Ground water transport models are relatively easy to develop if enough assumptions are made. Validation is needed before the output of any model is applied. Also, Pb-210 is a decay produce of radon and will be present in any water from an aquifer containing radium-226 or other radionuclides in its decay chain. This model must assume secular equilibrium.
Torres L, Yadav OP, Khan E. Holistic risk assessment of surface water contamination due to Pb-210 in oil produced water from the Bakken Shale. Chemosphere 2016 Nov 29;169:627-635. doi: 10.1016/j.chemosphere.2016.11.125.
A holistic risk assessment of surface water (SW) contamination due to lead-210 (Pb-210) in oil produced water (PW) from the Bakken Shale in North Dakota (ND) was conducted. Pb-210 is a relatively long-lived radionuclide and very mobile in water. Because of limited data on Pb-210, a simulation model was developed to determine its concentration based on its parent radium-226 and historical total dissolved solids levels in PW. Scenarios where PW spills could reach SW were analyzed by applying the four steps of the risk assessment process. These scenarios are: (1) storage tank overflow, (2) leakage in equipment, and (3) spills related to trucks used to transport PW. Furthermore, a survey was conducted in ND to quantify the risk perception of PW from different stakeholders. Findings from the study include a low probability of a PW spill reaching SW and simulated concentration of Pb-210 in drinking water higher than the recommended value established by the World Health Organization. Also, after including the results from the risk perception survey, the assessment indicates that the risk of contamination of the three scenarios evaluated is between medium-high to high.