Chemical Reaction In Porous Media Research Articles

A parameter-free and monolithic approach for multiscale simulations of flow, transport, and chemical reactions in porous media

Traditional approaches for transport in porous media rely on empirical hydrodynamic/transport parameters to quantify the interfacial exchange terms between fluid and solid, which leads to considerable uncertainties and also to a narrow application range of each method for realistic investigations of porous media. A parameter-free approach for flow, transport, and chemical reactions in porous media is presented in this paper. This approach adopts a novel, single-domain set of equations that are rigorously derived based on the elementary conservation laws describing the physical, continuous domain. The impact of the solid on nearby fluid being directly quantified in terms of the quantity to be solved, this avoids the introduction of empirical parameters. Various transport problems including external, conjugate, and reactive processes are properly formulated in this context, with the coupling between fluid and porous structures at different scales naturally solved in a monolithic manner. All these equations remain simple in terms of their numerical implementation, with solid structures represented by the porosity field on a background mesh. The application of the present method in both pore-scale and representative elementary volume (REV-scale) simulations are checked by performing a series of test cases, including interfacial momentum/heat/mass transport, conjugate heat/mass transfer, chemical reactions, and two practical applications containing reacting interfaces. An overall first-order convergence rate has been observed in both spatial and temporal accuracy tests.

Microscale Chaotic Mixing as a Driver for Chemical Reactions in Porous Media.

Mixing-induced reactions play a key role in a large range of biogeochemical and contaminant transport processes in the subsurface. Fluid flow through porous media was recently shown to exhibit chaotic mixing dynamics at the pore scale, enhancing microscale concentration gradients and controlling mixing rates. While this phenomenon is likely ubiquitous in environmental systems, it is not known how it affects chemical reactions. Here, we use refractive index matching and laser-induced fluorescence imaging of a bimolecular redox reaction to investigate the consequence of pore scale chaotic mixing on the reaction rates. The overestimation of measured reaction rates by the classical macrodispersion model highlights the persistence of incomplete mixing on the pore scale. We show that the reaction product formation is controlled by microscale chaotic mixing, which induces an exponential increase of the mixing interface and of the reaction rates. We derive a reactive transport model that captures experimental results and predicts that chaotic mixing has a first order control on reaction rates across a large range of time scales and Péclet and Damköhler numbers. These findings provide a new framework for understanding, assessing, and predicting mixing-induced reactions and their role on the fate and mobility of environmental compounds in natural porous media.

Well-posedness of a nonlinear stochastic model for a chemical reaction in porous media and applications

<p>In this paper, we considered a stochastic model of chemical reactive flows acting through porous media under the influence of nonlinear external random fluctuations, where the interchanges of chemical flow across the skeleton's surface are represented by a nonlinear function. We studied the existence and uniqueness of strong probabilistic solutions for the model under consideration. We also show the positivity for the concentration of the solute in the fluid face as well as the concentration of reactants on the surface of the skeleton under extra reasonable assumptions on the data. Initially, we approximated the solution of the nonlinear stochastic diffusion equation using Galerkin's approximation, and obtained important bound estimates along with probabilistic compactness results. Thereafter, we passed the limit and obtained a weak probabilistic solution. This was followed by the path-wise uniqueness of the solution, which leads to the existence and uniqueness of strong probabilistic solutions as a result of Yamada-Watanabe's theorem. Finally, we discuss some important numerical applications such as Langmuir and Freundlich kinetics using the extended stochastic non-conforming finite element method to illustrate the efficiency of this approach and compare it to the deterministic approach in both cases. Let us mention that well-posedness, positivity, and numerical simulations have not been considered so far for such a nonlinear stochastic model.</p>

Joint Effects of Heat Source and Magnetic Field on Unsteady Chemically Reacting Fluid Flow Towards A Vertically Inclined Plate in Addition of Cu-Nanoparticles

The primary goal of this evaluation task is to research the mathematical analysis for unstable, free convective incompressible viscous heat also mass transfer fluid movement across an inclined a plate that is vertically positioned in the occurrence of copper nanoparticles, Magnetism, thermal generator & chemical reaction in porous media. For this investigation, we assumed the effects of Cu-nanoparticles and Angle of inclination effects in the governing equations. Additionally, the effects of fluctuating temperature & concentration are studied. We established a set of basic equations for this fluid flow and translated nonlinear partial difference equations into linear incomplete comparisons, which were then answered using the implicit limited alteration technique. The impacts of several engineering fluid variables on flow variables such as velocity, temperature, & concentration profiles were explored in this research study via the use of graphs to show the findings. Along with the other findings, the mathematical standards of skin friction, heat transmission rate, & mass transmission constants are calculated and reported in tabular form. Finally, and perhaps most importantly, the mathematical consequences of the code validation programme are related to previously publish analytical results. In the instance of pure and nanofluids, the velocity profiles are shown to increase with rising values of the Heat transfer using the Grashof number, the mass movement Grashof number, the parameter for permeability, and the passage of time Increases in magnetic field component, the Schmidt number and the Prandtl number, the parameter for the heat source, the component of the chemical reaction, and the degree of inclination all result in a drop in the velocity profiles. With respect to temperature profiles, they have been on the rise with passing time, in contrast to the Prandtl number and the heat source parameter, for which the opposite trend has been seen. We discovered that the temperature and velocity profiles are both steeper for nanofluids than for pure fluids when the parameters are increased. The concentration profiles rise with increasing times, but the opposite is true for the Schmidt number. Moreover, increasing Chemical reaction parameter values result in decreasing profiles of concentrations.

Internal Biofilm Heterogeneities Enhance Solute Mixing and Chemical Reactions in Porous Media.

Bacterial biofilms can form in porous media that are of interest in industrial applications ranging from medical implants to biofilters as well as in environmental applications such as in situ groundwater remediation, where they can be critical locations for biogeochemical reactions. The presence of biofilms modifies porous media topology and hydrodynamics by clogging pores and consequently solutes transport and reactions kinetics. The interplay between highly heterogeneous flow fields found in porous media and microbial behavior, including biofilm growth, results in a spatially heterogeneous biofilm distribution in the porous media as well as internal heterogeneity across the thickness of the biofilm. Our study leverages highly resolved three-dimensional X-ray computed microtomography images of bacterial biofilms in a tubular reactor to numerically compute pore-scale fluid flow and solute transport by considering multiple equivalent stochastically generated internal permeability fields for the biofilm. We show that the internal heterogeneous permeability mainly impacts intermediate velocities when compared with homogeneous biofilm permeability. While the equivalent internal permeability fields of the biofilm do not impact fluid-fluid mixing, they significantly control a fast reaction. For biologically driven reactions such as nutrient or contaminant uptake by the biofilm, its internal permeability field controls the efficiency of the process. This study highlights the importance of considering the internal heterogeneity of biofilms to better predict reactivity in industrial and environmental bioclogged porous systems.

CompLaB v1.0: a scalable pore-scale model for flow, biogeochemistry, microbial metabolism, and biofilm dynamics

Abstract. Microbial activity and chemical reactions in porous media depend on the local conditions at the pore scale and can involve complex feedback with fluid flow and mass transport. We present a modeling framework that quantitatively accounts for the interactions between the bio(geo)chemical and physical processes and that can integrate genome-scale microbial metabolic information into a dynamically changing, spatially explicit representation of environmental conditions. The model couples a lattice Boltzmann implementation of Navier–Stokes (flow) and advection–diffusion-reaction (mass conservation) equations. Reaction formulations can include both kinetic rate expressions and flux balance analysis, thereby integrating reactive transport modeling and systems biology. We also show that the use of surrogate models such as neural network representations of in silico cell models can speed up computations significantly, facilitating applications to complex environmental systems. Parallelization enables simulations that resolve heterogeneity at multiple scales, and a cellular automaton module provides additional capabilities to simulate biofilm dynamics. The code thus constitutes a platform suitable for a range of environmental, engineering and – potentially – medical applications, in particular ones that involve the simulation of microbial dynamics.

Analytical Solution of Unsteady MHD Casson Fluid with Thermal Radiation and Chemical Reaction in Porous Medium

One of non-Newtonian fluid, Casson fluid, has a diversify application in the manufacturing and engineering sector due to its elasticity behaviour. This study provides the analytical solution of unsteady Casson fluid with the presence of thermal radiation and chemical reaction in a porous medium. Formulation of this fluid model is initiated with the partial differential equation (PDE) of the momentum and energy equations as well as the concentration equation. By applying the proper non-dimensional variables, these equations are then converted into dimensionless form. Subsequently, the derivation of the exact solutions for the concentration, temperature and velocity profiles is conducted with the operation of the Laplace transform method that satisfies both initial and boundary equations. Graphical illustrations, which portray the various effects on this study are generated. It has been revealed that as the thermal radiation, chemical species and porosity increases, so does the velocity profile. However, MHD and Casson parameter shown opposite behaviour in the velocity profiles.

Prediction of local concentration fields in porous media with chemical reaction using a multi scale convolutional neural network

The study of solute transport in porous media is of interest in many chemical engineering systems. Some example applications include packed bed catalytic reactors, filtration devices, and batteries. The pore scale modeling of these systems is time consuming and may require large computing resources, for this reason computational fluid dynamics (CFD) simulations are not practical if a large number of simulations is required, like in multiscale modeling, where a model at a large scale calls for pore scale simulations. It has been shown that neural networks can be trained with a dataset of flow simulations and then predict fields orders of magnitude faster, and with less computational resources, in new domains. However, it is crucial to provide the neural network with an effective description of the domain and the undergoing operating conditions to be able to train models that generalize accurately in unseen samples. Therefore, research is needed to employ neural networks in new complex systems. The appropriate training of a network for predicting coupled flow and solute transport processes is an outstanding problem due to the complex interplay between geometry and operating conditions. In this work, we train a multi scale convolutional neural network (MSNet) with a diverse dataset of simulations of transport and chemical reaction in porous media to predict the local concentration fields in images of porous media. Our dataset contains a wide diversity of sphere pack arrangements under different operating conditions (Péclet and Reynolds numbers). We train a robust model by employing different input descriptors that represent the medium and the different operating conditions of each system. Our trained model is able to provide nearly instantaneous predictions, compared to around twenty hours of the CFD workflow, with less than 3.5% error on new geometries and transport conditions. Thus the model could be easily integrated in a multiscale workflow where fast response is needed.

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.

Simulation of Structure Change in Porous Media During Gas–Solid Reactions Using Cellular Automata Model

In some gas–solid reactions, a new solid substance is produced. The product acts as a shield and prevents the collision between gas and solid reactants which further causes an incomplete reaction. If the molar volume of the new product differs from the solid reactant, the inner structure of porous media is changed as well. In this paper, we discuss such gas–solid reactions in porous media using the two-dimensional lattice gas cellular automata FHP-III model. We simulate the fluid flow and chemical reaction in different porous media. We also show the effects of porosity and morphology of the solid, and reaction probability on the reaction process. Results obtained from the simulations agree closely with the theory of gas–solid reactions and diffusion theories. Hence, the proposed model is a good choice to simulate gas–solid chemical reactions in porous media at the mesoscopic level.

An analytical model for dissolution of deposited asphaltene during CO<sub align="right">2 injection from the porous media

Carbon dioxide (CO2) based enhanced oil recovery (EOR) technique has a couple of benefits: mitigate CO2 emissions and increase recovery of oil from a reservoir. However, oil recovery is dependent on the composition of crude oil. Saturate-aromatic-resin-asphaltene (SARA) analysis shows that crude oil is composed of saturates, aromatics, resins, and asphaltene. It is found that asphaltene poses complex and severe formation damage problems and reduces the recovery of oil. After primary production with the change in pressure, temperature, and composition, the asphaltene may flocculate, precipitate and deposit in porous media. In this study, an analytical model is derived for the dissolution of deposited asphaltene. The derived model is used to develop a simulator that solves the dissolution of deposited asphaltene from porous media. The results of the derived model show good match with the laboratory results and also found important parameters that may lead to asphaltene dissolution. Our results show that asphaltene dissolution is affected by asphaltene concentration and its solubility, properties of host rock (heterogeneities), force of adhesion, and CO2 injection rate and period. The model does not consider CO2-rock chemical reactions in porous media. However, its consideration can increase reservoir porosity and permeability. [Received: May 24, 2017; Accepted: December 24, 2017]

An analytical model for dissolution of deposited asphaltene during CO<sub align="right">2 injection from the porous media

Carbon dioxide (CO2) based enhanced oil recovery (EOR) technique has a couple of benefits: mitigate CO2 emissions and increase recovery of oil from a reservoir. However, oil recovery is dependent on the composition of crude oil. Saturate-aromatic-resin-asphaltene (SARA) analysis shows that crude oil is composed of saturates, aromatics, resins, and asphaltene. It is found that asphaltene poses complex and severe formation damage problems and reduces the recovery of oil. After primary production with the change in pressure, temperature, and composition, the asphaltene may flocculate, precipitate and deposit in porous media. In this study, an analytical model is derived for the dissolution of deposited asphaltene. The derived model is used to develop a simulator that solves the dissolution of deposited asphaltene from porous media. The results of the derived model show good match with the laboratory results and also found important parameters that may lead to asphaltene dissolution. Our results show that asphaltene dissolution is affected by asphaltene concentration and its solubility, properties of host rock (heterogeneities), force of adhesion, and CO2 injection rate and period. The model does not consider CO2-rock chemical reactions in porous media. However, its consideration can increase reservoir porosity and permeability. [Received: May 24, 2017; Accepted: December 24, 2017]

Mathematical modelling of in situ combustion and gasification

The total worldwide resources of oil sands, heavy oil, oil shale and coal far exceed those of conventional light oil. In situ combustion and gasification are techniques that can potentially recover the energy from these unconventional hydrocarbon resources. In situ combustion can be used to produce oil, especially viscous and immobile crudes, by heating the oil and reducing the viscosity of the hydrocarbon liquids allowing them to flow to production wells. In situ gasification can be used to convert deep carbonaceous materials into synthesis gas which can be used at surface for power generation and petrochemical applications. While both in situ combustion for oil recovery and in situ gasification of coal have been developed and demonstrated over many decades, the commercial applications of these techniques have been limited to date. There are many physical processes occurring during in situ combustion, including multi-phase flow, heat and mass transfer, chemical reactions in porous media and geomechanics. A key tool in analysing and optimising the technologies involves using numerical models to simulate the processes. This paper presents a brief review of mathematical modelling of in situ combustion and gasification with an emphasis on developing a generalised framework and describing some of the key challenges and opportunities.

Interactions between gas flow and reversible chemical reaction in porous media

Taking into consideration the gas compressibility and chemical reaction reversibility, a model was developed to study the interactions between gas flow and chemical reaction in porous media and resolved by the finite volume method on the basis of the gas-solid reaction aA(g) + bB(s) ⇄ cC(g) + dD(s). The numerical analysis shows that the equilibrium constant is an important factor influencing the process of gas-solid reaction. The stoichiometric coefficients, molar masses of reactant gas, product gas and inert gas are the main factors influencing the density of gas mixture. The equilibrium constant influences the gas flow in porous media obviously when the stoichiometric coefficients satisfy a/c≠1.

Asymptotic analysis of a semi-linear elliptic system in perforated domains: Well-posedness and correctors for the homogenization limit

In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume chemical reactions in porous media. Our interest lies in deriving homogenization limits (upscaling) for alike systems and particularly in justifying rigorously the obtained averaged descriptions. Essentially, we prove the well-posedness of the microscopic problem ensuring also the positivity and boundedness of the involved concentrations and then use the structure of the two scale expansions to derive corrector estimates delimitating this way the convergence rate of the asymptotic approximates to the macroscopic limit concentrations. Our techniques include Moser-like iteration techniques, a variational formulation, two-scale asymptotic expansions as well as energy-like estimates.

Comparison of the surface ion density of silica gel evaluated via spectral induced polarization versus acid–base titration

Surface complexation models are widely used with batch adsorption experiments to characterize and predict surface geochemical processes in porous media. In contrast, the spectral induced polarization (SIP) method has recently been used to non-invasively monitor in situ subsurface chemical reactions in porous media, such as ion adsorption processes on mineral surfaces. Here we compare these tools for investigating surface site density changes during pH-dependent sodium adsorption on a silica gel. Continuous SIP measurements were conducted using a lab scale column packed with silica gel. A constant inflow of 0.05M NaCl solution was introduced to the column while the influent pH was changed from 7.0 to 10.0 over the course of the experiment. The SIP measurements indicate that the pH change caused a 38.49±0.30μScm−1 increase in the imaginary conductivity of the silica gel. This increase is thought to result from deprotonation of silanol groups on the silica gel surface caused by the rise in pH, followed by sorption of Na+ cations. Fitting the SIP data using the mechanistic model of Leroy et al. (Leroyet al., 2008), which is based on the triple layer model of a mineral surface, we estimated an increase in the silica gel surface site density of 26.9×1016sitesm−2. We independently used a potentiometric acid–base titration data for the silica gel to calibrate the triple layer model using the software FITEQL and observed a total increase in the surface site density for sodium sorption of 11.2×1016sitesm−2, which is approximately 2.4 times smaller than the value estimated using the SIP model. By simulating the SIP response based on the calibrated surface complexation model, we found a moderate association between the measured and estimated imaginary conductivity (R2=0.65). These results suggest that the surface complexation model used here does not capture all mechanisms contributing to polarization of the silica gel captured by the SIP data.

A coupled transport model for water splitting within a porous metal oxide thermochemical reactor using the random walk particle tracking method

Water splitting using an iron-based looping processes is a promising method to produce high purity hydrogen. The cyclical, heterogeneous oxidation and reduction reactions are carried out within high surface area stable porous structures as the solid reactant. The random walk method is used to simulate chemical reaction and species transport, as it is capable of handling stiff reaction kinetics and varying hydrodynamic dispersion tensors caused by pore-level velocity fluctuations. The original random walk formulation is extended to account for bulk density variations and source terms due to the chemical reaction. The species transport equation is recast in the form of the Fokker–Planck equation, and the trajectories of fluid particles are obtained by solving an appropriate Langevin equation that has additional drift terms as a result of spatial variations in bulk density and dispersion tensor. The source term is accounted for by changing the composition of fluid particles based on the reaction kinetics. The extended approach for each new term is validated against exact solutions or highly resolved finite difference solutions. Finally, a new coupled model for bulk fluid flow, species transport, and chemical reaction in porous media is developed and applied to simulate a bench-scale water splitting reactor with a porous iron-silica fixed bed structure. Excellent agreement with the measured hydrogen production rate at different operating conditions is obtained.

Simulation of gas exothermic chemical reaction in porous media reactor with lattice Boltzmann method

Exothermic reactor is the main part in a chemical heat pump. It involves complex multi-component exothermal chemical reaction in catalyst-filled porous media. The lattice Boltzmann method (LBM) is developed to simulate the characteristics of fluid flow, heat and mass transfer coupling chemical reaction in the exothermic reactor of the isopropanol/acetone/hydrogen chemical heat pump system. Fractal theory is used to structure a porous medium model in the reactor. The simulation results show that LBM is suitable for the simulation and the conversion has an optimal value with different inlet velocities.

On diffusion, dispersion and reaction in porous media

The upscaling process of mass transport with chemical reaction in porous media is carried out using the method of volume averaging under diffusive and dispersive conditions. We study cases in which the (first-order) reaction takes place in the fluid that saturates the porous medium or when the reaction occurs at the solid–fluid interface. The upscaling process leads to average transport equations, which are expressed in terms of effective medium coefficients for (diffusive or dispersive) mass transport and reaction that are computed by solving the associated closure problems. Our analysis shows that these effective coefficients depend, in general, upon the nature and magnitude of the microscopic reaction rate as well as of the essential geometrical structure of the solid matrix and the flow rate. This study also shows that if the reaction rate at the microscale is arbitrarily large, the capabilities of the upscaled models are hindered, which is in agreement with the breakdown of the physical sense of the microscale formulation.

On the effective diffusivity under chemical reaction in porous media

This paper addresses the question of whether effective diffusivities in porous materials under reactive and nonreactive conditions are equal. Previous studies have considered the problem with first-order reactions, suggesting that the effective diffusivity is unaffected by the reaction mechanisms. However, these studies were made under the assumption of heterogeneous reaction ( i.e., the reaction takes place on the solid surface). In contrast to such studies, the present work shows that the effective diffusivity is affected by homogeneous reaction ( i.e., the reaction takes place in the fluid phase bulk). The results, obtained from volume-averaging methods for first-order kinetics, show that the effective diffusivity is an increasing function of the Thiele modulus.