Details

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


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


Lecture Notes in Geosystems Mathematics and Computing

von: Matthias Albert Augustin

53,49 €

Verlag: Birkhäuser
Format: PDF
Veröffentl.: 15.07.2015
ISBN/EAN: 9783319170794
Sprache: englisch

Dieses eBook enthält ein Wasserzeichen.

Beschreibungen

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.<br>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.<br>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.
1.Introduction.- 2. Preliminaries.- 3. Physical and Mathematical Foundation.- 4. Boundary Layer Potentials in Poroelasticity.- 5. Methods of Fundamental Solutions in Poroelasticity.- 6. Numerical Results.- 7. Conclusion and Outlook.- A. Fundamental Stresses and Fluid Velocities.- Bibliography.<br><br>
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.<br>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.<br>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.
First approach to use a method of fundamental solutions for a coupled system of PDEs of different types, in particular a vector-valued elliptic one and a scalar-valued one of Sobolev-evolution type Progress in deep geothermics New methods in 3D numerics for poroelasticity Includes supplementary material: sn.pub/extras

Diese Produkte könnten Sie auch interessieren:

Classical Fourier Analysis
Classical Fourier Analysis
von: Loukas Grafakos
PDF ebook
50,24 €
Nonsmooth Dynamics of Contacting Thermoelastic Bodies
Nonsmooth Dynamics of Contacting Thermoelastic Bodies
von: Jan Awrejcewicz, Yuriy Pyr'yev
PDF ebook
106,99 €
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
von: Kenneth Meyer, Glen Hall, Dan Offin
PDF ebook
106,99 €