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.     

Genesis of tin and tantalum mineralization in pegmatites from the Bynoe area,Pine Creek Geosyncline,Northern Territory

The tin‐ and tantalum‐bearing pegmatites of the Bynoe area are located in the western Pine Creek Geosyncline. They are emplaced within psammopelitic rocks in the contact aureole of the Two Sisters Granite. The latter is a Palaeoproterozoic, fractionated, granite with S‐type characteristics and comprises a syn‐ to late‐orogenic, variably foliated, medium‐grained biotite granite and a post‐orogenic, coarse‐grained biotite‐muscovite granite. The pegmatites comprise a border zone of fine grained muscovite + quartz followed inward by a wall zone of coarse grained muscovite + quartz which is in turn followed by an intermediate zone of quartz + feldspar + muscovite. A core zone of massive quartz is present in some occurrences. Feldspars in the intermediate zone are almost completely altered to kaolinite. This zone contains the bulk of cassiterite, tantalite and columbite mineralization. Fluid inclusions in pegmatitic quartz indicate that early Type A (CO₂ + H₂O ± CH₄) inclusions were trapped at the H₂O‐CO₂ solvus at P～100 MPa, T～300°C (range 240–328°C) and salinity ～6 wt% eq NaCl. Pressure‐salinity corrected temperatures on Type B (H₂O + ～20% vapour), C (H₂O + < 15% vapour) and D (H₂O + halite + vapour) inclusions also fall within the range of Type A inclusions. Oxygen and hydrogen isotope data show that kaolin was either formed in isotopic equilibrium with meteoric waters or subsequent to its formation, from hydrothermal fluid, underwent isotopic exchange with meteoric waters. Fluid inclusion waters from core zone quartz show enrichment in deuterium suggesting metamorphic influence. Isotope values on muscovite are consistent with a magmatic origin. It is suggested that the pegmatites were derived from the post‐orogenic phase of the Two Sisters Granite. Precipitation of cassiterite took place at about 300°C from an aqueous fluid largely as a result of increase in pH due to feldspar alteration.     

Selecting Equivalent Strength for Intact Rocks in Heterogeneous Rock Masses

Many surface and underground structures are constructed in heterogeneous rock formations. These formations have a combination of weak and strong rock layers. Due to the alternation of the weak and strong layers, selecting the equivalent and appropriate geomechanical parameters for these formations is challenging. One of these problems is choosing the equivalent strength (i.e., uniaxial compressive strength) of intact rock for a group of rocks. Based on the volume of weak and strong parts and their strength, the equivalent strength of heterogeneous rocks changes. Marinos and Hoek (Bull Eng Geol Environ 60(2):85–92, 2001) presented the “weighted average method” for defining the uniaxial compressive strength (UCS) of heterogeneous rock masses based on the volume of weak and strong parts. Laubscher (1977) used the volume ratio of the strength of a weak part to a strong part (UCS weak/UCS strong) to determine the equivalent strength. In this study, the two methods are compared and their validity is evaluated by experimental data and numerical analyses. The geomechanical parameters of two heterogeneous formations (Aghajari and Lahbari) in the west of Iran were estimated using these methods. The results of the present study obtained through numerical analyses using particle flow code are compared with those of previous studies and discussed. Laboratory and numerical results show UCS decrease and approach to weak strength with an increasing in volume of weak part. When strength ratio of strong to weak rock increase, equivalent strength decrease more severely. The findings show that Laubscher’s method gives more appropriate results than the weighted average method.     

Understanding nesting ecology and behaviour of green marine turtles at Setiu,Terengganu, Malaysia

In this paper, we emphasize the importance of understanding the nesting ecology and nesting behaviour of green marine turtles (Chelonia mydas). Data were collected from 2007 until 2012 from nesting beaches at Setiu Terengganu, Malaysia. We focused on one of the beaches, Telaga Papan, based on data collected in 2012. We recorded the distribution of nesting areas, the emergence hour and the correlation between successful nesting attempts and false crawls. Telaga Papan had a significantly higher distribution of green marine turtle nesting compared with the other five beaches (ANOVA, F_5,42 = 8.874, P < 0.01, mean = 36.750 ± 3.727). The highest number of successful nesting attempts was recorded in 2012 (mean = 28.714). A majority of the species landed between 22:00 and 23:59 h (25%). There was a strong correlation between successful nesting attempts and false crawls (r_s = 0.883, P = 0.02). Based on these findings on the nesting ecology and nesting behaviour of green marine turtles, we suggest that scientific research, strict monitoring, awareness programs and policy implementation should be carried out proactively. Such activities are necessary to reduce the anthropogenic pressures at the nesting beaches as well as to ensure more successful nesting attempts of green marine turtles in Setiu.     

Regional bivariate modeling of droughts using L-comoments and copulas

The regional bivariate modeling of drought characteristics using the copulas provides valuable information for water resources management and drought risk assessment. The regional frequency analysis (RFA) can specify the similar sites within a region using L-comoments approach. One of the important steps in the RFA is estimating regional parameters of the copula function. In the present study, an optimization-based method along with the adjusted charged system search are introduced and applied to estimate the regional parameters of the copula models. The capability of the proposed methodology is illustrated by copula functions on drought events. Three commonly used copulas containing Clayton, Frank and Gumbel are employed to derive the joint distribution of drought severity and duration. The result of the new method are compared to the method of moments and after applying several goodness-of-fit tests, the results indicate that the new method provides higher accuracy than the classic one. Furthermore, the results of the upper tail dependence coefficient indicate that the Gumbel copula is the best-fitted copula among the other ones for modeling drought characteristics.     

Full-range equation for wave boundary layer thickness

Full-range equation covering all the flow regimes in a wave boundary layer is proposed for the boundary layer thickness. The results are compared with the available experimental data and good agreement has been found. In case of wave boundary layers, there are three definitions of boundary layer thickness in use. Therefore, the full-range equation is derived for three of the definitions. The findings of this study may be useful in calculating suspended sediment transport in coastal environments and studying wave–current combined motion.     

Integrated methodology for flood risk assessment and application in urban communities of Pakistan

Flood disasters and its consequent damages are on the rise globally. Pakistan has been experiencing an increase in flood frequency and severity along with resultant damages in the past. In addition to the regular practices of loss and damage estimation, current focus is on risk assessment of hazard-prone communities. Risk measurement is complex as scholars engaged in disaster science and management use different quantitative models with diverse interpretations. This study tries to provide clarity in conceptualizing disaster risk and proposes a risk assessment methodology with constituent components such as hazard, vulnerability (exposure and sensitivity) and coping/adaptive capacity. Three communities from different urban centers in Pakistan have been selected based on high flood frequency and intensity. A primary survey was conducted in selected urban communities to capture data on a number of variables relating to flood hazard, vulnerability and capacity to compute flood risk index. Households were categorized into different risk levels, such as can manage risk, can survive and cope, and cannot cope. It was found that risk levels varied significantly across the households of the three communities. Metropolitan city was found to be highly vulnerable as compared to smaller cities due to weak capacity. Households living in medium town had devised coping mechanisms to manage risk. The proposed methodology is tested and found operational for risk assessment of flood-prone areas and communities irrespective of locations and countries.     

Applications of particle-tracking techniques to bank infiltration: a case study from El Paso,Texas, USA

This paper presents results of a small scale study that utilized particle-tracking techniques to evaluate transport of river water through an alluvial aquifer in a bank infiltration testing site in El Paso, Texas, USA. The particle-tracking survey was used to better define filtration parameters. Several simulations were generated to allow visualization of the effects of well placement and pumping rate on flow paths, travel time, the size of the pumping influence zone, and proportion of river-derived water and groundwater mixing in the pumping well. Simulations indicate that migration of river water into the aquifer is generally slow. Most water does not arrive at the well by the end of an 18-day pumping period at 0.54 m³/min pumping rate for a well located 18 m from the river. Forty-four percent of the water pumped from the well was river water. The models provided important information needed to design appropriate sampling schedules for bank filtration practices and ensured meeting adequate soil-retention times. The pumping rate has more effect on river water travel time than the location of the pumping well from the river. The examples presented in this paper indicate that operating the pumping well at a doubled distance from the river increased the time required for the water to travel to the well, but did not greatly change the capture zone.     

Integrated petrographic,mineralogical, and geochemical study of the upper Kaimur Group of rocks,Son Valley,India: Implications for provenance,source area weathering and tectonic setting

The upper Kaimur Group (UKG) of the Vindhyan Supergroup in central India, primarily consists of three rock types-Dhandraul sandstone, Scarp sandstone and Bijaigarh shale. The present study aims to reconstruct the parent rock assemblages, their tectonic provenance, mineralogy, weathering intensity, hydraulic sorting and depositional tectonic setting. Samples from the UKG rocks representing the Dhandraul sandstone, Scarp sandstone and Bijaigarh shale were studied using a combination of petrographic, mineralogical, and geochemical techniques. Texturally, medium to coarse grained UKG sandstones are mature and moderate to well sorted. Deficiency of feldspars in these sandstones indicates that the rocks are extensively recycled from distant sources. Their average modal composition for Scarp (avg. Qt₉₉ F₀.₂L_0.8) and Dhandraul (avg. Qt₉₉ F_0.1L_0.8) sandstones, classifies them as quartz arenite to sub-litharenite types, which is consistent with geochemical study. Major element concentrations revealed that sandstones have high SiO₂, K₂O < Na₂O, and low Fe₂O₃, which are supported by the modal data. On the other hand, sandstone samples are enriched in most trace elements such as Ce, Sr, V, Sc and Zr and depleted in U and Th. The CIA values (43.17–76.48) of the UKG rocks indicate low to moderate weathering, either of the original source or during transport before deposition, which may have related to low-relief and humid climatic conditions in the source area. Further, petrographic and geochemical interpretations indicate that they are derived from craton interior to quartzose recycled sedimentary rocks and deposited in a passive continental margin. Therefore, granitic and low grade metamorphic rocks of Mahakoshal Group and Chotanagpur granite-gneiss, situated on the southern and south-eastern side of the Vindhyan basin are suggested as possible provenance for the UKG rocks.     

Long-range precipitation forecasts using paleoclimate reconstructions in the western United States

Long-range precipitation forecasts are useful when managing water supplies.Oceanicatmospheric oscillations have been shown to influence precipitation.Due to a longer cycle of some of the oscillations,a short instrumental record is a limitation in using them for long-range precipitation forecasts.The influence of oscillations over precipitation is observable within paleoclimate reconstructions;however,there have been no attempts to utilize these reconstructions in precipitation forecasting.A data-driven model,KStar,is used for obtaining long-range precipitation forecasts by extending the period of record through the use of reconstructions of oscillations.KStar is a nearest neighbor algorithm with an entropy-based distance function.Oceanic-atmospheric oscillation reconstructions include the El Nino-Southern Oscillation(ENSO),the Pacific Decadal Oscillation(PDO),the North Atlantic Oscillation(NAO),and the Atlantic Multi-decadal Oscillation(AMO).Precipitation is forecasted for 20 climate divisions in the western United States.A 10-year moving average is applied to aid in the identification of oscillation phases.A lead time approach is used to simulate a one-year forecast,with a 10-fold cross-validation technique to test the models.Reconstructions are used from 1658-1899,while the observed record is used from 1900-2007.The model is evaluated using mean absolute error(MAE),root mean squared error(RMSE),RMSE-observations standard deviation ratio(RSR),Pearson’s correlation coefficient(R),NashSutcliffe coefficient of efficiency(NSE),and linear error in probability space(LEPS) skill score(SK).The role of individual and coupled oscillations is evaluated by dropping oscillations in the model.The results indicate ’good’ precipitation estimates using the KStar model.This modeling technique is expected to be useful for long-term water resources planning and management.