Using graph search algorithms for a rigorous application of emergy algebra rules

¹ Public Research Centre Henri Tudor, Resource Centre for Environmental Technologies, 66 rue de Luxembourg, 4002 Esch-sur-Alzette, Luxembourg
e-mail: antonino.marvuglia@tudor.lu
² Cork Constraint Computation Centre, University College Cork, Western Gateway Building, Cork Ireland
³ LITIS, Normandy University, 25 rue Philippe Lebon CS 80540, 76058 Le Havre Cedex, France
⁴ Université de Toulouse INSA, UPS, INP, LISBP, INRA UMR792, CNRS UMR5504, 135 av. de Rangueil, 31077 Toulouse, France

Received: 31 January 2013
Accepted: 6 February 2013

Abstract

Emergy evaluation (EME) is an environmental assessment method which is gaining international recognition and has increasingly been applied during the last decade. Emergy represents the memory of the geobiosphere exergy (environmental work) – measured in solar emjoules (seJ) – that has been used in the past or accumulated over time to make a natural resource available. The rationale behind the concept of Emergy is the consideration that all different forms of energy can be sorted under a hierarchy and measured with the common metric of the seJ, which is then the yardstick through which all energy inputs and outputs can be compared with each other. For this reason EME is suggested to be a suitable method of environmental accounting for a wide set of natural resources, and can be used to define guidelines for sustainable consumption of resources. Despite those interesting features, EME is still affected by several drawbacks in its calculation procedures and in its general methodological background, which prevent it from being accepted by a wider community. The main operational hurdle lays in the set of mathematical rules (known as Emergy algebra rules) governing EME, which do not follow logic of conservation and make their automatic implementation very difficult. This work presents an open source code specifically created for allowing a rigorous Emergy calculation (complying with all the Emergy algebra rules). We modeled the Emergy values circulating in multi-component systems with an oriented graph, formalized the problem in a matrix-based structure and developed a variant of the well-known track summing algorithm to obtain the total Emergy flow associated with the investigated product. The calculation routine (written in C++) implements the Depth First Search (DFS) strategy for graph searches. The most important features of the calculation routine are: (1) its ability to read the input in matrix form without the need of drawing a graph; (2) its rigorous implementation of the Emergy rules; (3) its low running time, which makes the algorithm applicable to any system described at the level of detail nowadays made possible by the use of the available life cycle inventory (LCI) databases. A version of the Emergy calculation routine based on the DFS algorithm has been completed and is being tested on case studies involving matrices of thousands of rows and columns, describing real product production systems.