Numerical Simulation of Fluid Flow and Geomechanics

Transcription

1 Numerical Simulation of Fluid Flow and Geomechanics Liuqi Wang, Humid Roshan & Rick Causebrook, Geoscience Australia University of New South Wales CAGS Summer School II, November 00

2 Outline Introduction Geomechanical roerties of Rock Stress and strain Couled simulation of fluid flow and geomechanics Case study

3 Introduction Full-hysics Comositional Simulation Convective and disersive flow Relative ermeability hysteresis Gas solubility in aqueous hase Aqueous chemical equilibrium reactions Mineral dissolution and reciitation kinetics CMG Training, 008 Vaorization of H O redictions of brine density and viscosity Leakage through ca rock and thermal caability

4 Couled Simulation of Fluid Flow and Geochemical Reaction Material Balance Equation for CO Couled simulation of fluid flow and geochemical reactions through the generation of comositional equation-of-state (EOS), which integrates the imortant geochemical simulations.

5 Introduction Main imact from CO injection: Higher formation ressure due to CO injection CO buoyancy force Risk: Destabilization of fault Leakage through ca rocks or wellbore Wellbore instability Reservoir Characterization Orientation of minimum and maimum horizontal stress Magnitude of minimum and maimum horizontal stress, ore ressure Structural modelling: Folding and unfolding, deformation, faulting, structural maing

6 Geomechanical roerty of Rock Tension and etension in a rod which is under aial tension and which is unrestricted laterally Uniaial Tension load Young s modulus: E L Young s modulus: Ratio of lateral contraction to longitudinal etension d ν L Bulk modulus: hydrostatic ressure K volumetric strain E K 3( ν )

7 Orientation of Ma and Min Horizontal Stresses Borehole Breakouts Drilling Induced Tensile Fractures Earthquake Focal Mechanisms Fault Breakout AZ HAZI tan( RB) + a tan cos( DEV )

8 ore ressure, Effective stress and Total Stress +αi (In 3D) total stress effective stress ore ressure α - Biot s number

9 Minimum Horizontal Stress ost shut-in ressure analysis on mini-hydraulic fracturing data Etended leak-off test (XLOT) (White, et al., 00) (Chen, 009) (Weiren Lin, et al., 008)

10 Vertical Stress Overburden stress or vertical stress, v, at deth of D s, with the average bulk density (RHOB, g/cc) and acceleration due to gravity, g: Trend line of RHOB: D s v RHOB gdd s 0 RHOB B Ae D s A and B are the regression constants

11 Rock Frictional Strength Rock rincial stress vs internal friction: [ ] friction coefficient of - ore ressure stress minimum rincial stress maimum rincial ) ( µ µ µ µ f h v f ) ( 3 µ Normal Fault: h H v Strike-sli Fault: h v H h H f ) ( 3 µ Reverse Fault: v h H v H f ) ( 3 µ v H f + ) ( ) ( µ or v h f + (µ)

12 Internal Friction for Three Different Faulting Regimes Normal Fault: Strike-sli Fault: v H H v h h Reverse Fault: H h v To further constrain the horizontal stress: Wellbore breakout angle (FMI, BHTV, etc.) Rock comressive strength

13 Eamle of ore ressure and Stress (Chen, 009)

14 Comressive and Shear Wave Slowness (Well Log Data) Shear modulus: G Bulk modulus: RHOB DTS Kbulk RHOB DT oisson s Ratio: ν 3 Kbulk G 6 Kbulk + G Young s modulus: 9 G Kbulk E 3 Kbulk + G Bulk comressibility: 000 RHOB DT 4 3 DTS C b Internal frictional angle: φ φ shale VSH + φ sandsone 4G 3 ( VSH) Unconfined comressive strength: UCS.35 DT.75 Cohesive strength: UCS sin φ S 0 cos φ Tensile strength: UCS T 0 DT - comressional VSH - volume fraction of VSH + 00 e RHOB bulk density log (g/cc) DTS - Shear wave slowness (µµs/ft shale DT ( VSH) Al-Qahtani et al, 00 Static geomechanical roerty: Linear regressioned from dynamic roerty wave slowness (µµs/ft

15 Stress Tensor Traction Force er Unit (T) Unit normal vector (n) stress tensor () ij

16 ( ) ii m Mean effective stress: Mean & rincial Effective Stress rincial effective stress: 3 3 : Assume that > > ij

17 Constitutive Laws Linear elasticity: Loading and unloading have the same stress ath Loading E Unloading : Effective stress : Strain E : Young s modulus Linear Elastic Model

18 Dislacement & Deformation Changing both the shae and the location: u - dislacement vector Bt - deformed configuration

19 Strain ij 0 0 lim lim u u AB AB A B + Normal Strain: Shear Strain: 0 0 lim D A B π γ 0 0 lim u u π π u u + γ + u u γ

20 Volumetric Strain Volumetric Strain change in volume initial volume + v ii + 33

21 Absolute ermeability Matri ermeability - Emirical formula (Li and Chalaturnyk) - Look-u Table Fracture ermeability - Barton-Bandis Model (BB Model)

22 Barton-Bandis Model A secondary fracture system is defined in the grid via dualermeability As ressure increase in the regular grid the stresses are altered, causing the normal stresses on the fractures to increase. Eventually the Stress breaks ast the Failure Enveloe of the rock, causing a fracture to aear (oen) and allow fluids to ass through. (CMG, 009)

23 Loose Couling Algorithm (Susan E. Minkoff et al., 003)

24 Geomechanical Simulation Couled with Comositional Simulator Finite element aroach: n 0 Reservoir Simulator, T n : no of time stes : ore ressure T: temerature u: dislacement : stress : strain n n+ Geomechanics Module u,, One Way Couling Simulation Two Way Couling Simulation (CMG, 009)

25 Two-way couled simulation: Case Study Leakage Risk of Carock Grid Dimension: m 0m (horizontal) Grid Number: orosity: 0.8 Kv/Kh Sgrm 0.3 Injection Well: (3,, ) erforation Interval: (3,, 5) to (3,, 7) Injection Rate: 0 4 m 3 /day (STG surface gas rate) Injection eriod: to Simulation eriod: to 00--

26 ermeability Model

27 Results-00yrs Later

28 Results-00yrs Later

29 Results-00yrs Later

30 Results-00yrs Later

31 Results-00yrs Later Total Cum Inj, mol E+08 CO Storage Amounts in Reservoir Moles kg Gaseous hase E E+00 Suercritical hase E E+07 Traed due to Hysteresis.54067E E+06 Dissolved in Water E E+06 (CMG, 009)

32 Summary Couled numerical simulation of fluid flow and geomechanics is based on the detailed reservoir characterisation of structure, etrohysical roerty and geomechanical roerty, ect. Couled simulation can imrove our understandings of both movement of CO lume and change of geomechanical attern. Besides the effective storage caacity assessment, the couled simulation can rovide the risk information of leakage.