Weighted geometric mean model for determining thermal conductivity of reservoir rocks: Current problems with applicability and the model modification

Abstract

Thermal conductivity is one of the fundamental physical parameters of rocks used in all fields of Earth science related to heat transfer in formations. Theoretical modeling of thermal conductivity plays a significant role when it is impossible to carry out measurements on rock samples or when it is necessary to account for variations in bulk thermal conductivity caused by natural or technological factors. Among many theoretical models for determining the thermal conductivity of reservoir rocks, the weighted geometric mean model or so-called Lichtenecker model is the most popular. We demonstrate that the model systematically underestimates the predicted thermal conductivity relative to the experimental results obtained from the thermal conductivity measurements on 20 collections of 1765 samples represented by sandstones, limestone dolomites, limestones, siltstones, and argillites in various saturation states. The underestimation value depends on lithology, porosity, and pore fluid and can reach 53% for high porous (27.6% of porosity) gas-saturated rocks: the average value of the underestimation is 20.5% for dried samples, 14.4% for kerosene-saturated, and 8.6% for water-saturated collections. It means that the applicability of the weighted geometric mean model for determining the thermal conductivity of reservoir rocks creates a serious risk of essential errors in the predicted data that requires revision and improvement of the theoretical model. It is shown that using the correction factor in the weighted geometric mean model resolves the problem leading to an average absolute relative deviation of less than 0.45% for dried and kerosene-saturated samples and less than 0.3% for water-saturated samples. We presented the technique for estimations of the factor for different rock types with corresponding results, and studied its relation with the pore space geometry of carbonate rocks using Effective Medium Theory. Interrelations were studied between the correction factor, rock types, pore fluid, and pore space characteristic - aspect ratio. The suggested improvement technique can be used in numerical calculations after modifying the corresponding option of thermo-hydrodynamic simulators or in theoretical calculations to decrease the uncertainty in bulk thermal conductivity and increase the reliability of calculation results.