Reactive Porous Media Research Articles

A coupled compressible two-phase flow with the biological dynamics modeling the anaerobic biodegradation process of waste in a landfill

In this article, we present and study a new coupled model combining the biological and the mechanical aspects describing respectively the process of the biogas production and the compressible two-phase leachate-biogas flow during the anaerobic biodegradation of organic matters in a landfill, which is considered a reactive porous medium. The model obtained is governed by a reaction-diffusion system for the bacterial activity coupled with a compressible two-phase flow system of a non-homogeneous porous medium. We carry out the analysis and the numerical approximation of the model within a variational framework. We propose a full discrete system based on a second-order BDF-time scheme and P1-conforming finite element and we derive an efficient algorithm for the coupled system. We perform some numerical simulations in 2D and 3D examples in agreement with the theoretical analysis.

Entropy generation in a chemically and thermally reinforced doubly stratified porous enclosure in a magnetic field

In this article, the study of chemical reaction and heat generation effects on the magnetohydrodynamic free convection in the thermal and mass stratified fluid-filled porous enclosure under the influence of cross-diffusion forces is extended to the entropy generation analysis for the design of relevant tools of engineering applications. Here, the multiphysics associated with natural convection in doubly stratified fluid containing chemically reactive square porous enclosure under uniform magnetic field furnishes novel flow dynamics modeling. Since the distinctive nature of the free convective flow mechanism is described by the complex heat and mass transfer process, the thermal investigation cannot be considered complete until the visual illustration of the transportation of heat and mass flux is provided. Therefore, the new heat flux and mass flux models are proposed for the multi-force effect on chemically reactive porous media under the effect of viscous dissipative heat generation to facilitate the directional manifestation of heat and mass flux transitions along with intensity. Additionally, the thermodynamical measures are established by the new entropy generation model and advanced Bejan number irreversibility characterization.

A spectral approach for homogenization of diffusion and heterogeneous reaction in porous media

Macroscopic models for diffusion and heterogeneous reversible reaction of two species in porous media are developed by using coupled homogenization technique and spectral approach. Three representative cases related to the order of magnitude of the macroscopic Damköhler number DaL, namely predominating reaction, diffusion-reaction of the same order and dominating diffusion, are considered. The concentrations are developed as time series in an eigenfunctions basis associated with periodic spectral problems formulated in the unit-cell, thus forming a new microscopic problem to be homogenized. Such an approach represents a powerful tool to upscale diffusion-reaction microscopic problems, especially for high Damköhler number values where classical asymptotic development fails. It enables to capture the physics at very short times, when the characteristic time of reaction involved is much faster than the diffusion one. This work allows us to formulate the complex macroscopic laws describing the heterogeneous diffusion/reaction problem for two species in high Damköhler number regime.

New insights into the effects of methane and oxygen on heat/mass transfer in reactive porous media

The partial replacement of a hydrogen-based gaseous fuel for solid fossil fuel plays a key role in increasing the sustainable energy share in sinter plants. The imbalanced heat distribution is a long-standing problem that can adversely affect the energy efficiency of sintering process, especially in the near-inlet region. In the present study, the impacts of methane and oxygen injection concentrations on sintering performance were numerically examined. Compared with previous studies, the maximum methane concentration examined was extended significantly from 1.0% to 5.5%, which is very close to the lean flammable limit (5.3%). Computations demonstrated that methane concentration had considerable effects on the methane combustion dynamics and solid fuel oxidation. In the near-inlet region, injecting methane at a high concentration (3.5%) remarkably expanded the melting zone and increased the melting quantity index. In addition, the results indicated that reacting flow with a low oxygen concentration could decrease the melting zone propagation speed in the near-inlet region, thereby improving the local sintering performance. However, the reacting flow with high methane concentration and low oxygen concentration had negative impacts on the sintering speed. The recommended operating conditions were determined based on parametric studies to achieve a tradeoff between the sinter quality and productivity.

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.

A new outlook and a model of reactions in porous media

AbstractA novel method based on cup‐mixing concentration and superficial velocity is presented for the analysis of reactions in isothermal fixed‐bed reactors. It is founded on experimentally observed profiles of concentration and velocity so as to preserve the heterogeneity of a reaction system. The domain of application of the model includes reaction systems at lower Reynolds numbers and Péclet numbers of less than 700 with a void fraction of for which the ratio of the bed‐length‐to‐particle diameter to particle Péclet number exceeds .

A fractional differential scheme for the effective transport properties of multiscale reactive porous media: Applications to clayey geomaterials

AbstractA new homogenization scheme is proposed to model the effects of surface phenomena occurring at the pore fluid/solid interface on the effective transport properties of multiscale and reactive geosystems, e.g., clayey geomaterials. This new scheme is a generalization of the so‐called differential scheme (DS) used to infer the effective properties of a composite made up of several materials. It is named the fractional differential scheme and is based on two key elements: (i) the concept of realizability of the DS itself and (ii) a fractional integral formulation of the DS for a porous medium considered as a two‐component composite. The formulation of the fractional DS introduces two parameters: a cementation exponent m and a fractional order α. The cementation exponent m is related to the microstructure of the material. The fractional order α accounts for the amplitude of the “surface” transport of ions resulting from the physico‐chemical interactions between hydrated cations and swelling clay minerals. Both parameters m and α are inverted from two sets of data: electrical conductivity measurements obtained on clayey rocks and effective diffusion coefficient measurements acquired from a Na‐montmorillonite geomaterial. The inversion results demonstrate that the fractional DS model is able to capture the dependence of the cation concentration on the effective transport properties of the clayey materials under study. Our results also show that the fractional order α can be considered an indirect indicator of the amplitude of physico‐chemical interactions between hydrated cations and swelling clay minerals occurring at the pore fluid/solid interface.

Detailed Modeling of Cork-Phenolic Ablators in Preparation for the Post-flight Analysis of the QARMAN Re-entry CubeSat

This work deals with the analysis of the cork P50, an ablative thermal protection material (TPM) used for the heat shield of the qarman Re-entry CubeSat. Developed for the European Space Agency (ESA) at the von Karman Institute (VKI) for Fluid Dynamics, qarman is a scientific demonstrator for Aerothermodynamic Research. The ability to model and predict the atypical behavior of the new cork-based materials is considered a critical research topic. Therefore, this work is motivated by the need to develop a numerical model able to respond to this demand, in preparation to the post-flight analysis of qarman. This study is focused on the main thermal response phenomena of the cork P50: pyrolysis and swelling. Pyrolysis was analyzed by means of the multi-physics Computational Fluid Dynamics (CFD) code argo, developed at Cenaero. Based on a unified flow-material solver, the Volume Averaged Navier–Stokes (VANS) equations were numerically solved to describe the interaction between a multi-species high enthalpy flow and a reactive porous medium, by means of a high-order Discontinuous Galerkin Method (DGM). Specifically, an accurate method to compute the pyrolysis production rate was implemented. The modeling of swelling was the most ambitious task, requiring the development of a physical model accounting for this phenomenon, for the purpose of a future implementation within argo. A 1D model was proposed, mainly based on an a priori assumption on the swelling velocity and the resolution of a nonlinear advection equation, by means of a Finite Difference Method (FDM). Once developed, the model was successfully tested through a matlab code, showing that the approach is promising and thus opening the way to further developments.

Volatiles effects on the thermal and chemical structures of H2 production in a hybrid porous media reactor using solar steam

A numerical simulation was performed to model the gasification of carbonaceous feedstocks inside a batch reactor operating on a hybrid filtration combustion mode in presence of solar steam aiming to hybridize conventional process. Results were validated against empirical data collected using sub-bituminous coal, focusing in the effect of implementing a volatilization model to the simulation. Temperature and concentration of gaseous products of the combustion wave were reported as function of steam presence, filtration velocity and fuel content inside the porous bed. Solar steam was produced in a hybrid thermal/electric boiler powered by a PV-array and heat pipes, achieving up to 19% of concentrated solar input in the generation of steam. Numerical simulations showed a good qualitative agreement with experimental results. The main numerical and empirical results showed that increasing the coal presence favored a normal thermal structure, observing a maximum temperature of 1,638 K at a 70% coal mass fraction, while an increase on the steam content resulted on a shift from a normal to an inverse thermal structure recording a peak temperature of 1,618 K at a 0.95 H2O/O2 fraction and 50% coal presence. Finally, H2 production was observed to increase with an increment of coal fractions which was only properly simulated when including a devolatilization model.

Water Film Thickness in Unsaturated Porous Media: Effect of Pore Size, Pore Solution Chemistry, and Mineral Type

AbstractThe thickness of the water film on minerals is key for a quantitative understanding of mass transport and reaction in porous media under air entrapment. How the film thickness changes with pore structure, ionic strength, pH, and type of mineral, however, is not fully understood. Here, we present a model to predict the film thickness in porous media under air entrapment. The model numerically solves the Poisson–Boltzmann equation combined with the electrical triple‐layer model to consider the overlapping of electric double layers (EDLs) in the film, where EDLs formed at the mineral/water and air/water interfaces interact with each other. Based on the model, we estimated the film thickness for silica, montmorillonite, calcite, and goethite for various ionic strengths and pH. With decreasing film thickness, the overlapping of EDLs reduces the surface charges but increases the electric potentials of silica/water and air/water interfaces. The predicted film thickness for silica generally agreed with the measured value. The film on calcite and goethite is significantly thinner than that on silica and montmorillonite because the surface charges for calcite and goethite have a sign opposite to that of the air/water interface. Our model shows that the pore radius, ionic strength, pH, and sign of surface charge are the primary factors controlling the film thickness. When the ionic strength and pH are similar to those of rainwater, river water, and groundwater, the typical film thicknesses for silica in silt, sand, and gravel were predicted to be <14 nm, 14–45 nm, and >23 nm, respectively.

Porosity‐Permeability Evolution During Simultaneous Mineral Dissolution and Precipitation

AbstractPermeability in reactive porous media evolves in complex ways that are hard to predict. Macroscopic empirical equations are often used to estimate permeability evolution but fail to reflect the impact of pore scale reactions on permeability. This work aims to understand the evolution of permeability in systems where mineral dissolution and precipitation occur simultaneously. Pore network models are used for permeability simulation of a Paluxy sandstone using pore and pore‐throat size distributions from the analysis of X‐ray CT images. Pore and pore‐throat radii are increased and decreased to reflect the effects of dissolution and precipitation reactions. Varying spatial distributions of reactions are simulated and the resulting porosity and permeability values compared with commonly used macroscopic equations. It is observed that when dissolution occurs at the inlet and precipitation at the outlet, porosity increases while permeability decreases. Similar results are also observed in the respective opposite scenario where precipitation occurs at the inlet and dissolution at the outlet. When dissolution and precipitation reactions are randomly distributed throughout the network, porosity increases with little change in permeability that is not captured by the empirical equations. When reactions are controlled by pore and pore‐throat sizes, such as dissolution occurring in pores and pore‐throats of small size and precipitation in pores and pore‐throats of larger size, porosity and permeability decrease. When precipitation occurs in pores and pore‐throats of smaller size and dissolution in pores and pore‐throats of larger size, porosity and permeability increase and is described relatively well by the Verma‐Pruess porosity‐permeability equation.

Numerical modelling of a three-zone combustion for heavy fuel oil in inert porous media reactor

Numerical model for heavy fuel oil and air mixtures combustion is presented to simulate the behavior of the fuel in an inert porous medium reactor for hydrogen production. Three-zone combustion of oil and petroleum cokes separated by temperature ranges starting from ambient temperature to 560 K, from 560 K to 673 K, and above 673 K, is presented. Hydrogen production is achieved using water gas shift equilibrium reaction on the combustion products at different temperatures. Results show a high enthalpy contribution due to coke combustion formed in the low temperature oxidation reaction, being the most important reaction in relation to its zone size. Simulations increasing filtration velocity (from 0.05 to 0.9 m/s) has a favorable effect on the maximum temperature and the combustion front velocity. The effect of the simplified combustion model lowers computational time, with acceptable results for temperature as well as hydrogen production in contrast to laboratory tests and other software simulation such as COMSOL Multiphysics.

A Parallel Coupled Lattice Boltzmann-Volume of Fluid Framework for Modeling Porous Media Evolution.

In this paper, we present a framework for the modeling and simulation of a subset of physical/chemical processes occurring on different spatial and temporal scales in porous materials. In order to improve our understanding of such processes on multiple spatio-temporal scales, small-scale simulations of transport and reaction are of vital importance. Due to the geometric complexity of the pore space and the need to consider a representative elementary volume, such simulations require substantial numerical resolutions, leading to potentially huge computation times. An efficient parallelization of such numerical methods is thus vital to obtain results in acceptable wall-clock time. The goal of this paper was to improve available approaches based on lattice Boltzmann methods (LBMs) to reliably and accurately predict the combined effects of mass transport and reaction in porous media. To this end, we relied on the factorized central moment LBM as a second-order accurate approach for modeling transport. In order to include morphological changes due to the dissolution of the solid phase, the volume of fluid method with the piece-wise linear interface construction algorithm was employed. These developments are being integrated into the LBM research code VirtualFluids. After the validation of the analytic test cases, we present an application of diffusion-controlled dissolution for a pore space obtained from computer tomography (CT) scans.

The Lagrangian kinematics of three-dimensional Darcy flow

Abstract

Experimental investigation of reverse flow porous medium reactor with premixed and non-premixed flames

Reverse flow porous medium reactor with premixed and non-premixed flames of methane and oxidant was experimentally investigated to evaluate its suitability for hydrogen (H2) and syngas production. Methane-air premixed, non-premixed, and non-premixed with steam were the tested cases for different inlet configurations. Thermal profiles, wave velocities, and H2 and carbon monoxide (CO) production for equivalence ratios (ϕ) of 2, 3 and 4 were analyzed. Methane-air premixed flames at ϕ = 2 obtained good performance with 1574 K average and 31% and 68% of H2 and CO yield, respectively. The H2/CO ratios in syngas registered were 1.1, 1.7 and 1.5 at equivalence ratios of ϕ = 2, 3, and 4, respectively. Methane-air non-premixed flames obtained higher temperature in the zone of methane injection but no higher syngas production when compared to the premixed case. The H2/CO ratios in syngas registered were 2 and 2.4 at equivalence ratios of ϕ = 2 and 3, respectively. Methane-air non-premixed with steam shows a similarity between the temperature of without steam cases, which implies the lower influence of the steam on the reaction mechanism. Results show that separate supply of reagents allows obtaining synthesis gas with a higher H2/CO ratio than premixed case.

A new technique of seawater intrusion control: development of geochemical cutoff wall.

The construction of a subsurface dam and/or physical cutoff barriers is one of the most known techniques used to prevent seawater intrusion during excessive exploitation of freshwater from a coastal aquifer. This method is widely used in many sites around the world (Japan, Brazil, India, Burkina Faso…). In this study, we present an innovative technique for constructing subsurface barriers based on geochemical reactions. A calcite cutoff wall is developed by mixing two aqueous solutions Na2CO3 and CaCl2 under pCO2 equal to 3.16·10-4 bar. The deposition of calcite in the mixing zone induces a high clogging, which greatly reduces the porosity and then the permeability of the aquifer into the injection zone. We use GEODENS code to study the effect of a developed geochemical cutoff wall on saltwater intrusion and to assess their protective effect on preventing seawater intrusion. The GEODENS code can solve these equations by a finite element procedure; it can handle density-dependent flow, transport, and geochemical reactions in porous media. The effect of depth and location of the geochemical cutoff wall is tested and results showed a significant reduction of seawater intrusion penetration length. According to the budget used in many barrier construction projects, we have shown that the developed geochemical cutoff wall presented in this work could produce a lower seawater intrusion penetration length than the traditionally used barriers at a very lower cost.

Pore-scale simulation of miscible viscous fingering with dissolution reaction in porous media

Global climate change is happening but may be mitigated by the technology of geological carbon dioxide (CO2) sequestration. To gain comprehensive insights into this approach, we perform pore-scale simulations of displacement between two miscible fluids in porous media using a new multiple-relaxation-time lattice Boltzmann model. This study marks the first attempt to investigate viscous fingering dynamics in miscible displacement, considering the coexistence of viscosity contrast and dissolution reaction. Simulation results capture different fingering patterns that depend on dissolution (Damköhler number Da), diffusion (Peclet number Pe), and viscosity contrast (viscosity ratio R). From simulations of unstable viscous flows, dissolution is found to delay fingering onset, slow down fingering propagation, and inhibit or reinforce the late-stage fingering intensity. In simulations with stable viscosity contrasts, the displacement features fingering phenomena when dissolution is fast enough. In addition, we conduct a parametric study to assess the impact of Pe, R, and Da. The results suggest that increasing Pe or R destabilizes fingering, but increasing Da first suppresses and gradually intensifies fingering. Finally, for every fixed Da, we determine the phase boundary between stable and unstable regimes in a Pe–R phase plane. A unified scaling law is developed to approximate boundary lines obtained under different Da values. By comparing reactive and nonreactive cases, we classify four distinct regimes: stable, unstable, reactive stable, and reactive unstable. These pore-scale insights are helpful in understanding and predicting the displacement stability during the geological CO2 sequestration, which is of importance to the pre-evaluation of the storage efficiency and safety.

Acid stimulation in carbonates: A laboratory test of a wormhole model based on Damköhler and Péclet numbers

Acid stimulation has been used worldwide as a stimulation technique either by matrix acidizing to remove the near-wellbore permeability impairment which is referred to as formation damage or acid fracturing to enhance the connectivity between wells and reservoirs. Carbonate acid stimulation improves the near-wellbore permeability through the creation of deeply penetrating fluid pathways referred to as wormholes. The stimulation success depends on the length and width of these wormholes. Here, we test the results of a theoretical study which suggests that the effect of acid flow in a reactive porous medium can be fully defined by just two significant dimensionless numbers, the non-dimensional Damköhler and Péclet numbers. The approach was validated in an idealized numerical study and is here tested in a systematically controlled laboratory experiment for real carbonate rocks. In order to obtain statistically meaningful results, we pushed the envelope by testing the prediction of the critical point for the wormholing phenomenon in a difficult domain, where sufficient randomly distributed pathways exist such that the wormholing domain is rarely achieved. The result confirmed that for a randomly-structured highly porous media, the critical point for dissolution pattern formation including the wormholing phenomenon can be fully captured by a domain diagram of inverse Damköhler versus Péclet number as predicted by the theoretical model. The model also holds for moderately tight formations, however, breaks down when the natural permeability drops well below 100 mDarcy. We conclude that the result of this research can be applied to reliably predict the wormholes initiation and various dissolution structures under various injection rate and HCl-concentration.

Time increasing rates of infiltration and reaction in porous media at the percolation thresholds.

The infiltration of a solute in a fractal porous medium is usually anomalous, but chemical reactions of the solute and that material may increase the porosity and affect the evolution of the infiltration. We study this problem in two- and three-dimensional lattices with randomly distributed porous sites at the critical percolation thresholds and with a border in contact with a reservoir of an aggressive solute. The solute infiltrates that medium by diffusion and the reactions with the impermeable sites produce new porous sites with a probability r, which is proportional to the ratio of reaction and diffusion rates at the scale of a lattice site. Numerical simulations for r≪1 show initial subdiffusive scaling and long time Fickean scaling of the infiltrated volumes or areas, but with an intermediate regime with time increasing rates of infiltration and reaction. The anomalous exponent of the initial regime agrees with a relation previously applied to infinitely ramified fractals. We develop a scaling approach that explains the subsequent time increase of the infiltration rate, the dependence of this rate on r, and the crossover to the Fickean regime. The exponents of the scaling relations depend on the fractal dimensions of the critical percolation clusters and on the dimensions of random walks in those clusters. The time increase of the reaction rate is also justified by that reasoning. As r decreases, there is an increase in the number of time decades of the intermediate regime, which suggests that the time increasing rates are more likely to be observed is slowly reacting systems.

Natural gas-supported gasification of polyethylene and wood mixtures in a porous medium reactor

Valorisation of plastic waste or forest-agroindustrial residues poses an opportunity to reduce landfilling and to obtain value-added products simultaneously. Through thermal partial oxidation, hydrocarbon fuels can be gasified and converted into syngas. Particularly, hybrid porous media reactors allow gasifying low-grade fuels in an efficient eco-friendly way. In this work, the natural gas-supported gasification of polyethylene and wood mixtures in a porous bed reactor is studied. The reactor is designed and built to operate in semi-continuous mode. The temperature evolution, the reaction wave propagation rate, and the resulting concentration of the main gas species (H2, CO, CH4, CO2, NOx, and UHC) were measured for different polyethylene and wood mixtures, keeping an optimum natural gas-to-air ratio of 0.8. The influence of the gasification conditions on the reaction pathways and the process development is analysed by sampling the system in two representative moments. The maximum syngas production was 23.86 vol%, which was obtained when loading only 100% polyethylene, while the maximum energy return on investment of 49% was registered for the highest biomass fraction in mixture. The semi-continuous operation design was validated based on the thermal behaviour and the combustion wave displacement. This experimental work shows promising results in the search for solutions to gasify solid wastes in continuous mode.