Modelling Density Driven Flow and Solute Transport ...

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Modeling multi-phase flow in porous medium– a case for reservoir simulation. Mayur Pal, PhD. Maersk Oil Research and Technology Centre. Dept. of Hydrology ...
Modeling multi-phase flow in porous medium– a case for reservoir simulation Mayur Pal, PhD Maersk Oil Research and Technology Centre

Dept. of Hydrology - IIT Roorkee February 2016

Outline • • • •

Overview – subsurface reservoir modelling Why simulate ? How to simulate ? Some numerical schemes for improved simulation results • Results and some challenges

Subsurface reservoir modelling workflow

Petrophysical

Geological

Reservoir simulation

Overview – subsurface reservoir modelling

• Subsurface reservoir characterization • Static properties – structure, depth, porosity, permeability and aquifer Strength etc. • Dynamic properties – Relative permeability, capillary pressure and initial saturations

Reservoir Structure

• Seismic imaging for structure length, width, depth, layering, faults/fractures • Outcrop analog studies • Combined with geological knowledge • Results in creation of geological model

Static Properties - Porosity

• Porosity – fraction of rock occupied by voids/pores • Porosity is an intensive property that describes fluid storage of rock • Pore space is occupied by oil/water or gas • Gives an estimate of the volume of Oil or Gas within subsurface

Static Properties - Permeability

• Permeability – Is ability of a fluid to flow through connected pores • Permeability is a function of connected porosity of the rock • Permeability of a reservoir is a major factor which dictates flow/production of oil/gas from well bore • Permeability is measured through logs/well tests and core flooding experiments under controlled conditions

Dynamic Properties – Relative Permeability and Capillary Pressure

• Relative permeability – is ability of one fluid to move within the connected pore space in presence of another fluid • Capillarity/Capillary Pressure – Is the difference of pressure that exist across the interface of two immiscible fluid phases • Relative permeability and capillary pressure controls the flow of oil/gas/water within connected pores

What is reservoir simulation ? • A subdivision of the reservoir in space and time allowing variation in physical properties • Grid blocks and time steps – Flow between grid blocks – Storage within grid blocks

• System of equations describing interlock flows and storage • At each time step calculate production/injection and revise pressure and saturation distribution

Reservoir Simulation Workflow

• • • • •

Creation of a highly detailed model Input – static and dynamic properties Results in a multi-million cell model Huge demand on computing power Upscale reservoir simulation model

Why Simulate ? • Rapid assessment of alternative reservoir development strategies in complex reservoirs • Competitive forces • Study of complex fluid flow and dynamics for which analytical alternatives are not available • Improved efficiency of computers act as enablers for reservoir simulation • Helps in production forecasting • Multiple scenarios for planning of facilities • Determination of fluid movement in time and space

Types of reservoir models

Simulation Equations and Data Requirements • Darcy’s Law for two-phase water and oil:

vw  

krw

vo  

kro

• Two-Phase flow equations for water and oil:

w

o

K (pw   wg wh) K (po   og oh)

 Sw     vw  n   qw t w  S0     vo  n   qo t o

Reservoir Simulation – Flow Equations • With So+Sw = 1, assuming zero Pc , Sw = S • All phase pressures Pw = Po = P and λα= kri/μα , α = w,o

• Results in coupled set of equations   ( ( S ) KP )  g S     ( f ( S ) ( S ) KP)  Q t

• Coupled saturation and pressure equation, coupling via mobility λ(S) • Hyperbolic saturation eqn., elliptic pressure eqn.

Reservoir Simulation – Numerical Formulation Incompressible:

Compressible:

  Kt p,    q 

S w     f w   qw t

Discretization:

Discretization:

Reservoir Simulation – Numerical Formulation

Reservoir Simulation – Numerical Schemes

• Fully implicit – Commercial simulators • Implicit pressure and explicit saturation (IMPES) • Single-point upstream weighting for saturations • Multi-point upstream weighting for saturations • Higher-order methods

Reservoir Simulation – Need for higher order numerical Schemes

Standard TPFA Kx = 1 mD Ky = 50 mD

Higher Order MPFA-O

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Flow Simulation Results

Challenges • Number of challenges exists: – Upscaling multi-million cell models – Upscaling effectives properties like permeability, relative permeability, capillary pressure etc. – Faster computation of coupled flow equations – Effectively capturing subsurface heterogeneities in a simulation model – Identify end-members to use in RTM approach – CO2 capture and utilization for Enhance Oil recovery – Reduction in carbon emissions

Question ?