Fully Coupled Geomechanics, Multi-Phase, Thermal and Equation of State Compositional Simulator Jean H. Prévost, Lee Y. Chin*, Zhihua Weng e-mail: prevost@princeton.edu URL: http://www.princeton.edu/~prevost URL: http://www.princeton.edu/~dynaflow URL: http://denali.princeton.edu collaborators: G. Scherer, R. Fuller, B. Huet sponsors: BP, Ford Department of Civil and Environmental Engineering Princeton University *ConocoPhillips, Bartlesville, Oklahoma Princeton University 2/7/28 1
Research Focus: CO2 leaks Research Focus Wells cement degradation / leakage paths: Geochemical interaction with wells cement» cement degradation; seal loss Leakage:» thru seepage across overburden T» via abandoned wells (damage due to injection) Super-critical/sub-critical CO 2 flow; crossing saturation line; CO 2 bubbling/condensing Thermal/heat transfer effects w/ rock P L G Princeton University 2/7/28 2
Dynaflow Fully Coupled Multiphysics Simulator Geomechanics Multi-Phase flow; Multi-components Heat flow (including heat of reaction) Flash via equation of state Modular flash and geochemistry Transportable to other codes (e.g., Eclipse) Related models: TOUGH2 (K. Pruess, LBL): similar flash capabilities but not modular; no coupled poromechanics; no cement geochemistry NUFT (Nitao, Wolery, J. Johnson, LLNL): no extensive thermodynamic data base for cement geochemistry; no coupled poromechanics FLOTRAN (Lichtner, J. Carey, LANL): reactive transport; no coupled poromechanics ECLIPSE (Schlumberger), VIP (Halliburton),.: no accurate CO 2 flash; no cement geochemistry; no coupled poromechanics
finite element based (arbitrary meshing)» Galerkin, stabilized Galerkin (SUPG)» Finite volume (cell centered; vertex centered) staggered implementation to allow flexible/versatile algorithmic options for integration of coupling effects multiphase flows» compressible; incompressible flows» miscible; immiscible flows» heat transfers fluid flows fully coupled with geomechanics reactive transports capabilities for cement attack/degradation by CO 2 (B.H.) eos based flash (L.Y.C.) 1D/2D/3D capabilities Dynaflow parallel computing on shared and/or distributed memory/architectures (openmp/mpi) Princeton University 2/7/28 4
Modeling Leakage If a gap exists, the escaping (super-critical) fluid will react with the cement, but it will also boil Simulation shows advance of boiling front (gas, aqueous phase and CO 2 -rich liquid Other flash models are unable to handle this case
. adiabatic CO2 leak (Nc=2, Np=3) Princeton University 1/28/28 [ ] [ ] domain : x =., L Area = 1 1 L = 6. m initial conditions : T( x, t = ) = 15 CO2 H2O Z x t Z x t + T( x=, t = ) = 15 C 2 1. / (, ) (, ) Px ( =, t= ) = 5.23 MPa, Px ( = Lt, = ) =.1MPa (, = ) =, (, = ) = 1. boundary conditions : g = m s T = T x t P = P x t C + + Px ( =, t= ) = 5.73 MPa, Δ P =.5 MPa, P( x = L, t = ) =.1MPa CO2 Z x t + ( =, = ) = 1. g % L x P 6 T
adiabatic CO2 leak (Nc=2, Np=3) Princeton University 1/28/28 7
Radial steam injection (Nc=3, Np=3) r r 1 [ ] domain : r = r, r r =.1m r = 25. m initial conditions : Trt (, = ) = 65 Prt (, = ) = 6.MPa 1 1 C3 16 Z r t Z r t Z r t C HO 2 (, = ) =.4, (, = ) =.4, (, = ) =.2 boundary conditions : + Tr ( = r, t= ) = 3 C T= Trt (,) P= Prt (,) C + Pr ( = r, t= ) = 7. MPa, Δ P= 1.MPa + ( =, = ) = 1. HO 2 Z r r t r Princeton University 1/28/28 8
Radial steam injection (Nc=3, Np=3) 1d1x; time = 1, 1 days 35 1 3 S_L.8 25 2 temp.6.4 15 S_Aq 1 S_G.2 Princeton University 1/28/28 5 2 4 6 8 1 radial_distance (m) 9
Radial steam injection (Nc=3, Np=3) Loss of injectivity 35 3 25 1d1x; time = 1, 1 days pressure 7 6.5 2 6 15 1 temperature 5.5 Princeton University 1/28/28 5 5 2 4 6 8 1 radial_distance (m) 1
Geomechanics and Well Leakage Pressure created by injection of CO 2 deforms overburden Simulation investigates stresses from bending of cap rock and shear of cement relative to cap rock Overburden stress = 9 MPa σ ' = 1.4 MPa H, reservoir 2 m Cement Abandoned well Overburden 48 m depth = 1 km r o r i r 1 Void t s Δp 1 cement/rock interface Cap rock (shale) Reservoir 1 m Not to scale!!! 2 m 1 m t Steel
interface (slide-line) elements Modeling the well (cement)-rock interface beam τ Cohesion k 1 ε Schematic of interface element Tangential constitutive relation for interface elements 12
Material properties Geological layers Young's Modulus Poisson's ratio Density Permeability E (Pa) υ ρ (kg/m 3 ) κ (m 2 ) Overburden 3.45E+9.35 2.5E+3 1.E-15 (1 md) Reservoir 2.E+9.4 2.6E+3 1.E-13 (1 md) Shale 1.E+1.35 2.5E+3 1.E-17 (1 μd) 13
Material properties Geological layers Parameters Young's Modulus of cement E c (Pa) Value Poisson's ratio of cement υ c.2 6.9E+9 Materials Young's Modulus of steel E s (Pa) 2.7E+11 Poisson's ratio of steel υ s.28 Young's Modulus of composite beam E (Pa) 5.15E+1 Inner radius r i (m) Outer radius c or r o (m) Beam thickness t (m) 7.74E-2 1.21E-1 4.33E-2 Dimensions Steel layer thickness t s (m) 1.15E-2 Solid section area, A (m 2 ) Bending inertia, I (m 4 ) 2.69E-2 5.53E-4 S, I/c (m 3 ) 4.58E-3 EI (N.m 2 ) 2.85E+7 Rock-cement Tangential stiffness k 1 (Pa) 3.E+9 interface Normal stiffness k 2 (Pa) 2.E+12 Cohesion (Pa) 4.E+5 14
Finite element mesh 3D Well 15
Finite element mesh 2D axisymmetric 16
Beam bending: 3-layer formation (w/ shale) σ σ bending bending = N / A+ M / S 3MPa 2.E-4 2D axisymmetric 3D.4.E+ 2D axisymmetric 3D Bending moment (MN.m) 1.E-4.E+ -1.E-4.2 Bending stress (MPa) -.2 Bending moment (MN.m) -4.E-5-8.E-5-1.2E-4 -.1 -.2 Bending stress (MPa) -.3 -.4-2.E-4 5 1 15 2 25 3 Elevation from datum (m) Spatial distribution of bending moment/stress at t = 3 days 17-1.6E-4 1-4 1-3 1-2 1-1 1 1 1 1 2 1 3 Time (month) Time history for maximum bending moment/stress
shear stress in formation 3.E-2 3.E-2 2.5E-2 2.5E-2 Shear stress (MPa) 2.E-2 1.5E-2 1.E-2 Shear stress (MPa) 2.E-2 1.5E-2 1.E-2 5.E-3 2D axisymmetric 3D 5.E-3 2D axisymmetric 3D.E+ 5 1 15 2 25 3 Elevation from datum (m).e+ 1-3 1-2 1-1 1 1 1 1 2 1 3 Time (month) Spatial distribution of shear stress t = 5 days Time history for maximum shear stress 18
w/ slip at rock-cement interface 8.E-5.E+ Bending moment (MN.m) 4.E-5.E+ -4.E-5-8.E-5.1 -.1 -.2 Bending stress (MPa) Bending moment (MN.m) -5.E-5-1.E-4-1.5E-4 -.1 -.2 -.3 Bending stress (MPa) -1.2E-4 5 1 15 2 25 3 Elevation from datum (m) 1-4 1-3 1-2 1-1 1 1 1 1 2 1 3 Time (month) Spatial distribution of bending moment/stress at t = 3 days Time history for maximum bending moment/stress 19
w/ slip at rock-cement interface 5.E-1 1.2E-3 Interface shear stress (MPa) 4.E-1 3.E-1 2.E-1 1.E-1 @3days @2years Relative displacement (m) 8.E-4 4.E-4.E+ beam-rock (LHS) beam-rock (RHS) between rocks.e+ 1 15 2 25 3 Elevation from datum (m) Spatial distribution of interface shear stress t = 3 days -4.E-4 5 1 15 2 25 3 Elevation from datum (m) Spatial distribution of interface shear displacement t = 3 days 2
w/ slip at rock-cement interface 5.E-1 8.E-4 Interface shear stress (MPa) 4.E-1 3.E-1 2.E-1 1.E-1 Interface shear stress Relative displacement 6.E-4 4.E-4 2.E-4.E+.E+ 1-4 1-3 1-2 1-1 1 1 1 1 2 1 3 Time (month) Relative displacement (m) 21 Time history for shear and relative displacement
Geomechanics and Well Leakage Pressure created by injection of CO2 deforms overlying formation Simulation investigates stresses from bending of cap rock (found to be negligible) and shear of cement relative to cap rock (causing sliding, and possibly leakage???)
Volumetric flow rate at injection site 5.E+3 5.E+4 Volumetric flow rate (m 3 /month) 4.E+3 3.E+3 2.E+3 1.E+3 t=3days t = 2 years Volumetric flow rate (m 3 /month) 4.E+4 3.E+4 2.E+4 1.E+4.E+ 2 4 6 8 1 Elevation from datum (m) Spatial distribution of volumetric flow rate.e+ 1-4 1-3 1-2 1-1 1 1 1 1 2 1 3 Time (month) Time history for total flow rate 23
Numerical results: Shear stress τ xy 24
Numerical results: Mises stress, Caprock failure? mobilized ϕ 17 shear stress τ 3 MPa 25
Future work Stabilize flash (Nc=2, Np=3) Investigate failure in cap rock Incorporate interface in 3D model Parametric studies Detailed leak simulation: viz., fluid (P,T, composition) cement exposure vs depth Princeton University 2/7/28 26
Hydrogeologic parameters = = 13 2 permeability : K 1 m 1 mdarcy porosity : ϕ =.15 pore compressibility : C =. relative permeability : Stone' s first 3 phase method a : Aqueous phase : SAq Sar kraq = Sar =.15 n= 3 1 Sar b : Liquid phase : ) ) S S Aq 1 S ( )(1 ) ar S S Sar S lr Aq krl = ) S Sa r 1 SAq Slr 1 Sar ) S = 1 S S S =.5 n= 3 c : Gas phase : SG Sgr krg = Sgr =.1 n= 3 1 Sar thermal parameters : rock density : ρr = 26 kg / m Princeton University 1/28/28 n G lr lr : = 2. / thermal conductivity KT W m C rock specific heat : n c R = 1 / m J kg C 3 n 27