Distribution rule of the in situ stress state and its influence on the permeability of a coal reservoir in the southern Qinshui Basin,China

The recent development of the coalbed methane (CBM) industry has a significant role in advancing hydraulic fracturing theory and technology. However, further development requires a better understanding of how fractures influence reservoir permeability. In situ stress data from 54 CBM wells in the southern Qinshui Basin, China, were obtained by the injection/falloff test method to analyse the effect of in situ stress on the permeability of the CBM reservoir. The types of in situ stress states were classified, and the coal reservoir permeability under different in situ stress states was analysed. The results indicate that the maximum horizontal principal stress (σ_H), minimum horizontal principal stress (σ_h) and vertical principal stress (σ_v) all have positive linear relationships with the coal seam burial depth. Three in situ stress states were observed from the shallow to deep regions of the CBM reservoir in the study area: σ_H?>?σ_h?>?σ_v, σ_H?>?σ_v?>?σ_h and σ_v?>?σ_H?>?σ_h, which account for 9, 76 and 15% of the test wells, respectively. Coal reservoir permeability decreases with increasing horizontal principal stress, whereas it first decreases with increasing σ_v, then increases and finally decreases. The variation in permeability with σ_v is due to the conversion of the in situ stress states. Coal reservoir permeability has obvious differences under different in situ stress states. The permeability is the largest when σ_v?>?σ_H?>?σ_h, followed by σ_H?>?σ_h?>?σ_v and smallest when σ_H?>?σ_v?>?σ_h. The permeability differences are caused by the fracture propagation shape of the rock strata under different in situ stress states.     

Towards a better understanding of the evolution of the flood risk in Mediterranean urban areas: the case of Barcelona

Dam failure constitutes a grave threat to human life. However, there is still a lack of systematic and comprehensive research on the loss of life (L) caused by dam break in China. From the perspective of protecting human life, a new calculation method for L occurred in dam break floods is put forward. Fourteen dam failure cases in China are selected as the basic data by three-dimensional stratified sampling, balancing spatial, vertical elevation and temporal representations, as well as considering various conditions of the dam collapse. The method includes three progressive steps: Firstly, some impact factors of loss of life (IFL) are selected by literature survey, i.e., severity of dam break flood (S _F), population at risk (P _R), understanding of dam break (U _B), warning time (T _W) and evacuation condition (E _C). And the other IFL of weather during dam break (W _B), dam break mode (M _B), water storage (S _W), building vulnerability (V _B), dam break time (T _B) and average distance from affected area to dam (D _D) are also taken into account to get a more comprehensive consideration. According to disaster system and disaster risk, these eleven IFL are divided into four categories. Through the improved entropy method, eight key IFL are further selected out of the eleven. Secondly, four L modules are built based on four categories, which are L-causing factor module (M ₁), L-prone environment module (M ₂), affected body module (M ₃) and rescue condition module (M ₄). Eventually, by using two methods of multivariate nonlinear regression and leave-one-out cross-validation in combination with coupled four modules, the calculation method for L is established. Compared with the results of Graham method and D&M method, the result of the proposed one is much closer to the actual value and performs better in fitting effect and regional applicability. In the application, L calculation and consequence assessment are carried out in the example of Hengjiang reservoir that has already broken down. At the same time, L calculation and risk prediction are used in the analysis of Yunshan reservoir, which is under planning. The proposed method can not only be applied to estimate L and its rate (f _L ) under various types of dam break conditions in China, but also provide a reliable consequence assessment and prediction approach to reduce the risk of L.     

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.     

Assessment of Reservoir Rock Properties from Rock Physics Modeling and Petrophysical Analysis of Borehole Logging Data to Lessen Uncertainty in Formation Characterization in Ratana Gas Field,Northern Potwar,Pakistan

Petrophysical evaluation and rock physics analysis are the important tools to relate the reservoir properties like porosity, permeability, pore fluids with seismic parameters. Nevertheless, the uncertainties always exist in the quantification of elastic and seismic parameters estimated through wireline logs and rock physics analysis. A workflow based on statistical relationships of rock physics and logs derived elastic and seismic parameters with porosity and the percentage error exist between them is given. The statistical linear regressions are developed for early Eocene Chorgali Formation between various petrophysically factors determined from borehole logging of well Ratana–03 drilled in tectonically disturbed zone and the seismic and elastic parameters estimated through rock physics modeling. The rock physics constraints such as seismic velocities, effective density and elastic moduli calculated from Gassmann fluid substation analysis are in harmony and close agreement to those estimated from borehole logs. The percentage errors between well logs and rock physics computed saturated bulk modulus (K _sat ), effective density (ρ _eff ), compressional and shear wave velocities (V _P and _V S) are 1.31%, 4.23 %, 5.25% and 4.01% respectively. The permeability of reservoir intervals show fairly strong linear relationship with the porosity, indicating that the reservoir interval of the Chorgali Formation is permeable and porous thus having large potential of hydrocarbon accumulation and production.     

Seismic Pullout Capacity of Inclined Anchor Plates in Sand

By using the lower bound finite elements limit analysis, the pullout capacity of an inclined strip anchor plate embedded in a cohesionless soil medium has been computed with an inclusion of pseudo-static horizontal earthquake body forces. The variation of the pullout capacity factor (F _γ ) with changes in horizontal earthquake acceleration co-efficient (α _h ) has been computed by varying the inclination angle (β) of the anchor plate between 0° and 90°. The results clearly reveal that the pullout capacity factor (F _γ ) decreases significantly with an increase in the value of α _h . The reduction in the pullout resistance due to seismic forces (1) becomes much more extensive for a vertical anchor plate as compared to the horizontal anchor, (2) decreases generally with increases in the soil friction angle (?) and (3) increases with an increase in friction angle between soil and anchor plate (δ). The developments of the failure zone around the anchor plate were also examined by varying α _h and β. The results obtained from the analysis compare well with the solutions reported in literature.     

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.     

Simultaneous inversion application for characterizing Hamra Quartzite tight sand reservoir: a case study from Hassi Messaoud (Algeria)

Channel sand acts as a stratigraphic trap for hydrocarbon accumulation in many parts of the world. Delineation of this type of reservoir is crucial as channel sand may be scarce, and inaccurate location of the drilling wells could lose a huge currency. The Hassi Messaoud (HMD) field was subjected to multiphase tectonic events, where deep-seated structures were rejuvenated leading to intensive fault complexity. The main effective tectonic events upon the studied area are the Hercynian compression and deep erosion till the Ordovician Hamra Quartzite (HQZ) oil reservoir, followed by active Triassic rifting and filling the deeply eroded areas or the graben areas by eruptive volcanic rocks at Triassic time. Hercynian erosion and volcanic rocks distribution introduce a big uncertainty to the reservoir structural model. Amplitude versus offset (AVO) method is used as a helpful tool to differentiate channel sand from surrounding formations. Several attributes (P-impedance, S-impedance, longitudinal velocity Vp, shear velocity Vs and density ρ) are estimated from pre-stack seismic inversion. They have different sensitivity to the reservoir properties. Derived attributes such as Lamé parameters, incompressibility × density (λρ) and rigidity × density (μρ) can provide key lithology and fluid indicators (Goodway et al. 1997, Goodway CSEG Rec 26(6):39-60 2001). Petrophysically relating AVO attributes both to λρ and μρ and to each other in Lambda–Mu–Rho (LMR) cross-plot space can be a good tool for AVO interpretation (Rutherford and Williams Geophysics 54:680–688 1989 and Castagna and Swan Lead Edge 16(4):337–342 1997). After proper data conditioning, simultaneous inversion of pre-stack angle gathers is performed to get acoustic wave impedance (P-impedance), elastic wave impedances (S-impedance) and density ρ, then to calculate λρ and μρ volumes. In the studied area, λρ and μρ are used as a very important key to separate reservoir sands. The λρ and μρ curves are generated at each well location. Cross plots showed a fair separation of sand in the formation, i.e. higher μρ and lower λρ can detect sand. The output λρ and μρ volumes after simultaneous inversion follow the distribution of the sand which is consistent with the wells penetrating the target reservoir. This finding on the extension of the sand reservoir in terms of λρ and μρ. 3D cross-plot zonations are used for lithology discrimination. In this study, well logs were used to constrain lithology and to control the zonation filters by reducing the limits ambiguity. Other types of advanced attributes are calculated and tested. The obtained (μρ–λρ) volume acts as a good indicator for the sand distribution. It was finally used as sand presence index in the area. Also μρ has shown a good linear relationship with porosity. To note that the porosity volume is created based on the linear relationship with μρ. A product of derived porosity and the sand presence index (μρ–λρ) provides a good tool for reservoir characterization and lead to reservoir management, future planning of the field, and setting location for new wells.     

Numerical Investigation of the Optimum Location for Vertical Drains in Gravity Dams

The seepage beneath a concrete dam causes an upward force acting to the dam foundation, known as uplift. Previous literatures show that implementation of drainage wells in gravity dam foundations causes a reduction in uplift forces. The main aim of these wells is to drain excess seepage flow bypassed from the cutoff wall and to reduce the uplift force. The location of the drains in the foundation plays a key role in reducing the pressure. In the present study, effect of the location of drain pipes from the upstream face of the dam (s), space among them (n) and drain’s diameter (d) in uplift force reduction is investigated. The processes of the study have been performed by the Seep/w software based on the finite element method. Results show that the use of a drain system reduced the uplift forces developed beneath the floor of the structure. If the drain is located close to the face of the dam, it may not be effective in reducing the uplift. On the other hand, shifting it too much away from the upstream face of the dam will lead to increased total uplift. It is, therefore, desirable to find out the location of the drain such that the total uplift is optimum. Optimum location of the vertical drains is not fixed, and by increasing vertical drains distances from each other and also decreasing drain diameter, optimum location would be shifted to the downstream. For example introduction of system of pipe drains to the floor of gravity dams reduced the uplift force acting on the floor by up to 80% for d/l = 0.0004, n/l = 0.024 and s/l = 0.08. This reduction in uplift becomes up to 65% for d/l = 0.0004, n/l = 0.048 and s/l = 0.12. The best location of the drain is such that the total uplift is minimum and this is presented in both design charts and algebraic equations in this study.     

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.     

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.     

Spatial information of soil hydraulic conductivity and performance of cokriging over kriging in a semi-arid basin scale

Unlike the studies in small parcels by systematic measurements, the spatial variability of soil properties is expected to increase in those over relatively large areas or scales. Spatial variability of soil hydraulic conductivity (K _h) is of significance for the environmental processes, such as soil erosion, plant growth, transport of the plant nutrients in a soil profile and ground water levels. However, its variability is not much and sufficiently known at basin scale. A study of testing the performance of cokriging of K _h compared with that of kriging was conducted in the catchment area of Sarayköy II Irrigation Dam in Cank?r?, Turkey. A total of 300 soil surface samples (0–10 cm) were collected from the catchment with irregular intervals. Of the selected soil properties, because the water-stable aggregates (WSA) indicated the highest relationship with the hydraulic conductivity by the Pearson correlation analysis, it is used as an auxiliary variable to predict K _h by the cokriging procedure. In addition, the sampling density was reduced randomly to n = 175, n = 150, n = 75 and n = 50 for K _h to determine if the superiority of cokriging over kriging would exist. Statistically, the results showed that all reduced K _h was as good as the complete K _h when its auxiliary relations with WSA were used in cokriging. Particularly, the results of the “Relative Reduction in MSE” (RMSE) revealed that the reduced data set of n = 75 produced the most accurate map than the others. In this basin-scaled study, there was a clear superiority of the cokriging procedure by the reduction in data although a very undulating topography and topographically different aspects, two different land uses with non-uniform vegetation density, different parent materials and soil textures were present in the area. Hence, using the statistically significant auxiliary relationship between K _h and WSA might bring about a very useful data set for watershed hydrological researches.     

Sequence signal processing of 2012 Ahar–Varzaghan earthquake (<Emphasis Type="Italic">M</Emphasis><Subscript>W</Subscript> 6.4) of NW Iran

Before starting seismic cycle of Ahar–Varzaghan 2012 event, a partial gap in the form of a pre-seismic calm sequence (seismicity rate, r = 0.46 event/year, b = 1.4) with duration of 303 days spatially has dominated over the entire seismogenic area. From April 17, 2012, to May 31, 2012, r significantly increased to 2.16, indicating strong foreshock sequence, and b value changed to 1.9, remarkably. In the last two months before the mainshock, foreshocks have partially migrated toward the earthquake fault (with a decrease in size, b = 2.0). Significantly, high rate of seismicity and low V _P /V _S (1.64) in the foreshocks sequence and also very high seismicity rate (17.3) and high V _P /V _S (1.76) in the aftershocks sequence make substantial differences between the seismic cycle and the background seismicity. Moreover, a significant E–W migration of the microseismicity was confirmed in the study area.     

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 effect of reservoir length on seismic performance of gravity dams to near- and far-fault ground motions

In this article, the effect of reservoir length on seismic performance of gravity dams to near- and far-fault ground motions is investigated. For this purpose, four finite element models of dam–reservoir–foundation interaction system are prepared by using the Lagrangian approach. In these models, the reservoir length varies from H to 4H (H: the height of dam). The Folsom gravity dam is selected as a numerical application. Two different ground motion records of 1989 Loma Prieta earthquake are used in the analyses. One of ground motions is recorded in near fault; the other is recorded in far fault. Also, the two records have the same peak ground acceleration. The study mainly consists of three parts to assess the effects of reservoir length on the seismic performance of the concrete gravity dam. In the first part, the linear time-history analyses of the four finite element models prepared for the Folsom gravity dam are performed. In the second part, the seismic performance of the dam is evaluated according to demand–capacity ratio and cumulative inelastic duration. Finally, the nonlinear time-history analyses of the finite element models of the dam are carried out by using Drucker–Prager yield criteria for dam concrete. It is seen from the analyses results that the seismic behavior of the concrete gravity dams is considerably affected from the length of the reservoir. The reservoir length of 3H is adequate for concrete gravity dams. The selection of ground motion is on of the important parts of seismic evaluation of gravity dams. Also, the frequency characteristics of the ground motion having the same peak ground acceleration affect the seismic performance of the dam. The near-fault ground motions are generally creates more stress on the dam body than far-fault ground motions. The used performance approach provides a systematic methodology for assessment of the seismic performance and necessity of nonlinear analyses for dam systems.     

Probabilistic seismic hazard assessment in the Constantine region,Northeast of Algeria

This paper presents a seismic hazard evaluation and develops an earthquake catalogue for the Constantine region over the period from 1357 to 2014. The study contributes to the improvement of seismic risk management by evaluating the seismic hazards in Northeast Algeria. A regional seismicity analysis was conducted based on reliable earthquake data obtained from various agencies (CRAAG, IGN, USGS and ISC). All magnitudes (M _l, m _b) and intensities (I ₀, I _MM, I _MSK and I _EMS) were converted to M _s magnitudes using the appropriate relationships. Earthquake hazard maps were created for the Constantine region. These maps were estimated in terms of spectral acceleration (SA) at periods of 0.1, 0.2, 0.5, 0.7, 0.9, 1.0, 1.5 and 2.0 s. Five seismogenic zones are proposed. This new method differs from the conventional method because it incorporates earthquake magnitude uncertainty and mixed datasets containing large historical events and recent data. The method can be used to estimate the b value of the Gutenberg-Richter relationship, annual activity rate λ(M) of an event and maximum possible magnitude M _max using incomplete and heterogeneous data files. In addition, an earthquake is considered a Poisson with an annual activity rate λ and with a doubly truncated exponential earthquake magnitude distribution. Map of seismic hazard and an earthquake catalogue, graphs and maps were created using geographic information systems (GIS), the Z-map code version 6 and Crisis software 2012.     

Earthquake hazard and risk assessment based on unified scaling law for earthquakes: Altai–Sayan Region

We apply the general concept of seismic risk analysis based on morphostructural analysis of the territory, pattern recognition of earthquake-prone nodes, and the Unified Scaling Law for Earthquakes, USLE, in another seismic region of Russia to the west from Lake Baikal, i.e., Altai–Sayan Region. The USLE generalizes the empirical Gutenberg–Richter relationship making use of apparently fractal distribution of earthquake sources of different size: \( \log_{10} N\left( {M,L} \right)\, = \,A\, + \,B \cdot \left( {5\, - \,M} \right)\, + \,C \cdot \log_{10} L, \) where N (M, L) is the expected annual number of earthquakes of a certain magnitude M within an seismically prone area of linear dimension L. The local estimates of A, B, and C allow determination of the expected maximum credible magnitude in a given time interval and the associated spread around ground shaking parameters (e.g., peak ground acceleration, PGA, or macroseismic intensity, I₀). Compilation of the corresponding seismic hazard map of Altai–Sayan Region and its rigorous testing against the available seismic evidences in the past is used to model regional maps of specific earthquake risks for population, cities, and infrastructures.     

A numerical approach to the design parameters of permanent stoppings (seals and bulkheads) in Turkish underground coal mines

Observing permanent seals with different physical and mechanical characteristics under various conditions in the field is almost impossible. In conjunction with the development of high-speed computer algorithms, numerical simulation has become one of the major means to study the dynamics of such problems. Therefore, this study covers only the numerical approach to analyze the stability of underground seals. In this regard, the purpose of this study is to provide an insight to the design of underground seals by numerically analyzing their behaviors under different static and dynamic explosion overpressures using a geo-technical commercial software FLAC3D. For this purpose, a series of numerical models were constructed for a typical seal in an underground gallery with different properties such as seal thickness, seal dimensions, gallery geometry, and strength of the seal material to investigate the stability of seals exposed to various static and dynamic explosion overpressures. A total of 896 numerical analyses (512 static and 384 dynamic) were performed and evaluated. Regarding the gallery geometry, it was found that seals constructed in trapeze-shaped galleries are more stable than those constructed in horseshoe-shaped galleries having the same dimensions. Moreover, the results showed that the seal stability increases with the increasing seal thickness rather than the strength of the seal material. The statistical analyses suggest that there is a very strong exponential relationship between the seal thickness and the maximum displacement measured at the midpoints of the outer surfaces of the seals. The coefficients of determination values obtained are in the range of 0.92–0.93 and 0.92–0.95 for static and dynamic analyses, respectively. We proposed formulas which use the longer dimension of the seal (W _max ), maximum allowable displacement on the seal (D _max ), explosion overpressure applied onto the seal (P _exp ), and compressive strength of the seal material (σ _c and σ _cd for static and dynamic conditions, respectively) to predict the minimum required seal thickness (T _s ) for static and dynamic conditions. The proposed formulas enable calculating the necessary seal thickness easily if the explosion overpressure (or hydrostatic pressure) is known or approximated.     

On the Existence,Uniqueness and Correctness of the Fracture Diameter Distribution Given the Fracture Trace Length Distribution

Based on the fracture trace length distribution, conditions for the existence, uniqueness, and correctness of the fracture diameter distribution are given using Warburton’s fracture model. In particular, a solution for the fracture diameter distribution exists and is unique for all trace length probability density functions, h _A (y), such that \(h_{A}(y)/\sqrt{y^{2}-x^{2}}\) is Lebesgue integrable on [x,∞). This condition is met by the uniform, exponential, gamma, lognormal, and power-law trace length distributions as well as by the trace length distributions that arise from a deterministic fracture diameter or from a discontinuous fracture diameter length distribution. Exponential, gamma, lognormal, and power-law trace length distributions satisfy necessary conditions for the diameter distribution to be non-negative, and necessary and sufficient conditions for the distribution to have unit integral over the real line. Negative values of the fracture diameter distribution arise when the trace has a uniform distribution and the lower bound of the fracture trace is greater than zero.     

Finite-difference modelling of anisotropic wave scattering in discrete fracture model

The presence of fractures in reservoir rocks causes scattering of seismic wave energy. In this paper, we utilize the finite-difference modelling technique to study these scattering effects to gain more insights into the effects and assess the validity of using anisotropic wave scattering energy as a diagnostic tool to characterize fractured hydrocarbon reservoirs. We use a simplified fractured reservoir model with four horizontal layers with a fractured-layer as the third layer. The fractures are represented by grid cells containing equivalent anisotropic medium by the use of the linear slip equivalent model. Our results show that the scattered energy, quantified through estimates of the seismic quality factor (Q) is anisotropic, exhibiting a characteristic elliptical (\(\cos 2\theta \)) variations relative to the survey azimuth angle \(\theta \). The fracture normal is inferred from the minor axis of the Q ellipse. This direction correlates with the direction of maximum wave scattering. Minimum wave scattering occurs in the fracture strike direction inferred from the major axis of the Q ellipse. These results provide more complete insights into anisotropic wave scattering characteristics in fractured media and thus, validate the practical utility of using anisotropic attenuation attribute as an additional diagnostic tool for delineation of fracture properties from seismic data.     

Numerical Analysis of Sill and Crown Pillar Stability for Multilevel Cut and Fill Stopes in Different Geomining Conditions

A steeply dipping orebody, having decreasing width with depth has been modeled considering horizontal cut and fill method of stoping at four different depth levels. The focus of the study is to identify and understand the behavior of crown and sill pillars in terms of varying stress and geo-mining conditions without reinforcement using finite element method. Analysis of stresses, displacements and extent of yield zones around the excavation is carried out by varying the rock mass conditions such as geological strength index, uniaxial compressive strength (UCS or σ _ci), modulus of elasticity (E), and thickness of crown and sill pillars (T). These analyses have been conducted based on 135 non-linear numerical models considering Drucker–Prager material model in plane strain condition. Results of the study provide valuable insight into the stress concentration factors of the pillars highlighting stress distributions, roof convergence, yield zones and support requirements. Finally, it suggests the optimum thickness of crown and sill pillar with varying thickness of orebody.