Rühaak, W. ; Guadagnini, A. ; Geiger, S. ; Bär, K. ; Gu, Y. ; Aretz, A. ; Homuth, S. ; Sass, I. (2015)
Upscaling thermal conductivities of sedimentary formations for geothermal exploration.
In: geothermics, 58
Article

Abstract

An important issue in the numerical simulation of geothermal reservoirs is the problem of scales. Dataare collected at a scale usually smaller than the one used to discretise the sedimentological units in thenumerical model. For instance, thermal conductivities sampled from field scale cores have measurementsupport in the order of centimeters to meters, whereas numerical models for heat flow require conduc-tivities representative of scales ranging between tens to hundreds of meters. We present a study aimedat demonstrating the upscaling of thermal conductivities. Based on the spatial characteristics of a largesample data set of thermal conductivities of permo-carboniferous sedimentary rocks, 10 different real-izations of the system are randomly generated at a fine scale of resolution and are then upscaled to fourdifferent resolutions using diverse averaging procedures (based on arithmetic, geometric, or harmonicaveraging) as well as renormalization. Results show that upscaling based on harmonic averaging of localvalues is superior in reproducing the original values while renormalization gives the poorest results.Generally it is demonstrated that the specific kind of upscaling has only a small impact on the resultingtemperature distribution. Due to the diffusive character of heat conduction all results tend towards thearithmetic mean value associated with the data.

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