A local model for analysis of pump and treat systems with vertical barrier walls

We present a mathematical model of local, steady groundwater flow near a vertical barrier wall. Flow features represented in the model include an impermeable arc-shaped barrier wall and multiple wells; distant boundary conditions are not included explicitly, but their effects on the local flow field are modelled by specifying a uniform flow at infinity and a constant areal recharge within a local domain. We develop an explicit closed-form solution to the boundary-value problem using the analytic element method. The solution is an extension of a harmonic solution presented by Anderson and Mesa [Anderson EI, Mesa E. The effects of vertical barrier walls on the hydraulic control of contaminated groundwater. Adv Water Resourc 2006;29(1):89–98] which does not include the effects of recharge. We demonstrate that the general solution with recharge consists of the harmonic solution superposed on a special case of the harmonic solution along with two elementary one-dimensional flow solutions. The results are used to investigate the effects of areal recharge on the capture zone envelopes of the pumping wells and on the reduction in discharge that can be achieved by including a barrier wall in a pump and treat design. We find that the benefits of including an open barrier wall in a design, measured as a reduction in the pumping rate required to contain a plume, increase for higher recharge rates. Dimensionless plots of capture zone envelopes are presented for a practical well and barrier wall configuration.