{
  "abstract": "Gas–liquid two-phase flow measurement in vertical annular pipes remains a challenge in petroleum engineering and related fields, due to the complex flow regimes and asymmetric cross-sectional geometry. In this study, a non-invasive soft-sensing method based on multi-scale differential pressure signals and machine learning is developed for flow rate prediction in vertical annular (inner/outer diameters 75/125 mm) counter-current gas–liquid two-phase flow. Experiments were conducted over a gas superficial velocity range of 0.06–2.91 m/s, a liquid superficial velocity range of 0.02–0.24 m/s, and five eccentricity levels (0–1.0). Differential pressure signals were simultaneously acquired at two spatial scales: a short-span (50 mm, approximately 1 D) and a long-span (1000 mm, approximately 20 D). A total of 53 features were extracted from the time domain, frequency domain (power spectral density), and time-frequency domain (discrete wavelet transform). Three predictive models – Random Forest (RF), XGBoost, and Multilayer Perceptron (MLP) – were constructed and hyperparameter-optimized via grid search. Results show that the XGBoost model exhibits the best generalization performance, achieving mean absolute percentage errors (MAPE) of 6.04% for gas superficial velocity and 27.17% for liquid superficial velocity. SHAP-based feature importance analysis indicates that the long-span (1000 mm) differential pressure features play a dominant role in flow rate prediction. Low-frequency energy and the signal mean are crucial for liquid velocity prediction, while high-frequency detail energy governs gas velocity prediction. Although the short-span (50 mm) features rank lower in global importance, they provide critical non-linear corrections under extreme conditions such as high gas velocity. The eccentricity feature (ecce) exhibits a data-driven nonlinear tendency: once the eccentricity exceeds 0.5, the SHAP values for both phases shift markedly negative. This trend is qualitatively consistent with the understanding that wall friction in the narrow gap increases under highly eccentric annular geometries. This study demonstrates that multi-scale differential pressure sensing combined with interpretable machine learning offers a feasible pathway for flow rate measurement in complex wellbore annuli without relying on specific flow regimes (e.g., Taylor bubble flow).",
  "abstract_shown": true,
  "affiliations": [
    "Gansu Key Laboratory of Efficient Utilization of Oil and Gas Resources in Longdong, College of Petroleum and Chemical Engineering, Longdong University",
    "College of New Energy, Longdong University",
    "PetroChina Changqing Oilfield Co"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 7,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Feng Cao"
    },
    {
      "affs": [
        0
      ],
      "name": "Anzhao Ji"
    },
    {
      "affs": [
        0
      ],
      "name": "Zhanjun Chen"
    },
    {
      "affs": [
        0
      ],
      "name": "Xuefen Liu"
    },
    {
      "affs": [
        0
      ],
      "name": "Peng Zhang"
    },
    {
      "affs": [
        1
      ],
      "name": "Fengfeng Yang"
    },
    {
      "affs": [
        2
      ],
      "name": "Huifeng Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fte6grv2s28ax.bib",
  "cited_by": 0,
  "doi": "10.1038/s41598-026-68538-y",
  "fulltext_url": "https://doi.org/10.1038/s41598-026-68538-y",
  "id": "fte6grv2s28ax",
  "issns": [
    "2045-2322"
  ],
  "landing_url": "https://doi.org/10.1038/s41598-026-68538-y",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "Q"
    ],
    [
      "lcc",
      "R"
    ],
    [
      "openalex",
      "2211|Flow Measurement and Analysis"
    ]
  ],
  "openalex": "W7151211976",
  "pdf_url": "https://www.nature.com/articles/s41598-026-68538-y_reference.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": "Nature Portfolio",
  "ris": "https://research.draconitic.com/paper/fte6grv2s28ax.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T14:21:19Z",
      "native_id": "0640d6ec4f1245a7b1859cb2c48a23c9",
      "source": "doaj",
      "url": "https://doi.org/10.1038/s41598-026-68538-y"
    }
  ],
  "subjects": [
    {
      "field": "medicine",
      "origin": "lcc:R",
      "subfield": "general"
    }
  ],
  "title": "Characteristics and flow measurement of gas-liquid two-phase counter-current flow in vertical annulus",
  "title_text": "Characteristics and flow measurement of gas-liquid two-phase counter-current flow in vertical annulus",
  "type": "peer-reviewed",
  "updated_at": "2026-11-03T14:20:46Z",
  "url": "https://research.draconitic.com/paper/fte6grv2s28ax",
  "venue": "Scientific Reports",
  "versions": []
}