Abstract
In this brief, a real-time inversion of petrophysical information in downhole firmware for nuclear magnetic resonance logging while drilling (NMR-LWD) based on a field-programmable gate array (FPGA) is proposed. Firstly, the inverse problem is introduced, the nonnegative least-squares (NNLS) problem is modeled and solved by the accelerated projected gradient descent (APGD) algorithm. Secondly, the efficient architecture for the APGD accelerator based on look-up tables (LUTs) is used in Intel’s 10M50 FPGA. Finally, a software cooling method based on a multi-core structure and periodic thermal management technology is deployed. The proposed scheme is applied to NMR-LWD, the effectiveness and feasibility of the proposed scheme are verified experimentally.
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Kuang L, Wang Z, Feng C, Zhao P, Mao R, Yu J (2020) Predicting oil saturation of shale-oil reservoirs using nuclear magnetic resonance logs. Interpretation 8(3):35–43. https://doi.org/10.1190/INT-2019-0150.1
Liu Z-d, Zhao J-z, Zhang P, Sun J-x (2018) Evaluating the CBM reservoirs using NMR logging data. Open Geosci 10(1):544–553. https://doi.org/10.1515/geo-2018-0043
Mwachaka SM, Wu A, Fu Q (2019) A review of mud pulse telemetry signal impairments modeling and suppression methods. J Petrol Explor Prod Technol 9(1):779–792. https://doi.org/10.1007/s13202-018-0483-y
Prammer M (2004) Nmr in well logging and hydrocarbon exploration. Appl Magn Reson 25(3–4):637–649
Zhang M, Duan S, Ling Q (2019) Estimation of T2 spectrum in nmr based on OMP algorithm. In: 2019 Chinese Control Conference (CCC), pp 3697–3702. https://doi.org/10.23919/ChiCC.2019.8866138
Testamanti MN, Rezaee R (2019) Considerations for the acquisition and inversion of NMR T2 data in shales. J Petrol Sci Eng 174:177–188. https://doi.org/10.1016/j.petrol.2018.10.109
Guo J, Xie R, Xiao L, Jin G, Gao L (2019) Nuclear magnetic resonance T1–T2 inversion with double objective functions. J Magn Reson 308:106562. https://doi.org/10.1016/j.jmr.2019.07.049
Zhu M, Liu N (2020) Research on NMR noise reduction method based on improved CEEMD. IEEE Access 8:122864–122873. https://doi.org/10.1109/ACCESS.2020.3007223
Chouzenoux E, Moussaoui S, Idier J, Mariette F (2010) Efficient maximum entropy reconstruction of nuclear magnetic resonance T1–T2 spectra. IEEE Trans Signal Process 58(12):6040–6051. https://doi.org/10.1109/TSP.2010.2071870
Guo J, Xie R (2018) An inversion of NMR echo data based on a normalized iterative hard thresholding algorithm. IEEE Geosci Remote Sens Lett 15(9):1332–1336. https://doi.org/10.1109/LGRS.2018.2844411
Ge X, Chen H, Fan Y, Liu J, Cai J, Liu J (2017) An improved pulse sequence and inversion algorithm of T2 spectrum. Comput Phys Commun 212:82–89. https://doi.org/10.1016/j.cpc.2016.10.012
Bortolotti V, Landi G, Zama F (2021) 2DNMR data inversion using locally adapted multi-penalty regularization. Comput Geosci 25:1215–1228. https://doi.org/10.48550/arXiv.2007.01268
Lan W, Zhang J, Peng J, Ma Y, Zhou S, Luo X (2020) Distributed thermal management system for downhole electronics at high temperature. Appl Therm Eng 180:115853. https://doi.org/10.1016/j.applthermaleng.2020.115853
Shang B, Hu J, Hu R, Cheng J, Luo X (2018) Modularized thermal storage unit of metal foam/paraffin composite. Int J Heat Mass Transf 125:596–603. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.117
Sinha A, Joshi YK (2011) Downhole electronics cooling using a thermoelectric device and heat exchanger arrangement. J Electron Packag 133(4):041005. https://doi.org/10.1115/1.4005290
Peng J, Cheng J, Wu L, Li Q (2020) Data acquisition and processing circuit for high-temperature logging up to \(200^{\circ }\text{ c }\). Microelectron Int 37(3):131–138. https://doi.org/10.1108/mi-09-2019-0059
Zhang J, Fan Y, Cheng J, Wu L, Xu Y (2018) A programmable pulse sequence generator for high temperature low-field NMR apparatus. Instrum Exp Tech 61(4):506–515. https://doi.org/10.1134/S0020441218040127
Cheng J, Xu Y, Wu L, Wang G (2016) A digital lock-in amplifier for use at temperatures of up to \(200^{\circ } \text{ c }\). Sensors 16(11):1899. https://doi.org/10.3390/s16111899
Ohme B, Johnson M (2009). Deep trek re-configurable processor for data acquisition (RPDA). https://doi.org/10.2172/982893
Watson J, Castro G (2012) High-temperature electronics pose design and reliability challenges. Analog Dialogue 46(2):3–9
Zhang J, Wu D, He D, Feng D, Yin M, Qin X, He J (2017) Extraordinary thermoelectric performance realized in n-type PBTE through multiphase nanostructure engineering. Adv Mater 29(39):1703148. https://doi.org/10.1002/adma.201703148
TEXAS INSTRUMENTS (2012) Digital signal controller TMS320F28335-HT data manual. Dallas, Texas. TEXAS INSTRUMENTS
Li C, Chen Q, Zhang F, Di M, Pan Z, Lu F, Wang A (2020) Under-fet thermal sensor enabling smart full-chip run-time thermal management. IEEE J Electron Devices Soc 8:1242–1248. https://doi.org/10.1109/JEDS.2020.3022730
Memik SO, Mukherjee R, Ni M, Long J (2008) Optimizing thermal sensor allocation for microprocessors. IEEE Trans Comput Aided Des Integr Circuits Syst 27(3):516–527. https://doi.org/10.1109/TCAD.2008.915538
Cochran R, Reda S (2009) Spectral techniques for high-resolution thermal characterization with limited sensor data. In: Proceedings of the 46th Annual Design Automation Conference, pp 478–483. https://doi.org/10.1145/1629911.1630037
Cher C-Y, Kursun E (2011) Exploring the effects of on-chip thermal variation on high-performance multicore architectures. ACM Trans Archit Code Optim (TACO) 8(1):1–22. https://doi.org/10.1145/1629911.1630037
Moreno GA, De Niz D (2012) An optimal real-time voltage and frequency scaling for uniform multiprocessors. In: 2012 IEEE International Conference on Embedded and Real-Time Computing Systems and Applications, pp 21–30. https://doi.org/10.1109/RTCSA.2012.51. IEEE
Kumar RN, Chandran V, Valarmathi R, Kumar DR (2018) Bitstream compression for high speed embedded systems using separated split look up tables (LUTs). J Comput Theor Nanosci 15(5):1719–1727. https://doi.org/10.1166/jctn.2018.7367
Zhang K, Qi B, Jiang Q, Tang L (2012) Real-time periodic task scheduling considering load-balance in multiprocessor environment. In: 2012 3rd IEEE International Conference on Network Infrastructure and Digital Content, pp 247–250. https://doi.org/10.1109/ICNIDC.2012.6418753. IEEE
He W, Zhang J, Li H, Liu S, Wang Y, Lv B, Wei J (2022) Optimal thermal management of server cooling system based cooling tower under different ambient temperatures. Appl Therm Eng 207:118176. https://doi.org/10.1016/j.applthermaleng.2022.118176
Yin X-C, Han P, Zhang J, Zhang F-Q, Wang N-L (2003) Application of wavelet transform in signal denoising. In: Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No. 03EX693), vol 1, pp 436–441. https://doi.org/10.1109/ICMLC.2003.1264517. IEEE
Zou Y, Xie R, Ding Y, Arad A (2016) Inversion of nuclear magnetic resonance echo data based on maximum entropy inversion of NMR echo data. Geophysics 81(1):1–8. https://doi.org/10.1190/geo2015-0200.1
Ou W, Yuan D, Liu Q, Cao Y (2018) Object tracking based on online representative sample selection via non-negative least square. Multimed Tools Appl 77:10569–10587. https://doi.org/10.1007/s11042-017-4672-3
Jin G, Xie R, Xu H, Guo J, Gao L (2019) A new method of NMR echo data inversion constrained by priori information. J China Univ Petrol (Ed Nat Sci) 43(2):53. https://doi.org/10.3969/j.issn.1673-5005.2019.02.006
Zhou S, Liu J, Sun H (2017) Study of one-dimensional magnetotelluric regularized inversion based on non-negative least squares method. Chin J Eng Geophys 14:253–261
Bertsekas DP (1976) On the Goldstein-Levitin-Polyak gradient projection method. IEEE Trans Autom Control 21(2):174–184. https://doi.org/10.1109/TAC.1976.1101194
Nurvitadhi E, Kwon D, Jafari A, Boutros A, Sim J, Tomson P, Sumbul H, Chen G, Knag P, Kumar R, et al. (2019) Why compete when you can work together: FPGA-ASIC integration for persistent RNNs. In: 2019 IEEE 27th Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM), pp 199–207. https://doi.org/10.1109/FCCM.2019.00035. IEEE
Fearnley J, Goldberg P, Hollender A, Savani R (2023) The complexity of gradient descent: CLS = PPAD \(\cap\) PLS. J ACM 70(1):1–74. https://doi.org/10.1145/3568163
Mora J, de la Torre E (2018) Accelerating the evolution of a systolic array-based evolvable hardware system. Microprocess Microsyst 56:144–156. https://doi.org/10.1016/j.micpro.2017.12.001
ITRS2011 (2011) ITRS: the international technology roadmap for semiconductors. https://www.itrs.net/reports.html
Akkurt R, Marsala AF, Seifert D, Al-Harbi A, Buenrostro C, Kruspe T, Thern HF, Kurz G, Blanz M, Kroken A (2009) Collaborative development of a slim LWD NMR tool: from concept to field testing. In: SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition, vol All Days, p 126041. https://doi.org/10.2118/126041-MS
Liang W, Fang C, Chong-Yang H, Guo-Hui D, Yi-Ming D (2016) Multi-exponential inversion of T-2 spectrum in NMR based on improved nonlinear fitting. Acta Physica Sin 65(10)
Zhang J, Zhang W, Luo G, Wei X, Liang Y, Cong J (2019) Frequency improvement of systolic array-based CNNS on FPGAS. In: 2019 IEEE International Symposium on Circuits and Systems (ISCAS), pp 1–4. https://doi.org/10.1109/ISCAS.2019.8702071
Pertijs MA, Aita AL, Makinwa KA, Huijsing JH (2010) Low-cost calibration techniques for smart temperature sensors. IEEE Sens J 10(6):1098–1105. https://doi.org/10.1109/JSEN.2010.2040730
Dong J, Liping Z, Yanchao Z, Deyu W (2019) Curve fitting and piecewise linear method for z-type temperature sensor. In: 2019 14th IEEE International Conference on Electronic Measurement & Instruments (ICEMI), pp 686–691. https://doi.org/10.1109/ICEMI46757.2019.9101410
Acknowledgements
This work was supported in part by the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, in part by the China-Poland Belt and Road Belt and Road Joint Laboratory on Measurement and Control Technology, Huazhong University of Science and Technology, in part by Oilfield Technology Research Institute, China Oilfield Services Limited.
Funding
This work was supported in part by the National Natural Science Foundation of China under Grant 61973132, and in part by the Key Project of Hubei Province under Grant 2021ACB001.
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CF carried out the implementation of the research technology and the experiment of the proposed algorithm, and made contributions to the writing of the manuscript and the adjustment and modification of the format of the picture. ML designed the images and contributed to the technical implementation, experimental characterization, and analysis of the proposed algorithm. WL provided support for the construction of the experimental platform. JC contributed to the study’s conception, design, and multiple reviews of the manuscript.
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Fan, C., Li, M., Liu, W. et al. FPGA-based downhole real-time inversion of petrophysical information for NMR-LWD tools with periodic thermal management. J Supercomput 80, 9640–9662 (2024). https://doi.org/10.1007/s11227-023-05827-7
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DOI: https://doi.org/10.1007/s11227-023-05827-7