A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs / by Matthias Albert Augustin.

Format:

Book

Author/Creator:

Augustin, Matthias Albert., Author.

Series:

Lecture Notes in Geosystems Mathematics and Computing, 2730-5996

Language:

English

Subjects (All):

Differential equations, Partial.

Numerical analysis.

Geophysics.

Partial Differential Equations.

Numerical Analysis.

Geophysics/Geodesy.

Local Subjects:

Partial Differential Equations.

Numerical Analysis.

Geophysics/Geodesy.

Physical Description:

1 online resource (245 p.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

3-319-17079-1