Predictive mixing law models of rock thermal conductivity: Applicability analysis

Thermal conductivity is defined as the ability of a material to conduct the heat. Rock thermal conductivity is influenced by several parameters such as mineral composition, geometrical factors, porosity, and saturation condition. Value of the rock thermal conductivity is necessary in all thermal processes in petroleum engineering such as thermal methods of enhanced oil recovery. Laboratory measurement of the thermal conductivity of rock samples is time-consuming and expensive. Therefore, a large number of correlations and models have been presented to predict the rock thermal conductivity. These correlations and models are divided into three categories, i.e. mixing models, empirical and semi-empirical correlations, and theoretical models. In this paper, it was attempted to investigate 15 different predictive mixing models of rock thermal conductivity and examine their applications for different rock types and different saturation conditions using 159 collected data points. Validity and applicability of these predictive models were discussed using graphical and statistical error analysis. Results indicated that geometric mean model and Albert model can provide an accurate estimation of rock thermal conductivity with average absolute relative deviation (AARD) of 11.58% and 13.87%, respectively. Moreover, the applicability of each model was evaluated for different conditions of rock type and saturation. This evaluation revealed that Walsh, Alishaev, and Zimmerman models are more accurate than geometric mean model and Albert model for some specific conditions of rock type and saturation. Indeed, Walsh model is the best predictive thermal conductivity model for air saturated crystalline rocks, Alishaev model is the best model for predicting thermal conductivity of water saturated crystalline rocks and Zimmerman model provides the best estimation of the thermal conductivity of water saturated dolomite rocks. It should be noted that structural properties, which affect the rock thermal conductivity, are not considered in the mixing models which is the main limitation of this type of predictive models.