their positions over successive time intervals leads to an assessment of the position of the
front at any time. In this development, the position of point P is followed where this point
is situated on the boundary between the injected water and the ambient groundwater.
After time At and under natural gradient conditions, it is assumed that the
cylindrical volume of the stored water is displaced down gradient a distance Bi from the
ASR well. The position of the injected bubble at this time is shown in Figure 3-2.
Direction of Regional B P
Groundwater Flow
ri= ri"'- __-(-0ii)
Oi. .i2
Figure 3-2. Plan view of the injected water after time At and after movement.
The displacement distance Bi is estimated from equation (3-4):
B = qAt (3-4)
The relation between parameters of Figure 3-2 can be written as:
ri,'= ri2 + B2 2rilB, cos(r 0/) (3-5)
or:
ri1'= ri + B2 + 2riB cos 01 (3-6)
where Oil is specified and ril is obtained from equation (3-3). In addition, there is:
sin0, sin(- 0i,)
(3-7)
B, ri'