Modeling 3D thermal fracture propagation by transient cooling using virtual multidimensional internal bonds

Thermal fracturing can play an important role in development of unconventional petroleum and geothermal resources. Thermal fractures can result from the nonlinear deformation of the rock in response to thermal stress related to cold water injection as well as heating. Before the rock reaches the final failure stage, material softening and bulk modulus degradation can cause changes in the thermo‐mechanical properties of the solid. In order to capture this aspect of the rock fracture, a virtual multidimensional internal bond‐based thermo‐mechanical model is derived to track elastic, softening, and the failure stages of the rock in response to the temporal changes of its temperature field. The variations in thermo‐mechanical properties of the rock are derived from a nonlinear constitutive model. To represent the thermo‐mechanical behavior of pre‐existing fractures, the element partition method is employed. Using the model, numerical simulation of 3D thermal fracture propagation in brittle rock is carried out. Results of numerical simulations provide evidence of model verification and illustrate nonlinear thermal response and fracture development in rock under uniform cooling. In addition, fracture coalescence in a cluster of fractures under thermal stress is illustrated, and the process of thermal fracturing from a wellbore is captured. Results underscore the importance of thermal stress in reservoir stimulation and show the effectiveness of the model to predict 3D thermal fracturing. Copyright © 2016 John Wiley & Sons, Ltd.     

Elastic fields in two joined transversely isotropic media of infinite extent as a result of rectangular loading

This paper presents the closed‐form solutions for the elastic fields in two bonded rocks induced by rectangular loadings. Each of the two bonded rocks behaves as a transversely isotropic linear elastic solid of semi‐infinite extent. They are completely bonded together at a horizontal surface. The rectangular loadings are body forces along either vertical or horizontal directions and are uniformly applied on a rectangular area. The rectangular area is embedded in the two bonded rocks and is parallel to the horizontal interface. The classical integral transforms are used in the solution formulation, and the elastic solutions are expressed in the forms of elementary harmonic functions for the rectangular loadings. The stresses and displacements in the rocks induced by both the horizontal and vertical body forces are also presented. The numerical results illustrate the important effect of the anisotropic bimaterial properties on the stress and displacement fields. The solutions can be easily implemented for numerical calculations and applied to problems encountered in rock mechanics and engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluation of a probabilistic approach to simulation of alkalinity and electrical conductivity at a river bank filtration site

In river bank filtration, impurities present in the river water travel with the bank filtrate towards the pumping well. During this passage, certain types of impurities, such as turbidity, total coliform, and so forth, may get attenuated; however, it is interesting to note that some of the instant raw river water quality parameters, such as alkalinity and electrical conductivity, increase after the passage of water through the porous medium. This occurs because water, when passing through the soil pores, absorbs many of the solutes that cause an increase in alkalinity and electrical conductivity. Measurements at a river bank filtration site for a year showed that alkalinity of 116–32 mg l^?1 in river water increased to 222.4–159.9 mg l^?1 in the river bank filtered water. Likewise, the electrical conductivity increased from 280–131 μS cm^?1 to 462–409.6 μS cm^?1. This study uses a probabilistic approach for investigating the variation of alkalinity and electrical conductivity of source water that varies with the natural logarithm of the concentration of influent water. The probabilistic approach has the potential of being used in simulating the variation of alkalinity and electrical conductivity in river bank filtrate. Copyright © 2011 John Wiley & Sons, Ltd.     

Analytic element modelling for strip aquifers

The Analytic Element Method (AEM) provides a convenient tool for groundwater flow analysis in unbounded continuous domains. The AEM is based on the superposition of analytic functions, known as elements, useful at both regional and local scales. In this study, analytic elements for strip aquifers are presented. Such aquifers occur in riverine or coastal deposits and in outcrop zones of confined aquifers. Local flow field is modelled indirectly, using a reference plane related to the aquifer domain through the Schwarz‐Christoffel transform. The regional flow is obtained as a solution of the one‐dimensional flow equation. The proposed methodology was tested by modelling two hypothetical situations, which were compared to exact solutions. It is shown that regional boundaries can be reproduced exactly while local fields are adequately reproduced with analytic elements. The developed elements are applied to simulate a real flow field in northeastern Brazil showing good agreement with measured water levels. Copyright © 2011 John Wiley & Sons, Ltd.     

Study of bond stress–slip relationship and radial dilation in prestressed concrete

This paper presents two test procedures for evaluating the bond stress–slip and the slip–radial dilation relationships when the prestressing force is transmitted by releasing the steel (wire or strand) in precast prestressed elements. The bond stress–slip relationship is obtained with short length specimens, to guarantee uniform bond stress, for three depths of the wire indentation (shallow, medium and deep). An analytical model for bond stress–slip relationship is proposed and compared with the experimental results. The model is also compared with the experimental results of other researchers. Since numerical models for studying bond‐splitting problems in prestressed concrete require experimental data about dilatancy angle (radial dilation), a test procedure is proposed to evaluate these parameters. The obtained values of the radial dilation are compared with the prior estimated by numerical modelling and good agreement is reached. Copyright © 2012 John Wiley & Sons, Ltd.     

锡石的晶体结构和形态的关系

本文对不同成因类型的锡石晶体形态进行了研究,并从PBC(周期性键链)理论出发,讨论了锡石晶体形态与晶体结构的关系。笔者认为,锡石晶体具有三种F面,即s{111}、e{101}、m{110},与Hartman对同样结构类型的金红石晶面性质划分有所差异。据锡石晶面结构性质所推导的理想晶体形态图,与晶体测量所得到的天然晶体形态图总体上相吻合。     

Bond—Valence Sum and Distortion of Coordination Polyhedra

By using the Lagrange‘s intermediate value theorem,it is derived mathematically that the structur-al distortion of a coordination polyhedron may lead to an increase in bond-valence sum of the cen-tral atom of ion .The applicabilities of the bond-valence model are discussed in the following two cases:the modeling of crystal structure ,and the indication of distortion degree of a coordination polyhedron.Also it is shown that a distorted polyhedron should be in favor of a longer average bond length or a smaller coordination number.     

The Fourier Integral Method: An efficient spectral method for simulation of random fields

The Fourier Integral Method (FIM) of spectral simulation, adapted to generate realizations of a random function in one, two, or three dimensions, is shown to be an efficient technique of non-conditional geostatistical simulation. The main contribution is the use of the fast Fourier transform for both numerical calculus of the density spectral function and as generator of random finite multidimensional sequences with imposed covariance. Results obtained with the FIM are compared with those obtained by other classic methods: Shinozuka and Jan Method in 1D and Turning Bands Method in 2D and 3D, the points for and against different methodologies are discussed. Moreover, with the FIM the simulation of nested structures, one of which can be a nugget effect and the simulation of both zonal and geometric anisotropy is straightforward. All steps taken to implement the FIM methodology are discussed.     

三分量地震资料中各向异性检测

各向异性研究是当令地震学研究领域中重要课题之一；三分量地震资料中各向异性的检测是各向异性理论研究成果解决地球科学实际问题的重要桥梁。本文简要描述了各向异性介质中横波分裂现象，分别介绍了现有的四种主要检测技术，即偏振图法、协方差拒阵法、质，点振动分辨率法及传输矩阵法，并对这四种技术作了一定的评述。