Modeling three‐dimensional hydraulic fracture propagation using virtual multidimensional internal bonds

Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.     

Complications for traditional land consolidation in Central Europe

An integral part of post-socialist transformation under the Washington Consensus has been the privatisation of previously state owned and/or co-operative farms. In many instances, there have been attempts at ‘turning back the clock’ to pre-War conditions, including land ownership structures. Frequently, the result has been the division of large, economically efficient units into numerous, small and economically barely viable private plots. Following accession to the European Union, these re-constituted peasant-scale structures pose a major challenge to the Union’s agricultural policy. As this paper demonstrates, a simple transfer of western European practices, such as land consolidation, is not possible. The particular legacies of the communist system have given land ownership particular values, legitimacy and personal identity, and emotional bonds. Simple technocratic solutions, as applied in the West earlier, are thus not feasible. Consequently, the paper points out, new forms and instruments of tackling disadvantageous agricultural structures need to be found.     

Simulation of hydraulic fracture propagation near a natural fracture using virtual multidimensional internal bonds

A virtual multidimensional internal bond (VMIB) model developed to simulate the propagation of hydraulic fractures using the finite‐element method is formulated within the framework of the virtual internal bond theory (VIB) that considers a solid as randomized material particles in the micro scale, and derives the macro constitutive relation from the cohesive law between the material particles with an implicit fracture criterion. Hydraulic pressure is applied using a new scheme that enables simulation of hydraulically driven cracks. When the model is applied to study hydraulic fracture propagation in the presence of a natural fracture, the results show the method to be very effective. It shows that although the in situ stress ratio is the dominant factor governing the propagation direction, a natural fault can also strongly influence the hydraulic fracture behavior. This influence is conditioned by the shear stiffness of the fault and the distance to the original hydraulic fracture. The model results show that when the fault is strong in shear, its impact on hydraulic fracture trajectory is weak and the hydraulic fracture will likely penetrate the fault. For a weak fault, however, the fracture tends to be arrested at the natural fault. The distance between the fault and the hydraulic fracture is also important; the fault influence increases with decreasing distance. The VMIB does not require selection of a fracture criterion and remeshing when the fracture propagates. Therefore, it is advantageous for modeling fracture initiation and propagation in naturally fractured rock. Copyright © 2010 John Wiley & Sons, Ltd.     

Water organisation at the solid–aqueous solution interfaceOrganisation de l'eau à l'interface solide–solution aqueuse

The aim of this review is to examine the present knowledge about water structure close to an interface or confined in porous spaces. First, the structure of liquid water is briefly described. Though its understanding remains incomplete, it appears that it is largely dominated by the hydrogen bond network and its dynamical evolution. The presence of any ‘foreign’ substance in water perturbs such a structure by changing at least locally the hydrogen bond network. For this reason, the presence of a solid interface significantly modifies the structure of the first adsorbed layers. Whatever the support, it is now clearly evidenced that structural perturbations are limited to distances lower than 10–15 Å from the interface. The nature, energetic heterogeneity and hydrophilicility/hydrophobicity of the solid surface influence the arrangement of water molecules. This surface organisation must definitely be considered when studying adsorption phenomena at the solid–aqueous solution interface. The relevance of such problems to geosciences is illustrated by a few situations in which water structure plays a prominent role. To cite this article: L.J. Michot et al., C. R. Geoscience 334 (2002) 611–631.     

Hydrogen bonding and vibrational properties of hydroxy groups in the crystal lattice of dioctahedral clay minerals by means of first principles calculations

The hydroxy groups of the crystal lattice of dioctahedral 2:1 phyllosilicates were investigated by means of quantum-mechanical calculation. The standard Kohn-Sham self-consistent density functional theory (DFT) method was applied using the generalized gradient approximation (GGA) with numerical atomic orbitals and double-zeta polarized functions as basis set. Isomorphous cation substitution of different cations in the octahedral and tetrahedral sheet was included along with several interlayer cations reproducing experimental crystal lattice parameters. The effect of these substitutions and the interlayer charge on the hydroxyl group properties was also studied. These structures represent different cation pairs among Al³⁺, Fe³⁺ and Mg²⁺ in the octahedral sheet of clays joined to OH groups. The geometrical disposition of the OH bond in the crystal lattice and the hydrogen bonds and other electrostatic interactions of this group were analyzed. The frequencies of different vibrational modes of the OH group [(OH), (OH) and (OH)] were calculated and compared with experimental data, finding a good agreement. These frequencies depend significantly on the nature of cations which are joined with, and the electrostatic interactions with, the interlayer cations. Besides, hydrogen-bonding interactions with tetrahedral oxygens are important for the vibrational properties of the OH groups; however, also the electrostatic interactions of these OH groups with the rest of tetrahedral oxygens within the tetrahedral cavity should be taken into account. The cation substitution effect on the vibration modes of the OH groups was analyzed reproducing the experimental behaviour.Dr. V. Botella passed away last February     

Multiscale modeling of a sensitive marine clay

This paper examines the mechanical behavior of a sensitive marine clay. Various laboratory tests on intact and reconstituted samples of Guinea Gulf marine clay were performed under isotropic compression and drained triaxial compression at constant confining stresses. Microstructure analysis on intact and reconstituted samples was also carried out under different loading conditions. The effect of inter‐aggregates bonding on mechanical properties is discussed. Based on experimental analysis, a new modeling method is proposed. In this approach, the clay is regarded as an assembly of aggregates of clay particles. An inter‐aggregate contact law is introduced relating contact forces to aggregates relative displacements. The deformation of the assembly can be obtained by integrating the movement of the inter‐aggregate contacts in all orientations. Thus, the effect of inter‐aggregates bonds and debonding is considered in a direct way. The model is evaluated through comparisons between the predicted and measured results on Guinea Gulf marine clay. The evolutions of local stresses, strains, and bonds in inter‐aggregates planes are discussed to explain the anisotropy induced by the applied loading. Copyright © 2010 John Wiley & Sons, Ltd.     

High-temperature single-crystal neutron diffraction study of natural chondrodite

The H-atom environment in a Tilly Foster chondrodite was analyzed using single-crystal neutron-diffraction data collected at 500, 700 and 900 K and previously published low temperature data collected at 10, 100 and 300 K on the same crystal (Mg_4.64Fe_0.28Mn_0.014Ti_0.023(Si_1.01O₄)₂F_1.16(OH)_0.84; Friedrich et al. in Am Mineral 86:981–989, 2001). The full mean square displacement matrix Σ of the O–H pair was determined from the temperature dependence of the anisotropic displacement parameters, enabling a proper correction of the O–H bond for thermal vibration without assumptions about the correlation of O and H movements. The results show that the perpendicular O–H motions in chondrodite are intermediate between the riding and the independent motion models. The corrected O–H bond lengths do not change with temperature whereas the corrected H···F distances show an increase of ~0.02 Å with temperature, as do the Mg–O distances. This result shows that spectroscopic observations on the strength of the covalent O–H bond cannot be interpreted unambiguously in terms of a corresponding behaviour of the associated H···O/F hydrogen bond.     

First-principles study of (MgH2SiO4)? n (Mg2SiO4) hydrous olivine structures. I. Crystal structure modelling of hydrous olivine Hy-2 a (MgH2SiO4) ? 3(Mg2SiO4)

 Recently, the Hy-2a hydrous olivine (MgH₂ SiO₄)·3(Mg₂SiO₄) occurring as nanometre-sized inclusions in mantle olivines has been found by TEM, and has been suggested to be a new DHMS phase (Khisina et al. 2001). A model of the crystal structure of Hy-2a has been proposed as a 2a-superstructure of olivine with one Me²⁺ -vacant octahedral layer in the (1 0 0) plane per Hy-2a unit cell (Khisina and Wirth 2002). In the present study the crystal structure of Hy-2a hydrous olivine is optimized by ab initio calculations. The aims of this study are: (1) verification of the suggested models of Hy-2a hydrous olivine structure; (2) calculation of the most stable configurations for Hy-2a structure with minimum static lattice energy, by assuming a possible formation of Me²⁺ vacancies in either M1 or M2 octahedral sites; (3) determination of the position of protons and hydrogen bonds in the Hy-2a structure. Several different possible configurations of the Hy-2a structure are optimized. The results support the idea of a stable olivine structure with ordered planar-segregated OH-bearing defects oriented parallel to (1 0 0). The data obtained indicate a preferred stability of the Hy-2a structure with the protons associated with M1 vacancies and bonded with O1 and O2 oxygen sites. The relative energy values of the optimized Hy-2a structure configurations correlate as a rule with the average shifts of atoms from their positions in pure forsterite structure. Received: 7 February 2002 / Accepted: 23 October 2002     

硅酸盐中金属离子对Si—O键影响的量子化学研究

本文用CNDO/2法,研究了不同金属离子对硅桥氧键(Si—O~(br))及硅端氧键(Si-O~(ter))的影响。得到了硅酸盐骨架中硅氧键的性质与氧的成键状态、配位数以及金属离子影响之间的规律性。用得到的这些规律,可望较好地研究矿物学、地球化学、硅酸盐材料及冶金炉渣结构等同题。     

Micro-FTIR spectroscopy of liptinite macerals in coal

Reflectance FTIR microspectroscopy has been used to investigate the chemical structure of the liptinite macerals, alginite, bituminite, sporinite, cutinite and resinite in bituminous coals of Carboniferous to Tertiary age. In comparison with the spectra of vitrinite in the same coals, the micro-FTIR spectra of liptinite macerals are characterized by stronger aliphatic CH_x absorptions at 3000–2800 and 1460–1450 cm⁻¹, less intense aromatic C=C ring stretching vibration and aromatic CH out of plane deformation at 1610–1560 and 900–700 cm⁻¹ respectively and various intense acid C=O group absorptions at 1740–1700 cm⁻¹. The peaks at 1000–900 cm⁻¹ due to aliphatic CH₂ wagging vibrations in olefins and at 730–720 cm⁻¹ due to CH₂ rocking vibration in long chain aliphatic substances ([CH₂]_n, n≥4), are characteristic of liptinite macerals. Collectively the micro-FTIR spectral characteristics indicate that liptinite is composed of greater numbers of long chain aliphatics, fewer aromatics and a broader range of oxygen-containing groups than other macerals. Marked differences exist in micro-FTIR spectra within the liptinite maceral group. Alginite has the strongest aliphatic and least aromatic absorptions followed by bituminite, resinite, cutinite and sporinite. The aliphatic components in alginite are the longest chained and least branched whereas those in sporinite are the shortest chained and most branched. Bituminite, resinite and cutinite are intermediate. Notable differences in micro-FTIR spectra of individual liptinite macerals, such as intensities and peak locations of aromatic C=C in alginite, C=O groups in bituminite and resinite and substituted aromatic CH and C–O–C groups in cutinite and sporinite, also exist, which are attributed to differences in depositional environments or biotaxonomy.