Recycling flows in emergy evaluation: A mathematical paradox?

This paper is a contribution to the emergy evaluation of systems involving recycling or reuse of waste. If waste exergy (its residual usefulness) is not negligible, wastes could serve as input to another process or be recycled. In cases of continuous waste recycle or reuse, what then is the role of emergy? Emergy is carried by matter and its value is shown to be the product of specific energy with mass flow rate and its transformity. This transformity (τ) given as the ratio of the total emergy input and the useful available energy in the product (exergy) is commonly calculated over a specific period of time (usually yearly) which makes transformity a time dependent factor. Assuming a process in which a part of the non-renewable input is an output (waste) from a previous system, for the waste to be reused, an emergy investment is needed. The transformity of the reused or recycled material should be calculated based on the pathway of the reused material at a certain time (T) which results in a specific transformity value (τ). In case of a second recycle of the same material that had undergone the previous recycle, the material pathway has a new time (T + T1) which results in a transformity value (τ1). Recycling flows as in the case of feedback is a dynamic process and as such the process introduces its own time period depending on its pathway which has to be considered in emergy evaluations. Through the inspiration of previous emergy studies, authors have tried to develop formulae which could be used in such cases of continuous recycling of material in this paper. The developed approach is then applied to a case study to give the reader a better understanding of the concept. As a result, a ‘factor’ is introduced which could be included on emergy evaluation tables to account for subsequent transformity changes in multiple recycling. This factor can be used to solve the difficulties in evaluating aggregated systems, serve as a correction factor to up-level such models keeping the correct evaluation and also solve problems of memory loss in emergy evaluation. The discussion deals with the questions; is it a pure mathematical paradox in the rules of emergy? Is it consistent with previous work? What were the previous solutions to avoid the cumulative problem in a reuse? What are the consequences?

► A contribution to emergy theory in discrete time applying to recycling is proposed. ► Under assumptions, the emergy of a recycled product is a geometric series. ► Emergy of a product under depreciation can be similar with Carnot principle.