Images Of Sandstone Research Articles

Impact of the cracks lost in the imaging process on computing linear elastic properties from 3D microtomographic images of Berea sandstone

With the current developments in imaging/computational techniques and resources, computational rock physics has been emerging as a new field of study. Properties of rocks are examined by carrying out extensive numerical simulations on rocks that have been digitized using high-resolution X-ray CT scans. The ultimate goal of computational rock physics is to supplement the traditional laboratory measurements, which are time consuming, with faster numerical simulations that allow the parameter space to be explored more thoroughly. We applied the finite-element method to compute the static effective elastic properties from 3D microtomographic images of Berea sandstone saturated with different fluids. From the computations, we found discrepancies between the numerical results and the laboratory measurements. The reason for such a problem is the loss of small features, such as fine cracks and micropores, in the digitized matrix during the imaging and aggregation process. We used a hybrid approach, combining the numerical computation and the effective media theories — the differential effective medium model and the Kuster-Toksöz model — to deduce the lost cracks by a very fast simulated annealing method. We analyzed the sensitivity of the inverted results — the distributions of crack aspect ratios and concentrations — to the clay content. We found that the inverted crack distribution is not so sensitive to clay content. Compared with the effect of cracks on the computed effective elastic properties, clay has only a secondary effect. Our approach can recover the lost cracks and is capable of predicting the effective elastic properties of the rocks from the microtomographic images for different fluid saturations. Compared with the traditional inversion schemes, based only on the effective media theories, this hybrid scheme has the advantage of utilizing the complex microstructures that are resolved in the imaging process, and it helps define the inversion space for crack distribution.

Relative Permeability Calculations from Two-Phase Flow Simulations Directly on Digital Images of Porous Rocks

We present results from a systematic study of relative permeability functions derived from two-phase lattice Boltzmann (LB) simulations on X-ray microtomography pore space images of Bentheimer and Berea sandstone. The simulations mimic both unsteady- and steady-state experiments for measuring relative permeability. For steady-state flow, we reproduce drainage and imbibition relative permeability curves that are in good agreement with available experimental steady-state data. Relative permeabilities from unsteady-state displacements are derived by explicit calculations using the Johnson, Bossler and Naumann method with input from simulated production and pressure profiles. We find that the nonwetting phase relative permeability for drainage is over-predicted compared to the steady-state data. This is due to transient dynamic effects causing viscous instabilities. Thus, the calculated unsteady-state relative permeabilities for the drainage is fundamentally different from the steady-state situation where transient effects have vanished. These effects have a larger impact on the invading nonwetting fluid than the defending wetting fluid. Unsteady-state imbibition relative permeabilities are comparable to the steady-state ones. However, the appearance of a piston-like front disguises most of the displacement and data can only be determined for a restricted range of saturations. Relative permeabilities derived from unsteady-state displacements exhibit clear rate effects, and residual saturations depend strongly on the capillary number. We conclude that the LB method can provide a versatile tool to compute multiphase flow properties from pore space images and to explore the effects of imposed flow and fluid conditions on these properties. Also, dynamic effects are properly captured by the method, giving the opportunity to examine differences between steady and unsteady-state setups.

Micropore Structure Representation of Sandstone in Petroleum Reservoirs Using an Atomic Force Microscope

The pore structure of sandstone in an oil reservoir is investigated using atomic force microscopy (AFM). At nanoscale resolution, AFM images of sandstone show us the fine structure. The real height data of images display the three-dimensional space structure of sandstone effectively. The three-dimensional analysis results show that the AFM images of sandstone have unique characteristics that, like fingerprints, can identify different structural properties of sandstones. The results demonstrate that AFM is an effective method used to represent original sandstone in petroleum reservoirs, and may help geologists to appreciate the sandstone in oil reservoirs fully.

Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations

Tomographic images taken inside and outside a compaction band in a field specimen of Aztec sandstone are analyzed by using numerical methods such as graph theory, level sets, and hybrid lattice Boltzmann/finite element techniques. The results reveal approximately an order of magnitude permeability reduction within the compaction band. This is less than the several orders of magnitude reduction measured from hydraulic experiments on compaction bands formed in laboratory experiments and about one order of magnitude less than inferences from two-dimensional images of Aztec sandstone. Geometrical analysis concludes that the elimination of connected pore space and increased tortuosities due to the porosity decrease are the major factors contributing to the permeability reduction. In addition, the multiscale flow simulations also indicate that permeability is fairly isotropic inside and outside the compaction band.

Automatic identification of microcracks observed on microscopic images of coarse-grained sandstone

Automatic identification of microcracks observed on microscopic images of coarse-grained sandstone

The Multiscale Pore Connectivity Network via Scaling Relationship Derived from a Sandstone Image

This paper presents a study on a multiscale pore connectivity network derived from a sandstone image. We first convert a grayscale sandstone image into pore and grain regions. The binary pore‐grain image is transformed into multiscale pore by performing morphological opening operations with increasing structuring element size. A pore connectivity network (PCN), which is a skeleton network that describes the structure of pore space from multiscale pore‐grain images, is extracted. The PCN can be computed by using morphological transformations with reference to three different probing rules (in the form of octagon, square, and rhombus). It is observed that the length of multiscale PCN varies with the number of opening transformations. This is due to the fact that the intricacy of the pore image is reduced with the increasing cycle of opening transformations. Next, we estimate the fractal dimensions of these multiscale PCNs using box‐counting method. The values obtained follow universal power‐law relationships. We further analyze the relationship of multidimensional opening in quantitative manner. A rescaled formula based on the linearity of decreasing fractal dimension values of pore space is proposed. This technique is applied to estimate the fractal dimensions of a sequence of multi‐dimensional sandstone image generated by morphological opening.

X-ray tomography measurements of power-law cluster size distributions for the nonwetting phase in sandstones

Three-dimensional images of sandstones containing residual nonwetting phase were obtained using synchrotron x-ray tomography with a resolution of approximately 9 μm. We determined the size distribution of disconnected nonwetting phase clusters (ganglia); the number of ganglia of size s is N(s)~s(-τ) with τ=2.05 . The vast majority of the residual phase was contained in large clusters, spanning many pores. This result implies that we have clusters of all sizes providing a huge surface area for geochemical reactions and dissolution while allowing mobilization of the residual phase during improved oil recovery in hydrocarbon reservoirs and carbon dioxide storage in aquifers.

A semi-analytical model for computation of capillary entry pressures and fluid configurations in uniformly-wet pore spaces from 2D rock images

A novel semi-analytical model for computation of capillary entry pressures and associated fluid configurations in arbitrary, potentially non-convex, 2D pore space geometries at uniform wettability is developed. The model computes all possible centre positions of circular arcs, and physically sound criteria are implemented to determine the set of these arcs that correspond to geometrically allowed interfaces. Interfaces and pore boundary segments are connected to form closed boundaries of identified geometrical regions. These regions are classified as either oil regions, located in the wider parts of the pore space, or as water regions located in pore space constrictions. All possible region combinations are identified and evaluated for each radius value in an iterative procedure to determine the favourable entry radius and corresponding configuration based on minimisation of free energy. The model has been validated by comparison with known analytical solutions in idealised pore geometries. In cases where different analytical solutions are geometrically possible, the model generates several oil and water regions, and the valid solution is determined by the region combination that corresponds to the most favourable entry pressure, consistent with the analytical solution. Entry pressure radii and configurations are computed in strongly non-convex pore spaces extracted from an image of Bentheimer sandstone, which demonstrates that the model captures successfully well-known characteristics of capillary behaviour at different wetting conditions. The computations also demonstrate the importance of selecting the fluid configuration of minimum change in free energy. In some cases, a merged region formed by a combination of oil and water regions corresponds to the favourable entry configuration of oil, whereas in other cases, an individual oil region may correspond to the favourable oil entry configuration. It is also demonstrated that oil entry configurations may constitute merged regions for weakly water-wet conditions and individual oil regions for strongly water-wet conditions in the same pore space. The computations show that the ratio of pore area to perimeter multiplied by the cosine of the contact angle under-predicts the entry pressure radii in Bentheimer sandstone pore spaces. An alternative formula is proposed for prediction of entry radii for nonzero contact angles based on the entry radii obtained for zero contact angles.

Network flow modeling via lattice-Boltzmann based channel conductance

Lattice-Boltzmann (LB) computations of single phase, pore-to-pore conductance are compared to models in which such conductances are computed via standard pore body–channel–pore body series resistance (SR), with the conductance of each individual element (pore body, channel) based on geometric shape factor measurements. The LB computations, based upon actual channel geometry derived from X-ray computed tomographic imagery, reveal that the variation in conductance for channels having similar shape factor is much larger than is adequately captured by the geometric models. Fits to the dependence of median value of conductance versus shape factor from the LB-based computations show a power law dependence of higher power than that predicted by the geometric models. We introduce two network flow models based upon the LB conductance computations: one model is based upon LB computations for each pore-to-pore connection; the second is based upon a power law fit to the relationship between computed conductance and throat shape factor. Bulk absolute permeabilities for Fontainebleau sandstone images are computed using the SR-based network models and the two LB-based models. Both LB-based network models produce bulk absolute permeability values that fit published data more accurately than the SR-based models.

An image processing algorithm for the reversed transformation of rotated microscope images

This paper presents an image processing algorithm for reversed transformation of rock structure images taken with polarizing microscope stage rotations. The algorithm is applied for the analysis of microscope images of Tumlin sandstone. The most important property of the proposed method is that the operation is based on global image information to find the best fit angle and vector. The idea of the algorithm is based on finding the optimal rotation angle and optimal translation vector, thus ensuring the best correspondence between analysed images. The criteria for optimization are formulated on the basis of the shapes of edges located on images. The proposed algorithm can be used as an alternative solution in the case when a rotating polarizer stage is not available. Moreover, the proposed algorithm makes it possible to use matched images for the automatic identification of the rock structures such as grain boundaries, cracks and pores.

Effect of network topology on two-phase imbibition relative permeability

In a previous study Arns et al. (2004, Transport Porous Media 55, 21-46) weconsideredtheroleoftopologyondrainagerelativepermeabilitycurvescomputed using network models derived from a suite of tomographic images of Fontainebleau sandstone. The present study extends the analysis to more complex imbibition dis- placements where the non-wetting fluid can be disconnected by snap-off as a result of swelling of wetting films in the corners of pores and throats. In contrast to the findings for drainage displacements which showed that relative permeabilities are significantly affected by network topology, the present study shows that the effect of topology on imbibition relative permeabilities depends on the level of snap-off. For strongly wetting conditions where snap-off dominates the displacement the effect of network topology is significantly smaller than for weakly wet conditions where snap-off is suppressed. For contact angles sufficiently large to completely suppress snap-off, the effect of topology on imbibition relative permeabilities is similar to that for drainage displacements. The findings are valid for random networks and for networks displaying short-range pore-throat and longer range spatial correlations.

Second-order analysis by variograms for curvature measures of two-phase structures

Second-order characteristics are important in the description of various geometrical structures occurring in foams, porous media, complex fluids, and phase separation processes. The classical second order characteristics are pair correlation functions, which are well-known in the context of point fields and mass distributions. This paper studies systematically these and further characteristics from a unified standpoint, based on four so-called curvature measures, volume, surface area, integral of mean curvature and Euler characteristic. Their statistical estimation is straightforward only in the case of the volume measure, for which the pair correlation function is traditionally called the two-point correlation function. For the other three measures a statistical method is described which yields smoothed surrogates for pair correlation functions, namely variograms. Variograms lead to an enhanced understanding of the variability of the geometry of two-phase structures and can help in finding suitable models. The use of the statistical method is demonstrated for simulated samples related to Poisson-Voronoi tessellations, for experimental 3D images of Fontainebleau sandstone and for two samples of industrial foams.

Reconstruction of pore space from a pore connectivity network via morphological transformations

SummaryPore and grain regions were separated via thresholding techniques from sandstone images. A mathematical morphology‐based framework was followed to pack the random pore space with overlapping and nonoverlapping disks. This framework has several advantages in implementation and is generally applicable to multiscale images. The random pore space was reconstructed in two ways from the minimum morphological information through: (a) overlapping and (b) nonoverlapping disks of various shapes and sizes. The structuring elements employed to carry out this analysis included octagon, square and rhombus templates. The results achieved through these two types of reconstruction of sandstone pores are compared. These results provided the basis on which to test the accuracy of these techniques. Reconstruction recovery was tested by computing shapiness indices for the reconstructed pores achieved through the two methods.

Imaging of Rock Pores by X-ray Computed Tomography

Three-dimensional measurements of the complex shapes of pores in porous rocks are essential for quantitative discussions of material transport in strata. X-ray computed tomography (CT) visualizes the three-dimensional distribution of X-ray linear absorption coefficients of rock samples, and is a useful non-destructive technique for measuring pore shape. Some examples of the application of X-ray CT to rock pore imaging are shown to facilitate petrophysical CT studies in Japan. The 3-dimensional pore images were obtained for sandy sediment, rhyolitic/andesitic lavas, and sandstone. Pore connectivity analysis and tortuosity estimate were demonstrated using sandstone image data.

Imaging of Rock Pores by X-ray Computed Tomography

Three-dimensional measurements of the complex shapes of pores in porous rocks are essential for quantitative discussions of material transport in strata. X-ray computed tomography (CT) visualizes the three-dimensional distribution of X-ray linear absorption coefficients of rock samples, and is a useful non-destructive technique for measuring pore shape. Some examples of the application of X-ray CT to rock pore imaging are shown to facilitate petrophysical CT studies in Japan. The 3-dimensional pore images were obtained for sandy sediment, rhyolitic/andesitic lavas, and sandstone. Pore connectivity analysis and tortuosity estimate were demonstrated using sandstone image data.

Virtual permeametry on microtomographic images

We show that accurate numerical micropermeametry measurements can be performed on three-dimensional (3D) digitized images of sedimentary rock. The sample size can be very small, making it possible to predict properties from core material not suited for laboratory testing (e.g., drill cuttings, sidewall core and damaged core plugs). Simulation of fluid permeability on microtomographic images of Fontainebleau sandstone on sample sizes of less than 1 mm 3 are in good agreement with experimental measurements over a wide range of porosities.

Effect of Network Topology on Relative Permeability

We consider the role of topology on drainage relative permeabilities derived from network models. We describe the topological properties of rock networks derived from a suite of tomographic images of Fontainbleau sandstone (Lindquist et al., 2000, J. Geophys. Res.105B, 21508). All rock networks display a broad distribution of coordination number and the presence of long-range topological bonds. We show the importance of accurately reproducing sample topology when deriving relative permeability curves from the model networks. Comparisons between the relative permeability curves for the rock networks and those computed on a regular cubic lattice with identical geometric characteristics (pore and throat size distributions) show poor agreement. Relative permeabilities computed on regular lattices and on diluted lattices with a similar average coordination number to the rock networks also display poor agreement. We find that relative permeability curves computed on stochastic networks which honour the full coordination number distribution of the rock networks produce reasonable agreement with the rock networks. We show that random and regular lattices with the same coordination number distribution produce similar relative permeabilities and that the introduction of longer-range topological bonds has only a small effect. We show that relative permeabilities for networks exhibiting pore–throat size correlations and sizes up to the core-scale still exhibit a significant dependence on network topology. The results show the importance of incorporating realistic 3D topologies in network models for predicting multiphase flow properties.

Relative permeability from tomographic images; effect of correlated heterogeneity

We examine the calculation of relative permeability and residual saturation using networks derived from tomographic images of Fontainebleau sandstone previously used to successfully calculate single-phase transport properties. In contrast to electrical conductivity and permeability calculations, we find that that computed relative permeabilities and residual saturations for samples of the same sandstone display a high degree of variability. Randomizing pores and throats to remove all correlations almost completely eliminates the variability between samples and produces smooth numerical data sets. We conclude that correlations in rock microstructure, which appear to have little effect on the calculation of single fluid properties, have a major effect on computed relative permeability and residual saturation.

Morphological decomposition of sandstone pore–space: fractal power-laws

Morphological decomposition procedure is applied to estimate fractal dimension of a pore–space, which is isolated from a sandstone microphotograph. The fractal dimensions that have been computed by considering various probing rules have precisely followed the universal power-law relationships proposed elsewhere. These results are derived by considering structuring elements such as octagon, square and rhombus that have been used to decompose the pore–space of sandstone image. The radii of the structuring elements are made to increase in a cyclic fashion. To perceive the decomposed pore image, a color-coding scheme is adapted, from which one can identify several sizes of these structuring elements that could be fit into this pore. This exercise facilitates testing of the relationship between the radius of the structuring elements that could be used to decompose the pore at different levels, and the number of decomposed shapes that could be fit into the pore while using the corresponding structuring element. From the number–radius relationship, the fractal dimensions of pore–space estimated, by considering these structuring elements, yield the values of 1.82, 1.76, and 1.79. These values are in conformity with the values arising from estimation of box dimension method, as well as the dimensions of the corresponding pore connectivity networks (PCNs).

PETROPHYSICAL PROPERTIES DERIVED FROM X-RAY CT IMAGES

A micro-CT facility for imaging, visualising and modelling sedimentary rock properties in three dimensions (3D) is described. The facility is capable of acquiring 3D X-ray CT images of full-diameter cores and core plugs at up to 2,0003 voxels with resolutions down to 2μm. This allows the 3D pore-space of a rock to be imaged and, with the aid of SEM, to identify regions of different mineralogy. Computational results are presented which demonstrate that accurate predictions of petrophysical properties can be made directly from the digitised tomographic images. Computations of both formation factor and permeability from micro-tomographic images of Fontainebleau sandstone are shown to be in excellent agreement with experimental measurements over a wide range of porosities. Computed elastic properties for dry and water-saturated conditions are shown to be consistent with the exact Gassmann’s equations and are in excellent agreement with experimental measurements. Experimental measurements of Vp/Vs ratio for cemented sandstone morphologies are very noisy and cannot be used to infer relationships between elastic properties, mineralogy and rock microstructure. Computations on tomographic images show that the Vp/Vs ratio exhibits predictable limiting behavior which holds for any number of solid phases and is insensitive to the manner in which the phases are distributed. This allows the development of more accurate empirical methods for deriving the full velocity-porosity relationship for cemented sands. The results demonstrate the feasibility of combining digitised images with numerical calculations to accurately predict petrophysical properties of individual rock morphologies.