Transcript Slide 1
FORCE 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 Simulation
Based in Calgary Canada
28 years of simulator development
Mainly in IOR and thermal methods
Over 70 staff
Became a public company
CMG:TSX
Established as research foundation
Fiscal
Fiscal
Fiscal
Fiscal
Fiscal
Fiscal
Fiscal
Fiscal
1978
1997
1998
1999
2000
2001
…
2005
CMG’s Offices
Moscow, Russia
Calgary, Alberta
London,
England
Beijing, China
Houston, Texas
Caracas, Venezuela
Head Office
Calgary, Canada
Over 270 Customers
in 44 Countries
STARS –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 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
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
EnCana
Foster Creek
$290,000,000
Husky
Tucker Lake
$350,000,000
Imperial
Current Cold Lake
Imperial
Mahkeses
Imperial
Nabiye, Mahihkan
Japan Canada
Hangingstone main
Nexen/OPTI
Long Lake
Suncor
Firebag Phase 1
Investment Total
$260,000,000
$30,000,000
~ $7,000,000,000
$650,000,000
$1,000,000,000
$250,000,000
$2,500,000,000
$600,000,000
$22,830,000,000
SAGD 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 Process
Isotropic unloading will increase f 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 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
Reservoir
Grid Types
Initial
and
Boundary
Conditions
Element
Types
Displacement
Equations
Tresca Model
Linear
Elasticity
von Mises Model
Mohr-Coulomb
Model
Drucker-Prager
Model
Elasto-plasticity
Non-linear
Elasticity
Straindisplacement
Relations
Constitutive
Laws
Pseudo
Dilation
Model
ElastoViscoplasticity
Plastic Cap Model
Hyper-elastic
Model
Hypo-elastic
Model
von Mises
Model
Drucker-Prager
Model
Calculation 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 - 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 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 cornerpoint 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
Coupling
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 f* for feedback to the flow
simulator
Basic Flow Equations
Conservation of fluid in a deformable porous medium
k
f f 1 v f p f g Q f 0
t
Currentporevolume Vp
f T rueporosity
Currentbulk volume Vb
f* Reservoir porosity
f 1 v ;f
*
v
Vb
Vb0
Currentporevolume Vp
0
Initialbulk volume Vb
k
*
f f f p f g Qf 0
t
Basic Geomechanics Equations
σ = σ' + αp
p
’
’
p
p : pore pressure
σ' : effective stress
σ : total stress
α : Biot’s number
Coupling Deformation-Pressure-Temperature Equation (1D):
d du d
E p ET r g
dz dz dz
Basic Equation Summary
Equation for Fluid Flow
k
*
f f f p f g Q f
t
0
Equation for Heat flow
k
*
f f U f (1 f * ) rU r f p f g H f
t
(T ) Qh 0
Equation for Deformable Medium
1
T
C : u u p T I r g
2
Described in Tran, Nghiem, and Buchanan (SPE 97879)
Equation Communication
From Reservoir Flow to GEOMECH
P and T appears in GEOMECH calculation
Feedback from GEOMECH to Reservoir Flow
Porosity Function
f* = f (P,T,v) or f (P,T,m)
Porosity Function f*
Tran, Settari and Nghiem (2004)
fn*1 fn* Cn0 pn1 pn Cn1 Tn1 Tn
1
C0n c0 c2a1 n Cn c1 c2a 2 n
E:
cb:
cr:
:
:
:
m:
n:
n+1:
Young's modulus
Bulk compressibility
Solid rock compressibility
Thermal expansion coefficient
Poisson's ratio
Biot number
Mean total stress
Time level n
Time level n+1
Iterative Two-way Coupling
n=0
Solving p, T , f*, k
Convergence
Newtonian
Iterations
NO
Coupling
Iterations
n=n+1
Solving u, and σ
Updating f* coefficients
NO
Convergence
YES
Porosity 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 Improvements
Tran, Settari and Nghiem (SPE 88989, 2004)
f*n 1 f*n C0n pn 1 pn C1n Tn 1 Tn
Tran, Nghiem and Buchanan (SPE 93244, 2005)
f*n1 f*n B0n1 pn1 pn B1n1 Tn1 Tn
Further improvements
Provide good match between GEOMECH and
reservoir simulator porosity
Porosity Comparison
Permeability
What about permeability?
Most flow simulators use a simple f vs k look up table
Permeability Function
k = k (f*) 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 Permeability
GEOMECH 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 - 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 - 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 in
Reservoir Simulation