Hydrodynamic analysis of spreading regimes and multi-component gas diffusion in the underground storage of radioactive wastes I.Panfilova, A.Pereira, S.C.Yusuf, O.Heidarov (LEMT A.Burnol, P.Audigan, M.Parmentier (BRGM)
Feb 11, 2016
Hydrodynamic analysis of spreading regimes
and multi-component gas diffusion in the underground storage of
radioactive wastes
I.Panfilova, A.Pereira, S.C.Yusuf, O.Heidarov (LEMTA)
A.Burnol, P.Audigan, M.Parmentier (BRGM)
ProblematicsGas mixture, composed by H2, N2, CO2, O2, SO2, etc., is accumulated in alveoli and begins to migrate in all directions caused by the segregation, dissolution and diffusion.
Storage cell of type B
ProblematicsUndercritical CO2:two-phase vertical raising
Overcritical CO2:Singler-phase horizontal spreading
ProblematicsUndercritical CO2:two-phase vertical raising
Overcritical CO2:Singler-phase horizontal spreading
Does it can be stopped ?
Does it can be stopped ?
Migration of gasInjected gas bubble can migrate along the limited distance and be trapped for the long-term security of storage by
-structural trapping-residual gas trapping -dissolution in water-capillary forces-reactivity
The combination of these effects prevents the gas migrating more than a few kilometers from the injection site before it is fully blocked in the cap rocks.
CO2 Storage ModelsVan der Meer : CO2 storage in saline aquifers.
The dissolution rates is determined by gravity segregation and viscous displacement.
Holt et al.: reservoir simulation to investigate the storage capacity defined as CO2 dissolved in formation brine.
Law and Bachu showed that a similar fraction of CO2 may dissolve into the brine and travel within the slow hydrodynamic system in the aquifer
Pruess et al.: CO2 storage in saline aquifers. The long-term total storage capacity could be on the order of 30 kg/m3 of aquifer volume for all trapping mechanisms.
Kochina et al and Barenblatt studied analytically the capillary trapping effects.
Undercritical CO2: Vertical gas raising
Mathematical model of gas raising
)(Sppp cwg
)()(
)()(
gpKSk
u
gpKSk
u
www
rww
ggg
rgg
For each fluid phase, Darcy’s law:
Two-phase mass balance:
0)()(0)())1((
www
ggg u
tSu
tS
Initial condition:
S
z
Segregation model
0
( )
1'( )
rw rg g
rg g rw w
c
c
k kf S
k k
dPJ SP dS
0( ,0) ( )(0, ) ( )
S x S xS t t
( ) ( ) 1wSW f s J S
Reduction to:0wWS
capillarity gravity
Analytical solution: diagrammatic technique
Fractional flow Welge tangent
Evaluation in time of multiple fronts
Dynamics of bubble raising
Axe vertical
Bubble streatching
The back velocity << The forward velocity
Therefore, the bubble stretches until it reaches uniform residual gas saturation :
Very different from raising in bulk water
Dynamics of bubble raising
Axe vertical
Raising with capillary pressure
221
1
** )1()1()( SBSASJJ(S)
( ) ( ) 1wSW f s J S
0wWS
Raising with Pc, Sres=0
Axe vertical
Overcritical CO2: Horizontal reactive spreading
Physical formulation- Single-phase liquid.
- 2 chemical components: CO2 et H2O.
-The solid is immobile and non deformable.
- Fluid flow is radial. - Both components of liquid are reactive (the reaction with the solid):
2 2 8CaAl Si O 2 2 5 4( )Al Si O OH
CO2 + 2H2O + anorthite = kaolinite + CaCO3
Mathematical model
21div div CO
r DC U C U C wt
anorCCkCw 21
00
tC
injr
CC 0
0r
C
anor
t
anor CC 00
C = CO2 molar concentration
CO2 + 2H2O + anorthite = kaolinite + CaCO3
Reaction kinetics:
Law of action mass:
Analytical solution
( , ) 12 2
( , ) 1
inj z
inj z inj zt
z W tC z t C eDzt Dz
C z t C e C e
stationary limit
Numerical result
limit of propagation for 10 years
Anorthite concentration
Solid phase saturation
Numerical study of gas spreading
Gocad ECLIPSE
Vertical cross-section. Gas saturation
10 years of gas injection, 90 years without injection (natural gas migration)
After 6 years of rest the gas bubble was stabilized
Vertical cross-section. Water saturation
Aqueous concentration of CO2
Aqueous concentration of CO2
Numerical study of gas spreading
RSW: 500 years after STOP RSW: 1100 years after STOP
RSW: after 10 years of gas injection RSW: 100 years after STOP
Numerical study of gas dissolution
RSW in 4 points in time (1100 years)
Depth
Time
Proposal for 2011 LEMTA:1.Multi-component reactive diffusion-convection with gravity around a cell of radioactive waste. 3 chemical components in liquid: H2O, H2 and CO2 or air.
Model: diffusion fluxes resulting from the non-equilibrium thermodynamics.
Method: the numerical code developed in LEMTA.
2. Macroscopic circulations in a limit volume of gas. Water surrounding the macroscopic gas bubble causes the rotational flow inside it. It may be captured only within the Brinkman model.
BRGM:A literature review is planned to study each of 3 binary systems (CO2-H2O, CO2-H2 et H2O-H2) and calculations initiated with the binary CO2-H2S pursued. The result will be achieved with a Master student (initially planned during the first year of the project).