Assessment of thermal conductivity of rocks using regression analyses and artificial neural networks

Yıl 2024, Cilt: 30 Sayı: 4, 556 - 563, 30.08.2024

Hilal Özer Aral , Ebru Başpınar Tuncay

Öz

This study investigated the thermal conductivity of natural stones (𝑘) through regression analyses and artificial neural networks (𝐴𝑁𝑁). In order to gather a sizable number of datasets for the aforementioned analytic methodologies, a thorough literature review was carried out. Based on different physicomechanical rock characteristics, like dry density (𝜌𝑑), effective porosity (𝑛𝑒), uniaxial compressive strength (𝑈𝐶𝑆), and pulse wave velocity (𝑉𝑝), seven estimated models (M1-M7) were created for the evaluation of 𝑘. The regression-based models (M1-M5) demonstrated that the considered rock properties influence the 𝑘 of natural stones at different degrees. Notably, the 𝑛𝑒 and 𝑉𝑝 were found to be highly correlative parameters for estimating the 𝑘 of natural stones. A number of statistical indicators were used to assess the performance of the developed models. The statistical evaluations indicated that the ANN-based models (M6, M7) provided more consistent results than the M1-M5 models. In addition, the mathematical expressions for ANN-based models were also given in the present study to let users carry out them more efficiently. In this case, this study is thought to ensure applicable and comprehensible information on the heat conduction of natural stones and can be described as a research study on how to model the 𝑘 of natural stones as a factor of various rock characteristics.

Anahtar Kelimeler

Thermal conductivity, Natural stone, Regression analysis, Artificial neural networks

Kayaçların termal iletkenliğinin regresyon analizleri ve yapay sinir ağları kullanılarak değerlendirilmesi

Öz

Bu çalışma, doğal taşların (𝑘) termal iletkenliğini regresyon analizleri ve yapay sinir ağları (YSA) yoluyla araştırmıştır. Bu amaçla, yukarıda belirtilen analiz yöntemleri için çok sayıda veri seti derlemek için kapsamlı bir literatür araştırması yapılmıştır. Kuru yoğunluk (ρd), etkin gözeneklilik (ne), tek eksenli basınç dayanımı (UCS) ve darbe dalga hızı (Vp), gibi farklı fizikomekanik kaya özelliklerine dayanarak, 𝑘'nin değerlendirilmesi için yedi tahmin modeli (M1-M7) kurulmuştur. Regresyona dayalı modeller (M1-M5), dikkate alınan kaya özelliklerinin doğal taşların 𝑘 değerini farklı derecelerde etkilediğini göstermiştir. Özellikle, ne ve Vp'nin doğal taşların 𝑘'sini tahmin etmek için yüksek oranda bağıntılı parametreler olduğu bulunmuştur. Kurulan modellerin performansı da çeşitli istatistiksel göstergeler kullanılarak değerlendirilmiştir. İstatistiksel değerlendirmeler, YSA tabanlı modellerin (M6, M7), M1-M5 modellerinden daha tutarlı sonuçlar verdiğini göstermiştir. Ayrıca, kullanıcıların bunları daha verimli bir şekilde uygulayabilmeleri için YSA tabanlı modeller için matematiksel ifadeler de bu çalışmada verilmiştir. Böylelikle, bu çalışmanın, doğal taşların ısı iletimi hakkında pratik ve anlaşılır bilgiler sağlayacağı düşünülmektedir ve farklı kaya özelliklerinin bir fonksiyonu olarak doğal taşların 𝑘'sının nasıl modelleneceğine dair bir vaka çalışması olarak tanımlanabilir.

Anahtar Kelimeler

Isı iletkenliği, Doğal taş, regresyon analizi, Yapay sinir ağları

Kaynakça

• [1] Ulusay R. “The present and future of rock testing: highlighting the ISRM suggested methods”. In: Proceedings of 7th Asian Rock Mechanics Symposium, Seoul, South Korea, 15-19 October 2012.
• [2] Wagner V, Bayer P, Bisch G, Kübert M, Blum P. “Hydraulic characterization of aquifers by thermal response testing: Validation by large-scale tank and field experiments”. Water Resources Research, 50(1), 71-85, 2013.
• [3] Popov Y, Beardsmore G, Clauser C, Roy S. “ISRM suggested methods for determining thermal properties of rocks from laboratory tests at atmospheric pressure”. Rock Mechanics and Rock Engineering, 49(10), 4179-4207, 2016.
• [4] Verma AK, Jha MK, Maheshwar S, Singh TN, Bajpai RK. “Temperature-dependent thermophysical properties of Ganurgarh shales from Bhander group, India”. Environmental Earth Sciences, 75(4), 1-11, 2016.
• [5] Finsterle S, Muller RA, Baltzer R, Payer J, Rector JW. “Thermal evolution near heat-generating nuclear waste canisters disposed in horizontal drillholes”. Energies, 12(4), 2-23, 2019.
• [6] Hamoush S, Abu-Lebdeh T, Picornell M, Amer S. “Development of sustainable engineered stone cladding for toughness, durability, and energy conservation”. Construction and Building Materials, 25(10), 4006-4016, 2011.
• [7] Helgeson HC. “Summary and critique of the thermodynamic properties of rock-forming minerals”. American Journal of Science, A, 278, 1-229, 1978.
• [8] Price GD, Ross NL. “The Stability of Minerals”. 1st ed. London, England, Chapman & Hall, 1992.
• [9] Šafanda J. “Effect of thermal conductivity anisotropy of rocks on the subsurface temperature field”. Geophysical Journal International, 120(2), 323-3639, 1995.
• [10] Popov Y, Tertychnyi V, Romushkevich R, Korobkov D, Pohl J. “Interrelations between thermal conductivity and other physical properties of rocks: experimental data, In Thermo-hydro-mechanical coupling in fractured rock”. Pure Applied Geophysics, 160, 1137-1161, 2003.
• [11] Wu S, Yu Z, Kang J, Zhang Y, Gao P. “Research on the anisotropy of thermal conductivity of rocks in Songliao Basin, China”. Renewable Energy, 179, 593-603, 2021.
• [12] Zimmerman RW. “Thermal conductivity of fluid-saturated rocks”. Journal of Petroleum Science and Engineering, 3(3), 219-227, 1989.
• [13] Tavman IH. “Effective thermal conductivity of granular porous materials”. International Communications in Heat and Mass Transfer, 23(2), 169-176, 1996.
• [14] Coletti C, Borghi A, Cossio R, Dalconi MC, Dalla Santa G, Peruzzo L, Sassi R, Vettorello A, Galgaro A. “A multi-scale methods comparison to provide granitoid rocks thermal conductivity”. Construction and Building Materials, 304, 1-13 2021.
• [15] Uğur İ, Özer Toklu H. “Effect of multi-cycle freeze-thaw tests on the physico-mechanical and thermal properties of some highly porous natural stones”. Bulletin of Engineering Geology and the Environment, 79(1), 255-267, 2020.
• [16] Yaşar E, Erdoğan Y, Güneyli H. “Determination of the thermal conductivity from physico-mechanical properties”. Bulletin of Engineering Geology and the Environment, 67(2), 219-225, 2008.
• [17] Barry-Macaulay D, Bouazza A, Singh RM, Wang B, Ranjith PG. “Thermal conductivity of soils and rocks from the Melbourne (Australia) region”. Engineering Geology, 164, 131-138, 2013.
• [18] Demirci A, Görgülü K, Durutürk YS. “Thermal conductivity of rocks and its variation with uniaxial and triaxial stress”, International Journal of Rock Mechanics and Mining Sciences, 41, 1133-1138, 2004.
• [19] Özkahraman H, Selver R, Işık EC. “Determination of the thermal conductivity of rock from P-wave velocity”., International Journal of Rock Mechanics and Mining Sciences, 4(4), 703-708, 2004.
• [20] Boulanouar A, Rahmouni A, Boukalouch M, Samaouali A, Géraud Y, Harnafi M, Sebbani J, “Determination of thermal conductivity and porosity of building stone from ultrasonic velocity measurements”. Geomaterials, 3, 138-144, 2013.
• [21] Xiong J, Lin H, Ding H, Pei H, Rong C, Liao W. “Investigation on thermal property parameters characteristics of rocks and its influence factors”. Natural Gas Industry B, 7(3), 298-308, 2020.
• [22] Shim BO, Park JM, Kim HC, Lee Y. “Statistical analysis on the thermal conductivity of rocks in the Republic of Korea”. In: Proceedings World Geothermal Congress, Bali, Indonesia, 25-29 April 2010.
• [23] Chen C, Zhu C, Zhang B, Tang B, Li K, Li W, Fu X. “Effect of temperature on the thermal conductivity of rocks and its implication for in situ correction”. Geofluids, 2021, 1-12, 2021.
• [24] Singh TN, Sinha S, Singh VK. “Prediction of thermal conductivity of rock through physicomechanical properties”. Building and Environment, 42(1), 146-155, 2007.
• [25] Khandelwal M. “Application of an expert system to predict thermal conductivity of rocks”. Neural Computing and Applications, 21(6), 1341-1347, 2012.
• [26] Verma AK, Jha MK, Gautam PK, Mishra AK, Vardhan H, Singh SK. “Prediction of thermal conductivity and damage in Indian Jalore granite for design of underground research laboratory”. Neural Computing and Applications, 33, 13183-13192, 2021.
• [27] Balkan E, Erkan K, Şalk M. “Thermal conductivity of major rock types in western and central Anatolia regions, Turkey”. Journal of Geophysics and Engineering, 14(4), 909-919, 2017.
• [28] Liu S, Feng C, Wang L, Li C. “Measurement and analysis of thermal conductivity of rocks in the Tarim Basin, Northwest China”. Acta Geologica Sinica‐English Edition, 85(3), 598-609, 2011.
• [29] Xiaoqing S, Ming J, Peiwen X. “Analysis of the thermophysical properties and influencing factors of various rock types from the guizhou province”. 2018 3rd International Conference on Advances in Energy and Environment Research, Guilin, China. 10-12 August 2018.
• [30] Tang B, Zhu C, Xu M, Chen T, Hu S. “Thermal conductivity of sedimentary rocks in the Sichuan basin, Southwest China”. Energy Exploration & Exploitation, 37(2), 691-720, 2019.
• [31] Andersson, E. Thermal properties in Different Rock Materials Based on Hot Disk and Mineral Mode -a Comparison between Petrographic Analysis and Laboratory Measurements. University of Gothenburg, Gothenburg, Sweden, 2016.
• [32] Blackwell DD, Steele JL. “Thermal Conductivity of Sedimentary Rocks: Measurement and Significance”. Editors: Naeser ND, McCulloh TH. Thermal history of sedimentary basins, 13-36, New York, USA, 1989.
• [33] Lindawati L, Yuliza NF, Irwansyah I. “Thermal conductivity of some marble stones available in South Aceh District”. In: IOP Conference Series: Materials Science and Engineering, IOP Publishing, Malacca, Malasia, 9-10 November, 2020.
• [34] Pasquale V, Verdoya M, Chiozzi P. “Measurements of rock thermal conductivity with a Transient Divided Bar”. Geothermics, 53, 183-189, 2015.
• [35] Özkahraman HT, Bolattürk A. “The use of tuff stone cladding in buildings for energy conservation”. Construction and Building Materials, 20(7), 435-440, 2006.
• [36] Yüksek S. “Mechanical properties of some building stones from volcanic deposits of mount Erciyes (Turkey)”. Materiales De Construcción, 69(334), 1-13, 2019.
• [37] Sarıışık A, Sarıışık G. “Investigation of engineering characteristics of Urfa stone used in restoration”. 16th International Symposium on Environmental Issues and Waste Management in Energy and Mineral Production, Istanbul, Turkey, 05–07 October 2016.
• [38] Sarıışık A, Sarıışık G. “Investigation of engineering characteristics of Mardin stone used in eco-building”. Cogent Engineering, 3(1), 1-3, 2016.
• [39] Zhao XG, Zhao Z, Guo Z, Cai M, Li X, Li PF, Chen L, Wang J. “Influence of thermal treatment on the thermal conductivity of Beishan granite”. Rock Mechanics and Rock Engineering, 51(7), 2055-2074, 2018.
• [40] Öner F, Türkmen S, Özbek A, Karakaya T. “Engineering properties of Hınıs ignimbrites and their usability as a building stone (Erzurum, Turkey)”. Environmental Geology, 50(2), 275-284, 2006.
• [41] Labus M, Labus K. “Thermal conductivity and diffusivity of fine-grained sedimentary rocks”. Journal of Thermal Analysis and Calorimetry, 132(3), 1669-1676, 2018.
• [42] Midttømme K, Roaldset E, Aagaard P. “Thermal conductivity of selected claystones and mudstones from England”. Clay Minerals, 33(1), 131-145, 1998.
• [43] Li X, Liu S, Feng C. “Thermal properties of sedimentary rocks in the Tarim Basin, northwestern China”. The American Association of Petroleum Geologists Bulletin, 103(7), 1605-1624, 2019.
• [44] Hussain S, Saneen S, Ahmad N, Javeed MA, Ali S. “Calculation of thermal conductivity of diorite rocks and their modeling”. International Journal of Basic and Applied Sciences, 12(2012), 111-123, 2012.
• [45] Tufan B, Kun M. “Thermal insulation performance and thermal conductivity evaluation of natural stones by infrared thermography”. Proceedings of the International Conference on Mining, Material and Metallurgical Engineering, Prague, Czech Republic, 11-12 August 2014.
• [46] Vosteen HD, Schellschmidt R. “Influence of temperature on thermal conductivity, thermal capacity and thermal diffusivity for different types of rock”. Physics and Chemistry of the Earth Parts A/B/C, 28(9-11), 499-509, 2003.
• [47] Jenkins DG, Quintana-Ascencio PF. “A solution to minimum sample size for regressions”. PLoS One, 15(2), 1-15, 2020.
• [48] Schoukens J, Ljung L. “Nonlinear system identification: A user-oriented road map”. IEEE Control Systems Magazine, 39(6), 28-99, 2019.
• [49] Singh R, Kainthola A, Singh TN. “Estimation of elastic constant of rocks using an ANFIS approach”. Applied Soft Computing, 12(1), 40-45, 2012.
• [50] Lawal AI, Idris MA. “An artificial neural network-based mathematical model for the prediction of blast-induced ground vibrations”. International Journal of Environmental Studies, 77(2), 318-334, 2020.
• [51] Kamalov F, Nazir A, Safaraliev M, Cherukuri AK, Zgheib R. “Comparative analysis of activation functions in neural networks”. In 2021 28th IEEE International Conference on Electronics, Circuits, and Systems (ICECS), Dubai, United Arab Emirates, 28 November-01 December 2021.
• [52] Tong, D. L, Mintram, R. “Genetic Algorithm-Neural Network (GANN): a study of neural network activation functions and depth of genetic algorithm search applied to feature selection”. International Journal of Machine Learning and Cybernetics, 1, 75-87, 2010.
• [53] Civalek, Ö. “Plak ve kabuklarin nöro-fuzzy tekniği ile lineer ve non-lineer statik-dinamik analizi”. Yüksek Lisans Tezi, Fırat Üniversitesi, Elazığ, Türkiye, 1998.
• [54] Keleşoğlu, Ö, FIRAT, A. “İç basinç altinda ince cidarli kabuklarin yapay sinir ağlari ile çözümü”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 10(3), 447-451, 2006.
• [55] Das SK. “10 Artificial neural networks in geotechnical engineering: modeling and application issues”. Metaheuristics in Water, Geotechnical and Transport Engineering, 45, 231-267, 2013.
• [56] Köken E. “Assessment of deformation properties of coal measure sandstones through regression analyses and artificial neural networks”. Archives of Mining Sciences, 66, 523–542, 2021.