Effect of deformation on the thermal conductivity of granular porous media with rough grain surface

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Department of Geological and Mining Engineering and Sciences


Heat transfer in granular porous media is an important phenomenon that is relevant to a wide variety of problems, including geothermal reservoirs and enhanced oil recovery by thermal methods. Resistance to flow of heat in the contact area between the grains strongly influences the effective thermal conductivity of such porous media. Extensive experiments have indicated that the roughness of the grains' surface follows self‐affine fractal stochastic functions, and thus, the contact resistance cannot be accounted for by models based on smooth surfaces. Despite the significance of rough contact area, the resistance has been accounted for by a fitting parameter in the models of heat transfer. In this Letter we report on a study of conduction in a packing of particles that contains a fluid of a given conductivity, with each grain having a rough self‐affine surface, and is under an external compressive pressure. The deformation of the contact area depends on the fractal dimension that characterizes the grains' rough surface, as well as their Young's modulus. Excellent qualitative agreement is obtained with experimental data. Deformation of granular porous media with grains that have rough self‐affine fractal surface is simulated. Thermal contact resistance between grains with rough surfaces is incorporated into the numerical simulation of heat conduction under compressive pressure. By increasing compressive pressure, thermal conductivity is enhanced more in the grains with smoother surfaces and lower Young's modulus. Excellent qualitative agreement is obtained with the experimental data.

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Geophysical Research Letters