Pore Space Geometry Research Articles

Specific surface area versus porosity from digital images: High-porosity granular samples

We micro-CT-scanned several granular packs, including glass beads of two different particle sizes and their mixtures, a natural dune sand, as well as two sieved samples of this sand and their mixtures. After segmenting these digital volumes into grains and pores, we computed their porosity (φ) and specific surface area (S). Moreover, we subsampled these segmented volumes and computed the respective φ and S of the subvolumes as well. The resulting data pairs exhibited fairly tight S versus φ trends. These trends, as observed among different samples, present a somewhat inconsistent picture. In some granular digital samples, S increases with increasing φ, while in others the opposite behavior is observed. To explain these behaviors, we analytically model the evolution of the pore-space geometry as that of a binary mixture of large and small particles. Where the small particles gradually fill the pores of an undisturbed large-particle frame, S becomes larger as φ reduces. The opposite behavior takes place where the disparate large particles are embedded into the continuum of the small particles. The smaller the number of the large particles the higher the porosity and the larger the specific surface area. Where the particles in a pack are of uniform size, S reduces with increasing φ. This theory quantitatively supports the observed experimental relations. The observed consistency between the experiment and theory means that the behaviors observed on microscopic samples are applicable at a much larger spatial scale.

Effects of Gas Trapping on Foam Mobility in a Model Fracture

In enhanced oil recovery, foam can effectively mitigate conformance problems and maintain a stable displacement front, by trapping gas and reducing its relative permeability in situ. In this study, to understand gas trapping in fractures and how it affects foam behavior, we report foam experiments in a 1-m-long glass model fracture with a hydraulic aperture of 80 upmu m. One wall of the fracture is rough, and the other is smooth. Between the two is a 2D porous medium representing the aperture in a fracture. The fracture model allows direct visualization of foam inside the fracture using a high-speed camera. This study is part of a continuing program to determine how foam behaves as a function of the geometry of the fracture pore space (AlQuaimi and Rossen in Energy & Fuels 33: 68-80, 2018a). We find that local equilibrium of foam (where the rate of bubble generation equals that of bubble destruction) has been achieved within the 1-m model fracture. Foam texture becomes finer, and less gas is trapped as interstitial velocity, and pressure gradient increase. Shear-thinning rheology of foam has also been observed. The fraction of trapped gas is significantly lower in our model (less than 7%) than in 3D geological pore networks. At the extreme, when velocity increases to 7 mm/s, there is no gas trapped inside the fracture. Our experimental results of trapped-gas fraction correlate well with the correlation of AlQuaimi and Rossen (SPE J 23: 788-802, 2018b) for fracture-like porous media. This suggests that the correlation can also be applied to gas trapping in fractures with other geometries.Article HighlightsWe have made a lab-scale 1-meter-long transparent glass model representing a geological fracture with roughened surface, and we have implemented a direct method of image analysis to quantify the texture of bubbles in the fracture and to link the texture with the strength of the foam;We have successfully created surfactant-stabilized foam flow inside the fracture and examined its stability along the 1-meter-long fracture;We explain the mechanism of gas trapping in fractures and how it affects foam behavior. We also discuss how viscous force and capillary force affect gas trapping in fractures at our experimental conditions.Graphic

Averaged Boltzmann’s Kinetics for Colloidal Transport in Porous Media

AbstractDue to the stochastic nature of pore space geometry, particle velocities in a colloidal‐suspension flux are also stochastically distributed. This phenomenon is captured by Boltzmann's kinetic equation. We formulate a BGK‐form of Boltzmann's equation for particulate flow with a particle capture rate proportional to the particle speed and derive an exact method for the model's averaging. The averaged equation is of the form of a reaction‐advection‐diffusion equation with the average particle speed lower than the carrier fluid velocity. This delay, reported in numerous laboratory studies, is explained by preferential capture of fast particles. The large‐scale model coefficients of delay, dispersion, and filtration are explicitly expressed via the microscale mixing length, equilibrium velocity distribution, and filtration coefficient. The properties of the averaged coefficients are discussed, and emerging dependencies between them are presented. The derived large‐scale equation resolves two paradoxes of the traditional model for suspension‐colloidal transport in porous media. The large‐scale equation closely matches the laboratory breakthrough curves.

A Monte Carlo Model of Gas-Liquid-Hydrate Three-phase Coexistence Constrained by Pore Geometry in Marine Sediments

Gas hydrates form at relatively high pressures in near-surface, organic-rich marine sediments, with the base of the hydrate stability field and the onset of partial gas saturation determined by temperature increases with depth. Because of pore-scale curvature and wetting effects, the transition between gas hydrate and free gas occurrence need not take place at a distinct depth or temperature boundary, but instead can be characterized by a zone of finite thickness in which methane gas bubbles and hydrate crystals coexist with the same aqueous solution. Previous treatments have idealized pores as spheres or cylinders, but real pores between sediment grains have irregular, largely convex walls that enable the highly curved surfaces of gas bubbles and/or hydrate crystals within a given pore to change with varying conditions. In partially hydrate-saturated sediments, for example, the gas–liquid surface energy perturbs the onset of gas–liquid equilibrium by an amount proportional to bubble-surface curvature, causing a commensurate change to the equilibrium methane solubility in the liquid phase. This solubility is also constrained by the curvature of coexisting hydrate crystals and hence the volume occupied by the hydrate phase. As a result, the thickness of the three-phase zone depends not only on the pore space geometry, but also on the saturation levels of the hydrate and gaseous phases. We evaluate local geometrical constraints in a synthetic 3D packing of spherical particles resembling real granular sediments, relate the changes in the relative proportions of the phases to the three-phase equilibrium conditions, and demonstrate how the boundaries of the three-phase zone at the base of the hydrate stability field are displaced as a function of pore size, while varying with saturation level. The predicted thickness of the three-phase zone varies from tens to hundreds of meters, is inversely dependent on host sediment grain size, and increases dramatically when pores near complete saturation with hydrate and gas, requiring that interfacial curvatures become large.

Pore-scale compositional modeling of gas-condensate flow: Effects of interfacial tension and flow velocity on relative permeability

Liquid dropout and retention in gas-condensate reservoirs, specially in the near wellbore region, obstruct gas flowing paths and impact negatively the produced fluid volume and composition. Yet, condensate banking forecasting is commonly inaccurate, as experiments seldom reproduce reservoir extreme conditions and complex fluid composition, while most pore-scale models oversimplify the physics of phase transitions between gas and condensate. To address this gap, a fully implicit isothermal compositional pore-network model for gas and condensate flow is presented. The proposed pore-networks consist of 3D structures of pores connected by constricted circular capillaries. Hydraulic conductances are calculated for the capillaries, which can exhibit single-phase flow or two-phase annular flow, according to local gas and liquid saturations, or be blocked by a liquid bridge, when capillary forces overcome viscous forces. A PT-flash based on the Peng-Robinson EoS is performed at control volumes defined for the pores at each time step, updating the phases properties. Flow analyses were carried based on coreflooding experiments reported in the literature, with matching fluid composition and flow conditions, and approximated pore-space geometry. Predicted and measured relative permeability curves showed good quantitative agreement, for two values of interfacial tension and three values of gas flow velocity.

Netflow Python library – A free software tool for the generation and analysis of pore or flow networks

State-of-the-art tomographic scanning techniques provide detailed pore-space geometries of natural porous media, which are central for the study of subsurface flow and transport. Due to experimental and computational limitations, the extraction of high-resolution images is limited to relatively small sample volumes. To reduce the amount of data and the physical complexity, pore-space geometries are routinely translated into pore network models. Subsequently, such networks are expanded in space with suitable computational methods to determine effective medium parameters at larger scales relevant in engineering applications. While existing methods can provide networks with effective flow parameters being consistent with experimental data for comparably homogeneous media such as bead packs and sandstones, these methods are inadequate for more complex heterogeneous rocks such as carbonates or become too expensive for large networks. The netflow Python library accompanying this paper extends existing methods by preserving pore clusters that are a key characteristic of heterogeneous rocks. To this end dendrograms are extracted from experimental data and perturbed when generating larger networks. Moreover, the methods included in the netflow library are implemented in computationally efficient ways and enable the generation of large periodic networks that virtually eliminate boundary effects, which interfere in existing methods.• The netflow Python library enables the generation of large irregular networks, as it preserves pore or node clusters which are present in certain natural rock types.• The netflow Python library allows for the generation and flow analysis of boundary-free periodic networks. It further includes methods to convert periodic networks into conventional cubical ones.

Using scaling factors for characterizing spatial and temporal variability of soil hydraulic properties of topsoils in areas heavily affected by soil erosion

Extensive agricultural use of land coupled with intensive water erosion at geomorphologically diverse areas with uniform soil substrate and originally similar soils can lead to high diversity in soil types and, correspondingly, to a high spatial and temporal variability of soil properties (including soil hydraulic properties). Therefore, this study aimed to propose a procedure to characterize the variability of soil hydraulic properties of topsoils and the soil–water regime. Soil hydraulic properties were measured after sowing and harvesting at 5 sampling points of 1 elevation transect at 5 experimental areas with diverse soil types. The reference soil hydraulic properties and 3 scaling factors (related to the pressure head, αh, water content, αθ, and hydraulic conductivity, αK) were used to characterize the spatial and temporal variability of soil hydraulic properties. The best correspondence between scaled soil hydraulic curves was observed for the Chernozem area, followed by the two Haplic Cambisols areas, Leptosol area and Luvisol area. In general, matching of the scaled curves increased with a decreasing variability of n values (i.e., increasing similarity of a soil pore space geometry) and increasing average n values (e.g., for pronounced S-shape soil water retention curves). The sampling day significantly affected αh, αK, and αθ in the Chernozem area; αh and αK in the Cambisol (developed on shale) area; and αh and αθ in the Leptosol area. While values for the Chernozem area indicated an improvement in soil hydrological conditions during the vegetation period, the values for the Luvisol, Leptosol, and Cambisol (developed on shale) areas indicated aggravation. No considerable changes were observed for the Cambisol (developed on granodiorite and shale) areas. The sampling position significantly affected αθ in both the Cambisol areas. At some locations (e.g., Chernozem area), the spatial variability reflected different erosion-accumulation processes within the transect. To illustrate a practical application of the scaling factors at such locations, the scaling factors obtained for the Chernozem area were linearly interpolated within the surface layer of the theoretical vertical two-layer soil transect, and HYDRUS-2D program was used to simulate water flow in the surface 50 cm layer. The results showed a more gradual wetting front after sowing than after harvesting.

Formation evaluation of reservoirs in Eocene, Niger Delta Nigeria using modified formation factor from Pickett’s plot

Formation factor evaluation was carried out across eight reservoirs in five wells in a field in the Niger Delta region of Nigeria. Formation factor is very vital in assessment of petrophysical parameters, it is important to use in-situ wireline logs to evaluate the petrophysical constants. The identified reservoir in the study area show good accumulation of hydrocarbon having net pay zone between 5.00 and 83.50 ft and density porosity between 0.17 and 0.35. In-situ log was used to evaluate porosity exponent with the help of Pickett’s plot, the porosity exponent values are between 1.65 and 2.52 in the study area. These values of porosity exponent are seen to be influence by the values of volume of shale, this indicates that the porosity exponent is affected by grain size, pore space and pore geometry. A modified formation factor equation from the Archie’s equation using porosity exponent from Pickett’s plot was used for formation evaluation of each of the wells. Most of the wells showed an over estimation (between 2.06 and 2.52) of porosity exponent expect for well BS02 (1.65) that indicates under estimation of the porosity exponent. The over estimation of formation factor as compared to Archie’s equation is between 8.89% (BS01 R1) and 48.88% (BN01 R2), while for under estimation of formation factor as observed in well BS02 is between 39.02 (BS02 R1) and 41.29% (BS02 R2). The study has been able to propose an average formation factor equation as $$\left( {F = \frac{1}{{\phi^{2.17} }}} \right)$$ for the delineated reservoir in the study area.

Two-Stage Alignment of FIB-SEM Images of Rock Samples.

Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) tomography provides a stack of images that represent serial slices of the sample. These images are displaced relatively to each other, and an alignment procedure is required. Traditional methods for alignment of a 3D image are based on a comparison of two adjacent slices. However, such algorithms are easily confused by anisotropy in the sample structure or even experiment geometry in the case of porous media. This may lead to significant distortions in the pore space geometry, if there are no stable fiducial marks in the frame. In this paper, we propose a new method, which meaningfully extends existing alignment procedures. Our technique allows the correction of random misalignments between slices and, at the same time, preserves the overall geometrical structure of the specimen. We consider displacements produced by existing alignment algorithms as a signal and decompose it into low and high-frequency components. Final transformations exclude slow variations and contain only high frequency variations that represent random shifts that need to be corrected. The proposed algorithm can operate with not only translations but also with arbitrary affine transformations. We demonstrate the performance of our approach on a synthetic dataset and two real FIB-SEM images of natural rock.

Pore-scale imaging with measurement of relative permeability and capillary pressure on the same reservoir sandstone sample under water-wet and mixed-wet conditions

Using micro-CT imaging and differential pressure measurements, we design a comparative study in which we simultaneously measure relative permeability and capillary pressure on the same reservoir sandstone sample under water-wet and mixed-wet conditions during steady-state waterflooding experiments. This allows us to isolate the impact of wettability on a pore-by-pore basis and its effect on the macroscopic parameters, capillary pressure and relative permeability, while keeping the pore-space geometry unchanged.First, oil and brine were injected through a water-wet reservoir sandstone sample at a fixed total flow rate, but in a sequence of increasing brine fractional flows with micro-CT scans of the fluid phases taken in each step. Then the sample was brought back to initial water saturation and the surface wettability of the sample was altered after prolonged contact with crude oil and the same measurement procedure was repeated on the altered-wettability sample which we call mixed-wet.Geometric contact angles were measured, which discriminated the water-wet and mixed-wet cases with average values of 75° and 89° respectively. Additionally, an energy balance was used to determine the effective contact angles for displacement which indicated that a higher advancing contact angle of 116° was needed to displace oil in the mixed-wet case. For the water-wet experiment the filling sequence was pore-size dependent, with a strong correlation between pore size and oil occupancy. However, in the mixed-wet experiment the principal determinant of the filling sequence was the wettability rather than the pore size, and there was no correlation between pore size and the residual oil occupancy.The oil-water interfacial area had a larger maximum in the mixed-wet case which was supported by the observation of sheet or saddle-like menisci shapes present throughout the sample volume that impede the flow. These shapes were quantified by much larger negative Gaussian curvature which indicated better connectivity of the phases, consistent with the lower residual oil saturation. Mean curvature and associated capillary pressure were positive for the water-wet case but decreased to a negative value for the mixed-wet case pointing to forced displacement from oil-wet pores. This analysis explained why the relative permeabilities for the mixed-wet case were lower than for the water-wet case for the same fractional flow.

Direct fluid flow simulation at pore scale with regularized hydrodynamic equations

Laboratory analysis of rock samples (core material) is one of the main tools used in an analysis of oil and gas field development and methods to enhance oil recovery. A number of drawbacks are intrinsic to the laboratory techniques, among which we note the practical impossibility of carrying out parametric studies on one sample, the impossibility (and / or high cost) of taking into account reservoir conditions, and the impossibility of analyzing non-cemented rocks (sludge). With the development of computational capabilities and computed tomography methods, the “digital rock physics” technology, which consists in direct simulation of physical processes in a rock sample with resolved pore space geometry, is gaining popularity today. This technology complements the traditional laboratory studies and compensates for a number of their shortcomings. The presented work is devoted to the direct simulation of fluid flow within the scope of the digital rock physics. For simulation regularized (according to quasi-hydrodynamic technique) hydrodynamic equations are used. Both single-phase single-component flows and two-phase two-component flows, taking into account interfacial tension, are discussed. The results of simulations of fluid flows both in model domains and in domains corresponding to the pore space of real rocks are presented.

Geometrically derived efficiency of slow immiscible displacement in porous media.

The efficiency of a displacement is the fraction of applied work over the change in free energy. This displacement efficiency is essential for linking wettability to applied work during displacement processes. We quantify the efficiency of slow immiscible displacements in porous media from pore space geometry. For this end, we introduce pore-scale definitions for thermodynamically reversible (ison) and irreverisble (rheon) processes. We argue that the efficiency of slow primary displacement is described by the geometry of the pore space for porous media with a sufficient number of pore bodies. This article introduces how to calculate such geometry-based efficiency locally, and integrating this local efficiency over the pore space yields an aggregate efficiency for the primary displacement in the porous medium. Further, we show how the geometrical characterization of the displacement efficiency links the efficiency to the constriction factor from transport processes governed by the Laplace equation. This enables estimation of displacement efficiency from traditional and widely available measurements for porous media. We present a thermodynamically based wettability calculation based on the local efficiency and a method to approximate this thermodynamically based wettability from traditional experiments.

Predicting permeability via statistical learning on higher-order microstructural information

Quantitative structure–property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure facilitates prediction of permeability, a key property that has been extensively studied in material science, geophysics and chemical engineering. In this work, we study the predictability of different structural descriptors via both linear regressions and neural networks. A large data set of 30,000 virtual, porous microstructures of different types, including both granular and continuous solid phases, is created for this end. We compute permeabilities of these structures using the lattice Boltzmann method, and characterize the pore space geometry using one-point correlation functions (porosity, specific surface), two-point surface-surface, surface-void, and void-void correlation functions, as well as the geodesic tortuosity as an implicit descriptor. Then, we study the prediction of the permeability using different combinations of these descriptors. We obtain significant improvements of performance when compared to a Kozeny-Carman regression with only lowest-order descriptors (porosity and specific surface). We find that combining all three two-point correlation functions and tortuosity provides the best prediction of permeability, with the void-void correlation function being the most informative individual descriptor. Moreover, the combination of porosity, specific surface, and geodesic tortuosity provides very good predictive performance. This shows that higher-order correlation functions are extremely useful for forming a general model for predicting physical properties of complex materials. Additionally, our results suggest that artificial neural networks are superior to the more conventional regression methods for establishing quantitative structure–property relationships. We make the data and code used publicly available to facilitate further development of permeability prediction methods.

On the Birth of Structural and Crystallographic Fabric Signals in Polar Snow: A Case Study From the EastGRIP Snowpack

The role of near-surface snow processes for the formation of climate signals through densification into deep polar firn is still barely understood. To this end we have analyzed a shallow snow pit (0-3 meters) from EastGRIP (Greenland) and derived high-resolution profiles of different types of mechanically relevant fabric tensors. The structural fabric, which characterizes the anisotropic geometry of ice matrix and pore space, was obtained by X-ray tomography. The crystallographic fabric, which characterizes the anisotropic distribution of the c-axis (or optical axis) orientations of snow crystals, was obtained from automatic analysis of thin sections. The structural fabric profile unambiguously reveals the seasonal cycles at EastGRIP, as a consequence of temperature gradient metamorphism, and in contrast to featureless signals of parameters like density or specific surface area. The crystallographic fabric profile unambiguously reveals a signal of cluster-type texture already at shallow depth. We make use of order of magnitude estimates for the formation time of both fabric signals and discuss potential coupling effects in the context of snow and firn densification.

Geometrical and Topological Analysis of Pore Space in Sandstones Based on X-ray Computed Tomography

The pore geometry and topology properties of pore space in rocks are significant for a better understanding of the complex hydrologic and elastic properties. However, geometry and topology information about the sandstone pore structures is not fully available. In this study, we obtained the topological and geometrical pore parameters from a representative elementary volume (REV) for fluid flow in sandstone samples. For comparison, eight types of sandstones with various porosities were studied based on the X-ray micro-computed tomography technique. In this study, the REV size was selected based on the parameters from the respective pore network models (PNM), not just the porosity. Our analysis indicates that despite different porosity, all the sandstone samples have highly triangular-shaped pores and a high degree of pore structural isotropy. The high porosity group sandstones exhibit wider ranges of pore sizes than the low porosity group sandstones. Compared to the high porosity group sandstones, the low porosity group sandstones samples showing a higher global aspect ratio, indicating some pores exist in the form of bottlenecks. The pore topological properties of different sandstones show a high dependence of the porosity. The high porosity group sandstones obtain large coordination numbers, large connectivity densities and low tortuosities. The results from this study will help better understand the complex pore structure and the fluid flow in sandstone.

4D petroelastic modeling based on a presalt well

After their initial discovery in 2006, followed by an accumulated production of over 2 billion barrels of oil equivalent, the presalt carbonate reservoirs of offshore Brazil are now candidates for time-lapse seismic analysis. Therefore, we have conducted a 4D feasibility study in a Brazilian presalt reservoir well, which is composed of two types of carbonate rocks: microbialite and coquina. We evaluated two petroelastic models to obtain the acoustic impedance (AI) and shear impedance (SI) needed to estimate potential time-lapse differences ([Formula: see text], [Formula: see text], and [Formula: see text]). For this, we used the Gassmann and Xu-Payne models, in which the latter considers the pore geometry of the rock in its equations. Our analysis of both models shows that changes in pressure and saturation are very similar, and we can conclude that, despite being a carbonate, the application of Gassmann’s model is sufficient for the 4D feasibility studies conducted in the deemed reservoir because it does not require pore space geometry parameters, as does the Xu-Payne model. The analysis of the time-lapse attributes provided us with a greater comprehension of the 4D scenarios modeled, some of which presented detectability of changes in the microbialite and coquina.

Improving watershed-based pore-network extraction method using maximum inscribed ball pore-body positioning

Pore-scale modeling is a rapidly evolving area of research because modeling multiphase flow directly on 3D pore geometries is of utmost importance in wide variety of research areas, including oil and gas development, hydrology and material sciences. Although there are numerous methods to model flow, only so-called pore-network models are computationally effective enough to perform simulations in large modeling domains, and they are orders of magnitude faster than direct modeling approaches. However, pore-network models require a simplification of the 3D pore geometry to perform simulations, which are usually referred to as pore-network extraction. Such extraction poses a separate problem because it must provide an accurate description of the pore space geometry and topology. Different methods have been proposed in the literature. Recently, watershed-based approaches have been popular due to their effectiveness in working with porous media images of any porosity. A watershed algorithm requires seed placement to segment the space into distinct pores. We propose a hybrid algorithm combining the power of watersheds in finding intersections between pores with the advantages of the maximum inscribed ball technique, which is very effective in finding pore centers. We rigorously verify and test our novel methodology on artificial and X-ray microtomography images of wide variety of porous materials: sphere packings, carbonate, soil, ceramic and sandstone samples. Comparison against a purely watershed-based method and results based solely on the maximum inscribed balls–based method (in terms of pore/throat total number, pore size distributions and connection statistics, and multiphase flow properties including capillary curves and relative permeabilities) revealed the accuracy of our novel technique, consistency with existing classical techniques and great potential in analysing 3D pore images of any complexity. On the other hand, comparison of extracted pore-network topology (as based on Euler number) revealed significant differences between different methodologies, which is rather surprising considering the similarities in two-phase flow properties. While analysing permeability results, we also compared two popular pore-throat partitioning models and advocated in favor of the weight model usually utilized within watershed-based extracted pore networks. Our results illuminate problems in current pore-network models and outline some potential ways to improve their accuracy in future research.

Bistability in the unstable flow of polymer solutions through pore constriction arrays

Polymer solutions are often injected in porous media for applications such as oil recovery and groundwater remediation. As the fluid navigates the tortuous pore space, elastic stresses build up, causing the flow to become unstable at sufficiently large injection rates. However, it is poorly understood how the spatial and temporal characteristics of this unstable flow depend on pore space geometry, which can vary widely between different porous media. We investigate this dependence by systematically varying the spacing between pore constrictions in a one-dimensional ordered array. We find that when the pore spacing is large, unstable eddies form upstream of each constriction, similar to observations of an isolated constriction. By contrast, when the pore spacing is sufficiently small, the flow in the different pores exhibits a surprising bistability, stochastically switching between two distinct unstable flow states. We hypothesize that this unusual behaviour arises from the interplay between elongation and relaxation of polymers as they are advected through the pore space. Consistent with this idea, we find that the flow state in a given pore persists for long times; moreover, flow states are strongly correlated between neighbouring pores. Thus, the characteristics of unstable flow are not determined just by injection conditions and the geometry of the individual pores, but also depend on the spacing between pores. Ultimately, these results help to elucidate the rich array of behaviours that can arise in polymer solution flow through porous media.

A Novel Porous Media Permeability Model Based on Fractal Theory and Ideal Particle Pore-Space Geometry Assumption

In this paper, a novel porous media permeability model is established by using particle model, capillary bundle model and fractal theory. The three-dimensional irregular spatial characteristics composed of two ideal particles are considered in the model. Compared with previous models, the results of our model are closer to the experimental data. The results show that the tortuosity fractal dimension is negatively correlated with porosity, while the pore area fractal dimension is positively correlated with porosity; The permeability is negatively correlated with the tortuosity fractal dimension and positively correlated with the integral fractal dimension of pore surface and particle radius. When the tortuosity fractal dimension is close to 1 and the pore area fractal dimension is close to 2, the faster the permeability changes, the greater the impact. Different particle arrangement has great influence on porous media permeability. When the porosity is close to 0 and close to 1, the greater the difference coefficient is, the more the permeability of different arrangement is affected. In addition, the larger the particle radius is, the greater the permeability difference coefficient will be, and the greater the permeability difference will be for different particle arrangements. With the increase of fractal dimension, the permeability difference coefficient first decreases and then increases. When the pore area fractal dimension approaches 2, the permeability difference coefficient changes faster and reaches the minimum value, and when the tortuosity fractal dimension approaches 1, the permeability difference coefficient changes faster and reaches the minimum value. Our research is helpful to further understand the connotation of medium transmission in porous media.

A lattice-Boltzmann study of permeability-porosity relationships and mineral precipitation patterns in fractured porous media

Mineral precipitation can drastically alter a reservoir’s ability to transmit mass and energy during various engineering/natural subsurface processes, such as geothermal energy extraction and geological carbon dioxide sequestration. However, it is still challenging to explain the relationships among permeability, porosity, and precipitation patterns in reservoirs, particularly in fracture-dominated reservoirs. Here, we investigate the pore-scale behavior of single-species mineral precipitation reactions in a fractured porous medium, using a phase field lattice-Boltzmann method. Parallel to the main flow direction, the medium is divided into two halves, one with a low-permeability matrix and one with a high-permeability matrix. Each matrix contains one flow-through and one dead-end fracture. A wide range of species diffusivity and reaction rates is explored to cover regimes from advection- to diffusion-dominated, and from transport- to reaction-limited. By employing the ratio of the Damkohler (Da) and the Peclet (Pe) number, four distinct precipitation patterns can be identified, namely (1) no precipitation (Da/Pe 100), (3) fracture isolation (1 1), and (4) diffusive precipitation (1 < Da/Pe < 100 and Pe < 0.1). Using moment analyses, we discuss in detail the development of the species (i.e., reactant) concentration and mineral precipitation fields for various species transport regimes. Finally, we establish a general relationship among mineral precipitation pattern, porosity, and permeability. Our study provides insights into the feedback loop of fluid flow, species transport, mineral precipitation, pore space geometry changes, and permeability in fractured porous media.