Geology Reference
In-Depth Information
small activation energy is justified by the observation within
numerical experiments that a larger activation energy would
predict too large a flexural rigidity or too thick an elastic
plate near sea-mounts (Watts and Zhong
2000
). This rheol-
ogy is an obvious simplification, but it allows us to explore
the general behaviour of the upper mantle with a geologi-
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'
Appendix 3: Calculation of R
o
The calculation of R
o
is similar to previous studies based on
the transformation rate of vitrinite (Burnham and Sweeney
1989
; Ungerer
1990
); it is assumed that the vitrinite trans-
formation can be described by a set of N independent
Arrhenius first-order kinetic reactions:
x
i
t
dx
i
dt
¼
E
i
RT
abs
A
i
exp
ðÞ
ð
12
19
Þ
:
dx
i
where
dt
is the rate of the
i
th reaction,
A
i
the Arrhenius
frequency factor (
s
1
),
E
i
the activation energy (kcal/mole),
R the gas constant (0.001987 kcal/mole K),
T
abs
the absolute
temperature and
x
i
the initial hydrocarbon potential for the
i
t
h reaction (mg hydrocarbon/TOC).
x
i
(
t
) can be determined
by integration of the previous equation:
RT
abs
RT
0
abs
0
@
0
@
1
A
1
A
T
2
exp
E
i
T
0
exp
E
i
þ
x
i
t
ðÞ
¼
x
i
tðÞ
1
exp
A
i
R
E
i
T
T
0
tt
0
ð
12
20
Þ
:
We have used a spectrum of 15 reactions (46-74 kJ) to
determine the transformation rate of vitrinite and then an
empirical relationship for the conversion to R
o
. The effect of
pressure, which tends to decrease the R
o
value for a given
heating rate (Carr
1999
), has not been included.
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