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Development of an X-ray computed tomography (CT) system with sparse sources: application to three-phase pipe flow visualization


This paper describes the application of a two-beam X-ray computed tomography (CT) system to multiphase (gas–oil–water) flow measurement. Two high-voltage (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.

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A i,j :

Area fraction of the jth beam within the pipe that is occupied by the (i, j)th element, dimensionless

D :

Pipe diameter, m

E :

X-ray energy, keV

I :

X-ray intensity, W

I 0 :

Scaling factor in Eq. 1, W m−2

N :

Number of elements on each axis of the reconstructed image, dimensionless

U mix :

Mixture velocity, m s−1

x :

Path length of material, m

X i,j :

Local phase fraction in the (i, j)th element, dimensionless

\(\ifmmode\expandafter\hat\else\expandafter\^\fi{X}_{{i,j}} \) :

Adjusted local phase fraction in the (i, j)th element, dimensionless

X d :

Efficiency of the linear array detector, dimensionless

μ :

Attenuation coefficient

σ :

Smoothing factor, dimensionless

φ :

Phase fraction, dimensionless

\(\ifmmode\expandafter\hat\else\expandafter\^\fi{\phi }\) :

Adjusted phase fraction, dimensionless


Hard spectrum


Maximal value


Soft spectrum


Air (or gas) phase


Oil phase


Water phase


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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 Français du Pétrole, Norsk Hydro, Scandpower, Shell, SINTEF, Statoil, Total. The authors wish to express their sincere gratitude for this support.

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Hu, B., Stewart, C., Hale, C.P. et al. Development of an X-ray computed tomography (CT) system with sparse sources: application to three-phase pipe flow visualization. Exp Fluids 39, 667–678 (2005).

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  • Multiphase Flow
  • Projection Data
  • Phase Fraction
  • Tomographic Image
  • Slug Flow