Marina V. Karsanina

Improving pattern reconstruction using directional correlation functions

In this letter we introduce a new method to calculate correlation functions in four principal directions (i.e. two orthogonal and two diagonal) and separately utilize them for image reconstruction. We show that this method is particularly suitable for anisotropic porous media but that it also improves image reconstruction for isotropic structures. Based on the analysis of numerous reconstructions of four binary patterns using different sets of two-point probability and linear (for both phases) correlation functions, we quantify the accuracy of each set. Averaging of correlation functions in all directions almost always results in poorer reconstructions. Addition of separate directions significantly improves the quality of replicas with only a minor increase in computational effort.

Universal Stochastic Multiscale Image Fusion: An Example Application for Shale Rock.

Spatial data captured with sensors of different resolution would provide a maximum degree of information if the data were to be merged into a single image representing all scales. We develop a general solution for merging multiscale categorical spatial data into a single dataset using stochastic reconstructions with rescaled correlation functions. The versatility of the method is demonstrated by merging three images of shale rock representing macro, micro and nanoscale spatial information on mineral, organic matter and porosity distribution. Merging multiscale images of shale rock is pivotal to quantify more reliably petrophysical properties needed for production optimization and environmental impacts minimization. Images obtained by X-ray microtomography and scanning electron microscopy were fused into a single image with predefined resolution. The methodology is sufficiently generic for implementation of other stochastic reconstruction techniques, any number of scales, any number of material phases, and any number of images for a given scale. The methodology can be further used to assess effective properties of fused porous media images or to compress voluminous spatial datasets for efficient data storage. Practical applications are not limited to petroleum engineering or more broadly geosciences, but will also find their way in material sciences, climatology, and remote sensing.

Universal spatial correlation functions for describing and reconstructing soil microstructure.

Structural features of porous materials such as soil define the majority of its physical properties, including water infiltration and redistribution, multi-phase flow (e.g. simultaneous water/air flow, or gas exchange between biologically active soil root zone and atmosphere) and solute transport. To characterize soil microstructure, conventional soil science uses such metrics as pore size and pore-size distributions and thin section-derived morphological indicators. However, these descriptors provide only limited amount of information about the complex arrangement of soil structure and have limited capability to reconstruct structural features or predict physical properties. We introduce three different spatial correlation functions as a comprehensive tool to characterize soil microstructure: 1) two-point probability functions, 2) linear functions, and 3) two-point cluster functions. This novel approach was tested on thin-sections (2.21×2.21 cm2) representing eight soils with different pore space configurations. The two-point probability and linear correlation functions were subsequently used as a part of simulated annealing optimization procedures to reconstruct soil structure. Comparison of original and reconstructed images was based on morphological characteristics, cluster correlation functions, total number of pores and pore-size distribution. Results showed excellent agreement for soils with isolated pores, but relatively poor correspondence for soils exhibiting dual-porosity features (i.e. superposition of pores and micro-cracks). Insufficient information content in the correlation function sets used for reconstruction may have contributed to the observed discrepancies. Improved reconstructions may be obtained by adding cluster and other correlation functions into reconstruction sets. Correlation functions and the associated stochastic reconstruction algorithms introduced here are universally applicable in soil science, such as for soil classification, pore-scale modelling of soil properties, soil degradation monitoring, and description of spatial dynamics of soil microbial activity.

Improving stochastic reconstructions by weighting correlation functions in an objective function

Spatial correlation functions (CFs) are prominent descriptors of any structure. In this letter, we show for the first time how proper weighting of CFs in an objective function can lead to significant improvements in reconstruction accuracy and in the likelihood of convergence. We develop a simple weighting scheme and display its effectiveness on two- and three-dimensional structures utilizing up to 27 CFs in one set. Proper weighting of the objective functions led to completely accurate reconstructions not achievable by conventional unweighted approaches. The proposed approach combining numerous CFs can potentially characterize and reconstruct structures of any complexity.

Description and reconstruction of the soil pore space using correlation functions

In this paper a method for the description and reconstruction of the soil pore space using correlation functions has been examined. The reconstruction procedure employed here is the best way of verification of the potential descriptor of the soil pore space. Thin sections representing eight major types of pore space in zonal loamy soils and parent materials of the Russian Plain with pores of different shapes and orientations have been chosen for this study. Comparison based on the morphological analysis of the original pore space images and their correlation function reconstructions obtained using simulated annealing technique indicates that this method of reconstruction adequately describes the isometric soil pore space with isometric dissected, isometric slightly dissected, and rounded pores. The two-point correlation functions calculated with the use of the orthogonal method proved to be different for the examined types of soil pore space; they reflect the soil porosity, specific surface, and pore structure correlations at different lengths. The results of this study allow us to conclude that the description of the soil pore space with the help of correlation functions is a promising approach, but requires more development. Further directions of the development of this method for describing the soil pore space and determining the soil physical processes are outlined.

Determining Physical Properties of Unconventional Reservoir Rocks: from Laboratory Methods to Pore-Scale Modeling

With the rapid progress of imaging methods it is now possible to obtain detailed rock structure information on different scales, ranging from nanometers to micrometers. Such knowledge facilitates use of pore-scale modeling approaches to predict numerous physical properties based on three dimensional structural data. Pore-scale modeling approaches can simulate different processes in the rock under natural conditions (pressure, temperature, etc.), which are more difficult to simulate in the laboratory. This is especially important for unconventional reservoir rocks such as the Bazhen formation siliceous rocks (black shales) used in this study. Based on X-ray microtomography and SEM imaging we develop a detailed categorization of different types of porosities (including micro, i.e. larger than µm size, and nano, i.e. sub-micron size, porosities) for samples of Bazhen siliceous rocks. Standard pore-scale modeling techniques do not account for different flow regimes within different pore sizes. Thus, we develop a pore-network model with different physics of gas flow for micro- and nanoporosity. High-resolution images are used for stochastic reconstructions of 3D structure and subsequently used for modeling of gas permeability. Resulting permeability values are in a good agreement with gas permeabilities measured for Bazhenov siliceous rocks. Finally, we present a framework to model gas permeability of unconventional reservoir rocks using multi-scale 3D structure information based on microCT scans and high resolution SEM/FIB-SEM imaging techniques. Nomenclature

Solution of the stokes equation in three-dimensional geometry by the finite-difference method

The recent progress in the methods for the study of the three-dimensional structure of porous and composite materials (microtomography, confocal microscopy, and FIB-SEM) and the significant improvement in the available computational resources make it possible to simulate various processes directly in the three dimensional geometry of samples of such materials (pore-scale modeling) in order to determine their effective properties or to get a more detailed understanding of the studied processes, such as filtration. In this work, we solve the Stokes equation by the finite-difference method using schemes of the second and fourth orders of accuracy in a three-dimensional domain whose geometry reproduces the microstructure of the investigated rock samples. The numerical values of permeability obtained for a sample of sandstone are consistent with the data of laboratory measurements.

Studying structure and determining permeability of materials based on X-Ray microtomography data (using porous ceramics as an example)

Modern noninvasive methods for probing the three-dimensional structure of materials, such as X-ray tomography, make it possible not only to obtain precise data on the structure of a sample but also to use them for assessing effective properties of the material by numerical methods. We have studied the pore structure of three samples of permeable porous ceramics by X-ray microtomography and numerically determined the permeability by solving the Stokes equation in the three-dimensional geometry of the pore structure. The data thus obtained are in excellent agreement with results of laboratory measurements. Morphological analysis of the pore structure (pore size distribution) allowed us to explain the results obtained for three samples of ceramics produced from granules of various sizes and shapes.