Quantifying Recycling and Losses of Cr and Ni in Steel Throughout

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Quantifying recycling and losses of Cr and Ni in steel throughout multiple life cycles using MaTrace-alloy Shinichiro Nakamura, Yasushi Kondo, Kenichi Nakajima, Hajime Ohno, and Stefan Pauliuk Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b01683 • Publication Date (Web): 14 Aug 2017 Downloaded from http://pubs.acs.org on August 14, 2017

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Environmental Science & Technology

Quantifying recycling and losses of Cr and Ni in steel throughout multiple life cycles using MaTrace-alloy Shinichiro Nakamura,∗,† Yasushi Kondo,† Kenichi Nakajima,‡ Hajime Ohno,¶ and Stefan Pauliuk§ 1

†Graduate School of Economics, Waseda University, Tokyo, 169-8050, Japan ‡Center for Material Cycles and Waste Management Research, National Institute for Environmental Studies, Tsukuba, 305-8506, Japan ¶Graduate School of Engineering, Tohoku University, Sendai, 980-8579, Japan §Faculty of Environment and Natural Resources, University of Freiburg, Freiburg, 79085, Germany E-mail: [email protected] Phone: +81-3-5286-1267. Fax: +81-3-3204-8961

2

Abstract

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Alloying metals are indispensable ingredients of high quality alloy steel such as

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austenitic stainless steel, the cyclical use of which is vital for sustainable resource man-

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agement. Under the current practice of recycling, however, different metals are likely

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to be mixed in an uncontrolled manner, resulting in function losses and dissipation

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of metals with distinctive functions, and in the contamination of recycled steels. The

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latter could result in dilution loss, if metal scrap needed dilution with virgin iron to

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reduce the contamination below critical levels. Management of these losses resulting

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from mixing in repeated recycling of metals requires tracking of metals over multiple

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life cycles of products with compositional details. A new model (MaTrace-alloy) was

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developed that tracks the fate of metals embodied in each of products over multiple life

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cycles of products, involving accumulation, discard, and recycling, with compositional

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details at the level of both alloys and products. The model was implemented for the

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flow of Cr and Ni in the Japanese steel cycle involving 27 steel species and 115 final

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products. It was found that, under a high level of scrap sorting, greater than 70 %

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of the initial functionality of Cr and Ni could be retained over a period of 100 years,

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whereas under a poor level of sorting, it could plunge to less than 30%, demonstrating

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the relevance of waste management technology in circular economy policies.

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Introduction

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Recycling of postconsumer and fabrication scrap is the principal strategy for reducing pri-

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mary metal production and its associated resource depletion and environmental impacts.

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Current loss rates in anthropogenic metal cycles, however, suggest that a large potential for

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recycling still remains unexploited. 1 Moreover, even if a metal is recycled, it may end up in

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low quality applications where its original function is not required (cascading or down-cycling;

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losses of function) 2 or as a contaminant (tramp element). 1,3 Policy makers have recognized

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the importance of closing metal cycles, and the circular economy strategies issued by the

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Government of China and the EU Commission bear witness to this development. 4,5

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To assess the sustainability of metal use and to guide resource policy development, a

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prospective assessment of anthropogenic metal cycles is necessary. 6 Many components of

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end-of-life (EOL) products end up in mixed scrap groups where high-specialty-metal alloys of

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high-values are diluted, rendering the alloying elements in those groups without function. 3,7

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Alloying elements can also become contaminants themselves if they end up in the wrong

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secondary metal 8 . 9–12 Proper consideration of the coupling among multiple metal cycles is

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imperative for prospective metal cycle models to be useful to understand the relation between 2 ACS Paragon Plus Environment

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the purity of the scrap flows, i.e., their alloy content, and the quality and quantity of the

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resulting secondary materials.

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Dynamic material flow analysis (dMFA) has been widely used to capture the magnitudes

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of metal cycles, including the future supply of fabrication and postconsumer scrap. Whereas

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former dMFA studies tended to focus on a single metal only and paid less attention to

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interaction with other metal cycles, 13–16 an increasing number of studies has evolved recently

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that consider the interaction among multiple metal cycles. This is particularly the case for

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aluminum alloys. 2,17–20 Løvik et al. 2 considered 26 Al alloys used for the automotive sector

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with compositional details in 10 alloying elements. dMFA studies of ferrous metal cycles

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mostly focus on steel alloys involving Cr and Ni (shown below). A notable exception is

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Daehn et al. 21 on copper contamination of secondary steel.

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The European Commission has listed iron (Fe) and its alloying elements chromium (Cr),

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manganese (Mn), molybdenum (Mo), and nickel (Ni) as being of high relative economic

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importance. 22 The cycles of the steel alloying elements are strongly coupled to the iron

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cycle. For example, a share of 85% of global Cr and 61% of global Ni production are used

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as alloying elements in stainless steel production. 11 In Japan, 97% of Cr and 95% of Ni

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are consumed in steel making as alloying elements, 11 which emphasizes the importance of

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the steel recycling process in determining the recovery of Cr, Mn, Mo, and Ni from EOL

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products. With current waste management and remelting practices, however, the function

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of the alloying elements is lost in most cases. Even though the overall EOL recovery rate for

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steel is more than 80,% 23 the absolute losses and the losses of the alloying elements of steel

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to slag or to alloys in which they have no function is therefore substantial.

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Ohno et. al. 24 quantified the unintentional flows of the alloying elements, Cr, Ni, and

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Mo, that occur in steel materials, due to the mixing during end-of-life (EOL) processes.

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They found that Cr lost to slag, and Ni dissipated into carbon steel scrap represent major

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losses and are becoming a source of contamination of secondary steels. Diener and Tillman 7

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reported that the ratio of steel scrap being sold to carbon steel producers versus alloyed



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steel producers was estimated by material handlers as more than 3:1. According to Daigo

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et. al., 11 the recycling rate is much higher for austenitic stainless steel than for ferritic

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stainless steel. All common carbon steels are ferromagnetic, as are stainless steels, except for

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austenitic stainless steels. A magnetic separator can separate austenitic stainless steels from

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mixed steel scrap. However, ferromagnetic steels, including ferritic stainless steels and other

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alloyed steels, cannot be separated by a magnetic separator and, thus, are mixed into carbon

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steel scrap groups. The stainless steel scrap mixed into carbon steel scrap was estimated by

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Reck et al. 25 to have reached 32% of postconsumer stainless steel scrap flows. As for Ni, it

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was estimated that 80% of postconsumer Ni scrap is recovered within the Ni cycle whereas

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20% becomes a constituent of carbon and copper scrap. 26 A significant amount of Ni is used

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in applications that use low concentrations of Ni (e.g., electronics and alloys), where Ni may

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be recovered as a minor constituent of carbon steel or copper alloy scrap, but not as Ni metal

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or alloy. 26

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Considering these empirical findings, the once-prevailing modeling assumption that sec-

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ondary metals are a perfect substitute for primary metals and that a metal can be represented

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by a single category has been rightfully criticized by several authors 27,28 and needs to be re-

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visited. Moreover, the consequences of current and future waste management practice on

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overall metal loss, secondary alloy composition, and tramp element contamination needs to

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be studied more systematically.

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The MaTrace model 29 was built to study how scrap flows extracted from EOL products

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are recycled and then distributed across the different economic sectors into new products.

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To date, it has been a prospective material cycle model with focus on a single metal, thus

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suffering from the shortcomings described above. Extending the scope of MaTrace from a

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single metal to several metals combined into alloys will allow us to trace different metals si-

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multaneously through the waste streams, estimate the amounts of secondary alloys produced

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and their tramp metal contents, and quantify losses and nonfunctional recycling of alloying

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metals.


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This work introduces MaTrace-alloy, a supply-driven dynamic MFA model with the fol-

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lowing novel features. First, it explicitly considers the mixing of different metals over time

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via recycling. Secondly, it determines the temporal distribution of the alloying elements

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in each age cohort of steel-containing products into other product categories. Thirdly, its

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simultaneous consideration of different species of alloys and materials allows one to estimate

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the extent of functional losses. Finally, it enables one to derive a material cycle use index

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that takes into account losses to nonfunctional recycling. The architecture of the model is

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depicted in Figure S1 in the supporting information (SI).

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We present the model and apply it in a case study on tracing the fate of the steel alloying

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elements Cr and Ni in the Japanese steel cycle over a 100-year period. This case study was

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chosen both because of the relevance of Ni and Cr losses in the steel industry (described

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above) and because of good data availability. Henceforth, we use the term non-carbon (nc)

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alloy steel to refer to alloy steels other than carbon steel, acknowledging that the latter can

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also be regarded as an alloy.

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Methodology

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MaTrace-alloy

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We extended the scope of MaTrace from a single metal to multiple metals combined into

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alloys based on the following set of simplifying assumptions.

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1. A product is a combination of alloys.

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2. EoL products are disassembled into a certain combination of scrap, each of which

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111

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consists of alloys. 3. A refinery process is the only process that can re-arrange the metal composition of its feed (scrap), and transform into a new alloy.



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Non-alloy components of products are not considered. Reuse of parts and components in

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their original functions is also not considered. The last assumption implies that the metal

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composition of an alloy remains conserved unless submitted to a refinery process. 7 This

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assumption does not hold for alloys designed for dissipative applications, such as Zn coated

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steel, and for applications subject to tear and wear, such as cutting tools. 30 The fact that

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the shares of in-use dissipations in flows are negligible for Fe, Cr, and Ni justifies the use of

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this assumption. 30 Write q(t) for the amount of products in alloy mass produced from the EoL products recovered in year t; the dimension of q(t) is product × 1. The MaTrace-alloy gives the evolution of the products over time as ( ) (( ) ) T q(t) = Λ ⊙ D(t) diag R ⊙ ΩΓV (t) ιm ιa

(1)

with

V (t) =

t ∑

uˆ(t, r)C T (t − r)

(2)

r=0

and ( ) u(t, r) = B(t − r) δ ⊙ ϕ(r) ⊙ q(t − r) ,

(3)

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where C (metal × alloy) refers to the metal composition of alloys, B (alloy × product) to

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the alloy composition of products, Γ (scrap × alloy) to the scrap transformation of alloys

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recovered from EoL products, Ω (alloy×scrap) to the allocation of scrap to refinery processes,

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R (metal×alloy) to the yield of metals at the refinement of scrap into new alloys, D (product×

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alloy) to the allocation of new alloys to products, Λ (product×alloy) to manufacturing yields,

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δ (product × 1) to recovery yields of EoL products, ϕ(r) (product × 1) to the fraction of

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products that is discarded after r years of use, ι’s to a vector of unities for summation, ⊙ to 6 ACS Paragon Plus Environment

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the Hadamard product, diag(v) = vˆ to the diagonal matrix the main diagonal of which the

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components of a vector v are placed on, and T to the transpose operator.

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Leaving details of its derivation to SI, we give a brief description of the logic behind this

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equation. The term u (alloy × 1) gives the amount of alloys recovered at year t from EoL

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products that were produced at t − r and discarded at t. Multiplying with the material

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composition of alloys, C, and summing up over all r < t, (the transpose of) the term V

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(alloy × metal) gives the metal composition of EoL alloys recovered at t. The EoL alloys are

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then allocated to scrap categories via Γ, and scrap is further allocated to refinery processes

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via Ω. Submitted to refinery processes, the metals in scrap are rearranged via R into new

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alloys, which are subsequently allocated to new products via D. The sum of components of

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Γ over EoL alloys is smaller than unity due to scrap losses (shredder residues). In R, refinery

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losses (slag and dust) are considered by its elements taking values smaller than unity. The

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fact that the composition matrices B and C occur not as constants but as variables to be

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determined in the model represents a distinguishing feature of the present model that makes

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possible to consider the mixing (and/or dissipation) of metals in recycling processes.

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For the case of a single material, (1) reduces to the MaTrace model 29 (see SI for details).

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Data

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The model was applied to the large-scale input-output data on the steel flows for Japan

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developed by Ohno, 24 which involves 27 steel species (of which 8 are carbon steels and 19 are

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nc-alloy steels) and 3 metals (Cr, Fe, and Ni). Five types of scrap were considered: austenitic

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stainless steel scrap, ferritic stainless steel scrap, Ni alloy scrap, other alloy steel scrap, and

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carbon steel scrap. Detailed classifications of alloys and scrap are given in Table S2 of SI.

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Because our focus is on developing a new methodology, it was assumed for simplicity that

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the material embodied in exports would follow the same lifetime and EoL- and recycling

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processes as in Japan. Relaxation of this stringent assumption can be facilitated by its

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extension to the Multi-Regional-Input-Output (MRIO) framework. 31 Note that the initial 7 ACS Paragon Plus Environment


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values q(0) can include imports, which is indeed the case for this study.

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We now give a brief description about the choice of default values for Γ(metal × alloy =

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3×27) and R(scrap×alloy = 5×27) (see the SI for details). The former refers to scrap sorting

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processes, and, hence, to the quality of scrap to be fed into refinery processes. The latter

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processes, in which the metals in scrap are rearranged to make new alloys, are represented

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by R. For Γ, we followed Daigo et. al., 11 and assumed that 90% of austenitic stainless steel

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is sorted as austenitic stainless steel scrap, whereas this rate is only 40% for ferritic stainless

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steel, with the rest ending up in carbon steel scrap. For R, we took 0.986 for Cr in nc-alloy

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steel processes and 1.0 for Ni in all the refinery processes. 10,11 As for the ratio by which Cr is

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distributed to liquid metal in carbon steel processes, 0.5 was chosen as the default value. To

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account for its wide variability, 32 a sensitivity analysis was conducted on this ratio (results

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reported in the SI).

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Measuring the circularity of metal use

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The EU action plan for the circular economy states that “to assess progress towards a more

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circular economy and the effectiveness of action at EU and national level, it is important to

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have a set of reliable indicators”. 4 Here, we offer Cumulative Service Index (CSI) as part of

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the indicator family for the circular economy. The CSI, µi (T ), is a measure of the cumulative

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service over a certain time period T that is provided by a unit of material i taken into use

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at the start of the period, and is given by

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T ∑ 1∑ ∑ wij xij (t)/ wij xij (0) µi (T ) = T t=0 j∈alloys j∈alloys

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where xij (t) refers to the fraction of metal i that occurs in alloy j that occurs in products in

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service at t, and wij to the weight attached to it (SI gives details of deriving xij (t)). Product

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lifetime and recycling rates play vital roles in determining the degree of closure of metal

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cycles in the long run. This index was originally introduced by Pauliuk et al. 31 to address


(4)

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these two aspects of a circular economy, and was termed “circularity index.”. We chose to

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rename it by using ‘cumulative’ to emphasize its time dimension.

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This index gives a relative measure of the cumulative weighted mass of metal i present

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in the system over time interval T in terms of an ideal reference case, where the metal

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remains in its initial applications. By definition µi (0) = 1: initially, all the metal is used

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in products with their original functions. Over time, it would decline due to the occurrence

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of losses of material and functional nature. Once dissipated into carbon steel, Cr and Ni

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cannot be recovered for upgraded use in nc-alloy steel under the current economic and

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technical conditions of remelting processes. 33 Accordingly, an increase over time of the index

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is excluded.

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Functional aspects of metal use can be accommodated by an appropriate choice of the

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weights wij . One option would be to use monetary values based on metal prices. However,

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the highly volatile nature of metal prices makes its use as weighting factors difficult for

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analysis focusing on development over many years, as is the present case. Following Ciacci

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et al., 30 we chose to use embodied energy as a measure of functionality: the functional

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difference of metals was evaluated based on the amounts of embodied energy (“cradle to

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gate cumulative energy demand per metal") given by Nuss et al. 34 (Table 1). The term

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“Not used in products” in Table 1 corresponds to the not-recovered fraction of potentially

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recyclable, currently unrecyclable, and unspecified streams of EoL alloys in Ciacci et al. 35 (in-

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use dissipation is not considered because of its negligible share). Functionalities of Cr and Ni

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relative to Fe are represented by larger amounts of energy required for their production. Their

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distinguishing functions, such as corrosion resistance and hardenability, are indispensable for

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nc-alloy steel. 36 Once dissipated into carbon steel, however, their distinguishing functions

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are no longer required, and, thus, are wasted. This was represented by putting the function

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values for Cr and Ni equal to zero unless they are used in nc-alloy steel (as an alternative

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case, we also considered the case where the energy value was set equal to that of Fe when

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applied to carbon steel). For Fe, its value is set to zero when it is no longer used in products.



Table 1: Quantifying functionality of metals among locations based on embodied energy

Fe Cr Ni

Non-carbon alloy steel 23.1 40.2 111

Locations Carbon steel 23.1 0 0

Not used in products 0 0 0

Source: The data on embodied energy (“cradle to gate cumulative energy demand (GJeq/103 kg) per metal") were taken from Nuss et al. 34 204

Scenarios on scrap sorting

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To address the effects of scrap sorting on the quality of recycling, 24,37 two additional schemes

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of sorting were considered, a maximum level of alloy-based sorting (“maximum sorting” for

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short) and a minimum level of sorting (“minimum sorting” for short). Under the “maximum

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sorting” scenario, all the nc-alloy steels are sorted as nc-alloy steel scrap, and none end up

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in carbon steel scrap. The “minimum sorting” scenario refers to the opposite case where all

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the nc-alloy steels end up as carbon steel scrap, except for austenitic stainless steel and Ni

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alloys, of which 40% are sorted as nc-alloy steel scrap with the rest sorted as carbon steel

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scrap (the same level as ferritic stainless scrap under the default scenario). These sorting

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schemes are accommodated in Γ (see the SI).

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We set the time horizon to 100 yeas because of the long lifetime of steel in buildings and

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infrastructure, which adds some determinacy to distant future steel scenarios. This order of

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time horizon is not uncommon for stock-driven scenario work on steel, 15,16,21,29,31 but it is

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clear that the range of possible results grows substantially with the time horizon.

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Results

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Figure 1 gives the transition among different products (aggregated into five categories) and

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losses of the location of Cr and Ni under alternative scrap sorting scenarios across 100 years

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(results with a more detailed classification of products are given in the SI ). The results for 10 ACS Paragon Plus Environment

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Fe were similar to our previous results, 29 and are shown in the SI (Figure S4).

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The top panel in Figure 1 refers to the default (current) scrap sorting and shows that

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of the amounts of Cr embodied in the initial endowments of products, 40% is lost after 50

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years, and 70% is lost after 100 years, with the refinery losses (slag) occupying the dominant

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share, followed by collection losses, scrap losses, and manufacturing losses. Smaller losses are

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observed for Ni, with 20% of the initial endowments lost after 50 years, 45% lost after 100

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years, and the collection losses of EOL products occupying the largest share, followed by scrap

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losses, and manufacturing losses, with no slag losses occurring thanks to its thermodynamic

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properties (Ni is nobler than Fe).

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Another remarkable feature is the change over time in the location of the metals among

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different products. Whereas cars and machinery constituted their major applications initially

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(84% for Cr and 75% for Ni), their shares decline to around 50% after 100 years, with the

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rest occupied by buildings and civil engineering.

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The “maximum sorting” scenario (the panel in the middle of Figure 1) results in a sig-

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nificant reduction in metal losses for Cr, which is mostly attributed to the sizable reduction

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in refinery losses. In contrast to Cr, a slight increase in the material losses was observed for

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Ni: alloy-based scrap sorting did not appear to contribute to reducing the material losses

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for Ni. Common to both Cr and Ni is that their applications to products preserve their

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initial patterns, mostly consisting of cars and machinery, with the shares of buildings and

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civil engineering remaining below 20%, and that the recovery losses of EOL products occupy

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the largest share of losses, followed by scrap losses, and manufacturing losses.

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The “minimum sorting” scenario (the bottom panel of Figure 1) results in a significant

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increase in the material losses of Cr because of drastic increases in refinery losses, with the

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losses reaching around 90% after 100 years, whereas a slight decline in the losses is observed

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for Ni. Common to both Cr and Ni is the rapid shift in their applications from cars and

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machinery to buildings and civil engineering, with the shares of the former declining to

248

around 30% for Cr and 50% for Ni, after 40 years.



5

4

Cr: default sorting

10

Ni: default sorting

10

3

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2.5

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2

6

1.5 4

1

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0.5 0

0 20

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Cr: max sorting

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Ni: min sorting

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2.5

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1.5 4

1

2

0.5 0

0 20

Cars Buildings Recovery loss

40

60

80

100

20

Machinery Civil engineering Refinery loss

40

60

Other products Collection loss Manufacturing loss

Figure 1: The location of Cr and Ni among different products under alternative schemes of scrap sorting. The horizontal axis refers to the years after initial production. The vertical axis refers to the mass of each metal in 103 kg.


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Another way of tracing the fate of metals, which is made possible by the MaTrace-

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alloy model, is to look at the transition in their alloy locations (Figure 2). The panel in

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the middle shows that, under the “maximum sorting” scenario, Cr and Ni remain in their

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initial applications, nc-alloy steels, whereas under the default sorting (the top panel), their

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increasing fractions are dissipated into carbon steels. Under the “minimum sorting” scenario

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(the bottom panel), their initial applications to nc-alloy steels are almost entirely replaced

255

with those to carbon steels. For Cr, this results in sizable refinery (slag) losses because it

256

is less noble than Fe. For Ni, it results in sizable functional losses because of its dissipation

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into carbon steels, where its function is not required.

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Besides causing functional losses, the elevation in the level of Cr and Ni in carbon steels

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can turn the metals into undesirable contaminants that compromise the quality of recycled

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carbon steels (Figure 3). The result obtained for the default scenario of the concentration of

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Cr, where it reaching around 0.17%, is in good agreement with Oda et. al., 12 who found the

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concentration of 0.15% to 0.19% for samples taken from Japanese electric arc furnace (EAF)

263

facilities. Under the “minimum sorting” scenario, the concentration of Cr in carbon steel can

264

reach a level well above 0.3% exceeding the maximum admissible concentration, 38 whereas

265

the level remains well below that under the default sorting scenario. The concentration of Ni

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in carbon steel remains at a level lower than that of Cr, in most cases, because of its higher

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recovery rate as austenitic scrap or Ni scrap. In contrast to Cr, however, once it is dissipated

268

into carbon steel, its concentration remains kept at that level, or even tends to rise, because

269

of its conservation in refinery processes. Under the “minimum sorting” scenario, this feature

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of Ni renders its concentration non-negligible over time when the same cohort is repeatedly

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recycled without any dilution; it could exceed 0.2% after 30 years. Whereas this level of

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Ni concentration is regarded as unproblematic when considered in isolation, simultaneous

273

occurrence with Cr can make it problematic because of their mutually reinforcing effects as

274

contaminants. 38 We will return to this point at the end of this section.

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The “maximum sorting” scenario appeared to reduce the material losses of Ni, if only



5

4

Cr: default sorting

×10

Ni: default sorting

×10

3

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2.5

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×10

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Ni: max sorting

×10

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×10

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Ni: min sorting

×10

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Austenitic

Ferritic

Other non-carbon steel

Carbon steel

Collection loss

Scrap loss

Refinery loss

Manufacturing loss

Figure 2: The location of Cr and Ni among different alloys under alternative sorting schemes. The horizontal axis refers to the years after initial production. The vertical axis refers to the mass of each metal in 103 kg.


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10-3

4

Crdefault-sort Nidefault-sort

3.5

Cr

Cr and Ni Concentration

3

max-sort

Nimax-sort Crmin-sort Ni

2.5

min-sort

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0.5

0 0

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100

Years after initial production

Figure 3: Effects on Ni and Cr concentration in electric arc furnace (EAF) carbon steel (steel bar) produced from a given products cohort under default sorting.



276

by a small margin. This is attributed to the shift under the “minimum sorting” scenario of

277

the applications of Ni from the initial one mostly consisting of cars and machinery, high-

278

function applications, to those dominated by construction and civil engineering items. The

279

longer product lives of the latter items induce a smaller number of products cycles over

280

a given period, and, hence, smaller amounts of associated losses. This results in a trade-

281

off relationship between high-function applications and material losses, as pointed out by

282

Pauliuk et. al. 31

283

The above observation, however, was made based on the losses in terms of mass only,

284

without any consideration of function losses. The cumulative service index (4) with the

285

weights w referring to the function of metals occurring in different alloys in terms of embodied

286

energy enables one to consider function losses of metals. The results in Figure 4 show

287

that under the “minimum sorting” scenario the dissipation of high functional metals into

288

applications, where their functions are not needed, results in sizable function losses. This is

289

in particular the case for Ni. Hidden behind the seemingly slight reduction in material losses

290

of Ni under minimum sorting, in terms of mass, is thus a drastic increase in the losses in

291

terms of embodied energy with µ(100) falling from 0.76 under ”maximum sorting” scenario

292

to 0.3. Depending on the level of scrap sorting, µ(T ) can differ by more than 40 points in

293

terms of embodied energy for both Cr and Ni. Noteworthy for Ni is that, in terms of mass,

294

the difference in µ(100) among the sortring levels is negligible, or even slightly reversed.

295

Reliance solely on mass criteria can greatly underestimate the effects of improving the level

296

of scrap sorting. Under the “maximum sorting” scenario, the average energy losses could be

297

kept at well below 30% of the initial level for both Cr and Ni, whereas they could exceed

298

70% under the “minimum scrap sorting”. This demonstrates the inadequacy of considering

299

the efficiency of recycling in terms of mass only, neglecting its functional aspects.

300

The above results on µ(T ) were obtained by allocating zero function values to Cr and Ni

301

for applications other than nc-alloy steels: applied to carbon steel, they were evaluated with

302

zero values, just as the case they were no longer used in any product. This can be regarded


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303

as an extreme case. As an alternative, we considered the case where the energy value was

304

set equal to that of Fe when applied to carbon steel, but to zero when no longer used in any

305

product. It turned out that whereas the extent of reduction in µ(T ) under the “minimum

306

sorting” scenario decreased, the results remained unaltered qualitatively (see Figure S5 in

307

the SI). Cr

1 0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3 0.2 0.1 0 20

0.3

default-energy max-energy min-energy default-mass max-mass min-mass 40

60

Ni

1

default-energy max-energy min-energy default-mass max-mass min-mass

0.2 0.1

80

100

0 20

40

60

80

100

Figure 4: The cumulative service index, µ(T ), over time under alternative sorting scenarios and weights for Cr (left) and Ni (right): “default.”, “max.”, and “min.” refer to the level of sorting. “energy.” and “mass.” respectively refer to the weighting in terms of energy (Table 1) and mass. The horizontal axis refers to the years after initial production.

308

The ratio by which Cr is distributed between molten metal and slag in an EAF is known

309

to be subject to wide variations. 11,32 The above results were obtained for a particular value of

310

the ratio, a representative one taken from the literature. 10,11 To assess the effects of the ratio

311

on the cumulative service index and the concentration of Cr in carbon steel, a sensitivity

312

analysis was conducted by altering it in the range of 30% to 95% . As for scrap sorting,

313

the default case was assumed. It is obvious that the mass-based cumulative service index

314

increases with the ratio of Cr ending up in metal. Less obvious is its effects on the energy-

315

based cumulative service index. It turned out that the energy-based cumulative service index 17 ACS Paragon Plus Environment


316

was hardly affected by the increase in the ratio (Figure S7 in the SI). Another noticeable

317

effect of the increase in the ratio is the increase in the concentration of Cr in secondary steels

318

toward, or even surpassing, the tolerated levels (Figure S6 in the SI).

319

Dissipation of Cr and Ni in carbon steel represents their function losses, but would not

320

cause any harm to carbon steel provided their concentrations remain within the admissible

321

levels. 39 If the admissible levels were exceeded, however, their presence could compromise

322

the functionality of carbon steel, and needs to be taken care of by adding Fe from primary

323

or clean EoL sources to dilute their concentration. 40 This amount of Fe for dilution can be

324

regarded as a loss. For the cases where this was found relevant, we estimated the amount of Fe

325

required for dilution, and obtained the cumulative service index µ(T ) of Fe that incorporates

326

this loss. It was found that whereas the required rate of dilution could reach as high as 30%,

327

its effect on the cumulative service index of Fe was negligible. See SI, Figures 8 and 9, for

328

further details.

329

Discussion

330

Our results demonstrate the importance of paying due attention to function recycling, the

331

significance of which has been pointed in the literature. 7,9,24,37,41,42 Reliance on the rate of

332

recycling based on mass only or neglect of the functional aspects of recycling can result

333

in a serious underestimation of the potential benefits resulting from high levels of scrap

334

sorting. For instance, it was found above that, evaluated in terms of mass alone, alloy-based

335

sorting of Ni would appear to make little differences to its circular use, whereas in terms of

336

energy use, it could result in sizable differences. Our evaluation of functionality was based

337

on embodied energy. Use of different weights in the CSI (4) would yield different results, at

338

least quantitatively, if not qualitatively. One possible choice would be to use the criticality

339

index developed by Graedel et al. 43,44

340

This study did not consider the amounts of energy required for recycling, among others,


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341

remelting of scrap via an EAF. Under high levels of scrap sorting, larger shares of scrap metals

342

find their way into applications, such as machinery, characterized by shorter lives than into

343

construction and civil engineering items characterized by longer product lives, resulting in an

344

increase in the number of times metals are remelted. On the other hand, recycling contributes

345

to saving the production of virgin steels, which are mostly produced based on basic oxygen

346

furnace (BOF) processes. Given the significant differences in energy requirements between

347

the BOF and EAF routes (28-31 GJ/t versus 9-12.5 GJ/t, respectively 8 ), it seems safe to

348

assume that the inclusion of energy requirements associated with remelting processes would

349

not alter the above results, at least qualitatively. Complementing the present MFA results

350

with detailed life-cycle inventory analysis of the processes involved, including both EAF and

351

BOF processes, would be an important direction for future research.

352

This study was concerned with tracing the fate of a single cohort, providing a micro-

353

foundation of dynamic MFA involving multi-materials. Accordingly, the issue of contamina-

354

tion was discussed for a single cohort. In reality, the material flows consist of an aggregate of

355

cohorts of different vintages. 29 Extension of MaTrace-alloy to accommodate this mixing of

356

flows originating from different vintages would provide a deeper understanding of dynamic

357

material flows.

358

We close this paper by mentioning major limitations of the present model, the relaxation

359

of which would provide directions for future research. The first limitation to be mentioned is

360

the lack of geographical resolution. Countries/regions differ in products lives, the structure

361

of final demand, and in technologies of manufacturing, refining, and waste management,

362

among others. 45 Spatial extension of the model to a global level as performed for the single

363

material MaTrace by Pauliuk et. al. 31 would enable one to consider these spatial differences.

364

Secondly, the parameters of the model were assumed to remain unchanged over time (up

365

to 100 years!) except for those relevant to the sorting scenarios, whereas the composition

366

parameters B and C are endogenously determined, and variable. One way for relaxing this

367

strong assumption is resorting to more realistic future scenarios involving changes in final



368

demand and technology, including design changes and reduction of yield losses, as discussed

369

in Allwood. 3 With regard to alloy steels, one should consider the increasing use of elements

370

of significant criticality such as Nb, V, and Co, which would have significant consequences

371

when their functionality is lost over repeated recycling. 44,46 Another possibility would be

372

to endogenize some model parameters instead of providing exogenously by scenarios. For

373

instance, the parameter referring to the sorting of EoL materials to different categories of

374

scrap, Γ, could be derived based on an optimization procedure, say, cost minimization, as in

375

Gaustad et al. 19 Further extensions would follow by relaxing some of the three assumptions

376

introduced above. Among others, dissipative use of materials 30,35 can be accommodated

377

by relaxing assumption 3. It is hoped that these contribute to our better understanding of

378

material cycles.

379

Acknowledgement

380

We thank Tetsuya Nagasaka and the reviewers for helpful comments and Wataru Takayanagi

381

for drawing the graphical abstract. This work was supported by JSPS KAKENHI Grant

382

Number JP15K00641 and the program “Science of Science, Technology and Innovation Pol-

383

icy” in Research Institute of Science and Technology for Society (RISTEX), Japan Science

384

and Technology Agency (JST).

385

Supporting Information Available

386

Sankey diagram depicting the system definition, mathematical model formulation, data used,

387

and results with detailed products categories. This material is available free of charge via

388

the Internet at http://pubs.acs.org/.


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Quantifying Recycling and Losses of Cr and Ni in Steel Throughout

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