Introduction to Reservoir Geomechanics

Transcription

1 Introduction to Reservoir Geomechanics 1 Introduction Definitions and some challenges of reservoir geomechanics. Modeling of coupled phenomena. 2 Constitutive Laws: Behavior of Rocks Fundamentals of Pore-Mechanics. 3 Constitutive Laws: Behavior of Fractures Geomechanics of Fractured Media. 4 Reservoir Geomechanics Elements of a geomechanical model and applications. 5 Unconventional Reservoirs Naturally fractured reservoirs, hydraulic fracture, proppant and fracture closure model, validation (microseismicity). 6 Advanced Topics Injection of reactive fluids and rock integrity.

2 Geochemical Coupling

3 Civil Engineering Heave in a tunnel excavated in sulphate bearing rock (Belchen tunnel)

4 Mining Engineering Castellanza et al. (2005) Effects of weathering of pillars in abandoned iron mines (Northern France)

5 Chemical mechanism: new material characterization Long term stability of mineworkins and quarries (De Genaro, 2006): (and solid phase)

6 New Motivation: Brazilian Pre-Salt Reservoirs (ultra-deep waters reservoir): Reservoir and cap rocks integrity (geomechanical and chemical) Reservoir properties (coupled HMC phenomena) CO2 injection (multiphase multispecies modeling) Carbonatic Oil Reservoirs Tupi Reservoir

7 CO2 underground geological storage: Carbonate reservoirs: new deformational mechanisms can take place in the medium Rock-fluid chemical interactions Waterweakening Chemo-mechanical mechanism

8 CO2 underground geological storage: Carbonate reservoirs: new deformational mechanisms can take place in the medium CO 2 + H 2 O = HCO 3- + H + (water acidification) CaCO 3 (s) + H + = Ca 2+ + HCO 3 - (calcite dissolution) Waterweakening Chemo-mechanical mechanism

9 CO2 Storage in Geological Formations How can the geological CO 2 storage be done? Oil fields 1- Depleted reservoirs (gas/oil) 2- Enhanced oil recovery Saline Aquifers; 3- Deep unused saline watersaturated reservoir rocks. Coal layers. 4- Deep Unmineable coal 5- ECBM Recovery IPCC (2005)

10 CO2 Storage in Geological Formations How does CO2 behave when injected into geological formations? Supercritical CO 2 (gas as a liquid density) More reactive: Exhibit the propensity to dissolve materials

11 CO2 Storage in Geological Formations What can happen in porous media following CO2 injection? CO 2(g)?? Main mechanisms to storage CO 2 into geological formations Physical Chemical Fluid flow due to natural hydraulic gradientes and injection process; Buoyancy caused by the density differences between CO2 and the formation fluid; Diffusion, dispersion and fingering caused by constrast between CO2 injected and formation fluids; Dissolution into the formation fluid and porous media Precipitation/ mineralization into the porous media Adsorption of CO2 onto organic material Pore space trapping Others

12 CO2 Storage in Geological Formations What can happen in porous media following CO2 injection? Dissolution of porous media ionized react absorbed 1. CO 2(g) 2. CO 2(aq) 3. CO 2(aq) + H 2 O (l) H 2 CO 3(aq) 4. H 2 CO 3(aq) HCO 3 (aq) + H + (aq)

13 CO2 Storage in Geological Formations What can happen in porous media following CO2 injection? Dissolution of porous media Solid phase liquid phase ionized react absorbed 1. CO 2(g) 2. CO 2(aq) 3. CO 2(aq) + H 2 O (l) H 2 CO 3(aq) 4. H 2 CO 3(aq) HCO 3 (aq) + H + (aq) 5. CaCO 3 (s) + H + (aq) HCO 3 (aq) + Ca 2+ (aq)

14 CO2 Storage in Geological Formations What can happen in porous media following CO2 injection? Precipitation and mineralization into the porous media Solid phase Liquid phase ionized react absorbed 1. CO 2(g) 2. CO 2(aq) 3. CO 2(aq) + H 2 O (l) H 2 CO 3(aq) 4. H 2 CO 3(aq) HCO 3 (aq) + H + (aq) 5. HCO 3 (aq) + Ca 2+ (aq) CaCO 3 (s) + H + (aq)

15 CO2 Storage in Geological Formations What can happen in porous media following CO2 injection? Efectiveness geological storage depends on a combination of Physical (hydrodinamic, structural and stratigrafic) and Geochemical processes Under a layer with low permeability Structural & stratigraphic trapping Solubility trapping Capillarity Residual CO2 trapping Mineral trapping

16 CO2 Storage in Geological Formations Challenges: quantify changes of porosity and permeability due to precipitation. Distributed precipitation Changes in Porosity and Permeability Precipitation located Formation of disconnected porous The permeability is greatly affected, not porosity. The only way to solve this problem is by perfoming experiments Randhol & Larsen, 2010 (SINTEF Petroleum Research) III International Seminar on Oilfield Water Management

17 Coupled THM and Reactive Transport Problem

18 Multiphase multispecies approach SOLID GAS LIQUID The species are: mineral (-) : main mineral water air (w) : as liquid or evaporated in the gas phase (a) : dry air, as gas or dissolved in the liquid phase chemical species : interacting (reactive) species The three phases are: gas (g) : mixture of dry air and water vapour liquid (l) : water + air dissolved + dissolved chemical species solid (s) : main mineral + absorbed cations + precipitated minerals

19 Reactive transport equations t ( S c ) j R ( i 1,..., N) w w i i i Total Flow: Chemical reactions j i c q D c S w i w w i w c u w i Advective Non-advective (dispersion and diffusion) Solid velocity

20 Reactive transport equations t ( S c ) j R ( i 1,..., N) w w i i i CHEMICAL INTERACTION OF N INTERACTING SPECIES Slow reactions: kinetics controlled Fast reactions: equilibrium controlled PHENOMENA CONSIDERED Homogeneous reactions Aqueous complex formation Acid/base reactions Oxidation/reduction reactions Heterogeneous reactions Cation exchange Dissolution/precipitation of minerals (equilibrium and kinetics) Other reactions Radioactive decay Linear sorption

21 ) 1,..., ( ) ( N i R c S t i i i l l j CHEMICAL INTERACTION OF N INTERACTING SPECIES Fast reactions: equilibrium controlled A chemical equilibrium model is uses based on the minimization of Gibbs free energy x c x i c j N i x i x i N j c j c j n n n n G minimize 1 1, Slow reactions: kinetics controlled Rate of species production in kineticscontrolled reactions Newton-Raphson algorithm Lagrange multipliers to incorporate the restrictions of the system ) 1,..., ( 1 c N i x i ij c j U j N j n n n x ) 1,..., ( 0 c c j N j n ) 1,..., ( 0 x x i N i n n r p m m l l m k A S r 1 c mj N j v j m m m p a Q K Q 1 ; exp 25 T R E k k a m Reactive transport equations =

22 Reactive Transport Equations NUMERICAL IMPLEMENTATION NEWTON-RAPHSON ( S ) irrev l lu j lua j l l Ua j Sl lu j Rj 0 ( j 1,..., Nc) t q D u Analogy with the mechanical problem Mechanical problem: local global b 0 Reactive transport problem: c i c i U j Transport Equation Tangent matrix Ua U k j, X U k

23 HM-C Couplings Mechanical problem for geomaterials: Equilibrium Equation: σ b 0 Principle of Effective Stresses: σ σ' p f I New mechanisms!!! Stress-strain relationship: dσ' Ddε + L dp c + H dx d Specific for each geomaterial

24 HM-C Couplings HYDRO-MECHANICAL COUPLINGS: Rock porosity: t 1 1. u 0 s s (mass conservation of solids) (material derivative ) d dt t u d dt 1 d s d 1 dt dt s v (changes of porosity as a function of volumetric strains) Rock permeability: k k i exp b i

25 HM-C Couplings HYDRO-MECHANICAL COUPLINGS: Rock porosity: Chemical coupling: Porosity will change also due to mineral dissolution/precipitation!!!!! (new term in mass conservation equation) t 1 1. u f0 s s (mass conservation of solids) (material derivative ) d dt t u d dt 1 d s d 1 dt dt s v + dissolution/precipitation term Rock permeability: k k i exp b i

26 HM-C Couplings Changes of porosity due to mineral dissolution/precipitation: D Dt (1 ) s Ds Dt (1 ) u Dv Dt T v v c T m m chemical changes of porosity total mineral volume v 3 : molar volume (m /mol) of mineral m : concentration (mol/m 3 m m c m of rock) of mineral m Intrinsic permeability changes: k( ) k(mechanical, thermical and chemical problems)

27 Numerical implementation (Compiler: Intel Fortran; IDE: CodeBlocks; OS: Linux) Numerical approach Finite elements in space Finite differences in time Implicit time integration Simultaneous solution of the mechanical, hydraulic, thermal and reactive transport equations Full Newton-Raphson for iterative procedure to solve the set of nonlinear equations Solver (non-symmetric matrix) LU decomposition and backsubstitution Conjugate Gradient Squared Method with block diagonal preconditioning PARDISO (MKL) Convergence tolerances in terms of variable corrections and residuals Coupled to a reactive transport module Main features Coupled thermo-hydro-mechanicalchemical (THMC) analyses in 1, 2 and 3 dimensions Partial analyses are possible General treatment of transport processes Specific consideration of unsaturated porous media under non-isothermal conditions: Constitutive laws (thermal, hydraulic, mechanical) Equilibrium restrictions (vapour pressure, air dissolution) Chemical equilibrium and kinetics for chemical species interaction Thermo-hydro-mechanical joint element Sequential and parallel versions Staggered fully-coupled scheme THM C

28 Numerical implementation (Compiler: Intel Fortran; IDE: CodeBlocks; OS: Linux) Numerical approach Finite elements in space Finite differences in time Implicit time integration Simultaneous solution of the mechanical, hydraulic, thermal and reactive transport equations Full Newton-Raphson for iterative procedure to solve the set of nonlinear equations Solver (non-symmetric matrix) LU decomposition and backsubstitution Conjugate Gradient Squared Method with block diagonal preconditioning PARDISO (MKL) Convergence tolerances in terms of variable corrections and residuals Coupled to a reactive transport module Main features Coupled thermo-hydro-mechanicalchemical (THMC) analyses in 1, 2 and 3 dimensions Partial analyses are possible General treatment of transport processes Specific consideration of unsaturated porous media under non-isothermal conditions: Constitutive laws (thermal, hydraulic, mechanical) Equilibrium restrictions (vapour pressure, air dissolution) Chemical equilibrium and kinetics for chemical species interaction Thermo-hydro-mechanical joint element Sequential and parallel versions Staggered fully-coupled scheme THM C

29 Geochemical Integrity of reservoir and cap rocks Compaction and subsidence Creep in salt rocks Hydraulic fracturing Fault reactivation Reservoir Geomechanics Wellbore/Reservoir geomechanics

30 RESEARCH LINES LABORATORY TESTS Integrity of Carbonate Rocks Subjected to Mechanical and Chemical Actions Matrix: Fracture: before after

31 RESEARCH LINES LABORATORY TESTS Integrity of Carbonate Rocks Subjected to Mechanical and Chemical Actions Matrix: Fracture: Porosity

32 2D and 3D MODEL Injection of an under-saturated water Pressure at the top: P + P ; P =0.1MPa Dissolution front of mineral Pressure at the bottom: P Initially: - porosity and permeability: constants - mineral: randomically distributed

33 2D and 3D MODEL Injection of an under-saturated water Pressure at the top: P + P ; P =0.1MPa D Dt K K e K 0 10 b 75 (1 ) 0 b( 0 ) 18 s I Ds Dt (m 2 Dissolution front of mineral ) (1 ) u DvT Dt Tendency to develop preferencial paths (channels for fluid flow) Pressure at the bottom: P Initially: - porosity and permeability: constants - mineral: randomically distributed

34 2D MODEL Injection of an under-saturated water Concentração do mineral Porosidade Permeabilidade Fluxo

35 (Pereira & Fernandes, 2009) 2D and 3D MODEL

36 Clique aqui!

37 Clique aqui!

38 Clique aqui!

39 Clique aqui!

40 HM-C Couplings Chemo-mechanical constitutive model: v v c che vol T m m D Dt total mineral volume 3 : molar volume (m /mol) of mineral m : concentration (mol/m :parameter che vol 1 (1 ) of rock) of mineral m Linear-elastic law including chemical (volumetric) strains: 3 m Dv Dt v m c m T Cristal Growth Chemical compaction D e ( m che vol )

41 Case history: tunnel in sulphate bearing rock High-speed Railway Madrid Barcelona Pyrenees Zaragoza Barcelona Madrid B arcelona Tunnels in Stretches IVb & V Iberian Range km 45º Mediterranean 3º Sea Catalan Costal Range length: 629 km Tunnel Length (m) Maximum Cover (m) Excavated Cross-Section (m 2 ) Camp Magre Railway Authority Tunnels in Section Lleida-Martorell Lilla Puig Cabrer Camp Magre Lilla Puig Cabrer

42 Case history: tunnel in sulphate bearing rock Lilla Tunnel R = 6.46 m Excavated in by drill and blast (head and bench) from the two portals

43 Case history: tunnel in sulphate bearing rock m a.s.l North portal (Lleida) Geological Profile South portal (Martorell) Quaternary Middle Eocene Early Eocene Colluvion Limestone Claystone & Siltstone Marl Anhydritic-Gypsiferous Claystone The Tertiary Anhydritic-Gypsiferous Claystone from the Lilla Tunnel the excavated material cross-shaped fibrous gypsum veins slickenside

44 Case history: tunnel in sulphate bearing rock Heave in the flat slab section

45 Lilla tunnel: field observations Time (days) Heave in Stations with severe expansive behaviour. Flat slab section Vertical displacement (mm) /20/02 12/1/02 12/19/02 Construction of the invert 1/17/03 3/20/03 6/19/03 9/15/03 12/15/ Slab axis reference at 9/20/02 2/2/04

46 Lilla tunnel: field observations Total Radial Pressures at the invert sections 6.0 Dec-02 Jan-03 Feb-03 Mar-03 Apr-03 May-03 Jun-03 Jul-03 Aug-03 Sep-03 Oct-03 Nov-03 Dec-03 Jan-04 Feb-04 Mar-04 Apr-04 May-04 Jun-04 Jul-04 Invert: 60 cm 5.0 R = 6.46 m CPTR-3 Invert: 40 cm CPTR-1 Total radial pressure (MPa) Concreting the inverts CPTR-3 CPTR-2 CPTR CPTR CPTR CPTR CPTR CPTR Time (days)

47 Heave in sulphate bearing rock: analysis Anhydrite/gypsum system Anhydrite: Ca 2+ + SO 2-4 Gypsum: Ca 2+ + SO H 2 O Anhydrite Gypsum The molar volume of gypsum is 62% larger than that of anhydrite Direct transformation is apparently not possible Conversion from anhydrite to gypsum is via dissolution - precipitation

48 Sulphate-Bearing Clayey Rocks Expansive Behaviour TRANSFORMATION OF ANHYDRITE INTO GYPSUM IN AN OPEN SYSTEM Orthorhombic Monoclinic Anhydrite: Gs = 2.96 Gypsum: Gs = 2.32 V = 62% Water 2 mols 36 cm 3 + Anhydrite 1 mol cm 3 Gypsum 1 mol cm 3 2 H2O CaSO4 CaSO4 2 H2O

49 Heave in sulphate bearing rock: analysis

50 HM-C Couplings grain mass loss due to mineral dissolution produces a pronounced horizontal stress drop under zero lateral strain conditions rearrangement of the internal granular structure (discrete element simulation results confirm that the internal friction is fully mobilized at kmin )

51 Sample dimensions: 10x10x10cm 3D PLUG MODEL Injection of an under-saturated water Pressure at the top: P + P ; P =0.1MPa Dissolution front of mineral Pressure at the bottom: P Initially: - porosity and permeability: constants

52 HM-C Couplings Constant initial mineral concentration distribution 0.3 vertical displ. (cm) 0 0 time (s) 1.0e lateral stress (MPa) time (s) 1.0e8

53 HM-C Couplings Randomic initial mineral concentration distribution 0 vertical displ. (cm) time (s) 1.0e8 Higher vertical stresses in remaining mineral zones 2.34 lateral stress (MPa) time (s) 1.0e8

54 HM-C Couplings Assuming elastoplastic Mohr-Coulomb law: D( p m che vol ) vertical displ. (cm) time (s) 1.0e lateral stress (MPa) time (s) 1.0e8

55 HM-C Couplings How to increase the lateral stress?? τ Introducing material degradation (eg., decreasing of cohesion) 2.34 h v lateral stress (MPa) time (s) 1.0e8

56 At well and reservoir scales... Cement dissolution under load can cause: Chemically Induced Reservoir Compaction Material degradation (decreasing of shear strength): - Wellbore stability - Faults

57 CONCLUSIONS A numerical tool capable to evaluate the integrity of reservoir and cap rocks has been presented considering a number of HM and HMC phenomena. Consideration of chemical effects requires the incorporation of: New (environmental) variable: concentration of chemical species New balance equation: reactive transport equation Chemical models accounting for kinetics and chemical equilibrium are required Mineral concentration was adopted as a state variable of a simplified chemo-mechanical constitutive model that was able to reproduce qualitatively deformations induced by cement dissolution.