Caractérisation 3D de l

Caractérisation 3D de l'hétérogénéité de la perméabilité à l'échelle de l'échantillon, 3D Chatacterization of Permeability Heterogeneity at the Core Scale

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Sous la direction de Mostafa Fourar
Thèse soutenue le 21 octobre 2008: INPL
L’objet de cette thèse est de développer des méthodologies permettant d’identifier la distribution spatiale des valeurs de perméabilité dans des échantillons de roches. Nous avons tout d’abord développé en laboratoire des expériences d’injection de fluide miscible très visqueux dans des échantillons initialement saturés par une saumure peu visqueuse. Pendant l’injection, l’évolution au cours du temps de la pression différentielle entre les deux faces de l’échantillon a été enregistrée par des capteurs de pression. En outre, des mesures scanner ont fourni une carte 3D de la porosité ainsi que des cartes 3D décrivant la distribution spatiale des concentrations dans l’échantillon à différents temps. Nous avons mis en place une méthode d’interprétation donnant directement le profil 1D de la perméabilité le long de la direction d’écoulement à partir de la pression différentielle mesurée au cours du temps. Cette méthode a été validée numériquement et expérimentalement. Puis, afin d’affiner la description de l’agencement des valeurs de perméabilité dans l’échantillon, c’est à dire d’obtenir un modèle 3D de perméabilité représentatif de l’échantillon, nous avons développé une méthodologie itérative de calage des pressions et des concentrations. Cette méthode passe par deux étapes : une optimisation simple pour capturer l’hétérogénéité dans la direction de l’écoulement et une optimisation complexe pour capturer l’hétérogénéité transverse. Cette méthode a été validée à partir de tests numériques. La méthode a été appliquée à deux des expériences d’injection de fluide visqueux. Nous avons pu alors déterminer des modèles de perméabilité capables de reproduire assez bien les données de pression et de concentration acquises pendant l’injection
-Perméabilité
-Darcy
-History-matching
-CT-scan
-Ecoulement miscible visqueux
-Hétérogénéités
The objective of this study is to develop new methodologies to identify the spatial distribution of permeability values inside the heterogeneous core samples. We developed laboratory viscous miscible displacements by injecting high viscosity glycerin into the core samples initially saturated by low viscosity brine. The pressure drop across the samples was measured as a function of time until breakthrough. Meanwhile, CT scan measurements provided a 3D porosity map plus several 3D maps of concentration distribution inside the core samples at different times. A simple permeability mapping technique was developed deducing a one-dimensional permeability profile along the flow direction from the measured pressure drop data. The method was validated with both numerical and laboratory experiments. To go beyond one-dimensional characterization of permeability into cores, we developed an iterative process for matching pressure and concentration data. This method consisted of two steps: a simple optimization for capturing the permeability heterogeneity along the flow direction axis and a complex optimization for capturing transversal permeability heterogeneities. The methodology was validated by numerical data. It was also applied to the data collected from two laboratory viscous miscible displacements. We showed that the final 3D permeability models reproduce well the measured pressure drop and concentration data
-Local permeability heterogeneity
-History-matching
-Optimization
-CT measurement
-Viscous miscible displacement
Source: http://www.theses.fr/2008INPL049N/document

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Ajouté le 25 octobre 2011
Nombre de lectures 35
Langue English
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LIENS




Code de la propriété intellectuelle. Articles L 122.4
Code de la propriété intellectuelle. Articles L 335.2 – L 335.10
http://www.cfcopies.com/V2/leg/leg_droi.php
http://www.culture.gouv.fr/culture/infos-pratiques/droits/protection.htm
`THESE
DE L’INSTITUT NATIONAL POLYTECHNIQUE DE
LORRAINE
´ ´ ´ ´ECOLE DOCTORALE ENERGIE MECANIQUE MATERIAUX
pour obtenir le titre de
DOCTEUR DE L’INPL
Sp´ecialit´e:M´ecanique Energ´etique
Pr´esent´ee et soutenue par
AmirSOLTANI
´ ´ ´ ´ ´ ´CARACTERISATION 3D DE L’HETEROGENEITEDELA
´ ´ ` ´ ´PERMEABILITE AL’ECHELLE DE L’ECHANTILLON
soutenue le 21 octobre 2008 devant le jury compos´ede:
Christian DAVID, professeur, universit´e de Cergy-Pontoise Rapporteur
Fred DELAY, professeur, universit´edePoitiers Rapp
MostafaFOURAR, professeur, INPL Directeur
MickaeleLE RAVALEC-DUPIN,ing´enieur de recherche, IFP Co-Directeur
PatrickEGERMANN, Chef du groupe R&D stockage, GDF Suez Examinateur
DidierLASSEUX,charg´e de recherche CNRS, ENSAM Bordeaux
BenoitNOETINGER,ing´enieur de recherche, IFP Invit´eTable des mati`eres
R´ esume 1
Remerciements 3
1 Introduction 4
1.1 L’h´et´erog´en´eit´e`al’´echelle de l’´echantillon jusqu’`al’´echelle du r´eservoir . . . 5
1.2 H´et´erog´en´eit´eetdonn´esdegisement...................... 6
1.3 H´et´erog´en´eit´eetmod´elisation num´erique.................... 7
1.4 H´et´erog´en´eit´eetg´eostatistique.......................... 9
1.5 Objectifs de la th`ese............................... 10
2 Etat de l’art 12
2.1 Caract´erisation al` ’´echelle du r´eservoir ..................... 12
2.2´ al` ’´echelle de la carotte et du pore . . . . . . . . . . . . . . . 13
3 Caract´erisation unidimensionnelle de l’h´et´erog´en´eit´edelaperm´eabilit´e18
3.1 Introduction.................................... 18
3.2 Description de la m´ethodologie ......................... 18
3.3 Echantillons de roche et mod`eles num´eriques.................. 20
3.3.1 Echantillons de roche . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3.2 Mod`eles num´eriques ........................... 20
3.4 Validation num´erique............................... 21
3.4.1 Calcul des d´eriv´es............................ 21
3.4.2 D´eplacementimmiscible......................... 2
3.4.3 D´eplacementmiscible. 2
3.5 Validation exp´erimentale............................. 2
3.6 Conclusion..................................... 26
4 Caract´erisation tridimensionnelle de l’h´et´erog´en´eit´edelaperm´eabilit´e27
4.1 Introduction 27
4.2 Param´etrage du mod`eledeperm´eabilit´e..................... 27
i4.2.1 D´efinitiondelafonctionobjectif..................... 28
4.3 Boucledecalage ................................. 29
4.3.1 Optimisationsimple ........................... 29
4.3.2 Optimisationgraduelle 29
4.4 Validation num´erique............................... 30
4.4.1 Mod`eles num´eriques . 30
4.4.2 M´ethodologie............................... 31
4.4.3 R´esultatsdestestsdevalidation..................... 31
4.5 Application aux exp´eriencesenlaboratoire................... 32
4.5.1 R´esultatspourlecomposite2...................... 32
4.5.2 R´esultats pour le gr`esSG20. 32
4.6 Conclusion..................................... 3
Conclusions et perspectives 34
Annexe 38
1 Introduction 39
1.1 Heterogeneity from the core to the entire reservoir . . . . . . . . . . . . . . . 40
1.2 Reservoirdataandheterogeneity........................ 41
1.3 Numericalmodelingandheterogeneity..................... 42
1.4 Geostatisticsandheterogeneity......................... 45
1.5 Objectivesofthestudy.............................. 45
2 Literature Review 48
2.1 Field scale permeability characterization . . . . . . . . . . . . . . . . . . . . 48
2.2 Core scale permeability c . . . . . . . . . . . . . . . . . . . . 50
2.3 Concludingremarks................................ 5
3 Core Analysis and Measurements 56
3.1 Laboratoryexperiments ............................. 56
3.1.1 Experimentaldevicesandsetup..................... 57
3.1.2 Experimentalprocedure......................... 60
3.2 Coredescription.................................. 61
3.2.1 Naturalcoresamples........................... 61
3.2.2 Numericalcoresamples.......................... 67
3.3 Preliminarydataanalysis ............................ 68
3.3.1 Petrophysicalanalysis 68
3.3.2 Statisticalanalysis............................ 70
3.4 Chaptersummary................................. 78
ii4 One-Dimensional Permeability Characterization 79
4.1 Descriptionofthemethodology......................... 79
4.2 Numericalvalidation............................... 81
4.2.1 Sensitivityanalysis............................ 81
4.2.2 Numericaldifferentiation 87
4.2.3 Numericalimmiscibledisplacement................... 89
4.2.4 Numericalmiscibledisplacement .................... 92
4.3 Experimentalvalidation. 94
4.3.1 Experimentalresults........................... 95
4.4 Concludingremarks................................102
5 Three Dimensional Permeability Characterization: Theory 104
5.1 Optimizationproblem ..............................104
5.1.1 Definition of the objective function . . . . . . . . . . . . . . . . . . . 105
5.2 Optimizationmethods107
5.3 Parametrizationtechniques............................108
5.3.1 Pilotpointtechnique...........................109
5.3.2 Gradualdeformationmethod ......................109
5.4 Optimizationworkflow11
5.4.1 Simpleoptimization .112
5.4.2 Gradualoptimization.13
5.5 Concludingremarks................................15
6 Three Dimensional Permeability Characterization: Dynamic Data 116
6.1 Numerical models and the available data . . . . . . . . . . . . . . . . . . . . 116
6.1.1 Numericaldataanalysis.........................117
6.2 Laboratory experiments and the available data . . . . . . . . . . . . . . . . . 123
6.2.1 Laboratory data analysis and processing . . . . . . . . . . . . . . . . 123
6.3 Concludingremarks.139
7 Three Dimensional Permeability Characterization: Application 140
7.1 PumaFlownumericalsimulator.........................140
7.2 Numericalvalidation...............................143
7.2.1 Model-3..................................14
7.2.2 Model-4153
7.3 Experimentalvalidation.............................159
7.3.1 Composite2................................160
7.3.2 SandstoneSG20..............................16
7.4 Concludingremarks.179
Conclusions and Perspectives 181
iiiBibliography 185
ivTable des figures
1.1 Heterogeneityfrommicrotogigascopicscales ................. 40
1.2 Computed porosity as a function of the volume considered for a numerical
sandstonesample................................. 41
1.3 Schematic of vertical permeability variation in a reservoir . . . . . . . . . . . 44
3.1 Thecore-holderasembly............................. 57
3.2 Thedistributionplugwithspiralpatern.................... 58
3.3 X-ray CT scanning and the resulting two-dimensional matrix of CT data . . 59
3.4 Theexperimentalsetup. 60
3.5 Thinsectionsofdifferentcoresamples ..................... 63
3.6 Tomography profiles computed for different core samples . . . . . . . . . . . 65
3.7 Cross sectional CT images of plug1-1 and plug1-2 used in composite 1 . . . . 65
3.8 Cross CT i of plug1-3 and plug1-4 used in composite 1 . . . . 66
3.9 Cross sectional CT images of Fontainebleau plug used inside composite 2 . . 66
3.10 Cross sectional CT i of samples LJ001, K13 and SG20 . . . . . . . . . 67
3.11 The relative class frequencies of porosity data for composite 2, sample K13
andSG20..................................... 73
3.12 The experimental variograms of porosity data for composite 2 and sample SG20 76
3.13 The modeled variograms of porosity data for composite 2 and sample SG20 . 77
4.1 Schematic view of the pressure drop across the core sample . . . . . . . . . . 80
4.2 The permeability field for the numerical model with 80× 35× 35 grid cells . 84
4.3 Cumulative production and watercut against dimensionless time for the 80×
35×35model................................... 84
4.4 The permeability field with 80× 107×107gridcels ............. 85
4.5 Cumulative production and watercut against dimensionless time for the up-
scaled model (for cells along axis X) ...................... 86
4.6 Cumulative production and watercut against d time for the up-
scaled model (for cells along axis Y and Z)................... 87
4.7 Δp(t) and its time derivative fluctuations for a homogeneous model . . . . . 88
4.8 Filtering small scale Δp(t)timederivativefluctuations ............ 89
v4.9 Comparison of the processed permeabilities with the absolute ones for the
homogeneousmodel................................ 89
4.10 The permeability field for the numerical Model-2 . . . . . . . . . . . . . . . . 90
4.11 Numerical pressure drop data for Model-1 and Model-2 . . . . . . . . . . . . 90
4.12 2D images of the 3D simulated concentration maps at different times for nu-
merical Model-1 and Model-2 (immiscible displacement) . . . . . . . . . . . 91
4.13 Comparison of the processed numerical permeabilities with the absolute ones
forModel-1andModel-2(immiscibledisplacement).............. 92
4.14 Numerical pressure drops for Model-1 and Model-2 when performing miscible
displacement.................................... 93
4.15 Comparison of the processed numerical permeabilities with the absolute ones
for Model-1 and Model-2 (miscible displacement) . . . . . . . . . . . . . . . 93
4.16 2D images of the 3D simulated concentration maps at different times for nu-
merical Model-1 and Model-2 (miscible displacement) . . . . . . . . . . . . . 94
4.17 2D images of the 3D concentration maps at different times for composite 2 . 96
4.18 Comparison of the processed experimental permeabilities with absolute ones
forcomposite1andcomposite2......................... 97
4.19 Inlet-outlet pressure drop data before and after scaling for composite 1 and 2 98
4.20 Comparison of the processed permeabilities with the absolute ones for two cut
parts of the low permeability lavoux . . . . . . . . . . . . . . . . . . . . . . . 99
4.21 Inlet-outlet pressure drop data against injection time for sample LJ001 . . . 100
4.22 Comparison of processed permeabilities with the minipermeameter results for
LJ01.......................................10
4.23 The processed permeabilities for the coarse-grained sandstone K13 . . . . . . 101
4.24 2D images of the 3D concentration maps for the coarse-grained sandstone K13 102
5.1 Schematic of realization chain during a gradual deformation based optimization111
5.2 CONDOR workflow used for a simple calibration of the 3D permeability field 113
5.3 C workflow used for a gradual deformation based calibration of the
3D permeability field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.1 Cross sectional images of the 3D porosity map for Model-3 . . . . . . . . . . 118
6.2 Cross i of the 3D permeability map for Model-3 . . . . . . . . 119
6.3 Reference inlet-outlet pressure drop data for numerical Model-3 . . . . . . . 119
6.4 R concentration maps for numerical Model-3 . . . . . . . . . . . . . 120
6.5 Cross sectional images of the 3D permeability map for Model-4 . . . . . . . . 121
6.6 Reference inlet-outlet pressure drop data for numerical Model-4 . . . . . . . 122
6.7 R concentration maps for numerical Model-4 . . . . . . . . . . . . . 122
6.8 The inlet-outlet pressure drop data against injection time for composite 2 . . 124
6.9 Schematic of the sample SG20 numerical model . . . . . . . . . . . . . . . . 126
6.10 Original cross sectional images of the 3D porosity map for composite 2 . . . 127
vi6.11 Processed cross sectional images of the 3D porosity map for composite 2 . . 128
6.12 The arithmetic average of composite 2 and SG20 porosity values per slice . . 129
6.13VisualizationoftheCTnoise ..........................129
6.14 Cross sectional images of the 3D porosity map for sample SG20 . . . . . . . 130
6.15 2D images of the 3D concentration maps obtained at successive times for
composite2....................................132
6.16 The frequency distribution of some concentration images for composite 2 . . 133
6.17 A 2D concentration image taken at a distance of 61.2 mm from the inlet face
ofcomposite2...................................133
6.18 Comparison of an original and processed concentration data for composite 2 134
6.19 2D images of the 3D concentration maps for sandstone SG20 taken at two
sucesivetimes(normalinjection) .......................136
6.20 2D images of the 3D concentration maps for sandstone SG20 taken at two
sucesivetimes(normalinjection)137
6.21 2D images of the 3D concentration maps for sandstone SG20 taken at two
sucesivetimes(inverseinjection)137
6.22 2D images of the 3D concentration maps for sandstone SG20 taken at two
sucesivetimes(inverseinjection)138
6.23 2D images of the 3D concentration maps for sandstone SG20 taken at two
successivetimes(inverseinjection) .......................139
7.1 The relative permeability data used in PumaFlow simulator . . . . . . . . . 142
7.2 Comparison of the reference and the simulated Δp(t) for the primary opti-
mizationofModel-3................................147
7.3 The evolution of different parameters for primary calibration of Model-3 . . . 147
7.4 The ev of different p for second primary optimization of
Model-3......................................149
7.5 Comparison of a the reference and simulated concentration maps for primary
optimizationofModel-3.............................150
7.6 Evolution of the objective function for Model-3 during the gradual deforma-
tionbasedoptimization..............................151
7.7 Comparison of the reference and simulated Δp(t) for Model-3 after the gradual
deformationbasedoptimization.........................152
7.8 of a the reference and simulated concentration maps for the grad-
ualdeformationbasedoptimizationofModel-3.................152
7.9 The evolution of different parameters for Model-3 during the gradual defor-
mationbasedoptimization............................153
7.10 Comparison of the reference and the simulated Δp(t) for the primary opti-
mizationofModel-4................................154
7.11 of a the reference and the simulated concentration maps for the
primaryoptimizationofModel-4.........................156
vii7.12 Comparison of the reference and the simulated Δp(t) for the gradual defor-
mationbasedoptimizationofModel-4 .....................156
7.13 Evolution of the objective function for the gradual deformation based opti-
mizationofModel-4................................157
7.14 The evolution of different parameters for Model-4 during the gradual defor-
mationbasedoptimization............................158
7.15 Comparison of a the reference and the simulated concentration maps for the
gradualdeformationbasedoptimizationofModel-4..............159
7.16 of the reference and the simulated Δp(t) for the primary opti-
mizationofcomposite2 .............................161
7.17 The evolution of different parameters for composite 2 during the primary
optimization....................................162
7.18 Comparison of the reference and the simulated concentration maps for the
primaryoptimizationofcomposite2 ......................163
7.19 Evolution of the objective function for composite 2 during the gradual defor-
mationbasedoptimization............................164
7.20 Evolution of the different parameters for composite 2 during the gradual de-
formationbasedoptimization ..........................165
7.21 Comparison of the reference and the simulated concentration maps for the
gradual deformation based optimization of composite 2 . . . . . . . . . . . . 165
7.22 of the reference and the simulated Δp(t) for the primary opti-
mizationofSG20(normalinjection).......................167
7.23 Comparison of the reference and the simulated Δp(t) for the primary opti-
mizationofSG20(inverseinjection)167
7.24 of the reference and the simulated concentration maps for the
sample SG20 after the primary optimization (normal injection) . . . . . . . . 168
7.25 Comparison of the reference and the simulated Δp(t) for the gradual defor-
mation based optimization of SG20 (normal injection) . . . . . . . . . . . . . 169
7.26 The evolution of the inversion parameters for the sample SG20 during the
gradual deformation based optimization (normal injection) . . . . . . . . . . 171
7.27 Comparison of the reference and the simulated concentration maps for the
sample SG20 after the gradual deformation based optimization (normal injec-
tion)........................................172
7.28 Comparison of the reference and the simulated concentration maps for the
sample SG20 after the primary optimization (inverse injection) . . . . . . . . 173
7.29 The evolution of the inversion parameters for the sample SG20 during the
gradual deformation based optimization (inverse injection) . . . . . . . . . . 174
7.30 Comparison of the reference and the simulated Δp(t) for the gradual defor-
mation based optimization of SG20 (inverse injection) . . . . . . . . . . . . . 175
viii