gamma ray tomography

File:UiB GRT.jpg

Gamma ray tomography experienced substantial advancements starting in the 1990s, notably driven by research conducted at the University of Bergen, Norway.{{Cite journal |last1=Johansen |first1=G. A. |last2=Frøystein |first2=T. |date=1994-01-01 |title=Gamma detectors for tomographic flow imaging |url=https://linkinghub.elsevier.com/retrieve/pii/0955598694900043 |journal=Flow Measurement and Instrumentation |volume=5 |issue=1 |pages=15–21 |doi=10.1016/0955-5986(94)90004-3 |bibcode=1994FloMI...5...15J |issn=0955-5986}}{{Cite journal |last1=Johansen |first1=G.A. |last2=Frøystein |first2=T. |last3=Hjertaker |first3=B.T. |last4=Isaksen |first4=Ø. |last5=Olsen |first5=Ø. |last6=Strandos |first6=S.K. |last7=Skoglund |first7=T.O. |last8=Åbro |first8=E. |last9=Hammer |first9=E.A. |date=February 1995 |title=The development of a dual mode tomography for three-component flow imaging |url=https://linkinghub.elsevier.com/retrieve/pii/092304679402913X |journal=The Chemical Engineering Journal and the Biochemical Engineering Journal |language=en |volume=56 |issue=3 |pages=175–182 |doi=10.1016/0923-0467(94)02913-X}} The university pioneered high-speed gamma-ray tomography setups optimized for studying complex multiphase flows, establishing itself as a leader in industrial tomography research.

A significant development occurred with the second-generation gamma ray tomography system, collaboratively designed by the University of Bergen and {{ill|Prototech|no}} for the Saskatchewan Research Council (SRC).{{Cite web |title=Improved Tool for Monitoring Complex Fluid Dynamics |url=https://www.gceocean.no/news/posts/2017/january/improved-tool-for-monitoring-complex-fluid-dynamics/ |access-date=2025-03-26 |website=GCE Ocean Technology |language=en}} Delivered in 2016, this advanced unit significantly enhanced real-time imaging capabilities, capturing up to 100 frames per second with improved spatial resolution. This unit has since become integral to SRC's Pipe Flow Technology Centre, facilitating advanced analysis of slurry pipeline dynamics and predictive modeling of multiphase flows.{{Cite web |title=This Gamma Ray Tomography Unit is the First of Its Kind in the World for Modelling Slurries {{!}} Saskatchewan Research Council |url=https://www.src.sk.ca/blog/gamma-ray-tomography-unit-first-its-kind-world-modelling-slurries |access-date=2025-03-26 |website=www.src.sk.ca}}

Gamma ray tomography operates based on gamma-ray densitometry, governed by Beer–Lambert's law:

$I=I\_0Be^\; \{-\backslash int\{\backslash mu(x)dx\}\}$

Here, $I$ is the measured intensity, $I\_0$ is the source intensity, $B$ is the build-up factor, $\backslash mu$ is the linear attenuation coefficient, and $x$ is the path length between the source and detector.

According to this principle, a narrow beam of monochromatic gamma radiation emitted from a source attenuates exponentially when passing through a material, enabling measurement of the material's density distribution along defined paths. Multiple gamma-ray sources and detectors arranged around the investigated material facilitate detailed cross-sectional image reconstruction using algorithms such as the Iterative Least Squares Technique (ILST).{{Cite journal |last1=Kawata |first1=S. |last2=Nalcioglu |first2=O. |date=June 1985 |title=Constrained Iterative Reconstruction by the Conjugate Gradient Method |url=https://ieeexplore.ieee.org/document/4307698 |journal=IEEE Transactions on Medical Imaging |volume=4 |issue=2 |pages=65–71 |doi=10.1109/TMI.1985.4307698 |pmid=18243953 |issn=1558-254X}}{{Cite journal |last1=Maad |first1=R. |last2=Hjertaker |first2=B. T. |last3=Johansen |first3=G. A. |last4=Olsen |first4=Ø. |date=2010-12-01 |title=Dynamic characterization of a high speed gamma-ray tomograph |url=https://linkinghub.elsevier.com/retrieve/pii/S0955598610000890 |journal=Flow Measurement and Instrumentation |volume=21 |issue=4 |pages=538–545 |doi=10.1016/j.flowmeasinst.2010.10.001 |bibcode=2010FloMI..21..538M |issn=0955-5986}}

The linear attenuation coefficient $\backslash mu$ depends on material properties and photon energy. To optimize measurement accuracy, careful selection of the geometry dimensions and radioactive source with an appropriate photon energy level is crucial. The relative uncertainty in gamma densitometry measurements can be expressed as:

$\{\backslash sigma\_\backslash mu\; \backslash over\; \{\backslash mu\}\}\; =\; \{\{1\backslash over\backslash mu\; x\}\; \backslash sqrt\{e^\{\backslash mu\; x\}\backslash over\; I\_0\; \backslash tau\; \}\}$

where $\backslash sigma\_\backslash mu$ is the absolute uncertainty of $\backslash mu$, $x$ is the distance between the source and detector, and $\backslash tau$ is the integration time. Since the function $\{\backslash sqrt\{e^\{x\}\}/x\}$ has a minimum at $x=2$, selecting the product $\backslash mu\; x$ close to this value minimizes uncertainty.

Typical multiphase flow setups for gamma ray tomography require high temporal resolution. Rather than using scanning setups, these configurations consist of fixed pairs of radioactive sources and detector arrays symmetrically arranged around the pipe center. Gamma radiation emitted from radioactive sources such as Americium-241 is collimated into a fan-shaped beam covering the pipe's cross-section. Opposite these sources, detector arrays individually collimated capture narrow-beam measurements, allowing detailed cross-sectional imaging of phase distributions and densities. Semiconductor-based CdZnTe detectors are commonly utilized.

File:Multiphase pipe flow.gif

Though not widely implemented in daily industrial operations due to cost and complexity, gamma ray tomography remains an essential reference instrument in multiphase flow research and metering. It provides critical bench-marking data to validate and calibrate alternative multiphase measurement techniques, significantly enhancing multiphase flow research capabilities. It has also been used extensively to study different multiphase flows like slurry flow,{{Cite journal |last1=Hashemi |first1=S. A. |last2=Spelay |first2=R. B. |last3=Sanders |first3=R. S. |last4=Hjertaker |first4=B. T. |date=2021-08-01 |title=A novel method to improve Electrical Resistance Tomography measurements on slurries containing clays |url=https://linkinghub.elsevier.com/retrieve/pii/S0955598621000820 |journal=Flow Measurement and Instrumentation |volume=80 |pages=101973 |doi=10.1016/j.flowmeasinst.2021.101973 |bibcode=2021FloMI..8001973H |issn=0955-5986}} and oil-water-gas flow in various geometries.{{Cite journal |last1=Hjertaker |first1=B.T. |last2=Tjugum |first2=S.-A. |last3=Hallanger |first3=A. |last4=Maad |first4=R. |date=August 2018 |title=Characterization of multiphase flow blind-T mixing using high speed gamma-ray tomometry |url=https://linkinghub.elsevier.com/retrieve/pii/S0955598617300432 |journal=Flow Measurement and Instrumentation |language=en |volume=62 |pages=205–212 |doi=10.1016/j.flowmeasinst.2017.10.001|bibcode=2018FloMI..62..205H }}{{Cite journal |last1=Stavland |first1=S. H. |last2=Tjugum |first2=S. -A. |last3=Hallanger |first3=A. |last4=Sætre |first4=C. |last5=Maad |first5=R. |last6=Hjertaker |first6=B. T. |date=2024-09-01 |title=Characterization of multiphase flow through Venturi nozzle using gamma-ray tomography |url=https://linkinghub.elsevier.com/retrieve/pii/S0955598624000517 |journal=Flow Measurement and Instrumentation |volume=98 |pages=102571 |doi=10.1016/j.flowmeasinst.2024.102571 |bibcode=2024FloMI..9802571S |issn=0955-5986}}

Combining gamma ray tomography with techniques like electrical capacitance tomography (ECT){{Cite journal |last1=Stavland |first1=Stian Husevik |last2=Arellano |first2=Yessica |last3=Hunt |first3=Andy |last4=Maad |first4=Rachid |last5=Hjertaker |first5=Bjorn Tore |date=2021 |title=Multimodal Two-Phase Flow Measurement Using Dual Plane ECT and GRT |url=https://ieeexplore.ieee.org/document/9244228 |journal=IEEE Transactions on Instrumentation and Measurement |volume=70 |pages=1–12 |doi=10.1109/TIM.2020.3034615 |bibcode=2021ITIM...7034615S |hdl=11250/2757374 |issn=0018-9456|hdl-access=free }} or electrical resistance tomography (ERT) enhances multiphase characterization by utilizing complementary high spatial and temporal resolutions of these modalities.

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Category:Crystallography