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Presented at the 32nd Oil Shale Symposium, October 15-17, 2012, Colorado School of Mines, Golden, CO, USA.
Sharad Kelkar, Rajesh Pawar Los Alamos National Laboratory
Nazish Hoda, Chen Fang
ExxonMobil Upstream Research Company
Development of Numerical Simulation Capabilities for In Situ Heating of Oil Shale
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Full physics modeling of in situ heating processes is challenging
Mimicking in situ heating processes requires coupled thermal, mechanical, chemical, and multiphase flow modeling
Heating Element
Heat transport
Pyrolysis
Creation of flow pathways by fluid generation
Migration of generated fluids
Toe Connector Well
Production Wells Process Heater Wells
Electrically Conductive Material Conductive Heating and
Oil Shale Conversion
3
Each aspect of oil shale simulation physics is complex in its own right
• Thermal modeling
• Chemical modeling
• Mechanical modeling
• Multiphase flow
QTTCtTC
pp +∇⋅∇=∇+∂
∂)()(.
)(κU
)exp(,1 RT
EAfcfria
ii
N
jiiiij −== ∏
=
γ
T∇+⋅==+⋅∇ ασCε Fσ ,0
g) - ρµ
Pk
i
rii ∇⋅−= (Kq
4
Oil shale simulator’s feature list is extensive owing to complex properties of oil shale
Bedding plane
Transversely isotropic thermal and mechanical properties
Thermal and mechanical properties depend on temperature
Strong flow-mechanics coupling required to capture porosity/permeability creation during pyrolysis and by rock failure
Typically, rock is non-porous and impermeable
Fractures
Pyrolysis
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LANL’s FEHM simulator is an ideal spring board for oil shale simulator development
• FEHM: Finite Element Heat and Mass • Has the coupled thermal-flow-mechanics simulation
capability applicable to elastic response
• Control volume-finite element (CVFE) approximation: • Control volume for mass/energy balance • Finite element for stress
• FEHM has been verified through extensive applications:
• Groundwater modeling
• Contaminant transport and reactions
• Methane hydrate reservoir production • CO2 sequestration
• Geothermal
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Developing new thermal-hydrological-mechanical-chemical (THMC) modeling capabilities in FEHM • Thermal:
• Anisotropic, temperature-dependent thermal properties
• Hydrological (multiphase flow): • Black oil model: accounts for water boiling
• EOS based properties
• Mechanical: • Anisotropic, temperature-dependent mechanical and
fracturing properties
• Plastic/elastic deformation models
• Stress-dependent changes in porosity and permeability
• Chemical: • Kerogen conversion into oil/gas/coke and subsequent
reactions
• User-specified stoichiometry and kinetics
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Problem description: • Heater
• Q: 4 kW • Parabolic heat distribution
• No heat flux condition • Temperature dependent thermal and
mechanical properties • No pyrolysis
He
ate
r
328’
OB 450’
UB: 450’
Mahagony: 100’
Benchmarked new temperature dependent thermal and mechanical property variation capabilities against Abaqus
Thermal properties Mechanical properties
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FEHM and Abaqus results compare well!!
• Results compare well • Thermal softening of rock impacts
stress evolution in the heated zone
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Problem description: • Heater: Q = 0.7 kW • Permeability, K = 10 mD • Porosity, φ = 0.3 • Sw = 0.1, SKerogen = 0.9 • PInitial = PBHP = 0.1 Mpa • Rxn:
Kerogen ⇒ Oil + Gas + Coke Oil ⇒ Gas + Coke
He
ate
r
10 m
1 m
X
Y
Z
Producer
Benchmarked FEHM’s new multiphase flow and kerogen conversion capabilities against CMG’s STARS
90 days
Presence of water impacts thermal conduction and, as a consequence, conversion extent
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Implicit-coupling required to model steep changes in rock properties and time- scale separation
• Physical phenomena take place at very different time-scales • Kerogen conversion and permeability/porosity enhancement: on the
order of hours • Time scale of flow: on the order of days
• Steep changes in material properties with time • Mechanical properties (Young’s modulus and thermal expansivity)
show nonlinear temperature dependence.
• Enhancement in permeability takes place at a very small time scale
• Large variations in fluid pressure, temperature, saturations, and stresses
• With explicit coupling, very small time step needed to model steep changes; impractical for commercial scale simulation.
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Derivative of mass flux term with respect to displacements
Implicit-coupling: Formulation
• Thermal and multiphase flow problem solved on a control volume (CV)
• Stress calculations done on a finite element mesh
• Mapping between CV node and finite element node
k
eij
ijijijijij
k
ij
uFPPlAK
uq
∂
∂−⋅⋅⋅=
∂
∂ −
)()/(µρ
γ
∑ ∑−
−
−
⋅⋅∂
∂=
∂
∂
ijelements gpe
eij
eijk
ij
IBDJVe
FNu
F ||1.1σ
Kij: Absolute permeability γij: Relative permeability Fij: Effective permeability P: Pressure uk: Displacement σe: Average stress tensor Ve: volume of element Aij/lij: ratio of area to length J: Jacobian ρ/µ: Ratio of density to viscosity D, B, I: stress-strain, strain-displacement,
and identity matrices
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Implicit-coupling shows significant computational advantages over explicit-coupling
Permeability generation because of pore pressure build-up
• Implicitly-coupled model needs only 12 Newton-Raphson iterations compared to 42 needed by explicitly coupled simulator.
• Explicit method does not converge for time step > 2x10-3 days, however, implicit is stable for time steps beyond 1 day
Problem description: • 5 DOF per node: displacements, temperature, and pressure • Initial Permeability = 1 µD, • Porosity = 0.2 • Young’s modulus = 10 GPa • Poisson’s ratio: 0.25 • Water injection rate: 0.04 kg/s • Temperature: 250C • Fluid Compressibility = 100 x water
Water Injection
Fixed P
Pore Pressure
Perm
eabi
lity
Fact
or
1000
1
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New THMC modeling capabilities in FEHM enable comprehensive modeling of in situ conversion processes
Ø New thermal-hydrological-mechanical-chemical (THMC) capabilities have been developed in FEHM to numerically simulate in situ conversion processes
Ø Some THMC modeling capabilities extensively benchmarked against CMG’s STARS and Abaqus
Ø Implicit-coupling between flow and mechanics critical to model steep changes in properties, especially for commercial scale simulations.
Ø Future developments include: - Extend the implicitly coupled code to multiphase flow accounting for
kerogen conversion - Extend implicitly-coupled code to account for plastic deformation
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Acknowledgments
This work was conducted under the collaborative research and development agreement between LANL and ExxonMobil URC The implicit-coupling capability developed in FEHM was funded through US DOE’s Carbon Sequestration Program ExxonMobil Oil Shale Team: Sandra Hopko, Michele Thomas, William Symington, Michael Lin,
and Pengbo Lu LANL Oil Shale Team: Chris Bradley, Doran Greening