Reactive Porous Media Research Articles

Effective thermal conductivity in granular media with devolatilization: the Lattice Boltzmann modelling

Flow thermomechanics in reactive porous media is of importance in industry including the thermal processing of fossil fuel (coking understood as a slow pyrolysis) involving devolatilisation. On the way to provide a detailed description of the process, a multi-scale approach was chosen to estimate effective transport coefficients. For this case the Lattice Boltzmann method (LBM) was used due to its advantages to accurately model multi-physics and chemistry in a random geometry of granular media. After account for earlier studies, the paper presents description of the model with improved boundary conditions and a benchmark case. Results from meso-scale LBM calculations are presented and discussed regarding the spatial resolution and the choice of relaxation parameter along its influence on the accuracy compared with empirical formulae. Regarding the estimation of effective thermal conductivity coefficient it is shown that occurrence of devolatilization has a crucial effect by reducing heat transfer. Some quantitative results characterise the propagation of thermal front; also presented is the evolution of effective thermal conductivity. The work is a step forward towards a physically sound simulation of thermal processing of fossil fuel.

A method for measuring fluid pressure and solid deformation profiles in uniaxial porous media flows.

Flow through rigid, reactive, or deformable porous media has relevance to the dynamical behavior studied across a broad range of problems in science and engineering. Here, we describe an apparatus designed to simultaneously measure the pervadic pressure profile, fluid volume flux, and deformation in an evolving poroelastic medium. We demonstrate the apparatus in measurements of flow-induced compression of a soft latex foam. The approach can be used in both rigid and reactive porous media.

Understanding pressure changes in smouldering thermal porous media reactors

The use of thermal porous media reactors for environmental applications is growing rapidly. Understanding the pressures increases inherent in such systems is central to their success. Numerical modelling of thermal processes in porous media, supported by experiments, quantifies and explains the pressure increases occurring during gas injection into smouldering treatment systems. Air flux and pressure gradient are revealed to be linked by the pneumatic conductivity of the porous bed at two scales. Locally, air density, viscosity, and velocity are coupled to temperature. However, the air pressure gradient increases globally due to a global reduction in pneumatic conductivity. Finally, a new, simple method to estimate the maximum bed pressure drop for thermal porous media reactors is presented. Overall, this work provides the first quantitative analysis of these local and global phenomena in such systems and provides a simple design tool for engineers.

Design, testing, and implementation of a real-time system for monitoring flow in horizontal wells

The Horizontal Reactive Media Treatment Well (HRX Well®) is a technology capable of collecting and treating groundwater passively. To monitor the internal flow rate, ensuring it remains at an acceptable level and maintains the desired capture zone size in the aquifer, Point Velocity Probes (PVPs) were adapted for the task. The modified PVP was assessed for its performance in a mock-HRX Well setting, which consisted of a laboratory sand column, similar in diameter to the HRX Well cartridges that would house the PVP in the field, with flow directed along the longitudinal axis of the probe. Experiments were conducted to assess 1) the effects of friction between the fluid and the probe surface, which could bias a velocity measurement low, and 2) the effect of gas in the porous medium, potentially generated by some reactive media, on PVP signals and measurements of velocity. It was determined that PVP length exerted no discernable effect on the quality of the PVP performance. However, the effects of gas in the porous medium were varied. Compared to velocity estimates assuming a fully saturated porous medium, the bias to velocity measurements was negative if gas was limited to locations near a PVP's injection-detection array, such as might occur by inadvertent bubble injection during the tracer pulses. The bias was positive if the gas was generated uniformly throughout the porous medium, such as might occur in a reactive porous medium like granular iron, or one featuring vigorous biological activity. A field trial of the HRX Well was subsequently undertaken with internal PVPs. The PVPs identified a missing seal that was later retrofit, and documented flow in the HRX Well at velocities in the range of 1.3 to 4.0 m/d, which compared well with expectations based on a site model that predicted velocities of 1.3 to 2.3 m/d. The results of this study demonstrate that HRX Wells perform hydraulically as designed, and that PVPs are effective devices for tracking flow rates within them in near real-time.

The impact of mineral reactive surface area variation on simulated mineral reactions and reaction rates

Reactive transport modeling is an essential tool to simulate complex geochemical reactions in porous media that can impact formation properties including porosity and permeability. However, simulating these reactions is challenging due to uncertainties in model parameters, particularly mineral surface areas. Imaging has emerged as a powerful means of estimating model parameters including porosity and mineral abundance, accessibility and accessible surface area. However, these parameters, particularly mineral accessible surface area, vary with image resolution. This work aims to enhance understanding of the impact of image resolution and other means of estimating mineral reactive surface area on simulated mineral reactions and reaction rates. Mineral surface areas calculated from images with resolutions of 0.34 μm and 5.71 μm were used to simulate mineral reactions in the context of geologic CO2 sequestration in the Paluxy formation at the continuum scale. Additional simulations were carried out using BET surface areas collected from the literature and geometric surface areas. Simulations were run for 7300 days and mineral volume fractions and effluent ion concentrations tracked and compared. Variations in mineral surface areas measured from images are within 1 order of magnitude and yield similar simulation results, indicating the impact of image resolution on simulated reactions and reaction rates is minimum for the resolutions and sample considered. In comparison, surface areas obtained from BET and geometric approaches are 1–4 orders of magnitude higher than image-obtained surface areas and result in greater simulated reaction rates and extents. Minerals with high reaction rates (calcite and siderite) are most impacted by surface area values at short times where simulated mineral volume fractions at longer times agree relatively well, even for simulations with several orders of magnitude variation in surface area. Phases with lower reaction rates, such as K-feldspar and muscovite, are predominantly impacted over longer times where variations in surface areas impact reaction extents and porosity evolution. Overall, variations in surface areas due to image resolution are small and result in little variation in simulated reactions and reaction rates while there are significant variations in simulation results when other surface area estimates are used. These variations, however, depend on the reactivity of the mineral phase where surface areas of fast-reacting phases largely impact simulations at short (hours to days) timescales and surface areas of slower-reactive phases impact longer term simulations (years).

Multispecies Reactive Transport in a Microporous Rock: Impact of Flow Heterogeneity and Reversibility of Reaction

AbstractWe study the impact of pore space heterogeneity on mixing and reaction in porous media. We simulate the parallel injection of two streams of reactants at different pH in a three‐dimensional microporous consolidated rock whose pore space was resolved by differential micro‐CT imaging. As an exemplar of a heterogeneous medium, we consider the pore structure obtained from a Portland carbonate sample. We use direct numerical simulation to study the coupled impact of flow heterogeneity, characterized by a wide distribution of velocities and chemical reversibility on multispecies reaction. The flow field is found from the Darcy‐Brinkman equation while the advection‐diffusion equation describes transport, which is coupled to a general multispecies geochemical solver for homogeneous reactions; precipitation, and dissolution are ignored. We observe a highly nonuniform spatial distribution of concentration and rates of formation and consumption. For advection‐dominated transport, the heterogeneous flow field leads to significant transverse mixing in macropores at early times, followed by a slower mixing driven by diffusion between macropore and micropore regions. The effective rates of formation and consumption are species‐dependent and distinct in macroporosity and microporosity: while some species reach an asymptotic rate in well‐mixed regions, others still show a transient nonmonotonic behavior as a consequence of incomplete mixing. Our findings have important implications for the understanding of time‐ and space‐dependent reaction rate behavior: the coupled impact of pore space heterogeneity and reversible reactions need to be taken into account as key determinants to describe multispecies reactive transport.

Effect of magnetic field on stability in mushy layer during binary alloy solidification

During directional solidification of binary alloy mixtures, instability in the solid/liquid interface appears due to constitutional undercooling. As a result of this instability, a reactive porous medium, namely mushy layer, is formed, and it separates the liquid phase from the solid phase completely. The intrinsic structure of the mushy layer is of fine-scale dendritic crystal that shelters solute in the interstitial fluid. In a gravitational field, the rejection of lighter solute components from an advancing solidification front brings about unstable density gradient. Ensuing convective motions in the mush are driven by a density difference. The convection can change the solid matrix of the mushy layer. Hence, the dynamic response of the mushy layer is driven by interaction among heat transfer, solute transport and convection. As a contactless control tool, external magnetic field can change the heat and solute transport, which has a significant effect on the phase change process. Therefore, when magnetic field, thermal diffusion, solute transport and buoyancy convection are considered simultaneously in the phase transformation process, the mechanism of mushy region will become more complex and interesting. In this paper, the effect of external magnetic field on the stability of mushy layer during binary alloy solidification is studied. The coupling effects of magnetic field, temperature field, concentration field and convection are considered in the model. Including the direct mode and the oscillation mode, the resulting dispersion relation reveals the influence of magnetic field on the stability of mushy layer through linear stability analysis. It is found that the Lorentz force can reduce the instability effect which is caused by buoyancy convection. In the oscillation mode, an external magnetic field brings about a stabilizing effect on the mushy layer, but in the direct mode, the effect of external magnetic field on stability of the mushy layer is uncertain. In conclusion, the finding in this paper provides an important theoretical reference for improving products quality by applying an external magnetic field in the metals processing industry.

Improvement of remeshed Lagrangian methods for the simulation of dissolution processes at pore-scale

This article shows how to consistently and accurately manage the Lagrangian formulation of chemical reaction equations coupled with the superficial velocity formalism introduced in the late 80s by Quintard and Whitaker. Lagrangian methods prove very helpful in problems in which transport effects are strong or dominant, but they need to be periodically put back in a regular lattice, a process called remeshing. In the context of digital rock physics, we need to ensure positive concentrations and regularity to accurately handle stagnation point neighborhoods. These two conditions lead to the use of kernels resulting in extra-diffusion, which can be prohibitively high when the diffusion coefficient is small. This is the case especially for reactive porous media, and the phenomenon is reinforced in porous rock matrices due to Archie’s law. This article shows how to overcome this difficulty in the context of a two-scale porosity model applied in the Darcy-Brinkman-Stokes equations, and how to obtain simultaneous sign preservation, regularity and accurate diffusion, and apply it to dissolution processes at the pore scale of actual rocks.

Explaining persistent incomplete mixing in multicomponent reactive transport with Eulerian stochastic model

We present an Eulerian stochastic advection–diffusion–reaction (SADR) model and use it to explain incomplete mixing typically observed in transport experiments with bimolecular reactions. Unlike traditional advection–dispersion–reaction (ADR) models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, mechanical mixing is driven by random advective velocity whose variance is given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion process with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficient, but only the effective diffusion coefficient contributes to the mixing-controlled reactions. We use experimental results of Gramling et al. ** to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the ADR model, which overestimates the concentration of the reaction product by as much as 60%. We also show that the SADR model predicts an experimentally observed bell-shaped spatial distribution of the reactive product concentration, while the ADR model results in a concentration distribution with an unphysical kink.

Transport of produced water through reactive porous media

During hydraulic fracturing (or fracking) large volumes of wastewater (flow-back and produced water) are generated, which are naturally rich in heavy metals and radionuclides, such as radium. Spills may occur during operations and contaminate the groundwater. Therefore, there is an urgent need to identify a practice that can mitigate the negative impact of accidental leaks on water resources. Here, we present an experimental and modeling work on the transport of alkaline earth elements in produced water, which are congeners of radium, namely, barium (Ba2+), strontium (Sr2+), calcium (Ca2+), and magnesium (Mg2+) in addition to sodium (Na+). Column-flood tests were conducted using produced water from a shale-gas site and reactive porous media made of ubiquitous minerals such as sand, hydrous ferric oxide, activated alumina, and manganese oxide. In all cases, no retardation of the ions was observed at the salinity conditions of the produced water, but strong retardation in the pH front was measured, indicating that adsorption indeed occurred. When using manganese oxide and upon dilution of produced water, the concentration fronts of all major divalent cations were retarded. However, a fast wave of solute, traveling at the average flow velocity, emerged. This phenomenon confirmed that significant adsorption occurred under those conditions. But, pH-dependent adsorption and hydrodynamic dispersion favored fast solute transport.Overall, these results suggest that manganese oxide could be used as a reactive material in the lining of temporary storage tanks and in the well cases in order to retard the migration of the major toxic elements in produced water. However, mixing must be controlled to avoid the emergence of an instability at the concentration fronts favoring the formation of fast waves.

Mathematical modelling of the agglomeration in a reactive porous medium with variable permeability

When processing low-grade fuels, such as waste and biomass, the problems associated with bed agglomeration often arise. In this work, one of the variants of the agglomeration model is proposed, in which local permeability decreases as a result of the physicochemical process caused by heating, and the agglomeration centers (particles of the melting material) are randomly distributed in a two-dimensional porous medium. A relatively simple model allows the study of the development of thermohydrodynamic inhomogeneities in the fixed granular bed and evaluation of its hydraulic resistance at different fractions of melting material.

Performance of a novel single-tubular ammonia-based reactor driven by concentrated solar power

Because of high concentrating ratios of Concentrated Solar Power Technologies (CSP), and maturity of industrial ammonia synthesis process, the high-temperature ammonia thermochemical energy storage based on CSP technology has a promising potential. As a prototype of a tubular ammonia reactor under un-uniform heat flux originating from a sunlight spot or line focusing, it is assumed that catalyst particles packed in it is isotropic, and the heat transfer and mass diffusion in the axial direction of the tube were ignored since the length-diameter aspect ratio of the tube is high. Consequently, employing the local thermal non-equilibrium method, a 3-dimensional model for an ammonia decomposition reaction in porous media was developed with semi-perimeter un-uniform heat flux. For further research, the diameter of catalyst particles, the porosity of packed particles and inflow modes were recognized as important factors. The results show that the particular axial or radial distributions of the porosity significantly affect the reaction characteristics. Especially, the distribution of radial linear reduction of porosity increases the ammonia conversion rate and reduced maximum wall temperature. At the same time, the smaller catalyst particles and the inflow mode of one-side in and one-side out all contribute to improving the performance of the tubular reactor. In general, the following measures can effectively improve the reactor performance: choose a smaller catalyst particle diameter, the porosity of catalyst particles packed decreases linearly along the radial direction from the center of the tube, and the inflow mode in the tube is one-side in and one-side out.

Macroscopic models for filtration and heterogeneous reactions in porous media

Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible (Valdés-Parada et al., 2011; Battiato and Tartakovsky, 2011a) due to the strong coupling between scales that characterise such systems. In this work, we show how the upscaling can be carried out by applying and extending the methods presented in Allaire and Raphael (2007), Mauri (1991). The approach relies on the decomposition of the microscale concentration into a reactive component, given by the eigenfunction of the advection-diffusion operator, the associated eigenvalue which represents the macroscopic effective reaction rate, and a non-reactive component. The latter can be then upscaled with a two-scale asymptotic expansion and the final macroscopic equation is obtained for the leading order. The same method can also be used to overcome another classical assumption, namely of non solenoidal velocity fields, such as the case of deposition of charged colloidal particles driven by electrostatic potential forces. The whole upscaling procedure, which consists in solving three cell problems, is implemented for arbitrarily complex two- and three-dimensional periodic structures using the open-source finite volume library OpenFOAM®. We provide details on the implementation and test the methodology for two-dimensional periodic arrays of spheres, and we compare the results against fully resolved numerical simulations, demonstrating the accuracy and generality of the upscaling approach. The effective velocity, dispersion and reaction coefficients are obtained for a wide range of Péclet and surface Damköhler numbers, and for Coulomb-like forces to the grains. Noticeably, all the effective transport parameters are significantly different from the non-reactive (conserved scalar) case, as the heterogeneity introduced by the reaction strongly affects the micro-scale profiles.

Fused Filament Fabrication 3‐D Printing of Reactive Porous Media

AbstractUnderstanding the impacts of porous media properties on geochemical reactions is challenging due to the highly heterogeneous nature of natural samples. This work explores the use of 3‐D printing to create synthetic rock samples with reactive properties mimicking those of natural samples. Here, X‐ray Computed Tomography and 3‐D printing were used to recreate the pore network structure and reactive properties of a Paluxy sandstone. Novel, reactive filaments for 3‐D printing synthetic rock samples were constructed from mixtures of high impact polystyrene and calcite. The distribution and accessible calcite surface area of printed samples were evaluated and compared to values for the real rock sample. Only a small fraction of the total calcite was on the surface of the printed sample, but the accessible calcite surface area was comparable to real samples such that 3‐D printing may be a feasible means of fabricating reactive porous media samples.

Heat transfer analysis of solar-driven high-temperature thermochemical reactor using NiFe-Aluminate RPCs

Converting solar energy efficiently into hydrogen is a promising way for renewable fuels technology. However, high-temperature heat transfer enhancement of solar thermochemical process is still a pertinent challenge for solar energy conversion into fuels. In this paper, high-temperature heat transfer enhancement accounting for radiation, conduction, and convection heat transfer in porous-medium reactor filled with application in hydrogen generation has been investigated. NiFe-Aluminate porous media is synthesized and used as solar radiant absorber and redox material. Experiments combined with numerical models are performed for analyzing thermal characteristics and chemical changes in solar receiver. The reacting medium is most heated by radiation heat transfer and higher temperature distribution is observed in the region exposed to high radiation heat flux. Heat distribution, O2 and H2 yield in the reacting medium are facilitated by convective reactive gas moving through the medium's pores. The temperature gradient caused by thermal transition at fluid-solid interface could be more decreased as much as the reaction chamber can store the transferred high-temperature heat flux. However, thermal losses due to radiation flux lost at the quartz glass are obviously inevitable.

Experimental studies of CO2-brine-rock interaction effects on permeability alteration during CO2-EOR

Carbon dioxide (CO2) sequestration through CO2 enhanced oil recovery (EOR) in oil reservoirs is one way to reduce this gas in the atmosphere. Undesirable chemical reactions that occur during these operations can affect the reservoir structure and characteristics. In this study, the effect of CO2-water-rock interaction on the rock permeability alteration and final oil recovery has been evaluated experimentally during CO2 injection into a carbonate rock. The effect of flow rate, displacement type and pressure were investigated during CO2 EOR injection. Different scenarios of miscible/immiscible displacement, secondary/tertiary recovery has been evaluated for different levels of connate water salinity and injection rate. The results show that the severity of damage is directly related to the injection rate, however change in displacement type from miscible to immiscible reduce the intensity of chemical reactions in porous medium. Moreover, in the tertiary CO2 injection, the chemical reactions become more severe due to the higher water saturations. Interestingly, this growth in the level of chemical reactions has a negligible impact on permeability reduction, since the major volume of possible reactions occurs in coarse and high permeable pores. Results reveal that damage is more intense in the case of more saline water.

Syngas Production From the Reforming of Typical Biogas Compositions in an Inert Porous Media Reactor.

Syngas production by inert porous media combustion of rich biogas–air mixtures was studied experimentally, focusing on carbon dioxide utilization and process efficiency. Different gas mixtures of natural gas and carbon dioxide, which simulated a typical biogas composition of 100:0, 70:30, 55:45, and 40:60 (CH4:CO2), were comparatively analyzed considering combustion waves temperatures and velocities, and chemical concentrations products, at high equivalence ratios of φ = 1.5 and φ = 2.0. Different CO2 concentrations on biogas composition showed higher H2 productions than on pure methane (100:0), mainly due to CO2 reforming reactions. Also, syngas production, hydrogen yields, and process efficiency by means of biogas filtration combustion were higher than under methane filtration combustion. Results of the thermochemical conversion of biogas show an alternative and promising non-catalytic technique to CO2 utilization.

Upscaling diffusion–reaction in porous media

In this work, we present the outlines of the periodic homogenization of the diffusion equation with chemical reaction at the interface, for different orders of magnitude of the Damkohler number. For large values of the Damkohler number, a non-classical homogenized model is obtained, where the homogenized diffusion tensor is strongly coupled with the chemical reaction rate. This homogenized model is particularly well adapted to describe, at the macroscopic level, diffusion with strong chemical reactions at the pore interfaces. The aim of this article is to highlight the transition between different regimes of diffusion–reaction according to the order of magnitude of the Damkohler number. In the last part of this work, we first consider a simple analytical example between two parallel plates, to understand the transition between the different possible regimes of diffusion–reaction. Finally, numerical simulations are performed on more complex two-dimensional elementary cells.

Permeability measurements using oscillatory flows

We describe a versatile apparatus for measuring the permeability of porous materials using oscillatory flows. The permeabilities are measured by an original spectral analysis of the pressure and fluid-displacement signals. The measurements are shown to be in very good agreement with classical drainage experiments performed on the same device. Our apparatus and methodology will be useful if small fluid displacements are required, for example in reactive porous media.

Microfluidic flow-through reactor and 3D Raman imaging for in situ assessment of mineral reactivity in porous and fractured porous media.

An in-depth understanding of dissolution and precipitation of minerals in porous and fractured porous media and the complex feedback on the transport of fluids is essential for various subsurface applications. In this context, we developed a novel non-destructive "lab-on-chip" approach for quantitative in situ assessments of mineralogical changes in porous media. Our experimental approach involves a microfluidic flow-through reactor of reactive homogeneous and heterogeneous (fractured) porous media coupled with high-resolution imaging. Here, the reactive medium consists of compacted celestine grains seeded in a reservoir within the microfluidic chip. This medium reacts with a barium chloride solution injected into the microreactor at a constant flow rate, leading to the dissolution of celestine and growth of barite. Various seeding processes of the mineral grains allow the creation of homogeneous reactive porous media or the introduction of large heterogeneities such as fractures. Hence, our approach enables high-resolution investigations of reactive transport in fractured porous media. The use of confocal Raman spectroscopic techniques enables the spatio-temporal visualization of the mineral transformation at the pore-scale in two- and three-dimensions. Moreover, advanced pore-scale modelling correlates the hydrological heterogeneities to the geochemical observations in the micro-reactor, which explains the observed discrepancies between homogeneous and heterogeneous reactive media. Eventually, the proposed methodology can be applied to other chemical systems to provide new insights into hydro-geochemical coupling in porous and fractured porous media as well as high-fidelity datasets to benchmark reactive transport codes that are currently under development.