Two-Dimensional Integral Equation Solution of Advective-Conductive Heat Transfer in Sparsely Fractured Water-Saturated Rocks with Heat Source
Publication: International Journal of Geomechanics
Volume 12, Issue 2
Abstract
Saturated sparsely fractured granite (average fracture spacing on the order of meters) is currently studied as the host rock for a potential high-level nuclear waste repository in China. As part of an effort to study the coupling of waste-decay induced heat conduction in the rock matrix and heat convection in the fractures, a mathematical model is proposed for two-dimensional advective-conductive heat transfer in sparsely fractured water-saturated rocks with heat source(s), and an integral-equation solution scheme is developed by using discrete Laplace transform and numerical integration. The model and solution procedure is verified against an analytical solution for a single-fracture case with 1D perpendicular-to-fracture heat conduction. Illustrative calculations reveal, among other things, that significant interactions exist between the heat source intensity and the locations, apertures, and water velocities of the fractures, and that the influence of water in the fractures on the temperature in the rock matrix increases with the magnitudes of the fracture apertures and the water velocities.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study is sponsored by the Natural Science Foundation of China under grant 50778014. The comments from two anonymous reviewers are sincerely appreciated, for they have helped greatly in improving the manuscript.
References
Cheng, A. H.-D., Ghassemi, A., and Detournay, E. (2001). “Integral equation solution of heat extraction from a fracture in hot dry rock.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 25(13), 1327–1338.
Cheng, A. H.-D., Sidauruk, P., and Abousleiman, Y. (1994). “Approximate inversion of the Laplace transform.” Mathematica J., 4(2), 76–82.
Doughty, C. (1999). “Investigation of conceptual and numerical approaches for evaluating moisture, gas, chemical, and heat transport in fractured unsaturated rock.” J. Contam. Hydrol.JCOHE6, 38(1–3), 69–106.
Ghassemi, A., Tarasovs, S., and Cheng, A. H.-D (2003). “An integral equation for three-dimensional heat extraction from planar fracture in hot dry rock.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 27(12), 989–1004.
Gringarten, A. C., Witherspoon, P. A., and Ohnishi, Y. (1975). “Theory of heat extraction from fractured hot dry rock.” J. Geophys. Res.JGREA2, 80(8), 1120–1124.
Lauwerier, H. A. (1955). “The transport of heat in an oil layer caused by the injection of hot fluid.” Appl. Sci. Res., Sect. AASRAA9, 5(2–3), 145–150.
McEwen, T. (2007). “Site selection and characterization.” Chapter 4, Deep geological disposal of radioactive waste, Alexander, W. R. and McKinley, L. E., eds., Elsevier, Oxford, UK.
McKinley, I. G., Alexander, W. R, and Blaser, P. C. (2007). “Development of geological disposal concepts.” Chapter 3, Deep geological disposal of radioactive waste, Alexander, W. R. and McKinley, L. E., eds., Elsevier, Oxford, UK.
Schulz, R. (1987). “Analytical model calculations for heat exchange in a confined aquifer.” J. Geophys.JGEOD4, 61, 12–20.
Stehfest, H. (1970). “Numerical inversion of Laplace transforms.” Commun. ACMCACMA2, 13(1), 47–49, 624.
Zhao, C., Hobbs, B. E., Mühlhaus, H. B., Ord, A., and Lin, G. (2002). “Analysis of steady-state heat transfer through mid-crustal vertical cracks with upward throughflow in hydrothermal systems.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 26(14), 1477–1491.
Zhou, X. X., Ghassemi, A., and Cheng, A. H.-D (2009). “A three-dimensional integral equation model for calculating poro- and thermoealstic stresses induced by cold water injection into a geothermal reservoir.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 33(14), 1613–1640.
Information & Authors
Information
Published In
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Jun 10, 2010
Accepted: Dec 27, 2010
Published online: Mar 15, 2012
Published in print: Apr 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.