Nonreactive Solute Transport Research Articles

Comparison of non-reactive solute transport models for the evaluation of fluid flow in packed beds with implications for heap leaching practice

This study investigated the effects of mean particle size fraction, bottom particle size, particle porosity and wettability on solution scale preferential flow behaviour via step input tracer tests in drip irrigated, narrowly and mixed-sized beds under steady state fluid flux. Nine solute transport models were used to quantify this behaviour reflected in the residence time distribution (RTD) profiles. Four were empirical models: three compartmental model configurations (CM-1, CM-2, CM-3) and tanks-in-series (TIS) model. The remainder five models were semi-empirical: advection dispersion (AD), piston exchange (PE), piston exchange - diffusion variant (PE-D), piston dispersion and exchange (PDE) and piston dispersion and exchange - diffusion variant (PDED). The model fit results showed that the mono-porosity TIS, AD and CM-2 models were the worst performers, while the dual porosity PDE and novel PDE-D models achieved the lowest average error values across the various systems. Higher levels of particle wettability coupled with capillary effects produced peculiar RTD curves that were relatively more difficult for the mono-porosity models to simulate. The model parameters investigated included the longitudinal dispersion coefficient (Dds), dead to total volume fraction (VD/VT), dynamic to total saturation fraction (βd/βT), overall mass transfer coefficient (Kma) and maximum diffusional pore length (X). The results showed that an increase in the average particle size within the beds led to higher VD/VT, Dds and X values, but lower βd/βT and Kma values. These indicate an overall increase in solution scale preferential flow behaviour. Decreased capillary suction and connectivity between particle pores and inter-particle voids were deemed responsible for the results. Higher levels of particle porosity acted as a buffer against these effects. Overall, the results highlight the benefit of the addition of fines (0.1–1 mm particles) during the agglomeration process in heaps to help reduce solution scale preferential flow behaviour and increase liquid hold-up. This is more necessary when the ore has low to moderate levels of porosity (surface area: <2 m2/g) and will also increase the modelling options available as most models performed better fitting data from such beds.

Links between soil pore structure, water flow and solute transport in the topsoil of an arable field: Does soil organic carbon matter?

An improved understanding of preferential solute transport in soil macropores would enable more reliable predictions of the fate of agrochemicals and the protection of water quality in agricultural landscapes. The objective of this study was to investigate how soil organic carbon (SOC) and soil texture shape soil pore structure and thereby determine the susceptibility to preferential transport under steady-state near-saturated flow conditions. To do so, we took intact topsoil samples from an arable field that has large variations in SOC content (1.1–2.7%) and clay content (8–42%). Soil pore structure was quantified by X-ray tomography and soil water retention measurements. Non-reactive solute transport experiments under steady-state near-saturated conditions were carried out at irrigation rates of 2 and 5 mm h−1 to quantify the degree of preferential transport. Near-saturated hydraulic conductivities at pressure heads of −1.3 and −6 cm were also measured using a tension disc infiltrometer. The results showed that larger abundances of small macropores (240–720 µm diameter) and mesopores (5–100 µm diameter) resulted in weaker preferential transport, due to larger hydraulic conductivities in the soil matrix that prevented the activation of water flow and solute transport in large macropores. In particular, the degree of preferential transport was most strongly and negatively correlated with the mesoporosity in the 30–100 µm diameter class. In contrast, the degree of preferential transport was not correlated with connectivity measures (e.g. the percolating fraction and critical pore diameter for the macropore network), probably because i.) the pore space of almost all samples was highly connected, being dominated by one percolating cluster, and ii.) only a part of this percolating macroporosity was active under the near-saturated conditions of the experiment. We also found that the degree of preferential transport was strongly and negatively correlated with clay content, whilst the effects of SOC were not significant. Nevertheless, macroporosity in the 240–720 µm diameter class and mesoporosity were positively correlated with SOC content in our soils and in some previous studies. Therefore, SOC sequestration in arable soils may potentially reduce the risk of preferential transport under near-saturated flow conditions through better developed networks of small macropores and mesopores.

Numerical investigation of solute migration and release from sediments driven by wave-induced accumulation of pore water pressure

Sediments with poor drainage conditions are prone to build-up of excess pore water pressure when exposed to dynamic wave loading. This results in accumulated seepage flow that may have a significant impact on migration of solutes in marine sediments. In this study, the complex interplay between solute transport and wave-induced seepage process is investigated through a pioneering approach that combines and synchronously solves the two-dimensional advection-dispersion equation governing nonreactive solute transport with the governing equations for wave-induced oscillatory and residual pore pressures. The simulated results have demonstrated that the accumulated seepage flow significantly contributes to the advective and dispersive fluxes of solute, where the advection leads to movement of the solute layer and the hydrodynamic dispersion primarily enlarges the thickness of solute layer. The distribution of residual pore water pressure along depth exhibits two patterns that are primarily influenced by the thickness of the seabed. When the seabed is thinner than 0.3 times the wavelength, the residual pore pressure increases monotonically with depth (Pattern I). In this situation, the solute always migrates upwards to the seabed surface. Otherwise, Pattern II depicts the distribution of residual pore pressure, where the peak value of residual pore pressure attains at a certain depth and may advance downwards with wave action time. In this case, the direction of solute migration in regions shallower than a certain depth (e.g., 0.6 times the thickness of sediment) may alternate over time but the solute can eventually be transported upwards to seabed surface. The parametric study shows that when the seabed thickness is 0.2–0.3 times the wavelength, accumulated seepage flow has less effect on solute migration, whereas decreasing relative density and shear modulus, as well as increasing soil permeability can enhance the effect of accumulated pore water pressure on solute migration.

A solute transport in deformable dual-porosity media using mixture-coupling theory

Rock, soil and many porous-like materials are often fractured or structured media, which can exhibit dual-porosity behaviour. Studies on solute transport in deformable dual-porosity media remain challenging due to the multi-physics coupled effects and the complex interaction between fractures (or macropores) and the porous matrix. Although several studies exist on constitutive modelling of coupled behaviour in deformable dual-porosity media, the previously developed models are not systematic in thermodynamical frameworks. This paper proposes a mixture coupling theory approach based on non-equilibrium thermodynamics to develop a solute transport model with consideration of hydromechanical coupling in dual-porosity media (referred to as the ST-HM model). This paper derives the constitutive equations of fully hydromechanical coupled behaviour in dual-porosity media and considers the pore and fracture porosity evolution influenced by both hydraulic and mechanical fields. Therefore, the governing equations of ST-HM are capable of predicting non-reactive solute transport with a fully hydromechanical coupled effect in dual-porosity media. Then, the model was verified against existing models and validated by relevant experimental results. Further, a numerical example shows that the presented model significantly improves the accuracy of the prediction of porosity, fluid pressure and solute concentration compared with previous models, which ignore the fully hydromechanical coupled effects on solute transport.

Numerical investigation of solute transport into deformable marine sediments driven by ocean waves

Most existing studies do not consider the effect that the deformability of submarine sediments may have on solute transport under the action of ocean waves. In this study a two-dimensional numerical model based on Biot’s poro-elastic consolidation theory and an advection–dispersion equation is established to investigate the transport of non-reactive solute into a deformable porous seabed under the influence of ocean waves. The numerical model is then validated against experimental and analytical results in order to demonstrate its accuracy and robustness. The simulation results indicate that ignoring the deformability of seabed soil and associated seepage force due to ocean waves may lead to a significant underestimation of the rate of solute transport in shallow layers of marine sediment, particularly fine sand or silt. The effects of parameters such as the shear modulus, non-dimensional mechanical dispersion coefficient (related to particle size and permeability), dimensionless sediment thickness, wave steepness and the relative water depth have on solute transport into deformable sediments were investigated. The results indicate that the ratio of the longitudinal coefficient of mechanical dispersion between deformable and non-deformable sediments that can represent the enhancement of solute migration due to soil deformation may reach up to 85. This becomes more pronounced as the shear modulus and permeability of sediments decrease and the depth of water increases when the sediment thickness is less than 0.8 times the wavelength. The rate of solute transport in deformable sediments reaches its maximum when the sediment thickness is about 0.2 times the wavelength. In fact, as the relative water depth increases from 0.1 to 0.3, the enhancement of solute migration due to wave-induced soil deformation increases by about 60%-80%. In comparison to linear waves, shallow water waves, e.g., the first-order cnoidal waves, can increase the transport of solute more due to its strong non-linear behaviour, particularly in deformable seabed.

Density and size-dependent bioturbation effects of the infaunal polychaete Nephtys incisa on sediment biogeochemistry and solute exchange

The impact of bioturbation on the geochemistry of aquatic sediments is known to depend on the benthic infauna species that are present. However, burrowing and activity patterns of each species may also change during the different stages of a life cycle. In this study, we examined the effects of four size classes of the polychaete Nephtys incisa on burrow networks and sediment biogeochemistry. In our experimental aquaria, the total biovolume (~ biomass) of Nephtys was kept constant, but different age classes were introduced, so the size and abundance varied between treatments. Despite differences in the geometry of burrow networks (due to varying density and size of burrows as revealed by X-radiography), the transport of nonreactive solutes (Br–) showed little difference between treatments. In contrast, the depth distribution of reactive solutes (Fe2+, Mn2+, TPO3– 4, TCO2, O2, pH) depended on oxidized sediment volumes and on spatial micro-heterogeneity related to burrowing patterns. Net fluxes of O2, TCO2, and NO– 3 fluxes were strongly affected by age-dependent burrowing patterns. Carbonate dissolution and remineralization rates (reflected by TCO 2fluxes) were enhanced as the size of individuals increased. NO– 3fluxes showed progressive change from dominance of nitrification (release) to denitrification (uptake) as burrow densities decreased with larger individuals. We conclude that different age-size classes of a single species at identical biovolume affect biogeo- chemical cycling differently, due to changes in burrow sizes and burrow densities. Because of redox reaction coupling associated with burrow geometries (Fe2+, Mn2+ oxidation patterns), similar magnitudes of nonlocal transport may be a misleading indicator of biogenic impacts. Our observations demonstrate that biogeochemical impacts must be evaluated in the context of size (age-) specific traits and population densities rather than biomass or biovolume alone.

Modeling transport, fate, and removal kinetics of nitrate and orthophosphate using recycled adsorbents for high and low-flow stormwater runoff treatment

Excessive nitrate and orthophosphate carried by the stormwater runoff potentially lead to eutrophication in surface water bodies. Various green infrastructures are used that commonly consider the biological treatment of nutrients from the runoff. Due to the leaching and clogging complexities in biological mechanisms, the selection of high-flow, eco-friendly, and recycled adsorbents has been advocated to promote the physiochemical treatment of nutrients as an alternative. In this study, column experiments were conducted to investigate the transport, fate, adsorption equilibria, and reaction kinetics of nitrate (NO3–N) and orthophosphate (PO4–P) onto three recycled adsorbents - recycled concrete aggregate (RCA), recycled crushed glass (RCG), rice husks (RH), and a layered media (LM), under high and low-flow conditions. The non-reactive solute transport in columns was investigated through the bromide tracer test. The HYDRUS-1D model was used to estimate adsorption coefficients and reaction kinetics of pollutants in unsaturated media columns. Our results indicated the maximum superficial pore velocity (v = 4.40 cm/s) and dispersion (α = 2.50 cm) in RCA at the low-flow condition. Overall, NO3–N removal at the exhaustion was low in all columns, ranging between 1 and 25%. Conversely, orthophosphate removal was significant (p < 0.05) in RCA (≤94%) under low flow conditions with increased reaction kinetics (kr,d = 3.45 min−1, kr,s = 0.55 min−1) and enhanced adsorption capacity at saturation (qmax = 1.87E+05–2.33E+05 mg/kg). In conclusion, the dissolved-phase reaction kinetics (kr,d) played a significant role apart from the physisorption for the satisfactory removal of orthophosphate in RCA.

Inclusion of slow infiltration in determining the influence time of saline sediments on reservoir water

The influence time of polluted sediments on water quality, as well as the influence degree, plays a key role in decision-making for sediment pollution control. However, factors that determine influence time, especially slow infiltration through sediments, are poorly known. Further, there is a lack of corresponding indexes and efficient models to accurately identify the critical moment in determining the influence time from the dynamic process of interaction between downward advection (infiltration) and upward diffusion at the sediment-water interface. Therefore, this article focuses on methods for determining the influence time of saline sediments on reservoir water salinisation. An alternative expression of Péclet number (Pe=uCD∂C/∂xx=0) is proposed to characterise the transient relative role of downward advection versus upward diffusion on the transport of non-reactive solutes; Pe = 1 can be used as an exact criterion for identifying the critical moment when saline sediments no longer affect the overlying water. We then developed a single-domain model that does not require an alternate run the two subdomains in solving processes, enabling to flexibly simulate sediment-water interactions, both effectively and efficiently. By combining this model with the alternative Pe, the influence time of saline sediments on reservoir water can be accurately determined. We used the planned Muguandao Coastal Reservoir, Qingdao, China, as an example to explore the effects of infiltration on the influence time. The influence time shortens with infiltration rates in a power function relationship and decreases from 970 years to 19.3 years in the rate range of (1–7) ×10−2 m/year. Furthermore, based on the simulation and sensitivity analysis, we suggest a simple formula (t=5.25D/u2) to directly predict the influence time of saline sediments on water salinisation for shallow mixed coastal reservoirs. The importance of understanding slow infiltration in determining the influence time is discussed.

Influence of Clay on Solute Transport in Saturated Homogeneous Mixed Media

In this study, four homogeneous porous media (HPM1-HPM4), consisting of distinct proportions of sand-sized and clay-sized solid beads, were prepared and used as single fracture infills. Flow and nonreactive solute transport experiments in HPM1-HPM4 under three flow rates were conducted, and the measured breakthrough curves (BTCs) were quantified using conventional advection-dispersion equation (ADE), mobile-immobile model (MIM), and continuous time random walk (CTRW) model with truncated power law transition time distribution. The measured BTCs showed stronger non-Fickian behaviour in HPM2-HPM4 (which had clay) than in HPM1 (which had no clay), implying that clay enhanced the non-Fickian transport. As the fraction of clay increased, the global error of ADE fits also increased, affirming the inefficiency of ADE in capturing the clay-induced non-Fickian behaviour. MIM and CTRW performed better in capturing the non-Fickian behaviour. Nonetheless, CTRW’s performance was robust. 12.5% and 25% of clay in HPM2 and HPM3, respectively, decreased the flowing fluid region and increased the solute exchange rate between the flowing and stagnant fluid regions in MIM. For CTRW, the power law exponent ( β CTRW ) values were 1.96, 1.75, and 1.63 in HPM1-HPM3, respectively, implying enhanced non-Fickian behaviour. However, for HPM4, whose clay fraction was 50%, the β CTRW value was 1.87, implying a deviation in the trend of non-Fickian enhancement with increasing clay fraction. This deviation indicated that non-Fickian behaviour enhancement depended on the fraction of clay present. Moreover, increasing flow rate enhanced the non-Fickian transport based on β CTRW .

Investigating the impact of exit effects on solute transport in macroporous media

Abstract. The effect of macropore flow on solute transport has spurred much research over the last forty years. In this study, non-reactive solute transport in water-saturated columns filled with porous media crossed by a macropore was experimentally and numerically investigated. The emphasis was put on the study of exit effects, whose very existence is inherent to the finite size of any experimental column. We specifically investigated the impact of a filter at the column outlet on water flow and solute transport in macroporous systems. Experiments involving breakthrough measurements and magnetic resonance imaging (MRI) showed that solute transport displayed some significant non-unidirectional features, with a strong mass exchange at the interface between the macropore and the matrix. Fluid dynamics and transport simulations indicated that this was due to the non-unidirectional nature of the flow field close to the outlet filter. The flow near the exit of the column was shown to be strongly impacted by the presence of the outlet filter, which acts as a barrier and redistributes water from the macropore to the matrix. This impact was apparent on the breakthrough curves and the MRI images. It was also confirmed by computer simulations and could, if not properly taken into account, impede the accurate inference of the transport properties of macroporous media from breakthrough experiments.

Modeling One-Dimensional Nonreactive Solute Transport in Open Channel Flows Under Uncertain Flow and Solute Loading Conditions

AbstractThe study of solute transport processes in open channel flows is important for water quality management and environment protection. Solute transported in open channel flows is usually uncer...

Short-term variations in tracer-test responses in a highly karstified watershed

Methods of modelling non-reactive solute transport based on artificial tracer tests have been widely developed in the past few decades. The dependence of solute transport parameters on boundary conditions has been investigated across different hydrological settings (low and high water level) but still not investigated at the short-term scale (i.e. hourly and daily scale). In this study, a campaign of several tracer tests was performed over a few days to investigate the short-term variations of tracer-test responses in a conduit-dominated karst system (Baget watershed, in the Pyrenees Mountains, France) during a recession without the influence of rainfall. Also, an improved method of interpreting artificial tracer test results, using a process engineering tool, is introduced, consisting of a Laplace-transform transfer function approach with respect to the residence-time distribution curve. Considering the karstic system as a chemical reactor, the introduction of a transfer function approach appears to be an efficient way to describe the solute transport. Moreover, the transfer function is parametrized depending on the spring discharge. The model is extended for testing source pollution scenarios.

Centrifugal Modeling and Validation of Solute Transport within Unsaturated Zone

Numerical modeling has been adopted to assess the feasibility of centrifugal simulation of solute transport within the unsaturated zone. A numerical model was developed to study the centrifugal simulation of nonreactive, adsorption, radionuclide, and reactive solutes. The results showed that it is feasible to conduct centrifugal experiments for nonreactive solute transport. For the solute transport containing physical processes or chemical reactions, if the reaction is very rapid or slow, it is feasible to conduct centrifugal experiments. For the solute transport with a product B generated, if the reaction is relatively slow, the centrifugal prediction of solute is suitable. The centrifugal prediction of solute A matches the prototype quite well, but the prediction of B is in poor quality. If B is the focus, it is not feasible to conduct centrifugal experiments; but if B is not important, the centrifugal modeling is suitable. This has significant implications for the centrifugal modeling application to solute transport simulation within the unsaturated zone.

Non-reactive solute transport modelling with time-dependent dispersion through stratified porous media

We present a numerical solution of the mobile–immobile model (MIM) with time-dependent dispersion coefficient to simulate solute transport through heterogeneous porous media. Observed experimental data of non-reactive solute transport through hydraulically coupled stratified porous media have been simulated using asymptotic and linear time-dependent dispersion functions. Non-Gaussian breakthrough curves comprising long tails are simulated well with the MIM incorporating asymptotic time-dependent dispersion model. The system is under the strong influence of physical nonequilibrium, which is evident by variable mass transfer coefficient estimated at different down-gradient distances. Asymptotic time-dependent functions are capable of capturing the rising limb of the solution phase breakthrough curves with improved accuracy, whereas tailing part simulation capabilities are similar for both asymptotic and linear time-dependent dispersion functions. Further, the temporal moment analysis demonstrated increased spreading, variance for linear dispersion model as compared with asymptotic dispersion model. It is also observed that the first-order mass transfer coefficient varies inversely with travel distance from the input source. It can be concluded from the study that MIM with time-dependent dispersion function is simpler yet sensitive to account for medium’s heterogeneity in a better manner even for small observation distances from the source.

Interplay between Molecular Diffusion and Advection during Solute Transport in Macroporous Media

Core Ideas BTCs in a macroporous medium cannot always be fitted by classical transport models. Classical transport models can be faulted in a simple heterogeneous porous medium. Molecular diffusion affects solute transport for sufficient mean residence time. The shape of the BTCs depends on the mean residence time of the solute. Solute transport in soils is known to differ from solute transport in homogeneous porous media. Nonequilibrium processes, like those induced by the presence of macropores, can strongly influence the breakthrough of solute in soils. Breakthrough experiments and effective models are often combined to study the physicochemical processes involved in solute transport. However, the complexity of flow pathways and the diversity of possible processes is challenging. In this work, the influence of flow rate and viscosity of the carrying liquid on nonreactive solute transport is investigated under saturated conditions in a macroporous synthetic medium. As expected, solute transport is strongly affected by physical nonequilibrium induced by the preferential flow within the macropore. Breakthrough occurs early, and the shape of the breakthrough curve is influenced both by the flow rate and the coefficient of molecular diffusion of the solute. We show that when the mean residence time of the solute in the macropore is small enough, solute transport in a macroporous column can be considered as isolated within the macropore. The increase of the residence time strongly affects the shape of the breakthrough, and, eventually, a plateau appears during the ascent of the breakthrough curve. We demonstrate experimentally that the existence of this plateau, which is not predicted by classical effective models, is related to the relative importance of molecular diffusion versus advection. Indeed, this plateau can become unobservable if the coefficient of molecular diffusion is reduced through the use of a sufficiently viscous carrying liquid.

Experimental and numerical investigations on the effect of fracture geometry and fracture aperture distribution on flow and solute transport in natural fractures

The impact of fracture geometry and aperture distribution on fluid movement and on non-reactive solute transport was investigated experimentally and numerically in single fractures. For this purpose a hydrothermally altered and an unaltered granite drill core with axial fractures were investigated. Using three injection and three extraction locations at top and bottom of the fractured cores, different dipole flow fields were examined. The conservative tracer (Amino-G) breakthrough curves were measured using fluorescence spectroscopy. Based on 3-D digital data obtained by micro-computed tomography 2.5-D numerical models were generated for both fractures by mapping the measured aperture distributions to the 2-D fracture geometries (x-y plane). Fluid flow and tracer transport were simulated using COMSOL Multiphysics®.By means of numerical simulations and tomographic imaging experimentally observed breakthrough curves can be understood and qualitatively reproduced. The experiments and simulations suggest that fluid flow in the altered fracture is governed by the 2-D fracture geometry in the x-y plane, while fluid flow in the unaltered fracture seems to be controlled by the aperture distribution. Moreover, we demonstrate that in our case simplified parallel-plate models fail to describe the experimental findings and that pronounced tailings can be attributed to complex internal heterogeneities. The results presented, implicate the necessity to incorporate complex domain geometries governing fluid flow and mass transport into transport modeling.

Prediction of Soil Formation as a Function of Age Using the Percolation Theory Approach

Recent modeling and comparison with field results showed that soil formation by chemical weathering, from bedrock or unconsolidated material, is limited largely by solute transport. Chemical weathering rates are proportional to solute velocities. Nonreactive solute transport described by non-Gaussian transport theory appears compatible with soil formation rates. This change in understanding opens new possibilities for predicting soil production and depth across orders of magnitude of time scales. Percolation theory for modeling the evolution of soil depth and production was applied to new and published data for alpine and Mediterranean soils. The first goal was to check whether the empirical data conform to the theory. Secondly we analyzed discrepancies between theory and observation to find out if the theory is incomplete, if modifications of existing experimental procedures are needed and what parameters might be estimated improperly. Not all input parameters required for current theoretical formulations (particle size, erosion and infiltration rates) are collected routinely in the field; thus, theory must address how to find these quantities from existing climate and soil data repositories, which implicitly introduces some uncertainties. Existing results for soil texture, typically reported at relevant field sites, had to be transformed to results for a median particle size, d50, a specific theoretical input parameter. The modeling tracked reasonably well the evolution of the alpine and Mediterranean soils. For the Alpine sites we found, however, that we consistently overestimated soil depths by approximately 45%. Particularly during early soil formation, chemical weathering is more severely limited by reaction kinetics than by solute transport. The kinetic limitation of mineral weathering can affect the system until 1kyr to a maximum of 10kyr of soil evolution. Thereafter, solute transport seems dominant. The trend and scatter of soil depth evolution is well captured, particularly for Mediterranean soils. We assume that some neglected processes, such as bioturbation, tree throw, and land use change contributed to local reorganization of the soil and thus to some differences to the model. Nonetheless, the model is able to generate soil depth and confirms decreasing production rates with age. A steady state for soils is not reached before about 100 kyr.

A non-negative and high-resolution finite volume method for the depth-integrated solute transport equation using an unstructured triangular mesh

This paper proposes a new high-resolution finite volume method for solving the two-dimensional (2D) solute transport equation using an unstructured mesh. A new simple r-factor algorithm is introduced into the Total Variation Diminishing flux limiter to achieve a more efficient yet accurate high-resolution scheme for solving the advection term. To avoid the physically-meaningless negative solutions resulted from using the Green–Gauss theorem, a nonlinear two-point flux approximation scheme is adopted to deal with the anisotropic diffusion term. The developed method can be readily coupled with a two-dimensional finite-volume-based flow models under unstructured triangular mesh. By integrating with the ELCIRC flow model, the proposed method was verified using three idealized benchmark cases (i.e., advection of a circle-shaped solute field, advection in a cyclogenesis flow field and transport of a initially square-shaped solute plume), and further applied to simulate the non-reactive solute transport process driven by irregular tides in the Deep Bay, eastern Pearl River Estuary of China. These cases are also simulated by models using other existing methods, including different r-factor for advection term and the Green–Gauss theorem for diffusion term. The comparison between the results from the new method and those from other existing methods demonstrated the new method could describe advection induced concentration shock and discontinuities, and anisotropic diffusion at high resolution without providing spurious oscillations and negative values.

A similarity solution for reaction front propagation in a fracture-matrix system.

We propose a new composite similarity variable, based on which a similarity solution is derived for reaction front propagation in fracture-matrix systems. The similarity solution neglects diffusion/dispersion within the fracture and assumes the existence of a sharp reaction front in the rock matrix. The reaction front location in the rock matrix is shown to follow a linear decrease with distance along the fracture. The reaction front propagation along the fracture is shown to scale like diffusion (i.e. as the square root of time). The similarity solution using the composite similarity variable appears to be applicable to a broad class of reactive transport problems involving mineral reactions in fracture-matrix systems. It also reproduces the solutions for non-reactive solute and heat transport when diffusion/dispersion/conduction are neglected in the fracture. We compared our similarity solution against numerical simulations for nonlinear reactive transport of an aqueous species with a mineral in the rock matrix. The similarity solutions agree very well with the numerical solutions, especially at later times when diffusion limitations are more pronounced.This article is part of the themed issue 'Energy and the subsurface'.

Percolation theory for solute transport in porous media: Geochemistry, geomorphology, and carbon cycling

AbstractUnderstanding 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.