Andrea Villa Ledizioni LediPublishing

134 Pages·2010·8.24 MB·English

Andrea Villa

Three Dimensional Geophysical Modeling:
from Physics to Numerical Simulation

Ledizioni LediPublishing
Andrea Villa
Department of Mathematics
University of Milan
Via C. Saldini n.50
20133 Milan - Italy

Series Editors:
Vincenzo Capasso,
Coordinator of the PhD Program in Mathematics and Statistics for
Computational Sciences;
Alfredo Lorenzi,
Coordinator of the PhD Program in Mathematics;
Bernhard Ruf,
Director of the Graduate School.

Editorial Assistant: Stefania Leonardi

© 2010 Andrea Villa
Open Access copy available at air.unimi.it
First Edition: September 2010
ISBN 978-88-95994-14-7
All rights reserved for the print copy.
For the digital copy rights please refer to air.unimi.it

Ledizioni LediPublishing
Via Alamanni 11 – 20141 Milano – Italy
http://www.ledipublishing.com
[email protected]
Andrea Villa
Three Dimensional Geophysical
Modeling: from Physics to
Numerical Simulation
September15,2010

In memoryofFaustoSaleri

Acknowledgements
Iwishtoacknowledgetheactualandformerjuniormembersofthenumericalgeol-
ogygroupatMOX:AnnaScotti,DavideSoresinetti,MatteoLongoni,FrancoDassi,
CristianoMalossi,MarcoCuffaroandAlessioFumagalli.
InamgratefultotheseniormembersofthenumericalgeologygroupatMOX:Prof.
AlfioQuarteroni,Prof.LucaFormaggia,Dr.FabioNobile,Dr.EdieMiglio,Dr.Si-
monaPerotto,Dr.CarloD’Angelo.
ManythankstoP.RuffoandG.Scrofaniforhavingsupportedourresearchprogram.
IwishalsotothankLauraBarbareschiandGabrieleVillafortheirlinguisticalhelp
andadvices.
vii

Contents
1 Introduction................................................... 1
2 Anoverviewonbasingeology.................................... 5
2.1 Aninsightintosedimentarybasins ............................ 5
2.2 Sedimentarybasingeology .................................. 6
2.3 Motivationsfornumericalsimulations ......................... 9
2.4 Uncertainty................................................ 9
3 Mathematicalmodelsforbasinsimulationandcompaction ......... 11
3.1 Compactionmodels ........................................ 12
3.1.1 Thegeometryofthebasin............................. 12
3.1.2 Volumeaveragingtheorems ........................... 13
3.1.3 Momentumequationaverage .......................... 16
3.1.4 Massequationaveraging.............................. 21
3.1.5 Averagedenergybalance.............................. 22
3.1.6 Constitutiveequations ................................ 23
3.1.7 Thecompletemacroscopicmodels...................... 25
3.1.8 Approximatedmodels ................................ 27
3.2 Numericalsolutionforcompactionmodels ..................... 29
3.2.1 Timediscretizationalgorithmfor(3.50) ................. 29
3.2.2 Timediscretizationalgorithmfor(3.51) ................. 30
3.2.3 Algorithmanalysis................................... 31
3.3 Numericalsolutionforaone-dimensionalcase .................. 33
3.3.1 Theone-dimensionalcaseandnumericaltechniques....... 33
3.3.2 Numericalresults .................................... 34
3.4 Nomenclature.............................................. 39
4 Multi-fluidtracking ............................................ 41
4.1 Abriefreviewoftheliterature................................ 41
4.2 Theproposedmethod ....................................... 42
4.3 Analysisofthemethod...................................... 48
ix
x Contents
4.4 Convergenceanalysisoftheonedimensionalcase ............... 52
4.5 Numericalresults........................................... 55
4.6 Results ................................................... 55
4.7 Nomenclature.............................................. 59
5 Numericalmodelsforbasicbasinsimulations ..................... 61
5.1 Physicalandmathematicalmodels ............................ 62
5.2 Timediscretization ......................................... 63
5.3 Velocityfieldsolver ........................................ 64
5.4 Tracking.................................................. 71
5.5 Algorithmworkflow ........................................ 76
5.6 Numericalresults........................................... 77
5.7 Nomenclature.............................................. 84
6 NumericalModelsforadvancedbasinsimulations ................. 87
6.1 Physicalandmathematicalmodels ............................ 89
6.1.1 Nomenclature ....................................... 89
6.1.2 Rheologicalmodels .................................. 90
6.1.3 Modelingthecompaction ............................. 91
6.1.4 Themodel.......................................... 93
6.2 Numericaldiscretization..................................... 93
6.3 Adaptivegridmovement .................................... 95
6.3.1 Gridmovementequations ............................. 95
6.3.2 Errorestimation ..................................... 98
6.3.3 Metricdefinition.....................................101
6.4 Thehandlingoffaults.......................................103
6.4.1 Afinitevolumescheme...............................103
6.4.2 Setreconstruction(continuouspart).....................104
6.4.3 Setreconstruction(discretepart) .......................106
6.4.4 Thereconstructionalgorithmappliedtoasimplecase......107
6.4.5 Localgridrefinement.................................108
6.5 Algorithmworkflow ........................................109
6.6 Numericalresults...........................................110
7 Conclusions ...................................................117
References.........................................................119