An algorithm for estimating radial gas holdup profiles in bubble columns from chordal densitometry measurements

Abstract

γ‐ray densitometry (also referred to as “column scanning” in industrial troubleshooting applications) is a non‐invasive, simple, and relatively inexpensive technique for measuring time‐averaged holdup profiles in multiphase flow systems. Most often, the projection data measured in densitometry is “chordal,” and not “radial,” owing to limitations of experimentation, particularly in challenging industrial environments. However, most of the theory of design and scale‐up is based on “radial profiles” of phase holdups and velocity. The inter‐conversion of chordal profiles to radial profiles is non‐trivial and often prone to error propagation, particularly when the number of projection scans is small. In this work, we propose an algorithm for estimating radial gas holdup profiles, which is not subject to error propagation since we use only the direct (forward) Abel transformation process. Details of the algorithm are discussed. As a test case, γ‐ray densitometry experiments performed on a bubble column are presented.

Overcoming the gamma‐ray computed tomography data processing pitfalls for bubble column equipped with vertical internal tubes

“…Various measurement devices can be used to measure gas holdup in bubble/slurry bubble columns, such as fiber optical probes, conductivity probes, differential pressure probes, ultrasonic techniques, electrical capacitance tomography, X-ray tomography, gamma-ray densitometry, and gamma-ray computed tomography (CT). [24][25][26][27][28][29][30] However, gamma-ray computed tomography is superior to other techniques due to its capability to visualize and measure gas holdup over the entire cross-sectional area of the column in dense and opaque flows that are not visible to other measurement devices due to their limitation to measure in single points (such as probe-based measurement) or their low penetration capability to pass through the high attenuating material (such as X-ray tomography). [31][32][33][34][35] In the past three decades, the CT technique has been successfully used to visualize and quantify gas-liquid distributions and their profiles in a bubble column without vertical internal tubes.…”