The method for determination of hydrate amount is based on Figure 6 and the assumptions of isotopic equilibrium between pore water and hydrate and 100% exclusion of Cl- during formation of hydrate.
First, values for the
concentration of Cl- and 
2H
are assigned to the ascending brine and the transport equations (Appendix A) are
used to generate flow-rate-independent curves (FRI-curves, see "Estimation
of Hydrate Amount" section, this paper) using these values as boundary
conditions (curves labeled 1, 2, and 3 in Fig.
6). The FRI-curves represent all possible combinations of in situ
pore-water Cl- concentrations and 2H
values ([Cl-]pw and 2Hpw)
for the chosen boundary conditions.
Second, a vector V is
constructed that starts from the FRI-curve ([Cl-]pw, 2Hpw)
and projects into the [Cl-]-2H
space with a slope given by
,
(B1)
where 
is the isotope fractionation factor between hydrate and water.
This vector represents the
change in [Cl-] and 2H
that takes place when pore water with an initial composition given by the point
([Cl-]pw, 2Hpw)
on the FRI-curve is diluted by hydrate meltwater. This is justified as follows.
Measured concentrations of
Cl- and 2H
([Cl-]m, 2Hm)
are volumetric averages of pore-water compositions ([Cl-]pw,
2Hpw)
and hydrate meltwater compositions (0, 2HH),
and
(B2)
,
(B3)
where f is the
volume fraction of hydrate meltwater. Because of the assumption of isotopic
equilibrium, 2HH
and 2Hpw
are related through:
.
(B4)
Following the example of Kvenvolden and Kastner (1990) the hydrogen isotope fractionation factor for the hydrate-water system is set equal to the fractionation factor for the ice-water system (1.021, Lehmann and Siegenthaler, 1991).
By evaluating
(B5)
from Equation B2, and
(B6)
from Equations B3 and B4, the slope of the vector may be derived from:
.
(B7)
Third, the starting point of the vector V is moved along the FRI-curve until it intersects a measured pore water or hydrate sample composition (Fig. 6). This step is repeated until each measured point is represented by a vector.
Fourth, the vector V is
decomposed into the vectors v1 and v2 (Fig.
6) which provides an estimate of the amount of hydrate based on the
measured Cl- concentrations and 2H
values respectively.