1970 – 1980, Various reservoir simulators (black oil, ... 1980 – 1990, Commercial
reservoir simulators. (fully implicit method, fast .... Three Recent Books (cont'd).
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
Reservoir Simulation Basin Modeling
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
Initial and boundary conditions
Measurements Lab experiments
Comparison Application
Analytical solution
Numerical model Verification
Lab scale
Simulation
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 threephase black oil (water, liquid, and gas) • Enhanced recovery: multicomponent, multiphase, isothermal or nonisothermal
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 Software Research
Geomodels
Validation & Applications
Field Scale Models Journeying to the Reservoir
Gridding
Numerical Models
Solvers & Parallelizatio n
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 •
Difficulties Large scale systems Heterogeneity
Irregular geometric features Complex well architecture
Surface facilities coupling
RESERVOIR SIMULATION
Strong coupling & nonlinearity
High resolution
Instability and fingering
Small diffusion
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
Current Research (cont’d)
THAI Model
Modelling Complex Layers & Slanted Wells
Wells
Water
Complex Flow Due to Heterogeneous Geology
Oil & Water Mixture Oil
Modelling of a Reservoir
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
