No abstract

No abstract

Understanding the time‐dependent scaling of chemical weathering has been a significant research goal for over a decade. A percolation theoretical treatment of nonreactive solute transport that was previously shown compatible with the scaling of chemical weathering rates is here shown to be compatible with soil formation rates, and with C and N sequestration rates in the soil as well. In this theoretical framework, the percolation backbone fractal dimensionality, which generates the long‐time tail of the solute arrival time distribution, also predicts the scaling of the reaction rates, while laboratory proportionality to the fluid flow velocity translates to an analogous relevance of the vertical infiltration rate in the field. The predicted proportionality of solute transport to net infiltration generates simultaneously the variability in soil formation rates across 4 orders of magnitude of precipitation and 12 orders of magnitude of time scales.

A new model for gas transport in fractal-like tight porous media J. Appl. Phys. 117, 174304 (2015) Transport in porous media is quite complex, and still yields occasional surprises. In geological porous media, the rate at which chemical reactions (e.g., weathering and dissolution) occur is found to diminish by orders of magnitude with increasing time or distance. The temporal rates of laboratory experiments and field observations differ, and extrapolating from laboratory experiments (in months) to field rates (in millions of years) can lead to order-of-magnitude errors.The reactions are transport-limited, but characterizing them using standard solute transport expressions can yield results in agreement with experiment only if spurious assumptions and parameters are introduced. We previously developed a theory of non-reactive solute transport based on applying critical path analysis to the cluster statistics of percolation. The fractal structure of the clusters can be used to generate solute distributions in both time and space. Solute velocities calculated from the temporal evolution of that distribution have the same time dependence as reaction-rate scaling in a wide range of field studies and laboratory experiments, covering some 10 decades in time. The present theory thus both explains a wide range of experiments, and also predicts changes in the scaling behavior in individual systems with increasing time and/or length scales. No other theory captures these variations in scaling by invoking a single physical mechanism. Because the successfully predicted chemical reactions include known results for silicate weathering rates, our theory provides a framework for understanding changes in the global carbon cycle, including its effects on extinctions, climate change, soil production, and denudation rates. It further provides a basis for understanding the fundamental time scales of hydrology and shallow geochemistry, as well as the basis of industrial agriculture. V C 2015 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4913257]Chemical reactions at the surfaces of porous media drive the weathering of silicate minerals in the earth's crust. This weathering affects surface denudation rates and the global carbon cycle, and thereby also climate change and extinctions through geologic time. But reactions within porous media exhibit non-trivial dependences on time, space, and measurement scales that cannot be interpreted as transport-limited in the context of Gaussian transport. Thus, the role of solute transport in controlling such reaction rates has been controversial. Because our transport theory, which is based on concepts from percolation theory, is the first theory that can actually predict nonGaussian solute transport in porous media, we are able to resolve the controversial aspects of chemical reaction rate scaling. In particular, we show that our calculated functional dependence of the solute velocity acts as a proxy for chemical reaction rates, proving that they are limited by transport. Importantly, the solute...

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 porositydependent 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.

The porosity dependence of the formation factor for geologic media is examined from the perspective of universal scaling laws from percolation and effective medium theories. Over much of the range of observed porosity, the expected percolation scaling is observed, but the values of the numerical prefactor do not conform to the simple predictions from percolation theory. Combining effective medium and percolation theories produces a numerical prefactor whose value depends on both the threshold porosity and the porosity above which the formation factor crosses from percolation to effective medium scaling. This change allows extraction of a numerical value of the prefactor, which is reasonably close to experimental values. Subsequent evaluation of the porosity dependence of the formation factor shows that difficulties in prior comparisons of theory and experiment are largely removed when percolation scaling is allowed to transition to effective medium scaling far above the percolation threshold.

No abstract

Accurate prediction of the saturation dependence of different modes of transport in porous media, such as those due to conductivity, air permeability, and diffusion, is of broad interest in engineering and natural resources management. Most current predictions use a "bundle of capillary tubes" concept, which, despite its widespread use, is a severely distorted idealization of natural porous media. In contrast, percolation theory provides a reliable and powerful means to model interconnectivity of disordered networks and porous materials. In this study, we invoke scaling concepts from percolation theory and effective medium theory to predict the saturation dependence of modes of transport — hydraulic and electrical conductivity, air permeability, and gas diffusion — in two disturbed soils. Universal scaling from percolation theory predicts the saturation dependence of air permeability and gas diffusion accurately, even when the percolation threshold for airflow is estimated from the porosity. We also find that the non-universal scaling obtained from the critical path analysis (CPA) of percolation theory can make excellent predictions of hydraulic and electrical conductivity under partially saturated conditions.