Detection of Water Holdup in Oil-Water Flows Using a Curved Microstrip Sensor with Resonance-Enhanced Response

Accurate water holdup measurement in oil-water flows remains challenging due to flow-regime-dependent dielectric distributions and the limited sensitivity of conventional amplitude- or phase-based sensing features. This paper proposes a curved microstrip transmission-line sensor that jointly exploits broadband scattering responses and resonance-frequency shifts to characterize water holdup. The curved geometry increases the effective electrical length within a compact footprint, strengthens field interaction with the surrounding medium, and introduces resonance behavior within the operating band. To improve the physical consistency of numerical modeling, the frequency-dependent complex permittivity of oil-water mixtures is experimentally measured using an open-ended coaxial probe and directly incorporated into full-wave electromagnetic simulations. Both emulsion and stratified oil-water conditions are investigated through simulation and experimental validation. The results show that, under emulsion conditions, the magnitude and phase of S₁₁ and S₂₁ exhibit clear monotonic responses to water holdup. Under stratified conditions, conventional magnitude and phase features exhibit reduced resolution due to the spatially non-uniform dielectric distribution. In this case, variations in water holdup primarily modify the interface position rather than the overall dielectric volume, resulting in relatively small perturbations to the effective permittivity experienced by the guided electromagnetic field. Nevertheless, the resonance frequency remains highly sensitive and shifts monotonically with water holdup. The proposed sensor combines a resonant frequency with broadband magnitude and phase responses, where the resonant frequency provides a stable and reliable indicator across different flow conditions. The results demonstrate the potential of curved microstrip transmission-line structures for compact and reliable water holdup measurement in complex oil-water flow environments.