Knowledge of porosity and saturation‐dependent thermal conductivities is necessary to investigate heat and water transfer in natural porous media such as rocks and soils. Thermal conductivity in a porous medium is affected by the complicated relationship between the topology and geometry of the pore space and the solid matrix. However, as water content increases from completely dry to fully saturated, the effect of the liquid phase on thermal conductivity may increase substantially. Although various methods have been proposed to model the porosity and saturation dependence of thermal conductivity, most are empirical or quasiphysical. In this study, we present a theoretical upscaling framework from percolation theory and the effective‐medium approximation, which is called percolation‐based effective‐medium approximation (P‐EMA). The proposed model predicts the thermal conductivity in porous media from endmember properties (e.g., air, solid matrix, and saturating fluid thermal conductivities), a scaling exponent, and a percolation threshold. In order to evaluate our porosity and saturation‐dependent models, we compare our theory with 193 porosity‐dependent thermal conductivity measurements and 25 saturation‐dependent thermal conductivity data sets and find excellent match. We also find values for the scaling exponent different than the universal value of 2, in insulator‐conductor systems, and also different from 0.76, the exponent in conductor‐superconductor mixtures, in three dimensions. These results indicate that the thermal conductivity under fully and partially saturated conditions conforms to nonuniversal behavior. This means the value of the scaling exponent changes from medium to medium and depends not only on structural and geometrical properties of the medium but also characteristics (e.g., wetting or nonwetting) of the saturating fluid.

Pore size distributions in rocks may be represented by fractal scaling, and fractal descriptions of pore systems may be used for prediction of petrophysical properties such as permeability, tortuosity, diffusivity, and electrical conductivity. Transverse relaxation time (T2) distributions determined by nuclear magnetic resonance (NMR) measurements may be used to determine the fractal scaling of the pore system, but the analysis is complicated when internal magnetic field gradients at the pore scale are sufficiently large. Through computations in ideal porous media and laboratory measurements of glass beads and sediment samples, we found that the effect of internal magnetic field gradients was most pronounced in rocks with larger pores and a high magnetic susceptibility contrast between the pore fluid and mineral grains. We quantified this behavior in terms of pore size and Carr-Purcell-Meiboom-Gill (CPMG) half-echo spacing through scaling arguments. We additionally found that the effects of internal field gradients may be mitigated in the laboratory by performing T2 measurements with different CPMG half-echo spacings and fitting the apparent fractal dimensions determined by the NMR measurements with a model to determine the true pore system fractal dimension.

We measured nuclear magnetic resonance (NMR) relaxation times on samples from Integrated Ocean Drilling Program Expedition 333 Sites C0011, C0012, and C0018. We compared our results to permeability, grain size, and specific surface measurements, pore size distributions from mercury injection capillary pressure, and mineralogy from X‐ray fluorescence. We found that permeability could be predicted from NMR measurements by including grain size and specific surface to quantify pore networks and that grain size is the most important factor in relating NMR response to permeability. Samples within zones of anomalously high porosity from Sites C0011 and C0012 were found to have different NMR‐permeability relationships than samples from outside these zones, suggesting that the porosity anomaly is related to a fundamental difference in pore structure. We additionally estimated the size of paramagnetic sites that cause proton relaxation and found that in most of our samples, paramagnetic material is present mainly as discrete, clay‐sized grains. This distribution of paramagnetic material may cause pronounced heterogeneity in NMR properties at the pore scale that is not accounted for in most NMR interpretation techniques. Our results provide important insight into the microstructure of marine sediments in the Nankai Trough.