Laboratoire d'Énergétique et de Mécanique Théorique et Appliquée
Ecole Nationale Supérieure de Géologie
Institut National Polytechnique de Lorraine
STREAMLINE SPLITTING THE THERMO- AND HYDRODYNAMICS
IN COMPOSITIONAL FLOW THROUGH POROUS MEDIA
APPLICATION TO H2-WATER IN RADIOACTIVE WASTE DEPOSITS
S. OLADYSHKIN, M. PANFILOV
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Sommaire
PresentatIon
Introduction
Flow Model
Limit compositional model
Streamline HT-splitting
Validation to the limit thermodynamic model
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Introduction
Physical description
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Hydrogen generation in a radioactive waste deposit
Gas generation:
H2 + CO2 + N2 + O2 + …
Storage pressure growth :
Corrosion in storage tank
- Initial :
100 bar
- Increased by H2 : 300 bar
Water
Monitoring problem :
H2 transport through porous media
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accompanied with radionuclides
Fluid structure
Phases :
Components :
Gas
Liquid
H2
CO2
N2
O2
H20
…
2 phases
Gas
Liquid
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Similar phenomena in an underground H2 storage
Well
Hydrogen storage
Well
GAS and LIQUID
H20 + H2 + CO2 + CH4 + …
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Phase behaviour
Critical point
L
Initial state
G
L+G
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Flow Model
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Compositional model
2 phases (gas & liquid)
N chemical components
Mass balance for each chemical component k :
Momentum balance for each phase (the Darcy law)
Phase equilibrium :
( = the chemical potential)
or
Phase state :
Closure relationships:
or
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Limit contrast
compositional model
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Canonical dimensionless form
of the compositional model
gas flow
liquid flow
transport of basic
chemical components
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Mathematical type of the system
Parabolic equation
Hyperbolic equation
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Characteristic parameters of
a gas-liquid system
gas flow
liquid flow
transport of basic
chemical components
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Characteristic parameters of the system
Perturbation parameter:
Perturbation propagation time
Reservoir depletion time
Parameter of relative phase mobility:
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Limit behaviour
gas flow
liquid flow
transport of basic
chemical components
Semi-stationarity :
p and C(k) are steady-state, while s is non stationary
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Streamline HT-splitting
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Integration of the transport subsystem
Asymptotic contrast compositional model :
gas flow
liquid flow
transport of basic
chemical components
This subsystem can be integrated along streamlines :
A differential thermodynamic system
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HT-splitting
Hydrodynamic subsystem (limit hydrodynamic model):
Thermodynamic subsystem (limit thermodynamic model):
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Split Thermodynamic Model
variation of the total composition
in an open system
Properties
The thermodynamic independent system is monovariant:
all the thermodynamic variables depend on pressure only
The new thermodynamic model is valid along streamlines
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Thermodynamic “Delta-law”
Due to the monovariance, the thermodynalmic differential equations may be simplified to a “Delta-law”:
“Delta-law”
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Interpretation of the delta-law
Individual gas volume
Individual condensate volume
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Split Hydrodynamic Model
gas
flow
liquid
flow
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Validation to the limit thermodynamic model
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Validation of the Delta-law
F1
F2
These functions have been calculated using Eclipse simulation
data for a dynamic system
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Flow simulation: Fluid properties
Phase plot
P
Initial conditions:
P0 = 315 bar
T = 363 K
Fluid composition
CH4
H2
C10H22
T
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Flow simulation: Flow problem
Well
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Validation of the Delta-law
“Delta-law”
F1
F2
These functions have been calculated using the Eclipse simulation data
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Validation of the total limit thermodynamic model
Composition variation in an open thermodynamic system
Liquid mole fractions
Gas mole fractions
Compositional Model (Eclipse) - points; Limit thermodynamic model - solid curves
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Finita
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