The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution. 相似文献
This study evaluated the spatial variability of streambed vertical hydraulic conductivity (Kv) in different stream morphologies in the Frenchman Creek Watershed, Western Nebraska, using different variogram models. Streambed Kv values were determined in situ using permeameter tests at 10 sites in Frenchman, Stinking Water and Spring Creeks during the dry season at baseflow conditions. Measurements were taken both in straight and meandering stream channels during a 5 day period at similar flow conditions. Each test site comprised of at least three transects and each transect comprised of at least three Kv measurements. Linear, Gaussian, exponential and spherical variogram models were used with Kriging gridding method for the 10 sites. As a goodness-of-fit statistic for the variogram models, cross-validation results showed differences in the median absolute deviation and the standard deviation of the cross-validation residuals. Results show that using the geometric means of the 10 sites for gridding performs better than using either all the Kv values from the 93 permeameter tests or 10 Kv values from the middle transects and centre permeameters. Incorporating both the spatial variability and the uncertainty involved in the measurement at a reach segment can yield more accurate grid results that can be useful in calibrating Kv at watershed or sub-watershed scales in distributed hydrological models. 相似文献
The aim of this paper is to formulate a micromechanics‐based approach to non‐aging viscoelastic behavior of materials with randomly distributed micro‐fractures. Unlike cracks, fractures are discontinuities that are able to transfer stresses and can therefore be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. Making use of the elastic‐viscoelastic correspondence principle together with a Mori‐Tanka homogenization scheme, the effective viscoelastic behavior is assessed from properties of the material constituents and damage parameters related to density and size of fractures. It is notably shown that the homogenized behavior thus formulated can be described in most cases by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximate model for the isotropic homogenized fractured medium is formulated within the class of Burger models. Although the approximation is basically developed for short‐term and long‐term behaviors, numerical applications indicate that the approximate Burger model accurately reproduce the homogenized viscoelastic behavior also in the transient conditions. 相似文献
Izvestiya, Atmospheric and Oceanic Physics - The problem of atmospheric correction for shortwave channels of a multispectral low-resolution scanning radiometer onboard the Meteor-M No. 2 satellite... 相似文献
Izvestiya, Atmospheric and Oceanic Physics - As a result of studies conducted in the city of Derbent, it is established that its monumental fortification structures erected at the end of the 560s... 相似文献
The use of spontaneous potential (SP) anomalies is well known in the geophysical literatures because of its effectiveness and significance in solving many complex problems in mineral exploration. The inverse problem of self-potential data interpretation is generally ill-posed and nonlinear. Methods based on derivative analysis usually fail to reach the optimal solution (global minimum) and trapped in a local minimum. A new simple heuristic solution to SP anomalies due to 2D inclined sheet of infinite horizontal length is investigated in this study to solve these problems. This method is based on utilizing whale optimization algorithm (WOA) as an effective heuristic solution to the inverse problem of self-potential field due to a 2D inclined sheet. In this context, the WOA was applied first to synthetic example, where the effect of the random noise was examined and the method revealed good results using proper MATLAB code. The technique was then applied on several real field profiles from different localities aiming to determine the parameters of mineralized zones or the associated shear zones. The inversion parameters revealed that WOA detected accurately the unknown parameters and showed a good validation when compared with the published inversion methods.
This paper applied a logistic-based fuzzy logic inference system to integrate critical factors that could control orogenic gold mineralization in part of the Kushaka schist belt, north-central Nigeria to develop a process-based mineral potential mapping (MPM) of the area. The critical factors from geophysical and geological dataset were weighted using logistic functions. The fuzzy logic inference system provides the capability to handle complex geological processes that culminated in orogenic gold mineralization as well as minimizing systemic uncertainties/fuzziness that often plague MPM. The results of this work show that granitic intrusions with fuzzy scores of 0.67–0.90 played a major role in generating high geothermal gradient in the area. Seventy percent of the existing gold mine sites in the area spatially coincide with metasedimentary rocks, having fuzzy scores of 0.7–0.9; this suggests metasedimentary rocks as being responsible for the production of gold fluid and ligands in the area. The evidence of hydrothermal activity, with fuzzy scores of 0.53 and 0.91, confirms the occurrence of mineralization associated with quartz veins and granite rocks. Lithological contacts and faults, having fuzzy scores of 0.60–0.80, presumably contribute to the localization of orogenic gold mineralization in the area. Emerging from the results, favorable zones for primary orogenic gold mineralization in the area occurred predominantly on granite gneiss and quartz veins. The mineral potential map was found consistent with the local geology, structural styles and hydrothermal alteration signatures in the area, and its validation using the existing locations of geochemical anomalies and prediction–area rate curve in the study area showed 75 and 72% agreement, respectively, thus confirming the reliability of the developed mineral potential map for resource management.
Natural Resources Research - Sand failure and production occurs when the formation stress exceeds the strength of the formation, which is derived majorly from the natural material that cements the... 相似文献