Fontainebleau Sandstone Research Articles

Time‐Dependent Deformations of Sandstone During Pore Fluid Pressure Oscillations: Implications for Natural and Induced Seismicity

AbstractIn tectonically active regions, natural seismicity is often correlated with the seasonal hydrology, suggesting that cyclic loading variations might trigger seismicity. Moreover, recent field observations suggest that cyclic fluid injection strategies into geological reservoirs could produce less seismicity than monotonic injections. Here we present 10 brittle creep laboratory triaxial experiments that bring new constraints on fluid‐rock interactions during cyclic pore fluid variations. The experiments were performed on Fontainebleau sandstone with various pore fluid pressure conditions: (i) with constant pore fluid pressure levels from 1 to 10 MPa, at constant Terzaghi effective pressure (Pc − Pf = 30 MPa); and (ii) with cyclic (sinusoidal) pore fluid pressure oscillations of varying amplitudes (from 0 to 8 MPa) and periods (from 30 to 3,000 s) around a mean value of 5 MPa. During deformation, the rock's mechanical properties and the high‐frequency acoustic emission signals were monitored to investigate the physics underlying the rupture processes. Under macroscopically drained conditions, rather than their amplitude, the period of the oscillations appeared to strongly affect the rock sample strength, time‐to‐failure, and dilatancy behavior. Moreover, even for small variations of pore fluid amplitude, and at all pore fluid pressure period, pore fluid pressure and acoustic emissions were strongly correlated. Our experiments demonstrate that pore fluid pressure oscillations may strongly affect rocks mechanical behavior and associated seismic activity.

Dynamic In Situ Three-Dimensional Imaging and Digital Volume Correlation Analysis to Quantify Strain Localization and Fracture Coalescence in Sandstone

Advances in triaxial compression deformation apparatus design, dynamic X-ray microtomography imaging, data analysis techniques, and digital volume correlation analysis provide unparalleled access to the in situ four-dimensional distribution of developing strain within rocks. To demonstrate the power of these new techniques and acquire detailed information about the micromechanics of damage evolution, deformation, and failure of porous rocks, we deformed 3-cm-scale cylindrical specimens of low-porosity Fontainebleau sandstone in an X-ray-transparent triaxial compression apparatus, and repeatedly recorded three-dimensional tomograms of the specimens as the differential stress was increased until macroscopic failure occurred. Experiments were performed at room temperature with confining pressure in the range of 10–20 MPa. Distinct grayscale subsets, indicative of density, enabled segmentation of the three-dimensional tomograms into intact rock matrix, pore space, and fractures. Digital volume correlation analysis of pairs of tomograms provided time series of three-dimensional incremental strain tensor fields throughout the experiments. After the yield stress was reached, the samples deformed first by dilatant opening and propagation of microfractures, and then by shear sliding via grain rotation and strain localization along faults. For two samples, damage and dilatancy occurred by grain boundary opening and then a sudden collapse of the granular rock framework at failure. For the third sample, a fault nucleated near the yield point and propagated in the sample through the development of transgranular microfractures. The results confirm findings of previous experimental studies on the same rock and provide new detailed quantifications of: (1) the proportion of shear versus dilatant strain in the sample, (2) the amount of dilatancy due to microfracture opening versus pore opening when a fault develops, and (3) the role of grain boundaries and pore walls in pinning microfracture propagation and slowing down the rate of damage accumulation as failure is approached. Our study demonstrates how the combination of high-resolution in situ dynamic X-ray microtomography imaging and digital volume image correlation analysis can be used to provide additional information to unravel brittle failure processes in rocks under stress conditions relevant to the upper crust.

Comparison of thermal and elastic properties of sandstones: Experiments and theoretical insights

We measured P-wave velocity, thermal conductivity and thermal diffusivity on 26 sandstone samples under dry and water-saturated conditions. Subsequently, we compared these measurements with predictions by frequently used models.Overall, these three properties decrease with porosity and increase with water saturation. Comparing data sets and models, we distinguish three main groups of sandstone samples: From the difference in the intrinsic elastic and thermal properties of the dominant mineral, two tendencies attributed to either quartz or another rock forming mineral are identified, which separate class 1 sandstone and samples from class 2 sandstones. Within class 1 clean sandstones, a sub-class (sub-class 1a) consists of similarly porous samples having different elastic and thermal properties. Based on elasticity, we attribute this effect to microcracks or grain contacts in the samples. While this feature does not affect the total porosity, it affects all of three physical properties strongly and in a similar way. Additionally, we define a second sub-class (sub-class 1b) for Fontainebleau sandstone with porosities above 13%. For these four samples, the effect of water saturation on the elastic and thermal properties is different.

Expansion and shrinkage of sandstones during spontaneous imbibition of fluids

The expansion of pure quartz sandstones is investigated during spontaneous imbibition of fluids. The selected Fontainebleau sandstone samples cover a wide variation in their petrophysical properties (e.g., porosity, permeability, P-wave velocity, and effective pore size), and demonstrate expansion and shrinkage during spontaneous imbibition of fluids with different surface tension. The capillary forces cause a spontaneous imbibition of the fluid into the pore space. The wetting of the mineral grains causes a volume strain to the matrix that can be recorded as an expansion. If the rigidity of the matrix is weak, a shrinkage of the sample is observed instead of expansion. The experiments have shown that the relative expansion depends on the surface tension of the imbibing fluid, the degree of saturation, the rigidity, and the effective pore radius of the sandstone sample.

Image Segmentation and Analysis of Pore Network Geometry in Two Natural Sandstones

We report the results of pore-network analysis of high resolution synchrotron microtomographic images of Fontainebleau and Berea Sandstones. We segment the gray-scale images of the rocks into constituent phases, and analyze the geometry of the pore network. The network consists of pores situated at the corner of grains and serve as the junction between elongated throats along grain edges. Our analysis indicates that the number of pores, their median coordination number, and fraction of connected pore space increases with an increase in porosity. In contrast, the width and length of throats decrease with an increase in total porosity. In each sample, the coordination number of pores is directly related to the radius of the pores, while the length of throats are also positively correlated with the throat radius. The permeability determined from the images increase with the total connected porosity of the samples and there is a change in the modeled permeability for each sample with flow direction. We observe that the dimensionless coefficient of variation of the throat lengths in all samples are nearly uniform around an average value of 0.64. The coefficient of variation of throat radii are generally higher than that of the radius of pores.

Prediction of permeability and formation factor of sandstone with hybrid lattice Boltzmann/finite element simulation on microtomographic images

In Fontainebleau sandstone, the evolution of transport properties with porosity is related to changes in both the size and connectivity of the pore space. Microcomputed tomography can be used to characterize the relevant geometric attributes, with the resolution that is sufficiently refined for realistic simulation of transport properties based on the 3D image. In this study, we adopted a hybrid computation scheme that is based on a hierarchical multi-scale approach. The specimen was partitioned into cubic sub-volumes for pore-scale simulation of hydraulic permeability and formation factor using the lattice Boltzmann method. The pore-scale results were then linked with finite element simulation in a homogenized scheme to compute and upscale the transport properties to specimen scale. The simulated permeability and formation factor have magnitude and anisotropy that are in good agreement with experimental rock physics data. Together with simulated and measured values of connected porosity and specific surface area, they provide useful insights into how pore geometry controls the evolution of the transport properties.

Quantifying Rock Weakening Due to Decreasing Calcite Mineral Content by Numerical Simulations.

The quantification of changes in geomechanical properties due to chemical reactions is of paramount importance for geological subsurface utilisation, since mineral dissolution generally reduces rock stiffness. In the present study, the effective elastic moduli of two digital rock samples, the Fontainebleau and Bentheim sandstones, are numerically determined based on micro-CT images. Reduction in rock stiffness due to the dissolution of 10% calcite cement by volume out of the pore network is quantified for three synthetic spatial calcite distributions (coating, partial filling and random) using representative sub-cubes derived from the digital rock samples. Due to the reduced calcite content, bulk and shear moduli decrease by 34% and 38% in maximum, respectively. Total porosity is clearly the dominant parameter, while spatial calcite distribution has a minor impact, except for a randomly chosen cement distribution within the pore network. Moreover, applying an initial stiffness reduced by 47% for the calcite cement results only in a slightly weaker mechanical behaviour. Using the quantitative approach introduced here substantially improves the accuracy of predictions in elastic rock properties compared to general analytical methods, and further enables quantification of uncertainties related to spatial variations in porosity and mineral distribution.

Fast Laplace solver approach to pore-scale permeability

We introduce a powerful and easily implemented method to calculate the permeability of porous media at the pore scale using an approximation based on the Poiseulle equation to calculate permeability to fluid flow with a Laplace solver. The method consists of calculating the Euclidean distance map of the fluid phase to assign local conductivities and lends itself naturally to the treatment of multiscale problems. We compare with analytical solutions as well as experimental measurements and lattice Boltzmann calculations of permeability for Fontainebleau sandstone. The solver is significantly more stable than the lattice Boltzmann approach, uses less memory, and is significantly faster. Permeabilities are in excellent agreement over a wide range of porosities.

Preisach description for solids with frictional cracks

The observation of a hysteretic stress–strain relationship is widespread for a large class of solids, such as rocks and other geomaterials, concretes, bones, etc. A common feature that unifies these materials is the presence of internal mechanical contacts in their structure, which can either be natural, or appear as the result of damage or fatigue in consolidated materials with an originally non-hysteretic mechanical response. Even though a number of physical mechanisms can be identified to account for mechanical hysteresis, at moderate and high strains, when typical internal contact displacements largely exceed the atomic size, a friction-based mechanism becomes of primary importance. As an alternative for a physics-based description, phenomenological approaches, ignoring the physical nature of hysteresis, are often used in numerical simulations. In this paper, we intend to bridge the physical mechanism of friction-based hysteresis with the phenomenological Preisach formalism, and derive the Preisach density in a compact analytical form for a model system that represents an elastic continuum with a large number of diversely oriented frictional cracks. We validate the physical crack friction model and its phenomenological Preisach counterpart with experimental data for Fontainebleau sandstone. The new formulations and the results could be of interest for materials scientists dealing with systems that show hysteretic elasticity and/or distributed damage, geomaterials or construction materials.

Measurements of the Relationship Between Microstructure, pH, and the Streaming and Zeta Potentials of Sandstones

A large number (1253) of high-quality streaming potential coefficient (C_mathrm{sp}) measurements have been carried out on Berea, Boise, Fontainebleau, and Lochaline sandstones (the latter two including both detrital and authigenic overgrowth forms), as a function of pore fluid salinity (C_mathrm{f}) and rock microstructure. All samples were saturated with fully equilibrated aqueous solutions of NaCl (10^{-5} and 4.5 mol/dm^{3}) upon which accurate measurements of their electrical conductivity and pH were taken. These C_mathrm{sp} measurements represent about a fivefold increase in streaming potential data available in the literature, are consistent with the pre-existing 266 measurements, and have lower experimental uncertainties. The C_mathrm{sp} measurements follow a pH-sensitive power law behaviour with respect to C_mathrm{f} at medium salinities (C_mathrm{sp} =-,1.44times 10^{-9} C_mathrm{f}^{-,1.127} , units: V/Pa and mol/dm^{3}) and show the effect of rock microstructure on the low salinity C_mathrm{sp} clearly, producing a smaller decrease in C_mathrm{sp} per decade reduction in C_mathrm{f} for samples with (i) lower porosity, (ii) larger cementation exponents, (iii) smaller grain sizes (and hence pore and pore throat sizes), and (iv) larger surface conduction. The C_mathrm{sp} measurements include 313 made at C_mathrm{f} > 1 mol/dm^{3}, which confirm the limiting high salinity C_mathrm{sp} behaviour noted by Vinogradov et al., which has been ascribed to the attainment of maximum charge density in the electrical double layer occurring when the Debye length approximates to the size of the hydrated metal ion. The zeta potential (zeta ) was calculated from each C_mathrm{sp} measurement. It was found that zeta is highly sensitive to pH but not sensitive to rock microstructure. It exhibits a pH-dependent logarithmic behaviour with respect to C_mathrm{f} at low to medium salinities (zeta =0.01133 log _{10} left( {C_mathrm{f} } right) +0.003505, units: V and mol/dm^{3}) and a limiting zeta potential (zeta potential offset) at high salinities of {zeta }_mathrm{o} = -,17.36pm 5.11 mV in the pH range 6–8, which is also pH dependent. The sensitivity of both C_mathrm{sp} and zeta to pH and of C_mathrm{sp} to rock microstructure indicates that C_mathrm{sp} and zeta measurements can only be interpreted together with accurate and equilibrated measurements of pore fluid conductivity and pH and supporting microstructural and surface conduction measurements for each sample.

The Effect of Heat Transfer and Polymer Concentration on Non-Newtonian Fluid from Pore-Scale Simulation of Rock X-ray Micro-CT.

Most of the pore-scale imaging and simulations of non-Newtonian fluid are based on the simplifying geometry of network modeling and overlook the fluid rheology and heat transfer. In the present paper, we developed a non-isothermal and non-Newtonian numerical model of the flow properties at pore-scale by simulation of the 3D micro-CT images using a Finite Volume Method (FVM). The numerical model is based on the resolution of the momentum and energy conservation equations. Owing to an adaptive mesh generation technique and appropriate boundary conditions, rock permeability and mobility are accurately computed. A temperature and concentration-dependent power-law viscosity model in line with the experimental measurement of the fluid rheology is adopted. The model is first applied at isothermal condition to 2 benchmark samples, namely Fontainebleau sandstone and Grosmont carbonate, and is found to be in good agreement with the Lattice Boltzmann method (LBM). Finally, at non-isothermal conditions, an effective mobility is introduced that enables to perform a numerical sensitivity study to fluid rheology, heat transfer, and operating conditions. While the mobility seems to evolve linearly with polymer concentration in agreement with a derived theoretical model, the effect of the temperature seems negligible by comparison. However, a sharp contrast is found between carbonate and sandstone under the effect of a constant temperature gradient. Besides concerning the flow index and consistency factor, a master curve is derived when normalizing the mobility for both the carbonate and the sandstone.

Using Resin-Based 3D Printing to Build Geometrically Accurate Proxies of Porous Sedimentary Rocks.

Three-dimensional (3D) printing is capable of transforming intricate digital models into tangible objects, allowing geoscientists to replicate the geometry of 3D pore networks of sedimentary rocks. We provide a refined method for building scalable pore-network models ("proxies") using stereolithography 3D printing that can be used in repeated flow experiments (e.g., core flooding, permeametry, porosimetry). Typically, this workflow involves two steps, model design and 3D printing. In this study, we explore how the addition of post-processing and validation can reduce uncertainty in the 3D-printed proxy accuracy (difference of proxy geometry from the digital model). Post-processing is a multi-step cleaning of porous proxies involving pressurized ethanol flushing and oven drying. Proxies are validated by: (1) helium porosimetry and (2) digital measurements of porosity from thin-section images of 3D-printed proxies. 3D printer resolution was determined by measuring the smallest open channel in 3D-printed "gap test" wafers. This resolution (400µm) was insufficient to build porosity of Fontainebleau sandstone (∼13%) from computed tomography data at the sample's natural scale, so proxies were printed at 15-, 23-, and 30-fold magnifications to validate the workflow. Helium porosities of the 3D-printed proxies differed from digital calculations by up to 7% points. Results improved after pressurized flushing with ethanol (e.g., porosity difference reduced to ∼1% point), though uncertainties remain regarding the nature of sub-micron "artifact" pores imparted by the 3D printing process. This study shows the benefits of including post-processing and validation in any workflow to produce porous rock proxies.

Resurrection of a reservoir sandstone from tomographic data using three-dimensional printing

Three-dimensional (3-D) printing provides an opportunity to build lab-testable models of reservoir rocks from tomographic data. This study combines tomography and 3-D printing to reproduce a sample of the Fontainebleau sandstone at different magnifications to test how this workflow can help characterization of transport properties at multiple scales. For this sandstone, literature analysis has given a porosity of 11%, permeability of 455 md, mean pore throat radius of 15 μm, and a mean grain size of 250 μm. Digital rock analysis of tomographic data from the same sample yielded a porosity of 13%, a permeability of 251 md, and a mean pore throat radius of 15.2 μm. The 3-D printer available for this study was not able to reproduce the sample’s pore system at its original scale. Instead, models were 3-D printed at 5-fold, 10-fold, and 15-fold magnifications. Mercury porosimetry performed on these 3-D models revealed differences in porosity (28%–37%) compared to the literature (11%) and to digital calculations (12.7%). Mercury may have intruded the smallest matrix pores of the printing powder and led to a greater than 50% increase in measured porosity. However, the 3-D printed models’ pore throat size distribution (15 μm) and permeability (350–443 md) match both literature data and digital rock analysis. The powder-based 3-D printing method was only able to replicate parts of the pore system (permeability and pore throats) but not the pore bodies. Other 3-D printing methods, such as resin-based stereolithography and photopolymerization, may have the potential to reproduce reservoir rock porosity more accurately.

Stress Dependence of Sandstone Electrical Properties and Deviations From Archie’s Law

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 181484, “Experimental and Numerical Investigations on Stress Dependence of Sandstone Electrical Properties and Deviations From Archie’s Law,” by M.F. Farid, J.-Y. Arns, W.V. Pinczewski, and C.H. Arns, University of New South Wales, prepared for the 2016 SPE Annual Technical Conference and Exhibition, Dubai, 26–28 September. The paper has not been peer reviewed. The resistivity index (RI) of Fontainebleau and Bentheimer sandstones was investigated at ambient and reservoir pressures down to low water saturations. The RI measurements show that both sandstones display Archie behavior at elevated pressure. However, at ambient pressure, the RI for Fontainebleau sandstone deviates from Archie behavior at low water saturations. The pore-space images suggest that the deviation from Archie behavior is attributable to the presence of conductive percolating grain-contact regions. Introduction Deviations from Archie’s law are known to occur, particularly at low water saturations, even for clean sandstones. It is unclear whether the deviations from Archie behavior observed at low pressures are also displayed at elevated pressures. In this paper, the authors present laboratory measurements of RI for two strongly water-wet sandstones at ambient and elevated pressures. The measurements are supplemented with high-resolution microcomputed-tomography (CT) imaging in dry and wet states at ambient pressure to determine an accurate description of the open resolved pore space and to attribute a finite porosity to fluid-saturated grain contacts at elevated pressure. Assuming that the main elements responding to effective stress are the grain contacts, grain-contact conductivities are estimated at elevated confining pressures with actual formation-factor measurements for saturated samples at the same confining pressures. These are compared with computations on the micro-CT images. For Bentheimer, which contains image-resolvable clay regions, the clay regions are considered as additional conductive pathways with different stress dependence. Methodology Experimental Procedure. Rock. The Fontainebleau sandstone samples used exhibit relatively low porosity in the range of 4 to 5%, with sample permeabilities of approximately 0.03 to 2.2 md at confining pressures of 500 to 6,000 psi. The Bentheimer sandstone samples used have a porosity of approximately 23.7 to 25.9%, with permeability of the intact samples at approximately 2,000 md over a range of 500 to 6,000 psi in confining pressure. Fluid. RI and drainage capillary pressure experiments were performed with brine (2% by weight sodium chloride) and air as the wetting and the non-wetting phases, respectively. The density and viscosity of brine were measured to be 1.0166 g/cm3 and 1.0 cp, while 0.00129 g/cm3 and 0.0185 cp were used for the density and viscosity of air, respectively. Core preparation, as well as image analysis and acquisition, is described in detail in the complete paper. In Fig. 1, the authors illustrate the final phase assignments for Fontainebleau sandstone, including grain/grain boundary labels for a few different saturations and boundary assignments.

Formation factor in Bentheimer and Fontainebleau sandstones: Theory compared with pore-scale numerical simulations

Accurate quantification of formation resistivity factor F (also called formation factor) provides useful insight into connectivity and pore space topology in fully saturated porous media. In particular the formation factor has been extensively used to estimate permeability in reservoir rocks. One of the widely applied models to estimate F is Archie's law (F=ϕ−m in which ϕ is total porosity and m is cementation exponent) that is known to be valid in rocks with negligible clay content, such as clean sandstones. In this study we compare formation factors determined by percolation and effective-medium theories as well as Archie's law with numerical simulations of electrical resistivity on digital rock models. These digital models represent Bentheimer and Fontainebleau sandstones and are derived either by reconstruction or directly from micro-tomographic images. Results show that the universal quadratic power law from percolation theory accurately estimates the calculated formation factor values in network models over the entire range of porosity. However, it crosses over to the linear scaling from the effective-medium approximation at the porosity of 0.75 in grid models. We also show that the effect of critical porosity, disregarded in Archie's law, is nontrivial, and the Archie model inaccurately estimates the formation factor in low-porosity homogeneous sandstones.

Microstructure Representation and Reconstruction of Heterogeneous Materials Via Deep Belief Network for Computational Material Design

Integrated Computational Materials Engineering (ICME) aims to accelerate optimal design of complex material systems by integrating material science and design automation. For tractable ICME, it is required that (1) a structural feature space be identified to allow reconstruction of new designs, and (2) the reconstruction process be property-preserving. The majority of existing structural presentation schemes relies on the designer's understanding of specific material systems to identify geometric and statistical features, which could be biased and insufficient for reconstructing physically meaningful microstructures of complex material systems. In this paper, we develop a feature learning mechanism based on convolutional deep belief network (CDBN) to automate a two-way conversion between microstructures and their lower-dimensional feature representations, and to achieve a 1000-fold dimension reduction from the microstructure space. The proposed model is applied to a wide spectrum of heterogeneous material systems with distinct microstructural features including Ti–6Al–4V alloy, Pb63–Sn37 alloy, Fontainebleau sandstone, and spherical colloids, to produce material reconstructions that are close to the original samples with respect to two-point correlation functions and mean critical fracture strength. This capability is not achieved by existing synthesis methods that rely on the Markovian assumption of material microstructures.

Pore-scale capillary pressure analysis using multi-scale X-ray micromotography

A multi-scale synchrotron-based X-ray microtomographic dataset of residually trapped air after gravity-driven brine imbibition was acquired for three samples with differing pore topologies and morphologies; image volumes were reconstructed with voxel sizes from 4.44µm down to 0.64µm. Capillary pressure distributions among the population of trapped ganglia were investigated by calculating interfacial curvature in order to assess the potential for remobilization of residually-trapped non-wetting ganglia due to differences in capillary pressure presented by neighbor ganglia. For each sample, sintered glass beads, Boise sandstone and Fontainebleau sandstone, sub-volumes with different voxel sizes were analyzed to quantify air/brine interfaces and interfacial curvatures and investigate the effect of image resolution on both fluid phase identification and curvature estimates. Results show that the method developed for interfacial curvature estimation leads to reliable capillary pressure estimates for gas ganglia. Higher resolution images increase confidence in curvature calculations, especially for the sandstone samples that display smaller gas-brine interfaces which are then represented by a higher number of voxels when imaged with a micron or sub-micron voxels size. The analysis of sub-volumes from the Boise and Fontainebleau dataset highlights the presence of a residually-trapped gas phase consisting of ganglia located in one or few pores and presenting significantly different capillary pressures, especially in the case of Fontainebleau sandstone. As a result, Ostwald ripening could occur, leading to gas transfer from ganglia with higher capillary pressure to surrounding ganglia with lower capillary pressures. More generally, at the pore-scale, most gas ganglia do present similar capillary pressures and Ostwald ripening would then not represent a major mechanism for residually-trapped gas transfer and remobilization.

Computing the elastic properties of sandstone submitted to progressive dissolution

We present a numerical method for estimating the stiffness-to-porosity relationships for evolving microstructures of Fontainebleau sandstone. The proposed study is linked to geological storage of CO2 and focuses on long-term and far field conditions, when the progressive degradation of the porous matrix can be assumed to be homogeneous at the sample scale. The method is based on microstructure sampling with respect to morphological descriptors extracted from microtomography. First, an efficient method of generation of accurate numerical media is proposed. The method is based on grain deposit, compaction and diagenesis and allows to reproduce user-defined morphological parameters. Second, two simple numerical models that mimic chemical degradation of porous aquifers are presented. Effective elastic properties are estimated within the framework of periodic homogenization and finite element approach. A fixed-point method on a self-consisted outer layer allows to consider non-periodic representative volume elements. Accurate predictions of elastic properties over a wide range of porosity are obtained. The overall evolutions of elastic behaviour due to the increase of porosity are in excellent agreement both, with experimental data and the results obtained by Arns et al.1.

Estimating permeability from thin sections without reconstruction: Digital rock study of 3D properties from 2D images

We present a new approach for predicting permeability of natural rocks using thin sections. Our approach involves two steps: (1) computing permeability of the thin sections for flow normal to the face, and (2) application of new robust 2D-3D transforms that relate thin section permeability to 3D rock permeability using calibration parameters. We perform step 1 using Lattice-Boltzmann and finite difference schemes, which are memory efficient. We discuss two models to perform step 2. Our two-step approach is fast and efficient, since it does not require reconstruction of the unknown 3D rock using 2D thin section information. We establish the applicability of this new approach using a dataset comprised of LBM-computed permeability of rock samples from various geologic formations, including Fontainebleau sandstone, Berea sandstone, Bituminous sand, and Grosmont carbonate. We find that for sandstones our approach predicts fairly accurate permeability with little calibration. Predicting permeability of carbonates from thin sections is more challenging due to microstructural complexity thus model parameters require more calibration. For general workflow, we propose to first calibrate the proposed models using the available 3D information on the rock microstructure (from microCT, SEM, etc.) and then predict the permeability for rocks from the same geological formation for which only 2D thin sections are available.

Forced oscillation measurements of seismic attenuation in fluid saturated sandstone

Adopting the method of forced oscillation, attenuation was studied in Fontainebleau sandstone (porosity 10%, permeability 10 mD) at seismic frequencies (1–100 Hz). Confining pressures of 5, 10, and 15 MPa were chosen to simulate reservoir conditions. First, the strain effect on attenuation was investigated in the dry sample for 11 different strains across the range 1 × 10−6–8 × 10−6, at the confining pressure of 5 MPa. The comparison showed that a strain of at least 5 × 10−6 is necessary to obtain a good signal to noise ratio. These results also indicate that nonlinear effects are absent for strains up to 8 × 10−6. For all the confining pressures, attenuation in the dry rock was low, while partial (90%) and full (100%) saturation with water yielded a higher magnitude and frequency dependence of attenuation. The observed high and frequency dependent attenuation was interpreted as being caused by squirt flow.