Staged Effective Medium Modeling and Experimental Validation for Rock Thermal Conductivity

The thermal conductivity (λ) of porous rocks as a function of total porosity, grain size, and fluid saturation is measured and modeled by combining high-precision experiments with a Staged Differential Effective-Medium (SDEM) modeling framework. A 1-D divided-bar apparatus with PID-controlled guard heaters with an integrated ultrasonic pulse-transmission system was developed to measure the thermal conductivity and P and S-wave velocities simultaneously. Measurements were made on Fontainebleau Sandstone cores and quartz sand packs of varying grain size effective stresses up to 2000psi. The sample properties were measured in both dry and water-saturated states. For the sand packs the thermal conductivity and compressional velocity are the highest and most stress-sensitive for the fine-grained material. In contrast the shear velocity is largest in the coarse-grained material. The SDEM model is adapted from previous acoustic models for use in understanding thermal conductivity. These joint models accurately reproduce the evolution of both thermal conductivity and bulk modulus during increasing compaction and varying saturation. A single parameter fits both the dry and saturated data which allows Gassmann-style fluid substitution for the thermal conductivity. This model improves the prediction of in-situ thermal conductivity from sonic well logs.