Atwood, D and S. Gorelick (1985) “HYDRAULIC-GRADIENT CONTROL FOR GROUNDWATER CONTAMINANT REMOVAL”, Journal of Hydrology, 76(1-2), pp. 85-106
The authors propose to use linear programming to optimize the containment of a contamination plume in groundwater. The Rocky Mountain Arsenal was selected as the location for the case study due to its frequent groundwater contamination problems. The paper discusses some specific characteristics of the model area, including flow boundaries and transmissivity.
The modelers were required to define what the boundary of the contamination would be, which was in terms of contaminant concentration, and they were also required to define governing equations for how groundwater and contaminants move in the aquifer. These governing equations make the model nonlinear, and thus the modelers had to initially assume the velocity gradient to make the model linear. They then took two different paths of solving the model: either they did a global optimization which solved for the entire simulation period, or they did a sequential solution using the head distribution from the previous 6 months as the initial conditions for the next 6 months.
The objective function in the linear equation was to minimize the sum of pumping and recharge rates. The paper then goes on to give the various equations used to model the defining characteristics of the pumping scenarios.
The results of this study are that the global solution has a constant sum of pumping and recharge rates, while the sequential solution increases the sum of the pumping and recharge rates over time.
This paper is interesting since it has proven that hydraulic gradient control makes a difference in containing a contamination plume. Also, by optimizing the procedure, the time of cleanup can be reduced up to two years, which can be a huge amount of money in pumping energy costs. This study was performed in 1985 and much more could be done with the model with more recent technology. That would be the next step in research, is making the model more complex to include the nonlinearities and using new optimization tools to solve that model.
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I'd also like to see an extension of this study using new optimization tools. These days, it should be no problem to adapt the authors' methods to minimize pumping costs (a quadratic objective function) rather than total pumping amount (linear). I wonder how similar or different the results would be.
ReplyDeleteA look at other approaches would be interesting as well. In the introduction, the authors mentioned that the method used by Aguado and Remson (1974) was good, but that it was limited to small steady-state problems because of "excessive computer storage requirements and numerical difficulties." That's probably not as true 25 years later.