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May 28, 2014 - Open-loop recycling is subject to loss of functionality of original materials, dissipation in forms that are difficult to recover, and ...
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MaTrace: Tracing the Fate of Materials over Time and Across Products in Open-Loop Recycling Shinichiro Nakamura,*,† Yasushi Kondo,† Shigemi Kagawa,‡ Kazuyo Matsubae,§ Kenichi Nakajima,⊥ and Tetsuya Nagasaka§ †

Graduate School of Economics, Waseda University, Tokyo, Japan Graduate School of Economics, Kyushu University, Fukuoka, Japan § Graduate School of Engineering, Tohoku University, Sendai, Japan, and ⊥ Center for Material Cycles and Waste Management Research, National Institute for Environmental Studies, Tsukuba, Japan ‡

S Supporting Information *

ABSTRACT: Even for metals, open-loop recycling is more common than closed-loop recycling due, among other factors, to the degradation of quality in the end-of-life (EoL) phase. Open-loop recycling is subject to loss of functionality of original materials, dissipation in forms that are difficult to recover, and recovered metals might need dilution with primary metals to meet quality requirements. Sustainable management of metal resources calls for the minimization of these losses. Imperative to this is quantitative tracking of the fate of materials across different stages, products, and losses. A new input-output analysis (IO) based model of dynamic material flow analysis (MFA) is presented that can trace the fate of materials over time and across products in open-loop recycling taking explicit consideration of losses and the quality of scrap into account. Application to car steel recovered from EoL vehicles (ELV) showed that after 50 years around 80% of the steel is used in products, mostly buildings and civil engineering (infrastructure), with the rest mostly resided in unrecovered obsolete infrastructure and refinery losses. Sensitivity analysis was conducted to evaluate the effects of changes in product lifespan, and the quality of scrap.

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INTRODUCTION A chemical element is basically stable and indestructible unless it undergoes natural radioactive decay or a nuclear process. As chemical elements, it may seem possible to recycle metals many times without losing functional quality, that is, in a closed-loop. In reality, however, open-loop recycling is typical for many of the metals used in consumer goods such as electronics or cars. Qualitative degradation of recovered scrap metals due to uncontrolled mixing of different metal species at the end of life (EoL) phase (dismantling, liberating, shredding, sorting, etc.) is its main cause.1−8 Open-loop recycling is associated with various types of material losses: loss of original functionality, dissipation of scarce resources, and the eventual need for dilution of recovered materials with primary materials to meet quality requirements.9−11 Sustainable management of metal resources calls for the minimization of these losses. Imperative to this is quantification of the dynamic flow of materials, that is, quantitative tracing of the fate of materials over time across products and different types of losses. This is the task of dynamic material flow analysis (MFA). Dynamic MFA has been successfully applied to reproducing historical flows and stocks of various metal resources and projecting their possible future developments at both national © 2014 American Chemical Society

and global levels accommodating the EoL phase and subsequent recycling.12−20 These studies did not trace the fate of metals contained in EoL products over successive rounds of recovery, refinement, and open-loop recycling, accounting for the losses incurred during every transformation process. Reuter et al. developed a sophisticated dynamic model of material cycles that fully accounts for physical- and thermodynamic constraints, detailed process knowledge, and product design including details on the ways in which parts and components are bonded/jointed, with application to cars,1,4,21,22 solders,23 and electronics24 (for a recent review, see refs 25 and 26). Their approach is distinguished by the rigorous consideration of the processes in which EoL products are converted into refined materials, inclusive of all byproducts and interconnections among relevant processes. The model can thus assess the quality of resulting scrap, based on a wide range of technological parameters relevant to product design and conversion processes. That model was not explicitly concerned Received: Revised: Accepted: Published: 7207

February 17, 2014 May 28, 2014 May 28, 2014 May 28, 2014 dx.doi.org/10.1021/es500820h | Environ. Sci. Technol. 2014, 48, 7207−7214

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successive rounds of recycling throughout the 100 years. To the best of our knowledge, this is the first IO-based MFA study to enable visual tracking of the fate of materials in this manner.

with tracing the fate of materials over successive rounds of open-loop recycling involving multiple products. Tracing the fate of materials over successive rounds of openloop recycling has been the focus of MFA studies based on Markov Chain (MC) modeling.27−31 Central to MC-based MFA is the Markovian transition matrix that encompasses all of the life stages of materials. With regard to mapping of materials to corresponding use categories, the transition matrix of the MC-based MFA, or its submatrix excluding the EoL and recycling phases, is identical to the product-to-uses-matrix in standard MFA.15,18 In both standard MFA and MC-based MFA, this matrix is obtained from various sources without resorting to any generic mathematical model, which makes it rather difficult to consider possible changes in technology, final demand, and institutional setting. While MC-based MFA can estimate the number of times materials are utilized, its formulation is static. MFA is closely connected to input-output analysis (IO).32,33 One advantage of IO is its provision of a general mathematical model for the product-to-use-matrix, meaning it can accommodate possible change in technology, final demand, and institutional setting in a highly transparent manner.34 Based on our previous studies,11,35,36 this study presents an IO-based dynamic model of MFA that can trace the fate of materials over time and across products in open-loop recycling, with explicit consideration of losses and quality of scrap. Figure 1 depicts the architecture of the model.

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THE MODEL Recovery of Materials from EoL Products. Write xj(r) for the mass of the material under consideration in final product j produced at time r, and ϕj(s) for the fraction of product j that is discarded after s years of use with ∑S∞= 0ϕj(S) = 1. The amount of material that occurs in EoL product j generated at t, zj(t), is then given by t

zj(t ) =

∑ φj(t − r)xj(r), (j = 1, ..., n; t = 1, 2, ...) r=0

(1)

where n is the number of final products, and the initial value xj(0) is given. Let ns be the number of scrap types that are recoverable from EoL products, and γsj ∈ [0,1] be the recovery yield of scrap of type s from EoL product j: the remainder (1 − γsj) × 100% is unrecovered, and is not recycled. The amount of scrap s recovered from the EoL products in year t is given by n

∑ γsjzj(t )(j = 1, ..., n; s = 1, ..., ns) (2)

j=1

Writing Γ for an ns × n matrix with γsj as its (s,j)-element, and z(t) for an n × 1 vector of zj(t)’s, the amount of ns types of scrap recovered in year t is given by Γz(t). While γsj can be further divided into yield of scrap recovery from collected EoL products and the yield of the collection of EoL products, for the sake of simplicity and availability of data they are not distinguished in this study. Recovered scrap thus obtained is then allocated to nR refining (recycling) processes with each of which producing a single refined material. Denoting by B an nR × ns matrix with its (i,j)element bij ∈ [0, 1] referring to the share of recovered scrap j allocated to the refining process i, and by θi ∈ [0, 1) the yield of this process, the amount of refined materials obtained from EoL products is given by the nR × 1 vector:

θB̂ Γz(t )

(3)

where θ̂ is a diagonal matrix with θi as its i-th diagonal element. By definition, for an nR × 1 vector of unities ιR, ιTRB=ιTs , since each type of scrap is entirely allocated to the refining processes (aT refers to the transpose of a vector a). Use of Recovered Secondary Materials. The refined secondary materials thus obtained are now ready to be processed into products. Ultimately, all the products are destined to become final products except the small fractions of materials discarded as production losses. The amounts of refined materials destined to a final product are proportional to the material content of the product. Let C be an n × nR matrix of the composition of final products in terms of refined materials, with its (i,r)-element cir referring to material r mass of a unit of final product i. Let y be an n × 1 vector of final demand with yi as its i-th element. Multiplication of y by C gives an nR × 1 vector with its i-th element referring to the amount of refined material r that is embedded in the final demand. The allocation of refined materials to the final products, or the material composition of final products, is then given by the n × nR matrix D:

Figure 1. Dynamic model of the flow of materials across products. The ovals denote the flow of inputs and outputs, rectangles denote processes where inputs are transformed into outputs, and hexagons denote allocation processes. Collection- and separation processes are combined into a single compartment due to data availability and simplicity. Greek symbols indicate parameters referring to relevant processes: γ, θ, λ, and ξ are process yield ratios, B is allocation of scraps to refinery processes, and D is allocation of refined materials to products. The symbols correspond to those used in the next section, except for some simplifications due to limited space.

The model is implemented to track, over a 100-year period, the fate of steel that was initially part of a car. Car steel was selected because it represents the largest use of high-quality steel produced via integrated use of blast furnace (BF)- and basic oxygen furnace (BOF) processes.37 Moreover, the extent of closed recycling of this material is known to be limited.11 The choice of the 100 year timespan was motivated by the long lifestimes of steel products.20 The fate of the car steel is tracked by visualizing the changing location of the material across different categories of final products and losses during

D = yC ̂ diag(y T C)−1 7208

(4)

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By definition, ιTn D = ιTn ŷC diag(yTC)−1 = yTC diag(yTC)−1 = ιTR, where ιn refers to a n × 1 vector of unities. The allocation matrix of materials to final products D is of critical importance in the dynamic MFA, and its estimation poses a great challenge. The MFA literature employs various terms for this important matrix, including “branching ratios” used by ref 38, “sector split coefficients”,39 “the share of each respective end use”,17 “product-to-uses matrix” (PTUM),15,18 and “the distributions of resources among consumption products”.40 Except for ref 40, that used IO to estimate D, all of the studies cited used estimates derived from published data sources, back calculations, expert interviews, and the prior literature. In this study, the material composition matrix C was estimated using WIO-MFA34,35 from the matrices of input coefficients referring to the inputs of products to products APP and to the inputs of materials to products AMP: ̃ (I − APP ̃ )−1 CT = AMP

where Ξ is an ns × n matrix with its (s,j)-element, ξsj, referring to the recovery yield of scrap s in the production process of product j. Accompanied with the flow of materials into products is the flow of materials that are no longer in use. Specifically, this includes the flow of losses occurring in the collection of EoL products, the refining of scrap, and the manufacturing of final products. Henceforth, losses refer to the portion of materials that are no longer in use as products. For t ≥ 1, the amount of aggregate losses occurring in t is, S(t ) = ιnT(z(t ) − x(t )), which can be divided into its components (see SI for details):

(5)

where γ = ιTS Γ. To the best of our knowledge, eqs 8 and 9 with z(t) given by eq 1 represent the first IO-based dynamic MFA model with open-loop recycling that explicitly takes into account scrap quality and losses incurred during the conversion processes. Because the model given by these equations aims to trace the fate of materials, it will henceforth be called the MaTrace model. The model can accommodate changing consumer behavior and market conditions by changes in the elements of matrix D (see eq 4). Thermodynamic constraints in the allocation of scrap to refining processes are also taken into account in the elements of matrix B, the technical foundations of which can be provided, among others, by our previous studies on the behavior of metals in refining processes based on thermodynamics.44 Changes in product design and technological innovation can be accommodated by matrices A and D. Transition in the products destination of material over time was addressed by refs 27−31 based on a Markov chain model with the Markovian transition matrix representing the probability by which material is allocated to alternative destinations. Matrix D in MaTrace can be regarded as equivalent to the submatrix excluding the EoL phase of the “transition probability matrix” of the Markov chain model (or absorbing Markov chain, AMC) used in those studies. MaTrace would reduce to an MC with a constant transition matrix if D is constant over time and the lifetime distribution is independent of vintage. Duchin and Levine40 incorporated a Markov chain model into the framework of IO, but without considering recycling and the generation of losses. Our derivation of D in eq 4 closely resembles their approach, except that MaTrace considers the presence of nonphysical flows and yield losses. Henceforth, it is assumed that the pattern of final demand represented by D is exogenously given to MaTrace, and is not affected by the generation of EoL products and recycling thereof: whatever amounts of materials are recovered can be absorbed by the final demand without causing any noticeable changes in the supply and demand conditions including the balance of scrap. This assumption is implicit in dynamic MFA13,14 and MFA-based MC models.27−29 It can be justified if the amount of materials recovered from an ELV is “small” relative to the demand for relevant materials in the whole economy, such that any change in the former would be negligible. This refers to the ceteris paribus assumption that is implicit in many LCA studies.45,46 A possible method of

where à IJ refers to the technical coefficients matrix AIJ that was adjusted to exclude nonphysical flows and yield losses.34,35 The WIO-MFA model, and hence C, is highly flexible in terms of resolution, provided that the corresponding data are available: previous applications include PVC,41 Ni, Cr, and Mo in steel alloys,37,42 and iron and aluminum in international trade.43 Duchin and Levine40 proposed a similar estimation procedure, but without adjustments for nonphysical flows and yield losses. Cullen et al.18 is similar to our approach in their use of matrices and consideration of yield losses. Multiplication of eq 3 by D gives the amount of refined materials available to become final products. In the absence of manufacturing losses, this gives the amount of final products that can be obtained from secondary materials recovered from EoL products x(t ) = DθB̂ Γz(t )

(6)

or, for its k-th element, final product k:

For the sake of simplicity, this paper deals with the case of a single material, where xj(t) is a scalar. Generalization to the case involving m > 1 types of materials can be facilitated by extending xj(t) to a 1 × m vector of materials by use of the composition matrix C, with corresponding extensions and modifications of model parameters (see the Discussion section for further details). An IO-Based Model of Dynamic MFA: MaTrace. Considering losses incurred in the production of final products, with λi ∈ [0, 1] referring to the yield ratio of final product i, the overall equation of the evolution of materials including the recycling of both process- and EoL wastes becomes (see the Supporting Information (SI) for detailed derivation) ̂ −1DθB̂ Γz(t ) x(t ) = λ (̂ I − DθB̂ Ξ(I − λ ))

(8) 7209

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parameters over the next 100 years were used for the baseline scenario, with the parameter values mentioned above used as initial values. Based on the findings by refs 17 and 47 that per capita in-use stocks of steel have saturated or close to saturation in many developed countries including Japan, possible developments of domestic final demand for steel-related final products were projected based on population projections.48 Export demand was assumed to remain unchanged (see SI for further details and the results). For parameters related to technology and lifetime, the following were assumed: The use of steel in a car decreases by 20% in 20 years due to improvements in steel (e.g., increased use of high-tensile steel49) and possible substitution by nonferrous materials. In line with the World Steel Association,50 the recovery rate Γ of EoL civil engineering objects increases from the initial 46.6% to 80% in 50 years. Quality enhancement of scrap due to the use of advanced sorting technology and product design increases its use in BOF from zero to the level equal to EF ordinary steel processes (37.5%) in 50 years. In 20 years, improvements in production- and maintenance technologies extend the average product life of a car from 12 to 15 years, and the life of buildings and civil engineering from 29 and 39 years to 60 years. This was implemented by allowing the scale parameter of the Weibull density to vary with the year of production. Results. The Evolution of Car Steel in EoL Products and Its Destinations. Figure 2 shows the evolution, under the

overcoming this limitation will be briefly mentioned in the Discussion.

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THE STOCK The stock of xi(r), r ≤ t, in use at t, xi̅ (t), gives the stock of material being used (resident) in product i at t: t

xi̅ (t ) =

t−r

∑ (1 − ∑ φi(s))xi(r) r=0

s=0

(10)

The stock of losses (i.e., the cumulative losses) at t is t S ̅ (t ) = ∑r = 0 S(r ). The conservation of masses implies for any t ≥ 0: n

∑ xi̅ (t ) + i=1

n

S ̅ (t ) =

∑ xj(0) j=1

(11)

The right side of eq 11 gives the initial endowment of the material in the system, while the left side gives its allocation over time until year t into products and losses.

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DATA AND RESULTS MaTrace is implemented for ferrous materials embedded in a passenger car by use of Japanese data. Since steel produced via the integrated use of BF- and BOF processes is the major ferrous input used in cars, namely, car steel,11,37 this case study traces the fate of BOF steel across products over time, similar to ref 29, whose concern was the fate of BF crude iron. For illustrative purposes, xj(0) = 100 kg for j = passenger car, and xj(0) = 0 for all other products. The path of evolution was calculated at 100 years, the choice of which was motivated by the long economic life of buildings and civil engineering objects (according to ref 20, a time horizon of at least 60 years is required). Data. The model was implemented for the WIO-MFA database with some 400 sectors, which was developed based on the Japanese Input-Output Table for 2005.42 The five types of EoL ferrous scrap in the database were aggregated into a single type, termed old scrap, which implies ns = 1. In accordance with ref 29, cars, buildings, civil engineering, machines, containers, and others were considered as final products of significant importance for ferrous materials (see SI for details on the definition of these product categories). Based on the WIOMFA calculation, it was found that 99% of the flow of EoL iron and steel scrap was ultimately destined for these six categories of final products. The initial values for parameters referring to the recovery of EoL products and process waste were taken from the literature (see Table S3 of SI). The lifetime density function ϕ (t) was specified by the two-parameter Weibull density.14 With the value of shape parameter set equal to 5 based on the literature,14 the scale parameter was obtained by equating the mean lifetime to the average lifetime. For refining (recycling) processes to which recovered scraps are allocated, we considered six steel processes: BF crude ordinary steel, BF crude special steel, EF crude ordinary steel, EF crude special steel, forged steel, and cast steel. The (initial) allocation and yield ratios of these processes were taken from ref 42. Further details, including the chosen values of parameters, and the allocation of intermediate products and secondary materials to final products, are given in SI. MaTrace is a flexible, multilevel material-flow model that can accommodate changes in final demand compositions, technology, and lifetime distributions. Possible changes in these

Figure 2. Evolution of the amount of car steel in EoL products and its destination for new products and losses (as percentages of the initial production in year 0). Results of baseline scenario.

baseline scenario, of the amount of car steel in EoL products, z(t) (eq 1), and its destination for new products, x(t) (eq 8), and losses, S(t ) (eq 9), since its initial occurrence in a car in year 0. The use in products includes both domestic and export uses. The amount decreases over time because a portion is lost during cycles of the recovery- and refining processes that are repeated when products reach the ends of their lifetimes. The portion of recovered car steel recycled into a new car turned out to be fairly small, around 7−8%, confirming the limited extent of closed-loop recycling (Table S6 in SI gives detailed numerical results). The portion recycled was predominantly destined for use in machines, civil engineering, and buildings. Because the use in the categories “Containers” and “Others” happened to be small, they were aggregated into “Others”. 7210

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After 20 years, the portion residing in cars dropped to less than 8% of the stock, with more than 80% residing in buildings, civil engineering, and machines. Around 10% of car steel resided in refinery losses. After 50 years, around 80% of the stock was still used in products, with buildings and civil engineering accounting for the vast majority. The remaining 20% was diverted to losses, of which 30% was in recovery losses and 70% in refinery losses. In 100 years, the share of products dropped to around 60%, with the rest mostly occurring as unrecovered EoL civil engineering and Others, and refinery losses. Changes in the structure of final demand caused by the projected decline in population size (detailed in SI) result in the declining share of buildings and a slight increase in the share of machines. Integration of the individual curves in Figure 3 over different intervals of years gives the share of location, or residence probability, of car steel among products and losses over different periods of time (Table S6 of SI). In the first 20 years following initial production, the residence probability in products was around 96%. Averaged over 100 years, it declined to 78%, with cars accounting for 15%, civil engineering 28%, buildings 26%, and machines 8%. Of the remaining 22%, 9% was in recovery losses, with civil engineering 2%, and 13% in refinery losses, with EF steel production 5%. The large share of EF steel in refinery losses corresponds to its dominant share in scrap use (Table S5 in the SI). EF steel losses mostly take the form of oxides/chlorides such as slag and dust, the recycling of which is reasonably well established.51−53

Production losses turned out to be negligibe, and were not visible. Recovery losses became visible after around 20 years, and remained at levels comparable to refinery losses. The pattern of evolution is characterized by three peaks. The first peak (at 12 years) is both the highest and the sharpest; it corresponds to the mean life of a car, and represents the first generation of ELV scrap (Figure S3 of SI gives the composition of z(t) in terms of EoL products). The negligible share of recovery losses in this round of recycling could be attributed to the high recovery rate of ELVs. The second peak (at 25 years) is much smaller and less pronounced than the first peak, and corresponds to the second-round generation of scrap originating mostly from machines, the majority of which was produced at the time of the first peak. The noticeable increase in recovery losses could be attributed to the lower recovery rate of EoL machines compared to ELVs (see Table S3 of SI for details). The third peak (at around 70 years) is much flatter than the second one and maight be better desctibed as a plateau; it corresponds to the third-round generation of scrap, mostly from EoL machines, buildings, and civil engineering objects of different age groups. Gradual extension of the lifetime of buildings and civil engineering objects contributes to the coexistence of many EoL items with different lifetimes, with the result that scrap generation plateaued. The gradual increase in the use-share of machines (and, to a lesser extent, cars) is attributed to the increased use of steel scrap to produce BOF steel as a result of improvements in scrap quality. Transitions in Stock Composition. Because of the mass conservation condition (eq 11), the stock of car steel used in products (eq 10) and the cumulated losses always add up to the initial amount of car steel. Using this property of MaTrace, Figure 3 shows the transition among different products and

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DISCUSSION Sensitivity Analysis. The case study was based on a set of assumptions on the implementation of changes and improvements in technology, including extended product lifetime. The results were subjected to sensitivity analysis to assess the significance of these assumptions. Figure 4 shows the results for

Figure 3. Transition in the composition of the stock of car steel originally used for passenger cars in products and losses. Exports are assumed to follow the same product lives and are submitted to the same EoL and recycling processes as in Japan. Results of baseline scenario.

losses of the location (or residence) of the stock of car steel during 100 years. This figure is obtained from Figure 2 by integrating the flow of products, weighted by the probability of survival (eq 10), and the losses. Following ref 29, it was assumed for simplicity that exported products follow exactly the same product lifecycles and EoL treatments as their domestic counterparts. After 15 years, with cars reaching the end of their lifetime, the fraction of car steel used in cars dropped to around 20% of the stock, with buildings, civil engineering, and machines occupying the rest, with no noticeable emergence of losses.

Figure 4. Results of sensitivity analysis.

the probability of residence in products and losses over 100 years: “No changes” refers to the case where the parameters for technology and lifetime are fixed at their initial values; “Lifetime” refers to the case where only the parameters referring to lifetime and recovery change, as in the baseline scenario, and the remaining parameters fixed at their initial values. Analogously, “Scrap quality” refers to the case where only the parameters referring to scrap quality change as in the baseline scenario. The result of changes in other technology 7211

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knowledge. One possible way of extending MaTrace along this line is briefly sketched in the SI, including a numerical example. Multimaterial extension of MaTrace can be facilitated by explicit consideration of the processes by which the materials embodied in EoL products are converted into new products and losses through scrap generation- and refining processes. It is usual that an EoL product is first disassembled into its parts and components (of varying depths and degrees of disassembly and liberation) before being converted into different scrap categories based on some sorting criteria. Accordingly, the composition details of scraps will depend on those of parts and components, and the way in which these are sorted among different scrap categories. Using WIO-MFA, the composition of a product in terms of its parts and components can be obtained from matrix à , and the material composition of parts and components from matrix C.34,42 The way in which the parts and components are sorted into different scrap categories can be represented by a product-specific mapping matrix, say, Γj. The allocation of different categories of scraps to refining processes, that is, the elements of matrix B, can then be obtained based on constrained optimization techniques.1,57−60 Extending the lifetimes of buildings and civil engineering was found to have significant effects on the residence time of car steel in products. Since the expenditure for these items represents a significant portion of GDP, their life extension, if extensively applied, would have far-reaching effects on the size and composition of final demand, and alter the allocation of materials to final products as represented by matrix D. The supply and demand balances of scrap would also be affected: however, such repercussions were ignored in the present study, under the assumption of ceteris paribus. For MaTrace to address these important aspects, it needs to be integrated into a fully dynamic IO model that is capable of considering the economywide scrap balances. An important recent contribution in this direction is a dynamic WIO model with endogenized generation of EoL products and scraps.61 For the sake of simplicity, it was assumed that the material embodied in exports would follow the same lifetime and EoLand recycling processes as in Japan, which will not hold in reality. Worldwide MFA has become significant with increases in the borderless movement of materials.17 Extension for MaTrace into a multiregional MFA model can be facilitated based on the framework of Multi-Regional-IO (MRIO),62−64 where x is divided not only by products but by countries; the parameters referring to technology and lifetime, A, Γ, and ϕ, extended to take into intercountry differences, and the parameters referring to refinery- and use destinations, B and D, are extended to take into account the export of scrap, materials, and final products. Data availability is always a challenge for this sort of IO-based analysis. For instance, no IO tables, including those for Japan,65 Korea,66 and the US,67 have resolution at the level of individual metal species except for major ones like iron and aluminum. Hybrid approaches, where IO data are combined with detailed process-level data,68,69 should be used to cope with this challenge.

parameters is not shown because the effects were negligible. In all the scenarios, the composition of final demand changes as in the baseline scenario. Under the “No changes” scenario, the residence probability in products declined from around 80% to less than 70%, that in cars and machines declined from 23% to 20%, and that in recovery losses increased from 9% to 19%. The “Lifetime” scenario indicates the effectiveness of life extension to increase the residence probability in products via reduction in recovery losses. The “Scrap quality” scenario indicates that the improvement in scrap quality is vital to increasing the residence probability in cars and machines, whereas it effects on the residence probability of other products were negligible. The production of cars and machines uses larger amounts of BOF steel per product than EF steel to meet their functional requirements.27,29 Accordingly, improved scrap quality can result in the substitution (to some extent) of ELV scrap for BF crude iron to produce cars and machines, and hence can contribute to the reduction of their environmental footprints.54 Policy Relevance. MaTrace can trace the process in which the materials embedded in a particular product made in a particular year are transferred over time into a variety of products and losses via successive cycles of disposal, recovery, and recycling: it can trace the fate of material embodied in a given product-cohort. Aggregation across all product-cohorts gives the material flows in standard dynamic MFAs:12,38,39 MaTrace provides a microstructure in terms of a single cohort of standard MFAs (see SI for further details). This feature of MaTrace makes it a useful planning and evaluation tool for sustainable resource management. While recycling is regarded as indispensable for sustainable resource management, its increase is often hampered by quality issues in the scrap stream.5,8,11 As demonstrated by the above case study, MaTrace can identify the location of hot spots contributing to these barriers. Its ability to trace the fate of materials in individual products can help designing recycling policies or regulations focusing on specific products/materials, such as scarce materials used in cars and electronics. The anticipated increase in the complexity of scrap streams due to accelerating rolling-out of new carbon-mitigation technologies reliant upon materials not previously widespread8,55 would increase the area of its application in policy planning and industry. Industry would find MaTrace useful not only for identifying hot spots in the sense mentioned above, but also to identify stakeholders whose involvement would be vital for increasing the long-term sustainable use of materials. The MaTrace methodology described here is still subject to a number of simplifying assumptions that need to be relaxed in order to enhance its policy relevance. Future Directions. The improvement of scrap quality is of great importance for sustainable materials management. In practice, however, the opposite might occur, with accumulation of contaminants5,7,54,56 during repeated recycling (recirculation) leading to declining scrap quality. The adverse effects of repeated recycling on scrap quality can be incorporated into MaTrace by establishing a link between the elements of matrix B referring to the allocation of scrap to refinery processes, and a measure of scrap quality that in turn depends on the number of times recycling was repeated given initial levels of contamination. From the modeling perspective, this provides a promising opportunity to relax the assumption of constant parameters in MaTrace through the use of robust process

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ASSOCIATED CONTENT

* Supporting Information S

Derivation of eqs (8) and (9), MFA of all the cohorts, details of the use of EoL scrap estimated by WIO-MFA, sectoral classification, allocation of intermediate products in final demand to final products, allocation of secondary materials to 7212

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final products, projected changes in the composition of final demand, summarized results of Figure 2, the generation of EoL products that originated from the initial amount of ELV, and a note about possible introduction into the model of the effects of changes in the quality of scrap in repeated recycling. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by JSPS KAKENHI (22360386), by The Iron and Steel Institute Japan (Research Group for Car Recycling from the Material Industries’ Perspective), and by Waseda University (University Research Initiatives 10b-07) .

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