From equations (3-3) and (3-16), it was seen in a single layer that the two-
dimensional horizontal geometry of injected water varied as a function of natural gradient
and the injection/recovery flow rates. Therefore, the radial extent of the cylindrical
volume of injected water for the ith layer is Ci and is equal to:
1 1
C, 4 ~Q11At 2 AQ, At 2 (3-35)
Li -)- (3-35)
And in using the definition ofyi, will have:
1
C, 2 (3-36)
Similarly, equation (3-16) converts to:
i
A, =-- (3-37)
The horizontal displacement B during time At for each layer is a function of
constant hydraulic gradient and layer specific hydraulic conductivity; thus,
K d(o At
B, ds (3-38)
Therefore, Cm, the concentration of the target solute in water recovered from each
layer can be estimated. The total concentration of target solute is the summation of flow-
weighted concentrations from all layers:
NL
CRtotalQR CR, QR (3-39)
1
From equation (3-29) and (3-30) and (3-39) the following is obtained: