The Nonlinear Relationship between Paper Recycling and Primary Pulp Requirements Modeling Paper Production and Recycling in Europe

Waste paper is suitable for recycling back into paper or for incineration for energy recovery. If waste paper is used for recycling, secondary pulp replaces virgin pulp. Fiber recycling is limited, however, because of physical constraints-particularly the breakage of fiber in the recycling process-and a permanent input of virgin fiber to the system is required. Therefore one can expect that the relationship between recycling rates and resource requirements is represented by a curved line rather than a straight one. In this article, we present a mathematical model which confirms that the relationship between recycling rates and primary pulp requirements can be described as nonlinear. Furthermore, we show that this nonlinear relationship leads to an optimal recycling rate with regard to energy consumption: 93% for paper produced from chemical pulp, and 81% for paper produced from mechanical pulp. Sensitivity testing additionally reveals that at low recycling rates increasing waste paper recycling is energy efficient, but it becomes less efficient at higher recycling rates. Close to the optimum recycling rates (within 10%), increasing or decreasing the rate affects the total energy requirement less than 0.3%.