Steffen Schlüter

Image processing of multiphase images obtained via X-ray microtomography: A review

Easier access to X-ray microtomography (μCT) facilities has provided much new insight from high-resolution imaging for various problems in porous media research. Pore space analysis with respect to functional properties usually requires segmentation of the intensity data into different classes. Image segmentation is a nontrivial problem that may have a profound impact on all subsequent image analyses. This review deals with two issues that are neglected in most of the recent studies on image segmentation: (i) focus on multiclass segmentation and (ii) detailed descriptions as to why a specific method may fail together with strategies for preventing the failure by applying suitable image enhancement prior to segmentation. In this way, the presented algorithms become very robust and are less prone to operator bias. Three different test images are examined: a synthetic image with ground-truth information, a synchrotron image of precision beads with three different fluids residing in the pore space, and a μCT image of a soil sample containing macropores, rocks, organic matter, and the soil matrix. Image blur is identified as the major cause for poor segmentation results. Other impairments of the raw data like noise, ring artifacts, and intensity variation can be removed with current image enhancement methods. Bayesian Markov random field segmentation, watershed segmentation, and converging active contours are well suited for multiclass segmentation, yet with different success to correct for partial volume effects and conserve small image features simultaneously.

Quantification of soil structure based on Minkowski functions

The structure of soils and other geologic media is a complex three-dimensional object. Most of the physical material properties including mechanical and hydraulic characteristics are immediately linked to the structure given by the pore space and its spatial distribution. It is an old dream and still a formidable challenge to relate structural features of porous media to their functional properties. Using tomographic techniques, soil structure can be directly observed at a range of spatial scales. In this paper we present a scale-invariant concept to quantify complex structures based on a limited set of meaningful morphological functions. They are based on d+1 Minkowski functionals as defined for d-dimensional bodies. These basic quantities are determined as a function of pore size or aggregate size obtained by filter procedures using mathematical morphology. The resulting Minkowski functions provide valuable information on the size of pores and aggregates, the pore surface area and the pore topology having the potential to be linked to physical properties. The theoretical background and the related algorithms are presented and the approach is demonstrated for the pore structure of an arable soil and the pore structure of a sand both obtained by X-ray micro-tomography. We also analyze the fundamental problem of limited resolution which is critical for any attempt to quantify structural features at any scale using samples of different size recorded at different resolutions. The results demonstrate that objects smaller than 5 voxels are critical for quantitative analysis.

Segmentation of X-ray microtomography images of soil using gradient masks

For many analyses, grey scale images from X-ray tomography and other sources need to be segmented into objects and background which often is a difficult task and afflicted by an arbitrary and subjective choice of threshold values. This is especially true if the volume fraction of objects is small and the histogram becomes unimodal. Bi-level segmentation based on region growing is a promising approach to cope with the fuzzy transition zone between object and background due to the partial volume effect, but until now there is no method to properly determine the required thresholds in case of unimodality. We propose an automatic and robust technique for threshold selection based on edge detection. The method uses gradient masks which are defined as regions of interest for the determination of threshold values. Its robustness is analysed by a systematic performance test and finally demonstrated for the segmentation of pores in different soils using images from X-ray tomography.

Pore-scale displacement mechanisms as a source of hysteresis for two-phase flow in porous media

The macroscopic description of the hysteretic behavior of two-phase flow in porous media remains a challenge. It is not obvious how to represent the underlying pore-scale processes at the Darcy-scale in a consistent way. Darcy-scale thermodynamic models do not completely eliminate hysteresis and our findings indicate that the shape of displacement fronts is an additional source of hysteresis that has not been considered before. This is a shortcoming because effective process behavior such as trapping efficiency of CO2 or oil production during water flooding are directly linked to pore-scale displacement mechanisms with very different front shape such as capillary fingering, flat frontal displacement, or cluster growth. Here we introduce fluid topology, expressed by the Euler characteristic of the nonwetting phase (χn), as a shape measure of displacement fronts. Using two high-quality data sets obtained by fast X-ray tomography, we show that χn is hysteretic between drainage and imbibition and characteristic for the underlying displacement pattern. In a more physical sense, the Euler characteristic can be interpreted as a parameter describing local fluid connectedness. It may provide the closing link between a topological characterization and macroscopic formulations of two-phase immiscible displacement in porous rock. Since fast X-ray tomography is currently becoming a mature technique, we expect a significant growth in high-quality data sets of real time fluid displacement processes in the future. The novel measures of fluid topology presented here have the potential to become standard metrics needed to fully explore them.

On the challenges of measuring interfacial characteristics of three‐phase fluid flow with x‐ray microtomography

Synchrotron‐based x‐ray computed microtomography contributes high‐resolution, three‐dimensional observations to investigations of multiphase fluid transport in porous media. Pore‐scale observations are valuable to the development and validation of new theory, as well as numerical models. Computed microtomography has been used previously to measure fluid content and interfacial areas in systems containing two fluids (air–water, oil–water) and to a limited extent to measure fluid content and entrapped fluid morphology in systems containing three fluids (air–oil–water). This study addresses challenges that arise when imaging three‐phase flow in spreading systems. The first challenge is related to wettability alteration. Observations reported herein suggest that the wettability of solid surfaces changed over the course of a three‐fluid phase flow experiment, a phenomenon that has not been observed in similar, previously conducted two‐fluid phase experiments. Follow‐up experiments showed that wettability alteration is significant when oil–solid contact is combined with x‐ray exposure, and is not reversed with a conventional cleaning procedure.

Time scales of relaxation dynamics during transient conditions in two‐phase flow

The relaxation dynamics towards a hydrostatic equilibrium after a change in phase saturation in porous media is governed by fluid reconfiguration at the pore scale. Little is known whether a hydrostatic equilibrium in which all interfaces come to rest is ever reached and which microscopic processes govern the time scales of relaxation. Here we apply fast synchrotron-based X-ray tomography (X-ray CT) to measure the slow relaxation dynamics of fluid interfaces in a glass bead pack after fast drainage of the sample. The relaxation of interfaces triggers internal redistribution of fluids, reduces the surface energy stored in the fluid interfaces and relaxes the contact angle towards the equilibrium value while the fluid topology remains unchanged. The equilibration of capillary pressures occurs in two stages: (i) a quick relaxation within seconds in which most of the pressure drop that built up during drainage is dissipated, a process that is to fast to be captured with fast X-ray CT, and (ii) a slow relaxation with characteristic time scales of 1-4 h which manifests itself as a spontaneous imbibition process that is well described by the Washburn equation for capillary rise in porous media. The slow relaxation implies that a hydrostatic equilibrium is hardly ever attained in practice when conducting two-phase experiments in which a flux boundary condition is changed from flow to no-flow. Implications for experiments with pressure boundary conditions are discussed.

Generating random fields with a truncated power-law variogram: A comparison of several numerical methods

In this study we describe and compare four numerical methods for the generation of random fields with a truncated power-law variogram; the Fourier method, the Randomization method, the Hybrid method as well as the Fourier-Wavelet method. We evaluate these methods with respect to their ability to represent the variogram function over a number of spatial scales as well as the Gaussianity of the generated fields. We furthermore compare these methods with respect to computational costs and investigate structural features.Results show that the Randomization method performs well if only a few number of spatial scales (4-6 orders of magnitude) need to be represented. Due to its simpler implementation it can be preferred over the Fourier-Wavelet method. For a larger interval of spatial scales (9-12 orders of magnitude) however, the Randomization method fails to represent the variogram. Under such circumstances the Hybrid method or the Fourier-Wavelet method should be used.The Matlab code, used for the simulations can be accessed on our institution website at http://www.ufz.de/index.php?en=32179. We investigate the generation of random fields with a truncated power-law variogram.Several methods are compared with respect to different criteria.The variogram function is reproduced over several spatial scales by the Hybrid method and the Fourier-Wavelet method.The reproduction of the variogram function strongly depends on its heavy tailing.The scale-invariance for structural properties in the fractal regime is achieved best by the Hybrid method.

Analysis of Soil Structure Turnover with Garnet Particles and X-Ray Microtomography.

Matter turnover in soil is tightly linked to soil structure which governs the heterogeneous distribution of habitats, reaction sites and pathways in soil. Thereby, the temporal dynamics of soil structure alteration is deemed to be important for essential ecosystem functions of soil but very little is known about it. A major reason for this knowledge gap is the lack of methods to study soil structure turnover directly at microscopic scales. Here we devise a conceptual approach and an image processing workflow to study soil structure turnover by labeling some initial state of soil structure with small garnet particles and tracking their fate with X-ray microtomography. The particles adhere to aggregate boundaries at the beginning of the experiment but gradually change their position relative to the nearest pore as structure formation progresses and pores are destructed or newly formed. A new metric based on the contact distances between particles and pores is proposed that allows for a direct quantification of soil structure turnover rates. The methodology is tested for a case study about soil compaction of a silty loam soil during stepwise increase of bulk density (ρ = {1.1, 1.3, 1.5} g/cm3). We demonstrate that the analysis of mean contact distances provides genuinely new insights about changing diffusion pathways that cannot be inferred neither from conventional pore space attributes (porosity, mean pore size, pore connectivity) nor from deformation analysis with digital image correlation. This structure labeling approach to quantify soil structure turnover provides a direct analogy to stable isotope labeling for the analysis of matter turnover and can be readily combined with each other.

How much is too much?—Influence of X-ray dose on root growth of faba bean (Vicia faba) and barley (Hordeum vulgare)

X-ray CT is a powerful technology to study root growth in soil in-situ. Root systems can be studied in its true 3D geometry over time. Hence, the same plant can be scanned multiple times during development. A downside is the potential of X-rays to interfere with biological processes and therefore plant growth. The aim of this study is to evaluate the influence of cumulative X-ray dose on Vicia faba and Hordeum vulgare during a growth period of 17 days. One control treatment without X-ray scanning was compared to two treatments being scanned every two and four days, respectively. Scanned treatments received a maximum cumulative dose of less than 8 Gy. Plant species differed in their susceptibility to X-ray dose. For Vicia faba, mean total root length was reduced significantly. Leave growth was reduced as well. Number and length of second order laterals was reduced significantly, as well as length of first order laterals. Hordeum vulgare showed no negative impact of X-ray dose on any of the root parameters. Large differences between the two species investigated were detected in respect to susceptibility to X-ray dose. Results indicate that for X-ray CT studies involving temporal resolution a control treatment without scanning is required.

Emergent Properties of Microbial Activity in Heterogeneous Soil Microenvironments: Different Research Approaches Are Slowly Converging, Yet Major Challenges Remain

Over the last 60 years, soil microbiologists have accumulated a wealth of experimental data showing that the bulk, macroscopic parameters (e.g., granulometry, pH, soil organic matter, and biomass contents) commonly used to characterize soils provide insufficient information to describe quantitatively the activity of soil microorganisms and some of its outcomes, like the emission of greenhouse gasses. Clearly, new, more appropriate macroscopic parameters are needed, which reflect better the spatial heterogeneity of soils at the microscale (i.e., the pore scale) that is commensurate with the habitat of many microorganisms. For a long time, spectroscopic and microscopic tools were lacking to quantify processes at that scale, but major technological advances over the last 15 years have made suitable equipment available to researchers. In this context, the objective of the present article is to review progress achieved to date in the significant research program that has ensued. This program can be rationalized as a sequence of steps, namely the quantification and modeling of the physical-, (bio)chemical-, and microbiological properties of soils, the integration of these different perspectives into a unified theory, its upscaling to the macroscopic scale, and, eventually, the development of new approaches to measure macroscopic soil characteristics. At this stage, significant progress has been achieved on the physical front, and to a lesser extent on the (bio)chemical one as well, both in terms of experiments and modeling. With regard to the microbial aspects, although a lot of work has been devoted to the modeling of bacterial and fungal activity in soils at the pore scale, the appropriateness of model assumptions cannot be readily assessed because of the scarcity of relevant experimental data. For significant progress to be made, it is crucial to make sure that research on the microbial components of soil systems does not keep lagging behind the work on the physical and (bio)chemical characteristics. Concerning the subsequent steps in the program, very little integration of the various disciplinary perspectives has occurred so far, and, as a result, researchers have not yet been able to tackle the scaling up to the macroscopic level. Many challenges, some of them daunting, remain on the path ahead. Fortunately, a number of these challenges may be resolved by brand new measuring equipment that will become commercially available in the very near future.