Fuller, Kathleen听1听;听Neupauer, Roseanna M.听2听;听Mays, David C.听3
1听Department of Civil Engineering, University of Colorado Boulder
2听Department of Civil Engineering, University of Colorado Boulder
3听Department of Civil Engineering, University of Colorado Denver
Contaminated groundwater remediation may be conducted by injecting a treatment solution into the area of concern, where it reacts with the pollutant. This reaction relies on contact at the interface between the treatment solution and the contaminant, which can be increased while retaining the contamination within a manageable area, by stretching and folding the materials together. To do so, water is injected or extracted from several wells, in a strategic pumping scheme. For this preliminary study, pumping schemes were limited to a number of constraints: two wells were used, though only one well was actively pumping water at any time, six equal time steps were used, pumping rates were limited to either one unit of injection or of extraction 鈥� although the final rate might have been higher to maintain a net extraction of zero, and the contaminant was not permitted to enter the active wells.
To find the optimal pumping scheme, resulting in the maximum interface length, a genetic algorithm was utilized, which is based upon the biological concept of 鈥渟urvival of the fittest鈥�. The most desirable members of a population have their genetic qualities passed onto the next generation. In this case, a population consisted of a number of feasible pumping scenarios and the fitness of each was the cumulative interface length during its performance. The genetic traits consisted of a choice of an active well and a selected pumping rate for each time step in the scheme. The offspring for the next generation were produced from existing members of the population either through exact replication, mutation of certain genes, or crossover with another member.
All possible pumping schemes were generated and the fitness of each was calculated. Penalties were deducted from the fitness value if any of the restrictions were violated. The optimal scenario, which produced the greatest interface was isolated and is shown in Figure 1.
The other schemes formed a set from which the initial population was randomly selected, then run through the genetic algorithm, which was implemented using the Optimizer Toolbox in MATLAB, to determine if it would find the ideal solution. As the Optimizer Toolbox will only minimize the fitness, the negative sum of the interface lengths during the pumping scheme in question was used as the fitness value. As shown in Figure 2, the genetic algorithm was able reach the optimal solution in six generations, although it did not do so consistently during other trials.