Mathematical model for formation decontamination by pumping with well bore mixing

This work presents a novel mathematical model to evaluate the effect of pumped well bore mixing volume on formation decontamination. The model equation is solved by the Laplace transform finite difference method. The developed model is applied to assess the effect of well bore mixing volume on contaminant remediation. The simulated results indicated that the well bore volume effect is pronounced for initial plumes with a small maximum contaminated radius, and in media such as bedrock formation where aquifer porosity and longitudinal dispersivity are small. In such systems, the pumped well bore mixing effect reduces the early contaminant concentrations, shifts the peak breakthrough curves to the right and spreading the breakthrough curve, and thus increases the decontamination time. If such a system does not account for pumped well mixing bore effect, estimates of decontamination time required to the regulatory level will be inaccurate.