FORCE Workshop – 21 st Nov. 2006

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

2. 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 1978 Fiscal 1997 Fiscal 1998 Fiscal 1999 Fiscal 2000 Fiscal 2001 Fiscal … Fiscal 2005

3. CMG’s Offices Moscow, Russia London, England Calgary, Alberta Beijing, China Houston, Texas Caracas, Venezuela Over 270 Customers in 44 Countries Head Office Calgary, Canada

4. 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

5. SAGD Process • Game changer for the Canadian oil industry • $80 billion investment over the next 10 years • Shallow 150-400m; poorly consolidated; immovable liquid

6. 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!

7. SAGD – Example (T and uvert)

8. 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

9. 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?

10. Geomechanics Module (GEOMECH)

11. 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

12. 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!

13. 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 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

14. 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

15. Basic Flow Equations • Conservation of fluid in a deformable porous medium

16. Basic Geomechanics Equations σ = σ' + αp p : pore pressure σ' : effective stress σ : total stress α : Biot’s number Coupling Deformation-Pressure-Temperature Equation (1D):

17. Basic Equation Summary • Equation for Fluid Flow • Equation for Heat flow • Equation for Deformable Medium • Described in Tran, Nghiem, and Buchanan (SPE 97879)

18. 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,ev) or f (P,T,sm)

19. Tran, Settari and Nghiem (2004) Porosity Function f* E: Young's modulus cb: Bulk compressibility cr: Solid rock compressibility : Thermal expansion coefficient : Poisson's ratio a: Biot number sm: Mean total stress n: Time level n n+1: Time level n+1

20. Iterative Two-way Coupling

21. 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

22. Porosity 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

23. Porosity Comparison

24. 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 ev (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

25. Fractured Model Permeability

26. 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

27. 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

28. 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!

29. Leading the Way in Reservoir Simulation