Real-time measurement of liquid holdup and electrical conductivity in stratified flow using an ANN-particle filter and conductance sensor

Abstract Accurate measurement of liquid film thickness is crucial for understanding stratified multiphase flows in various industrial applications, such as oil and gas production, chemical processing, and others. Conductance sensors are widely used for this purpose due to their simplicity and cost-effectiveness. However, they often suffer from inaccuracies caused by factors such as contact impedance, electrode polarization, and environmental noise, which can introduce significant measurement errors. To address these challenges, a novel approach combining a particle filter (PF) with an artificial neural network (ANN) was developed to enhance measurement accuracy. The ANN compensates for systematic errors in conductance sensor readings, while the PF incorporates measurement variability to improve the robustness of the estimation process. The proposed method was tested using simulated stratified flow conditions with liquid holdup ranging from 0.05 to 0.7 and electrical conductivities varying between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.0101</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mtext>S m</mml:mtext> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0.0508</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mtext>S m</mml:mtext> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . Results demonstrated an error margin of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>±</mml:mo> <mml:mn>10</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> for holdup and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>±</mml:mo> <mml:mn>5</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> for electrical conductivity, validating the method’s reliability. This hybrid approach improves measurement precision while maintaining cost efficiency, making it a practical solution for real-time industrial flow monitoring, particularly in environments where conventional methods struggle with accuracy.