limitations, and guidance is offered for appropriate use of the algorithm.
The primary postulate of this algorithm is that the rela- tionship between concentration and head difference con-
straints is unique and reliable. This assumption forms the basis for the updating method described in eqn 18. The use
of this assumption has two subsidiary assumptions. First, it is assumed that changing a head difference constraint does
not significantly affect those concentration values that are not associated with that head difference constraint. That is,
only a single gradient affects each concentration. Second, all concentrations that are affected by a given head differ-
ence constraint are affected in a consistent manner—for example, the concentrations increase or decrease together.
The validity and significance of these two assumptions are discussed in the examples below.
6.1 Influence of multiple head difference constraints on a single concentration
Intuitively, the assumption that a single concentration is only affected by a single head difference constraint might
be violated in circumstances where concentration at a single location is affected by pumping at several wells. Hence, one
might expect that significant competition effects might cause failure of the algorithm. While no proof can be offered
that this will never be a problem, our experience indicates that this will not be the problem that might be imagined.
For example, consider the problem depicted in Fig. 6. The problem set-up is such that the concentrations at locations g,
h, i, j, k, and l should be significantly impacted by pumping at wells 2 and 3. However, these concentrations are linked to
gradients I and II which are closely associated with well 1. Despite this apparent potential for interaction, a solution is
achieved after 53 iterations as depicted in Fig. 6b and 6c. That interference is occurring can be seen from examination
of Table 3 which shows the gradients and pumping rates associated with wells 1 and 3 along with the concentrations
at location h over the first five iterations. At iteration 3, gradient I is driven to a value of 0.8109. This increase in
gradient produces an increase in pumping at well 1 and a decrease in concentration at h. Having overshot the desired
decrease the concentration is now below the standard, the algorithm reduces gradient I at iteration 4 to get an increase
in concentration at h to just meet the standard. However, at the same iteration gradient III has increased causing well 3
to increase its pumping. This causes a further reduction in pumping due to the interference between pumping at well 3
and concentration at h. After one additional iteration, 5, the gradient increases again at I seeking to increase the concen-
tration. The new hydro-chemical regime produced by large pumping at 3 responds and the concentration increases.
Because the algorithm only utilizes information from the past step, it is able to recover from a change in the type of
response that is encountered at the concentration response point.
6.2 Multiple concentrations influencing a single head difference constraint
