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Feb 13, 2024 35 likes •633 views

Enhanced Geothermal Systems (EGS): Permeability Stimulation Through Hydraulic Fracturing in a Thermo-Poroelastic Framework CNRS CNRS Prepared by: ABUAISHA Murad Supervised by: LORET Benjamin Laboratoire 3SR, Universit de Grenoble CNRS

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Enhanced Geothermal Systems (EGS): Permeability Stimulation Through Hydraulic Fracturing in a Thermo-Poroelastic Framework

Prepared by: ABUAISHA Murad Supervised by: LORET Benjamin Laboratoire 3SR, Université de Grenoble CNRS Fellowship 03/2011 to 02/2014

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1/48 Deep geothermal energy:

Earth’s stored energy Gradient of temperature Mankind’s energy needs (electricity) Exploitation of geothermal energy http://www.mhi-global.com on 30/01/2014

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2/48 Exploitation – Enhanced Geothermal Systems (EGS)

Impermeable Hot Dry Rock (HDR) reservoirs Enhance/create geothermal resources by Hydraulic Fracturing

(Lund, [2007])

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3/48 Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by ABAQUS and FE domestic code
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat - Stabilization
  • Conclusion
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Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by ABAQUS and FE domestic code
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat - Stabilization
  • Conclusion
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Thermo-poroelasticity - Mathematics - Constitutive equations

Homogeneous single-porosity media

  • Stress mixture equation:
  • Change in mixture fluid content equation:
  • Darcy’s equation:
  • Fourier’s law of thermal conduction:
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Thermo-poroelasticity - Mathematics – Balance equations

  • Balance of momentum:
  • Balance of fluid mass:
  • Balance of energy:

(Thermal diffusivity)

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Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by ABAQUS
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat - Stabilization
  • Conclusion
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Thermo-poroelasticity – Simulations by ABAQUS

The transient BVP: Heat transfer effect compared to the abrupt changes due to the surcharge History of loading:

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Thermo-poroelasticity – Thermal to mechanical loading

Parametric study: Pore pressure profiles at

Case (1) Case (2)

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Thermo-poroelasticity – Thermal to mechanical loading

Conclusions:

  • 1. Pore pressure is significantly affected by fluid compressibility and thermal expansion
  • 2. Previous conclusion holds correct for the field of axial effective stress
  • 3. No changes in the axial strain field
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Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by the FE domestic code
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat - Stabilization
  • Conclusion
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Thermo-poroelasticity – Simulations by the Fortran 90 FE code

Validation of the first version of the FE code: The first version of the FE code was modified by Rachel Gelet, (Gelet PhD thesis, [2012]). The numerical responses of the FE code were correlated against two transient BVPs:

  • The previously discussed 1-D column.
  • A 2-D wellbore stability axisymmetric problem.
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Fortran 90 code – Wellbore stability BVP

(He and Jin, [2010]) Radial distributions at t = 280 s

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Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by ABAQUS and FE domestic code
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat - Stabilization
  • Conclusion
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Fracture evolution – Fracturing criterion

DDFM: Directionally Distributed Fracture Model Modes I and II with all possible fracture orientations (Shao et al., [2005]) Characteristics of the model:

  • A phenomenological including relevant micromechanical features
  • Working in the frame of LEFM

Assumptions for opting this model:

  • No fracture Interaction before the onset of fracture evolution
  • Initial isotropy
  • Mechanical behavior before macroscopic failure
  • Penny-shaped fractures embedded in an infinite body
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Fracturing criterion - Fracture evolution (r)

For a group of fractures in a specific direction n, the following forces are sovereign:

  • The stress normal to the fracture surface
  • The stress applied to the fracture plane
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Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by ABAQUS and FE domestic code
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat - Stabilization
  • Conclusion
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Fracturing criterion - Fracture aperture (w) change

Fracture aperture (w) is related to fracture face mismatch and local grain matrix interaction: Crack aperture reduction: Barton’s hyperbolic closure model

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Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by ABAQUS and FE domestic code
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat - Stabilization
  • Conclusion
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Fracture evolution – Permeability tensor

Inside a given fracture of orientation n:

  • Flow: Navier-Stokes equation for laminar flow
  • Macroscopic velocity field: Directional averaging
  • Fracture permeability tensor is obtained from the macroscopic velocity field:

Fracture density

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Assumptions for calculating the permeability tensor:

  • Fractures are interconnected and/or dead channels
  • No local pressure fluctuations
  • Permeability tensor is anisotropic in nature
  • Permeability tensor is contributed by two porosities:

Fracture evolution – Permeability tensor

  • Initial porosity
  • Fracture induced permeability
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Fracture evolution – Numerical and experimental results

Application to Lac du Bonnet granite:

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Numerical and experimental results – Fracture radius (r) evolution

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Fracture evolution – Fracture aperture (w) reduction

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Fracture evolution – Correlation & validation

Validation of the DDFM against experimental records: (Souley et al., [2001])

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Thermo-poroelasticity and Fracturing– Summary

Reflections and Conclusions:

  • 1. Thermo-poroelasticity
  • Constitutive and balance equations
  • Simulations by ABAQUS and Domestic FE code
  • 2. Permeability enhancement
  • Fracturing model (r and w)
  • Anisotropic permeability tensor
  • Validation of the model
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Hydraulic Fracturing (HF)

Definitions:

  • Tensile failure of boreholes

Thermal strain tensor Effect of thermal loading on HF:

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Hydraulic Fracturing – Borehole stability (tensile failure)

Continuum approaches for HF:

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Hydraulic Fracturing – Borehole stability (shear failure)

Borehole shear failure criteria

  • Stress concentration at the borehole wall
  • Analytical stress expressions at the borehole wall
  • Two most observed stress states corresponding to shear borehole failure
  • Mohr-Coulomb failure criterion:
  • Two expressions for minimum borehole pressure

at shear failure Shear borehole failure is not likely to happen during HF.

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Hydraulic Fracturing – Fracture mechanics

From continuum mechanics to fracture mechanics: Fracturing criterion (DDFM) Fracture radius (r) and aperture (w) Permeability tensor Thermo-poroelasticity

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Hydraulic Fracturing – Fracturing model

Hydraulic Fracturing Model (HFM) Only mode I of fracture evolution Starting from the DDFM: Parameterization of the model so that fractures propagate at

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Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by ABAQUS and FE domestic code
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat - Stabilization
  • Conclusion
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Hydraulic Fracturing – Circulation tests

Stimulation tests of Soultz–Sous–Forêts HDR reservoir: Phase 1 injection test at GPK1

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Circulation tests – Flow logging 1993 – Injected flow

Applied flow at GPK1: Strategy of the simulations:

  • Scheme 1
  • Scheme 2
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Circulation tests – Flow logging 1993 - Correlations

Conclusions:

  • 1. Asymptotic plateau for turbulent flow
  • 2. More effective HF for impermeable boundaries
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Circulation tests – Permeability enhancement

Phase 1 injection test at GPK1 1993: Modeling

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Permeability enhancement – Simulations

Without HF With HF Fluid velocity vectors at year 1 Seismic record (Bruel, [1995])

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Simulations – Temperature and pressure

Without HF With HF At year 5

(Lee and Ghassemi, [2011])

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Simulations – Longitudinal stress

Wiggles due to heat convection: DCM and SGS (AbuAisha thesis, [2014], ch. 6) Without HF with HF At year 5

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Simulations – Injection schedule

Without HF With HF Non-linear relation in injection logging with HF Termination of HF at injection pressure of 35.9 MPa Injection rate of 20 l/s at injection pressure of 39 MPa At injection well GPK1 (Bruel, [1995])

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Simulations – Impedance and efficiency

Without HF With HF Efficiency enhanced by about 50% (Murphy et al., [1995]) Designer point of view

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Simulations – Impedance and efficiency

Efficient fluid with HF is 4.922 Million Efficient fluid without HF is 5.364 Million

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Permeability enhancement – Summary

Reflections and Conclusions:

  • 1. HFM for mode I of fracture evolution
  • Validated against field data
  • Used in doing the stimulation of Soultz–Sous–Forêts HDR reservoir
  • 2. HF increased the efficiency of the reservoir by 50%
  • 3. 7% to 8% of the produced efficient fluid is lost over the effective age of the reservoir
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Permeability enhancement – Viscosity temperature change

Brine used: Models of (Francke and Thorade, [2010]) Brine of NaCl (22.5% concentration) at pressure range of 0.01 to 50 MPa Phase 1 injection test at GPK1 1993: Simulations with viscosity-temperature change Without HF

155 °C 50 °C 4 times viscosity increase

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No viscosity change With HF Termination of HF after 5 years with viscosity change HF counteracts the hindrance due to viscosity increase At injection well GPK1 With viscosity change

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Viscosity temperature change – Impedance and efficiency

No viscosity change With HF With viscosity change Longer but inefficient longevity of the reservoir

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Hydraulic Fracturing – Permeability enhancement HFM2

Hydraulic Fracturing Model (HFM2) Modes I and II of fracture propagation Shear slippage of inclined fractures

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Permeability enhancement HFM2 – Permeability history at GPK1

Phase 1 injection test at GPK1 1993: Stimulations using HFM2 at the injection well GPK1 Stabler growth of fractures

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Permeability enhancement HFM2 – Permeability contours

Longitudinal permeability contours HF while accounting for modes I & II At year 1 At year 2

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Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by ABAQUS and FE domestic code
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat – Stabilization
  • Conclusion
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Convection of heat – Definition

Fluid velocity multiplied by the gradient of its temperature: Solving the equation of balance of energy with dominant convection of heat – Difficulties Heat waves striking suddenly stiff boundaries: Bubnov-Galerkin methods are not efficient – Alternatives:

  • 1. Subgrid Scale (SGS) method
  • 2. Streamline-Upwind Petrov-Galerkin (SUPG) method
  • 3. The Discontinuity Capturing Method (DCM)
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Convection of heat – SGS Method

Application of the SUPG method is inefficient at small time steps and when activating HF. SGS: The transient term of a transient diffusion problem can be transformed into a reaction term by first discretizing in time instead of the conventional method of first discretizing in space.

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SGS Method - Simulations

Stabilization at early and intermediate time intervals:

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DCM- Simulations

Stabilization at late time intervals:

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Overview of the research:

  • Thermo-poroelasticity
  • Mathematics
  • Simulations by ABAQUS and FE domestic code
  • Fracture evolution and permeability enhancement
  • Fracturing criterion:

 Evolution of fracture radius  Fracture aperture change

  • Anisotropic permeability tensor
  • FE simulations of Hydraulic Fracturing (HF)
  • Circulation tests without and with considering HF
  • Designing HDR reservoirs: Impedance, efficiency and life-time
  • Convection of heat – Stabilization
  • Conclusion
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Conclusion

Building a frame work capable of describing permeability enhancement in a THM framework with:

  • fully integrated mechanical ingredients to describe HF (HFM and HFM2),
  • a computational aspect to implement HF models and thermo-poroelasticity
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Reflections and perspectives

  • 1. Investigating large and small scale heterogeneities of geothermal systems
  • 2. Fracture slippage and permeability reduction under compressive stresses
  • 3. Experimental laboratory tests
  • 4. Impact of temperature change on the viscosity of Non-Newtonian fluids
  • 5. Non-Darcian flow to describe inertial effects due to high fluid velocities
  • 6. Chemical enhancement of EGS
  • 8. CO2-based EGS
  • 7. HF in a dual-porosity thermo-poroelastic framework
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