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
• f 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

• ptimization 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 & Parallelizatio n 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

• f cells to reservoir models with over
• ne 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