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(a)
(b)
Fig. 2.15
Dynamics of moving carbonatite melt (a) and of CO
2
fluxes (b) in a subducting slab. Four processes are
considered. ''Subduction'' implies CO
2
delivery by subducting slab (in the uppermost 500m layer) and rate of
resulting carbonatite melt production in the transition zone. ''Porous flow'' denotes the rate of melt segregation in
the partially molten layer across the solidus of carbonated rock. ''Infiltration'' gives the rate and flux of
impregnation of ''dry'' overlying mantle by carbonatite melt segregated at the slab-mantle interface. ''Diapir''
denotes the rate and maximum flux of carbonatite melt upon ascent of a diapir with 1 km radius.
counterflux of solid through the melt must exist
(see Figure 2.3 in (Hammouda & Laporte, 2000)).
The rate of melt infiltration can be expressed
from characteristic diffusion distance (
x
) (Crank,
1975) as:
subducting slab (Staudigel
et al
., 1989; Hayes &
Waldbauer, 2006; Dasgupta & Hirschmann, 2010)
(Figure 2.15b). The actual
f
CO
2
Inf
is even smaller, be-
cause the melt fraction decreases rapidly with in-
creasing penetration distance. Furthermore,
f
CO
2
Inf
diminishes rapidly with time as the surrounding
gets saturated by carbonatite melt (Figure 2.15b).
Buoyant ascent of the melt diapir is possible if
the viscosity of the country rocks is low enough
(Fyfe, 1973). For a sphere moving under gravity in
a viscous medium, the velocity (
v
) of the sphere
is given by:
v
Inf
=
dx
/
dt
=
4
D
/
t
.
(2.4)
Silicate diffusivity (
D
) in carbonatite melt was
estimated to be 2
10
-
9
m
2
/s at the PT con-
ditions of the mantle transition zone (Shatskiy
et al
., 2013). Overall CO
2
flux associated with
the melt infiltration into surrounding mantle can
be expressed as:
×
2
gr
2
(
v
Diapir
=
ρ
S
−
ρ
L
)
/
(9
η
Dry
_
mantle
),
(2.6)
f
CO
2
Inf
C
CO
2
Melt
=
v
Inf
·
W
·
x
·
ρ
Melt
·
ϕ
E
·
/
100%,
(2.5)
where
g
is the gravitational acceleration,
r
is the
radius of the sphere,
ρ
S
−
ρ
L
is the density con-
trast between the sphere and the medium and
η
Dry
_
mantle
is the viscosity of the medium. Assum-
ing a mantle viscosity of 3
where
x
0.06 m/year is the average subduct-
ing rate (van Keken
et al
., 2011),
∼
0.2 is the
equilibrium (maximum) carbonatite melt volume
fraction in the silicate mantle near the interface
with the melt chamber (Hammouda & Laporte,
2000),
C
CO
2
Melt
ϕ
E
=
10
21
Pa
s (Forte
et al
.,
1991) the ascent rate of a sphere with
r
×
·
1km
will be negligibly slow, i.e. on the order of 10
-
5
m/year. In addition, the carbonatite melt cham-
ber must be surrounded by a low-viscosity silicate
layer enriched in carbonatite melt (Figure 2.15c).
Low viscosity of this layer would be due to the
specific deformation regime. Dislocation creep
=
33 wt % is the CO
2
content in the
melt (Shatskiy
et al
., 2013). According to our es-
timations using Eq. 5, the maximum initial CO
2
flux into pristine surrounding mantle is about
2
∼
10
11
g/year, which is three orders of magni-
tude lower than the annual CO
2
supply from the
×
