Quantifying and mitigating thermal interference for electrical capacitance tomography measurement of high-temperature fluidized beds

Abstract

Electrical capacitance tomography (ECT) is an indispensable non-intrusive diagnostic tool for fluidized beds. Although recent advancements have successfully yielded robust sensors capable of surviving high temperatures, temperature-induced permittivity variations pose a formidable challenge to accurate phase reconstruction in high-temperature applications. To systematically quantify and mitigate the unaddressed thermal interference, this study integrates a numerical framework, encompassing different sensor architectures with varying diameters to represent geometries from laboratory to industrial-scale reactors, with high-temperature experiments. The results reveal that although temperature fluctuations induce significant dielectric drifts, the normalized sensitivity distribution maintains exceptional stability. Conversely, raw capacitance measurements are highly susceptible to thermal perturbations within both packed bed and column wall. Crucially, increasing wall thickness drastically amplifies measurement errors for adjacent electrode pairs. To improve measurement robustness, excluding adjacent electrode measurements is shown to effectively suppress temperature-induced deviations and extend the permissible operating range. In exchange for sacrificing fine-scale boundary resolution, the resulting trade-off prioritizes core-region tomographic integrity, mitigating severe thermal interference. Furthermore, the study establishes a theoretical equivalence between thermal distortions and inherent noise, enabling direct application of noise-based criteria to define operational limits. These findings provide practical guidelines for the design and deployment of robust ECT systems in high-temperature environments.

Graphical abstract

Keywords

electrical capacitance tomography / gas-solids fluidized bed / high temperature / image reconstruction / sensitivity distribution

References

[1] Das H J , Mahanta P , Saikia R , Aamir M S . Performance evaluation of drying characteristics in conical bubbling fluidized bed dryer. Powder Technology, 2020, 374: 534–543

[2] Gidaspow D . High production circulating fluidized bed polymerization reactors. Powder Technology, 2019, 357: 108–116

[3] Lü P , Kong X , Wu C , Yuan Z , Ma L , Chang J . Modeling and simulation of biomass air-steam gasification in a fluidized bed. Frontiers of Chemical Engineering in China, 2008, 2(2): 209–213

[4] Tian P , Wei Y , Ye M , Liu Z . Methanol to olefins (MTO): from fundamentals to commercialization. ACS Catalysis, 2015, 5(3): 1922–1938

[5] Gao Z , Abbasian J , Arastoopour H . Modeling and numerical simulation of concentrated solar energy storage using fluidized bed systems. AIChE Journal, 2025, 71(6): e18730

[6] Parvathaneni S , Kodukula B , Andrade M W . Iron-ore reduction in fluidized beds: review of commercial technologies, status, and challenges. Industrial & Engineering Chemistry Research, 2024, 63(44): 18724–18733

[7] Wang Z , Lei Z , Hong R , Li M , He X . Plasma-enhanced synthesis of nitrogen-doped silicon carbide nanopowders in a fluidized-bed reactor for lithium-ion battery anodes. Chemical Engineering Journal, 2025, 514: 163086

[8] Wei X , Liu J , Zhu J . Scale-up effects of the flow structure in bubbling and turbulent fluidized beds. Powder Technology, 2021, 379: 223–230

[9] Lu B , Zhang J , Luo H , Wang W , Li H , Ye M , Liu Z , Li J . Numerical simulation of scale-up effects of methanol-to-olefins fluidized bed reactors. Chemical Engineering Science, 2017, 171: 244–255

[10] Errigo M , Windows-Yule C , Materazzi M , Werner D , Lettieri P . Non-invasive and non-intrusive diagnostic techniques for gas-solid fluidized beds—a review. Powder Technology, 2024, 431: 119098

[11] Tu Q , Ma Z , Wang H . Investigation of wet particle drying process in a fluidized bed dryer by CFD simulation and experimental measurement. Chemical Engineering Journal, 2023, 452: 139200

[12] van Ommen J R , Mudde R F . Measuring the gas-solids distribution in fluidized beds—a review. International Journal of Chemical Reactor Engineering, 2008, 6(1): 77–90

[13] Wu S , Meng F , He Y . Scale resolution of fiber optical signals in circulating fluidized bed. Chemical Engineering Science, 2018, 182: 162–170

[14] Yao J , Takei M . Application of process tomography to multiphase flow measurement in industrial and biomedical fields: a review. IEEE Sensors Journal, 2017, 17(24): 8196–8205

[15] Wang H , Yang W . Application of electrical capacitance tomography in circulating fluidised beds—a review. Applied Thermal Engineering, 2020, 176: 115311

[16] Yang W , Peng L . Image reconstruction algorithms for electrical capacitance tomography. Measurement Science and Technology, 2003, 14(1): R1–R13

[17] Huang K , Meng S , Zhang T , Ye M , Yang W , Liu Z . Study of fluidization behavior transition from Geldart B to A induced by high temperature using electrical capacitance tomography. Industrial & Engineering Chemistry Research, 2023, 62(42): 17201–17215

[18] Huang K , Meng S , Guo Q , Ye M , Shen J , Zhang T , Yang W , Liu Z . High-temperature electrical capacitance tomography for gas-solid fluidised beds. Measurement Science and Technology, 2018, 29(10): 104002

[19] Liu Y , Huang K , Xiang P , Zhao Z , Liu Y , Wang M , Pei C , Gong J . Effects of temperature on gas-solid bubbling fluidization with Geldart A particles characterized by electrical capacitance tomography and pressure drop measurements. Chemical Engineering Science, 2024, 298: 120376

[20] Wang D , Xu M , Marashdeh Q , Straiton B , Tong A , Fan L-S . Electrical capacitance volume tomography for characterization of gas-solid slugging fluidization with Geldart group D particles under high temperatures. Industrial & Engineering Chemistry Research, 2018, 57(7): 2687–2697

[21] Hirose Y , Sapkota A , Sugawara M , Takei M . Noninvasive real-time 2D imaging of temperature distribution during the plastic pellet cooling process by using electrical capacitance tomography. Measurement Science and Technology, 2016, 27(1): 015403

[22] Weiss M , Fischerauer A , Jess A , Fischerauer G . Non-invasive temperature monitoring in fixed-bed reactors by electrical capacitance tomography. Measurement Science and Technology, 2024, 35(9): 095407

[23] Wang S-N , Giorgio-Serchi F , Yang Y-J . A virtual platform of electrical tomography for multiphase flow imaging. Physics of Fluids, 2022, 34(10): 107104

[24] Youngquist R C , Storey J M , Nurge M A , Biagi C J . A derivation of the electrical capacitance tomography sensitivity matrix. Measurement Science and Technology, 2023, 34(2): 025404

[25] Jaworski A J , Bolton G T . The design of an electrical capacitance tomography sensor for use with media of high dielectric permittivity. Measurement Science and Technology, 2000, 11(6): 743–757

[26] Guo Q , Meng S , Wang D , Zhao Y , Ye M , Yang W , Liu Z . Investigation of gas-solid bubbling fluidized beds using ECT with a modified Tikhonov regularization technique. AIChE Journal, 2018, 64(1): 29–41

[27] Peng L , Ye J , Lu G , Yang W . Evaluation of effect of number of electrodes in ECT sensors on image quality. IEEE Sensors Journal, 2012, 12(5): 1554–1565

[28] Li A , Meng S , Huang K , Yang W , Ye M . On the concentration models in electrical capacitance tomography for gas-fluidized bed measurements. Chemical Engineering Journal, 2022, 435: 134989

[29] Banaei M , van Sint Annaland M , Kuipers J A M , Deen N G . On the accuracy of Landweber and Tikhonov reconstruction techniques in gas-solid fluidized bed applications. AIChE Journal, 2015, 61(12): 4102–4113

[30] Serial M R , Benders S , Rotzetter P , Brummerloh D L , Metzger J P , Gross S P , Nussbaum J , Müller C R , Pruessmann K P , Penn A . Temperature distribution in a gas-solid fixed bed probed by rapid magnetic resonance imaging. Chemical Engineering Science, 2023, 269: 118457

[31] COMSOL Multiphysics®, Version 5.3, COMSOL AB, Stockholm, Sweden, 2022

[32] Wang Y , Wu M , Xu F , Zhang S . The dielectric properties of quartz glass at high temperature. Journal of Sichuan University (Natural Science Edition), 2005, 42(S1): 393–398

[33] Chen L . Dielectric performance of a high purity HTCC alumina at high temperatures—a comparison study with other polycrystalline alumina. Additional Conferences (Device Packaging, HiTEC, HiTEN, and CICMT), 2014, 2014: 271–277

[34] Olmos A M , Carvajal M A , Morales D P , García A , Palma A J . Development of an electrical capacitance tomography system using four rotating electrodes. Sensors and Actuators A: Physical, 2008, 148(2): 366–375

[35] Yue S , Yue S , Zeng M . Measurement and application of soft-field effect in electrical tomography. IEEE Transactions on Instrumentation and Measurement, 2025, 74: 2541212

[36] Ahlgren P , Jarneving B , Rousseau R . Requirements for a cocitation similarity measure, with special reference to Pearson’s correlation coefficient. Journal of the American Society for Information Science and Technology, 2003, 54(6): 550–560

[37] Huang K , Meng S , Guo Q , Yang W , Zhang T , Ye M , Liu Z . Effect of electrode length of an electrical capacitance tomography sensor on gas-solid fluidized bed measurements. Industrial & Engineering Chemistry Research, 2019, 58(47): 21827–21841

[38] Dixon A G , Partopour B . Computational fluid dynamics for fixed bed reactor design. Annual Review of Chemical and Biomolecular Engineering, 2020, 11: 109–130

[39] Korup O , Goldsmith C F , Weinberg G , Geske M , Kandemir T , Schlögl R , Horn R . Catalytic partial oxidation of methane on platinum investigated by spatial reactor profiles, spatially resolved spectroscopy, and microkinetic modeling. Journal of Catalysis, 2013, 297: 1–16

[40] Kim M , Chae H-J , Kim T-W , Jeong K-E , Kim C-U , Jeong S-Y . Attrition resistance and catalytic performance of spray-dried SAPO-34 catalyst for MTO process: effect of catalyst phase and acidic solution. Journal of Industrial and Engineering Chemistry, 2011, 17(3): 621–627

[41] Scherzer J . Designing FCC catalysts with high-silica Y zeolites. Applied Catalysis, 1991, 75(1): 1–32

[42] Kryszyn J , Wanta D M , Smolik W T . Gain adjustment for signal-to-noise ratio improvement in electrical capacitance tomography system EVT4. IEEE Sensors Journal, 2017, 17(24): 8107–8116

[43] Huang K , Pei C , Meng S , Yang W , Li H , Ye M , Gong J . Effects of noise on fluidized bed characteristics measurements by electrical capacitance tomography. Chinese Journal of Chemical Engineering, 2025, 79: 219–233

[44] Rasel R K , Straiton B , Marashdeh Q , Teixeira F L . Toward water volume fraction calculation in multiphase flows using electrical capacitance tomography sensors. IEEE Sensors Journal, 2021, 21(6): 7702–7712

RIGHTS & PERMISSIONS

Higher Education Press