FORCE Workshop – 21st Nov. 2006FORCE Workshop – 21st Nov. 2006

Introduction to CMG CMG’s STARS simulator The SAGD Process GEOMECH and its features Discussion on iterative coupling

CMG’s porosity function Examples Future Work

Long History in SimulationLong History in Simulation

Based in Calgary Canada 28 years of simulator development Mainly in IOR and thermal methods Over 70 staff

Established as research foundation

Fiscal

1978

Fiscal

1997

Fiscal

1998

Fiscal

1999

Fiscal

2000

Fiscal

2001

Fiscal

…

Fiscal

2005

Became a public company CMG:TSX

CMG’s Offices CMG’s Offices

Over 270 Customers in 44 Countries

Houston, Texas

London, England

Head OfficeCalgary, Canada

Calgary, Alberta

Caracas, Venezuela

Beijing, China

Moscow, Russia

STARS –SimulatorSTARS –Simulator

Market Leader in Advanced Process Simulation STARS simulator

Thermal (CS, SAGD, ES-SAGD, and Air Injection)

Electrical Chemical (ASP, Foams, Gels, Microbial)

Compositional (CO2, N2, VAPEX, Gas Injection)

Geomechanical (Finite Element)

Over 1,400 licenses in use worldwide mainly for thermal and IOR process modelling work Particularly steam processes e.g. SAGD

SAGD ProcessSAGD Process

Game changer for the Canadian oil industry $80 billion investment over the

next 10 years Shallow 150-400m; poorly

consolidated; immovable liquid

BlackRock Ventures Hilda Lake $260,000,000

CNRL Horizon Ph I $8,000,000,000

ConocoPhillips/TFE/Devon Surmont $1,000,000,000

Deer Creek/Enerplus Joslyn Creek Phase 2 $500,000,000

Devon Jackfish $400,000,000

Devon Dover Pilot $30,000,000

EnCana Foster Creek $290,000,000

Husky Tucker Lake $350,000,000

Imperial Current Cold Lake ~ $7,000,000,000

Imperial Mahkeses $650,000,000

Imperial Nabiye, Mahihkan $1,000,000,000

Japan Canada Hangingstone main $250,000,000

Nexen/OPTI Long Lake $2,500,000,000

Suncor Firebag Phase 1 $600,000,000

Investment Total $22,830,000,000

SAGD ProcessSAGD Process

Geomechanics plays an important part from both a reservoir and surface expression perspective! Surface heave of up to 20cm has been reported (Wang and Kry,

1997) for cyclic steaming in the Canadian formations At Peace River, Shell uses surface tilt meters to monitor the

process Large stress changes associated with the process

Isotropic Unloading – pore pressure increase under high pressure steam injection

Shear Failure – thermal stresses at steam chamber boundary caused by the large thermal gradient normal to the front surface Typically 250C over a few metres!

SAGD – Example (T and uvert)SAGD – Example (T and uvert)

SAGD ProcessSAGD Process

Isotropic unloading will increase and k Although if temperature dominates these terms can actually

decrease! However, the thermally induced shearing process can significantly

increase permeability Up to 6 times vertically and 2.5 times horizontally (Li and

Chalaturnyk, 2004) Dependent on stress path, but shallow SAGD operations benefit

most from having low confining stress Major contributor to injectivity and overall enhancement of

production rates Stress state cannot be modelled by simple flow simulator table

look up approaches (pore pressure vs poro or perm multiplier) So it is important to be able to model the stress alterations and get

the geomechanical effect right, in order to understand fully the injection and production response of your SAGD system

SAGD SummarySAGD Summary

Huge investment in the SAGD process Geomechanical effects can have a strong effect on

the production and injection response of the system Surface expression also significant

Simple poro/perm tables do not capture the full geomechanical effect

Stress path is important to quantify the effect and magnitude of the reservoir alterations

So how does CMG deal with this situation?

Geomechanics Module (GEOMECH)Geomechanics Module (GEOMECH)

Calculation SpeedCalculation Speed

In the SAGD situation we know that geomechanics plays an important role, but can we afford to model it?

It is the calculation time that has typically determined whether it is worthwhile modelling geomechanics, and to what extent. Fluid flow typically requires the solution of 4 eqns per block Full 3D Geomechanics can require up to 24 eqns per block! So, GEOMECH solution can take up to 85% of the cpu time!

The memory requirement also increases similarly 150,000 cell; inverted nine spot steam flood; 529 wells

No geomech - 450Mb 2D geomech – 820Mb 3D geomech – 3760Mb

Calculation Speed - ExampleCalculation Speed - Example

Surmont, SAGD, 9 well pair (half pad) 1,722,780 Grid cells 6.5 year forecast Serial runtime on IBM 1.65GHz P5

32 days!

Add 3D geomechanics 200+ days expected with 40-50GB RAM!

Reservoir and Geomechanics GridsReservoir and Geomechanics Grids

Reservoir Flow Corner-point grids

Geomechanics Quadrilateral 8-node finite elements that match initial

corner-point grids 8 nodes initially co-incident with grid corners 2D Plain strain or full 3D Elements

Finite elements model deformations whereas corner-point grids remain the same during the simulation

The finite element deformation is converted into a change in porosity in corner-point grids As reservoir flow grid bulk volume is invariant

CouplingCoupling

Fully Coupled Primary unknowns – (P, T and u) Pressure; Temperature and

Displacement solved simultaneously The ultimate solution, but very computationally expensive

Explicit Coupled Flow information sent to GEOMECH module but results not fed

back to the flow module ie Flow is unaffected by GEOMECH Iterative Coupled

P and T solved first and then u i.e. the GEOMECH calculations are calculated one step behind the flow calculations

Information is passed between flow and GEOMECH modules Flexible, as the 2 modules can be coded independently, and

quick This coupling uses a modified porosity * for feedback to the

flow simulator

Basic Flow EquationsBasic Flow Equations

Conservation of fluid in a deformable porous medium

b

p

V

V

volumebulkCurrent

volumeporeCurrentporosityTrue

0b

p*

V

V

volumebulkInitial

volumeporeCurrentporosityservoirRe

v* 1

0Qgpk

t ffff*

0gk

1

fffvf Qpt

Basic Geomechanics EquationsBasic Geomechanics Equations

p : pore pressure

σ' : effective stress

σ : total stress

α : Biot’s number

σ = σ' + αp

gTEpdz

d

dz

duE

dz

dr

Coupling Deformation-Pressure-Temperature Equation (1D):

Basic Equation SummaryBasic Equation Summary

Equation for Fluid Flow

Equation for Heat flow

Equation for Deformable Medium

Described in Tran, Nghiem, and Buchanan (SPE 97879)

0g*

ffff Qpt

k

gTp rT

IuuC

2

1:

0)(g)1( **

hfffrrff QTHpUUt

k

Equation CommunicationEquation Communication

From Reservoir Flow to GEOMECH P and T appears in GEOMECH calculation

Feedback from GEOMECH to Reservoir Flow Porosity Function

* = f (P,T,v) or f (P,T,m)

Porosity Function *Porosity Function *

Tran, Settari and Nghiem (2004)

nnnnnnnn TTCppC 11

10**

1

E: Young's moduluscb: Bulk compressibilitycr: Solid rock compressibility: Thermal expansion coefficient: Poisson's ratio: Biot numberm: Mean total stressn: Time level nn+1: Time level n+1

n120

0n accC

n2211n accC

Iterative Two-way CouplingIterative Two-way Coupling

NO

YES

NO

n = 0

Convergence

Solving p, T , *, k

n = n + 1 Solving u, and σ

Convergence

Newtonian Iterations

Coupling Iterations

Updating * coefficients

Porosity FunctionPorosity Function

Crux of the iterative coupling method Approximation of actual geomechanics behavior Converts geomechanics behavior to a form that could be used

by a reservoir simulator Compressibility and Thermal Expansion Coefficients

Discrepancies can exist between simulator porosity and geomechanics porosity but a threshold forms part of the final coupling iteration convergence check For difficult problems (e.g. plastic deformation and shear failure),

large differences may exist between the 2 porosities and many coupling iterations may be necessary E.g. Dean’s problem # 3 requires 5 iterations (SPE 79709)

CMG’s porosity function formulation aims to reduce the total number of coupling iterations to as low a value as possible E.g. Dean’s problem # 1,2, and 4 required 1 iteration

Porosity Function ImprovementsPorosity Function Improvements

Tran, Settari and Nghiem (SPE 88989, 2004)

Tran, Nghiem and Buchanan (SPE 93244, 2005)

Further improvements Provide good match between GEOMECH and

reservoir simulator porosity

n1n1nn1n

0n

*n

*1n TTCppC

n1n1

1nn1n0

1n*n

*1n TTBppB

VPOROSGEO 14,1,1 SAGD3_GEOM_COUPLING_MOHR.irf

Time (Date)

Po

rosity - G

eo-C

orrected

: VP

OR

OS

GE

O 14,1,1

2000-4 2000-7 2000-10 2001-1 2001-4 2001-7 2001-10 2002-1

0.2998

0.3008

0.3018

0.3028

Porosity - Geo-Corrected: VPOROSGEO 14,1,1 Porosity - Geo-Corrected: VPOROSGEO 15,1,19 Porosity - Geo-Corrected: VPOROSGEO Average Void Porosity: VPOROS 14,1,1 Void Porosity: VPOROS 15,1,19 Void Porosity: VPOROS Average

Porosity ComparisonPorosity Comparison

PermeabilityPermeability

What about permeability? Most flow simulators use a simple vs k look up table

Permeability Function k = k (*) basic look up provided

Additionally ln(k/ko) = C v (Li and Chalaturnyk, 2004)

C is a matching parameter from lab measurements Table lookup (allows for anisotropy)

Ki/Koi (i=x,y,z) versus Mean effective stress Mean total stress Volumetric strain

Fractured Model PermeabilityFractured Model Permeability

GEOMECH Highlights - FeaturesGEOMECH Highlights - Features

Current Iterative two-way coupling and one-way coupling Geomechanics for Dual Porosity/Permeability Stress-dependent permeability Temperature-dependent geomechanics properties

Future (near current!) Improved constitutive models for SAGD operations

Generalised Plasticity Drucker Prager and Matsouka-Nakai augmented by Plastic Potential function; Friction Hardening; Cohesion

softening; and dilation angle based on Rowe’s dilatancy theory

GEOMECH Highlights - SpeedGEOMECH Highlights - Speed

Current Improved porosity function

Advantages of a fully coupled system without the associated cost Geomechanics grid larger, or smaller, than reservoir grid Control of the frequency for calling GEOMECH AIM and PARASOL

Future Generalised grid mapping

GEOMECH and flow grids can be dissimilar Less GEOMECH cells

Allow CMG’s Dynagrid functionality Further flow grid speed enhancement

Apply PARASOL to the GEOMECH calculations

Calculation Speed - ExampleCalculation Speed - Example

Surmont, SAGD, 9 well pair (half pad) Serial runtime on IBM 1.65GHz P5

32 days!

Add 3D geomechanics 200+ days expected with 40-50GB RAM!

Parallel (8cpu) + Dynagrid Currently: 32 days < 2 days Future: Add full 3D geomechanics 200+ days ???? ~4 days expected!

Leading the Way inLeading the Way in Reservoir SimulationReservoir Simulation