Scaling of geochemical reaction rates via advective solute transport

Abstract

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...

A Percolation‐Based Approach to Scaling Infiltration and Evapotranspiration

“…Finally, to confirm the accuracy of our above postulate, we test in Figure 5 the prediction in [32] regarding the relationship between A and S. Fitting of the data into a power-law form yields the relationship S ~ A 0.727 , which is in reasonably good agreement with our prediction in the discussion following Equation (8) (10) vs. scaled time , calculated from Equation (11), for 26 experiments from [32] (digitized from their Figure 2b). The infiltration data represent field measurements using double-ring infiltrometers and 26 infiltration tests carried out on a 9.6-ha grassland watershed (called R-5) near Chickasha, Oklahoma.…”

“…Existing scaling predictions from percolation theory of vertical solute transport, chemical weathering and soil formation [9,11,12,14] Replotting the data and predictions given in Figure 3 bi-logarithmically (same color coding) demonstrates that the data agree with the statistical nature of percolation. In particular, as times and corresponding length scales increase relative to pore-scale times, the statistical constraints from percolation theory become more restrictive, and large fluctuations related to small sample size become less important.…”

“…Existing scaling predictions from percolation theory of vertical solute transport, chemical weathering and soil formation [9,11,12,14] invoke 3D imbibition (or saturated) fractal dimensionality of the backbone, relating time and distance of solute transport. Here, by comparison with an analysis of a series of experiments by Sharma et al [32], it was shown that essentially the same scaling describes vertical infiltration.…”

“…Existing scaling predictions from percolation theory of vertical solute transport, chemical weathering and soil formation [9,11,12,14] [32], digitized from their Figure 5, for the relationship between S and A, the coefficients of the transient and steady-state terms of the infiltration equation, respectively. Note that the exponent observed from the data, 0.727 (black line), is in much closer agreement with our prediction using percolation theory, 0.77 (in red), than with the value in Philip's infiltration theory, 0.5 (in blue).…”

“…The contrast between the exponent 1.87 for the most likely time and 1.37 for the shortest distance (for 3D saturated conditions) helps explain why paths that do not appear to be extraordinarily tortuous (20 m in a 1 m column) can still retard the arrival of solutes by an enormous factor [11] (over 1000). Since we are interested in (1) vegetation growth and transpiration in 2D (optimal paths exponent); and (2) unsteady flow in 3D (for the wetting conditions in Philip's infiltration theory), we select here the following exponent values (from Equations (1)- (4)): (i) D opt (2D) =1.21 for vegetation growth, and (ii) D b (3D imbibition) = 1.861 for vertical infiltration.…”