Image Reconstruction in a Tomographic Multiphase Flow Meter: A Greedy Compressed Sensing Approach

Abstract

The need for flow measurements throughout the production cycle has led to the development of a variety of multiphase flow meters. An ultrasonic tomographic multiphase flow meter is being developed in which it can potentially replace radioactive and invasive types of multiphase flow meters. The meter is configured to generate cross-sectional images of the flow inside the pipe in a non-invasive manner yet with direct contact to the fluid. Image reconstruction is generally carried out via inversion which requires a high level of computation complexity and processing time. It can be further challenged by the limited amount of data available. Compressed Sensing (CS) optimizes the conventional structure for data acquisition and compression. CS is based upon recovering certain data from very few measurements. Loosely speaking, most CS algorithms fall into either two categories; convex optimization recovery and greedy pursuits. In this paper, CS greedy pursuit algorithms are used to reconstruct sound speed images to find the most suitable algorithm in terms of image quality. Specifically, we made a comparative analysis of three greedy CS algorithms; Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP), and Fast Bayesian Matching Pursuit (FBMP). We further compare the CS greedy reconstruction results to a conventional approach for image recovery based on the least-squares problem. Simulation results show that CS algorithms highly outperform the conventional approach for image recovery. Results demonstrate that high quality image recovery can be achieved using these simple greedy pursuit algorithms, sometimes even at increased system efficiency. Out of the three greedy algorithms, CoSaMP shows the highest quality for image recovery. Results also suggest that careful selection of the number of measurements used for recovery is necessary to obtain an accurate image reconstruction. As presented in this paper, our purpose is to adapt a CS approach, specifically greedy pursuit algorithms, for an efficient and an improved reconstruction of images generated by the ultrasonic tomographic multiphase flow meter to accurately quantify phase fractions in producing oil wells.