Overview
- 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
Part of the book series: Lecture Notes in Geosystems Mathematics and Computing (LNGMC)
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Table of contents (7 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs
Authors: Matthias Albert Augustin
Series Title: Lecture Notes in Geosystems Mathematics and Computing
DOI: https://doi.org/10.1007/978-3-319-17079-4
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-17078-7Published: 23 July 2015
eBook ISBN: 978-3-319-17079-4Published: 15 July 2015
Series ISSN: 2730-5996
Series E-ISSN: 2512-3211
Edition Number: 1
Number of Pages: XII, 235
Number of Illustrations: 37 b/w illustrations, 32 illustrations in colour
Topics: Partial Differential Equations, Numerical Analysis, Geophysics/Geodesy