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Register a new userVariety of stylolites morphologies and statistical characterization of the amount of heterogeneities in the rock
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Authors
Alexandre Brouste
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The surface roughness of several stylolites in limestones was measured using high resolution laser profilometry. The 1D signals obtained were statistically analyzed to determine the scaling behavior and calculate a roughness exponent, also called Hurst exponent. Statistical methods based on the characterization of a single Hurst exponent imply strong assumptions on the mathematical characteristics of the signal: the derivative of the signal (or local increments) should be stationary and have finite variance. The analysis of the measured stylolites show that these properties are not always verified simultaneously. The stylolite profiles show persistence and jumps and several stylolites are not regular, with alternating regular and irregular portions. A new statistical method is proposed here, based on a non-stationary but Gaussian model, to estimate the roughness of the profiles and quantify the heterogeneity of stylolites. This statistical method is based on two parameters: the local roughness (H) which describes the local amplitude of the stylolite, and the amount of irregularities on the signal (mu), which can be linked to the heterogeneities initially present in the rock before the stylolite formed. Using this technique, a classification of the stylolites in two families is proposed: those for which the morphology is homogeneous everywhere and those with alternating regular and irregular portions.
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Stylolites are ubiquitous geo-patterns observed in rocks in the upper crust, from geological reservoirs in sedimentary rocks to deformation zones, in folds, faults, and shear zones. These rough surfaces play a major role in the dissolution of rocks around stressed contacts, the transport of dissolved material and the precipitation in surrounding pores. Consequently, they play an active role in the evolution of rock microstructures and rheological properties in the Earths crust. They are observed individually or in networks, in proximity to fractures and joints, and in numerous geological settings. This review article deals with their geometrical and compositional characteristics and the factors leading to their genesis. The main questions this review focuses on are the following: How do they form? How can they be used to measure strain and formation stress? How do they control fluid flow in the upper crust? Geometrically, stylolites have fractal roughness, with fractal geometrical properties exhibiting typically three scaling regimes: a self-affine scaling with Hurst exponent 1.1+/-0.1 at small scale (up to tens or hundreds of microns), another one with Hurst exponent around 0.5 to 0.6 at intermediate scale (up to millimeters or centimeters), and in the case of sedimentary stylolites, a flat scaling at large scale. More complicated anisotropic scaling (scaling laws depending of the direction of the profile considered) is found in the case of tectonic stylolites. We report models based on first principles from physical chemistry and statistical physics, including a mechanical component for the free-energy associated with stress concentrations, and a precise tracking of the influence of grain-scale heterogeneities and disorder on the resulting (micro)structures. Experimental efforts to reproduce stylolites in the laboratory are also reviewed. We show that although micrometer-size stylolite teeth are obtained in laboratory experiments, teeth deforming numerous grains have not yet been obtained experimentally, which is understandable given the very long formation time of such geometries. Finally, the applications of stylolites as strain and stress markers, to determine paleostress magnitude are reviewed. We show that the scalings in stylolite heights and the crossover scale between these scalings can be used to determine the stress magnitude (its scalar value) perpendicular to the stylolite surface during the stylolite formation, and that the stress anisotropy in the stylolite plane can be determined for the case of tectonic stylolites. We also show that the crossover between medium (millimetric) scales and large (pluricentimetric) scales, in the case of sedimentary stylolites, provides a good marker for the total amount of dissolution, which is still valid even when the largest teeth start to dissolve -- which leads to the loss of information, since the total deformation is not anymore recorded in a single marker structure. We discuss the impact of the stylolites on the evolution of the transport properties of the hosting rock, and show that they promote a permeability increase parallel to the stylolites, whereas their effect on the permeability transverse to the stylolite can be negligible, or may reduce the permeability, depending on the development of the stylolite. Highlights: Stylolite formation depends on rock composition and structure, stress and fluids. Stylolite geometry, fractal and self-affine properties, network structure, are investigated. The experiments and physics-based numerical models for their formation are reviewed. Stylolites can be used as markers of strain, paleostress orientation and magnitude. Stylolites impact transport properties, as function of maturity and flow direction.
Field-scale properties of fractured rocks play crucial role in many subsurface applications, yet methodologies for identification of the statistical parameters of a discrete fracture network (DFN) are scarce. We present an inversion technique to infer two such parameters, fracture density and fractal dimension, from cross-borehole thermal experiments data. It is based on a particle-based heat-transfer model, whose evaluation is accelerated with a deep neural network (DNN) surrogate that is integrated into a grid search. The DNN is trained on a small number of heat-transfer model runs, and predicts the cumulative density function of the thermal field. The latter is used to compute fine posterior distributions of the (to-be-estimated) parameters. Our synthetic experiments reveal that fracture density is well constrained by data, while fractal dimension is harder to determine. Adding non-uniform prior information related to the DFN connectivity improves the inference of this parameter.
This article provides an overview of the current state of digital rock technology, with emphasis on industrial applications. We show how imaging and image analysis can be applied for rock typing and modeling of end-point saturations. Different methods to obtain a digital model of the pore space from pore scale images are presented, and the strengths and weaknesses of the different methods are discussed. We also show how imaging bridges the different subjects of geology, petrophysics and reservoir simulations, by being a common denominator for results in all these subjects. Network modeling is compared to direct simulations on grid models, and their respective strengths are discussed. Finally we present an example of digital rock technology applied to a sandstone oil reservoir. Results from digital rock modeling are compared to results from traditional laboratory experiments. We highlight the mutual benefits from conducting both traditional experiments and digital rock modeling.
SNOLAB is one of the deepest underground laboratories in the world with an overburden of 2092 m. The SNO+ detector is designed to achieve several fundamental physics goals as a low-background experiment, particularly measuring the Earths geoneutrino flux. Here we evaluate the effect of the 2 km overburden on the predicted crustal geoneutrino signal at SNO+. A refined 3D model of the 50 x 50 km upper crust surrounding the detector and a full calculation of survival probability are used to model the U and Th geoneutrino signal. Comparing this signal with that obtained by placing SNO+ at sea level, we highlight a $1.4^{+1.8}_{-0.9}$ TNU signal difference, corresponding to the ~5% of the total crustal contribution. Finally, the impact of the additional crust extending from sea level up to ~300 m was estimated.
Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the existing phase-field models, however, incorporates the impact of surface roughness on the mechanical response of fractures -- such as elastic deformability and shear-induced dilation -- despite the importance of this behavior for subsurface systems. To fill this gap, here we introduce the first framework for phase-field modeling of rough rock fractures. The framework transforms a displacement-jump-based discrete constitutive model for discontinuities into a strain-based continuous model, and then casts it into a phase-field formulation for frictional interfaces. We illustrate the framework by constructing a particular phase-field form employing a rock joint model originally formulated for discrete modeling. The results obtained by the new formulation show excellent agreement with those of a well-established discrete method for a variety of problems ranging from shearing of a single discontinuity to compression of fractured rocks. Consequently, our phase-field framework provides an unprecedented bridge between a discrete constitutive model for rough discontinuities -- common in rock mechanics -- and the continuous finite element method -- standard in computational mechanics -- without any algorithm to explicitly represent discontinuity geometry.
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