Hatfield et al. (2004) developed an alternate method where by non-linear tracer
elution functions may be used to calculate water flow, by super-imposing a linear
function over segments of the non-linear elution function. In this way, the elution may be
described by different linear equations for different ranges of relative mass remaining
(Figure 2-3). Using this technique, a new Rt may be calculated for each linear segment
of the elution curve
1
R, = (2-6)
,=1 Rdi
Here, i (i=1, 2,..., p) denotes each segment of the linear approximation, (, (P,
represents the mass fraction eluted according to the linear segment and Rd, is the
retardation factor for i (i=1, 2,..., p). These parameters are all determined directly from
the plot of the linearized pieces, where Rd, is obtained from the terminating abscissa of
segment i and pi is the intercept of segment i on the y-axis (Hatfield et al., 2004). The Rt
values calculated in Eq. (2-6) may then used in Eq. (2-5) for the appropriate M,.
G(T)
0 1-
02---
04 -
0 Rdl Su Rd3
Figure 2-3: Linearized segments fit to a general non-linear elution curve. Here, three
linear segments have been fit to the non-linear elution function G(r) where p,
and Rd, define each segment [Reprinted from Hatfield et al. 2004].