Supplementary material for "A quasi-Newton approach to gas-hydrate-oriented circuit fitting problems" (IWIS 2026)

Abstract Gas hydrates are among the greatest concerns within deep-sea petroleum extraction. Their fast growth rates, especially under favorable conditions such as high pressure and low temperature, can lead to severe pipe clogging and costly stoppages. However, hydrate monitoring in the oil industry is usually limited to temperature and pressure readings. These techniques detect the presence of the structures but lead to few insights into physical and electrical properties. As a solution to this limitation, impedance spectroscopy has been reported to accurately measure hydrate dynamics and, more importantly, at a fairly low cost. Impedance readings across the broad frequency range inherent to this method enable direct characterization of multiple hydrate-related phenomena. For instance, parameters such as volume, saturation, and salt levels can be derived through the frequency response. Furthermore, from the impedance measurements, it is possible to define an inverse problem to identify an approximate electrical circuit that generated said output. This task is known as electric circuit fitting. This paper proposes using a quasi-Newton minimizer as an alternative to usual estimators in the literature, targeting hydrate-oriented spectra. Four samples were selected, spanning different frequency ranges and acquisition hardware, to assess the method's viability across multiple scenarios. Results show that the proposed approach outperforms the most common algorithms for circuit-fitting problems, achieving improved fit scores and faster convergence. Additionally, this work provides an accurate framework for future efforts on hydrate-oriented electrical characterizations. Reproducing the paper results All the results presented in the paper can be reproduced by the scripts provided in the `results` directory. For each sample, an individual script is provided that can be run independently. The only infrastructure requirement is to have the framework recognized by the scripts and the raw data in an accessible directory (e.g., data at the root). Except for "time_benchmark.py", which reproduces the results in Table II, the other scripts pertain to Fig. 2 and Table I of the paper. With the environment activated, run each script in the terminal with:python3 ./<result_script_name>.py assuming the script is called from the results directory. Alternatively, run the script directly using the IDE's run command. Note: the result scripts for methane hydrate fitting require raw seawater data (with and without sand) at negative temperatures, extracted from the open dataset published in 10.1029/2020GL087645. Since that data does not belong to us, it was excluded from this archive. License All Python source code (.py) is made available under the MIT license. You can freely use and modify the code, without warranty, so long as you provide attribution to the authors. See LICENSE-MIT.txt for the full license text.