Poroelasticity


Book Description

This book treats the mechanics of porous materials infiltrated with a fluid (poromechanics), focussing on its linear theory (poroelasticity). Porous materials from inanimate bodies such as sand, soil and rock, living bodies such as plant tissue, animal flesh, or man-made materials can look very different due to their different origins, but as readers will see, the underlying physical principles governing their mechanical behaviors can be the same, making this work relevant not only to engineers but also to scientists across other scientific disciplines. Readers will find discussions of physical phenomena including soil consolidation, land subsidence, slope stability, borehole failure, hydraulic fracturing, water wave and seabed interaction, earthquake aftershock, fluid injection induced seismicity and heat induced pore pressure spalling as well as discussions of seismoelectric and seismoelectromagnetic effects. The work also explores the biomechanics of cartilage, bone and blood vessels. Chapters present theory using an intuitive, phenomenological approach at the bulk continuum level, and a thermodynamics-based variational energy approach at the micromechanical level. The physical mechanisms covered extend from the quasi-static theory of poroelasticity to poroelastodynamics, poroviscoelasticity, porothermoelasticity, and porochemoelasticity. Closed form analytical solutions are derived in details. This book provides an excellent introduction to linear poroelasticity and is especially relevant to those involved in civil engineering, petroleum and reservoir engineering, rock mechanics, hydrology, geophysics, and biomechanics.




Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology


Book Description

The theory of linear poroelasticity describes the interaction between mechanical effects and adding or removing fluid from rock. It is critical to the study of such geological phenomena as earthquakes and landslides and is important for numerous engineering projects, including dams, groundwater withdrawal, and petroleum extraction. Now an advanced text synthesizes in one place, with one notation, numerous classical solutions and applications of this highly useful theory. The introductory chapter recounts parallel developments in geomechanics, hydrogeology, and reservoir engineering that are unified by the tenets of poroelasticity. Next, the theory's constitutive and governing equations and their associated material parameters are described. These equations are then specialized for different simplifying geometries: unbounded problem domains, uniaxial strain, plane strain, radial symmetry, and axisymmetry. Example problems from geomechanics, hydrogeology, and petroleum engineering are incorporated throughout to illustrate poroelastic behavior and solution methods for a wide variety of real-world scenarios. The final chapter provides outlines for finite-element and boundary-element formulations of the field's governing equations. Whether read as a course of study or consulted as a reference by researchers and professionals, this volume's user-friendly presentation makes accessible one of geophysics' most important subjects and will do much to reduce poroelasticity's reputation as difficult to master.




Thermo-Poroelasticity and Geomechanics


Book Description

A full account of thermo-poroelasticity and thermo-poromechanics with derivations to problems, for both experienced and novice researchers.




Mechanics of Poroelastic Media


Book Description

In Mechanics of Poroelastic Media the classical theory of poroelasticity developed by Biot is developed and extended to the study of problems in geomechanics, biomechanics, environmental mechanics and materials science. The contributions are grouped into sections covering constitutive modelling, analytical aspects, numerical modelling, and applications to problems. The applications of the classical theory of poroelasticity to a wider class of problems will be of particular interest. The text is a standard reference for researchers interested in developing mathematical models of poroelasticity in geoenvironmental mechanics, and in the application of advanced theories of poroelastic biomaterials to the mechanics of biomaterials.




Variational Continuum Multiphase Poroelasticity


Book Description

This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such as in geomechanics and biomechanics. The theory is derived based on a purely-variational deduction, rooted in the least-Action principle, by considering a minimal set of kinematic descriptors. The treatment herein considered keeps a specific focus on the derivation of most general medium-independent governing equations. It is shown that VMTPM recovers paradigms of consolidated use in multiphase poroelasticity such as Terzaghi's stress partitioning principle and Biot's equations for wave propagation. In particular, the variational treatment permits the derivation of a general medium-independent stress partitioning law, and the proposed variational theory predicts that the external stress, the fluid pressure, and the stress tensor work-associated with the macroscopic strain of the solid phase are partitioned according to a relation which, from a formal point of view, turns out to be strictly compliant with Terzaghi's law, irrespective of the microstructural and constitutive features of a given medium. Moreover, it is shown that some experimental observations on saturated sandstones, generally considered as proof of deviations from Terzaghi's law, are ordinarily predicted by VMTPM. As a peculiar prediction of VMTPM, the book shows that the phenomenon of compression-induced liquefaction experimentally observed in cohesionless mixtures can be obtained as a natural implication of this theory by a purely rational deduction. A characterization of the phenomenon of crack closure in fractured media is also inferred in terms of macroscopic strain and stress paths. Altogether the results reported in this monograph exemplify the capability of VMTPM to describe and predict a large class of linear and nonlinear mechanical behaviors observed in two-phase saturated materials.




Poromechanics


Book Description

Modelling and predicting how porous media deform when subjected to external actions and physical phenomena, including the effect of saturating fluids, are of importance to the understanding of geophysics and civil engineering (including soil and rock mechanics and petroleum engineering), as well as in newer areas such as biomechanics and agricultural engineering. Starting from the highly successful First Edition, Coussy has completely re-written Mechanics of Porous Continua/Poromechanics to include: New material for: Partially saturated porous media Reactive porous media Macroscopic electrical effects A single theoretical framework to the subject to explain the interdisciplinary nature of the subject Exercises at the end of each chapter to aid understanding The unified approach taken by this text makes it a valuable addition to the bookshelf of every PhD student and researcher in civil engineering, petroleum engineering, geophysics, biomechanics and material science.




Mathematical Models for Poroelastic Flows


Book Description

The book is devoted to rigorous derivation of macroscopic mathematical models as a homogenization of exact mathematical models at the microscopic level. The idea is quite natural: one first must describe the joint motion of the elastic skeleton and the fluid in pores at the microscopic level by means of classical continuum mechanics, and then use homogenization to find appropriate approximation models (homogenized equations). The Navier-Stokes equations still hold at this scale of the pore size in the order of 5 – 15 microns. Thus, as we have mentioned above, the macroscopic mathematical models obtained are still within the limits of physical applicability. These mathematical models describe different physical processes of liquid filtration and acoustics in poroelastic media, such as isothermal or non-isothermal filtration, hydraulic shock, isothermal or non-isothermal acoustics, diffusion-convection, filtration and acoustics in composite media or in porous fractured reservoirs. Our research is based upon the Nguetseng two-scale convergent method.




Poroelastic Structures


Book Description

Introduction. Modeling of Poroelastic Beams. Basic equations. Characteristic times. Note on a beam impermeable at both ends. Equations in non-dimensional form. Analytical Solutions for Quasi-Static Beams. Simply-supported beams with permeable ends. Beams subjected to loads suddenly applied and constant thereafter. Finite Element Formulation and Solutions for Quasi-Static Beams. Introduction. Variational principles. Finite element formulation. Examples and discussion. Vibrations of Poroelastic Beams. Initial value problems. Forced harmonic vibrations. Closure. Large Deflection Analysis of Poroelastic Beams. Governing equations. Equations in non-dimensional forms when & egr;0 =0. Numerical formulation. Numerical procedure for the finite difference method. Examples and discussion. Stability of Poroelastic Columns. Buckling of columns. Limits of critical load. Time-dependence of critical load and deflections. Post-buckling: formulation. Post-buckling: results and discussion. Imp ...




A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs


Book Description

This monograph focuses on the numerical methods needed in the context of developing a reliable simulation tool to promote the use of renewable energy. One very promising source of energy is the heat stored in the Earth’s crust, which is harnessed by so-called geothermal facilities. Scientists from fields like geology, geo-engineering, geophysics and especially geomathematics are called upon to help make geothermics a reliable and safe energy production method. One of the challenges they face involves modeling the mechanical stresses at work in a reservoir. The aim of this thesis is to develop a numerical solution scheme by means of which the fluid pressure and rock stresses in a geothermal reservoir can be determined prior to well drilling and during production. For this purpose, the method should (i) include poroelastic effects, (ii) provide a means of including thermoelastic effects, (iii) be inexpensive in terms of memory and computational power, and (iv) be flexible with regard to the locations of data points. After introducing the basic equations and their relations to more familiar ones (the heat equation, Stokes equations, Cauchy-Navier equation), the “method of fundamental solutions” and its potential value concerning our task are discussed. Based on the properties of the fundamental solutions, theoretical results are established and numerical examples of stress field simulations are presented to assess the method’s performance. The first-ever 3D graphics calculated for these topics, which neither requiring meshing of the domain nor involving a time-stepping scheme, make this a pioneering volume.




Petroleum Related Rock Mechanics


Book Description

Engineers and geologists in the petroleum industry will find Petroleum Related Rock Mechanics, 2e, a powerful resource in providing a basis of rock mechanical knowledge - a knowledge which can greatly assist in the understanding of field behavior, design of test programs and the design of field operations. Not only does this text give an introduction to applications of rock mechanics within the petroleum industry, it has a strong focus on basics, drilling, production and reservoir engineering. Assessment of rock mechanical parameters is covered in depth, as is acoustic wave propagation in rocks, with possible link to 4D seismics as well as log interpretation. - Learn the basic principles behind rock mechanics from leading academic and industry experts - Quick reference and guide for engineers and geologists working in the field - Keep informed and up to date on all the latest methods and fundamental concepts