Transcript Slide 1

FORCE Workshop – 21st Nov. 2006
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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
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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
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
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  ET   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  pn1  pn   Cn1 Tn1  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*n1  f*n  B0n1 pn1  pn   B1n1 Tn1  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
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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
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Currently: 32 days
< 2 days
Future: Add full 3D geomechanics
200+ days
????
~4 days expected!
Leading the Way in
Reservoir Simulation