exploring the global journey of nickel with markov chain

R E S E A R C H A N D A N A LYS I S

Exploring the Global Journey of Nickel

with Markov Chain Models

Matthew J. Eckelman, Barbara K. Reck, and T. E. Graedel

Keywords:

industrial ecology

Markov chains

metal cycles

resource efficiency

scrap recycling

technological lifetime

Supporting information is available

on the JIE Web site

Summary

Markov chain (MC) modeling is a versatile tool in policy analysis and has been applied

in several forms to analyze resource flows. This article builds on previous discussions of

the relationship among absorbing Markov chains (AMCs), material flow analysis (MFA),

and input-output (IO) analysis, and presents a full-scale application of MC modeling for

a particular globally relevant, nonrenewable resource, namely nickel. The MC model pre-

sented here is built on comprehensive, recently compiled nickel flow data for 52 geographic

regions. Considering all possible cycles of recycling and reuse, nickel extracted in 2005 is

estimated to have a technological lifetime of 73 ± 7 years. During its global journey, nickel

enters use, for some application somewhere in the world, an average of three times, the

largest share of which occurs in China. Nickel entering fabrication in 2005 is estimated to

enter use approximately four times. Over time, nickel is lost to the environment and as a

tramp element in carbon steel; the final distribution of nickel among these absorbing states

is 78% and 22%, respectively. Of all the nickel in ore extracted in 2005, fully 28% will even-

tually end up in the tailings, slag, and landfills of China. MC results are also combined with

geographically specific life cycle inventory data to determine the overall energy invested in

nickel during its many cycles of use. MCs provide a powerful tool for tracking resources

through the network of global production, use, and waste management, and opportunities

for further integration with other modeling efforts are also discussed.

Introduction

Markov chain (MC) modeling is a versatile tool in policy

analysis, used to examine such disparate systems-level prob-

lems as unemployment, drug addiction, and industrial pollution.

These systems are all marked by the existence of multiple states,

where agents (people or pollutants) can move from one state

to another, or stay where they are. Markov models use a proba-

bilistic formulation of the transitions among different states to

illuminate the long-run behavior of the system (Howard 1971;

Stokey and Zeckhauser 1978). Such models can also be applied

to natural resource management, in particular to questions of

Address correspondence to: Matthew J. Eckelman, Dept. of Civil & Environmental Engineering, 360 Huntington Ave., Boston, MA, USA 02115. Email: m.eckelman@

neu.edu

c© 2011 by Yale UniversityDOI: 10.1111/j.1530-9290.2011.00425.x

Volume 00, Number 00

how physical materials flow through the economy, and have

thus been explored in combination with other tools that have

the same purview, including material flow analysis (MFA) and

input-output (IO) analysis. In this article we build on previous

discussions of the relationship among these tools and present a

full-scale application of MC modeling for a particular globally

relevant, nonrenewable resource, namely nickel.

Markov Chain Models in Industrial Ecology

Mathematically MC models are similar in their construc-

tion and assumptions to IO models: they both are matrix-based

www.wileyonlinelibrary.com/journal/jie Journal of Industrial Ecology 1


approaches that specify transitions (physical or monetary flows,

in the case of IO) through a system of distinct states, or sec-

tors. One important mathematical condition of MCs is that

the probability of a given transition must be independent of all

previous transitions, so that these are “memory-less” models.

In a recent article, Duchin and Levine (2010) formalize the

relationship between a subset of MC models called absorbing

Markov chains (AMCs) and IO by expressing the former in IO

notation, specifically in terms of Ghosh matrices (1958), based

on earlier work by Suh (2005). The authors further present an

integrated formulation to explore what they term “resource-

specific networks” by rewriting IO results in terms of AMCs.

Instead of starting with final demand for a product or ser-

vice and using IO models to determine economic inputs and

related environmental burdens upstream, MCs start with a spe-

cific resource or supply sector and determine the flows of this

resource downstream—either direct flows or those embedded in

products. These downstream flows comprise a resource-specific

network, and MC results can be used to explore certain net-

work parameters: What is the average length of its path and

how many times does it pass through each state? How is the re-

source allocated to consumption sectors? The ability to answer

such questions is a common feature of MC models, but the pre-

cise meaning of each question differs between MC models based

on IO and those based on MFA (or more precisely, substance

flow analysis [SFA]), as discussed below.

The development of these two branches of MCs is presented

in the comprehensive literature review of Duchin and Levine

(2010), and here we further differentiate these types of models

through a discussion of the scope and assumptions of each, as

they have distinct but complementary capabilities.

The core of an MC model is the state transition matrix, de-

noted A which specifies the probability that a resource in one

state or economic sector (such as copper undergoing fabrica-

tion) will move to another state or sector (such as appliance

manufacturing). In IO models, these probabilities are deter-

mined by the relative monetary flows among economic sectors.

As IO models typically cover all sectors of the economy, includ-

ing the extraction of processing of many different resources, an

MC model based on IO can consider the flows of multiple ma-

terials. In contrast, MCs based on MFA use the distribution of

physical flows of material among economic sectors to populate

the state transition matrix (Yamada et al. 2006). While the for-

mulation of Duchin and Levine (2010) allows for models with

arbitrary or mixed units, MCs based on MFA have generally

been restricted to physical units of a single material (and so are

more accurately based on SFA). The substance tracked has typ-

ically been a metal, with previous work covering iron and steel

(Matsuno et al. 2007), copper (Daigo et al 2009), and stain-

less steel in Japan (Hashimoto et al. 2010), as well as copper

globally (Eckelman and Daigo 2008). Metals are particularly

well suited to MC modeling because their immutability makes

them relatively easy to track through various system states using

mass-balance techniques.

Data availability drives the scope of each type of model: the

IO-based model of Duchin and Levine is an assumed one-region

model, but in principle MCs could be applied to global multire-

gion IO models as well (Duchin 2005; Tukker et al. 2009), all

the way down to the level of one country per region (Lenzen

et al. 2010). MFA-based MC models, on the other hand, are

spatially restricted by the level of detail in the underlying MFA

data, which for global studies also generally reach their finest

level of detail at the country level (Graedel et al. 2004). How-

ever, unlike IO models, which suffer from well-known problems

of aggregation of many different materials and products into a

single sector, MFA-based MC models can be used to track any

specific resource, including minor but technologically crucial

resources, such as tantalum.

The other major feature of MCs is the presence of absorbing,

or “trapping,” states–those from which the probability of mov-

ing to other states in the system is zero. In the model of Duchin

and Levine (2010), the absorbing states are set as final con-

sumption, under the assumption that consumer goods will not

reenter the economy after they are purchased. This has major

implications for the temporal scope of IO-based MC models and

for the conceptual meaning of the model. IO-based MC models

examine the flows of a resource through economic space: re-

sources travel from supply sectors to intermediate production,

among these production sectors and eventually “trapped” to the

absorbing states of final consumption in the form of final prod-

ucts. In this framework, the number of times that a resource

passes through an intermediate production sector represents

the importance of that resource for intermediate production

itself–the role of copper-containing machinery needed to make

copper-containing appliances, for example. There is no tem-

poral aspect, per se, and so the assumption of a static state

transition matrix is not unreasonable.

MFA-based MC models, on the other hand, were developed

explicitly to consider recycling, and present the number of times

that metal is reused by an economy as a key metric. Here, final

consumption is simply the “first use” of a resource. At the end of

their useful lives, products that contain the resource in question

enter the waste management sector, from which they either

move back into a production sector and a second use, setting up

a physical resource loop, or are lost with the relevant resource

to an environmental sink, such as a landfill. In this framework,

the number of times that a physical resource passes through a

sector represents the reuse and recycling performance of that

resource. A resource will cycle through the economy, passing

in and out of use with each recycling loop, until eventually all

units of the resource are lost to the environmental sinks that

are the absorbing states of these models.

Because MFA-based MC models include a use phase, the

lifetimes of the material or substance in each end-use sector

are important parameters, and so these models trace a resource

both through space and through time. Consequently, another

key metric of MFA-based MC models is the “technological life-

time” of a resource, or the time-weighted path of a resource

in the economy averaged over all possible paths. This can

also be thought of, generally, as the average residence time

of the resource in the resource network. Although quite useful

for business and policy analysis, the inclusion of the temporal

2 Journal of Industrial Ecology


Scrap

Mi W

S U

Mfg

Stock

F

R

Landfilltailings

Import/E

xport

oreLithosphere

IW

Import

/Exp

ort

Import/Exp.

Import/Export

IW

blended or concentrated

nickel ore

EOL

refined nickel

intermediate nickel

nickel in final goods

nickel matte

nickel to other scrap

markets

Imp

ort/E

xp

ort

IW

Mi Mine & Mill

S SmelterR Refinery

F FabricationMfg ManufacturingU Use

W Waste Management & Recycling

IW Industrial Wastes

EOL End-of-Life flows

Mfg

Scrap

Export

Final Goods

11

units of Gg/yr Ni

18

107 89

IW

1

Figure 1 The anthropogenic nickel cycle, with selected 2005 data for Germany, adapted from Reck and colleagues (2008).

dimension introduces several methodological difficulties that

will be discussed later in the present article.

Global Flows of Nickel

The subject of the present study is the global cycle of nickel,

a resource-intensive, technologically critical metal with a wide

variety of uses. Reck and colleagues (2008) have constructed

a comprehensive assessment of nickel flows in the year 2000

through the economies of 52 major countries, country groups,

and territories (hereafter called countries) covering all stages

of nickel’s life cycle, from production to disposal and recycling.

The work has been updated to year 2005 flows (Reck and Rotter

forthcoming) and these results form the backbone of the present

Markov model, as described in the Methods section. Figure 1

shows a generic schematic diagram of the nickel cycle with

selected data on the manufacture and use of final goods in

Germany.

Previously the most spatially comprehensive MFA-based

MC model was that of Eckelman and Daigo (2008), which

considered global flows of copper across eight world regions.

On a global average basis, each atom of copper extracted from

the ground was found to enter use 1.9 times and have a techno-

logical lifetime of only 60 years, despite copper’s assumed lim-

itless potential for recycling. Global, multiregion models have

several advantages over one-region models, in that they can

account for different patterns in production, end-use sectors,

and recycling systems. The present analysis brings these global

multiregion models to the national level, which is the smallest

organizational level possible given the availability of economic

and trade statistics on which the MFA models are based. Such

a level of detail is desirable, as regional assessments can mask

significant variations among countries in each region, and most

of the policies that could be informed by Markov models (such

as control of metal emissions to the environment or the balance

of trade) occur at the national level.

These 2005 nickel data are modeled as an MFA-based MC

in order to explore the movement of nickel through the global

economy and to answer a number of interesting, long-run ques-

tions, several of which are suggested in the Next Steps section

of Duchin and Levine (2010):

• For a unit of material extracted in a given region, (a) where

does the material go after a given number of cycles through

the global economy and (b) what is its final fate? Because

MFA-based MC models trace physical flows, they allow

us to see how nickel moves stepwise in the global system

from an initial geologic distribution among nations, to

another distribution after an arbitrary k number of steps,

to a final distribution among absorbing states after infinite

steps.

• How many times does a unit of metal mobilized by hu-

mans actually get used, including all possible routes and

cycles of recycling and reprocessing? This efficiency of use

metric is explored from the starting points of the natu-

ral resource (metal ore in the ground) and the technical

resource (primary refined metal).

Eckelman et al., Exploring the Global Journey of Ni with Markov Models 3


• How long does a unit of nickel last in society—what is its

technological lifetime?

• What are the geographically specific energy savings as-

sociated with our global system of nickel recycling over

multiple cycles of use?

The model and results that follow represent a full-scale ap-

plication of MCs to understanding global material flows of this

important resource, with a novel model extension to explore

questions related to embodied energy.

Methods

The model formulation used here is analogous to that pre-

sented in Eckelman and Daigo (2008), with a number of im-

portant modifications. First, the model in the present article

uses country-level material flow data instead of regional data,

which increases the size of the overall state transition matrix

by an order of magnitude and allows for more specific insights

into the flows and final fate of nickel. Second, because of the

losses of nickel to carbon steel and other alloys during recycling

‘carbon steel’ has been added as a separate absorbing state in the

model. While nickel losses to the environment are considered

on a country basis (with 52 separate absorbing states), losses to

‘carbon steel’ are considered on a global basis (with only one ab-

sorbing state). The third important modification concerns trade

of nickel and nickel-containing products among countries. In

previous work, markets were introduced as separate states in the

MC model, as this realistically reflects that metal products and

semiproducts are global commodities. Transitions into and out

of these international markets were each counted as individ-

ual steps in the model, so that metal exported from a country

required two steps to enter the importing economy (one into

the market and the other out of the market), but metal used

domestically required only one step to enter the next life cycle

phase. This structure is adequate for modeling total technolog-

ical lifetimes over infinite model steps, but is not suitable for

clear, stepwise interpretation of the results, which is a major

goal here. Therefore the state transition matrix used here was

expanded by adding dummy states between each domestic pro-

duction state, so that nickel moves between states such as smelt-

ing, refining, and use in two transitions, regardless of whether

or not the nickel is traded internationally or not. Finally, the

fourth major modification is the inclusion of country-level en-

ergy use data in order to assess the accumulation of embodied

energy throughout the global journey of nickel. This was done

by postmultiplication of the Leontief inverse of the state tran-

sition matrix with a vector of primary energy use for nickel

production in each country which was derived from an inves-

tigation of facility-level energy and greenhouse gas emissions

in the global nickel industry (Eckelman 2010). Methodological

details on the MC model formulation used here are described

fully in the supporting information available on the Journal’s

Web site, both in relation to earlier work on copper (Eckelman

and Daigo 2008) and the generalized AMC model described by

Duchin and Levine (2010).

Model uncertainty is a major issue in a long-term study en-

compassing disparate data sources, particularly with regards to

waste management statistics. A sensitivity analysis was per-

formed on the end-of-life recycling rates in each country to

determine the influence of these parameters on the final results,

and an uncertainty analysis was done to explore model un-

certainty associated with the lifetime distributions of nickel in

each end-use category. Details are again given in the supporting

information on the Web. There is also uncertainty related to

the use of a static state transition matrix based solely on 2005

material flows, which is discussed in the Modeling Considera-

tions section in relation to possible dynamic extensions to MC

models.

Results and Discussion

Stepwise transitions and losses of nickel

Figure 2 shows the fate of nickel as it moves through the

global economy over the first 50 steps of the MC. The initial

state of the nickel (step 0) is as nickel ore in each mining coun-

try, with the degree of shading representative of each country’s

share of global ore production in 2005. (Other possible initial

states are discussed later in this section.) Unshaded countries

are either not included in the set of 52 major economies con-

sidered here or contain less than 0.1% of global 2005 nickel at

a given step in the MC. The graph on the right-hand side of the

figure depicts the location of nickel in aggregate, either within

the global economy or lost to the environment or carbon steel

absorbing states. In this initial state, 100% of global nickel is in

the economy (as ore), ready to be processed.

In the next MC step, some ore and concentrate are exported,

some nickel is lost to tailings (appearing in the Environment

box), and the remainder stays in each country for further pro-

cessing. Nickel losses to tailings can be observed in the sharp

uptick in the amount of nickel lost to the environment at the

step 1 mark, seen in the right-hand graph.

This pattern continues: For each step, nickel in a given

sector of the global economy moves to adjacent sectors in the

MC, either in other countries through international trade or

within the domestic economy, while some portion may be lost

to the local environment or to global carbon steel recycling. By

the time nickel has entered manufacturing in most countries

(step 5), the global distribution has changed dramatically from

the initial extraction state, with nickel found in nearly every

country considered in the analysis. Unsurprisingly, nickel at this

step is most abundant in China, Japan, South Korea, Germany,

and the United States, where a large portion of the world’s

manufacturing is conducted. Nickel then enters use (step 6),

and after a certain lifetime in a building, an airplane, or a piece of

industrial machinery, for example, it comes out of use and enters

waste management (step 7). At this point, there is another sharp

increase in nickel losses to the environment and nickel lost to

carbon steel appears for the first time in the right-hand graph of

figure 2. After this point, a stepwise interpretation of the results

becomes difficult, as nickel-containing scrap can enter a new



0% 50% 100%

0

5

10

15

20

25

30

35

40

45

50

Environment

Carbon Steel

Markov step 3RefiningImport of matteExport of refined

Markov step 02005 distribution of

global nickel ore

Markov step 1MiningExport of concentrateLosses to environment

Markov step 5Manufacturing and useWide distribution of nickel

Markov step 30Several cycles of recyclingUse concentrated in ChinaNotable trade still occuringSignificant loss to CS

Markov step 50Remaining use ChinaInsignificant tradeLoss to env. (75%)Loss in CS (21%)

share of 2005 Ni

Losses t

o C

arb

on

Ste

el

Pro

duction

, U

se

, &

Tra

de

Lo

sses t

o th

e E

nvir

onm

ent

…

Environment

Carbon Steel

Environment

Carbon Steel

Environment

Carbon Steel

Environment

Carbon Steel

Environment

Carbon Steel

……

…

0% 75%

Figure 2 Stepwise global movement of nickel down 50 steps of the Markov chain, in percentage of total 2005 extraction, for individual

countries, regions, and global sinks (left), and globally aggregated (right); 0.1% cutoff for shading.

cycle of production in either the smelting or fabrication stages,

so that there is no longer a one-to-one correspondence between

the number of steps down the MC and the general location of

nickel in its life cycle.

After 30 steps of the MC, the picture is again quite differ-

ent. A large portion of the nickel originally produced in 2005

has been lost to carbon steel and the environment, with only

24% still in the global economy. Of this, nearly half is found in

China, either as nickel-containing scrap being processed into

new goods, or as products in use in that country. The trend con-

tinues such that after 50 steps of the MC only 4% of the nickel

that began as ore in 2005 is still in the global economy, with



the majority of this material in China. Numerical values for the

first 10 steps, as well as a short video showing the progression of

global nickel flows over 50 steps, can be found in the supporting

information on the Web.

Figure 3 shows the distribution of nickel lost to the environ-

ment in different countries after a large number of MC steps

(k = 10,000) from the starting state of 2005 global ore extrac-

tion. Losses occur with every step of the MC and every cycle of

production, use, and recycling of nickel in the global economy.

Nickel loss is concentrated in a few countries, with fully 28%

lost to the environment in China. This means that of all the

nickel in ore extracted in 2005, 28% of that nickel will even-

tually end up in the tailings, slag, and landfills in China. These

losses will occur by a variety of routes, either through Chinese

mining and smelting (Chinese primary nickel production was

only about 5% of the global total for 2005, although this propor-

tion has increased in subsequent years), or through industrial

waste generated during fabrication and manufacturing of goods

(for which China is the dominant player globally), or, most

importantly, through discards of nickel-containing products to

landfills. These results are consistent with China’s influence on

the global cycle of stainless steel (Reck et al. 2010).

There are also significant losses of nickel in the major pro-

ducing countries of Australia, Canada, and Russia, which even-

tually will hold 4%, 5%, and 5.5% of the nickel extracted in

2005, respectively. Major refining, fabricating, manufacturing,

and end-user countries also experience nickel losses to their

respective environments, including the United States (6%),

South Korea (2.5%), and Japan (2.1%). The figures for all other

countries are 2% or less.

After a large number of steps, all nickel must reside in the ab-

sorbing states of the MC model. In total, approximately 78% of

all nickel extracted is lost to the environment absorbing states,

while the remaining 22% is lost to the other absorbing state of

carbon steel. Figures 2 and 3 depict the fate of nickel from an

initial distribution of all countries that mined the metal in 2005,

and so follow an annual cohort of metal through space and time.

However, it is also illuminating to consider the global fate of

nickel produced in just one specific country as a measure of how

interconnected the country is in the worldwide “nickel econ-

omy.” Figures depicting the final distribution of environmental

losses of nickel mined in the three major extracting countries—

Russia, Canada, and Australia—are presented in the supporting

information on the Web. All three of these cases display the

same pattern: major losses are concentrated in the particular

mining country itself, in China, and, to a much lesser degree,

in the United States.

Number of uses of nickel

The next question posed in the introduction concerns the

total number of times that the 2005 cohort of nickel enters use

in some form, summed over all end-use sectors in all countries

and all cycles of use until no nickel is left in circulation. This is

not an intuitive concept given the weighted averaging involved,

but it is a useful metric for identifying hotspots of use—end-use

sectors in the global economy where nickel is used multiple

times—and informs the general discussion of metal recycling

and resource efficiency. Virgin nickel extracted in 2005 will

be used a total of 3.0 times over its technological lifetime,

averaged over all possible routes of recycling and trade. This is

a significant difference from the 1.9 global uses experienced by

copper, as estimated in a previous study for year 2000 production

(Eckelman and Daigo 2008). In that case, the most frequent

use of copper was in electrical infrastructure in Asia. Nickel

is used most often in China, with the country’s six end-use

sectors comprising approximately 1.3 of the average 3.0 lifetime

number of uses. In other words, nickel extracted globally in 2005

is expected to be put into use at some point, somewhere in the

world, an average of three times and is expected to pass through

China’s economy specifically 1.3 times. In contrast, nickel will

spend only 0.3 of its lifetime uses in the United States, much of

which is during the first time it is being used. Nickel also sees

significant lifetime uses (>0.1) in South Korea, Spain, Italy, and

Germany.

The discrepancy in the results between China and the other

large end-users of nickel is surprising, as is the notable absence

of significant results for Japan. It is important to distinguish the

lifetime use results presented here that track a cohort of mined

nickel from a specific year, in this case from 2005, and the more

familiar statistic in the metal industry of end use (referring to

the first cycle of use in a Markov model). China’s lifetime uses

result can be explained as a combination of high levels of nickel

entering end use (392 gigagrams [Gg],1 fully one-quarter of the

global total), domestic reprocessing of nickel scrap, and net

import of scrap from international markets. In considering the

specific cohort of nickel from 2005, the portion that entered

end use in China will largely stay in the country for the sec-

ond cycle of production, minus losses to landfill for that scrap

that eludes collection and recycling. Despite China’s status as a

global exporter of goods, most nickel is used domestically, with

the highest export category being metal goods (17% exported),

and so most of the nickel that is reprocessed in China stays

in China for a second use, is collected and reprocessed domes-

tically, enters a third use, and so on. These subsequent uses

account for China’s leading result, with a similar phenomenon

contributing to South Korea’s significant result. Japan is also

a large end user of nickel (118 Gg), but exports a portion of

its scrap for foreign reprocessing and does not subsequently im-

port many nickel-containing final goods, thus losing secondary

metal with each cycle. The distinctions in scrap import and

export between the two countries may seem insignificant, but

they are magnified by the many cycles of nickel flows run by the

Markov model, leading to a large difference in the final results.

Up to this point, all of the results have assumed an initial

state of nickel as ore mined in 2005. One of the largest single

losses of nickel to the environment is nickel in tailings dur-

ing ore extraction and processing. For mining companies that

aim to minimize losses to tailings, it is useful to consider the

global journey of nickel using ore as an initial state, as advances

in nickel ore processing techniques can positively impact the

total result. Nickel-related companies that are not involved in



Figure 3 Distribution of environmental losses of nickel extracted in 2005.

nickel production, however, have no control over nickel lost to

tailings (or slag during smelting), and so it may be more useful

for them to assume an implicit first time of nickel use that treats

the initial state as nickel entering fabrication in 2005. The

largest nickel fabricators in 2005 were China, Japan, South Ko-

rea, Belgium–Luxembourg, Finland, Germany, and the United

States. If we follow that procedure and switch the initial state in

the present global nickel model from nickel in ore to nickel en-

tering fabrication, the lifetime number of uses increases from 3.0

to 3.9 (one implicit first time use of nickel and 2.9 subsequent

uses). This revised result may be a better indicator of nickel’s

current recycling performance (which generally excludes min-

ing operations) for companies and groups that engage in some

sort of recycling or reprocessing activities.

Accrual of time and embodied energy over the global

journey of nickel

The final two questions posed in the introduction consider

the age and embodied energy that accrue to nickel as it moves

through the global economy. First, considering the time that

nickel spends in each end-use sector in each country, as well as

the time required for production, trade, and waste management,

the total technological lifetime of nickel is approximately 73

years (±7 years from the uncertainty analysis presented in the

supporting information on the Web). This means that an ar-

bitrary unit of nickel extracted in 2005 will last, on average,

more than seven decades before being lost to the environment

or to carbon steel. While the potential lifetime of nickel in the

economy is nearly infinite because of the immutability and re-

cyclability of metals, this result reflects actual practices as of

2005. In fact, the average lifetime of nickel may further shorten

if nickel’s use in certain specialty applications grows. Products

like electronics or certain alloys only use small amounts of

nickel that, at end of life, are unlikely to be recycled for their

nickel content. This characteristic shows the strong influence

of product design on recycling rates and total technological

lifetimes.

Finally, the movement of nickel through its technological

lifetime requires energy at nearly every step: during primary pro-

duction, processing, remelting of scrap into new products, and

transportation. The total embodied energy of nickel weighted

over all of its possible routes through the global economy is esti-

mated to be 580 gigajoules per tonne (GJ/t),2 or about 195 GJ/t

per use. This is approximately 30% less than the energy re-

quired to produce Class I refined nickel from virgin ore (Eckel-

man 2010), which indicates the energy benefits of recycling and

the investment of energy that is lost when nickel is discarded.

These are aggregate results, but MC modeling also allows for

a detailed investigation of energy use, particularly with regards

to geography and time. Russia is the largest producer of virgin

nickel and, unsurprisingly, its production facilities are responsi-

ble for the largest share of energy used during this first life cycle

of nickel. But when considering all possible cycles of nickel,

China emerges as the location where the largest share of en-

ergy is used, due to its dual role as a major metal producer and

manufacturer of nickel-containing products. These geograph-

ical considerations are vital when considering energy-related

emissions (such as greenhouse gases) that are highly dependent

on the local mix of energy and conversion technologies, as well

as any company policies or the use of financial instruments

associated with managing these emissions.

Modeling Considerations

We would now like to revisit the temporal aspect of the MC

model. It is important to note that the steps of figure 1 are not

time steps, they are transition steps, stepwise. The time that

nickel spends in use is much longer than the time it spends

in manufacturing, for example. This time heterogeneity has no

effect on the number of uses or technological lifetime results

considered here, but it does make interpretation of the results

more challenging for business and policy analysis. Introducing

uniform time steps would enable users to read the model results

across time and to estimate the distribution of global resources

at some given year in the future. Such a feature would bring

MFA-based MCs closer to continuous-variable dynamic MFA

models that depict material flows coming in and out of stock

(Muller 2006). While we do not do so here, it is possible to

convert A into a time-homogenous state transition matrix by



partitioning each state into individual years (or discretizing the

continuous lifetime distributions for nickel in each end use), as

suggested in Stokey and Zeckhauser (1978), and carried out by

Davis and colleagues (2007) for iron and steel in the UK. Do-

ing so would essentially convert the model from an event-based

to an interval-based approach, allowing for flexibility in mod-

eling lifetime distributions and other temporal considerations

endogenously; however, such a structure would also increase

the size of A by approximately two orders of magnitude.

Another important point to note is that the elements of A

are based on the flows of nickel in a given year, in this case 2005,

and is therefore static. So even though MC models explore the

future flows of metal over several decades, they do so under the

assumption that the relative structure of nickel production and

consumption stays constant. It was not the goal of this work

to forecast the future economic structure of nickel supply and

demand, but one way to introduce dynamics into the MC model

presented here would be to create a series of transition matri-

ces that vary through time, followed by performing a strictly

stepwise analysis of the model results. Dynamics could also be

introduced by varying the lifetime or energy use vectors, which

would be a relatively straightforward way to model technolog-

ical change and increasing efficiency in nickel production and

processing facilities.

The present article has discussed IO- and MFA-based MC

models as distinct and complementary, but there are ways in

which they might be combined. As pointed out by Duchin and

Levine (2010), the integration of waste flows into IO tables, as

exemplified in the work of Nakamura and colleagues (2007),

would allow for meaningful tracking of resources through recy-

cling and reuse activities, but doing so for global multiregion

IO tables is a huge undertaking. It may also be useful to con-

sider a particular subset of resources (metals, for example), for

which some global waste management data have already been

compiled, as an early target for integration. Further use of ge-

ographic information, such as physical distance between states

or more country-specific life cycle inventory data will also be a

fruitful area of exploration for MC models.

Using MC Model Results

On a macroscopic level, the results presented here are use-

ful for understanding the global economy of nickel and, as a

valuable technological material, such information helps us be

strategic about its finitude. The location of production facili-

ties is obviously well known, and the present analysis details

what happens to nickel after production through its entire life-

time: where it goes, where and how it is used, how long it

lasts, and how much energy humans invest in it over its tech-

nological lifetime. These results can be used to inform policy

discussions around nickel, particularly those related to allocat-

ing the environmental impacts of nickel production to different

life cycle stages (Yamada et al. 2006). In the context of green-

house gas emissions and carbon credits, these discussions may

help to determine which industry sectors will receive credits for

recycling and which will not, and thus they carry significant

economic implications. The results can also be used as inputs

to other techno-economic models, such as those determining

future supplies of secondary scrap metal based on current inputs

(Hatayama et al. 2010) or those mapping the location of metals

in use (Rauch 2009).

The results also present a challenge to industry, as the cur-

rent statistic of 3.0 lifetime uses (or 3.9 uses for refined nickel)

can, in theory, be extended significantly with efforts in scrap

collection, recycling, and reprocessing. The results for energy

expended over nickel’s lifetime showcase the energy benefits of

recycling nickel, and can be used to quantify the total amount

of reduced energy use by the nickel industry for a specific co-

hort of nickel (as opposed to energy saved through recycling

during a particular year, as is currently done). The nickel indus-

try may also use the energy results as a benchmark with which

to highlight the benefits of future energy investments in nickel

processing facilities or technology. Spatial information on the

location of nickel that is lost during its technological journey

may be seen as an opportunity by industrial actors that could

use the results in focusing recovery efforts, extending product

lifetimes, or even eventually treating current environmental

sinks as sources of secondary material.

Acknowledgements

The authors gratefully acknowledge conversations with

Ichiro Daigo, Seiji Hashimoto, Faye Duchin, and Steven

Levine, the comments provided by three anonymous review-

ers, and the financial support of the Nickel Institute. Partial

funding for Matthew Eckelman was provided by the U.S. En-

vironmental Protection Agency’s Science to Achieve Results

(STAR) Fellowship.

Notes

1. One gigagram (Gg) = 106 kilograms (kg, SI) = 103 tonnes

(t) ≈ 1.102 × 103 short tons.

2. One gigajoule (GJ) = 109 joules (J, SI) ≈ 2.39 × 105 kilocalories

(kcal) ≈ 9.48 x 105 British thermal units (Btu). One metric ton

(t) = 103 kilograms (kg, SI) ≈ 1.102 short tons.

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About the Authors

Matthew Eckelman was at the time of writing a lecturer

at Yale University in New Haven, CT, USA and is now an

assistant professor in the Department of Civil & Environmental

Engineering at Northeastern University in Boston, MA, USA.

Barbara Reck is an associate research scholar and Thomas

Graedel is the Clifford R. Musser Professor of Industrial Ecology

at the School of Forestry & Environmental Studies at Yale

University.

Supporting Information

Additional supporting information may be found in the online version of this article:

Supporting Information S1: This supporting document contains

1. details on the mathematical formulation of the country-level MC model in relation to model formulations described

in previous work;

2. figures S1-1–S1-3, depicting the distribution of environmental losses of nickel initially mined in the three largest

extracting countries, Russia, Canada, and Australia; and

3. details of the methods and results of the uncertainty analysis that accompanied the AMC model of the global resource

flows of nickel.

Supporting Information S2: This supporting information provides a table with stepwise country-level results of nickel flows

from global production in 2005 and country-level results of the total number of uses the nickel experiences.

Supporting Information S3: This supporting information provides a Microsoft PowerPoint slideshow that animates stepwise

the global flows of nickel using a series of annotated maps.

Please note: Wiley-Blackwell is not responsible for the content or functionality of any supporting information supplied by

the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.


exploring the global journey of nickel with markov chain

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