Chemical reactions are driven by non‐equilibrium and can be fully described by the spatio‐temporal distribution of the reaction rate. We present an analytical approach for the computation of reaction rates under local non‐equilibrium conditions for a precipitation/dissolution problem. We derive an original non‐linear partial differential equation for the reaction rate r and present a series expansion of r for large Damköhler numbers, i.e., fast local scale reactions. The impact of local scale non‐equilibrium conditions on the transport‐controlled reaction rate is studied for reactive transport in a column.

Analysis of the space‐time evolution of reactive solutes in porous systems is complex owing to the presence of different types of chemical reactions. The complete description of a reactive transport scenario entails calculating the spatial and temporal distribution of species concentrations and reaction rates. Here we develop an exact explicit expression for the space‐time distribution of reaction rates for a scenario where the geochemical system can be described by an arbitrary number of equilibrium (fast) reactions and one kinetic (slow) reaction, in the absence of non‐constant‐activity immobile species. The key result is that the equilibrium reaction rate is the sum of two terms representing the availability of reactants. One term involves diffusion and dispersion and represents the contribution of mixing. The other term includes the contribution of the kinetic reaction. The approach also yields the local concentrations of all dissolved species. Yet the latter are not needed for the direct computation of equilibrium reaction rates. We illustrate the approach by means of a simple reactive transport scenario, involving a common ion effect in the presence of a kinetic and an equilibrium reaction leading to precipitation and dissolution processes within a one‐dimensional fully saturated porous medium. The example highlights the highly nonlinear and nonmonotonic response of the system to the controlling input parameters.

Fine particle deposition within riverbeds plays a major role in riverine ecology and biogeochemistry by altering hyporheic exchange flux. Moreover, it is ubiquitous within streams and rivers across all flow stages. However, the dynamics of fine particle deposition are still not completely understood in rivers, and continuum models like the advection dispersion equation require modifications to represent the processes accurately. To enhance understanding of fine particle dynamics, we developed a novel numerical particle tracking model that simulates fine particle deposition as a stochastic process under losing, neutral, and gaining streamflow conditions. These flow conditions generate three different velocity profiles by combining the free surface and groundwater flows. In addition, a novel aspect of our model is the storage of filtered particles to estimate concentration fields within the bed. Our simulated results are qualitatively compared with previous laboratory flume experimental results of kaolinite deposition under similar conditions. The model indicates that fine particle deposition patterns and residence time functions depend heavily on the exchange flux between stream and groundwater, as well as bed filtration properties as the deposition of particles occurs at greater depths in the losing stream condition than in the neutral and gaining cases. Therefore, the spatial pattern of particle deposition is a direct result of pore water velocity profiles, while the concentration depends on filtration dynamics within the bed.