Ensuring the Safety of an Extraction Well from an Upgradient Point Source of Pollution in a Computationally Constrained Setting

Shallow groundwater is an important resource, especially in low- and middle-income countries; however, shallow groundwater is particularly vulnerable to point sources of pollution such as latrines or unlined waste disposal ponds. The objective of this paper is to derive a quantitative criterion for siting an extraction well and an upgradient point source of pollution to ensure that they are hydraulically disconnected, i.e., that no water flows from the point source to the well. To achieve this objective, we modeled the flow of shallow groundwater considering uniform regional flow, a single point source of pollution, and a single extraction well. For any set of flow rates and upgradient point source distance, we sought the minimum “off-center distance” ymin (i.e., the distance in the direction perpendicular to regional flow) that ensures the well and the point source are hydraulically disconnected. For constituencies with access to computing resources and coding expertise, we used a computer-based method for determining ymin that is exact to within the accuracy of a root-finding algorithm; this approach is recommended when computer access is available. For constituencies lacking these resources, we determined a simple, closed-form, approximate solution for ymin that has an average error of less than 3% for the conditions we tested. For a subset of scenarios in which the point source is sufficiently far upgradient of the well (n = 77), the root mean square relative error of the approximate solution is only 0.52%. We found that ymin depends on a length parameter (Qw + Qps)/QR, where Qw is the extraction rate of the well, Qps is the injection rate of the point source, and QR is the regional groundwater flow rate per unit of perpendicular length. Either the exact solution or the closed-form approximation can help to site wells near point sources of pollution, or to site point sources near wells, in a manner that protects the health of the well user. The approximate solution is valuable because many constituencies that rely on shallow wells for water supply and latrines for sanitation also lack access to the computer resources necessary to apply the exact solution.