-ray tube and by using a 4,5 mm aluminum filter to harden radiation. Measured 8-bit value Ι [-] V = 35 kv without filter V = 6 kv without filter V = 6 kv filtered with 4,5 mm aluminum Integral value of solids concentration L(1-ε) [mm] Figure 5: Calibration of the x-ray computed tomography system DGZfP Proceedings BB 67-CD 28 Poster 11

7 The three different calibration functions also show the operative range of this tomographic system. In order to measure low solids concentrations with an optimum of resolution the voltage V applied to the x-ray tube should be the minimum possible without using any filter. In our case with a tube diameter of.19 m average solids concentrations (1-ε) from almost up to 3 Vol-% can be detected with 35 kev applied. High voltage V should be increased and radiation should be filtered to measure highest concentrations. With a voltage of 6 kev an a 4,5 mm aluminum filter it is possible to use the system for average solids concentrations up to 2 Vol-%. The problem of applying higher voltage however is that resolution for low concentrations is worse and using filters increases the time for one measurement because of lower radiation intensities. So far it is possible to calculate the integral value of solids concentration for each approximately linear beam. To calculate the local solids distribution inside the tube, it is necessary, to know integral values for a number of different directions across the whole fan beam at a time. The calculation of local values is carried out by an Algebraic-Reconstruction-Technique (ART), which is an iterative algorithm to solve underdeterminated linear equation systems. For industrial applications ART is rather used than e.g. Fourier inversion or convolutional backprojection, because it shows better results with limited data and it is very easy to incorporate prior knowledge like restrictions in the reconstruction area (Williams and Xie, 1993). Due to the statistic nature of the generation of x-rays a minimum recording time at each direction is necessary to achieve a given resolution of the solids concentration. As a consequence, only time averaged solids concentrations can be obtained. One solids concentration profile needs about 2 to 4 minutes to be measured, depending on the concentration inside the tube. However, the main advantage of this technique is the non-intrusive measurement of local solids concentrations even near to the wall of the tube, where other systems like intrusive probes deliver no reliable results because of too large measurement volumes. In addition to that, the spatial resolution of the system is relatively high. The system used allows a minimum spatial resolution of.2 mm. Finally x-ray computed tomography is insensitive to electronic charging of the gas-solids flow in the riser, which normally is a great problem especially for capacitance probes. Riser Setup The x-ray computed tomography system used is installed at a cold-running riser with an inner diameter of.19 m and 15 m height and can be moved to four different elevations. Figure 6 shows a sketch of the riser set-up built up to investigate the behavior of high-loaded riser-reactors. The riser consists of tube elements made of stainless steel. In order to measure the solids distribution inside the riser with the tomographic system four.5 m long acrylic glass tube elements are inserted between the stainless steel elements. With acrylic glass tube elements instead of stainless steel elements the decrease in intensity only because of tube material is reduced. Air is provided by a blower and mixed with solids in the gas-solids-distributor. This should realize a well distributed gas-solids-flow at the beginning of the tubular reactor. Both phases flow against the direction of gravity, vertically upwards, which explains the name for this type of reactor. At the end of the reaction zone both phases are quickly and completely separated in two cyclones in series. Solids move DGZfP Proceedings BB 67-CD 29 Poster 11

8 downwards through a hopper with a valve into the downer and then through an angled standpipe back into the gas-solids distributor. The gas flow rate through the riser is measured by an orifice meter. There are 18 differential pressure transducers along the riser height to observe static pressure. The solid flux circulating in the plant can be measured by closing the valve below the hopper and weighing the variation of solid accumulation inside the hopper. Experiments have been carried out with narrowly size distributed glass beads between 5 and 7 µm, which are ideal spherical and insensitive to breakage and attrition, at superficial gas velocities U G from 2 to 7 m/s. This leads to solids circulating mass fluxes G S from 3 up to 6 kg/(m²s) and average solids concentrations (1-ε) av. of 1.8 to 17.2 Vol-%. 18: : : 12.1 elevation 4: : : : 9.6 elevation 3: : : 8.1 1: 7.6 cyclone 2 cyclone 1 hopper valve Results an Discussion Axial pressure profile Integral information about the flow conditions inside a circulating fluidized bed can be obtained by pressure profile readings. Figure 7 shows the axial development of the pressure with reference to the first pressure tap at the top of the riser tube for a specific mass flow rate of G S = 195 kg/(m²s) and a superficial gas velocity U G = 2.7 m/s. The axial pressure profile shows the typical shape for a riser with a lower steady-state section characterized by a high constant pressure gradient, an upper steady-state section with a low constant pressure gradient and the Transport Disengaging Height (TDH) (Grace et al., 1997; Molerus and Wirth, 1991; Wirth, 199) between these sections from about 5 m up to 9 m. 9: 7.1 elevation 2: 6.8 8: 6. 7: 5. elevation 1: 4.4 3: 1.4 2:.9 1:.4.5 6: 4. 5: 3.4 4: 2.4 Ø.19 Ø.19 Ø.15 RISER DOWNER acrylic glass valve angled standpipe gas-solids-distributor Figure 6: Sketch of the riser setup DGZfP Proceedings BB 67-CD 21 Poster 11

9 14 Height above distributor h [m] Static pressure p [hpa] Figure 7: Axial pressure profile (G S = 195 kg/(m²s), U G = 2.7 m/s) X-ray computed tomography Figure 8 shows results from the tomographic system measured at the same operating conditions as the axial pressure profile in Figure 7. In this case the radial concentration profiles are reconstructed from 128 angular projections to a 256 x 256 reconstruction grid according to a spatial resolution of.8 mm. At each angular position the x-ray linear detector is read out 2 times and the results are averaged. This implies an integration time of about 15 s for each of the 128 projections and in total a time of 3 minutes for one radial concentration profile. In Figure 8 the tube material is shown as an intense black circle enclosing the radial solids concentration profile. All three radial concentration profiles show a parabolic shape with a maximum concentration close to the wall and a minimum concentration in the center of the tube. The mean value of solids concentration (1-ε) av. over the whole cross section decreases from elevation 1 to elevation 4, i.e. from the bottom of the riser to the top. At the bottom local solids concentration up to 45 Vol-% are reached near the wall of the riser, which is close the minimum fluidization concentration. This corresponds to the pressure profile, where high pressure gradients indicate high solids concentration, if acceleration and friction effects are neglected. DGZfP Proceedings BB 67-CD 211 Poster 11

10 ,2,15,1,5, (1-ε) elevation 4 (h = 11.6 m): (1-ε) av. = 2.3 Vol-%,4,3,2,1 (1-ε) elevation 2 (h = 6.8 m): (1-ε) av. = 5. Vol-%,,8,6,4,2 (1-ε) elevation 1 (h = 4.4 m): (1-ε) av. = 15.8 Vol-%, Figure 8: Results of x-ray computed tomography (G S = 195 kg/(m²s), U G = 2.7 m/s) DGZfP Proceedings BB 67-CD 212 Poster 11

11 Since all profiles in this paper show approximately radial symmetry, solids concentration profiles over the radial position r in the tube have been calculated by averaging circular rings of the tomographic profiles. The results are presented in Figure 9 and Figure 1. In Figure 9 profiles of absolute solids concentrations (1-ε) are plotted, whereas Figure 1 shows solids concentrations with regard to the cross-sectional area weighted solids concentration(1-ε) av.. Both figures show the increase of solids concentration from the top of the riser down to the bottom and from the center of the tube to the wall. According to Figure 1 solids distribution is getting more uniform from the bottom up to the top of the riser. Moreover it is remarkable, that solid concentration decreases rapidly close to the wall at every elevation, but remains higher than in the center of the tube. Absolute solids concentration (1-ε) [-],45,4,35,3,25,2,15,1,5 elevation 4 elevation 2 elevation 1, Radial position r [mm] Figure 9: Radial profile of absolute solids concentration (G S = 195 kg/(m²s), U G = 2.7 m/s) Rel. solids concentration (1-ε)/(1-ε) av 3, 2,5 2, 1,5 1,,5 elevation 4 elevation 2 elevation 1, Radial position r [mm] Figure. 1: Radial profile of relative solids concentration (G S = 195 kg/(m²s), U G = 2.7 m/s) DGZfP Proceedings BB 67-CD 213 Poster 11

12 This effect already have been observed in a square circulating fluidized bed measured with γ-radiation (Wirth et al., 1991), but can not easily be detected by many probe systems, because of poor spatial resolution and because of wall effects influencing most of the sensing techniques used. Even with a computed tomography system accuracy of measurements near the wall of the tube is reduced because of an orthogonal grid necessary for the reconstruction algorithm. Comparison of x-ray computed tomography to pressure profiles From pressure profiles mean values of solids concentration between two pressure taps can be calculated according to the following equation: ( 1 ε) = 1 p ( ρ ρ ) g h S F (6) If acceleration and friction effects are neglected, the mean value of solids concentration is calculated from the pressure drop p over the distance between two pressure taps h with the knowledge of solids density ρ S and fluid density ρ F. Figure 11 shows the axial solids concentration profile calculated from the pressure profile in Figure Height above distributor h [m] pressure profile tomographic measurement,5,1,15,2,25,3,35 Absolute solids concentration (1-ε) [-] Figure 11: Axial solids concentration profile (G S = 195 kg/(m²s), U G = 2.7 m/s) Figure 11 also contains mean values of the tomographic measurements at the considered elevations. They show good coincidence to the values calculated from the pressure profile, however especially at the highest elevation relative deviations up to 1 % have been observed at higher superficial gas velocities than 2.7 m/s because of exit effects influencing pressure readings. DGZfP Proceedings BB 67-CD 214 Poster 11

13 First results of dual energy x-ray CT A lot of commercial applications like fluid catalytic cracking are carried out in a threephase flow inside the CFB, where liquid educts are injected additionally to the circulating catalyst. In that case the attenuation due to the liquid cannot be neglected in comparison to the solids. If the computed tomography system is used as described above, liquid cannot be separated from solids and appears like solids with lower concentration in the reconstruction area. In order to investigate three-phase flows in a CFB the tomographic system is operated at two different x-ray energies. If the attenuation due to the gas is neglected and the attenuation properties of fluid and solids are significantly different, then the two materials can be imaged separately (Engler and Friedman, 199). As mentioned above the linear absorption coefficient µ, which describes the attenuation of different materials, is influenced by a number of variables. Therefore the whole system has to be calibrated by measuring the attenuation of different integral concentrations of respective materials. The integral solids and fluid concentration radiated by the x-ray beam can be varied with different layers L of material having a specific volume concentration (1-ε S ) respectively c F. Figure 12 shows values of the linear detector I/I for different integral values of solids L. (1-ε S ) and fluid concentration L. c F, which have been measured for aluminum silicate and water at two voltages V applied to the x- ray tube aluminum silicate 45 kev aluminum silicate 6 kev water 45 kev water 6 kev Measured 8-bit value I/I [-] Integral value of solids and fluid concentration L. (1-ε S ) and L. c F [mm] Figure 12: Calibration of the x-ray computed tomography system for three-phase flows If the system is used for gas-solids flows only one calibration function at one voltage is necessary. From the measured 8-bit value I/I given by the x-ray linear detector the integral value of solids concentration L. (1-ε S ) along the beam path can be calculated and then processed by the reconstruction algorithm. In case of dual-energy computed tomography an equation system can be written according to Beer s law in order to calculate the integral solids and fluid concentrations from two tomographic measurements (I/I ) 45 kev and (I/I ) 6 kev carried out with two different x-ray voltages V : DGZfP Proceedings BB 67-CD 215 Poster 11

14 I I 45 kev = exp L µ S () s ( ε ) µ () 45 kev 1 S ds F s 45 kev c F ds L (7) I I 6 kev = exp L µ S () s ( ε ) µ () 6 kev 1 S ds F s 6 kev cf ds L (8) The unknown integral solids concentration L. (1-ε S ) and the unknown integral fluid concentration L. c F can be calculated simultaneously using the results of the calibration process. In order to accelerate this calculation during the reconstruction process the equation system (Equation 7 and 8) can be solved in advance for all possible combinations of (I/I ) 45 kev and (I/I ) 6 kev. Then the integral values of solids and fluid concentration L. (1-ε S ) and L. c F are used to reconstruct the solids and fluid concentration distribution in the measuring area with the help of ART. To prove the reliability of such a strategy two objects made of extremely thin latex one filled with aluminum silicate and one with water have been investigated. The attenuation of the thin latex layer around the object can be neglected in comparison to solids and fluid, what has been tested before. Figure 13 shows the dimensions and volume concentrations of the test object consisting of aluminum silicate in the left and water in the right. This object has been measured with single-energy and dual-energy computed tomography. The concentration distribution shown in Figure 14 has been received by operating the x-ray computed tomography system at 6 kev and by using the calibration function of water during the reconstruction process. Due to similar attenuation coefficients of both materials for one x-ray energy no distinction between aluminum silicate and water is possible. When using the tomographic system with two different energies and calculating integral solids and fluid concentrations according to Equation 7 and 8 in preparation to the reconstruction process, both materials can be distinguished as seen in Figure 15 and 16. aluminum silicate: (1-ε S ) =.571 water: c F = 1. Figure 13: Dimensions and volume concentrations of the test object for dual-energy computed tomography DGZfP Proceedings BB 67-CD 216 Poster 11

15 Figure 14: Test object measured with 6 kev and reconstructed with calibration of water Figure 15: Aluminum silicate Figure 16: Water reconstructed reconstructed from dual- energy CT: from dual-energy CT: c F =.887 (1-ε S ) =.588 After the reconstruction process the position of each single material can be obtained very precisely, however the local concentration distributions are not as uniform as they are in the real object. Moreover the cross sectional average of fluid concentration c F differs slightly from the real value. This may be improved, when the difference between the two voltages applied to the x-ray source is increased. With dual-energy computed tomography it is possible to separate various combinations of two different materials e.g. polyvinyl-chloride and water have been tested successfully. As a next step to the investigation of three-phase flows inside a commercially used CFB water injection into a gas-solids flow will be investigated as a simple example of multiphase flows. Conclusions X-ray computed tomography has been used to determine local solids distribution in a cold-running CFB. In comparison to other measuring techniques, especially various kinds of intrusive probes, it combines high spatial resolution with high accuracy. After a simple calibration process this system consisting of a 6 kev x-ray source and a 8- bit x-ray linear detector allows one to measure average solids concentration up to 17.2 Vol-% in a.19 m tube with a minimum spatial resolution of.2 mm. Radial solids concentration profiles show a typical core-annulus structure in the riser with high concentrations close to the wall and a minimum in the center of the tube. DGZfP Proceedings BB 67-CD 217 Poster 11

16 Directly at the wall solids concentration is decreasing rapidly, but is still higher than in the center of the tube. This could cause problems in predicting wall-to-bed heat transfer, if prevalent core-annulus models are used for calculation. Mean values of solids concentration over the cross section of the tube calculated from tomographic profiles show good accordance to values calculated from pressure readings. However, entrance and exit effects influencing pressure profiles cause deviations between both measuring techniques up to 1 %. The main disadvantage of x-ray computed tomography is a rather long acquisition time of about 2 to 3 minutes, which leads to time-averaged results and requires a plant running in steadystate. In addition to investigating gas-solids flow inside a CFB the x-ray computed tomography system has been used to determine two different materials like aluminum silicate and water as a first step to the investigation of three-phase flows. With the help of test objects it has been shown that it is possible to separate two different materials if the x-ray computed tomography system is operated with two different x- ray energies. Notation c 8 velocity of light = m/s c F concentration of fluid - e electronic charge = C E energy of x-ray ev g gravitational acceleration = 9,8665 m/s h height of the riser facility m h Planck s constant = Js I x-ray intensity - I intensity of the x-ray source - L thickness of absorbing material m G S specific solids mass flux kg/(m²s) p static pressure Pa r radial position m s coordinate along an x-ray beam m T transmission factor - U G superficial gas velocity m/s V high voltage applied to the x-ray tube V Z atomic number - ε porosity - 1-ε, 1-ε S solids volume fraction - (1-ε) av. area weighted average solids concentration - λ wavelength m λ cutoff wavelength m µ linear absorption coefficient 1/m η = µ/ρ mass absorption coefficient m²/kg ρ coordinate along a projection m ρ F density of fluid kg/m³ ρ S density of solids kg/m³ DGZfP Proceedings BB 67-CD 218 Poster 11

17 References Berruti, F, Chaouki, J., Godfroy, L., Pugsley, T.S., Patience, G.S.: Hydrodynamics of Circulating Fluidized Bed Risers: A Review, Can. J. Chem. Eng. 73 (1995), pp Chaouki, J., Larachi, F., Dudukovic, M.P. (eds.): Non-Invasive Monitoring of Multiphase Flows, Elsevier, Amsterdam, 1997 Contractor, R. M., Chaouki, J.: Circulating Fluidized Bed as a Catalytic Reactor, in: Circulating Fluidized Bed Technology III, Toronto, 199 Goedicke, F.: Strömungsmechanik und Wärmeübergang in Zirkulierenden Wirbelschichten, PhD-Thesis, ETH Zürich, 1992 Gordon, R.: A Tutorial on ART, IEEE Transactions on Nuclear Science 21 (1974), pp Grace, J.R., Avidan, A.A., Knowlton, T.M.: Circulating Fluidized Beds, Blackie Academic & Professional, London, 1997 Hering, E.: Physik für Ingenieure, VDI-Verlag, Düsseldorf, 1992 Herman, G.T., Lent, A., Rowland, S.W.: ART: Mathematics and Applications, J. theor. Biol. 42 (1973), pp Hubbell, J.H.: XCOM: Photo Cross Section Database, Issangya, A.S., Rai, D., Grace, J.R., Lim, K.S.: Flow Behavior in the Riser of a High- Density Circulating Fluidized Bed, AIChE Symposium Series No. 317, Vol. 93 (1998), pp Minder, W., Liechti, A.: Röntgenphysik, Springer Verlag, Wien, 1955 Molerus, O., Wirth, K.-E.: State Diagrams of Gas/Solid Flows with Partial Phase Separation, Powder and Particle 9 (1991), pp Morneburg, H. (ed.): Bildgebende Systeme für die medizinische Diagnostik, Publicis MCD Verlag, München, 1995 Mulligan, J. F.: Introductory College Physics, McGraw-Hill Book Company, New York, 1985 Schnitzlein, M.G., Weinstein, H.: Design Parameters Determining Solid Hold-up in Fast Fluidized Bed System, in: Circulating Fluidized Bed Technology II, Basu, P., Large, J.F. (eds.), Pergamon Press, New York, 1988, pp Scott, D.M., Williams, R.A. (eds.): Frontiers in Industrial Process Tomography, Engineering Foundation, New-York, 1996 Wei, F., Yang, G.-Q., Jin, Y., Yu, Z.-Q.: The Characteristics of Cluster in a High Density Circulating Fluidized Bed, Can. J. Chem. Eng. 73 (1995), pp Williams, R.A., Xie, C.-G.: Tomographic Techniques for Characterizing Particulate Processes, Part. Part. Syst. Charact. 1 (1993), pp Wirth, K.-E.: Zirkulierende Wirbelschichten, Springer Verlag, Berlin, 199 Wirth, K.-E., Seiter, M., Molerus, O.: Concentration and Velocities of Solids in Area Close to the Walls in Circulating Fluidized Bed Systems, VGB Kraftwerkstechnik 1 (1991), pp Zhu, J.-X., Bi, H.-T.: Distinction Between Low Density and High Density Circulating Fluidized Beds, Can. J. Chem. Eng. 73 (1995), pp DGZfP Proceedings BB 67-CD 219 Poster 11