Advances in the iterative coupling between flow-geomechanical simulators E-Book

Yuri Nunes Saraiva

• Herausgeber: Editora Dialética
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 107

Veröffentlichungsjahr: 2022

Beschreibung

Numerical analysis for reservoir engineering scenarios is necessary due to the importance of predict the consequences and products of water or oil exploitation, as well as the vast quantity of variables that are associated with hydraulic engineering, oil, and rock geomechanics. Due to this, the present work consists to show the relative activities for geomechanical coupling and flux simulation based on paper SPE – 79709 of Dean et al. (2006). This way, the used software for coupling was IMEX (2019), in the explicit iterative coupling, with geomechanics and flux model of the same simulator and, posteriorly, was used the geomechanics simulator FLAC3D 6.0 associated with the flux model of IMEX and programming with MATLAB and FISH to transfer the data between simulators. In addition, the results demonstrate the satisfactory obtention of convergence of the problems proposed by Dean et al. (2006), in IMEX with geomechanics. For iterative coupling between FLAC3D and IMEX was obtained good behavior convergence of problem 1. At the end of the simulations, a reservoir model is elaborated based on this problem with the inclusion of a horizontal fracture near the region of the producing well. This type of coupling allows an accurate study with the highest level of complexity and inclusion of variables to reservoir behavior, as the inclusion of fractures and constitutive models.

Leseprobe

To my Grandfather Mário Sales Nunes (In memoriam) an example of a man who is integrated and a struggler.

To Luana Karine (In memoriam) example of a person who fights for a dream.

ACKNOWLEDGEMENTS

To God for the gift of life and for being the driving force in the search for knowledge and for overcoming battles.

To my parents, Clésio Jean de Almeida Saraiva and Luci Ane Nunes Saraiva for always supporting my decisions, as well as to my brothers Natália, Mariana, and Jean, who accompany me throughout the journey.

To Natasha Nogueira Prado, who accompanied me through the whole process and constantly supports me.

My advisor Professor Francisco Chagas da Silva Filho, PhD. And my co-advisor Professor Luis Glauber Rodrigues, PhD. For all knowledge and experience shared, as well as for trusting in the dedication and engaged work.

To Professor Silvrano Adonias Dantas Neto, PhD, and Professor Francisco Pinheiro Lima-Filho, Dsc. For accepting the invitation to examine the dissertation and contribute with their vast knowledge and experiences.

To Herberth Arturo Vasques Haro, Dsc. For sharing moments of numerical simulations and search for knowledge, and to Madson Magalhães, Dsc. For sharing knowledge about programming language.

To Petrobras for providing the support, software licenses, computational structure, and laboratory.

To my friends and colleagues Helson, Emanuelle, Tiago, and all the other GSIM lab collaborators for sharing moments of research and knowledge.

SYMBOLS

σh

Horizontal stress;

σv

Vertical stress;

i,j

Shear stress at respective coordinates;

i,i

Normal stress at respective coordinates;

Interfacial energy between oil and solid;

Interfacial energy between water and solid;

Interacial energy between oil and water;

Angle of contact between oil-water-solid measured through the water phase;

Pressure;

Universal gas constant;

Temperature;

Gas volume in ft3 per one gas mole;

Bulk volume;

Pore volume;

Grain volume;

Porosity;

Initial porosity;

Volumetric strain;

Coefficient for incompressible solids equals 1;

(T – Ti)

Temperature variation;

Final volume;

Initial volume;

Rock compressibility;

Relative permeability;

Absolute permeability;

Effective permeability to the fluid at a given fluid saturation;

Shear stress;

τ0

Cohesive resistance;

Friction angle;

σ

Effective normal stress;

Final shear stress;

μ

Internal friction coefficient;

Higher main stress;

Lower main stress;

Friction index;

Confinement stress;

Index for intact rock;

e

Specific constants for or type of rock;

Bulk compressibility;

Formation compressibility;

Reservoir net thickness;

Pressure depletion;

Porous rock compressibility;

Young modulus;

Biot coefficient;

Poisson coefficient;

m

Mean total stress.

SUMÁRIO

Capa

Folha de Rosto

Créditos

1 INTRODUCTION

1.2. TOPIC AND JUSTIFICATION

1.3. GENERAL AND SPECIFIC PURPOSE

2 THEORETICAL BACKGROUND

2.1. STRESS

2.2. EFFECTS OF FLUIDS ON PORES

2.3. BASIC PHASE BEHAVIOR

2.4. WETTABILITY

2.5. STATE EQUATIONS

2.6. SCALE EFFECT

2.7. POROSITY

2.8. COMPRESSIBILITY

2.9. PERMEABILITY

2.10. CONSTITUTIVE MODELS OF FAILURE CRITERIA

2.10.1 Von-Mises criteria:

2.10.2 Mohr-Coulomb criteria:

2.10.3 Hoek-Brown Criteria:

2.11. SUBSIDENCE

2.12. RESERVOIR CLASSIFICATION

2.13. RESERVOIR WELLS

2.14. RESERVOIR BEHAVIOR

2.15. RESERVOIR SIMULATION MODEL

2.16. NEW POROSITY AND PERMEABILITY CALCULATION THROUGH ITERATIVE COUPLING

3 METHODOLOGY

3.1. PROBLEMS DESCRIPTION

3.1.1. Problem 1

3.1.2. Problem 2

3.1.3. Problem 3

3.1.4. Problem 4

3.2. IMEX 2019 EXPLICIT ITERATIVE COUPLING

3.2.1. Problem 1

3.2.2. Problem 2

3.2.3. Problem 3

3.2.4. Problem 4

3.3. EXTERNAL EXPLICIT ITERATIVE COUPLING WITH FLAC3D 6.0, IMEX E MATLAB

3.3.1. Mesh design

3.3.2. Initial conditions

3.3.3. Master file

3.3.4. Initial pore pressure list

3.3.5. FISH programming

3.4 FRACTURED MODEL

4 RESULTS

4.1. DESCRIPTION OF RESULTS OF DEAN ET AL. (2006)

4.1.1. Problem 1

4.1.2. Problem 2

4.1.3. Problem 3

4.1.4. Problem 4

4.2. IMEX 2019 RESULTS

4.2.1. Problem 1

4.2.2. Problem 2

4.2.3. Problem 3

4.2.4. Problem 4

4.3. FLAC3D 6.0 RESULTS

4.3.1. Volumetric strain

4.3.2. Subsidence

4.3.3. Average mechanical ratio

4.4. FRACTURED RESERVOIR

CONCLUSIONS AND RECOMMENDATIONS

REFERENCES

APPENDICES

APPENDIX A IMEX CMG 2019 PROBLEM 1 PROGRAMMING.

APPENDIX B IMEX CMG 2019 PROBLEM 2 PROGRAMMING.

APPENDIX C IMEX CMG 2019 PROBLEM 3 PROGRAMMING.

APPENDIX D IMEX CMG 2019 PROBLEM 4 PROGRAMMING.

APPENDIX E GRID BLOCK CREATION IN FLAC3D.

APPENDIX F INITIAL CONDITIONS

APPENDIX G PORE PRESSURE LIST

APPENDIX H FISH PROGRAMMING

APPENDIX I DEAN ET AL. RESULTS (2006)

APPENDIX J IMEX CMG 2019 EXPLICIT ITERATIVE COUPLING.

Landmarks

cover

title-page

copyright-page

table of contents

bibliography

1 INTRODUCTION

Based on the need to control the complexities associated with the oil and water reservoir system, from the preliminary reservoir capacity study to the depletion and abandonment of the fluid extraction field, the simulation of oil and water reservoirs is important because it is possible to mitigate and predict future behaviors, as well as to adjust the analysis with the actual depletion and field tests.

The analysis of the geomechanical behavior through simulation guarantees to follow the development of phenomena such as subsidence and development of the stresses associated with the model, with consequent relief of stresses, or increase of stresses, providing the activation of failures, creation of fractures, or also pressure loss with low production and loss of injection material.

The choice of theme is based on the need for careful monitoring of the geomechanical behavior associated with the reservoir, whether it is confined to rock with fractures that influence the depletion or not, or the reservoir confined with compositional fluid or just black oil.

Initially, studies on preliminary knowledge on reservoir engineering were conducted, with learning and use of specific computer simulators for the analysis of oil and water reservoirs, with associated geomechanics module.

Subsequently, the use of another simulator, specifically for geomechanics, and the application of flow simulators in porous media and rock mechanics in iterative coupling to obtain accurate results of geomechanical behavior.

1.2. TOPIC AND JUSTIFICATION

Studies and analysis of the behavior of oil and water reservoirs are highly developed due to the importance of the energy capacity that, in the case of oil, it provides, either for fuel generation or the generation of oil products.

The environmental impacts that may occur with an imprecise analysis or without using the due importance to preliminary studies, during the execution phase and later phase of abandonment of the exploration field may be irreparable and provide a drastic impact on mankind.

Therefore, preliminary studies and reservoir simulations are important to predict and mitigate future actions, to provide the preparation for future events during exploration, reducing the uncertainties associated with the oil reservoir system.

1.3. GENERAL AND SPECIFIC PURPOSE

The general objective is to compare the total coupling proposed by Dean et al. (2006) with the iterative coupling developed in this work, using the commercial software CMG IMEX 2019, MATLAB, and FLAC3D 6.0, proposing the numerical analysis of oil reservoirs with the well-defined flow and geomechanical properties. This way, simulations are performed with a simplified method, providing a scenario with a higher level of complexity and representativity of results.

The specific objectives are to monitor the development of geomechanical efforts and reservoir behavior when changing the boundary conditions and properties of the fluid under analysis.

2 THEORETICAL BACKGROUND

The theoretical background consists of the analysis of issues related to the flow-stress coupling described below, which involves reservoir flow behavior and geomechanics associated with reservoir rock, properties that affect oil recovery, as well as the safety analysis of depletion development.

2.1. STRESS

According to Zoback (2007), depletion can cause changes in the stress state of the reservoir, thus, being beneficial or harmful, to production in different ways. Therefore, knowledge of stresses in depth is fundamentally important to address a wide range of practical problems in geomechanics within oil, gas, geothermal reservoirs, and overlapping formations. Sun et al. (2020) state that the numerical uniaxial strain test that represents the reservoir stress path can be used to obtain the changes of porosity and permeability as a function of effective stress.

According to AadnØy (2014), in situ stress data plays a key role at various stages of oil and gas well planning, construction, operation, and production. Knowledge of in situ stresses and the mechanical properties of the rock formation is crucial for the assessment of well construction and production, so before performing any rock stress analysis and rupture assessment, it is necessary to have complete knowledge of in situ stresses.

Jaeger & Cook (2007) defines the theory of stress in three dimensions as a direct extension of the two-dimensional theory. A generic three-dimensional plane will have a normal unitary vector. Mohr’s circular representation of the two-dimensional stress state can be used in three dimensions, as shown in Figure 1.

Figure 1 - Three-dimensional stress state.

Source: Jaeger & Cook, 2007.

Three mutually perpendicular stresses exist at each point underground, as shown in Figure 2. Other sources of vertical stress include stresses resulting from geological conditions, such as magma or salt domes penetrating the areas surrounding the rock formation. This overload stress usually tends to propagate and expand the underlying rocks and horizontal lateral directions due to the Poisson effect. This lateral movement is limited by the presence of adjacent materials, which then make the maximum and minimum horizontal stresses form, AadnØy (2014).

Figure 2 - Three-dimensional block stresses.

Source: Author, 2020.

Where:

σh – Horizontal stress;

σv – Vertical stress.

Ju et al. (2020) defines that stress sensitivity is used to describe petrophysical parameters of oil reservoir rocks that change with the variation in effective stress. Normally, the reservoir rock permeability decreases when the effective stress increases.

According to Hudson and Harrison (1997) it is more convenient to consider normal and shear components concerning a given set of axes, usually a rectangular x, y, z Cartesian system. In this case, the body can be considered sliced into three orientations corresponding to the visible faces of the cube shown in Figure 3.

Figure 3 – Stress state components of a block.

Source: Hudson & Harrison, 1997.

Where:

i,j – Shear stress at respective coordinates;

i,i – Normal stress at respective coordinates.

For the geomechanics analysis, the stress state is used as a departure point. Usually, it is assumed that σv is the principal stress, therefore, the other two lie in the horizontal plane. This assumption should be verified in cases of regional vulcanism, strong structural deformation, high geographical relief, and differential compaction during burial, Dusseault (2011).

2.2. EFFECTS OF FLUIDS ON PORES

According to AadnØy (2014), pore pressure is a key factor in production and has a significant effect on well construction and well hole stability. A pore pressure curve is required to select the slurry weights and installation points of the support coatings. Pore pressure derived from profiles and other sources is not accurate, so the pressure curves of the pores have significant uncertainty.

According to Jaeger & Cook (2007), rocks are typically porous to a certain extent, and the pore space of rock will be filled with fluids under pressure. The porous liquid is usually water but can be oil, gas, or molten rock. Porous fluid can affect rock failure in two ways, due to the purely mechanical effect of pore pressure, or due to chemical interactions between rock and fluid. Concerning the mechanical effect of the pore fluid pressure, this would work as tensile stress. According to Longuemare et al. (2002), in conventional formulations of fluid flow, the variation of pore volume only depends on the pore pressure variation through the pore volume compressibility coefficient. In the other hand, Goral et al. (2020) observed a minor effect of reservoir confinement in porosity and permeability, related to the morphology of the pore, in the extension of stress and of fluid flow connected paths.

According to Rosa (2002), the properties of the fluids and rocks that make up petroleum reservoirs should preferably be determined experimentally in laboratory analysis. But in some situations, this is not possible due to economic or operational reasons. Therefore, the properties of the fluids and the reservoir rock can be calculated through state equations or estimated using charts, abacuses, or empirical correlations available in the literature. Zhao et al. (2020) determine, in the recovery process, the flow of oil, gas, and water by their relative permeability in the reservoir.