Reactive Flows In Porous Media Research Articles

Visualization of Multiphase Reactive Flow and Mass Transfer in Functionalized Microfluidic Porous Media.

Multiphase reactive flow in porous media is an important research topic in many natural and industrial processes. In the present work, photolithography is adopted to fabricate multicomponent mineral porous media in a microchannel, microfluidics experiments are conducted to capture the multiphase reactive flow, methyl violet 2B is employed to visualize the real-time concentration field of the acid solution and a sophisticated image processing method is developed to obtain the quantitative results of the distribution of different phases. With the advanced methods, experiments are conducted with different acid concentration and inlet velocity in different porous structures with different phenomena captured. Under a low acid concentration, the reaction will be single phase. In the gaseous cases with higher acid concentration, preferential flow paths with faster flow and reaction are formed by the multiphase hydrodynamic instabilities. In the experiments with different inlet velocities, it is observed that a higher inlet velocity will lead to a faster reaction but less gas bubbles generated. In contrast, more gas bubbles would be generated and block the flow and reaction under a lower inlet velocity. Finally, in heterogeneous structures, fractures or cavities would significantly redirect the flow and promote the formation of preferential flow path nearby.

Numerical modeling of reactive flow in porous media at the pore scale

AbstractDifferent numerical algorithms for the solution of a class of unsteady convection‐diffusion‐reaction (CDR) equations are presented and compared in this paper. The fully implicit in time discretizations are usually preferred because they are unconditionally stable for linear problems. However, when implicit discretization is used for nonlinear problems, iterations over the nonlinearity have to be performed. Picard (simple linearization) or Newton's methods can be used for this purpose. An alternative to the fully implicit discretization is fractional time‐step methods, e.g. splitting with respect to physicochemical processes. The study of the latter class of discretization is especially interesting in the case when only the reactive term contains nonlinearity, while the convection and diffusion operators are linear. The CDR models used to describe processes in catalytic filters belong to this class. Numerical experiments for CDR equation with controllable stiffness of reaction term for different transport regimes, which are described by Peclet and Damkohler numbers are demonstrated and analyzed.

Homogenization of a nonlinear stochastic model with nonlinear random forces for chemical reactive flows in porous media

In this study, we establish new homogenization results for chemical reactive fluxes in porous media using a nonlinear stochastic model with nonlinear random forces. This model is mathematically represented by a linear stochastic response equation, a nonlinear boundary condition, a nonlinear stochastic diffusion equation, and external nonlinear random forces that affect the solute concentration and diffusion in the fluid phase. A homogenized model made up of a nonlinear stochastic diffusion equation with extra terms reflecting the impact of the adsorption and chemical reactions occurring on the boundaries of the perforations and a stochastic differential equation with extra nonlinear term representing the limit for the surface problem is derived using the periodic unfolding operator method and probabilistic compactness results. To guarantee that the entire sequence converges, we also show the uniqueness result for the limit problem. Finally, we go over some applications for the interaction of chemical fluxes.

PORE SCALE INVESTIGATION ON THE EFFECT OF TEMPERATURE ON THREE-PHASE REACTIVE FLOW IN POROUS MEDIA USING THE LATTICE BOLTZMANN METHOD

In this study, the process of carbonate rock acidification with three-phase immiscible fluid [water, oil, and supercritical carbon dioxide (scCO<sub>2</sub>)] reactive flow in nonisothermal condition at pore scale was simulated by the lattice Boltzmann method (LBM). The three immiscible fluids' flow, solute transport, and heat transfer were solved by the Shan-Chen multiphase multicomponent lattice Boltzmann model, mass transport lattice Boltzmann model, and multicomponent thermal lattice Boltzmann model, respectively. The solid phase was updated by the volume-of-pixel method. In addition, the effect of temperature on the multiphase multicomponent reactive flow was numerically investigated. The results show that the dissolution rate is determined by three-phase distribution. The increase of temperature can accelerate the dissolution rate and decrease the inhibition influence of the non-acid phase on dissolution. Furthermore, the influence of temperature decreases with the increase of inlet velocity and oil wettability.

Numerical modeling and analysis of the matrix acidizing process in fractured sandstone rocks with the Extended–FEM

Significant natural fractures develop in deep sandstone reservoirs. However, the previous numerical simulation for matrix acidizing in sandstone rocks always focused on the reactive flow in porous media. A series of responses between multiple types of acids and minerals in fracture and matrix pores have been a significant setback for seeking the mechanism of acid flow in fractured sandstone rocks. This paper, established a multistage reactive-transport model for fractured sandstone rocks based on the two-scale continuum model to explore the effects of fractures on the reactive flow. The weak forms of fluid flow and solute transport equations are derived using the Galerkin method to couple the matrix and fracture domains, and the extended finite element method was used to solve the discretization model. Additionally, we presented numerical simulations under 2D linear flow conditions with specific and sensitive analyses about fracture and matrix properties. Numerical cases showed that the wormhole-shaped structure generated by acid dissolution is hard to develop even in highly heterogeneous fractured sandstone rocks due to the low reaction rate between mud acid and minerals. However, fractures that are not parallel to the flow direction can accelerated acid flow in the formation and reduced Si(OH)4 precipitation. Increasing the injection rate can not change the dissolution patterns of sandstone, but expanded the acid diffusion range and decreased Si(OH)4 precipitation in fractured sandstone.

Large-deposit non-linear chemical reactive flows in porous media: Identifiability and observability

This work discusses the use of additional pressure drop measurements in the characterisation of chemical reactive flow in porous media resulting in insoluble solid deposition. Previous studies of this problem have used outlet breakthrough concentration of one species and pressure drop across the sample during the commingled injection of reacting species, to determine model coefficients. In this work, we consider the introduction of additional measurements of pressure drop across subsections of the sample. The recently derived analytical model is compared to laboratory data to demonstrate the validity of both the model and additional measurement data. The effect of measuring different quantities is assessed by considering the identifiability of the model parameters. All parameters exhibit finite confidence intervals, however, datasets neglecting breakthrough concentration result in higher parameter uncertainty. Higher parameter uncertainty is shown to result in uncertainty in deposit profiles and prediction of pressure drop at higher length scales, demonstrating the importance of limiting parameter uncertainty through experimental design.

Analytical solution for large-deposit non-linear reactive flows in porous media

We discuss reactive flows in porous media that exhibit an irreversible chemical reaction between two components, resulting in large solid-product deposition. Previous works used the analytical solution for the linear problem with low deposition to determine model parameters from the reactant breakthrough concentrations and pressure drop growth across the core during laboratory coreflood. The present work derives an exact analytical solution for the non-linear problem with large solid-product deposition. We use the solution for interpretation of the laboratory data, and determination of the type curves for the measured values. Seven sets of experimental data are shown to closely match the data from the analytical model, which validates the analytical model.

Lattice Boltzmann Simulation of Multicomponent Porous Media Flows With Chemical Reaction

Flows with chemical reactions in porous media are fundamental phenomena encountered in many natural, industrial, and scientific areas. For such flows, most existing studies use continuum assumptions and focus on volume-averaged properties on macroscopic scales. Considering the complex porous structures and fluid–solid interactions in realistic situations, this study develops a sophisticated lattice Boltzmann (LB) model for simulating reactive flows in porous media on the pore scale. In the present model, separate LB equations are built for multicomponent flows and chemical species evolutions, source terms are derived for heat and mass transfer, boundary schemes are formulated for surface reaction, and correction terms are introduced for temperature-dependent density. Thus, the present LB model offers a capability to capture pore-scale information of compressible/incompressible fluid motions, homogeneous reaction between miscible fluids, and heterogeneous reaction at the fluid–solid interface in porous media. Different scenarios of density fingering with homogeneous reaction are investigated, with effects of viscosity contrast being clarified. Furthermore, by introducing thermal flows, the solid coke combustion is modeled in porous media. During coke combustion, fluid viscosity is affected by heat and mass transfer, which results in unstable combustion fronts.

Reactive Flows in Porous Media: Challenges in Theoretical and Numerical Methods.

We review theoretical and computational research, primarily from the past 10 years, addressing the flow of reactive fluids in porous media. The focus is on systems where chemical reactions at the solid-fluid interface cause dissolution of the surrounding porous matrix, creating nonlinear feedback mechanisms that can often lead to greatly enhanced permeability. We discuss insights into the evolution of geological forms that can be inferred from these feedback mechanisms, as well as some geotechnical applications such as enhanced oil recovery, hydraulic fracturing, and carbon sequestration. Until recently, most practical applications of reactive transport have been based on Darcy-scale modeling, where averaged equations for the flow and reactant transport are solved. We summarize the successes and limitations of volume averaging, which leads to Darcy-scale equations, as an introduction to pore-scale modeling. Pore-scale modeling is computationally intensive but offers new insights as well as tests of averaging theories and pore-network models. We include recent research devoted to validation of pore-scale simulations, particularly the use of visual observations from microfluidic experiments.

Pore-scale investigation on reactive flow in porous media considering dissolution and precipitation by LBM

The reactive transport process in oil gas reservoirs is complicated due to the coupling between dissolution and precipitation. In the present study, based on lattice Boltzmann method, the coupled dissolution and precipitation process in randomly generated porous media by quartet structure generation is investigated at the scale of geological pores. The fluid velocity, temperature and concentration in porous media are solved by multicomponent flow lattice Boltzmann model, multicomponent thermal lattice Boltzmann model and mass transport lattice Boltzmann model, respectively. The solid phase is updated by volume of pixel method. The results show that the dissolution reaction rate has a positive impact on the consumption of reactants. For different precipitation reaction rates, there exists an optimal value resulting in abundant precipitate and sparse solid distribution. Reaction equilibrium constant affects reaction rates slightly but influence the solid morphology heavily. The coupled dissolution and precipitation process accelerates with the increase of Peclet number, but the precipitate produced increases with the decrease of Peclet number.

An efficient symmetric finite volume element method for second-order variable coefficient parabolic integro-differential equations

This paper is devoted to develop a symmetric finite volume element (FVE) method to solve second-order variable coefficient parabolic integro-differential equations, arising in modeling of nonlocal reactive flows in porous media. Based on barycenter dual mesh, one semi-discrete and two fully discrete backward Euler and Crank–Nicolson symmetric FVE schemes are presented. Then, the optimal order error estimates in $$L^{2}$$ -norm are derived for the semi-discrete and two fully discrete schemes. Numerical experiments are performed to examine the convergence rate and verify the effectiveness and usefulness of the new numerical schemes.

Process-based upscaling of reactive flow in geological formations

Recently, there is an increased interest in reactive flow in porous media, in groundwater, agricultural and fuel recovery applications. Reactive flow modeling involves vastly different reaction rates, i.e., differing by many orders of magnitude. Solving the ensuing model equations can be computationally intensive. Categorizing reactions according to their speeds makes it possible to greatly simplify the relevant model equations. Indeed some reactions proceed so slow that they can be disregarded. Other reactions occur so fast that they are well described by thermodynamic equilibrium in the time and spatial region of interest. At intermediate rates kinetics needs to be taken into account. In this paper, we categorize selected reactions as slow, fast or intermediate. We model 2D radially symmetric reactive flow with a reaction-convection-diffusion equation. We show that we can subdivide the PeDaII phasespace in three regions. Region I (slow reaction); reaction can be ignored, region II (intermediate reaction); initially kinetics need to be taken into account, region III (fast reaction); all reaction takes places in a very narrow region around the injection point. We investigate these aspects for a few specific examples. We compute the location in phase space of a few selected minerals depending on salinity and temperature. We note that the conditions, e.g., salinity and temperature may be essential for assigning the reaction to the correct region in phase space. The methodology described can be applied to any mineral precipitation/decomposition problem and consequently greatly simplifies reactive flow modeling in porous media.

Multi-stage preconditioners for thermal–compositional–reactive flow in porous media

We present a family of multi-stage preconditioners for coupled thermal-compositional-reactive reservoir simulation problems. The most common preconditioner used in industrial practice, the Constrained Pressure Residual (CPR) method, was designed for isothermal models and does not offer a specific strategy for the energy equation. For thermal simulations, inadequate treatment of the temperature unknown can cause severe conver-gence degradation. When strong thermal diffusion is present, the energy equation exhibits significant elliptic behavior that cannot be accurately corrected by CPR's second stage. In this work, we use Schur-complement decompositions to extract a temperature subsystem and apply an Algebraic MultiGrid (AMG) approximation as an additional preconditioning stage to improve the treatment of the energy equation. We present results for several two-dimensional hot air injection problems using an extra heavy oil, including challenging reactive In-Situ Combustion (ISC) cases. We show improved performance and robustness across different thermal regimes, from advection dominated (high Péclet number) to diffusion dominated (low Péclet number). The number of linear iterations is reduced by 40–85% compared to standard CPR for both homogeneous and heterogeneous media, and the new methods exhibit almost no sensitivity to the thermal regime.

Differential diffusion effects on density-driven instability of reactive flows in porous media

Based on the lattice Boltzmann (LB) method, pore-scale simulations are performed to investigate the differential diffusion effects on the density-driven instability (DI) with chemical reaction A + B → C in porous media. A partially miscible stratification is considered, and thus only solutes from the top fluid can diffuse down into the host fluid in pore spaces. Tests with different values of the Rayleigh number Ra r and the diffusion coefficient D r of species r ( r = A , B , C ) are considered. The results demonstrate eight distinct scenarios of DI, and four of them are not observed in equal diffusivity simulations. Two differential diffusion effects, namely, the double-diffusive (DD) and the diffusive-layer convection (DLC) mechanisms, can act upon the gravity field and give rise to new fingering phenomena. The DD mechanism comes into play and results in a local minimum density layer if Ra B / Ra C is small and D B > D C ; and DLC becomes significant and brings in a local maximum density layer if Ra B / Ra C is large and D B < D C . On one hand, when fluid density increases with dissolved A , the DD-induced minimum can act as an inhibiting barrier to suppress fingering propagation, although it can be eventually penetrated by fingering tips; and the DLC-induced maximum can introduce the second DI below the first one. On the other hand, when the dissolution of A contributes to decreasing fluid density, both the DD-induced minimum and the DLC-induced maximum can help trigger the development of DI. Finally, quantitative results are provided to indicate that fingering propagates into the host fluid more deeply with larger D B / D C , and the dissolution of A decreases with the increasing difference between D B and D C .

Pore-scale investigation on reactive flow in porous media with immiscible phase using lattice Boltzmann method

Reactive flow happens during carbonate rock acidification. In the present study, carbonate rock dissolution process is investigated by lattice Boltzmann method at pore scale. The two immiscible fluids flow, solute transport and heat transfer are solved by the Shan-Chen multiphase multicomponent lattice Boltzmann model, mass transport lattice Boltzmann model and multicomponent thermal lattice Boltzmann model, respectively. The solid phase is updated by Volume of Pixel method. The results show that the immiscible phase has negative effect on dissolution, while positive effect on acid penetration. The immiscible phase effect is influenced by the inlet velocity, porous media porosity, surface wettability and temperature. The increasing inlet velocity and temperature accelerate the dissolution rate, but decrease the degree of immiscible phase suppression on dissolution. The surface wettability impact on dissolution process is influenced by the immiscible phase distribution. The porosity affects the degree of immiscible phase suppression on dissolution process slightly.

Modeling geochemical reactions of citric acid with ankerite cement during sandstone matrix acidizing

Reactive flows in porous media have complex behavior that is influenced by the properties of rocks (e.g., composition, structure) and fluids. In this study, the interaction of citric acid, as a weak acid, with a sandstone core containing ankerite cement was investigated during matrix acidizing. The model, developed in Python, implemented a global implicit numerical approach to consider acid-rock geochemical interactions. The effect of multi-step dissociation of citric acid on lowering rock pH was investigated. The sugar-lump approach was used to estimate the behavior of the ions concentration originated from the variation of the reactive surface area (RSA). The model outputs were validated against matrix sandstone acidizing experiments from the literature. By assuming ankerite as the main reactive mineral and considering several other aqueous reactions, the ions concentration changes (e.g., Ca2+, Fe2+, and Mg2+) of the acidizing experiments were correctly predicted. The effect of the uncertainty of the input parameters on the predictions of the model (i.e., ions concentration) was evaluated using the Monte Carlo method. The geochemical model explained the reaction rate evolution during citric acid injection and evaluated its capacity on dissolving carbonate cement (i.e., ankerite). During the acidizing process, the sandstone RSA increases, achieves a maximum value, and finally decreases. Moreover, the results indicate that the dissociation steps of citric acid have a direct effect on the prediction of acidizing performance.

A coupled geochemical and fluid flow model to simulate permeability decline resulting from scale formation in porous media

Scale precipitation due to the mixing of incompatible injected water with formation brine and its subsequent deposition in porous media is an unpleasant phenomenon in water injection projects that can lead to severe injectivity and productivity decline. As a result of the complexity of geochemical reactions, modelling scale precipitation and deposition is a challenge. This paper presents a coupled geochemical and fluid flow model to simulate reactive flow in porous media which models pressure difference increase resulting from scale formation during water injection into porous media. To simulate chemical reactions during scale formation and subsequent rock permeability decline, PHREEQC software was coupled with a fluid transport model. The pressure difference and outlet ion concentration from three laboratory data were successfully matched. The coupled model that is proposed considers injected and formation water compositions and their associated chemical reactions. The formation damage coefficient is the single optimisation parameter of the proposed model. With matching parameters from experimental data, the proposed model can be used for predicting well injectivity decline and sensitivity analysis.

Instabilities of nonisothermal nanocatalytic reactive flows in porous media

Instabilities of nonisothermal nanocatalytic reactive flows in porous media

Dynamics of Miscible Nanocatalytic Reactive Flows in Porous Media

Catalysis at the nanoscale plays an increasingly important role in subjects ranging from energy and environment to medical sciences, but our physical understanding of the dynamics and effectiveness of nanocatalysts in porous media is lacking. The authors theoretically investigate the factors needed for success in $i\phantom{\rule{0}{0ex}}n$ $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u$ nanocatalyst applications, such as heavy-oil upgrading and soil remediation, and they discuss the physical mechanisms behind the dynamics of mixing during nanocatalytic miscible displacement in porous media. This insight will aid the optimal design and utilization of nanocatalysts.

Streamline simulation of a reactive advective flow with discontinuous flux function

Reactive transport in porous media with dissolution and precipitation has important applications in oil and gas industry and groundwater remediation. In this work, we present a simulation method for reactive flow in porous media of two salts that share an ion. The method consists of a front-tracking solver that uses the Riemann solutions of the underlying set of hyperbolic partial differential equations. In addition to the discontinuities stemming from the nonlinearities of the flux function, the flux function for the corresponding advection reaction equation also admits discontinuities for a heterogeneous medium. Here, we solve the Riemann problem for the governing nonlinear hyperbolic system with a discontinuous flux function. We use mass balance across the interface and the non-decreasing sequence of velocity of waves to seek the unique solution for this problem. Furthermore, a model is provided for mixing of streamlines at the well to estimate the amount of precipitate. In the use of streamline methods, we have modified the definition of time-of-flight to allow the model to be easily utilised for the heteregeneous case. The simulation method is applied to model dissolution through injection of an unsaturated fluid. It is shown that the first dissolution shock, which causes induced precipitation due to the co-ion effect, results in accumulation of precipitate at the well.