Atwood, D and S. Gorelick (1985). “Hydraulic Gradient Control for Groundwater Contaminant Removal”, Journal of Hydrology. 76(1-2), pp. 85-106.

Summary:

The paper covers a research project using linear programming in order to determine the optimal techniques from removing polluted groundwater from the aquifer below Rocky Mountain Arsenal near Denver. The researchers determined that contaminant removal would be accomplished by pumping the contaminated water from the aquifer. In order to keep the contaminated plume in place, the researchers decided to use wells surrounding the contaminated plume to either pump of inject water to ensure that the hydraulic gradient would keep the plume from spreading.

The researchers first selected the best of four possible locations for the well that would actually pump the contaminated water by trial and error, assuming that that well would pump at a certain constant rate. Then, the researchers developed a linear program to determine how much water should be pumped or injected from each of the surrounding wells. The objective function used was to minimize the total amount of pumping and injecting done by adjusting pumping/injecting rates at the surrounding wells. Constraints were that the central well should pump at a certain, constant velocity while the pumping and injection pattern of the surrounding wells should result in an inward pointing gradient.

The researchers looked into two optimization techniques: global optimization, in which they calculate the optimal pumping/recharge schedule by solving just one run of their optimization schedule, and sequential optimization, in which they divided the toxin removal into 32 pumping periods and calculated the best pumping/injection for each well for each period.

The research resulted in the optimal solution of pumping and injection being selected. The paper states that global optimization resulted in a “different and better solution than the sequential strategy.” They state that this is because the global strategy is capable of looking ahead into the long term.

Discussion:

This paper seems significant since it is about using linear programming (which we have been studying lately in CVEN665) to solve a realistic problem. I found this paper interesting since the researchers were using things which we have been studying in CVEN 665 (linear programming) and applying them to real life problems (groundwater contamination). Although the problem being solved is quite complicated, I was able to understand theoretically what the researchers were attempting, which is helpful when learning the best ways of applying a theoretical concept such as linear programming to an actual problem.

Although not a fault, I found that the fact this paper is from 1984 could limit its practical applications in modern engineering. Many of the assumptions and formulations used were selected and justified by the intentions of making calculations easier. The authors actually discussed computation times and the computers being used several times, which, while providing insight into some of their choices may not be useful to the modern engineer. Furthermore, near the end of the paper, the authors state that the global solution is better than the sequential solutions, but technological limitations prevent them from exploring this in any depth. I think this would be a logical next step—attempting to create some sort of hybrid global-sequential strategy to further optimize the solution.

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Andrew,

ReplyDeleteWhat an honor it is to post commentary on the blog of a modern day renaissance thousandaire. I enjoyed your perspective on this article. I too found that the authors did an excellent job of applying a theoretical concept to a practical problem. Although the problem in question was complex, their application of theory made it much easier to understand.

I hadn't given much thought to the age of this article, but I agree with your reasoning. There are probably ways of solving this problem today with which the modern engineer should have familiarity. Nevertheless, I admire the creativity of the authors' approach, since limitations in computational power often force your methodology to be more unique and efficient.

I'd like to hear more about this hybrid approach you speak of...

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