Prediction of Effective Thermal Conductivity of Fluid Saturated Porous Media: in situ Thermo Physical Measurements

Abstract

The density related properties of igneous (dunite and gabbro) and sedimentary (limestone) rocks are measured at room temperature and normal pressure, using ASTM Standards. Dunite samples are taken from Chillas near Gilgit and gabbro samples from Warsik near Peshawar, both of these places are located in north of Pakistan. The limestones are taken from Nammal Gorge sections, Western Salt Range, Pakistan. The thermal properties are determined using the well known transient plane source (TPS) technique. The thermal parameters of dunite are measured in temperature range from 83K to 483K, using air as saturant in pore spaces. The thermal properties of gabbro samples are reported using air as well as water as saturants in pore spaces at room temperature where as the thermal properties of limestones are measured in temperature range from 293K to 443K. All of the measurements on thermal parameters are carried out at normal pressure. Precise measurements on thermal conductivity are difficult to conduct and are very time consuming. Consequently, a lot of work is done on the prediction of effective thermal conductivity of porous media. To become a part of these efforts, an empirical model is proposed, as given below: 1 λ e = 1 λ s + mΦ λ f Where λ e is the effective thermal conductivity, λ f is the thermal conductivity of fluid in pore spaces, λ s is the thermal conductivity of solid phase, Φ is the fractional porosity and m is the empirical coefficient whose value can be determined by the method of least squares. The results of this proposal are compared with the existing models and the corresponding improvements are reported.⎛ 1 ⎞ Using the concept that thermal resistivity ⎜ ⎟ is a linear function of temperature, the ⎝ λ ⎠ above model is then extended to involve the effect of temperature, given as: 1 λ e = 1 λ s + mΦ ⎛ T ⎜ λ f ⎜ ⎝ T o ⎞ ⎟ ⎟ , ⎠ where T o is certain reference temperature. An exponential decay trial is also given for the prediction of effective thermal conductivity of porous media under ambient conditions, as: λ e = λ s e − zΦ λ s λ f , where z is the empirical coefficient. This formula is tested on gabbro samples with air and water as fluids in pore spaces. The results of this relation are again compared with the results obtained from the existing models and the corresponding variations are discussed.