A Fast Electrical Resistivity-Based Algorithm to Measure and Visualize Two-Phase Swirling Flows

Abstract

Electrical resistance tomography (ERT) has been used in the literature to monitor the gas–liquid separation. However, the image reconstruction algorithms used in the studies take a considerable amount of time to generate the tomograms, which is far above the time scales of the flow inside the inline separator and, as a consequence, the technique is not fast enough to capture all the relevant dynamics of the process, vital for control applications. This article proposes a new strategy based on the physics behind the measurement and simple logics to monitor the separation with a high temporal resolution by minimizing both the amount of data and the calculations required to reconstruct one frame of the flow. To demonstrate its potential, the electronics of an ERT system are used together with a high-speed camera to measure the flow inside an inline swirl separator. For the 16-electrode system used in this study, only 12 measurements are required to reconstruct the whole flow distribution with the proposed algorithm, 10× less than the minimum number of measurements of ERT (120). In terms of computational effort, the technique was shown to be 1000× faster than solving the inverse problem non-iteratively via the Gauss–Newton approach, one of the computationally cheapest techniques available. Therefore, this novel algorithm has the potential to achieve measurement speeds in the order of 104 times the ERT speed in the context of inline swirl separation, pointing to flow measurements at around 10kHz while keeping the average estimation error below 6 mm in the worst-case scenario.

Towards Tomography-Based Real-Time Control of Multiphase Flows: A Proof of Concept in Inline Fluid Separation

“…The fast acquisition of flow data is one of the reasons for the many successful applications of tomography in the study of multiphase flows mentioned at the beginning of the section, and the slow image reconstruction was the reason behind the limitation of tomography to offline or slow applications; the recent increase in computational power together with the development of optimized reconstruction algorithms finally allows acquiring and reconstructing tomographic data at speeds compatible with the intrinsic multiphase flow dynamics [35,36], opening the door to applications of the real-time control of the distribution of phases of multiphase flows, strongly connected to the equipment performance, using tomography.…”

“…In order to speed-up the ERT measurements, which is fundamental to control applications, the inline swirl separator application-specific reconstruction algorithm of [36] is used in this work. The algorithm, which is detailed in Section 3.4, reconstructs the gas core size and position directly from the current measurements using equations that are simple and fast to compute, providing a feedback of the separation much faster than applications based on the inverse problem.…”

“…The Flow Watch ERT system from Rocsole Ltd was able to provide reliable measurements of gas-liquid swirling flows in previous works [35,36] and was used in the experiments of this paper. It operates in the voltage-current (VC) scheme, i.e., the measurements were performed imposing a voltage in one electrode (source), while measuring the current in the others, which were kept grounded (sink), and a frame of the flow was obtained when every electrode of the system acted as the source (Section 2).…”

“…The application-specific ERT reconstruction algorithm of [36] was used to reconstruct in real-time the gas core inside the inline fluid separator based on the raw data of current measured by the acquisition system. The algorithm is based on the voltage (V)-current (I) measurements of opposite electrodes (following Figure 4, electrodes 1 (V) and 9 (I), 2 (V), and 10 (I), 3 (V) and 11 (I), .…”

“…The radial position of the centroid of the gas core, r, is linked to the standard deviation of ∆i m,m+8 , and the angular position of the gas core, θ, is obtained analyzing ∆i m,m+8 together with four additional 90°current measurements, obtained between electrodes 1 and 5, 5 and 9, 9 and 13, and 13 and 1. Since the gas core is well centered in the conditions explored in Section 5, only the core size (d) is used in this paper, and the reader is referred to [36] for details regarding the calculation of the position of the core.…”