Reactive Transport In Porous Media Research Articles

Upscaling the reaction rates in porous media from pore- to Darcy-scale

Modeling and prediction of reactive transport in porous media are challenging due to the complexity of the characterization of reactions across spatial and time scales. The application of reaction rates obtained from batch experiments to porous media is not valid because it disregards the influences of flow pathways, distribution of residence time, transport limitations within the porous media, as well as neglecting the impact of surface mineralogy heterogeneity. In this study, we presented how the pore-scale modeling can help to improve the Darcy-scale simulations. First, the reactive transport was simulated in a pore-network model and was validated against the experiments. Then, the pore-network results were averaged to obtain the effective reaction rates as a function of pore velocity, the inlet concentration, and the resident concentration. The upscaled function was incorporated into the Darcy-scale model and showed a significant improvement in predicting the concentration profiles. Notably, the use of batch reaction rates in the Darcy model (ADRE-batch) led to significant underestimation, up to 93%, of the required pore volume injection for complete contaminant removal from the simulation domain.

Shannon entropy of transport self-organization due to dissolution–precipitation reaction at varying Peclet numbers in 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 interaction between the reactive dissolution and precipitation 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. It has been shown that the emergence of preferential flow paths can be considered to be a manifestation of transport self-organization in porous media as these 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 processes 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. 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. Scalability of the parameters, which characterize the evolution of the reactive process, with the Peclet number in an initially homogeneous field is derived using a simple one-dimensional ADRE model with a linear adsorption reaction term and is then confirmed through numerical simulations, with the global reaction rate, the mean value, and the variance of the hydraulic-conductivity distribution in the field all exhibiting dependency on the reciprocal of the Peclet number. 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 interaction between the transport and reactive processes. By studying the influence of the 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 self-organization of the breakthrough curve exhibits the opposite tendencies, which are observed from the perspective of a thermodynamic analogy. The hydraulic power, required to maintain the driving head pressure difference between the inlet and outlet of the field, was shown to increase with the increasing variance, as well as with the increasing mean value of the hydraulic-conductivity distribution in the field, using a simple analytic model. This was confirmed by numerical experiments. This increase in power, supplied to the flow in the field, results in an increase in the level of transport self-organization. Employing a thermodynamic framework to investigate the dynamic reaction–transport interaction in porous media may prove to be beneficial whenever the need exists to establish relations between the intensification of the preferential flow path phenomenon, represented by a decline in the Shannon entropy of the transport, with the amount of reaction that occurred in the porous medium and the change in its heterogeneity.

BioReactPy: An open-source software for simulation of microbial-mediated reactive processes in porous media

This paper provides a new open-source software, named BioReactPy, for simulation of microbial-mediated coupled processes of flow and reactive transport in porous media. The software is based on the micro-continuum approach, and geochemistry is handled in a fully coupled manner with biomass-nutrient growth treated with Monod equation in a single integrated framework, without dependencies on third party packages. The distinguishing features of the software, its design principles, and formulation of multiphysics problems and discretizations are discussed. Validation of the Python implementation using several established benchmarks for flow, reactive transport, and biomass growth is presented. The flexibility of the framework is then illustrated by simulations of highly non-linearly coupled flow and microbial reactive transport at conditions relevant to carbon mineralization for CO2 storage. All results can be reproduced by openly available simulation scripts.

In-situ multicore fibre-based pH mapping through obstacles in integrated microfluidic devices.

Microfluidic systems with integrated sensors are ideal platforms to study and emulate processes such as complex multiphase flow and reactive transport in porous media, numerical modeling of bulk systems in medicine, and in engineering. Existing commercial optical fibre sensing systems used in integrated microfluidic devices are based on single-core fibres, limiting the spatial resolution in parameter measurements in such application scenarios. Here, we propose a multicore fibre-based pH system for in-situ pH mapping with tens of micrometer spatial resolution in microfluidic devices. The demonstration uses custom laser-manufactured glass microfluidic devices (called further micromodels) consisting of two round ports. The micromodels comprise two lintels for the injection of various pH buffers and an outlet. The two-port system facilitates the injection of various pH solutions using independent pressure pumps. The multicore fibre imaging system provides spatial information about the pH environment from the intensity distribution of fluorescence emission from the sensor attached to the fibre end facet, making use of the cores in the fibre as independent measurement channels. As proof-of-concept, we performed pH measurements in micromodels through obstacles (glass and rock beads), showing that the particle features can be clearly distinguishable from the intensity distribution from the fibre sensor.

P3D-BRNS v1.0.0: a three-dimensional, multiphase, multicomponent, pore-scale reactive transport modelling package for simulating biogeochemical processes in subsurface environments

Abstract. The porous microenvironment of soil offers various environmental functions which are governed by physical and reactive processes. Understanding reactive transport processes in porous media is essential for many natural systems (soils, aquifers, aquatic sediments or subsurface reservoirs) or technological processes (water treatment or ceramic and fuel cell technologies). In particular, in the vadose zone of the terrestrial subsurface the spatially and temporally varying saturation of the aqueous and the gas phase leads to systems that involve complex flow and transport processes as well as reactive transformations of chemical compounds in the porous material. To describe these interacting processes and their dynamics at the pore scale requires a well-suited modelling framework accounting for the proper description of all relevant processes at a high spatial resolution. Here we present P3D-BRNS as a new open-source modelling toolbox harnessing the core libraries of OpenFOAM and coupled externally to the Biogeochemical Reaction Network Simulator (BRNS). The native OpenFOAM volume-of-fluid solver is extended to have an improved representation of the fluid–fluid interface. The solvers are further developed to couple the reaction module which can be tailored for a specific reactive transport simulation. P3D-RBNS is benchmarked against three different flow and reactive transport processes: (1) fluid–fluid configuration in a capillary corner, (2) mass transfer across the fluid–fluid interface and (3) microbial growth with a high degree of accuracy. Our model allows for simulation of the spatio-temporal distribution of all biochemical species in the porous structure (obtained from μ-CT images), for conditions that are commonly found in the laboratory and environmental systems. With our coupled computational model, we provide a reliable and efficient tool for simulating multiphase, reactive transport in porous media.

Temperature-dependent dynamics of electrokinetic conservative and reactive transport in porous media: A model-based analysis

Electrokinetic techniques employ direct current electric fields to enhance the transport of amendments in low permeability porous media and have been demonstrated effective for in situ remediation of both organic contaminants and heavy metals. The application of electric potential gradients give rise to coupled chemical, hydraulic and electric fluxes, which are at the basis of the main transport mechanisms: electromigration and electroosmosis. Previous research has highlighted the significant impacts of charge interactions and fluid composition, including temperature-dependent properties such as electrolyte conductivity and density, on these transport phenomena. However, current models of electrokinetic applications often assume isothermal conditions and overlook the production of heat resulting from Joule heating.This study provides a detailed model-based investigation, systematically exploring the effects of temperature on electrokinetic conservative and reactive transport in porous media. By incorporating temperature-dependent material properties and progressively investigating the impact of temperature on each transport mechanism, we analyze the effects of temperature variations in both 1D and 2D systems. The study reveals how temperature dynamically influences the physical, chemical and electrostatic processes controlling electrokinetic transport. A temperature increase results in a higher speed of amendments delivery by both electromigration and electroosmosis and increases the kinetics of degradation reactions. The simulations also reveal a feedback mechanism in which higher aqueous conductivity results in increased Joule heating, leading to a faster temperature rise and, subsequently, to higher electrolyte conductivity. Finally, we estimate the electric energy requirements of the system at varying temperatures and show how these changes impact the rate of contaminant removal.

Reactive transport modeling of scale precipitation and deposition during incompatible water injection in carbonate reservoirs

Seawater injection is an efficient enhanced oil recovery (EOR) method that capitalizes on the chemical composition differences between the injecting seawater and in-situ formation water, which leads to physicochemical interactions between the rock and fluids. These rock and fluid interactions result in changes of rock wettability and subsequent improved microscopic sweep efficiency. However, the ion imbalance resulting from seawater injection and its incompatibility with the in-situ formation water may interfere with the rock and fluids equilibrium state, causing scale precipitation and subsequent deposition which can negatively impact rock quality, well productivity and reservoir performance. In this study, an accurate, robust, and general approach is presented by coupling a geochemical module with a compositional two-phase fluid flow model to handle reactive transport in porous media. The proposed coupled model, so-called ad-scale model, is capable of simulating carbonate rock dissolution and sulfate scale formation/deposition for evaluating reservoir performance under incompatible water injection. The model predictions were validated using experimental data. This model was also utilized to predict water injection rate into a carbonate formation. It was obtained that both the reacting and non-reacting component profiles were accurately predicted using the proposed coupled model. The water injection rate prediction was also validated and showed high accuracy with absolute error and coefficient of determination values of 9.02% and 0.99, respectively. In addition, a sensitivity analysis was performed on water composition, which showed a strong dependence of reservoir and well performance on water composition.Graphical abstractThis diagram elucidates what exactly happens during incompatible water injection in the mixing zones near the injection well (right half of the figure) or production well (left half of the figure) where most of the geochemical phenomena occur.

Effect of control domains of fractures and caves on reactive transport in porous media

It is often highly difficult to predict the main flow path of reactive fluids in porous media with complexly distributed fractures and/or caves. Based on Darcy's law, this research defines the control domain of fractures/caves that represents the interference range of fractures/caves. This control domain can be used to identify the connectivity possibility between fractures/caves and predict the flow paths of reactive fluids at the optimal flow rate. Furthermore, after simplifying the geometry of fractures/caves, a threshold geometric aspect ratio of 20 is set to distinguish fractures and caves, concerning the flow mechanisms, by clarifying the ranges of control domains. Moreover, the control domain theory is combined with the two-scale continuum model for acidizing carbonate rocks to estimate the flow paths of acid in fractured-vuggy carbonate rocks at an optimal flow rate, thereby validating the accuracy of the reactive fluid main flow path estimation based on the control domain theory. The primary criterion to determine the reactive transport in porous media with complex fracture/cave distribution is the overlap degrees of control domains of adjacent isobaric bodies along their width and length directions, while the directions of isobaric bodies offer supplementary material. If the control domains of two isobaric bodies overlap with each other perpendicular to the flow direction, these isobaric bodies have higher odds of connected fluid flow.

Space–time upscaling of reactive transport in porous media

Reactive transport in saturated/unsaturated porous media is numerically upscaled to the space–time scale of a hypothetical measurement through coarse-grained space–time (CGST) averages. The reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged microscopic quantities. The latter are further used to verify the CGST-GRW numerical approach. The upscaling approach is applied to biodegradation processes in saturated aquifers and variably saturated soils and the CGST averages are compared to classical volume averages. One finds that if the process is characterized by slow variations in time, as in homogeneous reaction systems, the differences between the two averages are negligible. Instead, the differences are significant and can be extremely large in simulations of time-dependent biodegradation processes in both variably saturated soils and saturated aquifers.

Simulation of reactive transport in porous media using Meshless Local Petrov Galerkin (MLPG) and combination of Meshless Weak and Strong (MWS) form methods

In this paper, two meshless methods, namely, a weak form Meshless Local Petrov Galerkin (MLPG) method, and Meshless Weak Strong (MWS) form method, obtained by combining MLPG with a strong form Radial Point Collocation Method (RPCM), are presented for simulation of advection-dispersion-reaction phenomena of the contaminants in the porous media. The first-order decay and sorption reactions are considered in this study. The Crank Nicolson scheme is applied for the time discretization. The weak form MLPG is a truly meshless and robust numerical technique, that can be applied to complex aquifer systems with derivative boundaries. However, in this method, the computational time is increased due to the integration, which is not essential for simple problems. Thus, the MLPG method is further coupled with a strong form RPCM with an aim of decreasing the background integration, by modelling only the nodes around the derivative boundaries using MLPG method and the other nodes by a direct RPCM which do not require integration. The proposed MWS model automatically converts into a complete RPCM model if there are no derivative boundaries. Thus, this model being both accurate and computationally efficient is suitable for simple and moderately complex aquifer systems and MLPG is the most stable and reliable method for modelling the most complex aquifer problems. Both the developed models are tested with available analytical solutions and applied for hypothetical case studies. The results prove the efficiency of the models and the applicability of each model is described in detail.

Effects of physicochemical properties and structural heterogeneity on mineral precipitation and dissolution in saturated porous media

Physicochemical properties, such as solute concentration, flow acidity and flow rate, regulate flow and reactive transport in porous media. Mineral precipitation – dissolution (PD) dynamically changes the pore structural heterogeneity and affects the physicochemical properties, yet the interplay between the PD process and structural heterogeneity remains unclear. This study took the precipitation of Ca2+ and CO32− (Ca2++CO32−⇌CaCO3) as an example to study the reactive transport behavior under different physicochemical conditions in saturated, heterogeneous-packed porous media. A series of column breakthrough experiments and numerical simulations of the coupled flow and PD processes were conducted. X-ray computed tomography (XCT) and pore morphology analysis were also applied to investigate the effects of calcite precipitation on pore structure. Results demonstrate that solute concentration, flow acidity, and flow rates in homogeneous columns significantly altered the time of the PD process to reach equilibrium, leading to immediate chemical environmental changes, and thus impact reactive transport behavior. Preferential flow paths in heterogeneous-packed columns could lead to early breakthroughs and thereby promoted the transport of calcium carbonate (CaCO3) in saturated porous media. XCT images revealed that surface roughness played an important role in Ca2+ precipitation, i.e., CaCO3 clustered more on concave surface than convex surface, reshaping a round coat outside grain particles. The CaCO3 precipitation could also narrow or even block the pore throats, and thus decrease the pore connectivity, which hinders the breakthrough behavior. Our study provided experimental evidence for a predictive understanding of Ca2+ reactive transport as well as new insights into the changes in soil structural heterogeneity and transport properties during the PD process.

Scalable semismooth Newton methods with multilevel domain decomposition for subsurface flow and reactive transport in porous media

Large-scale modeling and predictive simulations of the subsurface flow and reactive transport system in porous media is significantly challenging, due to the high nonlinearity of the governing equations and the strong heterogeneity of material coefficients. The design of novel mathematical models and state-of-the-art methods for the flow simulation through porous media typically needs to satisfy the so-called bound-preserving property, i.e., the computed solution should stay inside a physically meaningful range. This paper presents a robust, scalable numerical framework based on the variational inequality formulation and the semismooth Newton method in a fully implicit manner, to model and simulate highly nonlinear flows without violating the boundedness requirement of the solution. Rigorous theoretical analysis for the variational inequality formulation of the problem is provided for facilitating the design of algorithms. Specifically, our approach further enhances the numerical formulation by utilizing a family of multilevel monolithic overlapping Schwarz methods for efficiently preconditioning, and the parallel implementation of the bound-preserving solver is based on the fast and robust domain decomposition technique. Numerical experiments are presented to demonstrate the efficiency and parallel scalability of the solution strategy for both standard benchmarks as well as realistic flow problems involving strong heterogeneity and high nonlinearity. We also show that the proposed framework is more robust and efficient than the commonly used inexact Newton algorithm in terms of the bound-preserving property.

Comparative investigation of a lattice Boltzmann boundary treatment of multiphase mass transport with heterogeneous chemical reactions.

Multiphase reactive transport in porous media is an important component of many natural and engineering processes. In the present study, boundary schemes for the continuum species transport-lattice Boltzmann (CST-LB) mass transport model and the multicomponent pseudopotential model are proposed to simulate heterogeneous chemical reactions in a multiphase system. For the CST-LB model, a lattice-interface-tracking scheme for the heterogeneous chemical reaction boundary is provided. Meanwhile, a local-average virtual density boundary scheme for the multicomponent pseudopotential model is formulated based on the work of Li etal. [Li, Yu, and Luo, Phys. Rev. E 100, 053313 (2019)10.1103/PhysRevE.100.053313]. With these boundary treatments, a numerical implementation is put forward that couples the multiphase fluid flow, interfacial species transport, heterogeneous chemical reactions, and porous matrix structural evolution. A series of comparison benchmark cases are investigated to evaluate the numerical performance for different pseudopotential wetting boundary treatments, and an application case of multiphase dissolution in porous media is conducted to validate the present models' ability to solve complex problems. By applying the present LB models with reasonable boundary treatments, multiphase reactive transport in various natural or engineering scenarios can be simulated accurately.

Dimensionality effects on multicomponent ionic transport and surface complexation in porous media

Coulombic interactions between charged species in pore water and at surface/solution interfaces are of pivotal importance for multicomponent reactive transport in porous media. In this study, we investigate the impact of domain dimensionality on electrostatically coupled dispersion and surface-solution reactions during transport of acidic plumes and major ions in porous media.Column and quasi two-dimensional flow-through experiments were performed, with identical silica porous media and under the same advection-dominated conditions. Equal mass fluxes of different electrolyte solutions (i.e., HCl - pH ∼ 2.8, NaBr - 100 mM, HCl - pH ∼ 2.8 plus NaBr - 100 mM) were continuously injected in the 1-D and 2-D experiments and breakthrough curves of pH and major ions were measured at the outlet of the domains. The presence of pronounced ionic strength gradients in the transverse direction in the 2-D setup caused distinct retardation and transport behaviors of protons and major ions which were not observed in the one-dimensional column experiments. Furthermore, in the cases of salt electrolytes injection, considerably enhanced release of H+ (>61%) from the quartz surface was observed in the multidimensional system compared to the one-dimensional setup.Reactive transport modeling was performed to reproduce the experimental outcomes and to analyse the coupling between transport processes, based on the Nernst-Planck formulation of diffusive/dispersive fluxes and on surface complexation reactions at the solid-solution interface. Electrostatic interactions between Na+, Br−, and H+, and deprotonation of the quartz surface upon the formation of sodium outer-sphere complexes, are the primary controllers of the spatial and temporal features displayed by the pH and major ions measurements. The reactive transport simulations allowed us to interpret the experimental observations, to visualize the distribution and spatio-temporal evolution of dissolved and solid species, to identify a spatially heterogeneous zonation of Coulombic interactions with distinct behavior at the fringe and core of the injected plumes in the multidimensional setup, and to quantify the different components of the Nerst-Planck fluxes of the charged solutes. This study demonstrates that the domain dimensionality directly affects electrostatic interactions between charged aqueous species in the pore water and surface complexation reactions at the solid-solution interface. The non-trivial effects of dimensionality on multicomponent ionic transport result in a significantly different behavior in 1-D and 2-D systems.

An Improved Tandem Neural Network Architecture for Inverse Modeling of Multicomponent Reactive Transport in Porous Media

AbstractParameter estimation for reactive transport models (RTMs) is important in improving their predictive capacity for accurately simulating subsurface hydrogeochemical processes. This paper introduces a deep learning approach called the tandem neural network architecture (TNNA), which consists of a forward network and a reverse network to estimate input parameters for RTMs. The TNNA approach has a limitation in that the approximation error from the forward network often results in biased inversion results. To solve this problem, we proposed to enhance TNNA using an adaptive updating strategy (AUS), which locally reduces the approximation error of the forward network. The developed framework updates the forward network by iteratively using local sampling and transfer learning. The TNNA‐AUS was verified by a cation exchange example. The results show that TNNA‐AUS successfully reduces the inversion bias and improves the computational efficiency and inversion accuracy, compared with the global improvement strategy of adding training samples according to the prior distribution of model parameters. After verification, the TNNA‐AUS was applied to a real‐world and well‐documented RTM problem of the Aquia aquifer, Maryland, USA. The inversion results demonstrate that the developed TNNA‐AUS algorithm is an excellent tool for us to understand the complex subsurface hydrogeochemical processes and estimate the associated reaction parameters.

Predicting Fluid Properties in the MUFITS Reservoir Simulator with User-Supplied Modules

We present a recent development of the MUFITS reservoir simulator aiming at modelling the transport of fluids whose properties and phase equilibria are calculated in a user-supplied external shared library. Both the explicit correlations and tabulated data for the fluid parameters can be implemented in the library that we name the EoS-module (Equation of State-module). An iterative approach—which, for example, is based on the phase equilibria calculation through the Gibbs energy minimisation (GEM) method, can also be used in the EoS-module. A considerable effort has been undertaken to minimise the number of program procedures exported by the shared library. This should facilitate and ease the usage of the developed software extension by the scientific community. Furthermore, we supplement the article with the source code of two simple EoS-modules that can serve as templates in other modelling and software development efforts. The EoS-modules are also useful for coupling MUFITS with other elaborate software for fluid property prediction. To demonstrate such a possibility, we supplement the article with the source code of a more complicated EoS-module that couples MUFITS with the geochemical code GEMS3K. This module is used in a simple 1-D benchmark study showing the capabilities of MUFITS for modelling reactive transport in porous media.

Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport

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.

Random‐Walk Modeling of Reactive Transport in Porous Media With a Reduced‐Order Chemical Basis of Conservative Components

AbstractIn this work we employ a reduced‐order basis of conservative chemical components to model reactive transport using a Lagrangian (particle tracking) method. While this practice is well‐understood in the Eulerian (grid‐based) context, its adaptation to a Lagrangian context requires a novel reformulation of particle transport properties. Because the number of conservative‐species particles need not change during simulation, spatial resolution stays constant in time, and there is no increase in computational expense due to increasing numbers of product particles. Additionally, this treatment simplifies the interaction between equilibrium and kinetic reactions and allows the use of species‐dependent transport operators at the same time. We apply this method to model a suite of simple test problems that include equilibrium and kinetic reactions, and results exhibit excellent match with base‐case Eulerian results. Finally, we apply the new method to model a 2D problem concerning the mobilization of cadmium by a CO2 leak, showing the potential applicability of the proposed methodology.

A mathematical model for thermal single-phase flow and reactive transport in fractured porous media

In this paper we present a mathematical model and a numerical workflow for the simulation of a thermal single-phase flow with reactive transport in porous media, in the presence of fractures. The latter are thin regions which might behave as high or low permeability channels depending on their physical parameters, and are thus of paramount importance in underground flow problems. Chemical reactions may alter the local properties of the porous media as well as the fracture walls, changing the flow path and possibly occluding some portions of the fractures or zones in the porous media. To solve numerically the coupled problem we propose a temporal splitting scheme so that the equations describing each physical process are solved sequentially. Numerical tests show the accuracy of the proposed model and the ability to capture complex phenomena, where one or multiple fractures are present.

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

In order to test the performance of the incomplete mixing model including the advection-dispersion-reaction equation (IM-ADRE) in simulating bimolecular reactive transport in fractured media, the laboratory-controlled experiments and numerical modeling were conducted in a single rough-wall fracture. Bimolecular reaction of aniline (AN) + 1, 2-napthoquinone-4-sulfonic acid (NQS) → 1, 2-naphthoquinone-4-aminobenzen (NQAB) was employed. Three different flow rates (0.15, 0.825 and 1.5 mL/s) and three fracture apertures (2, 3 and 4 mm) were considered in the experiment. The numerical simulation was analyzed and discussed based on the Péclet (Pe) number and Damköhler (Da) number. The results showed that although the spatial distribution of product concentration varied with the Pe number, the IM-ADRE model could simulate it well. The discrepancy between the simulated and measured peak product concentrations was less than 0.7%, which was far less than the value of 5% in previous study (Qian et al., 2015) produced by the IM-ADRE model used to modeling the reactive transport in porous media. This meant that the IM-ADRE model was effective for simulating and predicting the experimental results of bimolecular reactive transport in a single rough-wall fracture. Due to the instability of the product, the simulated value of the peak product concentration was always higher than the experimental value. Through further analysis of the model parameters, it was found that the hydrodynamic dispersion coefficient (D) changed significantly with the change of Pe number. The parameters m and β0 were linearly correlated with the Pe number. In addition, the IM-ADRE model was more sensitive to the parameters m and β0 but less sensitive to D.