Application of mathematical optimization to exploit regional nutrient recycling potential of biogas plant digestate

Nutrients can be circulated back to agriculture from waste streams through anaerobic digestion and digestate processing. Digestate processing, however, is making slow progress as circulated nutrient products have not been cost competitive compared to fossil fertilizers and not designed from the farmer's perspective to truly match with the regional nutrient need. In this study, the aim is to assess apply mathematical optimization to the design of a cost-optimal processing route for a biogas plant's digestate to produce fertilizer products based on specified regional needs. Another aim is to analyze whether such a cost-optimal solution can fully exploit the nutrient recycling potential, that is, the efficiency of such a solution in returning nutrients to agriculture. The results indicate that mathematical optimization allows the design of a cost-optimal digestate production routes based on the region's nutrient need and characteristics. The true cost optimum was found for a design combining three processing technologies and producing four nutrient products, which when mixed, would fulfil farmer's fertilization needs. However, there seems to be a conflict between an optimal economic design and a full exploitation of recycling potential as only 25% of the digestate's phosphorus was utilized within the case region. This is because only 29% of the digestate mass was used and processed as fertilizer, as the concentration of required nutrients was deemed too low for economic use. The proposed mathematical model could be implemented as tool to assist in biogas plant investment decisions.