Development of an emergy computation algorithm for complex systems using depth first search and track summing methods

Although emergy analysis provides a more comprehensive view of sustainability than other methods, it has been criticized from both theoretical and practical aspects due to its complicated approach, especially when dealing with large sized systems and allocating emergy involved with feedbacks or with input streams that have splits and co-products. The aim of this study was to provide a practical sustainability decision-making software tool to cover all the emergy rules by reformulating and improving previous emergy accounting procedures using the MATLAB language algorithm. The code consisted of the two components of (i) searching the emergy pathways, where the algorithm is adapted from the depth first search method, and (ii) the computation of emergy based on emergy algebra, where the track summing method was deployed. The algorithm was validated on three case studies, comprised of two complex systems with feedbacks, splits and co-products and one case of an industrial symbiosis with a closed loop of materials and energy through reuse and recycle. Three emergy size distribution behaviors (symbiosis, serial and parallel) were revealed and classification of the process behavior could be used to reduce the calculation complexity in further emergy applications.