【论文题目】 NUMERICAL AND ANALYTICAL MODELING OFSANDING ONSET PREDICTION
【论文作者】 XIANJIE YI
【院校】 Texas A&M University
【时间】 August 2003
【内容简介】
To provide technical support for sand control decision-making, it is necessary to predict the production condition at which sand production occurs. Sanding onset prediction involves simulating the stress state on the surface of an oil/gas producing cavity (e.g. borehole, perforation tunnel) and applying appropriate sand production criterion to predict the fluid pressure or pressure gradient at which sand production occurs. In this work, we present numerical and analytical poroelastoplastic stress models describing stress around producing cavity and verify those models against each other. Using those models, we evaluate the stress state on the cavity surface and derive sanding onset prediction models in terms of fluid pressure or pressure gradient based on the given sand production criterion. We then run field case studies and validate the sanding onset prediction models. Rock strength criterion plays important roles in sanding onset prediction. We investigate how the sanding onset prediction results vary with the selection of one or another rock strength criterion. In this work, we present four commonly used rock strength criteria in sanding onset prediction and wellbore stability studies: Mohr-Coulomb, Hoek-Brown, Drucker-Prager, and Modified Lade criteria. In each of the criterion, there are two or more parameters involved. In the literature, a two-step procedure is applied to determine the parameters in the rock strength criterion. First, the Mohr-Coulomb parameters like cohesion So and internal friction angle ff are regressed from the laboratory test data. Then, the parameters in other criteria are calculated using the regressed Mohr-Coulomb parameters. We propose that the best way to evaluate the parameters in a specific rock strength criterion is to perform direct regression of the laboratory test data using that criterion. Using this methodology, we demonstrate that the effect of various rock strength criteria on sanding onset prediction is less dramatic than using the commonly used method. With this methodology, the uncertainties of the effect of rock strength criterion on sanding onset prediction are also reduced.
【目录】
ABSTRACT..................................................................................................................... iii
ACKNOWLEDGEMENTS ...............................................................................................v
TABLE OF CONTENTS................................................................................................. vi
LIST OF FIGURES.......................................................................................................... ix
LIST OF TABLES .......................................................................................................... xii
CHAPTER
I INTRODUCTION..................................................................................................1
1.1 Statement of the problem .................................................................................1
1.2 Objectives of this research ...............................................................................1
1.3 Summary of results...........................................................................................2
II LITERATURE REVIEW.......................................................................................4
2.1 Sand arch stability ............................................................................................4
2.2 Perforation tunnel stability ...............................................................................7
2.3 Open hole stability ...........................................................................................9
2.3.1 Analytical axisymmetrical plane strain model ..................................9
2.3.2 Analytical 2D plane strain model....................................................10
2.3.3 Numerical model .............................................................................11
2.4 Sand production criterion ...............................................................................11
2.4.1 Tensile failure..................................................................................12
2.4.2 Shear failure and rock strength criterion .........................................12
2.4.3 Pore collapse ...................................................................................13
III ANALYTICAL MODELS FOR SANDING ONSET PREDICTION ................16
3.1 Analytical model for wellbore/perforation tunnel failure induced
sand production-Isotropic in-situ stress case ..................................................16
3.1.1 Poroelasticity solution and shear failure sanding criterion .............17
3.1.2 Poroelastoplasticity solution and tensile failure sanding
criterion ...........................................................................................19
3.2 Analytical model for wellbore/perforation tunnel failure induced
sand production-Anisotropic in-situ stress case..............................................22
3.3 Analytical model for perforation tip failure induced sand production...........26
3.3.1 Poroelasticity solution and shear failure sanding criterion .............26
3.3.2 Poroelastoplasticity solution and tensile failure sanding
criterion ...........................................................................................27
IV NUMERICAL MODEL FOR SANDING ONSET PREDICTION ....................30
4.1 3D stress model ..............................................................................................30
4.2 3D transient fluid flow model ........................................................................31
4.3 Mohr-Coulomb plasticity ...............................................................................32
4.3.1 Mohr-Coulomb in terms of stress invariants……………………...32
4.3.2 Flow rule……………………………..……………...…….………34
4.3.3 Elastoplastic stress-strain matrix………………………………….34
4.4 Finite element solution to the 3D stress model ..............................................36
4.5 Finite element solution to the 3D fluid flow model .......................................37
4.6 Verification of the numerical models.............................................................37
4.6.1 Verification of the 3D fluid flow model..........................................37
4.6.2 Verification of the 3D stress model.................................................43
4.7 Comparison of numerical model and analytical model..................................47
4.8 Uncertainty assessment of sanding onset prediction model...........................50
V EFFECT OF ROCK STRENGTH CRITERION ON SANDING
ONSET PREDICTION .......................................................................................54
5.1 Rock strength criterion ...................................................................................56
5.1.1 Mohr-Coulomb criterion .................................................................56
5.1.2 Hoek-Brown criterion .....................................................................57
5.1.3 Drucker-Prager criterion .................................................................58
5.1.4 Modified Lade criterion ..................................................................61
5.2 Near wellbore poroelastic stress model..........................................................61
5.3 Determination of rock strength criterion parameters .....................................62
5.4 Application of rock strength criterion in sand production prediction ............68
VI SANDING ONSET PREDICTION CASE STUDIES.........................................75
6.1 Sand production in gas fields in the Northern and Central Adriatic Sea .......75
6.2 Sand production in Well #3 ...........................................................................84
VII SUMMARY AND CONCLUSIONS...................................................................90
NOMENCLATURE.........................................................................................................92
REFERENCES.................................................................................................................98
APPENDIX A ................................................................................................................107
APPENDIX B ................................................................................................................118
APPENDIX C ................................................................................................................120
APPENDIX D ................................................................................................................125
APPENDIX E.................................................................................................................128
VITA ..............................................................................................................................132
