{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T10:49:44Z","timestamp":1791629384747,"version":"4.3.4"},"reference-count":39,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T00:00:00Z","timestamp":1790467200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T00:00:00Z","timestamp":1790467200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CNPC Logging Co., Ltd. Technology Development Project","award":["2025-1422"],"award-info":[{"award-number":["2025-1422"]}]},{"name":"National Science and Technology Major Project of China","award":["2025ZD1402103"],"award-info":[{"award-number":["2025ZD1402103"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate downhole temperature sensing and low-flow characterization remain challenging in horizontal and highly deviated wells because of nonuniform cross-sectional flow, temperature drift, and probe-to-probe response differences. This study develops an array-based dual-mode constant-temperature-difference (CTD) sensing system for low-flow downhole applications. The system integrates one upstream temperature-sensing probe and six downstream heated sensing probes with pulse width modulation (PWM)-based CTD regulation, particle swarm optimization\u2013genetic algorithm\u2013proportional\u2013integral\u2013derivative (PSO\u2013GA\u2013PID) parameter tuning, probe-specific polynomial calibration, and depth-matched baseline compensation. The resulting framework is intended to improve the heating stability and consistency of the distributed thermal responses. Simulations using representative CTD thermal dynamics, together with repeated stochastic optimization, show that PSO refinement improves the repeatability of PID parameter tuning and reduces transient deviation. Experimental tests further show that PSO\u2013GA\u2013PID achieves a mean overshoot of 4.34% and a mean integral of time-weighted absolute error (ITAE) of 807.08, both lower than those of GA\u2013PID. After polynomial calibration, the absolute temperature errors of all probes remain within \u00b10.6 \u00b0C over 10\u201360 \u00b0C and \u00b10.3 \u00b0C over 60\u2013150 \u00b0C. Under single-phase water conditions, dual-mode baseline compensation reduces the maximum duty-cycle difference among the six sensing probes from 6.1\u20137.6 to 2.6\u20134.0 percentage points. The compensated heating duty cycle increases monotonically with flow rate and exhibits higher sensitivity over 0\u201330 m3\/d than over 30\u201360 m3\/d, providing a measurable basis for subsequent flow-rate calibration. Additional water-cut experiments show that the duty-cycle\u2013flow relationship depends on fluid composition, indicating the need for composition-specific calibration under oil\u2013water two-phase conditions. These results demonstrate the feasibility of the integrated array-based CTD sensing and compensation framework for stable multipoint thermal response characterization under controlled low-flow conditions.<\/jats:p>","DOI":"10.3390\/s26196133","type":"journal-article","created":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T15:57:57Z","timestamp":1790611077000},"page":"6133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Array-Based CTD Thermal Sensing for Low-Flow Downhole Applications with Dual-Mode Compensation"],"prefix":"10.3390","volume":"26","author":[{"given":"Zihan","family":"Lin","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":"data-curation","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8520-2060","authenticated-orcid":false,"given":"Yong","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Yangtze University, Jingzhou 434023, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8804-9778","authenticated-orcid":false,"given":"Yifei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Yangtze University, Jingzhou 434023, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"supervision","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"}]},{"given":"Ruyi","family":"Gan","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Yangtze University, Jingzhou 434023, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"supervision","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Mei","family":"Wang","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"}]},{"given":"Qiang","family":"Chen","sequence":"additional","affiliation":[{"name":"China Petroleum Logging Co., Ltd., Xi\u2019an 710077, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhu, Y., Wang, X., Kang, Y., Guo, C., He, Q., and Li, C. 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