transformed hydraulic conductivities that were then used to simulate water quality
changes in recovered water from an ASR well located in stratified aquifer:
F(x) 0.5 1+ 1- exp 2xom 2j_ (3-50)
Lo.
Fn, X
-3 -2 -1 0 1 2 3 4 5 6 7
Figure 3-12. Cumulative probability function, F(xo), for N: (2, 2).
Figure 3-12 shows the cumulative probability function, F(xo), for N: (2, 2). To
generate a suite of hydraulic conductivities that are then used to characterize a uniformly
layered aquifer, it is necessary that the conductivity assigned to each layer reflect a
fraction of aquifer thickness that honors the assumed underlying log-normal conductivity
distribution; hence, equation (3-50) is first rearranged to give xo:
x0 =m' +cr'-0.57zLn( -(2F(xo)-1)2) (3-51)
Next, F(xo) is incrementally increased by AF(xo) from 0 and 1, where the value of
AF(xo) is equal to fraction of total aquifer thickness represented by a single layer. From
each value F(xo) a unique conductivity value ofx, is estimated from equation (3-51). The
resultant hypothetical aquifer will then have a lognormal distribution of conductivities
with the mean conductivity of m and standard deviation of -.