{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T12:12:48Z","timestamp":1789042368181,"version":"build-2803163510"},"reference-count":39,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T00:00:00Z","timestamp":1788998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deep Earth Probe and Mineral Resources Exploration\u2014National Science and Technology Major Project","award":["2024ZD1003000"],"award-info":[{"award-number":["2024ZD1003000"]}]},{"name":"Drilling and Production Engineering Technology Research Institute, CNPC Chuanqing Drilling Engineering Co. Ltd."}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Discriminating gas injection rates in drilling fluids is essential for monitoring downhole gas influx. However, each gas bubble traversing the sensing zone causes ultrasonic and resistivity readings to depart from the baselines recorded without gas injection, while a single acquisition cycle captures only a random snapshot of the bubble distribution. In this work, a sliding window framework is developed that combines ultrasonic and resistivity measurements to distinguish gas injection rates in a vertical static liquid column. Ultrasonic and resistivity indices are extracted from individual acquisition cycles, aggregated within a 2.5 s sliding window containing five consecutive acquisition cycles, and fused by normalizing classwise products without introducing trainable parameters. Experiments were conducted in freshwater and 2.0gcm\u22123 water-based mud at four discrete injection rates from 0 to 0.3Lmin\u22121. Evaluation used cross-validation with data split by experimental repetition. The fusion framework achieved a macro F1 of 84.7% \u00b1 4.3% in water-based mud, a gain of 6.3 percentage points over the best result from either channel alone. The classwise product also gave the highest mean macro F1 among three evaluated nontrainable fusion rules in both media. The resulting fusion framework supports gas injection rate discrimination under static column conditions.<\/jats:p>","DOI":"10.3390\/s26185749","type":"journal-article","created":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T11:38:39Z","timestamp":1789040319000},"page":"5749","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ultrasonic and Resistivity Sensor Fusion for Discriminating Gas Injection Rates"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-0139-8519","authenticated-orcid":false,"given":"Juehui","family":"Wang","sequence":"first","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Yangtze University, Jingzhou 434023, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8986-7917","authenticated-orcid":false,"given":"Xiuquan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Yangtze University, Jingzhou 434023, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1497-6932","authenticated-orcid":false,"given":"Gui","family":"Tang","sequence":"additional","affiliation":[{"name":"Drilling and Production Engineering Technology Research Institute, CNPC Chuanqing Drilling Engineering Co., Ltd., Guanghan 618300, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"resources","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-3212-8844","authenticated-orcid":false,"given":"Yilin","family":"Yao","sequence":"additional","affiliation":[{"name":"Drilling and Production Engineering Technology Research Institute, CNPC Chuanqing Drilling Engineering Co., Ltd., Guanghan 618300, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3093-1083","authenticated-orcid":false,"given":"Qiuyue","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Yangtze University, Jingzhou 434023, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0344-8981","authenticated-orcid":false,"given":"Weijie","family":"Li","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0513-2456","authenticated-orcid":false,"given":"Mingzhang","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Yangtze University, Jingzhou 434023, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"212134","DOI":"10.1016\/j.geoen.2023.212134","article-title":"Early gas kick detection-inversion-control integrated system: The significance of applications of managed pressure drilling: A review","volume":"229","author":"Chen","year":"2023","journal-title":"Geoenergy Sci. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1002\/ese3.70367","article-title":"Research on the mechanism and suppression method of gas migration velocity under gas invasion conditions in ultra-deep well drilling","volume":"14","author":"Ren","year":"2026","journal-title":"Energy Sci. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Azab, H.M., Elfakharany, T., Salem, A.M., and Zankoor, A.S. (2026). Technological transformation and recent advances in early kick detection during drilling operations: A comprehensive review. Processes, 14.","DOI":"10.3390\/pr14111832"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"205297","DOI":"10.1016\/j.jgsce.2024.205297","article-title":"Downhole detection of gas kick using low-frequency elastic wave: Multiphysics modeling and its implications","volume":"125","author":"Wang","year":"2024","journal-title":"Gas Sci. Eng."},{"key":"ref_5","unstructured":"Zhang, H., Gao, Y., Zhao, X., and Wang, X. (2023). Study on the applicability of downhole sonic gas invasion monitoring acoustic models. Proceedings of the International Technical Symposium on Deepwater Oil and Gas Engineering, Beijing, China, 13\u201315 October 2023, Springer."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2599","DOI":"10.1016\/j.petsci.2026.01.034","article-title":"A quantitative interpretation method of gas kick driven by physics-informed neural network","volume":"23","author":"Yang","year":"2026","journal-title":"Pet. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"114932","DOI":"10.1016\/j.measurement.2024.114932","article-title":"Bulk resistance and contact impedance: Particular solution for annulus, homogeneous domain and dimensional analysis of the complete electrode model","volume":"235","author":"Lourett","year":"2024","journal-title":"Measurement"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"115803","DOI":"10.1016\/j.measurement.2024.115803","article-title":"Correction of the electrode polarization and ionic conductance effects in the measurements of permittivity and loss of the dielectric materials","volume":"242","author":"Dhar","year":"2025","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"111199","DOI":"10.1016\/j.expthermflusci.2024.111199","article-title":"Bubble size distribution and turbulence characterization in a bubbly flow in the presence of surfactant","volume":"155","author":"Hoque","year":"2024","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"11825","DOI":"10.1038\/s41598-023-38937-6","article-title":"Effect of bubble size on ultrasound backscatter from bubble clouds in the context of gas kick detection in boreholes","volume":"13","author":"Indimath","year":"2023","journal-title":"Sci. Rep."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"091501","DOI":"10.1063\/5.0049046","article-title":"Review of ultrasonic measurement methods for two-phase flow","volume":"92","author":"Fan","year":"2021","journal-title":"Rev. Sci. Instrum."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"102614","DOI":"10.1016\/j.flowmeasinst.2024.102614","article-title":"The development of the ultrasonic flowmeter sensors for mass flow rate measurement: A comprehensive review","volume":"97","author":"Afandi","year":"2024","journal-title":"Flow Meas. Instrum."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"102314","DOI":"10.1016\/j.flowmeasinst.2023.102314","article-title":"Mass flow rate measurement of gas-liquid two-phase flow using acoustic-optical-Venturi multisensors","volume":"90","author":"Li","year":"2023","journal-title":"Flow Meas. Instrum."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"109654","DOI":"10.1016\/j.measurement.2021.109654","article-title":"Development of a high-speed ultrasonic tomography system for measurements of rising bubbles in a horizontal cross-section","volume":"182","author":"Murakawa","year":"2021","journal-title":"Measurement"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"015134","DOI":"10.1088\/1361-6501\/ad9624","article-title":"Gas volume fraction measurement based on ultrasonic array sensors in gas-liquid two-phase flow","volume":"36","author":"Guo","year":"2025","journal-title":"Meas. Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"120457","DOI":"10.1016\/j.oceaneng.2025.120457","article-title":"Gas kick monitoring in deep-water drilling risers based on ultrasonic Doppler spectroscopy","volume":"321","author":"Zhang","year":"2025","journal-title":"Ocean Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"063104","DOI":"10.1063\/5.0336804","article-title":"Quantitative identification method of gas kick in deep-water drilling","volume":"38","author":"Zhang","year":"2026","journal-title":"Phys. Fluids"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"27252","DOI":"10.1109\/JSEN.2021.3124625","article-title":"Electrical impedance sensors for multi-phase flow measurement: A review","volume":"21","author":"Cui","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"129173","DOI":"10.1016\/j.applthermaleng.2025.129173","article-title":"A review of gas-liquid two-phase flow measurement: Sensing technologies and intelligent data analysis methods","volume":"284","author":"Fan","year":"2026","journal-title":"Appl. Therm. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"102763","DOI":"10.1016\/j.flowmeasinst.2024.102763","article-title":"Gas-liquid two-phase flow measurement by using electrical tomography sensors and Venturi","volume":"102","author":"Hu","year":"2025","journal-title":"Flow Meas. Instrum."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"102828","DOI":"10.1016\/j.flowmeasinst.2025.102828","article-title":"Void fraction measurement of gas-liquid two-phase flow based on a multi-frequency CCEIT system","volume":"102","author":"Han","year":"2025","journal-title":"Flow Meas. Instrum."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102393","DOI":"10.1016\/j.flowmeasinst.2023.102393","article-title":"Research on the measurement method of gas-water two-phase flow based on dual-sensor system","volume":"93","author":"Xu","year":"2023","journal-title":"Flow Meas. Instrum."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"103243","DOI":"10.1016\/j.flowmeasinst.2026.103243","article-title":"A spatiotemporal feature fusion approach for identifying gas-liquid two-phase flow pattern","volume":"109","author":"Shi","year":"2026","journal-title":"Flow Meas. Instrum."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"103087","DOI":"10.1016\/j.flowmeasinst.2025.103087","article-title":"Gas-liquid two-phase flow pattern classification based on multi-channel feature fusion and near-infrared absorption","volume":"107","author":"Li","year":"2026","journal-title":"Flow Meas. Instrum."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Yin, Q.S., Yin, Z.M., Xu, Z.Q., Li, M.B., Zhang, L.B., Yang, J., Sui, D., and Guo, Y.Y. (Pet. Sci., 2026). Machine learning for gas kick detection in deepwater drilling: A review with multi-source data fusion, Pet. Sci., in press.","DOI":"10.1016\/j.petsci.2026.06.012"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"29603","DOI":"10.1109\/JSEN.2024.3437292","article-title":"Integrating machine learning with sensor technology for multiphase flow measurement: A review","volume":"24","author":"Bao","year":"2024","journal-title":"IEEE Sens. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"25314","DOI":"10.1109\/JSEN.2025.3574085","article-title":"Mass flow rate measurement of gas-liquid two-phase flow using multi-sensor data fusion and soft computing model","volume":"25","author":"Suo","year":"2025","journal-title":"IEEE Sens. J."},{"key":"ref_28","first-page":"1","article-title":"Convolutional attention network for electrical\/ultrasound dual-modal fusion 2-D image reconstruction","volume":"73","author":"Li","year":"2024","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_29","first-page":"1","article-title":"Combinational multimodality tomography system for industrial multiphase flow imaging","volume":"72","author":"Tan","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Abu Alsaud, S., Katterbaue, K., and Alshehri, A. (2024, January 22\u201324). Optimizing underbalanced coiled tubing drilling monitoring via advanced in-line sensing AI framework. Proceedings of the SPE Conference at Oman Petroleum & Energy Show, Muscat, Oman.","DOI":"10.2118\/218798-MS"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1121\/1.397599","article-title":"Linear pressure waves in bubbly liquids: Comparison between theory and experiments","volume":"85","author":"Commander","year":"1989","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"106979","DOI":"10.1016\/j.ijmecsci.2021.106979","article-title":"Modelling of low-frequency acoustic wave propagation in dilute gas-bubbly liquids","volume":"216","author":"Wang","year":"2022","journal-title":"Int. J. Mech. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"12913","DOI":"10.1109\/JSEN.2020.3042206","article-title":"Conductance sensors for multiphase flow measurement: A review","volume":"21","author":"Shi","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"065513","DOI":"10.1088\/2631-8695\/ae4f5b","article-title":"Measurement of Taylor bubble parameters using ultrasonic reflection and cross-correlation","volume":"8","author":"Ma","year":"2026","journal-title":"Eng. Res. Express"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Bragan\u00e7a, H., Colonna, J.G., Oliveira, H.A.B.F., and Souto, E. (2022). How validation methodology influences human activity recognition mobile systems. Sensors, 22.","DOI":"10.3390\/s22062360"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Srinivas, S. (1993). A generalization of the noisy-or model. Uncertainty in Artificial Intelligence: Proceedings of the Ninth Conference, Morgan Kaufmann.","DOI":"10.1016\/B978-1-4832-1451-1.50030-5"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"118281","DOI":"10.1016\/j.measurement.2025.118281","article-title":"Wire-mesh sensor technique for void fraction measurement in gas-liquid two-phase flow under varying conductivity conditions","volume":"256","author":"Yuan","year":"2025","journal-title":"Measurement"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"075303","DOI":"10.1088\/1361-6501\/ade558","article-title":"Identification method of gas-liquid two-phase flow pattern based on dual-domain multi-scale feature fusion framework","volume":"36","author":"Li","year":"2025","journal-title":"Meas. Sci. Technol."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Garcia, M.M., Sattar, M.A., Atmani, H., Legendre, D., Babout, L., Schleicher, E., Hampel, U., and Portela, L.M. (2022). Towards tomography-based real-time control of multiphase flows: A proof of concept in inline fluid separation. Sensors, 22.","DOI":"10.3390\/s22124443"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5749\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T11:41:18Z","timestamp":1789040478000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5749"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,10]]},"references-count":39,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26185749"],"URL":"https:\/\/doi.org\/10.3390\/s26185749","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,10]]}}}