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 gas

Injected 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

t

Su

t

S

Initial condition:

S

z

Segregation model

0

( )

1'( )

rw rg g

rg g rw w

c

c

k kf S

k k

dPJ S

P dS

0( ,0) ( )

(0, ) ( )

S x S x

S t t

( ) ( ) 1w

SW 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()( SBSASJ

J(S)

( ) ( ) 1w

SW 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

21

div div COr D

CU C U C w

t

anorCCkCw 21

00

tC

inj

rCC

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 e

Dzt 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).