Modeling and Simulation for Multiphase Flow in Petroleum Reservoirs

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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