Hydraulic Gradient Control for Groundwater contaminant removal

Fisher Atwood D, Gorelick S.M.(1985)." Hydraulic Gradient Control for Groundwater Contaminant Removal", Journal of Hydrology, Vol 76(1985) 85-106.

Summary

This article provides the insight as to how linear programming was used to optimize the selection of wells for groundwater purification. The Rocky Mountain Arsenal near Denver Colorado was selected as the site for groundwater purification. The Arsenal which is a military base also process toxic chemicals. Poor disposal techniques over decades have resulted in contamination of the water table. A system of wells removes contaminated water. The optimization routine selects the best wells and their pumping and recharge schedule while controlling the hydraulic gradient.

Much of the study at the initial stages was concentrated to determine the hydrological parameters like the hydraulic head distribution, transmissivity, effective porosity and storage coefficients of the Arsenal. The key requirement of the groundwater pumping is that it should be hydraulic gradient controlled. This prevents the contaminant plume boundary from migrating beyond its original boundaries. If there is no hydraulic control while pumping studies showed that over the years the plume will move outside the model area selected for the study. However optimization for hydraulic control introduces non-linearity to the problem and thus it could not be solved in a single linear programming attempt. The pumping/recharge rate which is a decision variable which is unknown. The groundwater velocity is also an unknown and the non linearity is introduced by multiplying unknown velocities and concentrations in the advection dispersion equation. Thus a two step process was introduced to deal with the non linearity issue.

The first stage consisted of tracking the plume boundary. This was done by assuming a velocity vector as the true velocity is an unknown. This was derived by observing the effects of a successful hydraulic control. The speed at which a contaminant is removed depends on the number of the pumps, their placement and the pumping rates. So next the location of the most effective well was identified. The plume geometry is derived from experimentation. The second stage consisted of identifying optimal well selections and rates. The objective was to minimize the pumping rates. The hydraulic gradient control is the first constraint. The pumping rate and the non negativity of the velocity vectors are the other constraints. The process was to be completed in equal length time periods of pumping and each time period was associated with a certain specific position of the plume. A time period of 18 yrs was identified to complete the process and further divided in 8 yrs and it consisted of a total of 32 pumping periods. During trial runs proper location of wells were selected by mixed integer programming. Drawdown responses for each well location was derived and converted into a gradient. The resulting constrain matrix was evaluated with a convergence criteria of 1.10^-9 was solved using MINOS.

Discussion

The two stage optimization problem was solved by two optimization technique’s namely global optimization and sequential optimization, and comparisons were drawn between the two techniques. The sequential strategy would require periodically updating the plume configuration and determining new well locations for management problem 2 but for an accurate comparison identical well locations were used. The result from global optimization showed that recharge rates are relatively high for the first half year. Than the rates drop in the next 1 to 2 yrs thus indicating that lower rates are suitable for maintain the inward hydraulic gradient. As the target gradient increases with time for the rest of the management stage 1 the recharge rates show a steady rise. The results of the management problem II differs in case of global optimization from the first period. For pumping rates there is a steady rise but however this is not the case with recharge rates. For the last pumping period the pumping or recharge rates increase or decrease dramatically and there is an uncertainty in the explanations. The result from the sequential optimization differs from that of the global optimization. The well selection and pumping schedules are different. For stage I the entire hydraulic gradient is controlled by recharge wells alone and pumping wells are used only during the second stage. However the cumulative rates show that the global solution is better than the sequential solution. Although the values are mostly same during stage I they differ in stage II. The global rates are much less at the last stages of the pumping period. However other criteria like economic and social if considered might give sequential method an edge over global method.

The process described for the Arsenal ground water purification is general and can be applied to other locations as well. A future line of work for this model could be by introducing constrains related to economy and other factors affecting the system. It would be interesting to see and compare the results from the two optimization techniques.