Assignment # 2

Article Reference:
Dorothy Fisher Atwood, Steven M. Gorelick, Hydraulic Gradient Control for Ground Water Contaminant Removal, 1985, Journal of Hydrology

Summary:
The paper explains about how linear programming can be used in optimizing the well location and recharging/pumping schedules so as to minimize total pumping and recharge. The planning procedure comprises of two stages, first to simulate the ground water flow and solute transport model and study the removal of contaminant under the assumed velocity; secondly the analyze the model with the relevant constraints and objectives is fed into the linear program for finding out the optimized solution.

In view of the increase of groundwater pollution incidents, aquifer planning and restoring has become of great interest. The present paper illustrates the methodology of controlling the hydraulic gradient for removal of the contaminants from the groundwater. Initially one of the techniques used for groundwater management as considered by Molz and Bell (1977) was using embedding systems method, in which the constraints for the linear model included are groundwater flow equation, pumping rates and hydraulic gradients. But this technique was limited to using for small steady state flow problems. Further Remson and Gorelick (1980) applied embedded systems approach to identify the well location and rates to prevent the contaminant plume from migrating. Another technique in groundwater modeling is response matrix which is used in conjunction with linear and quadratic programming to find out the optimizing solution to maximize the well yields and minimizing the production cost.

The Rocky Mountain Arsenal near Denver, Colorado, U.S.A which was the military facility to manufacture and process toxic chemicals for military and industrial use. This area has a history of groundwater contamination because of the poor disposal techniques. For carrying out the study, model area (about 3 km2) considered is the north boundary of the Rocky Mountain Arsenal, as the flow in the unconfined aquifer is from south to north; therefore goal of the design is to prevent further migration of contaminant during the aquifer cleanup. The model area was discretized into 702 finite difference nodes approximating the boundaries. South west flux boundary was calculated by running the steady state simulation, constant north head boundary was based on the water levels, Western and eastern boundaries are represented as no-flow boundaries. The parameters of hydro-geologic considered in the study are derived from the groundwater and solute transport models.

The hydraulic gradient control design procedure comprises of two design stages. In stage I, simulation of solute transport is used to locate the shrinking plume boundary. For locating the plume boundary with respect to the potential gradient control wells, the contaminant transport is simulated through time and using an assumed velocity field. To reduce the contamination level to safe level the following factors play main role; number of wells, location and pumping rates of the contaminant removal wells. By trial and error most effective location of the well was selected which would restore the water quality of the groundwater more effectively. With the found well location study of plume boundary reduction over the years was carried out. It was found that with the selected well location the entire plume can be removed in over 12 years. This geometry of the plume if further considered for carrying out stage II.

In stage II, linear programming combined with ground water flow simulation is used to find out optimum well location and pumping/recharge rates are estimated which would minimize the migration of the plume by controlling the hydraulic gradient. Objective function of the problem would be minimizing the pumping and recharging rate of the well for the management period of 32 pumping periods, constraints would be the hydraulic gradient control which will have decision variables associated with pumping and recharging.

There are two different solution strategies considered in the study of the project area. Sequential strategy uses series of sequential optimization for each pumping period. On the other hand single global optimization uses for total 32 pumping periods. Though the pumping/recharge rates are comparable between the two strategies, well selection and schedules of pumping are different. It was observed that cumulative pumping/recharge rates of global optimization was about 10% better than sequential solution over the entire pumping periods. From the above two strategies it can concluded that global optimization is more advantageous as it considers the entire time period and therefore constraints are considered for the entire time horizon. Selection between both the strategies can be based on the criteria of economic or social considerations.

Global strategy solution was cross checked by running the solute transport model with the resulted optimum pumping/recharge rates. Comparison study was carried with and without the hydraulic gradient control wells on the redistribution of the contaminant. When there was no control of hydraulic gradient on the wells then the pumping effect was negligible and after about 4 year the plume started moving outside the model area. With the hydraulic gradient control wells, the plume contained in the original boundaries and helped in restoring the aquifer.

Discussion:
The paper was interesting as it gives us idea of how linear programming is applied in finding out the optimum location of the wells and their pumping/recharge rates for the contaminant removal with the hydraulic gradient control. The paper gave a good insight of the two solution strategies, their advantages and limitations. Comparative study of how the solutions differ for the study area when we consider these two solution strategies was very informative.

In the paper, during the beginning of the problem itself it is assumed that it has existing well network, therefore cost impact is not taken into consideration. It would be interesting to see how the solution is affected by the cost implications. Modeling the linear program corresponding to the cost also would give a more realistic optimized solution.