scholarly journals Three-dimensional analytical poromechanical solutions for an arbitrarily inclined borehole subjected to fluid injection

2019 ◽  
Vol 475 (2221) ◽  
pp. 20180658 ◽  
Author(s):  
S. L. Chen
Keyword(s):  
Stress Responses ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Gas Production ◽  
Element Analysis ◽  
Expansion Theorem ◽  
Inclined Borehole

Hydraulic fracturing is the primary method of stimulation in unconventional reservoirs, playing a significant role in oil and gas production enhancement. A key issue for the analysis of hydraulic fracture initiation is to accurately determine the stress distributions in the vicinity of the borehole caused by the injection of pressurized fluids. This paper develops an exact, three-dimensional, poroelastic coupled analytical solution for such stress analysis of an arbitrarily inclined borehole subjected concurrently to a finite-length fluid discharge and in situ stresses, using Fourier expansion theorem and the Laplace–Fourier integral transform technique. The complicated boundary conditions, which involve the mixed boundary values at the borehole surface and the coupling between the total radial stress and injection-induced pore pressure over the sectioned borehole interval, as well as the fully three-dimensional far field in situ stresses, are addressed in a novel way and deliberately/elegantly decomposed into five fundamental, easier to handle modes. The rigour and definitive nature of the proposed analytical methodology facilitates fundamental understanding of the mechanism underlying the stress responses of the borehole and porous medium. It can be and is used here as a benchmark for the numerical solutions obtained from the finite-element analysis commercial program (ABAQUS).

Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium

2005 ◽  
Vol 72 (1) ◽  
pp. 102-114 ◽  
Author(s):  
Younane Abousleiman ◽  
Shailesh Ekbote
Keyword(s):  
Transverse Isotropy ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Systematic Analysis ◽  
General Anisotropy ◽  
Pressure Distributions ◽  
In Situ Conditions ◽  
Poroelastic Material ◽  
Inclined Borehole

A porothermoelastic solution of the general problem of the inclined borehole in a transversely isotropic porous material is presented herein and compared with the isotropic porothermoelastic solution. The governing equations are outlined for the case of general anisotropy and specialized for a transversely isotropic poroelastic material under nonhydrostatic and nonisothermal in situ conditions. A superposition scheme is employed to obtain the analytical solutions within the isotropic and transversely isotropic poromechanics theory. The borehole generator is assumed to coincide with the material axis of symmetry, in the case of transverse isotropy, yet subjected to a three-dimensional state of stress. A systematic analysis has been carried out to evaluate the effect of the anisotropy of the poromechanical material parameters as well as the thermal material properties on stress and pore pressure distributions and the potential impact on the overall stability of deep wellbore drilling.

Stability of D-shaped tunnels in a Mohr–Coulomb material under anisotropic stress conditions

2006 ◽  
Vol 43 (3) ◽  
pp. 273-281 ◽  
Author(s):  
M A Meguid ◽  
R K Rowe
Keyword(s):  
Finite Element ◽  
Rock Mass ◽  
Three Dimensional ◽  
In Situ Stress ◽  
Stress Conditions ◽  
Element Analysis ◽  
Overburden Pressure ◽  
Face Stability ◽  
Rock Mass Strength

The near-face stability of D-shaped tunnels excavated in a Mohr–Coulomb material subjected to anisotropic in situ stress conditions is investigated in the present study. The construction of the intake tunnel of the Darlington Nuclear Generating Station is analyzed using three-dimensional elasto-plastic finite element analysis. The induced displacement and stresses around the tunnel opening as the face advances are compared to the field measurements recorded during the tunnel excavation. The effect of rock mass strength reduction on the tunnel deformation, face stability, and distribution of stresses at the tunnel circumference is investigated for different in situ stress conditions. When the ratio of rock mass strength to overburden pressure falls below 0.5, excessive deformation occurrs and squeezing of the rock mass becomes a problem that can cause instability of both the tunnel circumference and the face.Key words: weak rock, tunnelling, horizontal stresses, three-dimensional, finite element, excavation, face stability.

scholarly journals Three-Dimensional Investigation of the Stokes Eigenmodes in Hollow Circular Cylinder

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Adil El Baroudi ◽  
Fulgence Razafimahery
Keyword(s):  
Present Method ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Finite Depth ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Element Analysis ◽  
Fluid Medium ◽  
Stokes Eigenmodes ◽  
Good Agreement

This paper studies the influence of boundary conditions on a fluid medium of finite depth. We determine the frequencies and the modal shapes of the fluid. The fluid is assumed to be incompressible and viscous. A potential technique is used to obtain in three-dimensional cylindrical coordinates a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier-Stokes equation. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effect of the fluid thickness on the Stokes eigenmodes is also investigated. It is found that frequencies are strongly influenced.

A CO-ROTATIONAL FORMULATION FOR GEOMETRICALLY NONLINEAR FINITE ELEMENT ANALYSIS OF SPATIAL BEAMS

1994 ◽  
Vol 18 (1) ◽  
pp. 65-88 ◽  
Author(s):  
L. Jiang ◽  
M.W. Chernuka
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Internal Force ◽  
Beam Element ◽  
Geometrically Nonlinear ◽  
Element Analysis ◽  
Finite Element Program ◽  
Geometrically Nonlinear Analysis ◽  
Spatial Beams

A co-rotational procedure is presented in this paper for handling arbitrarily large three-dimensional rotations associated with geometrically nonlinear analysis of spatial beam structures. This procedure has been incorporated into two commonly used 3-D beam elements, the 2-node cubic beam element and the 3-node superparametric beam element, in our in-house general purpose finite element program, VAST. In the present procedure, the element tangent stiffness matrices are generated by using the standard updated Lagrangian formulation, while a co-rotational formulation is employed to update the internal force vectors during the Newton-Raphson iterations, A number of example problems have been analyzed and the result are in good agreement with analytical or published numerical solutions.

scholarly journals Numerical and Experimental Study of the Mechanical Response of Diatom Frustules

Nanomaterials ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 959 ◽  
Author(s):  
Emre Topal ◽  
Harishankaran Rajendran ◽  
Izabela Zgłobicka ◽  
Jürgen Gluch ◽  
Zhongquan Liao ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Finite Element ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Element Analysis ◽  
Didymosphenia Geminata ◽  
Novel Approach ◽  
Transmission Electron ◽  
Micro Indentation

Diatom frustules, with their hierarchical three-dimensional patterned silica structures at nano to micrometer dimensions, can be a paragon for the design of lightweight structural materials. However, the mechanical properties of frustules, especially the species with pennate symmetry, have not been studied systematically. A novel approach combining in situ micro-indentation and high-resolution X-ray computed tomography (XCT)-based finite element analysis (FEA) at the identical sample is developed and applied to Didymosphenia geminata frustule. Furthermore, scanning electron microscopy and transmission electron microscopy investigations are conducted to obtain detailed information regarding the resolvable structures and the composition. During the in situ micro-indentation studies of Didymosphenia geminata frustule, a mainly elastic deformation behavior with displacement discontinuities/non-linearities is observed. To extract material properties from obtained load-displacement curves in the elastic region, elastic finite element method (FEM) simulations are conducted. Young’s modulus is determined as 31.8 GPa. The method described in this paper allows understanding of the mechanical behavior of very complex structures.

Mechanics of Small Utility Cuts in Urban Street Pavements: Implications for Restoration

1998 ◽  
Vol 1629 (1) ◽  
pp. 226-233 ◽  
Author(s):  
Mewburn H. Humphrey ◽  
Neville A. Parker
Keyword(s):  
Flexible Pavements ◽  
Three Dimensional ◽  
Element Analysis ◽  
Urban Street ◽  
Excavation Process ◽  
Dimensional Finite Element ◽  
Pavement Structure ◽  
Three Dimensional Finite Element

The results of a three-dimensional finite element analysis of the impacts of small utility cuts in urban street pavements are presented. The analysis was restricted to flexible pavements for cuts of the order of 915 mm (3 ft) square. Using ANSYS Solid 45 Version 5.2 on a one-eighth area, the excavation process was simulated using a stress relief approach, in which the material was assumed to be removed in successive layers. Starting with gravity loading on the uncut model, the element stress results from the previous removal were used to compute the new effective confining stresses of the respective layers. The in situ material properties were typical of flexible pavements in an urban street. The analysis presented a clear picture of the magnitude and extent of the distress induced on the pavement structure below and surrounding the cut. The analysis also showed how the restraining action of the asphalt layer is reflected in its arching up from heave and granular material thrusting, causing tension at the bottom and compression at the top. The results suggested that for unsupported depths of up to 1524 mm (5 ft), material distress may extend approximately 1068 mm (3.5 ft) into the pavement structure. Implications for methodology and economics of restoration are discussed, including determination of optimum cutback and recompaction of the affected area of pavement.

In Situ Tooth Replica Custom Implant: A 3-Dimensional Finite Element Stress and Strain Analysis

2013 ◽  
Vol 39 (5) ◽  
pp. 559-573 ◽  
Author(s):  
Wael Aly Ghuneim
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Biomechanical Study ◽  
Vertical Force ◽  
Element Analysis ◽  
3 Dimensional ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

This study is a phase of a biomechanical study, a part of a research program concerned with the new concept of in situ tooth replication. The purpose of the study was to evaluate tooth replica under each of two possible circumstances: (1) attachment via periodontal ligament and (2) osseointegration. Replicas were made of Cortoss, a bioactive glass, bone substitute. Three-dimensional finite element analysis was used to assess the stresses and strains resulting from each of 2 types of loads: off-vertical pressure and vertical point force acting on natural mandibular second premolar and corresponding replicas. Natural tooth tolerated 19 MPa pressure or 85 N vertical force, periodontally attached replica tolerated 15 MPa pressure or 80 N force, and osseointegrated replica tolerated 23 MPa pressure or 217 N force.

Correlated Studies of Cellular Interactions Using TEM, Freeze Etching, and SEM

1974 ◽  
Vol 32 ◽  
pp. 320-321
Author(s):  
J. P. Revel
Keyword(s):  
Developmental Stages ◽  
Three Dimensional ◽  
Cell Movement ◽  
Cellular Interactions ◽  
Serial Sections ◽  
Cell Sheets ◽  
Freeze Etching ◽  
Early Developmental

Movement of individual cells or of cell sheets and complex patterns of folding play a prominent role in the early developmental stages of the embryo. Our understanding of these processes is based on three- dimensional reconstructions laboriously prepared from serial sections, and from autoradiographic and other studies. Many concepts have also evolved from extrapolation of investigations of cell movement carried out in vitro. The scanning electron microscope now allows us to examine some of these events in situ. It is possible to prepare dissections of embryos and even of tissues of adult animals which reveal existing relationships between various structures more readily than used to be possible vithout an SEM.

In vitro and in vivo polysaccharides assembly: ultrastructural and cytochemical study of growing plant cell wall components.

1978 ◽  
Vol 36 (2) ◽  
pp. 434-435
Author(s):  
D. Reis ◽  
B. Vian ◽  
J. C. Roland
Keyword(s):  
Cell Wall ◽  
Self Assembly ◽  
Plant Cell Wall ◽  
Higher Plants ◽  
Three Dimensional ◽  
Cytochemical Study ◽  
Wall Components

Wall morphogenesis in higher plants is a problem still open to controversy. Until now the possibility of a transmembrane control and the involvement of microtubules were mostly envisaged. Self-assembly processes have been observed in the case of walls of Chlamydomonas and bacteria. Spontaneous gelling interactions between xanthan and galactomannan from Ceratonia have been analyzed very recently. The present work provides indications that some processes of spontaneous aggregation could occur in higher plants during the formation and expansion of cell wall.Observations were performed on hypocotyl of mung bean (Phaseolus aureus) for which growth characteristics and wall composition have been previously defined.In situ, the walls of actively growing cells (primary walls) show an ordered three-dimensional organization (fig. 1). The wall is typically polylamellate with multifibrillar layers alternately transverse and longitudinal. Between these layers intermediate strata exist in which the orientation of microfibrils progressively rotates. Thus a progressive change in the morphogenetic activity occurs.

In situ investigation of the primary recrystallization of alpha titanium in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 634-635
Author(s):  
S. Naka ◽  
R. Penelle ◽  
R. Valle
Keyword(s):  
Dimensional Analysis ◽  
Texture Evolution ◽  
Cold Work ◽  
Three Dimensional ◽  
Primary Recrystallization ◽  
Thin Foils ◽  
In Situ Investigation ◽  
Grain Growth Model ◽  
Alpha Titanium

The in situ experimentation technique in HVEM seems to be particularly suitable to clarify the processes involved in recrystallization. The material under investigation was unidirectionally cold-rolled titanium of commercial purity. The problem was approached in two different ways. The three-dimensional analysis of textures was used to describe the texture evolution during the primary recrystallization. Observations of bulk-annealed specimens or thin foils annealed in the microscope were also made in order to provide information concerning the mechanisms involved in the formation of new grains. In contrast to the already published work on titanium, this investigation takes into consideration different values of the cold-work ratio, the temperature and the annealing time.Two different models are commonly used to explain the recrystallization textures i.e. the selective grain growth model (Beck) or the oriented nucleation model (Burgers). The three-dimensional analysis of both the rolling and recrystallization textures was performed to identify the mechanismsl involved in the recrystallization of titanium.

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