Bioretention basins are a common stormwater best management practice (BMP) used to mitigate the hydrologic consequences of urbanization. Dry wells, also known as vadose-zone wells, have been used extensively in bioretention basins in Maricopa County, Arizona to decrease total drain time and recharge groundwater. A mixed integer nonlinear programming (MINLP) model has been developed for the minimum cost design of bioretention basins with dry wells.

The model developed simultaneously determines the peak stormwater inflow from watershed parameters and optimizes the size of the basin and the number and depth of dry wells based on infiltration, evapotranspiration (ET), and dry well characteristics and cost inputs. The modified rational method is used for the design storm hydrograph, and the Green-Ampt method is used for infiltration. ET rates are calculated using the Penman Monteith method or the Hargreaves-Samani method. The dry well flow rate is determined using an equation developed for reverse auger-hole flow.

The first phase of development of the model is to expand a nonlinear programming (NLP) for the optimal design of infiltration basins for use with bioretention basins. Next a single dry well is added to the NLP bioretention basin optimization model. Finally the number of dry wells in the basin is modeled as an integer variable creating a MINLP problem. The NLP models and MINLP model are solved using the General Algebraic Modeling System (GAMS). Two example applications demonstrate the efficiency and practicality of the model.