Mark T. Brown

1Environmental Engineering Sciences, University of Florida， 1953 Museum Road, Gainesville, FL 32611, USA

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Emergy and Form： Accounting Principles for Recycle Pathways

Mark T. Brown1,?

1Environmental Engineering Sciences, University of Florida， 1953 Museum Road, Gainesville, FL 32611, USA

Submission Info

Communicated by Sergio Ulgiati

Emergy

Recycle

By-products

Form

A brief exploration of the concept of information is undertaken to parse the different meanings and measures. We agree with Odum （1996） that information might best be expressed as complexity and posit that the shape or form of an object is a type of information and with increasing complexity of form there is a corresponding increase in emergy required to make it. We also agree with Odum that an increase in concentration of a material increases its emergy per mass （i.e. its UEV） and a decrease in concentration as when a material is dispersed requires a decrease in the emergy stored.

We present new thoughts related to the emergy in form as distinct from the emergy of the materials that make up the form. We suggest that the emergy of form is lost when the form is consumed, but the emergy of the substance is maintained. We define recycle pathways in such a way as to clarify emergy accounting for products and by-products.

These considerations are important when evaluating “circular economies”where products and by-products are recycled once their useful life is finished. This proposed method of dealing with recycled material is a refinement of the emergy accounting procedure.

? 2015 L&H Scientific Publishing, LLC. All rights reserved.

“It is the pervading law of all things organic and inorganic, of all things physical and metaphysical, of all things human and all things superhuman, of all true manifestations of the head, of the heart, of the soul, that the life is recognizable in its expression, that form ever follows function. This is the law."

American architect, Louis Sullivan

1. Introduction

1.1 Information

Information may be one the least understood concepts in modern scientific discourse. It has many meanings and even more ways of quantitatively describing it. The earliest historical meaning of the word information in English （the 14thcentury） was the act of informing, or giving form or shape to the mind, as in education, instruction, or training. In the mid-20thcentury, Claude Shannon （1948） mathematically defined information as a quantity, divorced from any concept of meaning or learning and used the word “bit”, a contraction of binary digit as the basic unit of information. In the latter half of the 20thcentury information took on even more meanings, often without reference to a person being informed, sometimes contrasted with data but which can be produced by processing data. Others have used the word information to describe sequences （ie DNA）stored, or something that can be transmitted, stored and communicated by inanimate things.

Odum （1988, 1996, 2001） defined an information maintenance cycle in his now much reproduced diagram of the cycle of scientific information being generated, tested and adopted （Figure 1） in a cyclic process, driven by available energy. He likened it to the information cycle inherent in the life cycle of salmon fish （Figure 2）. He recognized a hierarchy of information and introduced the concept of shared information （Odum； 1988）.

Fig. 1. The scientific information maintenance cycle adopted from Odum （1996） showing the generation of new information by research groups that test and select then share the information at national meetings or published journals. The shared information acts as reinforcement for the generation of new information. The entire cycle requires input of outside energy and resources to maintain all phases of the cycle.

As an interesting aside, that has some relevance, N?rretranders （1998） proposed the term exformation for explicitly discarded information. He suggested, that exformation is the totality of everything an individual may know about something, but is not actually communicated when it is spoken about. Whereas information is the measurable words actually communicated.

In this paper we will restrict our inquiry to a definition of information that is related to form1Form is the shape, organization, visual appearance, constitution or configuration of an object., or the idea that the form or shape that something takes is inFORMation. We are particularly interested in the relationship between form and function, which we suggest is the information content of the physical shape. We address the concept of form as information and define it quantitatively as the emergy required to create form, and then suggest that this conceptual framework may be useful in evaluating the transformity or specific emergy of recycled matter. We then quantitatively explore this framework for three product unit process chains, an agricultural product, an aluminum can, and an aluminum can produced with 50% recycled matter.

Fig. 2. The life cycle of salmon showing the increasing emergy of the lifecycle, until the time of egg dispersal, when the total emergy is divided by the number of eggs, thus the emergy per individual declines. （After Odum, 2007）

1.2 Form， Function and Information

Louis Sullivan （1896） suggested that “...form ever follows function.” The idea that form and function are inseparable. It's not difficult to realize that the form enables the function and that the function of a product is only possible if the form remains intact. Further, consider that the form of an object is information, then one can say that the information inherent in an object enables the function. Should the information be lost, the function is lost. An aluminum can filled with soft drink has a particular form that allows it to be a container. If the can is crushed, its function is lost, and we suggest that some of the information of its form is lost as well.

1.3 Information and Emergy

The term emformation was proposed by Scienceman （1987） as the emegy per bit of information. Odum （1996）suggested that emergy per bit could be calculated as a measure of information placed on the scale of the energy hierarchy. He proposed that useless complexity would have low emergy per bit since “l(fā)ittle work has been exerted to make it useful”, while highly evolved information would have high emergy per bit “because of the larger and longer flows of emergy required for its development and maintenance. Jorgensen et al. （2004）evaluated the emergy and exergy of genetic information, finding an interesting relationship between the emergy cost of carriers of information （organisms） and the information carried （genes）. As the complexity of the information increased from bacteria to mammals（i.e. genetic code）, the emergy costs of maintaining thecarrier increased faster, leading them to conclude that complexity of the carrier increases faster than the complexity of the information carried.

1.4 Form and Emergy

In this paper we suggest that the emergy required to create form can be separate from the emergy of the materials in the form. Form itself is relative. If we begin with the atom, then a certain configuration of atoms leads to the FORMation of a molecule, molecules form macro-molecules, which form cells, tissues, organs, organisms ecosystems, and so forth. Each successive form resides at a different hierarchical level and we might say that the form at any level is more complex than the form at the proceeding level, since it is composed of units of the proceeding level.

The same material can take on many different forms, which we might call parallel forms, and which we define as the reformation of the same material into different forms at the same hierarchical level （e.g. bottles, bags, pipes or toys made from the same polyethylene plastic）. The same material can also be formed into new products in a hierarchical sense, which we might call hierarchical forms （e.g. cellulose, made into paper, then combined into a book） where each form represents a different hierarchical level. By hierarchic forms we mean that each form is contained within a scalar hierarchy, wherein a form is derived from a given form, which in turn may give rise to yet another form.

Least we become totally entwined in a semantic knot of our own making, let us also mention that all substance has form. We may, however, add some clarity if we also state that a given object's scalar hierarchy might be measured by the emergy required to make it. We are implying that all “things”, or objects, have form that is separate from their substance. Further, form and substance are two different aspects of a given object.

1.5 Materials and Emergy

Odum suggested a Sixth Energy Law （or possibly a corollary to his proposed 5thEnergy Law） for material processing as follows： “Material cycles are hierarchically organized in a spectrum measured by emergy/mass that determines mass flows, concentrations, production processes, and frequency of pulsed recycle” （Odum, 2000）. In reviewing principles relating energy, emergy, and materials Odum states

“…any increase in concentration of a material requires an increase in the emergy per mass（typical units are emjoules per gram）. When concentration increases in some part of a biogeochemical cycle, the emergy per mass increases. When the material disperses … the stored emergy decreases. The amount can be calculated by estimating what emergy is required to restore its concentration. （Odum 2000）

The important aspect of Odum's reasoning was the next to last sentence…the fact that when a material is dispersed （or recycled） the stored emergy decreases. He suggests that the amount of decrease can be estimated as the emergy required to concentrate it in the first place. Thus, in a sense, he is stating that the form emergy is lost since he suggests that the amount of decrease in emergy of dispersed materials can be estimated by how much emergy is required to restore its concentration.

Figure 3 is an aggregated system diagram of a material and emergy transformation hierarchy. Dispersed materials on the left are upgraded at each step in the hierarchy increasing concentration and emergy per unit mass. Since, at each step in the hierarchy some of the material is dispersed the quantity decreases at each step, but its concentration increases. Concentrating the material on the left requires coupling of the material to some available energy. At each transformation step, more available energy is degraded than stored. The contributions of the available energy used up at each transformation step add emergy to the stored material and therefore the emergy of the material at each step has that of the each preceding step plus the available energy used up at that step. As a result the emergy per mass increases with each increase in concentration of material.

Fig. 3. A material and energy hierarchy. Materials are concentrated with each transformation, while increasing quantities of energy are required, thus emergy per gram increases. Two recycle pathways are shown, a dispersal pathway where the materials carry no emergy, and product recycle pathways where the materials carry some emergy as they are recycled.

1.6 Recycle Pathways and Emergy Accounting

There are two pathways of recycle shown in Figure 3, a product recycle and a dispersed recycle. The product recycle represents pathways of recycle where a material still has form and concentration that is distinguishable from background. In this case, materials have some availability and emergy, but as Odum （2000） suggested, they have lost some emergy relative to their previous state. Notice that the product from each level can recycle to all lower levels of the hierarchy. And while it is probably most likely that products recycle to only one or possibly two levels below their position in the energy hierarchy, it is conceivable that they can recycle to all levels.

We strictly define product recycle as the return of material to a previous stage in a cyclic process.

We define dispersed recycle as the return of materials to the environment through actions that distribute them over wider area.

In Figure 3 the pathways of product recycle flow back to the right in the energy hierarchy. They do not flow out of the system as products, nor do the pathways flow into a separate system. It is very important that this distinction be made. There are many definitions of recycle, which include collecting, processing and reusing materials that would otherwise be discarded as waste. This sometimes results in the material being further “upgraded”. By our definition of recycle, a material must be returned to a previous stage in a cyclic process. If a waste product is upgraded （for instance using garbage to generate electricity）, we do not consider this product recycle by our definition and as a result the “up-graded” output of this process carries all the emergy of the waste product input.

The General Principle for recycle pathways is：

A recycled material returned to a previous stage in its cycle loses all its emergy in keeping with the 5themergy accounting rule2Emergy Accounting rules are given as an appendixwhich states... within a system， emergy cannot be counted twice： a） emergy in feedbacks ［recycle pathways］ cannot be double counted， and b） co-products， when reunited cannot be added to equal a sum greater than the source emergy from which they were derived.

The second type of recycle, dispersed recycle, represents the flows of material that are collectively dispersed or recycled toward background concentrations in the environment （land, oceans, or atmosphere） on the left of the diagram. These material flows have little or no availability as they are very near background con-centrations. Odum （2000） suggested, that the state of dispersed material on the right “…h(huán)as no availability or emergy （relative to the earth）….It is at the lowest energy state in its biogeochemical cycle.”

The General Principle for dispersal pathways is：

The emergy of products and materials decreases as they are dispersed and is proportional to the degree of dispersal. At backgound concentrations all emergy of form is lost.

Please note that materials that are dispersed carry some emergy and depending how they are dispersed, they may still have a significant amount of emergy. For instance, consider chemicals released into the air or water...since they have higher concentration at the point of dispersal, they carry the emergy of their concentration, only when the materials have reached background concentration do they lose all their emergy. The emergy on the dispersal pathway decreases proportionally with concentration, with the highest emergy at the point of release and no emergy at background concentration.

1.7 Form Emergy

Figure 4 suggests that the emergy of the form of an object （product） can be evaluated separately from the emergy of the material. Generally, transformation process require inputs of materials, energy and information, and the product has the sum of the emergies of the inputs. However, we might separate the inputs for the purposes of evaluating the emergy in the form, into two input flows of emergy： （1） the emergy of the material, and （2） the emergy of the energy and information required to create the new form. The outputs （flows to the right） suggest that the use of the product and the recycle of it have different effects on the emergy of the form. When used, and or upgraded, the product carries the total emergy （emergy in the material and emergy in the form）. When recycled, the recycled product loses some form emergy.

Fig. 4. Form and matter might be considered separately when evaluating emergy of recycle. When matter is used, the emergy of the matter and the emergy of the form is used, however when recycled, the emergy of the matter is recycled, but the emergy of the form is used up.

The concept of form emergy has important implications relative to emergy evaluations of whole systems that include recycle. When a product is recycled, depending on the recycle pathway, the recycled product may lose some or all of its form emergy. We suggested in earlier work （Brown and Buranakarn, 2000） that when something is recycled, we value its emergy equal to the emergy of the inputs at the level of the energy chain to which it is recycled. Further, as long as an object is increasing in complexity or concentration it carries the emergy of materials and all the form emergy. Therefore, an object whose useful life is used up, but another use if found （for instance, cooking oil that is converted into bio-diesel） carries all the emergy required to make it. It is only recycle pathways and dispersal pathways that lose form emergy.

1.8 Products， By-Products and Co-Products

A product is something that is produced by, or results from a process. It is of higher quality than the materials that it is produced from, and is often referred to as having been “up-graded” from the input matter or energy. A by-product is an incidental or secondary product produced in a process in addition to the principle product. Generally it is not valued as highly as the product. A co-product is a product produced along with or jointly with a different product in a process in which both are valued. Figure 5 illustrates the different ways of showing products, co-products and by-products in a system diagram.

Fig. 5. Diagram illustrating difference between product, co-product and by-product.

2. Case Studies

We next provide two examples to make our case. The first is the unit process production chain that produces a vegetable, brings it to market, prepares and then consumes it. Our second example is the production chain of an aluminum beer can.

2.1 Case Study 1： Vegetable production （Broccoli）

Figure 6 shows the unit process chain diagram for the production of one serving （100g） fresh broccoli, beginning with the agriculture field and ending with human consumption （data are from Milà i Canals et al. 2008）. The process chain results in production of human service and human waste. Labor is not included in this evaluation. At each transformation step, emergy is added to the broccoli and the quantity of broccoli decreases. In order to provide a 100g serving of broccoli, the farm produces 195g of plant biomass of which only 133g is picked and transported to the regional distribution center （RDC）. There, 3g are lost and emergy is added for packaging and transport to the retail store, where another 2g are lost and emergy is added in the form of cooling, lighting etc. Once the broccoli is purchased, 28g are lost in the preparation, and cooking adds a significant quantity of emergy. Finally the broccoli is eaten, with the result that it contributes to the emergy of the human and produces 100g of human waste.

Fig. 6. Unit process chain diagram for the production of one serving （100g） fresh broccoli.

It is interesting to note that the single largest input to the emergy of the broccoli is the input during preparation （over 500% increase from 6.1 E10 sej to 3.9 E11 sej）. The emergy support of the human （2.1 E12 sej）, we assume it takes 15 minutes to eat the broccoli, is over 5 times that of the broccoli.

The following questions arise after considering the flow diagram：

What is the emergy of the “waste” or by-product broccoli at each step of the chain？

What is the emergy assigned to dispersed recycle？

What is the emergy of the broccoli consumed by the human？

2.1.1 Emergy of the “by-product” broccoli

The emergy of the by-products at each step depends on whether it is assigned to a product recycle pathway or a dispersed pathway. At the farm, the total broccoli grown to provide a 100 gram serving is 195 grams （see Figure 7a： 133 grams picked and shipped and 62 grams left in the field）. Therefore, the emergy assigned to biomass is the total input （5.1 E10 sej） divided by the total biomass （195 grams） or 5.1 E10 sej/195 g = 2.68 E8 sej/g. For the purposes of assigning emergy to the biomass left behind, the emergy is 2.68 E8 sej/g times the quantity （62 grams） or 1.62E10 sej. On the other hand, the emergy assigned to the broccoli florets （the portion we eat） is the total emergy required, thus the UEV of this flow is 3.83 E8 sej/g （5.1 E10 sej/133g） as it leaves the farm.

So the general principles to compute the emergy of farm products and wastes at the farm are：

1. Compute the emergy and UEV of agricultural by-products by treating them as a split of the total productivity, and

2. Compute the emergy and UEV of the upgraded product by summing all inputs and assigning that emergy to the product.

As the broccoli moves through the chain, the assignment of emergy to by-product follows the same algebra （see Figure 7b）. The emergy that is added at each step in the chain contributes to the concentration of the broccoli, from the farm to the distribution center, to the store, to the home and finally cooked and eaten. At each step the broccoli is more concentrated and therefore has higher quality. The by-products at each of the stages beyond the farm include the emergy of concentration. As shown in Figure 7b the emergy of the byproducts is computed like that at the farm. The total inputs are divided by the quantity of broccoli before the by-product is generated to compute its UEV. The remaining broccoli, that which is “upgraded” and shipped to the next step in the chain, is divided into the total inputs to obtain its UEV.

The general principles here are （refer to Figure 7b）：

3. Treat the by-product at each stage as a split of the total quantity after summing all inputs and assigning that emergy to the total quantity, the UEV is then computed by dividing the total emergy by the total material.

4. Compute the emergy and UEV of the upgraded product by summing all inputs and assigning that emergy to the product.

For the most part, there are no product recycle pathways within the farm to table production chain, as most by-products follow a dispersal pathway whether to composting, or solid waste land-fill. However some chains, the by-products at each stage can be used for another type of food, either for humans, or feed for animals, or fuel. In the latter cases, the by-products do not disperse, but are concentrated further and the by-products car-ry the emergy as computed above. If they are dispersed, then they lose their form emergy （see below）

Fig. 7. Details of the broccoli supply chain showing （a） the farm system and the UEVs for waste biomass and the broccoli florets； （b） the RDC where some broccoli is wasted （3g） and the UEVs for waste and “up-graded florets”； and （c） cooking and consumption where nearly 25% of the broccoli is wasted in preparation and 100% becomes human waste and the UEVs of waste and broccoli.

3.1.2 Emergy assigned to dispersed recycle

Dispersed recycle pathways no longer increase form or concentration, but instead are actions that disperse matter back toward background concentrations. By-products that are not up-graded, but instead are thrown away follow a dispersal pathway as does the broccoli converted to human waste （Figure 7c）. Along the unit process chain, at each step, the broccoli has become more concentrated from farm to the dinner table and therefore its emergy has increased. At the home preparation stage some of the broccoli is trimmed off and thrown away（28g）. That which is thrown away carries only the emergy of the previous stages in the hierarchy and does not carry the emergy of cooking （note that the split of the waste happened before the cooking emergy is added）. Further, at this stage in the chain, the broccoli changes form. Until this point, the broccoli form was being added to, that is, the emergy input at each stage was increasing its concentration and to a certain extent, increasing the information in the form. As the broccoli is cooked and then eaten, the broccoli loses its form （and of course some minerals and nutrients）, becoming less complex. We suggest that the emergy that is added to the broccoli during cooking and eating does not add to the value of the broccoli as human waste and that the UEV assigned to the human waste is the same as the UEV of the broccoli waste before cooking. If the human waste is dispersed by spreading on land, its stored emergy decreases.

The general principle here, is：

5. The emergy assigned to a material at its point of dispersal is the emergy of the material and all form emergy up to that point.

6. As a material becomes more dispersed, it loses its form emergy in proportion to its dispersal until it has only the material emergy related to background.

2.1.3 Emergy of broccoli consumed by humans

For the human to eat and enjoy the broccoli, it is trimmed （a loss of 28 grams） and cooked （Figure 7c）. The emergy assigned to the broccoli as it is consumed is the sum of the input broccoli emergy and the emergy of preparation. The emergy required to provide 100g of broccoli to the human is the sum of all the inputs and totals 3.9 E11 sej. Therefore the UEV of the broccoli at this point is 3.9 E9 sej/g （3.9 E11 sej/100g）. Note that we have included human support emergy （equal to 15 minutes of emergy support ［2.1 E12 sej］, the time necessary to consume the broccoli） in the diagram. The life support emergy is NOT assigned to the human waste, but is assigned to the output of human labor. The emergy of the broccoli is relatively small compared to the human life support emergy （and in reality would be double counted if added since the human life support emergy includes all food as well as other emergy inputs）.

2.2 Case Study 2： Aluminum can

Figure 8 shows a unit process chain diagram for the production of one aluminum can that includes the material and energy inputs beginning with bauxite in the ground and ending with the production of the can （data are from PE Americus, 2010）. The can weighs 1.5 g and holds 0.36 liters of beer. In the final two stages of the unit processes the can is filled with beer and the beer is then consumed by a human, which results in the “production” of human service, an empty beer can, and a quantity of urine. Labor is not included in this evaluation. The largest single input is the input required to produce the aluminum ingots （6.6E11 sej）. It is interesting to note that the emergy in the can is almost equal to the emergy in the beer. Emergy of the beer is 8.7 E11sej/can, while the emergy in the can is 8.0 E11 sej. Also the emergy supporting the human （2.1 E12 sej： we assume it takes 15 minutes to drink the beer） is about 2.4 times the emergy of the beer （8.7 E11 sej）.

Similar questions, as those for the broccoli, arise.

1. What is the emergy assigned to the by-products at each stage in the chain？

2. What is the emergy of the recycled can？

3. If the can is reused without recycling （i.e. it is used for another purpose）, what is its emergy and UEV？

4. What is the emergy of the beer when consumed by the human？

5. What is the emergy of the urine？

Fig. 8. Unit process chain diagram for the production of one aluminum beer can. Flows are in 1 E9 sej （top of flow） and grams （below flow）. Numbers in parentheses are UEVs of the output from each process.

Fig. 9. Details of the aluminum can supply chain showing （a） the production of alumina and the UEVs of the product and waste and （b） the UEVs of the finished can, filled with beer, human consumption and （c） the first stage in recycle where the can is crushed. Numbers in parentheses are UEVs of the output from each process.

2.2.1 Emergy of by-products

Notice in Figure 8 that at each stage in the unit process chain there are by-product flows （we are unsure if there are aluminum by-products from the can filling stage, thus we have not assigned any at this stage）. For clarity, we have reproduced several detailed unit processes to emphasize the by-products as shown in Figure 9. The top figure （Figure 9a） is typical of most of the unit processes. The form of the input material flow is changed （up-graded） into a more complex form with the input of emergy. The UEV of the by-product flow is computed after the addition of the up-grading emergy, therefore the UEV is the total emergy （sum of the material emergy and the up-grade emergy） divided by the total quantity of material, in this case 120g, yielding a by-product UEV of 6.6 E8 sej/g. The UEV of the up-graded material （aluminum oxide） is the total emergy divided by the quantity of up-graded material, or 7.9 E10 sej / 44g = 18.0 E8 sej. The by-products and upgraded materials at each step in the unit process chain are computed in this way.

At this point, the by-products may follow either a product up-grade, in which case the emergy assigned to them before further upgrading is the by-product emergy. Or they may follow a dispersed pathway in whichcase they lose some of their form emergy in proportion to the degree of dispersal. Or they may follow a product recycle pathway, in which case, they may eventually lose all their form emergy.

2.2.2 Emergy of the can as it is recycled

As the can and its contents can be easily split （Figure 9b）, we assume that the emergy of the empty can is 8.0 E11 sej （5.3 E11 sej/g）, however as soon as the can is crushed （Figure 9c）, we suggest that the form is lost and the emergy stored in the form is lost. The quantity of form emergy lost depends on how much emergy would be required to remake the form （Odum, 2000）, and we suggest that, in essence, what this means is that the quality of the can is reduced and some of it's stored emergy is lost. In this case we assign the emergy of sheet aluminum （4.5 E10 sej/g）. This is not to say, it is sheet aluminum, only that it has lost the emergy of the can form. In reality the crushed can will be shredded and re-melted （we will deal with this in a moment）.

The general principle here is：

When materials lose their form, they lose the form emergy in the material equal to that required to re-make the form.

2.2.3 Emergy of the beer consumed

The emergy of the beer （8.7 E11 sej） was estimated from data given by Kl?verpris et al. （2009）. The emergy assigned to the beer that is consumed by the human （1.67 E12 sej） includes the emergy of the can （8.0 E11 sej）, since one cannot have the beer without the can.

2.2.4 Emergy of the urine

Here we assume that all the beer becomes urine （Figure 9b）. The question arises, should the emergy of the urine include the support emergy （2.1 E12 sej） and the emergy of the can or only that of the beer？ We suggest that only the emergy of the beer （8.7 E11 sej）, not including the can, and not including the human support emergy be assigned to the urine since the beer and the can are easily split, and the human does not consume the can. The concentrated urine carries the emergy of the beer （UEV=8.7E11/355g = 2.45 E9 sej/g）, but as soon as it is dispersed （ie diluted with water, or spread out in the environment） its stored emergy is reduced in portion to its reduction in concentration.

2.2.5 Emergy of human service

Human service requires all inputs, thus we suggest that the emergy of human service would include the beer plus can, however since the human support emergy was computed from average emergy support, which would include, on average, the beer consumed in this short 15 minutes, we would not add the beer as it would be double counted.

2.3 Case Study 3： The recycled can

Once the can has been crushed, it no longer carries the emergy of the form of the can （Figure 9c）. Prior to crushing, the can carries all the emergy of the material and form. Upon crushing, the can loses a portion of the form emergy and carries only the emergy of the material and the form that it most closely resembles. Since it resembles sheet aluminum having lost the form of the can, we assign the UEV of sheet aluminum （4.5 E10 sej/g） to compute the emergy of the crushed can equal to 4.5 E10 sej/g * 1.5g = 6.8 E10 sej. The difference between this value and the emergy of the can （8.0 E11 sej/g） is the form emergy that is lost （8.0 E11 sej - 6.8 E10 sej = 7.3 E11 sej） upon crushing the can.

Following questions arise：

1. If the crushed can is recycled, what is the emergy and UEV of the crushed can when it re-enters the aluminum unit process chain？

2. How does the emergy and UEV of the final product （can） change with recycle？

Fig. 10. Unit process chain diagram for the production of one aluminum beer can when recycle rate is 50%. Flows are in 1 E9 sej （top of flow）and grams （below flow）. Numbers in parentheses are UEVs of the output from each process.

Fig. 11. Comparison of the emergy required to make one aluminum can from bauxite vs. making the can from 50% bauxite and 50% recycled aluminum.

2.3.1 Emergy and UEV of the recycled crushed can

Figure 10 shows a closed cycle where 50% of the needed raw materials comes from recycle of the can and scrap aluminum sheet. Notice that since it takes over 24 g of melted aluminum to make one 1.5 g can, therefore, one can （1.5 g） and 10.8 g of scrap aluminum sheet （total 12.3 g） are recycled to achieve a recycle rate of 50%.

The emergy assigned to the recycled can and scrap aluminum as it enters the shredding and decoating unit process is zero （0.0）. This is because in a closed system, once recycle pathways close a loop, their emergy cannot be counted twice. So the emergy of the can and scrap aluminum sheet is “l(fā)ost” in the recycle process. Notice also that as a result of recycle, the quantity of bauxite and the energy required to mine and melt it is reduced by half when compared to the aluminum can system in Figure 8. The emergy required to shred and re-melt the aluminum can and scrap is minor compared to the emergy required to melt the same quantity of alumina. Figure 11 shows the benefit of recycling. The top figure （Figure 11a） is a summary of the inputs to produce an aluminum can from bauxite and the bottom figure （Figure 11b） the inputs required to produce the can when 50% of the aluminum required is recycled.

There is a difference in the total emergy required to make an aluminum can of 348 E9 sej when the can is produced from bauxite only compared to a can produced with 50% recycle of scrap aluminum. The can made from 50% recycled aluminum requires about 46% less emergy to make. As a result the UEV of the can made from 50% recycled aluminum is 3.0 E11 sej/g compared to 5.3 E11 sej/g for the standard can.

3. Summary

We suggest that “form” is information and that the emergy in form is distinct from the emergy of materials that make up the form. Emergy stored in form can be evaluated as the emergy added to a product over and above the emergy of the material. Form of a material requires both energy and information to shape it. Stored emergy of form is lost when the form is consumed, but the emergy of the material is maintained.

Concentration in time and space increases the emergy of matter. Supply chains of unit processes are energy hierarchies that “upgrade” the form of materials and products and in the process increase their spatial concentration. Products and by-products, alike, have higher emergy at each step in an energy hierarchy. At any hierarchical step where the product or material is “downgraded” the stored emergy in form and concentration begins to disperse. The rate that emergy decreases is proportional to the decrease in form and in concentration.

Three case studies were explored, an agricultural unit process chain that produced a vegetable for human consumption, a unit process chain that produced an aluminum can, and similar aluminum can chain where 50% of the materials came from recycled aluminum. At each step in these chains, the emergy of products and by-products increased until the last step when the products were consumed. A method was proposed to compute the emergy and UEV of products and by-products at each step in the unit process chain as follows：

· Any product or by-product that is used for another purpose and is up-graded, carries all its emergy, its form emergy and its material emergy.

· Products and by-products that are recycled to a previous stage in their cycle lose all their emergy, however, emergy may be added to recycle them.

· Products and by-products that are dispersed lose their emergy in proportion to the change in form and/or their concentration relative to the background

When the intended use of a product is used up, for instance when food is consumed to support human work, the resulting by-product （human waste） is downgraded food, which loses some of its form emergy. However, if the downgraded product is then used in another process such as the production of methane gas, the human waste carries all the emergy of the food. It is necessary to distinguish between dispersal pathways and pathways where “wastes” are further up-graded to accurately account for the emergy of the materials. Dispersal pathways lose form emergy, while pathways which up-grade products or by-products increase stored emergy.

We distinguish between product recycle pathways and dispersal pathways. A product recycle is the return of material to a previous stage in a cyclic process. This implies that it is within the same system boundary.When recycled, the material has no emergy based on the 5themergy accounting principle. Material that follows a dispersal pathway loses emergy in proportion to it's concentration （or hierarchical level） until it reaches background concentration, in which case the stored emergy in its form is zero.

In a whole system context, we show the benefit of recycle and suggest that proper accounting of recycled materials requires a whole system perspective. In the case of the aluminum can, the recycled system used less emergy than the production system that did not recycle aluminum.

While these principles may seem to be a new approach, or result in a new emergy algebra, they are not, we are simply, 1） restating the fact that when material is cycled, it's emergy cannot be counted twice and 2） acknowledging Odum's （2000） statement related to material cycles....when materials are dispersed, they lose some of their stored emergy.

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Appendix： Emergy Accounting Rules

Rule 1： Emergy is the available energy （exergy） of one kind that is used up in transformations directly and indirectly to make a product or service.

Rule 2： In processes having one output， all independent emergy inputs are assigned to the processes' output.

Rule 3： When a pathway splits， the emergy is assigned to each branch of the split based on its percent of the total available energy flow （or mass） on the pathway before the split.

Rule 4： In processes having two or more co-products， all independent input emergy is assigned to each coproduct.

Rule 5： Within a system， emergy cannot be counted twice：

（a）emergy in feedbacks cannot be double counted

（b）co-products， when reunited cannot be added to equal a sum greater than the source emergy from which they were derived.

30 June 2014

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Email address： mtb@ufl.edu

ISSN 2325-6192, eISSN 2325-6206/$- see front materials ? 2012 L&H Scientific Publishing, LLC. All rights reserved.

10.5890/JEAM.2015.03.004

Accepted 18 August 2015

Available online 1 September 2015