Two - phase oil – gas pipe flow imaging by simulated annealing

We introduce a numerically improved image reconstruction technique for imaging two-phase oil–gas pipe flows using electrical capacitance tomography, based on simulated annealing and iterative linear forward modelling. In the simulated annealing method, a permittivity image is reconstructed by minimizing iteratively an energy function related to the difference between the measured ECT data and those calculated for an estimated permittivity distribution. The permittivity model is repeatedly updated, in a semi-random process that mimics the thermodynamic phenomenon of crystallization in a liquid that is being cooled. In this work, the forward problem is calculated by using a numerically optimized linear approach that makes use of the sensitivity matrix which is computed in the beginning of the process and is not subsequently updated. The images are refined as they go through the processes of cooling and random perturbation of model parameters until their calculated capacitance data match the measured data in a least-squares sense. As each new model is roughly the same as the previous one except for one perturbed parameter, the forward problem computation can be accelerated by avoiding redundant operations. We found this technique to be faster and more accurate than traditional linear methods commonly used in the context of this application. Abbreviations ECT electrical capacitance tomography FVM finite volume method GA genetic algorithms LBP linear back-projection SA simulated annealing VFSA very fast simulated annealing