An analytical solution to model aquaculture wetlands subject to intermittent loading and variable initial concentrations

Constructed wetlands are increasingly being used to treat intermittent releases of wastewaters from aquaculture ponds. Most constructed wetland design protocols are based on steady-state releases and as such are incapable of characterizing transient pollutant distribution arising from intermittent releases. Given the seasonal nature of aquaculture operations, the constructed wetland has to be developed using water from other nearby sources (termed as fill water in this study). In some instances, the pollutant concentrations in the fill water are noted to be greater than that measured in the aquaculture ponds. Also, the pollutants in the wetland may exhibit spatial variability due to geochemical interactions with wetland soils. These effects cannot be captured with existing steady-state design schemes. A mathematical model based on the tanks-in-series conceptualization is developed to overcome the aforementioned limitations. An analytical solution for multiple intermittent releases and spatially varying initial concentrations is obtained using Laplace transform and superposition techniques. The utility of the developed model is illustrated using an example based after a constructed wetland at the Loma Alta Shrimp Aquaculture Facility (LASAF) in South Texas. The developed model captures the extremely nonlinear relationship between the maximum discharge concentration and the hydraulic residence time. For the conditions assumed in this study, the extent of mixing is not of major concern when the spacing between the loadings is greater than 0.75 times the hydraulic residence time (HRT). Model results also suggest that the wetland should be oriented in a manner such that the internal geochemical production of the pollutant, if any, is near the inlet.