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Transcript
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
1
Sommaire
PresentatIon
Introduction
Flow Model
Limit compositional model
Streamline HT-splitting
Validation to the limit thermodynamic model
2
Introduction
Physical description
3
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
4
accompanied with radionuclides
Fluid structure
Phases :
Components :
Gas
Liquid
H2
CO2
N2
O2
H20
…
2 phases
Gas
Liquid
5
Similar phenomena in an underground H2 storage
Well
Hydrogen storage
Well
GAS and LIQUID
H20 + H2 + CO2 + CH4 + …
6
Phase behaviour
Critical point
L
Initial state
G
L+G
7
Flow Model
8
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
9
Limit contrast
compositional model
10
Canonical dimensionless form
of the compositional model
gas flow
liquid flow
transport of basic
chemical components
11
Mathematical type of the system
Parabolic equation
Hyperbolic equation
12
Characteristic parameters of
a gas-liquid system
gas flow
liquid flow
transport of basic
chemical components
13
Characteristic parameters of the system
Perturbation parameter:
Perturbation propagation time
Reservoir depletion time
Parameter of relative phase mobility:
14
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
15
Streamline HT-splitting
16
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
17
HT-splitting
Hydrodynamic subsystem (limit hydrodynamic model):
Thermodynamic subsystem (limit thermodynamic model):
18
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
19
Thermodynamic “Delta-law”
Due to the monovariance, the thermodynalmic differential equations may be simplified to a “Delta-law”:
“Delta-law”
20
Interpretation of the delta-law
Individual gas volume
Individual condensate volume
21
Split Hydrodynamic Model
gas
flow
liquid
flow
22
Validation to the limit thermodynamic model
23
Validation of the Delta-law
F1
F2
These functions have been calculated using Eclipse simulation
data for a dynamic system
24
Flow simulation: Fluid properties
Phase plot
P
Initial conditions:
P0 = 315 bar
T = 363 K
Fluid composition
CH4
H2
C10H22
T
25
Flow simulation: Flow problem
Well
26
Validation of the Delta-law
“Delta-law”
F1
F2
These functions have been calculated using the Eclipse simulation data
27
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
28
Finita
29