development of numerical simulation capabilities for in ... · volume (cv) • stress ... sandra...

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