Modeling and Simulation for Multiphase Flow in Petroleum Reservoirs - PowerPoint PPT Presentation

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 Development of a Measurements Model validation numerical model Mathematical Model and process Lab experiments Model verification identification Initial and Comparison boundary conditions Application Analytical solution Numerical model Simulation Verification Lab scale

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 P c =P o -P w

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 Geo- Research models Validation & Field Scale Applications Models Journeying to the Reservoir Solvers & Gridding Parallelizatio Numerical n Models

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 Surface systems facilities coupling High Heterogeneity resolution RESERVOIR Instability SIMULATION Irregular and geometric fingering features Strong Complex coupling & Small well nonlinearity diffusion architecture

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) Modelling Complex Layers & Slanted THAI Model Wells Wells Water Complex Flow Due to Oil & Water Mixture Heterogeneous Geology 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 • 1 st Edition out

Three Recent Books (cont’d) • Reservoir Simulation: Mathematical Techniques in Oil Recovery • Year 2007 • Z. Chen • NSF Summer School