Reactive Porous Media Research Articles

Electrical conductivity model for reactive porous media under partially saturated conditions with hysteresis effects

The electrical conductivity of a porous medium is strongly controlled by the structure of the medium at the microscale as the pore configuration governs the distribution of the conductive fluid. The pore structure thus plays a key role since different geometries translate in variations of the fluid distribution, causing different behaviors measurable at the macroscale. In this study, we present a new physically-based analytical model derived under the assumption that the pore structure can be represented by a bundle of tortuous capillary tubes with periodic variations of their radius and a fractal distribution of pore sizes. By upscaling the microscale properties of the porous medium, we obtain expressions to estimate the total and relative electrical conductivity. The proposed pore geometry allows us to include the hysteresis phenomenon in the electrical conductivity estimates. The variations on these estimates caused by pore structure changes due to reactive processes are accounted by assuming a uniform dissolution of the pores. Under this hypothesis, we describe the evolution of the electrical conductivity during reactive processes. The expressions of the proposed model have been tested with published data from different soil textures, showing a satisfactory agreement with the experimental data. Hysteretic behavior and mineral dissolution are also successfully addressed. By including hysteresis and mineral dissolution/precipitation in the estimates of the electrical conductivity, this new analytical model presents an improvement as it relates those macroscopic physical phenomena to its origins at the microscale. This opens up exciting possibilities for studies involving electrical conductivity measurements to monitor water movement, and hysteretic and reactive processes in porous media.

Optimization of methane partial oxidation for hydrogen production with local free space addition: An efficient combination of porous media reactor and thermoelectric conversion system

Thermoelectric technology plays a pivotal role in the efficient conversion and utilization of exhaust heat. Abundant waste heat resources are present in the tail gas of hydrogen production, significantly influenced by combustion characteristics. To investigate the impact of combustion performance on hydrogen yield and power output, an efficient porous media reactor was designed and integrated with a thermoelectric conversion system. The combustion characteristics of a thermoelectric system incorporating unsteady porous media were examined. Furthermore, the effects of the porous media’s structural parameters on temperature distribution, gas concentration, and power generation were analyzed under various operating conditions. The results revealed that radial free space structures exhibited higher hydrogen and methane conversion efficiencies compared to axial free space structures at verge and toroidal positions. However, the height of the radial free space exerted a more substantial influence on temperature distribution and gas production than the size of the free space itself. At a height of 39 mm, hydrogen concentration and yield reached their peak values of 14.5 % and 53 %, respectively. Combustion was found to significantly impact power generation, with a downward shift of the flame resulting in decreased power output. The inlet velocity was observed to affect the thermoelectric generator power, with a maximum steady-state power of 3.95 W achieved at a velocity of 16 cm/s. These findings provide practical guidance for the efficient utilization of industrial waste heat.

Experimental investigation of steam and carbon dioxide influence on methane filtration combustion in a reversal flow porous media reactor

A reverse flow porous medium reactor with premixed and non-premixed flames was experimentally investigated to evaluate the influence of steam and carbon dioxide on methane (CH4) filtration combustion for syngas production. Premixed, non-premixed, and non-premixed with steam were the tested cases for different injection configurations. Thermal profiles, combustion products, hydrogen (H2) and carbon monoxide (CO) yields for several equivalence ratios are analyzed. Non-premixed case exposed higher maximum temperatures due to the reactant accumulation at the crosswise injection position, with a temperature of 1615 K. The lack of homogenization of the reactants in this configuration leads to low H2 and high CO concentrations compared to the premixed case. The maximum CO yield was 92.81% for the non-premixed configuration with alternated air injection, while the maximum H2 yield was 37.8% for the premixed air-methane-steam case. It was found that the air-methane-carbon dioxide mixtures had lower temperatures, combustion wave velocities, and H2 and CO concentrations, compared to the air-methane, and air-methane-steam mixtures, but higher CH4 and CO2 concentrations. The premixed configuration with air-methane-carbon dioxide mixture showed higher temperatures, and H2 and CO concentrations, compared to the non-premixed configuration. Further studies are necessary to optimize the operation of these types of reactors.

Solar-driven gasification for syngas production at low temperatures using a rotary hybrid porous media reactor

Solar-based technologies play a crucial role in the energy transition towards a green circular economy. This work investigates the solar-driven steam gasification of carbon char particles at low temperatures using an indirectly irradiated rotary hybrid porous media reactor. The solar concentration system consists of a heliostat and parabolic dish with a focus on the emitter plate located at the bottom of the reactor, allowing allothermal conditions for hydrogen (H2) and syngas production. The hybrid bed is composed of carbon and alumina particles randomly mixed in a 50/50 proportion in mass. Three sets were tested varying rotation speed of the unit, i.e., Set A (0 rpm), Set B (15 rpm), and Set C (20 rpm). Numerical simulations were performed using a one-dimensional model assessing mass, energy and chemical conservation equations, considering a semi-global kinetic scheme, including three homogeneous and four heterogeneous chemical reactions. The optical design configuration of the solar system, in addition to the high heat recirculation enhanced by the rotation of the reactor, allowed maximum temperatures of 662 K (outer surface) and 573 K (reaction chamber). At this low-temperature range, a good agreement between numerical simulations and experiments was achieved, observing a H2/CO ratio of 0.088 (Set B) and 0.163 (Set C), representing a 5.7% and 3.1% deviation, respectively. Numerical results show an increase in the temperature would lead to a higher H2/CO ratio production. Further studies are necessary to assess hydrogen and syngas production under these operating conditions at high temperatures.

Efficient Energy Storage via Methane Production Using Protonic Ceramic Electrochemical Cells

Protonic ceramic electrochemical cells (PCECs) are promising energy storage technologies due to their high performance and ability to convert CO2 into value-added chemicals. However, there are many fundamental aspects of this technology that require investigation to better understand its interactions and opportunities. Thus, this paper focuses on the development of a steady-state PCEC model, encompassing intricate details of reactive porous-media transport, elementary catalytic chemistry, and electrochemistry within unit cells. The model is calibrated and validated using experimental data. The model presents the rate of methane production at different temperatures and revealed that efficient PCEC for co-electrolysis of CO2 and H2O is operated in the temperature range of 420–470 °C and the optimum being 450 °C at the rate of 0.0391 moldm−3 min−1. It provides insights into the effects of overpotentials on cell performance. At a current density of 3000 A/m2 the ohmic, concentration, and activation overpotentials amount to 0.65, 0.004, and 0.19 V, respectively. The results obtained from the model highlight the potential of PCECs as efficient CO2 sinks for decarbonization purposes and as a means of methane production. Furthermore, the model's findings offer valuable guidance for the design, selection of stacks, and choice of building materials in PCEC systems. The potential applications of PCECs as real-life fuel utilization technologies are justified with improved material development to reduce cell overpotentials, opening doors for scale-up and eventual commercialization. These findings contribute to the development of sustainable energy systems and advance the pursuit of decarbonization goals.

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.

Modelling soil-water retention curves subject to multiple wetting-drying cycles: An approach for expansive soils

This study proposes an innovative and simple method to quantify the effect of wetting–drying history on soil–water retention curve (SWRC) of expansive soils. This method is based on the increment relationship between degree of saturation and initial void ratio corresponding to irreversible swelling or shrinkage after each wetting–drying cycle, following the double-structure scheme for three-phase reactive porous media. The approach satisfies the intrinsic constraints for partially saturated porous media, and the incremental relationship can be applied in any existing SWRC equations for future water retention capacity prediction. In this respect, only one new rate function is proposed, which could be easily calibrated by relevant experimental data. The prediction of the model is verified through the comparison with relevant experimental data of two expansive clayey soils. To evaluate the general applicability of the proposed method, two typical SWRC equations proposed in literature were used. The results showed a very good agreement with experimental data subject to multiple wetting–drying cycles, indicating its potential as an effective tool for estimating preliminary SWRCs of expansive soils.

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.

Groundwater remediation by in-situ membrane ozonation: Removal of aliphatic 1,4-dioxane and monocyclic aromatic hydrocarbons

Groundwater contamination by widespread and persistent organic compounds requires extensive treatment efforts, for example by in-situ chemical oxidation (ISCO). In this study, we investigated ozone mass transfer and removal mechanisms of ozone-resistant monocyclic aromatic and non-aromatic compounds in a novel in-situ treatment method using ozone-permeable membranes as reactive barrier. Initial batch experiments confirmed fast depletion of ozone in presence of sub-stoichiometric benzoic acid (BA), in contrast to the non-aromatic 1,4-dioxane (DIOX), where ozone depleted much slower. Simulated in-situ membrane ozonation treatment of contaminated groundwater led to lower removal of 5 mg L−1 BA (52.7%) compared to DIOX (60.6%). Inhibited removal of BA compared to additional batch experiments could be explained by quick depletion of ozone by reactive intermediates on the membrane surface. Surprisingly, reactive porous media did not lead to substantial changes of in-situ DIOX oxidation, although a stronger impact of the media on DIOX oxidation was hypothesized. Furthermore, experimental ozone mass transfer coefficients were determined (3.94∙10−7 – 3.12∙10−6 m s−1) and compared to modeled values for different membrane types (polydimethylsiloxane and polytetrafluoroethylene). Finally, a mathematical model based on mass transfer data was developed to support upscaling efforts. We concluded that contaminant properties are crucial for the feasibility assessment of in-situ ozone membrane treatment technology.

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>

Stabilization of methane–hydrogen flames inside a divergent porous media reactor

The energy transition process triggered by the threat of climate change has created the need for cleaner heat generating systems. Using blends of hydrocarbons with increasing presence of green fuels, such as green hydrogen, has been proposed as an initial step of this process. The present study aims to investigate methane–hydrogen flames stabilized inside a divergent inert porous media burner. Experimentally, four stable operating points were found for the considered burner with a hydrogen presence between 0% and 30% in the fuel mixture at a constant thermal output of 2 kW. Temperatures are presented for each condition, noticing a decreasing trend as hydrogen presence was increased, since the equivalence ratio was gradually reduced to achieve stabilization. CO and NOx emissions were below 15 ppm for all studied cases. A 2-dimensional numerical model incorporating the GRI-Mech 3.0 mechanism was developed and validated against experimental data.The model revealed that the stabilized flame front is observed as a straight line that runs parallel to the radial coordinate. This line exhibits a slight curvature close to the burner wall, which is caused by heat losses and the influence of the divergent geometry. Solid surface temperature was not constant due to the reduced convective heat exchange with flue gases in the periphery of the burner. To reduce this issue a lower expansion angle is proposed as an alternative. In addition, changes in the chemical kinetics due to H2 addition were also evaluated. As results, a general trend towards reaction shifting was found with a 56% of the reactions being strongly promoted by H2 presence, which is associated with an increase in radical concentration in the flame front due to H2 decomposition.

A multiscale approach in modeling of chemically reactive porous media

Chemical reactions occur in geotechnical, biological and synthetic porous media. Swelling and shrinkage phenomena can be observed in clays, shales and gels, when they are in close contact with water. In petroleum engineering, wellbore-stability problems are caused by swelling or shrinking of the wellbore. Thus, it is significant to model the Chemo-Hydro-Mechanical (CHM) processes in porous media that include different physical and geometrical heterogeneities. In this paper, a multiscale computational homogenization approach is developed for the analysis of CHM problems. In this manner, the first-order homogenization technique is adopted for the two-scale formulation. The heterogeneities are assumed in the microscale level and a homogeneous domain is considered for the macroscale level, where the constitutive behavior is derived from the microscopic level. The governing equations and constitutive equations of the CHM processes are presented in the coupled manner. The primary variables are taken as the displacement, pore pressure, and solute concentration fields. Moreover, the transient terms are included in the microscale level to increase the accuracy of computations. Consequently, a generalized form of Hill-Mandel principle of macro-homogeneity is defined between the two scales. Appropriate microscopic boundary conditions, i.e. the linear and periodic boundary conditions, are employed to satisfy the averaging constraints. Finally, the accuracy and efficiency of the proposed computational multiscale method are illustrated through several numerical examples.

Efficient reforming of methane in a porous radiant reactor with regular structure: A novel experimental system for heat-hydrogen coproduction

As a high-energy clean fuel, hydrogen is one of the most promising energy carriers to achieve “carbon neutrality”. In order to produce hydrogen, a novel porous media heat-hydrogen coproduction system (PHH) with regular structure was built, and ceramic foam was added to improve thermal radiation performance. The effects of porous regular structure on the temperature distribution, products concentration, and thermal radiation efficiency were investigated at different operating conditions. The results indicated that the regular structure achieved higher hydrogen concentration and methane conversion efficiency than the irregular structure, especially at small-diameter pellets. Meanwhile, increasing the pellets diameter and decreasing the ceramic rings size reduced the radiation efficiency, but that improved the hydrogen production. The optimal thermal efficiency (26.5%) and radiation efficiency (33.2%) were obtained in the Ⅰ-type reactor at the equivalence ratio of 1.5. In addition, with the inlet velocity increasing from 10 to 14 cm/s, the combustion temperature and syngas energy conversion efficiency significantly increased. These results provide an essential reference for advancing the practical application of heat-hydrogen coproduction and the design of the regular structure in porous media reactor.

Oscillating reaction in porous media under saddle flow

Pattern formation due to oscillating reactions represents variable natural and engineering systems, but previous studies employed only simple flow conditions such as uniform flow and Poiseuille flow. We studied the oscillating reaction in porous media, where dispersion enhanced the spreading of diffusing components by merging and splitting flow channels. We considered the saddle flow, where the stretching rate is constant everywhere. We generated patterns with the Brusselator system and classified them by instability conditions and Péclet number (Pe), which was defined by the stretching rate. The results showed that each pattern formation was controlled by the stagnation point and stable and unstable manifolds of the flow field due to the heterogeneous flow fields and the resulting heterogeneous dispersion fields. The characteristics of the patterns, such as the position of stationary waves parallel to the unstable manifold and the size of local stationary patterns around the stagnation point, were also controlled by Pe.

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.

Enhanced Mixing and Reaction in Converging Flows: Theory and Pore‐Scale Imaging

AbstractMixing fronts at the interface of opposing flows are compressed at a constant rate. The resulting exponential stretching of fluid elements leads to enhanced chemical gradients and biogeochemical processes. This process is similar as what occurs in the pore space of 3D chaotic flows. However, it is so far not known how such fluid compression controls the amplitude of mixing and reaction rates in porous media. Here we derive analytical predictions for the mixing width, the maximum reaction rate and the reaction intensity in compressed mixing fronts as a function of the Péclet and Damköhler numbers. We developed an experimental setup providing pore scale measurements of mixing and reaction rates in mixing fronts at the interface of converging flows. The theory accurately predicts the scaling of mixing and reaction with the Péclet number both in porous micromodels and simple Hele‐Shaw cells. Additionally, we found that the presence of pore scale heterogeneities in the porous micromodels enhances reaction rates by a factor of 4 compared to the Hele‐Shaw cells. Using numerical simulations of pore scale velocity fields, we attributed this phenomenon to the enhancement of pore‐scale compression due to the presence of grains in accelerating flows. These findings provide new insights into the dynamics of mixing‐induced reactions in porous media.

Upscaled model for the diffusion/heterogeneous reaction in porous media: Boundary layer problem

Multi-species diffusion/heterogeneous reaction coupled problem in porous media involving a boundary layer problem is studied. The spectral approach developed in our previous work allows to derive a macroscopic model in the high Damköhler number regime combining homogenization technique and spectral approach. Such a homogenized model cannot describe the perturbation at the external boundary where the chemical equilibrium is not necessarily satisfied. We construct herein a modified model involving additional variables, which are rapidly-decaying functions, to capture the complex physics in the boundary layer. Numerical simulations underline the accuracy of the proposed correction in both steady and transient states.

Fluid-Solid Reaction in Porous Media as a Chaotic Restart Process.

Chemical and biological reactions at fluid-solid interfaces are central to a broad range of porous material applications and research. Pore-scale solute transport limitations can reduce reaction rates, with marked consequences for a wide spectrum of natural and engineered processes. Recent advances show that chaotic mixing occurs spontaneously in porous media, but its impact on surface reactions is unknown. We show that pore-scale chaotic mixing significantly increases reaction efficiency compared to nonchaotic flows. We find that reaction rates are well described in terms of diffusive first-passage times of reactants to the solid interface subjected to a stochastic restart process resulting from Lagrangian chaos. Under chaotic mixing, the shear layer at no-slip interfaces sets the restart rate and leads to a characteristic scaling of reaction efficiency with Péclet number, in excellent agreement with numerical simulations. Reaction rates are insensitive to the flow topology as long as flow is chaotic, suggesting the relevance of this process to a broad range of porous materials.

Phase-field modeling of thermal cracking in hardening mass concrete

The manuscript is concerned with the phase-field modeling of thermal cracking in massive hardening concrete structures. Owing to the exothermic reactions, known as hydration, a considerable amount of heat is generated during the setting and hardening of concrete. Since concrete has relatively low thermal conductivity and fairly high heat capacity, sharp temperature gradients may occur between the interior and exterior parts of massive concrete structures. This uneven temperature distribution results in a non-uniform thermal expansion that, in turn, may lead to thermal cracking in conjunction with restraining external boundary conditions. Hence, it is of key importance to conduct the crack risk assessment of massive concrete structures at various stages of their construction and thereafter where real-size experiments are often unrealizable. To this end, we develop a multi-field computational approach to simulate thermal cracking in hardening concrete. In particular, we propose a novel chemo-thermo-mechanical model developed within the framework of the theory of reactive porous media coupled with a quasi-brittle phase-field regularized cohesive zone model to explicitly account for the initiation and propagation of thermal cracks. In the model, chemical, thermal, mechanical, and phase-field fracture problems are coupled through the constitutive equations. To our best knowledge, this is the first study where a quasi-brittle phase-field fracture model is used to model thermal cracking in hardening massive concrete through a novel incremental formulation. The potential of the proposed approach is demonstrated through the benchmark thermomechanical problems of a normal concrete member and a roller-compacted concrete dam. In the latter, original multi-field interface elements are devised between the lifts.

A mesoscale model for heterogeneous reactions in porous media applied to reducing porous iron oxide

A mesoscale model based on the lattice gas cellular automata (LGCA) is proposed for heterogeneous reaction in porous media. This model features an entirely discretized reaction system, including discrete space, time, gas phases, and solid particle. To describe gas diffusion at solid nodes and gas–solid heterogeneous reaction on the phase boundary, two local probabilities are proposed, which are verified by the analytical solutions for gas diffusion and gas–solid reaction problems. This model was then applied to the hydrogen reduction of porous Fe3O4. The effects of the porosity, reaction rate constant (kl), and initial H2 concentration on the reduction were analyzed. The results indicate that the reaction rate increased with increasing porosity, kl, and H2 concentration. The solid product Fe was randomly distributed on the framework of Fe3O4 at smaller kl and concentrated around the unreacted Fe3O4 at higher kl, which is consistent with our experimental results.