modeling and simulation for multiphase flow in petroleum reservoirs
TRANSCRIPT
Modeling and Simulation for Multiphase Flow in Petroleum Reservoirs
Zhangxing Chen
University of Calgary
Sponsors
Synergia Polygen Ltd
Outline
• Part I: Modeling and Simulation of Conventional Oil
• Part II: Investigation of Compositional Grading
• Part III: Current Research in Heavy Oil Modeling
Outline, Part I
• My Research Background • Models • Current Developments • Difficulties • Conclusions and References
Basin Modeling Reservoir Simulation
From Basin Modeling to
Reservoir Filling to
Reservoir Simulation
Problem Description
Idealization
Conceptual Model
Mathematical Model Development of a numerical model
Model verification
Model validation and process identification
Measurements
Lab experiments
Analytical solution Numerical model Simulation
Initial and boundary conditions
Verification
Application
Lab scale
Comparison
Models: History of Numerical Reservoir Simulation
- 1950 – 1970, Study of dynamics of fluid flow and transport through porous media
- 1970 – 1980, Various reservoir simulators (black oil, compositional, thermal, dual porosity) based on the finite difference method
- 1980 – 1990, Commercial reservoir simulators (fully implicit method, fast solvers, EOS, vector computers) - 1990 – 2000, Workstation computer techniques, advanced
GUIs, integration with geo-modeling, geomechanics, parallel computer techniques (PVM, MPI, clusters)
- After 2000, Commercial unstructured grids simulators, large scale simulation on PC (64 bites), new history matching and optimization techniques, new computer hardware (multiple cores, GPUs, OpenMP, hybrid OpenMP-MPI, blue gene)
Models (cont’d): Oil production methods
• Primary recovery: simple natural decompression
• Secondary recovery: water injected
• Enhanced recovery: -Miscible displacement -Chemical processes -Thermal processes
Models (cont’d): Types of fluid flows in porous media
• Primary recovery: single-phase • Secondary recovery: two-phase
(above a bubble pressure) or three-phase black oil (water, liquid, and gas)
• Enhanced recovery: multicomponent, multiphase, isothermal or non-isothermal
Models (cont’d): Major laws
• Conservation of mass • Conservation of momentum • Conservation of energy
Models (cont’d): Single phase flow
- Mass conservation equation:
- Darcy’s law:
Models (cont’d): Two-phase flow
- Mass conservation equation
- Darcy’s law
Pc=Po-Pw
Models (cont’d): Three-phase flow
• Governing equations
• Darcy’s Law
Models (cont’d): Three-phase flow
– Constraint equation
– Capillary pressures
Models (cont’d): Compositional flow
Models (cont’d): Thermal flow
• Mass conservation • Darcy’s law • Phase package • Conservation of energy:
Models (cont’d): Mathematical Issues
• Existence of a solution • Uniqueness of the solution • Solution regularity
Current Developments
Geo-models
Field Scale Models
Gridding Solvers &
Parallelization
Validation & Applications
Software Research
Numerical Models
Journeying to the Reservoir
Current Developments (cont’d): Upscaling
• Mathematical techniques: homogenization, volume averaging, etc.
• Numerical upscaling: - purely numerical: renormalization, power law
averaging, harmonic mean, etc.
- multiscale methods
Current Developments (cont’d): Dynamical Gridding
– Irregular geometric feature presentation • boundaries (and
BCs) • faults • fractures • pinch-outs
Current Developments (cont’d): Dynamical Gridding
– Complex features • complicated well
architecture • local reaction
zones • different spatial
and temporal scales
• geomechanics
Current Developments (cont’d): Numerical Methods
– Finite difference methods – Finite volume (control
volume) methods – Finite element methods
Current Developments (cont’d): Fast Linear Solvers
• Large scale systems (million unknowns) • Coupling of different physical variables • Highly nonsymmetric and indefinite matrices • Ill conditioned systems • Matrix structure spoiled by well perforation and
unstructured grids • 80-90% of the total simulation time spent on the
solution of large linear systems • Limitation of problem size and space resolution on
a single processor
Current Developments (cont’d): Fast Linear Solvers • Fast and robust solvers: - ORTHOMIN (orthogonal minimum residual) - GMRES (generalized minimum residual) - BiCGSTAB (biconjugate gradient stabilized) • Efficient preconditioners: - ILU(k) - CPR (constrained pressure residual) - AMG (algebraic multigrid) • Taking advantage of modern parallel architecture
Strong coupling & nonlinearity
Small diffusion
High resolution Heterogeneity
Irregular geometric features
Complex well
architecture
Difficulties
Instability and
fingering
Large scale systems
RESERVOIR SIMULATION
Surface facilities coupling
Difficulties (cont’d): Upscaling
• Integration – Disparate data with different scales – Coupling of different flow, transport and
chemical processes
• Upscaling – Geological models with tens of millions
of cells to reservoir models with over one million cells
• Speed of computation – Fast enough for timely decisions
Difficulties (cont’d): Gridding
• Grid adaptivity in space and time
• Wells with complex features
• Easy integration
Difficulties (cont’d): Numerical Methods
– Multipoint upstream winding
– Multipoint flux approximation
– Instability and fingering
– Small diffusion/dispersion representation
– Mass and energy conservation
Difficulties (cont’d): Solvers
• Large scale systems (million unknowns and long time integration )
• Coupling of different physical variables • Highly nonsymmetric and indefinite
matrices • Matrix structure spoiled by well
perforation and unstructured grids • Ill conditioned systems • Limitation of problem size and space
resolution on a single processor
Current Research
Oil
Oil & Water Mixture
Water
Wells
Modelling of a Reservoir
Current Research (cont’d)
THAI Model
Modelling Complex Layers & Slanted
Wells
Complex Flow Due to Heterogeneous Geology
Validation of Simulator: n-Component (cont’d)
Rayleigh Number Validation
Reservoir with Baffles for n-Component Mixing (cont’d)
Conclusions
• Development of simulator integrating geological and reservoir processes
• Good features: flexibility, speed, accuracy, interface, etc.
• Incorporation of more physics: fluid flow, heat transfer, chemistry, and geomechanics
• All these mean significant savings in capital costs
Three Recent Books
• Finite Element Methods and Their Applications
• Z. Chen • Year 2005 • Over 1,000 copies sold
Three Recent Books (cont’d)
• Computational Methods for Multiphase Flows in Porous Media
• Year 2006 • Z. Chen, G. Huan and Y.
Ma • 1st Edition out
Three Recent Books (cont’d)
• Reservoir Simulation: Mathematical Techniques in Oil Recovery
• Year 2007 • Z. Chen • NSF Summer School