Experimental Investigation into Hydraulic Fracture Network Propagation in Gas Shales Using CT Scanning Technology

Multistage fracturing of the horizontal well is recognized as the main stimulation technology for shale gas development. The hydraulic fracture geometry and stimulated reservoir volume (SRV) is interpreted by using the microseismic mapping technology. In this paper, we used a computerized tomography (CT) scanning technique to reveal the fracture geometry created in natural bedding-developed shale (cubic block of 30 cm × 30 cm × 30 cm) by laboratory fracturing. Experimental results show that partially opened bedding planes are helpful in increasing fracture complexity in shale. However, they tend to dominate fracture patterns for vertical stress difference Δσ _v  ≤ 6 MPa, which decreases the vertical fracture number, resulting in the minimum SRV. A uniformly distributed complex fracture network requires the induced hydraulic fractures that can connect the pre-existing fractures as well as pulverize the continuum rock mass. In typical shale with a narrow (<0.05 mm) and closed natural fracture system, it is likely to create complex fracture for horizontal stress difference Δσ _h  ≤ 6 MPa and simple transverse fracture for Δσ _h  ≥ 9 MPa. However, high naturally fractured shale with a wide open natural fracture system (>0.1 mm) does not agree with the rule that low Δσ _h is favorable for uniformly creating a complex fracture network in zone. In such case, a moderate Δσ _h from 3 to 6 MPa is favorable for both the growth of new hydraulic fractures and the activation of a natural fracture system. Shale bedding, natural fracture, and geostress are objective formation conditions that we cannot change; we can only maximize the fracture complexity by controlling the engineering design for fluid viscosity, flow rate, and well completion type. Variable flow rate fracturing with low-viscosity slickwater fluid of 2.5 mPa s was proved to be an effective treatment to improve the connectivity of induced hydraulic fracture with pre-existing fractures. Moreover, the simultaneous fracturing can effectively reduce the stress difference and increase the fracture number, making it possible to generate a large-scale complex fracture network, even for high Δσ _h from 6 MPa to 12 MPa.     

The stress regime in a Rotliegend reservoir of the Northeast German Basin

In-situ stresses have significant impact, either positive or negative, on the short and long term behaviour of fractured reservoirs. The knowledge of the stress conditions are therefore important for planning and utilization of man-made geothermal reservoirs. The geothermal field Groß Schönebeck (40 km north of Berlin/Germany) belongs to the key sites in the northeastern German Basin. We present a stress state determination for this Lower Permian (Rotliegend) reservoir by an integrated approach of 3D structural modelling, 3D fault mapping, stress ratio definition based on frictional constraints, and slip-tendency analysis. The results indicate stress ratios of the minimum horizontal stress S _hmin being equal or increasing 0.55 times the amount of the vertical stress S _V (S _hmin ≥ 0.55S _V ) and of the maximum horizontal stress S _Hmax ≤ 0.78–1.00S _V in stress regimes from normal to strike slip faulting. Thus, acting stresses in the 4,100-m deep reservoir are S _V  = 100 MPa, S _hmin = 55 MPa and S _Hmax = 78?100 MPa. Values from hydraulic fracturing support these results. Various fault sets of the reservoir are characterized in terms of their potential to conduct geothermal fluids based on their slip and dilatation tendency. This combined approach can be adopted to any other geothermal site investigation.     

Cosmological tests based on the abundance of galaxy clusters

We present a new normalization for the linear density-perturbation spectrum in a multi-parameter model of the Universe. Using the differential mass function for the nearly galaxy clusters obtained from optical data, we have constructed a functional relation between the dispersion of the density contrast σ ₈ on the scale 8h ^?1 Mpc and the cosmological parameters Ω _m , Ω_Λ, h, n, f _v for each of three theoretical approximations of the mass function: Press-Schechter, Sheth-Tormen and Jenkins. An extended class of models of the Universe with general spatial curvature include four parameters for the matter components: baryons (Ω _b ), “cold” dark matter (Ω _c ), “hot” dark matter (Ω _v ), and the vacuum energy (Ω_Λ). It is shown that the most accurate normalization of the power spectrum is achieved with the Sheth-Tormen approximation.     

Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth

The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solution of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The spatiotemporal data are collected and processed providing information about the wave height probability and typical appearance of abnormally high waves (rogue waves). The waves are considered at different water depths ranging from deep to relatively shallow cases (k _p h > 0.8, where k _p is the peak wavenumber, and h is the local depth). The asymmetry between front and rear rogue wave slopes is identified; it becomes apparent for sufficiently high waves in rough sea states at all considered depths k _p h ≥ 1.2. The lifetimes of rogue events may reach up to 30–60 wave periods depending on the water depth. The maximum observed wave has a height of about three significant wave heights. A few randomly chosen in situ time series from the Baltic Sea are in agreement with the general picture of the numerical simulations.     

The space distribution of quasars

The space distribution of quasars from the 2dF and SDSS DR5 catalogs in the redshift interval 0.3 < z < 1.9 is analyzed. The distributions of quasars in both catalogs are found to have the following common features: (1) when the distance between the nearest objects exceeds 35h ^?1 Mpc (where h = H ₀/100 km/s Mpc is the dimensionless Hubble constant), the distribution of quasars virtually coincides with a uniform three-dimensional distribution; (2) on scale lengths of (5–35)h ^?1 Mpc, the fractal dimension of the quasar distribution is 2.3; (3) the amplitude of quasar clustering and the average distance between neighboring quasars increase slowly with z (at a significance level of about 1.5σ). Twenty large groups of quasars with sizes of (50–150)h ^?1 Mpc can be identified in the 2dF catalog at the 4σ significance level. These groups are incipient superclusters (two earlier known groups are confirmed). The space density of these groups is of the order of 7h ³ Gpc^?3.     

Permeability of granular soil employing flexible wall permeameter

Understanding the changes in permeability of soil, when soil is subjected to high confining pressure and flow pressure, which may alter the textural and geomechanical characteristics of soil, is of great importance to many geo-engineering activities such as, construction of high-rise buildings near the coast or the water bodies, earthen dams, pavement subgrades, reservoir, and shallow repositories. It is now possible to evaluate the changes in permeability of soil samples under varying conditions of confining pressure and flow pressure using flexible wall permeameter (FWP). In the present study, investigation was carried out on a cylindrical sample of granular soil employing FWP under varied conditions of confining pressure (σ₃)—50–300 kPa, which can simulate the stress conditions equivalent to depth of about 20 m under the earth’s crust, and a flow pressure (f_p)—20–120 kPa, which is mainly present near the small earthen embankment dams, landfill liners, and slurry walls near the soft granular soil with high groundwater table. The obtained results indicate a linear relationship between hydraulic conductivity (k) with effective confining pressure (σ_eff.), k, decreasing linearly with an incremental change in σ_eff.. Further, k increases significantly with an increase in f_p corresponding to each σ_eff., and q increases significantly with increase in the f_p corresponding to each (σ₃). It was also observed that corresponding to the low f_p of 20 kPa, the reduction in k is nonlinear with σ_3. The percentage reduction in k is observed to be 9, 13, and 27% corresponding to σ₃ of 50–100, 100–200, and 200-300 kPa, respectively.     

DEM simulations of sandstone under true triaxial compressive tests

Numerically simulated true triaxial compression tests (σ ₁ ≥ σ ₂ ≥ σ ₃) are conducted in this study to elucidate the failure mechanism of sandstone using 3D discrete element method (DEM), in particular the effect of the intermediate principal stress (σ ₂). Eight series of tests (σ ₃ = 0, 10, 20, 30, 40, 50, 70, and 100 MPa) are conducted. Within each series, σ ₂ is varied from σ ₂ = σ ₃ to σ ₂ = σ ₁ from test to test. For each test, σ ₁ is raised monotonically to failure while keeping σ ₂ and σ ₃ constant. The DEM simulations reveal the effect of σ ₂ on the variations of peak stress, Young’s modulus, failure plane angles, the brittle–ductile transition, and the evolution of failure modes, the effect beyond the well-understood effect of σ ₃. The simulation is in qualitative agreement with the results obtained experimentally. Detailed analyses performed on the particle-scale responses further the understanding of the microscopic mechanisms. The distribution of contact force becomes more homogeneous with the increase of σ ₃, which leads to the resulting damage being more localized rather than diffused. The interaction between contact force distribution and coalescence of cracks determines the processes and patterns of fracturing in the sample scale. σ ₂ is found to affect the microscopic stress distribution as well as structure evolution, and this effect weakens with the increase of σ ₃.     

Spectroscopic monitoring of SS 433: A search for long-term variations of kinematic model parameters

Between 1994 and 2006, we obtained uniform spectroscopic observations of SS 433 in the region of Hα. We determined Doppler shifts of the moving emission lines, Hα ₊ and Hα _?, and studied various irregularities in the profiles for the moving emission lines. The total number of Doppler shifts measured in these 13 years is 488 for Hα _? and 389 for Hα ₊. We have also used published data to study possible long-term variations of the SS 433 system, based on 755 Doppler shifts for Hα _? and 630 for Hα ₊ obtained over 28 years. We have derived improved kinematic model parameters for the precessing relativistic jets of S S 433 using five-and eight-parameter models. On average, the precession period was stable during the 28 years of observations (60 precession cycles), at 162.250^d ± 0.003^d. Phase jumps of the precession period and random variations of its length with amplitudes of ≈6% and ≈1%, respectively, were observed, but no secular changes in the precession period were detected. The nutation period, P _nut = 6.2876^d ± 0.00035^d, and its phase were stable during 28 years (more than 1600 nutation cycles). We find no secular variations of the nutation cycle. The ejection speed of the relativistic jets, v, was, on average, constant during the 28 years, β = v/c = 0.2561 ± 0.0157. No secular variation of β is detected. In general, S S 433 demonstrates remarkably stable long-term characteristics of its precession and nutation, as well as of the central “engine” near the relativistic object that collimates the plasma in the jets and accelerates it to v = 0.2561c. Our results support a model with a “slaved” accretion disk in S S 433, which follows the precession of the optical star’s rotation axis.     

Influences of loading direction and intermediate principal stress ratio on the initiation of strain localization in cross-anisotropic sand

Since cross-anisotropic sand behaves differently when the loading direction or the stress state changes, the influences of the loading direction and the intermediate principal stress ratio (b = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) on the initiation of strain localization need study. According to the loading angle (angle between the major principal stress direction and the normal of bedding plane), a 3D non-coaxial non-associated elasto-plasticity hardening model was proposed by modifying Lode angle formulation of the Mohr–Coulomb yield function and the stress–dilatancy function. By using bifurcation analysis, the model was used to predict the initiation of strain localization under plane strain and true triaxial conditions. The predictions of the plane strain tests show that the major principal strain at the bifurcation points increases with the loading angle, while the stress ratio decreases with the loading angle. According to the loading angle and the intermediate principal stress ratio, the true triaxial tests were analyzed in three sectors. The stress–strain behavior and the volumetric strain in each sector can be well captured by the proposed model. Strain localization occurs in most b value conditions in all three sectors except for those which are close to triaxial compression condition (b = 0). The difference between the peak shear strength corresponding to the strain localization and the ultimate shear strength corresponding to plastic limit becomes obvious when the b value is near 0.4. The influence of bifurcation on the shear strength becomes weak when the loading direction changes from perpendicular to the bedding plane to parallel. The bifurcation analysis based on the proposed model gives out major principal strain and peak shear strength at the initiation of strain localization; the given results are consistent with experiments.     

Detailed comparison of nine intact rock failure criteria using polyaxial intact coal strength data obtained through PFC<Superscript>3D</Superscript> simulations

Study of intact rock failure criteria is an important topic in rock mechanics. In this study, applicability of nine different intact rock failure criteria is investigated for intact coal strength data. PFC^3D modeling was used to simulate the laboratory polyaxial tests for cubic intact coal blocks of side dimension 110 mm under different confining stress combinations. A modified grid search procedure is proposed and used to find the best-fitting parameter values and to calculate the coefficient of determination (R ²) values for each criterion. Detailed comparisons of the nine criteria are made using the following aspects: R ² values, σ ₁ ? σ ₂ plots for different σ ₃, shapes on the deviatoric plane, linearity or nonlinearity on the meridian planes. Through the comparisons of R ² values, σ ₁ ? σ ₂ plots and meridian lines, the modified Wiebols–Cook and modified Lade criteria were found to fit the intact coal strength data best. The nine failure criteria are categorized into three types based on the appearances on the deviatoric plane.     

Orthogonal test and regression analysis of the strain on silty soil in Shanghai under metro loading

Cyclic triaxial test by means of the geotechnical digital system is conducted for the soil near the Guoquan Road Station of Metro Line 10 in Shanghai to analyze the strain characteristics and the variation law of saturated silty soil under subway loading. Orthogonal design method is used to arrange the experiment, considering the following factors: frequency ratio f _R, cyclic stress ratio σ _R, vibration time ratio N _R, and the interaction function among them. Results show that the cyclic stress ratio σ _R, the frequency ratio f _R, the vibration time ratio N _R, and the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R have a significant effect on the axial strain of the subway tunnel. The effect of the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R is also significant. From the analysis of variance and regression theory, the nonlinear regression equation of the cumulative plastic strain of silty soil under subway loading is established. Residual analysis proves that the equation is ideal and credible. The results have important value for the design of subway tunnels.     

Separation of chemical elements in the atmospheres of CP stars under the action of light induced drift

A mechanism for the separation of chemical elements and isotopes in the atmospheres of chemically peculiar (CP) stars due to light-induced drift (LID) of ions is discussed. The efficiency of separation due to LID is proportional to the relative difference of the transport frequencies for collisions of ions of heavy elements located in the excited state (collision frequency ν _e ) and ground state (collision frequency ν _g ) with neutral buffer particles (hydrogen and helium), (ν _e ? ν _g )/ν _g . The known interaction potentials are used to numerically compute the relative difference (ν _e ^H ? ν _g ^H )/νg H for collisions between the ions Be⁺, Mg⁺, Ca⁺, Sr⁺, Cd⁺, Ba⁺, Al⁺, and C⁺ and hydrogen atoms. These computations show that, at the temperatures characteristic of the atmospheres of CP stars, T = 7000?20 000 K, values of |ν _e ^H ?ν _g ^H |/ν _g ^H ≈ 0.1?0.4 are obtained. With such relative differences in the transport collision frequencies, the LID rate of ions in the atmospheres of coolCP stars (T < 10000 K) can reach ~0.1 cm/s,which exceeds the drift rate due to light pressure by an order of magnitude. This means that, under these conditions, the separation of chemical elements under the action of LID of ions could be an order of magnitude more efficient than separation due to light pressure. Roughly the same manifestations of LID and light pressure are also expected in the atmospheres of hotter stars (20 000 > T > 10 000 K). LID of heavy ions is manifest only weakly in very hot stars (T > 20 000 K).     

Masses of the visual components and black holes in X-ray novae: Effects of proximity of the components

It is shown that the approximation of the complex, tidally distorted shape of a star as a circular disc with local line profiles and a linear limb-darkening law, which is usually applied when deriving equatorial stellar rotation velocities from line profiles, leads to overestimation of the equatorial velocity V _rot sin i and underestimation of the component mass ratio q = M _x /M _v . A formula enabling correction of the effect of these simplifying assumptions on the shape of a star is used to re-determine the mass ratios q and the masses of the black holes M _x and visual components M _v in low-mass X-ray binary systems containing black holes. Taking into account the tidal–rotational distortion of the stellar shape can significantly increase the mass ratios q = M _x /M _v , reducing M _v , while M _x changes only slightly. The resulting distribution of M _v attains its maximum near M _v ? 0.35M _⊙, in disagreement with the results of population synthesis computations realizing standard models for Galactic X-ray novae with black holes. Possible ways to overcome this inconsistency are discussed. The derived distribution of M _x also differs strongly from the mass distribution for massive stars in the Galaxy.     

Collective supernova outbursts and the growth of supershells: Observational manifestations

Numerous supernova outbursts that are correlated in time and space are the main mechanism for the formation of powerful galactic winds and supershells of ionized hydrogen. Information about the dynamics and thermal properties of the gas in shells (bubbles) can be obtained from spectral observations, including those of optical recombination lines. The emission properties of the Hα and Hβ recombination lines and the velocity dispersion of the gas in bubbles formed by numerous supernova outbursts are studied. The appearance of the intensity vs. velocity dispersion (I(H _α)_?σ) diagram depends on the supernova rate and the age of the bubble. The temperature dependence of the I(H_α)/I(H _β) line-intensity ratio (the Balmer decrement) can be used to obtain additional constraints on the evolutionary status of a collective remnant formed by numerous supernova outbursts.     

A laboratory study of anisotropic geomaterials incorporating recent micromechanical understanding

This paper presents an experimental investigation revisiting the anisotropic stress–strain–strength behaviour of geomaterials in drained monotonic shear using hollow cylinder apparatus. The test programme has been designed to cover the effect of material anisotropy, preshearing, material density and intermediate principal stress on the behaviour of Leighton Buzzard sand. Experiments have also been performed on glass beads to understand the effect of particle shape. This paper explains phenomenological observations based on recently acquired understanding in micromechanics, with attention focused on strength anisotropy and deformation non-coaxiality, i.e. non-coincidence between the principal stress direction and the principal strain rate direction. The test results demonstrate that the effects of initial anisotropy produced during sample preparation are significant. The stress–strain–strength behaviour of the specimen shows strong dependence on the principal stress direction. Preloading history, material density and particle shape are also found to be influential. In particular, it was found that non-coaxiality is more significant in presheared specimens. The observations on the strength anisotropy and deformation non-coaxiality were explained based on the stress–force–fabric relationship. It was observed that intermediate principal stress parameter b(b = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) has a significant effect on the non-coaxiality of sand. The lower the b-value, the higher the degree of non-coaxiality is induced. Visual inspection of shear band formed at the end of HCA testing has also been presented. The inclinations of the shear bands at different loading directions can be predicted well by taking account of the relative direction of the mobilized planes to the bedding plane.     

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily over-consolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as half of the critical distance. This fracture criterion is known as the point method, and is part of the theory of critical distances, which is utilised in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, σ ₀, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, σ _c and σ _t. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (σ _c/σ _t = 3–50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low-confining stresses.     

The mass of the compact object in the X-ray binary her X-1/HZ her

We have obtained the first estimates of the masses of the components of the Her X-1/HZ Her X-ray binary system taking into account non-LTE effects in the formation of the H _γ absorption line: m _x = 1.8 M _⊙ and m _v = 2.5 M _⊙. These mass estimates were made in a Roche model based on the observed radial-velocity curve of the optical star, HZ Her. The masses for the X-ray pulsar and optical star obtained for an LTE model lie are m _x = 0.85 ± 0.15 M _⊙ and m _v = 1.87 ± 0.13 M _⊙. These mass estimates for the components of Her X-1/HZ Her derived from the radial-velocity curve should be considered tentative. Further mass estimates from high-precision observations of the orbital variability of the absorption profiles in a non-LTE model for the atmosphere of the optical component should be made.     

A Pulsar Time Scale Based on Parkes Observations in 1995–2010

Timing of highly stable millisecond pulsars provides the possibility of independently verifying terrestrial time scales on intervals longer than a year. An ensemble pulsar time scale is constructed based on pulsar timing data obtained on the 64-m Parkes telescope (Australia) in 1995–2010. Optimal Wiener filters were applied to enhance the accuracy of the ensemble time scale. The run of the time-scale difference PT_ens?TT(BIPM2011) does not exceed 0.8 ± 0.4 μs over the entire studied time interval. The fractional instability of the difference PT_ens?TT(BIPM2011) over 15 years is σ _z = (0.6 ± 1.6) × 10^?15, which corresponds to an upper limit for the energy density of the gravitational-wave background Ω _g h² ~ 10^?10 and variations in the gravitational potential ~10^?15 Hz at the frequency 2 × 10^?9 Hz.     

Fracture evolution and energy mechanism of deep-buried carbonaceous slate

In order to study the influence of confining pressure and water content on the mechanical properties, fracture evolution and energy damage mechanism of deep-buried carbonaceous slate, uniaxial and triaxial compression tests were carried out under natural and saturated states and acoustic emission monitored. The deep-buried carbonaceous slate samples were obtained at a depth of 1020 m from the Lanjiayan tunnel in Sichuan province, China, where the maximum in situ stress has been measured at 44.2 MPa. The results suggest that water has a significant softening effect on the strength and deformation characteristics of carbonaceous slate, but the effect decreases with an increase in the confining pressure. When both the confining pressure and water content are increased, the acoustic emission events and dissipated energy gradually increase at the pre-peak and post-peak stages. Thus, the AE evolution type seen in the natural state under low confining pressure usually presents as a main shock-type event, and it changes to a foreshock–main shock–after shock event when saturated and at high confining pressures. Based on the S-shaped energy evolution law, the damage evolution process of carbonaceous slate was analyzed. The damage stress thresholds σ _ea and σ _eb were obtained, which can be considered as the thresholds of the rock entering the energy-hardening and energy-softening stages. Finally, a new brittleness energy index BDE is proposed to describe the influence of confining pressure and water content on the damage mechanism of deep-buried carbonaceous slate.