Linear programming for regulation-compliant digestate disposal in Spanish biogas plants

Abstract

Anaerobic digestion converts organic feedstocks into biogas and a nutrient-rich digestate whose land application closes the nitrogen loop and offsets part of nearby croplands’ synthetic-fertilizer demand. Allocating digestate batches to eligible parcels is constrained by Spanish Royal Decrees 1051/2022 and 47/2022, by autonomous-community frameworks such as Catalonia’s Decree 153/2019, and by crop nutrient demand and soil status, yielding a large constrained planning problem. This work formulates a linear programming model over a 12 month horizon with monthly time steps that allocates whole or separated digestate to parcels, prioritising those closest to the plant, subject to nitrogen, heavy-metal and salinity limits. The model is re-solved every month within a rolling-horizon scheme stabilised by a penalty on changes to previously committed decisions. On a synthetic scenario of 2,000 parcels, all regulatory thresholds are met and the plant obtains a monthly application plan that can be recomputed as regulations change.