Optimal Wellfield Operation under Water Quality Constraints

A new approach to solving the problem of the optimal operation of a wellfield under water quality constraints is presented and tested. The approach is related to well activation in which all the wells are operated against an approximately constant head. Under these conditions, the hydraulic solutions of the network can be considered as a set of steady-state solutions that depend on the combination of operated wells. This setting is very practical because, in many cases, groups of wells pump water to the same receptor, which maintains an approximate constant head (for example, a relatively large reservoir or a treatment plant). The methodology utilizes mixed-integer linear programming (MILP) to optimize the combinations of wells that will pump the required volume of water given a threshold water quality constraint at minimum energy. This is by dividing the problem into two subproblems of hydraulics and water quality, whose solutions are combined and embedded into a MILP formulation. To overcome the complexity of water quality simulations, a predictive linear regression formulation is utilized to construct linear surrogate connections between the wells and the resulting water quality outcomes, which are then incorporated into a MILP optimization problem. Two example applications of increasing complexity are explored through base runs and sensitivity analyses. The results show that once the model is tuned to a specific water distribution system, an operational plan can be established that provides good approximate results without the need to construct a detailed simulation-evolutionary optimization algorithm framework.