Abstract

GAMIO, J. C.; ORTIZ-ALEMAN, C.  and  MARTIN, R.. Electrical capacitance tomography two-phase oil-gas pipe flow imaging by the linear back-projection algorithm. Geofís. Intl [online]. 2005, vol.44, n.3, pp.265-273. ISSN 2954-436X.

Electrical Capacitance Tomography (ECT) is a novel technology that can deal with the complexity of two-phase gas-oil flow measurement by explicitly deriving the component distributions on two adjacent planes along a pipeline. One of its most promising applications is the visualization of gas-oil flows. ECT offers some advantages over other tomography modalities, such as no radiation, rapid response, low-cost, being non-intrusive and non-invasive, and the ability to withstand high temperature and high pressure. The linear back-projection (LBP) algorithm is one of the most popular methods employed to perform image reconstruction in ECT. Despite its relatively poor accuracy, it is a simple and fast procedure capable of real-time operation in many applications, and it has remained a very popular choice. However, since it was first reported it has lacked a clear formal support in the context of this application. Its only justification has been that it was an adaptation of a method normally used in linear X-ray medical tomography, and the fact that it actually does produce useful (albeit only 'qualitative') images. In this paper, one illustrative way of interpreting LBP is presented. It is shown how LBP is actually based on the linearisation of a normalised form of the forward problem. More specifically, the normalised forward problem is approximated by means of a series of hyper-planes. The reconstruction matrix used in LBP is found to be a 'weighted' transpose of the linear operator (matrix) that defines the linearised normalised forward problem. The rows of this latter matrix contain the information of the sensitivity maps used in LBP.

Keywords : Capacitance tomography; linear back-projection; image reconstruction; flow imaging; inverse modelling.

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