Fontainebleau Sandstone Research Articles

Mechanisms of Confining Pressure Dependence of Resistivity Index for Tight Sandstones by Digital Core Analysis

SummaryResistivity measurements are a major input into hydrocarbon reserve estimation and are usually described by Archie’s laws. In this study, we use digital rock physics to analyze the mechanisms of non-Archie and Archie behavior of formation factor (FF) and resistivity index (RI) of low-porosity Fontainebleau (FB) sandstone for ambient conditions and under high confining pressure, respectively.FB sandstone was imaged by micro-X-ray computed tomography (micro-CT) at a resolution of 1 µm. Subresolution details of the grain contact width distribution along with their length were extracted from a set of scanning electron microscope (SEM) images. The nanoscale aperture of grain contacts, which is below tomogram resolution, is accounted for in micro-CT-based numerical calculations by assigning effective porosity and conductivity to individual voxels of the extracted grain contact network. A porosity reduction of grain contacts and open pore space as a function of applied confining pressure is introduced, capturing the pressure dependence. The concept was implemented by grain contact labeling, introducing an additional phase derived from a Euclidean distance transform (EDT). Subvoxel stress-strain effects were incorporated by attributing all compressibility effects to the pore space (open pore space and grain contacts), treating the solid phase as perfectly rigid. Voxel-scale input conductivities are assigned using Archie’s law followed by solving the Laplace equation for sample-scale rock resistivity and RI directly on the segmented image using the finite element method.For the numerical modeling of the FF and RI of low-porosity FB sandstone as a function of confining pressure, which depends on subresolution features, a set of hypotheses were tested. These are based on two segmentation scenarios incorporating the measured contact aperture distribution from SEM analysis—a homogeneous aperture-based segmentation by assuming all grain contacts as an average constant value and a heterogeneous aperture-based segmentation assigning two groups of grain contact apertures. The segmentation scenarios enable homogeneous and heterogeneous morphological change of grain contacts due to confining pressure effects. Furthermore, partial saturation of grain contacts is considered. In all cases, strong water-wetness was assumed, and discretization effects were analyzed carefully.The numerical results highlight the relative contribution of each of two conductive components of FB sandstone (open pores vs. grain contacts) over the full range of partial saturations. Of importance is the connectivity of the system, with discretization effects having a significant effect on FF, but a small effect on the RI. Grain contacts and confining pressure are found to have a significant impact on RI behavior of low-porosity FB sandstone. Both the grain contact network with homogeneous aperture and the heterogeneous grain contact network are able to describe experimental observations. However, it is not sufficient to assume a homogeneous change in contact area, and an inhomogeneous deformation of grain contact zones is required to match the experiment.

Diagenetic Trends of Synthetic Reservoir Sandstone Properties Assessed by Digital Rock Physics

Quantifying interactions and dependencies among geometric, hydraulic and mechanical properties of reservoir sandstones is of particular importance for the exploration and utilisation of the geological subsurface and can be assessed by synthetic sandstones comprising the microstructural complexity of natural rocks. In the present study, three highly resolved samples of the Fontainebleau, Berea and Bentheim sandstones are generated by means of a process-based approach, which combines the gravity-driven deposition of irregularly shaped grains and their diagenetic cementation by three different schemes. The resulting evolution in porosity, permeability and rock stiffness is examined and compared to the respective micro-computer tomographic (micro-CT) scans. The grain contact-preferential scheme implies a progressive clogging of small throats and consequently produces considerably less connected and stiffer samples than the two other schemes. By contrast, uniform quartz overgrowth continuously alters the pore space and leads to the lowest elastic properties. The proposed stress-dependent cementation scheme combines both approaches of contact-cement and quartz overgrowth, resulting in granulometric, hydraulic and elastic properties equivalent to those of the respective micro-CT scans, where bulk moduli slightly deviate by 0.8%, 4.9% and 2.5% for the Fontainebleau, Berea and Bentheim sandstone, respectively. The synthetic samples can be further altered to examine the impact of mineral dissolution or precipitation as well as fracturing on various petrophysical correlations, which is of particular relevance for numerous aspects of a sustainable subsurface utilisation.

A three‐dimensional multiscale damage‐poroelasticity model for fractured porous media

AbstractThe paper investigates the failure of brittle rocks within a multiscale/multiphysics computational modeling framework so as to explicitly incorporate both microstructural and hydromechanical aspects in their overall (nonlinear) fracture behavior. Herein, the rock is idealized as a microfissured porous medium via a representative elementary volume (REV) containing distributed oblate spheroidal open microcracks and spheroidal nanopores at the lower scales. A two‐scale analytical homogenization procedure is then performed on the REV, assuming a saturated pore space across the scales. The end result is a microstructurally enriched continuum damage‐poroelasticity constitutive model within the generalized Biot's framework that inherits the underlying small‐scale characteristics. A set of damage tensors is derived based on the directional density distribution of microcracks that operate on both the poromechanical and hydraulic properties. Microstructural evolution is modeled following changes in microcrack length, aperture, and number density, including nanoporosity. To this end, a robust localization procedure is used that accurately captures the macroscopic softening due to microcracking events, leading to a nonlinear (but path‐independent) model. To investigate the baseline features of the model, including the salient effects of microcracking on induced anisotropy and deterioration of poroelastic properties, numerical results of material point‐based computations are discussed in detail. Finally, predictions of the current model are validated against experiments on Fontainebleau sandstone.

Dual attenuation peaks revealing mesoscopic and microscopic fluid flow in partially oil-saturated Fontainebleau sandstones

SUMMARY We conducted stress–strain oscillation experiments on dry and partially oil-saturated Fontainebleau sandstone samples over the 1–2000 Hz band at different confining pressures to investigate the wave-induced fluid flow (WIFF) at mesoscopic and microscopic scales and their interaction. Three tested rock samples have similar porosity between 6 and 7 per cent and were partially saturated to different degrees with different oils. The measurement results exhibit a single or two attenuation peaks that are affected by the saturation degree, oil viscosity and confining pressure. One peak, exhibited by all samples, shifts to lower frequencies with increasing pressure, and is mainly attributed to grain contact- or microcrack-related squirt flow based on modelling of its characteristics and comparison with other experiment results for sandstones. The other peak is present at smaller frequencies and shifts to higher frequencies as the confining pressure increases, showing an opposite pressure dependence. This contrast is interpreted as the result of fluid flow patterns at different scales. We developed a dual-scale fluid flow model by incorporating the squirt flow effect into the patchy saturation model, which accounts for the interaction of WIFFs at microscopic and mesoscopic scales. This model provides a reasonable interpretation of the measurement results. Our broad-frequency-band measurements give physical evidence of WIFFs co-existing at two different scales, and combining with modelling results, it suggests that the WIFF mechanisms, related to pore microstructure and fluid distribution, interplay with each other and jointly control seismic attenuation and dispersion at reservoir conditions. These observations and modelling results are useful for quantitative seismic interpretation and reservoir characterization, specifically they have potential applications in time-lapse seismic analysis, fluid prediction and reservoir monitoring.

Elasto-plastic behavior of the Fontainebleau sandstone based on a refined continuous strain deviation approach

The elasto-plastic behavior of the Fontainebleau sandstone is studied from experimental and numerical points of view on the basis of a series of conventional triaxial compression tests. Five distinct stages of the axial strain curve are quantified in terms of four stress thresholds (crack closure stress σcc , crack initiation stress σci , crack damage stress σcd and short-term peak strength σp ). The onset of dilation and total volumetric strain reversal occur at axial stress level 30–50% and 50–80% of σp , respectively. A refined continuous strain deviation (RCSD) method is proposed to more accurately define the elastic parameters. Other internal state variables are determined accordingly. Some important information are gained as follows: (1) the Poisson’s ratio decreases with the increase of the confining pressure; (2) at the same stress level, the higher of the confining pressure, the smaller of the negative plastic volumetric strain (dilatancy); (3) the evolution of the friction-like coefficient and the plastic volumetric strain can be described with an exponential function and a hyperbolic function, respectively. A strictly experimental based constitutive model is proposed to study the elasto-plastic behavior of the Fontainebleau sandstone. All numerical aspects including formulations, algorithms and experimental validations, are presented in detail.

A rock-physics model to determine the pore microstructure of cracked porous rocks

SUMMARY Determining rock microstructure remains challenging, since a proper rock-physics model is needed to establish the relation between pore microstructure and elastic and transport properties. We present a model to estimate pore microstructure based on porosity, ultrasonic velocities and permeability, assuming that the microstructure consists on randomly oriented stiff equant pores and penny-shaped cracks. The stiff pore and crack porosity varying with differential pressure is estimated from the measured total porosity on the basis of a dual porosity model. The aspect ratio of pores and cracks and the crack density as a function of differential pressure are obtained from dry-rock P- and S-wave velocities, by using a differential effective medium model. These results are used to invert the pore radius from the matrix permeability by using a circular pore model. Above a crack density of 0.13, the crack radius can be estimated from permeability, and below that threshold, the radius is estimated from P-wave velocities, taking into account the wave dispersion induced by local fluid flow between pores and cracks. The approach is applied to experimental data for dry and saturated Fontainebleau sandstone and Chelmsford Granite.

A plugin for computing the pore/grain network tortuosity of a porous medium from 2D/3D MicroCT image

Tortuosity is an important geometrical parameter of the pore or grain network in a porous medium. Here we present and discuss an implementation of a plugin to estimate the pore/grain network tortuosity of a porous medium sample. The tortuosity is estimated according to the geometric reconstruction algorithm that can be applied to 2D or 3D μCT image samples. To illustrate the tortuosity plugin features, applications are given i) for the 2D case: three synthetic image samples being one horizontal straight line, one diagonal straight line and a curved line, and additionally it is considered a Dolomite Silurian rock sample, ii) for the 3D case: the pore network of a Berea and Fontainebleau sandstone and a Grosmont carbonte reservoir core samples; the grain network of a distal-radius trabecular bone sample and, finally, the pore network of a Rhodic Ferralsol soil sample. Some comments and discussions about the tortuosity estimated with the current algorithm are also addressed.

Capillary pressure characteristics of CO2-brine-sandstone systems

In carbon geo-sequestration (CGS), CO2 is collected from large industrial emitters and injected deep into the subsurface. In this context it is vital to know how much CO2 can be pressed into the storage rock matrix. The metric which measures this is the primary capillary pressure. Furthermore, once the CO2 resides in the pore space of the rock it can be trapped by capillary forces so that it cannot leak back to the surface. Such residual trapping also depends on the rock matrix and thermo-physical conditions. However, data is sparse for these key metrics, which presents a significant risk for CGS projects. We thus measured these parameters in two rock matrices as a function of various thermo-physical variables. The capillary pressure (Pc) measured ranged from 0.1 to 10 kPa for Bentheimer sandstone and from 10 to 100 kPa for Fontainebleau sandstone; this difference is due to different pore morphologies in the rocks. However, when scaled with contact angle, fluid and rock properties, the curves collapse onto a single master curve. Moreover, Pc during secondary drainage was higher than during primary drainage. 16–21% residual CO2 saturation (SCO2,r) was achieved with supercritical CO2; while higher SCO2,r (25–29%) was achieved with liquid CO2, which is attributed to a) a better sweep efficiency of liquid CO2 due to its higher viscosity, and b) to a change in wettability. We conclude that careful site selection is an important criterion for optimizing CGS projects as rock matrix properties and thermo-physical conditions play a key role.

Identification of sampling patterns for high-resolution compressed sensing MRI of porous materials: 'learning' from X-ray microcomputed tomography data.

There exists a strong motivation to increase the spatial resolution of magnetic resonance imaging (MRI) acquisitions so that MRI can be used as a microscopy technique in the study of porous materials. This work introduces a method for identifying novel data sampling patterns to achieve undersampling schemes for compressed sensing MRI (CS-MRI) acquisitions, enabling 3D spatial resolutions of 17.6 µm to be achieved. A data-driven learning approach is used to derive k-space undersampling schemes for 3D MRI acquisitions from 3D X-ray microcomputed tomography (µCT) datasets acquired at a higher spatial resolution than can be acquired using MRI. The performance of the new sampling approach was compared to other, well-established sampling strategies using simulated MRI data obtained from high-resolution µCT images of rock core plugs. These simulations were performed for a range of different k-space sampling fractions (0.125-0.375) using images of Ketton limestone. The method was then extended to consideration of imaging Estaillades limestone and Fontainebleau sandstone. The results show that the new sampling approach performs as well as or better than conventional variable density sampling and without need for time-consuming parameter optimisation. Further, a bespoke sampling pattern is produced for each rock type. The novel undersampling strategy was employed to acquire 3D magnetic resonance images of a Ketton limestone rock at spatial resolutions of 35 and 17.6 µm. The ability of the k-space sampling scheme produced using the new approach in enabling reconstruction of the pore space characteristics of the rock was then demonstrated by benchmarking against the pore space statistics obtained from high-resolution µCT data. The MRI data acquired at 17.6 µm resolution gave excellent agreement with the pore size distribution obtained from the X-ray microcomputed tomography dataset, while the pore coordination number distribution obtained from the MRI data was slightly skewed to lower coordination numbers. This approach provides a method of producing a k-space undersampling pattern for MRI acquisition at a spatial resolution for which a fully sampled acquisition at that spatial resolution would be impractically long. The approach can be easily extended to other CS-MRI techniques, such as spatially resolved flow and relaxation time mapping. LAY DESCRIPTION: Magnetic resonance imaging (MRI) is widely used to study the microstructure of, and fluid transport phenomena in porous media relevant for engineering applications. A major application is the study of water and hydrocarbon transport in porous sedimentary rocks, which typically have pore sizes smaller than 100 µm. The spatial resolution of routine MRI acquisitions, however, is limited to several hundred µm due to the relatively low sensitivity of the magnetic resonance method. Therefore, there exists a strong motivation to increase the spatial resolution of MRI by one to two orders of magnitude to be able to study these rocks at a pore scale. This work reports the initial step towards achieving this. Three-dimensional images of rock pore structure are acquired at both 35 and 17.6 µm spatial resolution. In ongoing work, these methods are now being incorporated into magnetic resonance velocity imaging methods, thereby enabling imaging of both pore structure and hydrodynamics at these much higher spatial resolutions than were hitherto possible. Although X-ray microcomputed tomography (µCT) produces high spatial resolution images, it is far more limited in being able to spatially map transport processes (i.e. flow) in porous media. This work reports a strategy for accelerating the image acquisition time such that sufficient signal-to-noise ratio (SNR) is achieved to increase the spatial resolution, that is, the voxel size within which there is sufficient SNR within the resulting image. To achieve this, a technique known as compressed sensing is used which exploits undersampling of the acquired data relative to the standard fully sampled image. In MRI, data are acquired in so-called k-space and Fourier transformed to yield the real space image. The challenge, when undersampling, is to optimise the specific points in k-space that are acquired because these will influence the quality of the resulting image. This work reports a straightforward, robust strategy for identifying the optimal sets of k-space points to acquire. The method introduced uses simulated MRI images calculated from high-resolution µCT images of the rocks of interest, from which optimised MRI sampling patterns are obtained. The method does not require any optimisation of parameters for its implementation, which is a significant advantage compared to other strategies. Moreover, we show that the pore space characteristics of the acquired MRI images are in excellent agreement with the same characteristics obtained from a high-resolution µCT image.

Macroscopic mechanical properties of porous rock with one saturating fluid

Effective frequency-dependent moduli and [Formula: see text]-factors are broadly used for characterizing the behavior of earth media in laboratory and field seismic observations. However, such properties are wavemode- and experiment-dependent and are often incomplete and/or inaccurate for modeling realistic situations. For example, viscoelastic moduli for porous fluid-saturated rock are usually derived for primary waves, but they may not apply to cases in which secondary waves are important, such as reflections in finely layered poroelastic media or quasistatic pore-fluid flows in laboratory experiments. To obtain a model applicable to all cases, equations of mechanics should be used, and mechanical properties of the material must be identified. To reveal and measure such properties for fluid-saturated porous rock, we have developed a Biot-consistent model based on Lagrangian continuum mechanics. The model is “minimal,” purely macroscopic, and independent of the macrostructure or patterns of pore-fluid flows; thus, it could represent many existing wave-induced fluid-flow (WIFF) as well as non-WIFF models. Due to its mechanical definition, the model should be applicable to all rock-physics experiments (linear creep, pore flow, low-frequency, resonant, or ultrasonic), any waves in the field (primary, secondary, standing, surface, etc.) under arbitrary boundary conditions, and also finite-difference and finite-element numerical modeling. When based on this model, numerical simulations require no integral equations, fractional derivatives, memory variables, or additional kinetic equations. We further use the model to invert for detailed elastic and viscous properties of fluid-saturated Berea and Fontainebleau sandstones from recently published low-frequency laboratory experiments. All rock properties inferred in the model are time- and frequency-independent, comparable to other physical observations, and the model closely predicts the data. The model can be approximately pore-fluid independent, which allows performing rigorous fluid substitution with viscous pore fluids. As an illustration, P-wave velocity dispersion and attenuation in water-, oil-, and gas-saturated sandstone are simulated.

Pore-scale permeability prediction for Newtonian and non-Newtonian fluids

Abstract. The flow of fluids through porous media such as groundwater flow or magma migration is a key process in geological sciences. Flow is controlled by the permeability of the rock; thus, an accurate determination and prediction of its value is of crucial importance. For this reason, permeability has been measured across different scales. As laboratory measurements exhibit a range of limitations, the numerical prediction of permeability at conditions where laboratory experiments struggle has become an important method to complement laboratory approaches. At high resolutions, this prediction becomes computationally very expensive, which makes it crucial to develop methods that maximize accuracy. In recent years, the flow of non-Newtonian fluids through porous media has gained additional importance due to, e.g., the use of nanofluids for enhanced oil recovery. Numerical methods to predict fluid flow in these cases are therefore required. Here, we employ the open-source finite difference solver LaMEM (Lithosphere and Mantle Evolution Model) to numerically predict the permeability of porous media at low Reynolds numbers for both Newtonian and non-Newtonian fluids. We employ a stencil rescaling method to better describe the solid–fluid interface. The accuracy of the code is verified by comparing numerical solutions to analytical ones for a set of simplified model setups. Results show that stencil rescaling significantly increases the accuracy at no additional computational cost. Finally, we use our modeling framework to predict the permeability of a Fontainebleau sandstone and demonstrate numerical convergence. Results show very good agreement with experimental estimates as well as with previous studies. We also demonstrate the ability of the code to simulate the flow of power-law fluids through porous media. As in the Newtonian case, results show good agreement with analytical solutions.

Direct numerical simulations of water flooding process through digitized porous rocks

Water flooding is a secondary oil recovery process where oil from porous rocks is displaced by high pressure water. In this paper we focus on the direct numerical simulation of multiphase flows through complex solid structures with wettability effects using a coupled immersed boundary and volume of fluid method (IBM-VOF). Our method is tested for a wide range of validation/verification cases. The water flooding process through Fontainebleau sandstone is simulated for porosities between 0.15 and 0.25, at representative pore-scale Reynolds and capillary numbers. First, we quantify the temporal change in oil saturation, phase pressure difference and oil/water interstitial velocities to study the mobility of oil through the rocks. Further, we focus on the oil-water interfacial surface area and the specific length scale to study the growth of viscous fingers inside pores. Finally, we evaluate different energies and dissipation rates to understand the energy exchange encountered in the water flooding process.

Nuclear magnetic resonance characterization of porosity-preserving microcrystalline quartz coatings in Fontainebleau sandstones

The almost-pure quartz–cemented Fontainebleau Formation (Paris Basin, France) sandstones are known to preserve their porosity because of microcrystalline quartz coatings. Here, we use nuclear magnetic resonance (NMR) techniques, petrography, scanning electron microscopy, porosity and permeability measurements, hysteresis, and mercury injection capillary pressure curves to identify and analyze their porosity structure. Nuclear magnetic resonance experiments include transverse relaxation time (T2) distributions and T2-filtered T2–T2 exchange (T2F-TREx), a technique that provides estimates on the diffusion coupling by comparing the evolution of families of pores in T2 distributions at different exchange times. Samples were divided according to their texture, composition, and abundance of microcrystalline quartz crystals, comprising group 1 samples with very low amounts of coatings and group 2 samples with entire grains coated by microquartz. Both groups show three (or four) peaks in NMR 2-MHz T2 distribution at approximately 1 (peak A), 10−1 (peak B), and 10−2 s (peak C); group 2 samples present a slight shift to shorter T2 times in comparison with other samples. The longest T2 peak A is because of intergranular macropores, whereas the shortest peak C is because of the microporosity associated with the microcrystalline quartz coating at the surface of the pores. Peak B is also because of microporosity associated with microcrystalline quartz, but with a different surface/volume ratio being likely related to flat-shaped pores within the microcrystalline coating. The T2F-TREx indicates the proton exchange is higher between macropores and the pore surface micropores (peak C) than between macropores and the internal flat-shaped micropores; no exchange between the two sets of micropores can be observed. Our results show the potential of NMR techniques in characterizing the microporosity in Fontainebleau sandstones, which is key for the mechanism of porosity preservation in these rocks.

Estimating elastic moduli of sandstones using two-dimensional pore space images

The elastic moduli (shear modulus and bulk modulus) of two different sandstones are estimated from two-dimensional images of the pore space. An image analysis technique was used to extract the area and perimeter of each pore. The shearablity and compressibility of each pore were calculated using the boundary element method and a perimeter-area scaling law. The effective shear modulus and bulk modulus of the rock were then estimated using the area-weighted mean pore shearablity, pore compressiblity and the differential effective medium theory. The method was applied to Fontainebleau and Berea sandstones. Comparison with experimental values of the shear moduli and bulk moduli showed good agreement.

Direct simulation of pore-scale two-phase visco-capillary flow on large digital rock images using a phase-field lattice Boltzmann method on general-purpose graphics processing units

We describe the underlying mathematics, validation, and applications of a novel Helmholtz free-energy—minimizing phase-field model solved within the framework of the lattice Boltzmann method (LBM) for efficiently simulating two-phase pore-scale flow directly on large 3D images of real rocks obtained from micro-computed tomography (micro-CT) scanning. The code implementation of the technique, coined as the eLBM (energy-based LBM), is performed in CUDA programming language to take maximum advantage of accelerated computing by use of multinode general-purpose graphics processing units (GPGPUs). eLBM’s momentum-balance solver is based on the multiple-relaxation-time (MRT) model. The Boltzmann equation is discretized in space, velocity (momentum), and time coordinates using a 3D 19-velocity grid (D3Q19 scheme), which provides the best compromise between accuracy and computational efficiency. The benefits of the MRT model over the conventional single-relaxation-time Bhatnagar-Gross-Krook (BGK) model are (I) enhanced numerical stability, (II) independent bulk and shear viscosities, and (III) viscosity-independent, nonslip boundary conditions. The drawback of the MRT model is that it is slightly more computationally demanding compared to the BGK model. This minor hurdle is easily overcome through a GPGPU implementation of the MRT model for eLBM. eLBM is, to our knowledge, the first industrial grade–distributed parallel implementation of an energy-based LBM taking advantage of multiple GPGPU nodes. The Cahn-Hilliard equation that governs the order-parameter distribution is fully integrated into the LBM framework that accelerates the pore-scale simulation on real systems significantly. While individual components of the eLBM simulator can be separately found in various references, our novel contributions are (1) integrating all computational and high-performance computing components together into a unified implementation and (2) providing comprehensive and definitive quantitative validation results with eLBM in terms of robustness and accuracy for a variety of flow domains including various types of real rock images. We successfully validate and apply the eLBM on several transient two-phase flow problems of gradually increasing complexity. Investigated problems include the following: (1) snap-off in constricted capillary tubes; (2) Haines jumps on a micromodel (during drainage), Ketton limestone image, and Fontainebleau and Castlegate sandstone images (during drainage and subsequent imbibition); and (3) capillary desaturation simulations on a Berea sandstone image including a comparison of numerically computed residual non-wetting-phase saturations (as a function of the capillary number) to data reported in the literature. Extensive physical validation tests and applications on large 3D rock images demonstrate the reliability, robustness, and efficacy of the eLBM as a direct visco-capillary pore-scale two-phase flow simulator for digital rock physics workflows.

Sensitivity of Acoustic Emission Triggering to Small Pore Pressure Cycling Perturbations During Brittle Creep

AbstractFluid‐induced stress perturbations in the crust at seismogenic depths caused by sources such as tidal or seasonal loading may trigger earthquakes. We investigate the role of small periodic pore pressure (Pp) perturbation in rupture nucleation by performing laboratory triaxial creep experiments on Fontainebleau sandstone, saturated in water, under sinusoidal Pp variations. Results show that recorded acoustic emissions (AEs) correlate with Pp as the rock approaches failure. More interestingly, AEs occur significantly more when Pp is decreasing, that is, when strain rate is maximum with a progressive increase of Pp‐AEs correlation in time as the rock approaches failure. This suggests that the correlation of small stress perturbations and AEs not only depends on Pp amplitude but also on the criticality of the rock. Observations at the laboratory scale support field observations where tidal loading may have modulated seismic rates during the nucleation phase of the 2004 Sumatra‐Andaman and 2011 Tohoku‐Oki earthquakes.

Rock compressibility from microcomputed tomography images: Controls on digital rock simulations

Rock compressibility is a major control of reservoir compaction, yet only limited core measurements are available to constrain estimates. Improved analytical and computational estimates of rock compressibility of reservoir rock can improve forecasts of reservoir production performance and the geomechanical integrity of compacting reservoirs. The fast-evolving digital rock technology can potentially overcome the need for simplification of pores (e.g., ellipsoids) to estimate rock compressibility as the computations are performed on an actual pore-scale image acquired using 3D microcomputed tomography (micro-CT). However, the computed compressibility using a digital image is impacted by numerous factors, including imaging conditions, image segmentation, constituent properties, choice of numerical simulator, rock field of view, how well the grain contacts are resolved in an image, and the treatment of grain-to-grain contacts. We have analyzed these factors and quantify their relative contribution to the rock moduli computed using micro-CT images of six rocks: a Fontainebleau sandstone sample, two Berea sandstone samples, a Castelgate sandstone sample, a grain pack, and a reservoir rock. We find that image-computed rock moduli are considerably stiffer than those inferred using laboratory-measured ultrasonic velocities. This disagreement cannot be solely explained by any one of the many controls when considered in isolation, but it can be ranked by their relative contribution to the overall rock compressibility. Among these factors, the image resolution generally has the largest impact on the quality of image-derived compressibility. For elasticity simulations, the quality of an image resolution is controlled by the ratio of the contact length and image voxel size. Images of poor resolution overestimate contact lengths, resulting in stiffer simulation results.

Methane transport through hierarchical silica micro-mesoporous materials: From non-equilibrium atomistic simulations to phenomenological correlations

Abstract Atomistic non-equilibrium molecular dynamics simulations were employed to quantify methane transport in hierarchical porous networks. Model amorphous silica materials were used as solid substrates, which allows us to construct pore networks with well-defined properties. The results show that the methane diffusivity and permeability through the pores strongly depend on the frameworks. Analysis of the vector fields for methane within the pores reveals the existence of local back-flow near the solid substrates, which disturbs methane transport. Varying the pore cross-sectional areas leads to changes in the entropy potential along the flow direction, which influences the molecular path length. The results show a linear relationship between methane transport (i.e., permeability) and a pore characteristic parameter that takes into consideration porosity, constriction factor, and tortuosity. This relation holds for hierarchical porous materials containing both micropores and mesopores. Diffusivity and permeability of methane through porous media are found to scale as a power function of porosity and constriction factor. These are measurable descriptors, suggesting that transport properties could be predicted for engineering and natural materials once characterisation data are available. For example, we show here that a power law can describe results obtained for Fontainebleau sandstone. The good agreement achieved suggests that using the approach presented not only enables the quantification of molecular effects influencing fluid transport, but also yields the reliable prediction of diffusivity and permeability of fluids through sedimentary rocks using as sole input macroscopic pore structure information.

Establishing Framework for 3D Printing Porous Rock Models in Curable Resins

Stereolithographic 3D printing is of paramount interest for researchers studying porous media because it is possible to use resins with a wide range of physical and chemical properties. Currently, these properties can be designed and adjusted to model the interaction of solids with fluids occupying the pore space, which is not feasible with natural materials. This ability enables replicating the pore network geometry of natural rocks as well as tuning the wettability of pore network surfaces. This study presents analysis of uncured liquid resins and porous rock models 3D-printed in those resins to establish the accuracy of the stereolithographic 3D printer in repeatedly printing the same pore network, as well as the fidelity of transport properties (e.g., porosity, pore sizes, wettability) to the model design. Viscosity of uncured resins was measured to predict the physical properties of the resulting cured models. A digital model of Fontainebleau sandstone was 3D-printed at three magnifications (15-, 23-, and 30-fold) from the original tomographic volume of 1 mm3 and in six resins (black, gray, clear, white, green, and yellow). The models were validated using the following techniques: helium pycnometry (for porosity); mercury porosimetry (for pore-throat size); and drop shape analyzer (for contact angles). Validation tests showed that green resin had the highest accuracy in replicating the rock’s pore network. White, yellow, and gray resins produced models with moderate accuracy with respect to their transport properties. Black and clear resins had the lowest accuracy and would need further analysis of their physical and chemical properties to be useful in reservoir rock replication.

Computation of grain size distribution in 2-D and 3-D binary images

Grain Size Distribution is one of the basic measurements for sediment classification. The conventional methods for grain size distribution include the sieve method, the laser diffraction method, and the point-count method. We aimed to develop a robust computer code that simulates these conventional methods. The code can measure grain size distribution on 2-D and 3-D binary images using a watershed algorithm to extract out individual grains, and using principal component algorithms to find the principal axes. The outputs include grain radius for different principal axes, grain volume, grain surface area, principal axes inclinations and azimuths, and the number of contacts for each grain. The calculated distribution can be volume-based, frequency-based, or grid-based. Digital microstructures used in this study include (1) identical sphere packs including a simple cubic pack and a Finney pack, and (2) natural rock geometry such as Berea sandstone, Castlegate sandstone, and Fontainebleau sandstone. Furthermore, we employed this code to provide additional value of information from μXCT images by using μXCT to create 2-D to 3-D model of the grain size distribution, solving what is commonly known as Wicksell's corpuscle problem. We showed that our workflow successfully models a generalized 2-D to 3-D grain size distribution for a particular set of natural rocks that we include in our study. We hope to be able to obtain more μXCT images in the future in order to create a universal model covering most types of natural rocks.