Capture zone models of a multi-well system in aquifers bounded with regular and irregular inflow boundaries

Being bounded by hydrological (inflow and barrier) boundaries, natural aquifers have regular/irregular shapes. Here, we consider aquifers bounded by segmental inflow (variable head) boundaries in which water is extracted/injected by a multi-well system. Steady state analytical and semi-analytical solutions are derived to delineate the capture envelopes of the multi-well system. The multi-well system includes any number of extraction or injection wells, each with an arbitrary flow rate. The aquifer is bounded by an arbitrary number of boundary segments, with and without uniform regional flow. The solution is fully analytical, and involves hypergeometric functions if the number of boundary segments exceeds three. A sensitivity analysis shows that number, position and extraction/injection rate of wells, numbers and geometry of boundary segments, distance between wells and boundaries, and direction and rate of regional flow independently and collectively control the size, shape and pattern of the capture zones. The derived solutions are useful for sustainable water resources management in terms of both quality and quantity.