Flow Measurement and Instrumentation 23 (2012) 66–75 Contents lists available at SciVerse ScienceDirect Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst A new constrained hierarchical reconstruction method for electrical capacitance tomography Samir Teniou ∗ , Mahmoud Meribout, Thuraya Al-Hanaei, Fatima Al-Zaabi, Rehab Banihashim, Sameya Al-Ghafri Department of Electrical Engineering, Petroleum Institute, Abu Dhabi 2533, United Arab Emirates article info Article history: Received 30 June 2011 Received in revised form 29 October 2011 Accepted 8 November 2011 Keywords: Electrical capacitance tomography Finite element method Hierarchical mesh Internal pressure and temperature sensors Regularized constrained Gauss–Newton abstract In permittivity distribution reconstruction using electrical capacitance tomography (ECT), it is usually required to divide the image area into a finite number of elements. Since finer meshes lead to more accurate results at the detriment of a slower reconstruction time, a good tradeoff is usually sought by researchers. In this paper, a new reconstruction method of the image area in a hierarchical manner is proposed. It consists of localizing gradually the regions of interest which hold the inhomogeneous phases by refining the pixels only around their boundaries. To improve even more the reconstructed images, this paper suggests a new ECT device consisting of a multitude of miniaturized pressure and temperature sensors distributed at different locations of a cross section of a pipeline (in addition to the electrical electrodes surrounding the pipe). Using these sensors, an estimation of the density distribution of the process across a section of the pipeline can be performed using the Bernoulli equation. This density data is then used as a hard constraint for the forward and inverse problem which uses the data acquired from the electrical electrodes. Experimental results on synthetic and real images show that the proposed scheme improves the accuracy and the quality of the reconstructed images while keeping the computation time significantly lower than other traditional methods. © 2011 Elsevier Ltd. All rights reserved. 1. Introduction In oil and gas industries there is a continuous need for measuring in real-time and online the amount of each individual phase passing through a given section of a pipeline. This would lead for instance to an effective reservoir management by remotely controlling the actuated control valves according to the actual composition and behavior of the fluid in a given upstream locations. With the continuous depletion of oil and gas reserves, this kind of reservoir control, namely smart field, is becoming a necessity for oil and gas companies for improving their productivity [1,2]. This triggered tremendous research efforts to design new embedded instruments for real-time multiphase flow composition measurement [3–5]. Process flow tomography refers to non-invasive methods with which the internal characteristics of pipeline flows are acquired from a set of measurements on or outside the domain of interest. This technique has achieved substantial improvements over other methods, such as the ones using gamma rays, for real-time flow estimation [6,7]. Among various tomography techniques such ∗ Corresponding author. Tel.: +971 26075462. E-mail addresses: steniou@pi.ac.ae (S. Teniou), mmeribout@pi.ac.ae (M. Meribout). as electrical, ultrasonic, X-ray, nuclear magnetic resonance, and microwaves [8], tomography techniques based on measurement of electrical properties have received significant attention in recent years [9–11]. Electrical Resistance Tomography (ERT), Electromagnetic Tomography (EMT), and Electrical Capacitance Tomography (ECT) which explore the conductive, inductive and capacitive properties of the flow respectively constitute the three main types of electrical-based tomography techniques. ECT, which is considered in this paper, provides in a relatively short amount of time the permittivity distribution of the multiphase process by measuring the capacitances between all pairs of electrodes surrounding this process. Thus, this technique can be adopted for applications requiring real-time measurement of flows composed of fluids having different dielectric values, such as flows composed of oil, gas and water [11,12]. In ECT, image reconstruction algorithms consist mainly to solve in one or several iterations the so-called forward and inverse problems [13]. In the forward problem, the inter-electrode capacitances are determined using an estimated permittivity distribution of the process. Hence, the non-linear relationship between these capacitances and the permittivity distribution may be derived from Maxwell’s equations [14], which is difficult to be solved analytically. This is the reason why the forward problem is usually solved numerically using for instance the Finite Difference Method (FDM) [15], suitable for rectangular sensors, the Finite 0955-5986/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2011.11.001