Development of a Mathematical Model for Estimating Rock Thermal Conductivity Using Analogy between Electricity Transmission and Heat Transfer

Document Type : Research Paper

Authors

Ahvaz Faculty of Petroleum, Petroleum University of Technology (PUT), Iran

Abstract

Thermal conductivity of a partially saturated rock sample depends on several parameters such as matrix properties, pore structure, pore filling fluids and their saturations. Indeed, complex pore structure of the rock causes many problems in prediction of its thermal conductivity at different saturation conditions. Numerous investigators presented different correlations and mechanistic predictive models to predict thermal conductivity of porous media. But, most of these models have focused on the prediction of thermal conductivity of single phase saturated porous medium. Analogy between electricity transmission and heat transfer through a rock can be considered as a basis to develop a model for prediction of thermal conductivity. In this paper, thermal conductivity of six carbonate plug samples from one of the Iranian reservoirs has been measured at vacuum condition. Also, for four samples of these six plugs, thermal conductivity has been determined at fully water saturated condition and four different water saturations using divided bar steady-state apparatus; in addition, the second phase has been air. This apparatus has been designed and constructed in Petroleum University of Technology (PUT). Finally, according to the results, it is obvious that rock thermal conductivity at vacuum condition decreases with an increase in porosity. Furthermore, thermal conductivity of partially saturated rock increases with an increase in water saturation. Moreover, a new model for predicting rock thermal conductivity of partially saturated rock has been presented based on the analogy between electricity transmission and heat transfer through the rock. Our experimental results confirmed the suitability of the proposed model.
 

Keywords

References

[1]. Albert K., Schulze M., Franz C., Koenigsdorff R. and Zosseder K., “Thermal conductivity estimation model considering the effect of water saturation explaining the heterogeneity of rock thermal conductivity,” Geothermics, Vol. 66, pp. 1-12, 2016. ##
[2]. Alishaev M. G., Abdulagatov I. M., and Abdulagatova Z. Z., “Effective thermal conductivity of fluid-saturated rocks: experiment and modeling”, Engineering Geology, Vol. 135, pp. 24-39, 2012. ##
[3]. Aurangzeb and Maqsood. A., “Modeling of the effective thermal conductivity of consolidated porous media with different saturants: a test case of gabbro rocks,” International Journal of Thermophysics, Vol. 28, No. 4, pp. 1371-1386, 2007. ##
[4]. Sugawara A. and Yoshizawa Y., “An investigation on the thermal conductivity of porous materials and its application to porous Rook,” Australian Journal of Physics, Vol. 14, No. 4, pp. 469-480, 1961. ##
[5]. Woodside. W., and Messmer. J., “Thermal conductivity of porous media. I. Unconsolidated sands,” Journal of Applied Physics, Vol. 32, No. 9,  pp. 1688-1699, 1961. ##
[6]. Brailsford A. and Major K., “The thermal conductivity of aggregates of several phases, including porous materials,” British Journal of Applied Physics, Vol. 15, No. 3, p. 313, 1964. ##
[7]. Anand J., Somerton W. H. and Gomma E., “Predicting thermal conductivities of formations from other known properties,” Society of Petroleum Engineers Journal, Vol. 13, No. 5, pp. 267-273, 1973. ##
[8]. Sekiguchi K., “A method for determining terrestrial heat flow in oil basinal areas,” Tectonophysics, Vol. 103, No.1, pp. 67-79, 1984. ##
[9]. Bauer T., “A general analytical approach toward the thermal conductivity of porous media,” International Journal of Heat and Mass Transfer, Vol. 36, No. 17, pp. 4181-4191, 1993. ##
[10]. Maqsood A. and Kamran K., “Thermophysical properties of porous sandstones: measurements and comparative study of some representative thermal conductivity models,” International Journal of Thermophysics, Vol. 26, No.5, pp. 1617-1632, 2005. ##
[11]. Popov Y., Tertychnyi V., Romushkevich R., Korobkov D. and Pohl J., “Interrelations between thermal conductivity and other physical properties of rocks: experimental data,” Pure and Applied Geophysics, Vol. 160, pp. 1137-1161, 2003. ##
[12]. Görgülü K., Duruturk Y. S., Demirci A. and Poyraz B., “Influences of uniaxial stress and moisture content on the thermal conductivity of rocks,” International Journal of Rock Mechanics and Mining Sciences, Vol. 45, No. 8, pp. 1439-1445, 2008. ##
[13]. Abdulagatova Z., Abdulagatov I. and Emirov V., “Effect of temperature and pressure on the thermal conductivity of sandstone,” International Journal of Rock Mechanics and Mining Sciences, Vol. 46, No. 6, pp. 1055-1071, 2009. ##
[14]. Nagaraj P. and Roy S., “Effect of water saturation on rock thermal conductivity measurements,” Tectonophysics, Vol. 626, pp. 137-143, 2014. ##
[15]. Mohammadmoradi P., Behrang A, Taheri S. and Kantzas A., “Thermal conductivity of partially saturated microstructures,” International Journal of Thermal Sciences, Vol. 112, pp. 289-303, 2017. ##
[16]. Abid M., Hammerschmidt U. and Köhler J., “Thermophysical properties of a fluid-saturated sandstone,” International Journal of Thermal Sciences, Vol. 76, pp. 43-50, 2014. ##
[17]. Somerton W. H., Keese J. A. and Chu S. L., “Thermal behavior of unconsolidated oil sands,” Society of Petroleum Engineers Journal, Vol. 14, No. 5, pp. 513-521, 1974. ##
[18]. Seto A. and Bharatha S., “Thermal conductivity estimation from temperature logs,” in SPE International Thermal Operations Symposium, Society of Petroleum Engineers, 1991. ##
[19]. Çanakci H., Demirboga R., Karakoc M. B. and Sirin O.,“Thermal conductivity of limestone from Gaziantep (Turkey),” Building and Environment, Vol. 42, No. 4, pp.1777-82, 2007. ##
Journal of Petroleum Research
Volume 29, 98-5 - Serial Number 108
January and February 2019
Pages 17-27

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