X-ray microtomography characterization of porosity, permeability and reactive surface changes during dissolution

Pore-scale study of effects of macroscopic pores and their distributions on reactive transport in hierarchical porous media

Considering the utility of backward-in-time simulations of multi-component reactive transport in porous media

In this work, a multicomponent lattice Boltzmann (LB) model is presented for simulating reactive transport in porous media at the pore scale. In the model, a set of distribution functions is introduced to simulate fluid flow and solute transport. The model takes into account advection, diffusion, homogeneous reactions among multiple aqueous species, and heterogeneous reactions between the aqueous solution and minerals, as well as changes in solid and pore geometry. Homogeneous reactions are described through local equilibrium mass action relations. Mineral reactions are treated kinetically through boundary conditions at the mineral surface. The LB equation for flow recovers the correct pore‐scale continuity and Navier‐Stokes equations. The LB equations for solute transport are modified to recover advection‐diffusion equations for total concentrations at the pore scale. The model is applied to a hypothetical three‐component system with two aqueous complexes and two mineral reactions in a simple pore geometry. The effects of advection, diffusion, reaction rate constants, equilibrium constants of both homogeneous and heterogeneous reactions, and chemical compositions on mineral alteration of the porous medium and solute concentration are analyzed.

This review comprehensively examines the application of the lattice Boltzmann method (LBM) for the simulation of reactive transport and dissolution–precipitation processes in porous media. It covers fundamental LBM theory, including governing equations, collision operators like Bhatnagar–Gross–Krook and multiple-relaxation-time, and key boundary condition schemes such as no-slip, Dirichlet, curved-wall, and reactive formulations. Special attention is given to advanced reactive boundary conditions by Kang et al., Ju et al., Weinmiller et al., Kashani et al., and Izadi et al., which enable accurate modeling of nonlinear reaction kinetics and curved interfaces. The review also compares interface-tracking methods, volume of fluid, and volume of pixel, highlighting their impact on dissolution pattern accuracy and computational efficiency. LBM is shown to effectively capture dissolution regimes (wormhole, face, uniform) influenced by Péclet and Damköhler numbers, temperature, wettability, porosity, and interfacial tension. The paper concludes by identifying persistent challenges such as modeling multiphase systems, non-isothermal effects, and upscaling pore-scale results and emphasizes the need for improved benchmarking, experimental validation, and advanced boundary conditions to enhance predictive capability in realistic porous media applications.

12 - Reactive transport in porous media—concepts and numerical approaches

We present a numerical framework for efficiently simulating partially miscible two-phase flow with multicomponent reactive transport in porous media using the global implicit approach. The mathematical model consists of coupled and nonlinear partial differential equations, ordinary differential equations, and algebraic equations. Our approach is based on a model-preserving reformulation using the reduction scheme of Krautle and Knabner (Water Resour. Res. 43(3), 2007), Hoffmann et al. (Comput. Geosci. 16(4):1081–1099, 2012) to transform the system. Moreover, a nonlinear, implicitly defined resolution function to reduce its size is employed. By choosing persistent primary variables and using a complementarity approach, mineral reactions and the local appearance and disappearance of the gas phase can be handled without a discontinuous switch of primary variables. In each time step of the Euler-implicit time stepping scheme, the discrete nonlinear systems are solved using the Semismooth Newton method for linearization using the global implicit approach. Thus, we obtain an efficient, robust, and stable simulation method allowing for large time steps and avoiding the potential drawbacks of splitting approaches.

Reactive Transport in Porous Media: P.C. Lichtner, C.I. Steefel and E.H. Oelkers(Eds.)

A comparison of published experimental data with a coupled lattice Boltzmann-analytic advection–diffusion method for reactive transport in porous media

Numerical investigation of pore and continuum scale formulations of bimolecular reactive transport in porous media

Stochastic parameter estimation and inversion have become increasingly popular in recent years. Nowadays, it is computationally reasonable and regular to solve complex inverse problems within the Bayesian framework. Applications of Bayesian inferences for inverse problems require investigation of the posterior distribution, which usually has a complex landscape and is highly dimensional. In these cases, Markov chain Monte Carlo methods (MCMC) are often used. This paper discusses a Bayesian approach for identifying adsorption and desorption rates in combination with a pore-scale reactive flow. Markov chain Monte Carlo sampling is used to estimate adsorption and desorption rates. The reactive transport in porous media is governed by incompressible Stokes equations, coupled with convection–diffusion equation for species’ transport. Adsorption and desorption are accounted via Robin boundary conditions. The Henry isotherm is considered for describing the reaction terms. The measured concentration at the outlet boundary is provided as additional information for the identification procedure. Metropolis–Hastings and Adaptive Metropolis algorithms are implemented. Credible intervals have been plotted from sampled posterior distributions for both algorithms. The impact of the noise in the measurements and influence of several measurements for Bayesian identification procedure is studied. Sample analysis using the autocorrelation function and acceptance rate is performed to estimate mixing of the Markov chain. As result, we conclude that MCMC sampling algorithm within the Bayesian framework is good enough to determine an admissible set of parameters via credible intervals.

We consider a Darcy-scale model for mineral precipitation and dissolution in a porous medium. This model is obtained by homogenization techniques starting at the scale of pores. The model is based on a phase-field approach to account for the evolution of the pore geometry and the outcome is a multi-scale strongly coupled non-linear system of equations. In this work we discuss a robust numerical scheme dealing with the scale separation in the model as well as the non-linear character of the equations. We combine mesh refinement with stable linearization techniques to illustrate the behaviour of the multi-scale iterative scheme.

Modelling multicomponent reactive transport in porous media with subgrid scale stabilized finite elements

Accelerated by urbanization, as well as by agricultural intensification and climate change, increasing nutrient fluxes towards surface waters and increasing water temperatures are increasing the probability for cyanobacterial harmful algal blooms. Significant deterioration of water quality occurs with such events when microcystins (MCs) are released as the most prominent algal toxins. Despite the typical assumption that MCs are removed during percolation, studies have found significant concentrations in groundwater bodies. In this article, advances and challenges associated with monitoring and modeling techniques for characterizing the fate of MCs are discussed. Missing insights in the mechanisms leading to elevated MC concentrations in the subsurface—ultimately limiting the reliability of risk assessments—are identified. An important aspect is the a priori identification of environmental conditions and corresponding events that support bloom formation in surface waters and subsequent transport into groundwater. Challenges associated with required improved monitoring and simulation techniques are formulated. In particular, the role of environmental conditions in urban regions as major drivers for heat and nutrient emissions controlling bloom formation, potentially limiting MC retardation, needs to be further investigated. Based on existing experimental studies on MC reactive transport in porous media, existing monitoring methods need to be refined and combined with suitable modeling approaches. A thorough data analysis can then support efforts for sustainable water management of urban regions under threat by algal toxins.

Analysis of reactive transport in natural and engineered porous media has benefited from the concept of mixing ratios, in particular as a basis for mathematical separation of transport and reactions processes. General use of solute age has also been recently explored as a way to describe solute mass transfer and/or as a proxy for reaction extent. Age here is defined as exposure time to the flow field. Pairing these concepts, we develop mixing ratio models that are structured on age. One‐dimensional transport is cast in terms of age‐structured mixing ratios in general and compared with conventional formulations of mixing ratio models, demonstrating that age is often a more natural independent variable than absolute time. Using this modeling framework, we then apply age‐structured mixing ratios to the problem of mixing‐limited reactive transport in one‐dimension by explicitly considering unmixed and mixed phases. In order to address mixing limitations under the entirety of transport including the preasymptotic dispersion timeframe, we use the same age variable to define the dispersion coefficient value in a local formulation of transport. Establishing an age‐dependent dispersion coefficient allows simulation of the whole transport time including both preasymptotic and asymptotic dispersion conditions with one model. In our application we explore use of this modeling approach to both synthetic preasymptotic data and experimental asymptotic data pertaining to one famous experiment.

Experimental and numerical study of bimolecular reactive transport in a single rough-wall fracture