Recycling and mathematics

Summary: Efficient recycling requires the use of sophisticated mathematical models to maximize product use and reuse and minimize energy consumption.

Recycling is the extraction of usable materials out of used objects. Materials that are often recycled at the start of the twenty-first century include metal, paper, glass, and plastic. One important mathematical problem of recycling is the comparison of environmental and monetary costs of recycling and virgin production. Mathematicians are also involved in developing new methods for recycling and modeling both economic and environmental impacts. The notion of “algorithm recycling” applies to resources used in some mathematical investigations. For example, statistical bootstrap recycling reuses samples to minimize demands on computational resources. Some mathematicians, scientists, educators, and others use recycling for education, recreation, and art. Mario Marin has designed polyhedral outdoor play spaces and kinetic sculptures from recycled and remaindered materials and has published many creative ways to recycle household objects, like plastic bottles, into interesting polyhedral structures. With regard to learning, some have even suggested a concept called “neuronal recycling,” which refers to adaption of neuronal circuits for new uses.

Proportion-Based Regulations and Labeling

To motivate recycling, companies and governments set rules that demand the recycling of a certain proportion of materials and the use of a certain proportion of recycled material in production. Because recycling is the third desirable option in the waste management hierarchy, after reduction of waste and reusing of objects and materials, setting high recycling quotas is never a goal in its own right. However, recycling is often preferable to disposal. Governments sometimes directly mandate minimum recycled content in certain classes of manufactured goods. Labeling laws, which require companies to display the percent of recycled content in goods and packages, may also promote recycling if consumers support it, or hinder recycling if consumers do not find recycled goods in this particular industry appealing. Companies advertise their recycling efforts—typically by disclosing the percent of recycled material—to present ecofriendly images to their customers.

A common scheme to promote the recycling of packaging is to include a refundable fee in the price of the product. Once the customer returns the packaging to the store, the fee is refunded.

Measuring Efficiency

Because recycling is a complex process, there are ecological and economical costs involved in it. For recycling to make sense, the benefits have to outweigh the costs. Computing costs and benefits is a complex problem. Costs are incurred at all stages of recycling: collecting materials, sorting them, and re-making them. Benefits include the reduction of landfill costs, reduction of pollution, and revenues from the use of recycled materials. In the cases of nonrenewable natural resources, recycling is the only option to keep using these resources in the future.

Metal Recycling

Because of the relative difficulty and high cost of mining and smelting of metals, and the ease of collecting and recycling, metals are the most recycled materials in the world. For example, recycling aluminum takes only 5% of the energy that it would take to make it from the raw materials. About three-quarters of steel and a third of aluminum is recycled in the United States as of 2010. Some applications of science and mathematics metal recycling involves the separation of impurities, such as paint.

Paper Recycling

One category of paper recycling, post-consumer paper, is familiar to most people because paper is ubiquitous in modern society. “Mill broke” is scraps that pulp mills accumulate from making paper, which they can also recycle. Preconsumer paper is scraps collected and recycled in paper mills. Unlike metal recycling, where the cost-benefit ratio is low, paper recycling is more complicated and controversial. For example, burning paper for energy may be more environmentally sound than recycling it and harvesting and replanting forests may be cheaper than recycling.

Estimates for energy saving are 40% to 65% for recycled paper, compared to creating new paper. However, pulp mills frequently produce energy by burning roots, bark, and other byproducts, whereas recycling plants have to be close enough to collection (usually urban) areas to minimize transport cost and frequently depend on fossil fuels for energy. Thus, the environmental costs of conserving the same amount of energy is different, as one process uses renewable resources and the other uses nonrenewable resources. Water and air pollution benefits of paper recycling are more pronounced than energy benefits because of highly toxic bleaching used in making new paper.

Plastic Recycling

Recycling of plastics involves a scientific challenge not found in recycling of other materials. Because of the ways polymer chains are formed in plastics, different plastics do not blend well. Removing dyes, glue, paper stickers, and other impurities is also difficult. Plastics are coded with the Resin Identification Codes, numbers 1–7, inside the triangular recycle symbol.

There are several processes for recycling plastic. The most straightforward is melting similar plastics together, with some steps to remove impurities. Heat compression mixes all types of plastics in high-heat, high-pressure drums. Thermal depolymerization is currently an experimental procedure that “reverses” the process of making plastic and turns it into a substance similar to crude oil. Another experimental procedure, called “monomer recycling,” reverses plastic-making halfway, turning polymers into the mix of monomer chemicals that formed them.

The short-term cost-benefit analysis may not support plastic recycling because of the high energy and labor requirements of the known processes. However, crude oil (the raw material of plastic) is a nonrenewable resource, which makes plastic recycling attractive in the long term.

Glass Recycling

The main benefits of glass recycling are saving landfill space and saving energy on producing new glass. However, because glass is sturdy and easy to clean, glass container reuse is vastly preferable to recycling. Through changing their infrastructures, along with using clear bottle standards and monetary incentives, some countries can reuse more than 95% of their glass bottles.

Crushed glass can be added to concrete. This process can be considered reuse rather than recycling because the glass is serving a different purpose. Measurements of glass-infused concrete include its insulation properties and strength properties, both of which are improved by the addition of glass. Also, concrete with glass is more aesthetically pleasing and can be used for countertops and other highly visible places.

Mathematical Modeling

Mathematical models are widely used in logistics—controlling the efficient flow and storage of goods, services, and information from the point of origin to the point of consumption. Reverse logistics is the extension of this principle that addresses concepts such as returns, source reduction, recycling, and reuse. Mathematicians have researched models for logistics that address these reversals of flows. For example, Italian researchers created a staged mathematical model of the options for recycling a broad range of appliances, electronic equipment, and other household items commonly thrown away. The model suggested that recycling can offer what is known as economies of scale to businesses, which are increasingly being held liable for end-of-life product disposal.

Others have used techniques such as dynamic quantitative models to simulate recycling systems and flows to better understand the driving variables and relationships among the activities and participants. These models can aid planners in making decisions about recycling policies and procedures. Nutrient recycling for trees, which has implications for issues such as global warming, has been modeled using linear and quadratic functions, along with data-based numerical simulations. However, some scientists argue that mathematical models must be contextually evaluated and used with caution for decision making and legislation. Models based on limited data may generate what appear to be useful results, but extrapolation or subsequent modeling can create bias and propagation of errors.

Bibliography

Environmental Protection Agency. “Wastes—Resource Conservation—Reduce, Reuse, Recycle.” http://www.epa.gov/osw/conserve/rrr/recycle.htm

La Mantia, Francesco. Handbook of Plastics Recycling. Shropshire, England: Smithers Rapra Technology, 2002.

Mancini, Candice. Garbage and Recycling (Global Viewpoints). Farmington Hills, MI: Greenhaven Press, 2010.

Newton, Michael, and Charles Geyer. “Bootstrap Recycling: A Monte Carlo Alternative to the Nested Bootstrap.” Journal of the American Statistical Association 89, no. 427 (1994).

Schlesinger, Mark. Aluminum Recycling. Oxfordshire, England: Taylor & Francis Group, 2007.