Assignment 2

Atwood, Dorothy Fisher, and Gorelick, Steven M. (1985) “Hydraulic Gradient Control for Groundwater Contaminant Removal,” Journal of Hydrology 76, 85-106.

Summary

This study entails a two-stage planning procedure that optimizes a pumping and recharge schedule for wells that will ultimately remove contaminated water. Stage I included a groundwater flow and solute transport model that simulated contaminant removal, and Stage II was a linear programming model that determined the optimal well selection and their schedules by minimizing total pumping and recharge. The stage II program includes the groundwater flow model from stage I as a constraint.

In stage I, the methodology of the plume containment was to control the hydraulic gradient that was aimed at containing and removing the contaminants. An important technique that they used in the groundwater management modeling was the response matrix, which showed the “influence of pumping or recharge of the wells at the potential well sites upon drawdowns at specified observation locations”.

The model that was developed by the authors was tested in the Rocky Mountain Arsenal in Colorado, which is an area where poor disposal of industrial and military chemicals exist. It was found that the northern boundary of the area had a steeper hydraulic gradient compared to the southern end, and the contaminant was more effectively removed in the southern part. This had a great influence on the well chosen, along with the pumping/recharge schedules.

In stage II, an objective function was formulated to minimize the sum of the pumping and recharge rates. The constraints for the model were non-negativity values for the decision variables, along with the hydraulic gradient constraints for the creation of an inward hydraulic gradient. The cost was not taken into account in the objective function, or even in the optimization model as a whole. The linear programming model was solved using the MINOS optimization package. Two solution strategies were used: global (a single global optimization for all pumping periods) and sequential (used a series of sequential optimizations for each pumping period). The results found were that pumping and recharge rates were similar between the two strategies, but the well selection and pumping schedules were quite different. The global optimization was advantageous because it solved the problem over the entire time span and took all constraints at one time. However there are arguments that the sequential optimization is preferred due to other non-hydraulic related criteria, such as social or economic concerns.

The authors discussed that the limitation of this methodology was that it can only be applied to small steady-state flow problems. Excessive computer storage requirements and numerical difficulties made the method infeasible for field-scale problems.

Discussion

This article created an optimization model used to identify the most advantageous wells, along with pumping and recharge rates. This work credited to hydraulic modeling methodology by linearizing nonlinearities in the system. It was also very beneficial that the authors decided to optimize the solution using two different methodologies: global versus sequential. This is because the readers were allowed to compare the results, along with the advantages and disadvantages of both. This proves that there is no right answer to this problem, and it is just relative to the perspective of the user.

The faults of this work deal with the scale in which the model can be applied. Applications of related subjects pertaining to this model are to be used on a larger scale. Also, the model had used information from other models, in which the work wasn’t autonomous entirely. This can be beneficial in the sense that the model must be relatively valid and accurate if it is being reproduced. However, problems could arise if there are not identical constraints and/or assumptions made in both the borrowed and the new models.

If I were to build on this research, I would look into hydraulic related models similar to this one, and see if they separated the models in their studies in a similar fashion as this one due to non-linearity of variables. I would also look into the numerical difficulties that were encountered in the model development that led the authors to claim that the model can only be used on a small scale. I would also see how I could incorporate cost into the objective function or constraints.