Mixed-Integer Programming Approach for Designing Land Application Systems at a Regional Scale

Sewage sludge disposal has become more difficult for wastewater-treatment plants because landfill operators are increasingly raising tipping fees and limiting the sludge they will accept. For this reason many municipalities are turning to land application as a means of beneficially disposing of sludges. We have developed a procedure for systemwide planning of biosolids (sewage sludge) land application systems. The system includes multiple treatment plants, agricultural regions, and crops. Our approach considers costs of the following: (1) Biosolids storage; (2) digestion; (3) composting; (4) transportation; and (5) land application over an extended planning horizon. We describe a mixed-integer programming (MIP) algorithm that can be used to simultaneously schedule capacity expansions and route transportation. The objective function minimizes long-term and short-term costs. We use an inventory-type approach to model nitrogen accumulation in the soil over time. Accumulated nitrogen limits the quantity of biosolids that can be applied to a given parcel of land. The model restricts certain crops to composted biosolids according to current Environmental Protection Agency (EPA) regulations. Sewage-treatment plants may opt to either compost their biosolids or upgrade their digestion system to meet U.S. federal standards for land application, and the model settles on an optimal pathogen treatment plan based on storage, transportation, and marketing constraints. The model is used to find an economically efficient solution for the sludge disposal needs of Eastern Municipal Water District (EMWD) in Riverside County, Calif. In this District, a combination of direct land application and composting proves optimal.