Page 146 - Physical Principles of Sedimentary Basin Analysis

128 Heat flow

b
a = 0.1, while the parameter b =−10.5 is just the scaling factor 2 .VR(%Ro)is
correlated to TTI by the functional relationship
%Ro = exp (p ln(TTI) + r) (6.105)
where the parameters p and r are calibrated against data sets. Several pairs of p and r
parameters have been reported in the literature, see for instance Waples (1980) and Issler
(1984) and Morrow and Issler (1993).
The TTI based computation of VR has been superseded by procedures based on
Arrhenius kinetics (Burnham and Sweeney, 1989, Sweeney and Burnham, 1990). The vit-
rinite is divided into a series of components where each component has its own reaction
rate. The decay of component i is given by a first-order reaction

dx i
=−k i x i (6.106)
dt
where x i is the amount of the component. An Arrhenius law gives the reaction rate

E i
k i = A i exp − . (6.107)
RT
where A i is the Arrhenius factor and E i is the activation energy. The temperature depends
on time and the reaction rate is therefore also time dependent. Integration of the first-order
equation (6.106) gives that the component i is
t
x i = x i,0 exp − k i (t) dt (6.108)
0
where x i,0 is the initial amount of component i in terms of normalized fractions. These
initial fractions therefore add up to zero, x i,0 = 1. The fractions x i,0 are also referred to
i
as stoichiometric factors, or weight fractions. The amount of each fraction that has reacted
is x i,0 − x i and the total amount that has reacted is the transformation ratio

Tr = (x i,0 − x i ) = 1 − x i (6.109)
i i
which is a number that increases from 0 towards 1 as the reactions go to completion. The
transformation ratio is mapped to VR by the expression
%Ro = exp(c + d Tr). (6.110)

The parameters c and d must be calibrated against data sets together with the parameters
for the Arrhenius kinetics and the initial fractions. The most common parameter set for VR
computations is the one suggested by Sweeney and Burnham (1990), see Table 6.3, which
was one of the earliest models for VR based on Arrhenius kinetics. These parameters have
become a “standard” in the computation of VR since they give a good match against a
large number of data sets, both from sedimentary basins as well as laboratory experiments.
There is also a need for a standard parameter set because it simplifies comparisons of
maturity studies. The VR model using the data set from Sweeney and Burnham (1990)is