Kirill M. Gerke

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.

Prediction and Evaluation of Time-Dependent Effective Self-diffusivity of Water and Other Effective Transport Properties Associated with Reconstructed Porous Solids

We reconstructed pore structures of three porous solids that differ from each other in morphology and topology of pore space. To achieve this, we used a stochastic method based on simulated annealing and X-ray computed microtomography. Simulated annealing was constrained by the following microstructural descriptors sampled along the principal and diagonal directions: the two-point probability function for the void phase and the lineal-path functions for both void and solid phases. The stochastic method also assumed the isotropic pore structures in accordance with a recent paper (Čapek et al. in Transp Porous Media 88(1): 87–106 (2011)). With the exception of the solid with the widest pores, we made tomographic volume images in high and low resolution, which enabled us to study the effect of resolution on microstructural descriptors and effective transport properties. A comparison of the two-point probability function and the lineal-path function sampled in the principal directions revealed that the pore structures derived from the tomographic volume images were slightly anisotropic, in opposition to the assumption of the stochastic method. Besides the anisotropy, other microstructural descriptors including the pore-size function and the total fraction of percolating cells indicated that the morphological and topological characteristics of the pore structures depended on the reconstruction method and its parameters. Particularly, the pore structures reproduced using the stochastic method contained wider pores than those obtained using X-ray tomography. Deviations between the pore structures derived from low- and high-resolution tomographic volume images were also observed and imputed to partial volume artefacts. Then, viscous flow of incompressible liquid, ordinary diffusion, Knudsen flow and self-diffusion of water in the reconstructed pore spaces were simulated. As counterparts, experimental data were measured by means of permeation and Wicke–Kallenbach cells and pulsed field gradient NMR. Deviations between the simulated quantities on the one hand and experimental data on the other hand were generally acceptable, which corroborated the pore-space models. As expected, the predictions based on the tomographic models of pore space were more successful than those derived from the stochastic models. The stationary effective transport properties, i.e. the effective permeability, the effective pore size and the geometric factor, were sensitive to a bias in long-range pore connectivity. Furthermore, the time-dependent effective diffusivity was found to be especially sensitive to relatively small morphological deviations between the real and reconstructed pore structures. It is concluded that the combined predictions of the effective permeability, the effective pore size, the geometric factor and time-dependent effective self-diffusivity of water are needed for the reliable evaluation of pore-space reconstruction.

Criteria for selecting fluorescent dye tracers for soil hydrological applications using Uranine as an example

Abstract Calibrating and verifying 2-D and 3-D vadose zone flow and transport models requires detailed information on water and solute redistribution. Among the different water flow and mass transfer determination methods, staining tracers have the best spatial resolution allowing visualization and quantification of fluid flow including preferential flow paths. Staining techniques have been used successfully for several decades; however, the hydrological community is still searching for an “ideal” vadose zone tracer regarding flow path visualization. To date, most research using staining dyes is carried out with Brilliant Blue FCF. Fluorescent dyes such as Uranine, however, have significant advantages over nonfluorescents which makes them a promising alternative. This paper presents the first analysis of key properties any fluorescent substance must possess to qualify as a staining fluorescent tracer in vadose zone hydrological applications. First, we summarize the main physico-chemical properties of Uranine and evaluate its staining tracer potential with conventional suitability indicators and visibility testing in a soil profile. Based on numerical analysis using the theory of fluorescence, we show that a low molar absorption coefficient is a crucial parameter to quantify concentration accurately. In addition, excitation of a tracer on wavelengths different from the maximum excitation wavelength can extend the linear range of the concentration-fluorescence relationship significantly. Finally, we develop criteria for evaluating the suitability of any potential fluorescent soil staining compound for soil hydrological applications: 1) high quantum yield, 2) low molar absorption coefficient, 3) fluorescence independent of temperature, 4) low photodecomposition rates, and 5) fluorescence stable across a wide range of pH values.

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