NL
CRtotal = CR, (3-40)
Modeling the Distribution of Hydraulic Conductivity in the Aquifer
The geometry of the subsurface plume of injected freshwater is influenced by the
aquifer properties and variation in hydraulic conductivity within the aquifer. In addition,
dispersion and mixing between the injected water and native water are also related to the
distribution of permeability within the storage zone
The dispersivity in a stratified aquifer was discussed by Gelhar (1993) and Dagan
(1994). A very simple description of mixing process in a heterogeneous aquifer can be
developed if we assume that the aquifer exhibits perfect stratification, in the sense that
horizontal hydraulic conductivity varies vertically through the depth of the aquifer
(Gelhar, 1993). The values of hydraulic conductivity can be modeled as a random space
function to account for their spatial variability and usually their logarithm tends to be
normally distributed (Dagan, 1994).
Theory
A lognormal variant such as hydraulic conductivity will have a mean value of m
and standard deviation o and is expressed in brief form as L: (m, a). Similarly a normal
variant (such as log transformed conductivities) will have a mean m' and standard
deviation o' which is expressed by N: (m', '). The lognormal variant is related to the
normal variant by the following equation:
L: (m, )= exp(N : (m',a')) (3-41)
The relationship between means and standard deviations of normal and lognormal
distributions is as follow (David, 1977):
a2 =m2(exp(c'2) 1) (3-42)