Complex Pore Geometry Research Articles

Polycaprolactone/β-Tricalcium Phosphate Composite Scaffolds with Advanced Pore Geometries Promote Human Mesenchymal Stromal Cells' Osteogenic Differentiation.

Critical-sized mandibular bone defects, arising from, for example, resections after tumor surgeries, are currently treated with autogenous bone grafts. This treatment is considered very invasive and is associated with limitations such as morbidity and graft resorption. Tissue engineering approaches propose to use 3D scaffolds that combine structural features, biomaterial properties, cells, and biomolecules to create biomimetic constructs. However, mimicking the complex anatomy and composition of the mandible poses a challenge in scaffold design. In our study, we evaluated the dual effect of complex pore geometry and material composition on the osteogenic potential of 3D printed scaffolds. The scaffolds were made of polycaprolactone (PCL) alone (TCP0), or with a high concentration of β-tricalcium phosphate (β-TCP) up to 40% w/w (TCP40), with two complex pore geometries, namely a star- (S) and a diamond-like (D) shape. Scanning electron microscopy and microcomputed tomography images confirmed high fidelity during the printing process. The D-scaffolds displayed higher compressive moduli than the corresponding S-scaffolds. TCP40 scaffolds in simulated body fluid showed deposition of minerals on the surface after 28 days. Subsequently, we assessed the differentiation of seeded bone marrow-derived human mesenchymal stromal cells (hMSCs) over 28 days. The early expression of RUNX2 in the cell nuclei confirmed the commitment toward an osteogenic phenotype. Moreover, alkaline phosphatase (ALP) activity and collagen deposition displayed an increasing trend in the D-scaffolds. Collagen type I was mainly present in the deposited extracellular matrix (ECM), confirming deposition of bone matrix. Finally, Alizarin Red staining showed successful mineralization on all the TCP40 samples, with higher values for the S-shaped scaffolds. Taken together, our study demonstrated that the complex pore architectures of scaffolds comprised TCP40 stimulated osteogenic differentiation and mineralization of hMSCs in vitro. Future research will aim to validate these findings in vivo.

Reply to the Discussion

Gassmann’s equations have been known for several decades and are widely used in geophysics. These equations are treated as exact if all the assumptions used in their derivation are fulfilled. However, a recent theoretical study claimed that Gassmann’s equations contain an error. Shortly after that, a 3D numerical calculation was performed on a simple pore geometry that verifies the validity of Gassmann’s equations. This pore geometry was simpler than those in real rocks but arbitrary. Furthermore, the pore geometry that was used did not contain any special features (among all possible geometries) that were tailored to make it consistent with Gassmann’s equations. In other recent studies, I also performed numerical calculations on several other more complex pore geometries that supported the validity of Gassmann’s equations. To further support the validity of these equations, I provide here one more convergence study using a more realistic geometry of the pore space. Given that there are several studies that rederive Gassmann’s equations using different methods and numerical studies that verify them for different pore geometries, it can be concluded that Gassmann’s equations can be used in geophysics without concern if their assumptions are fulfilled. MATLAB routines to reproduce the presented results are provided.

Effect of Multiscale Cracks on Seismic Wave Propagation in Tight Sandstones

AbstractSeismic wave propagation is affected by wave‐induced local fluid flow between stiff pores and multiscale fractures. To investigate this phenomenon, forced vibration (1–100 Hz) and ultrasonic (106 Hz) measurements are performed on two tight sandstones with complex pore geometry in dry and water‐saturated scenarios. Porosity, permeability, and ultrasonic velocities were also measured at different differential pressures. The results indicate that the nonlinear behavior of these properties is strongly influenced by the presence of cracks, and the correlations between the permeability/ultrasonic velocities and porosity are different. A wave propagation model is then developed in which penny‐shaped cracks are inclusions introduced stepwise into a porous medium to describe the wave anelasticity in a wide frequency band at different pressures. As a result, the model provides good agreement with the measured P‐wave velocity dispersion, and the pore aspect ratio spectrum and crack radii are determined. We then compare the estimated crack radii and pore size distributions from nuclear magnetic resonance spectroscopy. Published data of a tight sandstone and a low porosity sandstone in the frequency range (2–200, 106) and (1–3,000) Hz at different differential pressures are also analyzed to validate the model. The aspect ratios, volume fractions, and radii of pores/cracks are used to describe the measured permeability. The present work can provide new insights into the geophysical properties of reservoir rocks with complex pore geometry.

Using Multiscale Direct Simulation Approach to Understanding Transports Behavior Inside PEM Water Electrolyzer

In this work, numerical modeling techniques were developed to predict oxygen bubble evolution through complex pore geometries to provide information of gas transport pathways inside saturated porous transport layers (PTL). Each PTL undergoes an image processing technique that uses X-ray CT images to generate accurate 3D microstructures. An example of a generated PTL structure is shown in Figure 1.Historically, meshing of the complex geometry was tedious and non-automated. Due to the random particle size across the geometry, a constant base size for meshing resulted in an inadequate mesh for accurate predictions. The Lattice-Boltzmann method is therefore more commonly used because a lattice is easier than a finite volume mesh to generate. Although sufficiently fine lattices adhered to the topology of the physical structure, simulations required a timestep between 1e-8 and 1e-10 seconds, resulting in long computational time.Meshing techniques have improved and can now be applied to complex geometries. Using the finite volume method accompanied with an adaptive mesh and adaptive time scale, provides an accurate representation of the PTL structure and larger timesteps. A volume of fluid (VoF) method was used to model two phase flow, using liquid water and gaseous oxygen, through different PTL structures. Evolution, growth, size, velocity, and surface interaction of oxygen bubbles through microstructures were studied as also shown in Figure 2. Findings from the work will provide better understanding of oxygen evolution through saturated PTLs Figure 1

The critical role of fracture flow on two-phase matrix–fracture transfer mechanisms

We analyze the dynamics of imbibition in a fractured medium using the Direct Numerical Simulation of the Navier–Stokes equations. Pore geometries with homogeneous and heterogeneous pore distributions at the matrix and fracture interface are considered in this study. We evaluate the role of critical factors such as wettability, viscosity ratio, injection rate, and the magnitude of the interfacial tension on the pore-scale dynamic of mass exchange between matrix and fracture for 2D geometries consisting of a complex pore-geometry and a single fracture. Two different regimes are identified during the injection of wetting fluid through the fracture into the domain saturated with a non-wetting fluid: (1) co-operative (co-current) imbibition before the wetting phase breakthrough and, (2) counter-current imbibition follows afterwards. For the studied 2D geometries, the displacement efficiency is higher in the co-operative imbibition, while the counter-current imbibition occurs at a slow pace. Lower injection rates in the fracture are in favor of improving displacement efficiency in the porous matrix. Higher wettability and interfacial tension help the wetting fluid to penetrate further into the matrix and improve the displacement rate for both co-operative and counter-current modes of displacement.

Investigation of pore geometry influence on fluid flow in heterogeneous porous media: A pore-scale study

Brazilian pre-salt reservoirs are renowned for their intricate pore networks and vuggy nature, posing significant challenges in modeling and simulating fluid flow within these carbonate reservoirs. Despite possessing excellent petrophysical properties, such as high porosity and permeability, these reservoirs typically exhibit a notably low recovery factor, sometimes falling below 10%. Previous research has indicated that various enhanced oil recovery (EOR) methods, such as water alternating gas (WAG), can substantially augment the recovery factor in pre-salt reservoirs, resulting in improvements of up to 20%. Nevertheless, the fluid flow mechanism within Brazilian carbonate reservoirs, characterized by complex pore geometry, remains unclear. Our study examines the behavior of fluid flow in a similar heterogeneous porous material, utilizing a plug sample obtained from a vugular segment of a Brazilian stromatolite outcrop, known to share analogies with certain pre-salt reservoirs. We conducted single-phase and multi-phase core flooding experiments, complemented by medical-CT scanning, to generate flow streamlines and evaluate the efficiency of water flooding. Subsequently, micro-CT scanning of the core sample was performed, and two cross-sections from horizontal and vertical plates were constructed. These cross-sections were then employed as geometries in a numerical simulator, enabling us to investigate the impact of pore geometry on fluid flow. Analysis of the pore-scale modeling and experimental data unveiled that the presence of dead-end pores and vugs results in a significant portion of the fluid remaining stagnant within these regions. Consequently, the injected fluid exhibits channeling-like behavior, leading to rapid breakthrough and low areal swept efficiency. Additionally, the numerical simulation results demonstrated that, irrespective of the size of the dead-end regions, the pressure variation within the dead-end vugs and pores is negligible. Despite the stromatolite's favorable petrophysical properties, including relatively high porosity and permeability, as well as the presence of interconnected large vugs, the recovery factor during water flooding remained low due to early breakthrough. These findings align with field data obtained from pre-salt reservoirs, providing an explanation for the observed low recovery factor during water flooding in such reservoirs.

Adaptive mesh refinement in locally conservative level set methods for multiphase fluid displacements in porous media

Multiphase flow in porous media often occurs with the formation and coalescence of fluid ganglia. Accurate predictions of such mechanisms in complex pore geometries require simulation models with local mass conservation and with the option to improve resolution in areas of interest. In this work, we incorporate patch-based, structured adaptive mesh refinement capabilities into a method for local volume conservation that describes the behaviour of disconnected fluid ganglia during level set simulations of capillary-controlled displacement in porous media. We validate the model against analytical solutions for three-phase fluid configurations in idealized pores containing gas, oil, and water, by modelling the intermediate-wet oil layers as separate domains with their volumes preserved. Both the pressures and volumes of disconnected ganglia converge to analytical values with increased refinement levels of the adaptive mesh. Favourable results from strong and weak scaling tests emphasize that the number of patches per processor and the total number of patches are important parameters for efficient parallel simulations with adaptive mesh refinement. Simulations of two-phase imbibition and three-phase gas invasion on segmented 3D images of water-wet sandstone show that adaptive mesh refinement has the highest impact on three-phase displacements, especially concerning the behaviour of the conserved, intermediate-wet phase.

Pore-scale modelling of water sorption in nanopore systems of shale

Water vapor sorption in nanoporous media with complex pore structures, like shale, is not well understood. To address this, a pseudopotential lattice Boltzmann method (LBM) is developed to investigate water sorption behavior. The LBM model incorporates long-range molecular forces using a modified Shan-Chen model based on the Carnahan-Starling equation of state. The simulation results show that the presence of water films in nanopores can create a liquid pressure difference of up to 100 MPa between confined and free states. The adsorption theories based on simple pore shapes are not applicable to nanoporous systems with complex pore geometries. Additionally, when the relative humidity exceeds 1, water vapor condenses inside hydrophobic nanostructures while being attracted by neighboring liquid, leading to cluster formation. In water-wet nanoporous media, capillary condensation occurs progressively from small throats to large pores, and the sorption curves vary smoothly with pressure variation. In mixed-wet nanoporous media, the sorption curves exhibit no hysteresis in the early desorption stage, where the adsorption and desorption processes occur in the region around the hydrophobic particles and are reversible. Overall, this study provides valuable insights into water sorption behavior in nanopore systems of shale and sets the foundation for modelling liquid-vapor distribution in nanoporous media at the pore scale.

Multiscale reconstruction of porous media based on multiple dictionaries learning

Digital modeling of the microstructure is important for studying the physical and transport properties of porous media. Multiscale modeling for porous media can accurately characterize large-pores and fine-pores in a large-FoV (field of view) high-resolution three-dimensional pore structure model. This paper proposes a multiscale reconstruction algorithm based on multiple dictionaries learning, in which edge patterns and fine-pore patterns from homology high-resolution pore structure are introduced into low-resolution pore structure to build a fine multiscale pore structure model. The qualitative and quantitative comparisons of the experimental results show that the results of multiscale reconstruction are similar to the real high-resolution pore structure in terms of complex pore geometry and pore surface morphology. The geometric, topological and permeability properties of multiscale reconstruction results are almost identical to those of the real high-resolution pore structures. The experiments also demonstrate the proposal algorithm is capable of multiscale reconstruction without regard to the size of the input. This work provides an effective method for fine multiscale modeling of porous media.

Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS

In recent years, convolutional neural networks (CNNs) have experienced an increasing interest in their ability to perform a fast approximation of effective hydrodynamic parameters in porous media research and applications. This paper presents a novel methodology for permeability prediction from micro-CT scans of geological rock samples. The training data set for CNNs dedicated to permeability prediction consists of permeability labels that are typically generated by classical lattice Boltzmann methods (LBM) that simulate the flow through the pore space of the segmented image data. We instead perform direct numerical simulation (DNS) by solving the stationary Stokes equation in an efficient and distributed-parallel manner. As such, we circumvent the convergence issues of LBM that frequently are observed on complex pore geometries, and therefore, improve the generality and accuracy of our training data set. Using the DNS-computed permeabilities, a physics-informed CNN (PhyCNN) is trained by additionally providing a tailored characteristic quantity of the pore space. More precisely, by exploiting the connection to flow problems on a graph representation of the pore space, additional information about confined structures is provided to the network in terms of the maximum flow value, which is the key innovative component of our workflow. The robustness of this approach is reflected by very high prediction accuracy, which is observed for a variety of sandstone samples from archetypal rock formations.

Rock physics modelling‐based characterization of deep and tight mixed sedimentary (clastic and carbonate) reservoirs: A case study from North Potwar Basin of Pakistan

AbstractRock physics modelling in deeply buried tight carbonate reservoirs is more challenging than the clastic reservoir because of its complex pore systems. Therefore, modelling complex pore geometries in carbonates reservoir plays an important role in the geophysical measurements to infer pore‐type distribution and their volume fraction, which control the fluid flow properties governed by their complex geological history. This paper presents the use of a robust and practical integrated and iterative seismic petrophysics, and rock physics modelling workflow for the characterization of a deep tight mixed (carbonate and clastic) sedimentary reservoir of a recently discovered oil field located in the Potwar Basin onshore Pakistan. The case study incorporates a careful assessment of well‐log data quality, workflow used for well data conditioning and consequent improvement in data quality, seismic petrophysics and rock physics modelling results. Rock physics diagnostics identified data quality issues and rectified them using appropriate measures to ensure that the rock physics modelling scheme reliably predicts elastic logs honouring different pore types (reference, soft, stiff and cracks) distribution validating from the well observations. Two inclusion‐based rock physics models (Xu and Payne for carbonate and Keys and Xu for clastic) are used to predict rock elastic (P‐sonic, S‐sonic and density) properties responses. Utmost care is exercised to integrate all available data/information, such as Formation Micro‐Imager, mud‐log, testing data and calibrated pore‐type inversion results from well‐log data with the pore geometry revealed by Formation Micro‐Imager and core information. The rock physics modelling provided consistency between elastic and petrophysical properties by calibrating the estimated properties with the measure logs and improved understanding in terms of lithology and fluid separation in the tight carbonate interval. Finally, rock physics‐modelled elastic logs (P‐sonic, S‐sonic and density) are used along with seismic data (partial stacks) and horizons interpretation model to compute pre‐stack synthetic seismograms to calibrate with the preconditioned seismic data. A significant improvement in the well‐to‐seismic calibration is achieved from rock physics modelled logs compared with the original (measured) elastic logs at well location using pre‐stack seismic data, which, further, can help produce reliable reservoir rock properties of interest from the inversion of seismic data.

In-Situ Imaging of CO2 Trapping and Oil Recovery in Three-Phase Systems: Dependence on Pore Geometry and Wettability

SummaryCarbon dioxide (CO2) injection into reservoirs can be combined with enhanced oil recovery. Pore geometry and wettability are critical factors in CO2 trapping and oil recovery. However, their relationship has not been tackled and the influence of wettability is always controversial. To elucidate this intrinsic link, we prepared simple models using glass beads and angular grains, changed wettability by aging, and imaged the three-phase displacement process at high resolution. The results showed that the oil flow occurred through the ways of direct drainage and double imbibition, which is caused by the trapped CO2 under immiscible conditions. More residual CO2 was trapped in the angular grain sample and the water-wet sample, and more residual oil was trapped in the angular grain sample and the oil-wet sample. Under water-wet conditions, CO2 was easier to be trapped as the state of gas-in-oil-in-water or gas-in-water. While under oil-wet conditions, more CO2 was directly surrounded by oil and more small-size residual oil dispersed near the throats. The statistics of the residual clusters showed that the capillary-trapping capacity Ctrap of the angular grain sample was high (12.97% > 8.69%), but the oil recovery R2 was low (89.89% < 93.85%). The altered wettability (water-wet to oil-wet) increased the number of isolated CO2 clusters and the proportion of oil and CO2 in the smaller pores while decreasing the Ctrap (8.93% < 10.34%) and R2 (84.48% < 91.04%). The dissolution trapping and capillary trapping were maximized in the angular grain sample due to the increased surface-to-volume ratio of CO2 clusters and higher capillary force. The effect of wettability on dissolution trapping was slight, but the residual CO2 saturation was higher under water-wet conditions, thus the water-wet media were more conducive to CO2 trapping. We suggested that reservoirs with strong heterogeneity should be selected as CO2 storage sites, and the wettability of oil-wet rocks should be changed by using tertiary oil recovery technology to enhance CO2 storage efficiency and oil recovery. Our study provided direct evidence of the influence of pore geometry and wettability on residual CO2 and oil distribution, and clarified that complex pore geometry and water-wet systems were more conducive to CO2 trapping under immiscible conditions.

Porous Aluminum Oxide for Medical Applications Including Targeted Drug Delivery

A comprehensive review of the current level of research in the development of intelligent hybrid nanosystems based on porous inorganic materials, in particular porous alumina, has been carried out. Porous materials are of great interest for the development of controlled drug delivery platforms due to their high effective surface area and controlled pore size. One of the main determinants of the overall pore drug loading and release profile is pore geometry. Three-dimensional pore structures with complex pore geometries and increasing surface area are promising platform designs for sustained drug release. But there are certain structural and financial difficulties in their manufacture. Porous anodic alumina, which is easily and economically produced by electrochemical anodization, allows complex and reproducible three-dimensional pore geometries to be obtained. The unique physical and chemical properties of porous anodic alumina make this material a promising platform for controlled drug release. Porous anodic alumina has a highly ordered pore distribution, and its well-known electrochemical fabrication methods allow precise control of pore spacing, diameter, length, and pore geometry. The purpose of this work is to analyze the current level of research in the development of intelligent hybrid nanosystems based on porous alumina with different characteristics for use in medicine. The presented works have shown interesting opportunities for the development of intelligent, multifunctional optical devices with a microchip design. The design of implantable biosensors with the ability to monitor biological systems in vivo and in real time is promising for the use of porous anodic alumina immunosensors.

Temperature Effect on Water Adsorption and Desorption Processes in the Mesoporous Metal–Organic Framework MIL-101(Cr)

Mesoporous metal–organic frameworks (MOFs) are potential materials for efficient and reversible water adsorption and desorption processes. However, pore-filling/pore-emptying processes in mesoporous MOFs are complicated due to the complex pore geometry, nonuniform pore surface properties, and polarity of water molecules. In addition, the temperature effects on these processes are still unknown. Here, the temperature effect on the adsorption and desorption processes of water was investigated in a promising mesoporous MOF, namely, MIL-101(Cr). Experimentally measured water adsorption/desorption isotherms show a transition from a one-step to a two-step pore-filling/pore-emptying process with increasing temperature. Theoretical studies revealed that the corresponding mechanism of this transition is related to the relative pressures for the transition between two different stable adsorption states in two different-sized mesopores, the relative pressure at which the inner surface is completely covered with water, and the relative pressure at which condensed water overcomes the energy barrier from the metastable liquid state to the gas state.

Additive manufacturing of ceramic porous structures for acoustical applications

Ceramics offer the unique ability to withstand extreme temperatures and pressures without mechanical degradation-characteristics that make them ideal for acoustic applications in extreme environments. While ceramic forming is now a mature technology, traditional forming methods only allow two-dimensional design freedom, cannot create internal features, and often require expensive dies. Here, we propose the use of additive manufacturing (AM) to fabricate porous structures with complex pore geometries suitable for noise reduction applications. We fabricate cylindrical impedance tube test coupons of various pore geometries using a robocasting method that relies on clay extrusion. The printed green bodies are fired and sintered in an automated kiln to obtain the final ceramic sample. In this paper, we present the preliminary results from our wok on characterizing the relationships between the ceramic AM process parameters and the final ceramic part quality and dimensional accuracy. Finally, we investigate the acoustic absorption characteristics of the printed coupons using the normal incidence two microphone impedance tube method. Our results show that ceramics AM provides an attractive route to fabricate complex acoustic structures suitable for high temperature environments.

An accurate analytical model for squirt flow in anisotropic porous rocks — Part 1: Classical geometry

Seismic wave propagation in porous rocks that are saturated with a liquid exhibits significant dispersion and attenuation due to fluid flow at the pore scale, so-called squirt flow. This phenomenon takes place in compliant flat pores such as microcracks and grain contacts that are connected to stiffer isometric pores. Accurate quantitative description is crucial for inverting rock and fluid properties from seismic attributes such as attenuation. Up to now, many analytical models for squirt flow were proposed based on simplified geometries of the pore space. These models were either not compared with a numerical solution or showed poor accuracy. We have developed a new analytical model for squirt flow, which is validated against a 3D numerical solution for a simple pore geometry that has been classically used to explain squirt flow; that is why we refer to it as classical geometry. The pore space is represented by a flat cylindrical (penny-shaped) pore whose curved edge is fully connected to a toroidal (stiff) pore. Compared with correct numerical solutions, our analytical model provides very accurate predictions for the attenuation and dispersion across the whole frequency range. This includes correct low- and high-frequency limits of the stiffness modulus, the characteristic frequency, and the shape of the dispersion and attenuation curves. In a companion paper (part 2), we extend our analytical model to more complex pore geometries. We provide as supplemental information MATLAB and symbolic Maple routines to reproduce our main results.

Synchrotron 4D X-Ray Imaging Reveals Strain Localization at the Onset of System-Size Failure in Porous Reservoir Rocks

Understanding the mechanisms of strain localization leading to brittle failure in reservoir rocks can shed light on geomechanical processes such as porosity and permeability evolution during rock deformation, induced seismicity, fracturing, and subsidence in geological reservoirs. We perform triaxial compression tests on three types of porous reservoir rocks to reveal the local deformation mechanisms that control system-size failure. We deformed cylindrical samples of Adamswiller sandstone (23% porosity), Bentheim sandstone (23% porosity), and Anstrude limestone (20% porosity), using an X-ray transparent triaxial deformation apparatus. This apparatus enables the acquisition of three-dimensional synchrotron X-ray images, under in situ stress conditions. Analysis of the tomograms provide 3D distributions of the microfractures and dilatant pores from which we calculated the evolving macroporosity. Digital volume correlation analysis reveals the dominant strain localization mechanisms by providing the incremental strain components of pairs of tomograms. In the three rock types, damage localized as a single shear band or by the formation of conjugate bands at failure. The porosity evolution closely matches the evolution of the incremental strain components of dilation, contraction, and shear. With increasing confinement, the dominant strain in the sandstones shifts from dilative strain (Bentheim sandstone) to contractive strain (Adamswiller sandstone). Our study also links the formation of compactive shear bands with porosity variations in Anstrude limestone, which is characterized by a complex pore geometry. Scanning electron microscopy images indicate that the microscale mechanisms guiding strain localization are pore collapse and grain crushing in sandstones, and pore collapse, pore-emanated fractures and cataclasis in limestones. Our dynamic X-ray microtomography data brings unique insights on the correlation between the evolutions of rock microstructure, porosity evolution, and macroscopic strain during the approach to brittle failure in reservoir rocks.

Pore-Size Measurement from Eigenvalues of Magnetic Resonance Relaxation

Nonground eigenvalues are widely disregarded in magnetic resonance relaxation measurements of porous media due to difficulties involved in their measurement, detection, and the derivation of physically meaningful parameters from them. Such nonground eigenvalues may be experimentally observed in relaxation measurements, such as the relaxation correlation of ${T}_{1}\ensuremath{-}{T}_{2}$, and yield information on the pore size and surface relaxivity of porous media without calibration through other independent measurements. Nonground eigenvalue analysis of ${T}_{1}\ensuremath{-}{T}_{2}$ measurements on Berea sandstone undertaken at three static magnetic fields produces pore sizes consistent with those obtained through x-ray microtomography and SEM measurements. Similar agreement is found for a Bentheimer sandstone with a more complex pore geometry. A phase-encoding imaging variant of this method measures the imbibition confinement-size profile in Berea sandstone. It is suggested that the existence of nonground eigenmodes may be much more prevalent in simple magnetic resonance relaxation measurements than previously considered. Therefore, it is possible to measure pore size by matching numerical Brownstein-Tarr solutions with those of experiments in a wide variety of samples and magnetic resonance methods.

GeoChemFoam: Direct Modelling of Multiphase Reactive Transport in Real Pore Geometries with Equilibrium Reactions

GeoChemFoam is an open-source OpenFOAM-based toolbox that includes a range of additional packages that solve various flow processes from multiphase transport with interface transfer, to single-phase flow in multiscale porous media, to reactive transport with mineral dissolution. In this paper, we present a novel multiphase reactive transport solver for simulations on complex pore geometries, including microfluidic devices and micro-CT images, and its implementation in GeoChemFoam. The geochemical model includes bulk and surface equilibrium reactions. Multiphase flow is solved using the Volume-Of-Fluid method, and the transport of species is solved using the continuous species transfer method. The reactive transport equations are solved using a sequential operator splitting method, with the transport step solved using GeoChemFoam, and the reaction step solved using Phreeqc, the US geological survey’s geochemical software. The model and its implementation are validated by comparison with analytical solutions in 1D and 2D geometries. We then simulate multiphase reactive transport in two test pore geometries: a 3D pore cavity and a 3D micro-CT image of Bentheimer sandstone. In each case, we show the pore-scale simulation results can be used to develop upscaled models that are significantly more accurate than standard macro-scale equilibrium models.

Ternary segmentation and estimation of permeability for porous rocks based on 3D X-ray computed tomographic images by hidden Markov random field and Brinkman-force lattice Boltzmann model

Three-dimensional X-ray computed tomographic (CT) images of specimens often serve as a flow simulation domain for numerical analysis, particularly for permeability estimation, but there exists uncertainty in classifying image pixels into pore or solid structures due to the complex pore geometry and limited resolution of X-ray CT image. This limitation has been tackled by ternary segmentation of CT images into resolved pore, unresolved pore, and solid phases, but it is still challenging to segment each phase and estimate local permeability of unresolved pore. This study proposed the estimation of the hydraulic diameter of each unresolved pore voxel in CT images to evaluate the local permeability by a general porosity–permeability model. Hidden Markov random field (HMRF) was implemented to achieve reliable ternary segmentation of porous rock images with different resolutions by considering the statistical and spatial distribution of CT numbers. Brinkman-force lattice Boltzmann method (BF-LBM) was then used to compute permeability. The results showed that the estimated permeability of Berea sandstone and limestone was analogous to experimentally measured values. The proposed procedure, which does not require experimental characterization of the pore size distribution, can be used to nondestructively estimate the permeability of porous rocks using X-ray CT images while being less sensitive to image resolution.