Shannon Entropy of Transport Self-Organization Due to Dissolution/Precipitation Reaction at Varying Peclet Number in an Initially Homogeneous Porous Media

Abstract. Dissolution and precipitation processes in reactive transport in porous media are ubiquitous in a multitude of contexts within the field of Earth sciences. In particular, the dynamic coupling between the reactive precipitation / dissolution processes and the solute transport is of interest, as it is capable of giving rise to the emergence of preferential flow paths in the porous host matrix. This coupling is critical to a variety of Earth science scenarios, although the approaches to its characterization remain disputed. It has been shown that the emergence of preferential flow paths can be considered a manifestation of transport self-organization in porous media, as they create spatial gradients that distance the system from the state of perfect mixing and allow for a faster and more efficient fluid transport through the host matrix. To investigate the dynamic feedback between the transport and the reactive process in the field and its influence on the emergence of transport self-organization, we consider a two-dimensional Darcy-scale formulation of a reactive transport setup, where the precipitation and dissolution of the host matrix are driven by the injection of an acid compound, establishing local equilibrium with the resident fluid and an initially homogeneous porous matrix, composed of a calcite mineral. The coupled reactive process is simulated in a series of computational analyses employing the Lagrangian particle tracking (LPT) approach, capable of capturing the subtleties of the multiple scale heterogeneity phenomena. As the reactive process evolves, the dissolution / precipitation reactions are allowed to affect the local values of porosity and hydraulic conductivity in the host matrix, thus creating a dynamic feedback in the system. Subsequently, we employ computational non-reactive tracer tests to obtain the solute concentration data in the field, used to calculate the Shannon entropy of the transport. We employ the Shannon entropy to quantify the emergence of self-organization in the field, which we define as a relative reduction in entropy, compared to its maximum value. Our findings show that transport self-organization in an initially homogeneous field increases with time, along with the emergence of the field heterogeneity due to the interplay between transport and reactive process. By studying the influence of the transport Peclet number on the reactive process, we arrive at a conclusion that self-organization is more pronounced in diffusion-dominated flows, characterized by small Peclet values. The explanation for this lies in the fact that in a completely homogeneous field, the dominant mechanism to drive reactive components out of equilibrium is the stochasticity of diffusion. The self-organization of the breakthrough curve exhibits the opposite tendencies, that are explained from the thermodynamic perspective. The hydraulic power, required to maintain the driving head pressure difference between inlet and outlet, increases with the increasing variance of the hydraulic conductivity in the field due to the evolution of the reactive process in the field. This increase in power, supplied to the fluid traveling in the porous medium, results in an increase in the level of transport self-organization in the medium.