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

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.