Analysing the Uncertain Future of C opper with
Three Exploratory System Dynamics Models
Willem Auping (TU Delft/HCSS, w.l.auping@ tudelft.nl, WillemA uping@ HCSS.nl)
Enik Pruyt (TU Delft)
Jan Kwakkel (TU Delft)
Policy Analysis Section,
Faculty of Technology Policy and Management
Delft University of Technology
Jaffalaan 5, 2628BX, Delft, The Netherlands
March 2012, Conference paper for the 2012 SDS conference
Abstract
High copper prices, the prospect of a transition to a more sustainable energy mix
and increasing copper demands from emerging economies have not led to an in-
creased attention to the base metal copper in mineral scarcity discussions. The
copper system is well documented, but especially regarding the demand of copper
many uncertainties exist. In order to create insight in this systems behaviour in
the coming 40 years, an Exploratory System Dynamics Modelling and Analysis
study was performed. Three different models have been developed representing
different views on copper supply and demand. The behaviour of these models
shows crisis-like behaviour for the copper price, and often a declining consump-
tion of refined copper. Six different policy options have been explored, individu-
ally and in combinations, for their robustness in counteracting undesirable behav-
iours. The results of these tests are that emphasising recycling, and the develop-
ment of strategic reserves are potentially helpful.
Keywords: Copper, Mineral Scarcity, System Dynamics, EMA, ESDMA
1 Introduction
In the debate about mineral and metal scarcity, the focus is on several “risky” metals, like
lithium (A ngerer et al. 2009) and the rare earth metals (European Commission 2011). Almost
no attention exists for copper. This bulk metal however, can be considered to be a scarce
metal, in contrast to iron or aluminium (Gordon et al. 1987, 2). The vast quantity of copper
use (ICSG 2010) and the current high copper prices (LME 2011) make societal problems re-
garding this metal, like copper theft (Klis 2011), an almost inevitable consequence.
There seem to be two causes for the current high copper price: the energy transition
towards a more sustainable mix of energy sources (Kleijn and van der Voet 2010) and the
growing demand for minerals in fast developing economies like China and India (European
Commission 2011). The future development of copper demand however can be classified as
deeply uncertain. Deep uncertainty can be defined as: ,,where analysts do not know, or the
parties to a decision cannot agree on, (1) the appropriate conceptual models that describe the
2 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
relationships among the key driving forces that will shape the long-term future, (2) the proba-
bility distributions used to represent uncertainty about key variables and parameters in the
mathematical representations of these conceptual models, and/or (3) how to value the desira-
bility of alternative outcomes” (Lempert, Popper, and Bankes 2003). Another deeply uncer-
tain element in the copper system is the development of the ore grade in relation with mining
operations (Tilton 2003; Gordon, Bertram, and Graedel 2007; Tilton and Lagos 2007).
A novel method which allows exploring the influences deep uncertainties have on sys-
tem behaviour is Exploratory System Dynamics Modelling and Analysis, or ESDMA (Pruyt
2010; Pruyt et al. 2011; Pruyt and Kwakkel 2012). ESDMA is a combination of Exploratory
Modelling and Analysis (EMA), (Bankes 1993; Lempert, Popper, and Bankes 2003) and Sys-
tem Dynamics (SD) models especially developed to explore both parametric and structural
uncertainties. In this paper, the goal is to create plausible scenarios for Key Performance Indi-
cators (KPIs) in the copper system, explore possible undesirable effects in these scenarios,
and the influences the uncertainties have on this system behaviour. In light of this, several
policies that can address the identified undesirable effects have been developed and tested.
In this paper, the research methodology will be explained in section 2. This starts with
an overview of SD studies on the domain of scarcity issues and commodity cycles and is fol-
lowed by elaborations on EMA and ESDMA. The structure of the different copper models
used in this study will be explained in section 3. In section 4, the scenarios exhibited by these
models will be discussed. In section 5, some policy options for the copper system and the ef-
fects they have on the ensemble of scenarios are assessed. Section 6 contains the conclusions
both on future dynamics of the copper system and the use of the ESDMA methodology for
scarcity issues is presented.
2 Methodology
2.1 SD modelling of mineral and metal scarcity
System Dynamics (SD) (Forrester 1968; Sterman 2000) is a modelling method which is par-
ticularly useful for simulating systems which are characterized by strong feedback loops, de-
lays and stock-flow structures. The simulation of SD models has as goal to investigate modes
of dynamic behaviour over time.
SD modelling of mineral and metal scarcity has a long tradition. Probably the most
well-known example is the Limits to growth (Meadows et al. 1972), where minerals and met-
als are modelled as non-renewable resources. In many other examples geological, technologi-
cal and economic aspects about mineral depletion were combined (Sterman and Richardson
1985; Davidsen, Sterman, and Richardson 1987; Sterman, Richardson, and Davidsen 1988).
A more specific metal study was performed by the Dutch National Institute of Public
Health and Environment (Van Vuuren, Strengers, and De Vries 1999), where the long-term
structural dynamics for two categories of metals were studied. Some research aimed at cer-
tain specific metals, like the platinum group metals (Alonso, Field, and Kirchain 2008) or
magnesium (Urbance et al. 2002). In these studies the use of the metal is often linked to a
specific use for the metal, like electronics (Alonso, Field, and Kirchain 2008) or the automo-
tive industry (Urbance et al. 2002). No SD model was found however which exclusively fo-
cused on the global supply and demand of copper.
The copper models presented here try to unite geological, technological and economic
aspects of the copper system. This is however not be done in a traditional way, but by com-
bining SD techniques with the Exploratory Modelling and Analysis approach.
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper 3
2.2 Exploratory Modelling and Analysis
Exploratory Modelling and Analysis (EMA) is a research methodology that uses computa-
tional experiments to analyse deeply uncertain issues (Bankes 1993; A gusdinata 2008). EMA
consists quantitative modelling of the set of plausible models and uncertainties, the process of
exploiting the information contained in such a set through a large number of computational
experiments, the analysis of the results of these experiments, and the testing of policies for
robustness (Bankes 1993; A gusdinata 2008). Uncertainties may be caused by a variety of fac-
tors, including the infeasibility of critical experiments, impossibility of accurate measure-
ments or observations, immaturity of theory, openness of the system to unpredictable outside
perturbations, or nonlinearity of system behaviour, but is fundamentally a matter of not know-
ing enough to make predictions (Cambell et al. 1985; Hodges and Dewar 1992).
EMA can be useful when relevant information exists that can be exploited by building
models, but where this information is insufficient to specify a single model that accurately
describes the real system behaviour. In this circumstance, models can be constructed that are
consistent with the available information, but such models are not unique, which is an impor-
tant reason for specifying different model structures or even multiple models. These models
combined with other uncertainties allow for computational experiments that reveal how the
world would behave if the various guesses any particular combination of assumptions would
be correct. By conducting many such computational experiments, the implications of the vari-
ous guesses can be explored.
In this study, EMA was performed by making use of three SD models. This relatively
new method, called Exploratory System Dynamics Modelling and Analysis, or ESDMA
(Pruyt 2010; Pruyt et al. 2011; Pruyt and Kwakkel 2012) forms an extension to the traditional
SD approach in the way that it allows exploring the effects of both structural and parametric
uncertainties on the behaviour of KPIs in the explored system. By doing so, ESDMA follows
suggestions from classic SD literature, e.g. the comments in Groping in the Dark by Scolnik,
Cole, Rademaker and Bremer (Meadows, Richardson, and Bruckmann 1982, 149, 205, 207,
231). Thus in this case, special structures have been added to the models which allow switch-
ing between different structures about which deep uncertainty exists, apart from the different
model varieties that have been built. This makes it important in the model specification to
clearly distinguish which structures can be considered deeply uncertain and which possible
model definitions can be made regarding these uncertainties.
2.3 EMA visualisations
Exploring the effects of deep uncertainties requires many runs to adequately cover the uncer-
tainty space. This large amount of runs can be visualised in a way which is close to the tradi-
tional one-line base case visualisation, by plotting all runs in one figure. The result, the lines
graph, can be seen in Figure 1. Since the distribution of the lines over the different states gives
valuable information as well, a Kernel Density Estimation (KDE) (Rosenblatt 1956; Parzen
1962) of the end state is added at the right side of the picture. This distribution however does
not allow probabilistic interpretation, since uniform distributions and cardinal switches were
used as inputs for Latin Hypercube sampling (Iman, Campbell, and Helton 1981).
4 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
part of original demand iBauted
"oo 20102020 230 «2040 20500 1s "Sooo ——aoio ano SSC 18
Figure 1: Lines graph with KDE for part of Figure 2: Envelope graph with KDE for part of
original demand substituted original demand substituted
In cases where the extreme values are important for interpretation, the outer limits of
the run ensemble are most important. For that purpose, the ensemble figure was developed
(Figure 2). Combined with the KDE, it gives also a clear overview of the effectiveness of
policies over the ensemble of runs (e.g. see Figure 15).
Since in many cases the distribution of runs is important for other states than the end
state, a visualisation was needed that allows examining the distribution of runs for all time
steps. For this purpose, on the x-y-plane used for the lines or envelopes graph, the distribution
is given in the third dimension. This generates the picture visible in Figure 3. By rotating this
image (Figure 4), the distribution of the ensemble becomes clearer visible. The 3D envelopes
are often truncated to reduce the effect extreme values have on the visibility of the ensemble.
Figure 3: 3D envelopes, y axis and x axis asin Figure 4: 3D envelopes, rotated. The x axis is
2D graph, while z axis with distribution is to- from back to front, the y axis from left to right,
wards the viewer and the z axis with the distribution from stand-
ing on this plane
For further interpretation of the data, machine learning algorithms, like the Patient
Rule Induction (PRIM) (Friedman and Fisher 1999), Random Forests (Breiman 2001) and
clustering the behaviour could be used on the ESDMA data. These will provide more insight
in the ranges in which combinations of uncertainties cause certain behaviour.
3 Modelling the copper system
Parts of the structure of the copper system are, as was already described above, well docu-
mented, while other parts of the system are deeply uncertain. In order to develop an ensemble
of models that can explore these deep uncertainties, first the major deep uncertainties in the
copper system have to be identified (Table 1), for their specification will have a profound
influence on the behaviour exhibited by the KPI’s in the copper models. Some of these deep
uncertainties are composed of elements which are each a separate deep uncertainty. An exam-
ple is the demand evolution from a top down approach. This is composed of scenarios for the
global population (UNPD 2011), economic growth and the relation between copper demand
and the GDP per capita (Wouters and Bol 2009, 18).
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper 5
Table 1: Major deep uncertainties in the copper system
Uncertainty Type of uncertainty Description
Demand evolution Structural uncertainty The intrinsic demand for copper, i.e. the
demand without effects due to price and
substitution
Ore grade evolution Structural uncertainty The ore grade declines with mining of
copper
Price of energy evolution (Dynamic) parametric The price of the energy needed for copper
uncertainty production
Prices of substitutes evolu- (Dynamic) parametric The evolution of the price for substitutes
tion uncertainty for copper use
Economic growth (Dynamic) parametric The growth of the GDP globally or re-
uncertainty gionally
Resources/resource base Structural uncertainty What amount of copper is ultimately re-
coverable from the earth’s crust
Capacity evolution Structural uncertainty The capacity for (deep sea) mines, smelt-
ers and refineries
Copper supply and demand can be conceptualised along two important perspectives, being the
different uses for copper (Angerer et al. 2010) and the strongly regionalised mining, refining
and consumption of copper (ICSG 2010). For both perspectives a higher and lower aggregate
view of the system are chosen, since models designed from these views can potentially pro-
duce quite diverse behaviours. Therefore, in this study four different model varieties are pos-
sible (Table 2). The dynamic hypothesis is thus that these different models will generate par-
tially different behaviour, thus expanding the set of plausible scenarios for the future of the
copper system.
Table 2: Matrix of the copper models. Below each model name the corresponding number of
model uncertainties is given.
Regions
Dimension
1 3
Top down Regional
j 112 178
Bottom up Complete
167 341
The first parameter is the uses perspective, where the copper demand was conceptualised with
a top down demand with a single copper use, and bottom up demand with a division in six
major uses. The second parameter allows a geopolitical perspective with a global and a re-
gionalised demand.
Together, these two dimensions result in four possible models. Out of these four, three
models are discussed in this paper. For a description of these models see Appendix: model
descriptions. The first variety discussed is the top down model, with a global top down per-
spective on the demand evolution. This model is particularly interesting to explore the conse-
quences of the growing demand due to a growing number of people with an increasing
wealth. The second model is the bottom up model, which has a globalised bottom up perspec-
tive on the demand. In the specification of this model, the effects of the energy transition on
6 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
different uses of copper can be explored. In the third mode, the regional model, a regional top
down perspective was chosen. This allowed looking into the effects on the system in a market
which is not completely free and open. Finally, the fourth model, combining the perspectives
chosen in the bottom up and regional models, was not used in this study. As is visible in Table
2, this model had a very large number of uncertainties. Besides the obvious effects this had on
the computational requirements for fully exploring this uncertainty space, pinpointing the
effects specific parameters have on the behaviour of the K Pls is far more difficult.
In the specification of the copper models, as far as possible information from sources
describing the actual structure and functioning of the global copper supply, demand and sub-
stitution have been used, although this had as a consequence that the developed models are
considerably larger than usual exploratory SD models (Pruyt 2010, 2010).
Where conflicting mental models existed about the functioning of a particular part of
the system, different structures corresponding to these different views have been made to be
able to explore their effects. This is in line with the approach Forrester described (Forrester
1994, 12, 13). One exception is the ore grade discussion (Tilton 2003; Gordon, Bertram, and
Graedel 2007; Tilton and Lagos 2007). In the models a choice was made to explicitly let sub-
stitution influence the demand for copper and as such, via the evolution of the costs of copper
mining due to the lower ore grade, influence the demand for primary (i.e. mined) copper.
Technological aspects of the copper production regarding the reduction of costs due to learn-
ing effects have also been assumed to have little effect, due to the large experience in and
long history of copper mining (ICSG 2010, 9).
4 Behaviour of the copper models
For each model variety, 1000 sets of input variables were generated with the Latin Hypercube
sampling method (Iman, Campbell, and Helton 1981) over the uncertainty space, generating a
total set of 3000 results, which will be discussed now.
4.1 Top down model results
The results from the behaviour of the top down model showed in many cases a decline of the
global consumption of copper (Figure 5 and Figure 6). In Figure 5 the behaviour of this vari-
able is depicted with a lines graph, while Figure 6 shows the truncated 3D envelope.
Figure 5: Run lines for global consumption of Figure 6: Distribution of global consumption
copper, top down model of copper over time, top down model. Trun-
cated at 30 million t/Y ear
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper 7
distribution
Sao m0
Figure 7: Run lines for real price of copper, Figure 8: Distribution of real price of copper
top down model over time, top down model. Truncated at
100000 Dollar/t
"Shoo 2010 2020, 2030 240 20500 18
Figure 9: Run lines for part of original de- Figure 10: Distribution of part of original de-
mand substituted, top down model mand substituted over time, top down model
A typical characteristic of the copper consumption are the small boom and busts visi-
ble in many runs. These are caused by an increased demand in times of a low copper price,
which will be limited when the global inventories of refined copper are declining due to this
higher demand and the lower refining capacity, due to the lower prices in times of a relative
high availability of the metal.
The real price of copper shows behaviour characterised by strong rises and declines
(Figure 7). These are caused by disbalance between availability and intrinsic global demand
of copper. The long period for adjusting the capacities for mining and refining, combined with
long term effects of high and low copper prices and the substitution of copper have the big-
gest influence in this lack of adaptability in the copper supply system. On average, the behav-
iour in the runs for price is exponential growth, which is caused by the declining ore grades
and consequentially the rising marginal costs. This can be seen in the lower values for the
KDE in the later years of the run set (Figure 8).
Finally, the part of original demand substituted (Figure 9 and Figure 10) shows very
strong rises in substitution, mainly caused by long term price effects. A strong rise in substitu-
tion can form the basis for a strong decline in demand, causing the copper price to collapse.
This was potential copper system risk, identified already by (Rademaker and Kooroshy 2010,
3) and thus visible in the modelled copper system.
4.2 Bottom up model results
The bottom up model shows on average a higher copper consumption than the top down
model (Figure 11). This indicates that the top down method for estimating copper consump-
tion may not be accurate with regard to increases in copper demand due to the energy transi-
tion.
8 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
Another difference in the copper is the behaviour of the copper substitution. Since the
substitution threshold is also subscripted, the substitution happens at different moments, also
reducing the long term substitution effects and as a consequence, also the slopes of the part of
original demand substituted (Figure 12).
"$000 2 2020 203 FE 20500
Figure 11: Distribution of global consumption _‘ Figure 12: Run lines for part of original de-
of refined copper over time, bottom up model. _ mand substituted, bottom up model
Truncated at 30 million t/Y ear
4.3 Regional model results
The behaviour of the global consumption of refined copper in the regional model showed
even more booms and busts than the original top down model, but the declines after the cop-
per consumption peak were often less steep (Figure 13). This different behaviour can be ex-
plained by the ex- and import of different copper products and the resulting slower reaction
time of the model on copper scarcity, which develops regionally.
The regional model showed a stronger decline in copper consumption, more specific
copper mining, than the other two copper models. The lower rate of global mined copper pro-
duction depletes the reserve base, making the value of the global reserve base of copper di-
vided by the mining production, in the models called year left of copper mining, higher
(Figure 14). This figure shows after 2010 very low values for the KDE. This can thus only be
caused by a strong decline in the global mined copper production.
8 18
7
6 | global consumption of refined copper ps
distri
Shoo 2010 020 2030 240 2050) 3 Real price of copper
Figure 13: Run lines for global consumption of Figure 14: Distribution of year left of copper
copper, regional model mining over time, regional model. Truncated
at 500 year
4.4 Assessment of the outcomes
The declining copper consumption, the strong substitution effects and the volatile price devel-
opment are well perceivable in the real world copper system when existing dynamics regard-
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper 9
ing the development of mine, smelter and refinery capacity in combination with dynamics of
substitution and demand are taken into consideration.
The gradually declining copper consumption can be explained by the falling grade of
copper ore, which is a main factor in the increase of the marginal costs of copper mining. The
substitutes of copper, like aluminium, do not have this problem (Gordon et al. 1987). It is
therefore very likely that copper will become more expensive compared to its substitutes in
the coming period.
The strong substitution effects are most prone to exist after a longer period of high
copper prices. When these high prices first occur, consumers will in the short term take their
loss, while in the long term they will seek for alternatives for the high price asset. This long
term effect probably generates high substitution of copper products, causing the price to drop
when this reaches a certain turing point, reversing the situation. Especially with current high
copper prices, this is a very likely scenario to occur.
The alternating prices cannot be explained however with the long term oscillating sub-
stitution effects alone, since in isolation these effects would have a goal seeking behaviour for
the copper price in the direction of the price of the main substitute. The reactions of the de-
mand on the price level however can cause the disbalance between supply and demand, since
the demand changes in such a case faster than the delays in the form of permit terms allow the
supply to adjust. In this way, price volatility is almost inevitable to occur.
Not all behaviour exhibited by the models seems valid however. The small boom and
busts visible in Figure 5 were not observed in the historical data. Further the values of the
global consumption of copper seem to be rather low compared to the estimated consumption
of over 15 million tonne in 2000 and over 19 million ton in 2010 (ICSG 2010, 2011). A rea-
son for this could be that the copper models presented here do not take into account that addi-
tional profits can be made by coproduction of other potentially high valued metals present in
the ore, amongst which are gold, silver and several other metals (Verhoef, Dijkema, and
Reuter 2004). Coproduction will essentially lower the marginal costs for copper, making it
more competitive compared to the substitutes and thus allowing more consumption before the
metal is being substituted.
5 Policy options to avoid plausible undesirable behaviour
5.1 Potential copper system risks
Despite the lack of predefined system risks by the commissioning actor of this research, it is
possible to define some potentially undesirable behaviour and system risks for stakeholders
from a European perspective (Table 3). These risks allow thinking about ways in which these
effects can be countered by introducing policy options.
Table 3: Potential copper system risks
Nr. Name Criterion Stakeholder
1 High price Real copper price > 100000 Dollar/t Consumers
2 Copper crisis Change in price > factor 2 in 1/8th of a Consumers, producers
ear
3 High substitu- Part of original demand substituted > 0.8 Producers, investors
tion
4 LowR/Pratio Year left of copper mining < 10 Year Consumers
5 HighR/Pratio Year left of copper mining > 500 Y ear Producers, investors
10 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
5.2 Policy design
For the design of policy options in an ESDMA context, roughly two approaches can be cho-
sen. The first approach can be seen as closing the circle. The modeller selects problematic
behaviour pattems, tries to find which selection of input parameters cause these behaviour ,
for example with the random forest method (Breiman 2001), selects those that can be influ-
enced by policy makers, companies or investors and tries to develop policies that (combined)
have the biggest impact.
The second option is having an understanding of the system. The modeller needs to
know which stakeholders can have an influence on the system and at which points this influ-
ence “connects”. This influence needs to be developed into possible policy options.
In this research, the second method for policy design was chosen. This resulted in the
policies visible in Table 4. These policies were tested on the same experimental setup as dis-
cussed in section 4. Per policy option, 1000 additional runs were performed. In the runs, the
policies were tested individually, but also in four combinations. These were the recycling
policies (1 and 2), substitution policies (4 and 5), strategic recycling policies (1, 2 and 3) and
all policies (1 till 6). Therefore, in total 30000 runs were performed to test the policies on the
three model varieties.
Table 4: Policy options for the copper models. All policies start in 2015; policies 1, 2, 4, 5 and 6
have full effect in 2025. 1, 2, 4 and 5 with linear interpolation, 6 with an S-curve
Nr Name Connection Goal Type
1 Recycling 1 Collection rate cop- 0.95 Political
per products
2 Recycling 2 Recycling score 0.95 Technical
3 Strategic reserve Global inventories of 0.5* Global consumption Political
refined copper of refined copper;
Selling at over 1.3 *
MAX(Marginal costs)
4 Substitution 1 Substitution thresh- 0.7 * original Substitution Technical
old threshold
5 Substitution 2 Growth of effect of Minimum 0.7 Political
substitution
6 Deep sea Marginal costs deep 0.5 * original Production Technical
sea mining costs deep sea copper
5.3 Results of the policy options
As aresult of the recycling policies, it was possible to increase the global consumption of re-
fined copper (Figure 15 and Figure 16). The combination of these policies with the strategic
reserve policy even further amplified this effect, while the other policies did not add much to
this reduction of unwanted behaviour. The combination of all policies finally also has a posi-
tive effect on the crisis behaviour visible in the real price of copper (Figure 17).
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper 11
‘SwrategieRecyelingPolicie
AllPolicies
—"DeepSeaPoticy ] =
insu 624468
ie
Phonon
__—4/
aN GODND—UBTSOL1s SMM) ODT 3088
Figure 15: Envelopes for different system performance indicators and all policy options and
combinations, top down model
cal price of copper
“Sooo 2s
Figure 16: Global consumption of refined Figure 17: Real price of copper, top down model
copper, top down model with recycling with all policies
policies
The other policies, more in particular the two substitution policies and the deep sea policy did
not seem to have a positive effect in reducing unwanted behaviour in the copper system. The
policies showed similar behaviour in the other model varieties.
6 Conclusions and discussion
The global copper system is, besides being well documented on the supply side, heavily influ-
enced by deep uncertainties. In order to explore the effects these uncertainties have on the
behaviour of the copper system, three model varieties were built. All models showed scenar-
ios with on average rising copper prices, which however are characterised often by large peri-
odic fluctuations. The high average price levels can however, also with periodic fluctuations,
cause substitution on large scale of the use of copper. When all run data is taken together, this
will create an image of a decreasing demand of copper in the coming 40 years.
Although the copper models all showed these general conclusions, some distinct dif-
ferences in behaviour between the different model varieties were distinguishable. The top
down model often showed crisis like behaviour, due to a very fast substitution of copper de-
mand. In the other models, substitution behaviour showed less intensity. This is probably due
to the fact that when the effects of different uses and regions are strong, substitution of all
uses or in all regions will not happen synchronous. Further, it was visible that the demand
growth as modelled in the bottom up model was bigger than the effect solely due to the
emerging economies, which also resulted in higher prices for copper. Finally, the regional
12 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
model showed longer periods for the fluctuations in model behaviour. This is probably due to
the slower reactions in the system in the case of less transparency in the system.
Several policy options were tested over the set of scenarios generated by the three
model varieties. This resulted in the observation that especially improving the collection rate
of end-of-life copper products, the recycling efficiency rate and the counter cyclic investment
in strategic reserves showed effectiveness in countering undesirable behaviour in the copper
system.
By combining the methodologies EMA and SD in an ESDMA research, it was possi-
ble to explore a wide variety of different scenarios for the copper system. Creating three
model varieties highlighting different perspectives on the copper system enriched this set of
scenarios and added extra insights on the effects of the growing demand from the upcoming
economies, the energy transition and the effects of a less transparent copper market which
would not have been possible without using this extensive methodology.
An extra remark needs to be made regarding the size of the models. While modelling,
an explicit aim was to keep a connection between the terms used in literature regarding the
copper system and the terms used in the copper models. This resulted in a relative low aggre-
gation level, especially when compared to other ESDMA studies (see for example Pruyt
2010). While this may have added to the validity of the model structure, it also posed problem
in exploring the uncertainty space created by the models. It was therefore with these large
models not possible to fully explore all possible behaviour. Further, it was also more difficult
to pinpoint certain behaviour to specific parameters in the models.
Future research that builds on the experiences from this study are possible both on the
topic of modelling the copper system and a more extensive use of ESDMA. For building the
copper models some input from experts was used, but this could have been extended. This
could have added to the validity of the models and the interpretation of the outcomes. For the
outcomes, it is interesting to use clustering algorithms on the scenarios generated by the cop-
per models. This would create more insight in the different dynamics visible in the results and
the drivers of this behaviour. Finally, adding more adaptive policy design working on these
drivers could make it possible to counter undesirable effects in the copper system in a more
robust way.
Acknowledgements
The authors would like to thank Piet Hein van der Kleijn for his input regarding the functioning of
the copper system and Douwe Bonthuis for his input regarding equations used in the copper mod-
els. Further, the advice of Wil Thissen, Ton Bastein and Gerard Dijkema during the execution of
this research was very much appreciated.
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16 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
A Appendix: model descriptions
A.1 Top down model
The smallest of the models in this study is the copper model with top down demand (Gordon,
Betram, and Graedel 2006). This intrinsic demand is calculated by looking at the development
of the world population, the GDP per capita and the effect of GDP on copper demand. A con-
ceptualisation is visible in the causal loop diagram (CLD. Sterman 2000; Lane 2008) of Fig-
ure 18. In this figure, three important balancing feedback loops can be distinguished: the sup-
ply, demand and substitution loop. Major external uncertain influences (compare Table 1) are
coloured pink.
World population
/
Effect of GDP on
_— copper demand
_ yt
ina eoperc
wet denen
Coppecsipply kh) Copp pee (——A Copper demand XN
ae | i
swpplyioop —/ Demand op
(bh Comper
en ee
_Ssbstiton bop 4 price of sibs
Figure 18: Simple CLD of the top down copper model
A.1.1 Copper stocks
The copper stocks sub model (Figure 20) forms a well-documented, possibly even the best
documented part of system (Lossin 2005; ICSG 2010). This sub model contains a stock flow
structure from resource base, resources, reserve base via mining and refining to the global
consumption of refined copper to copper use. When global copper in use has reached the end
of its lifetime, it is partially collected via the global secondary copper to scrap and recycled in
copper recovered from scrap. These stocks and flows outline the physical and technical back-
bone of the system.
As was mentioned above, some discussion exists about the relevance of the resource
base for the availability of copper in relation with the development of the ore grade of copper
(Tilton and Lagos 2007; Gordon, Bertram, and Graedel 2007). In this research the assumption
is made that the price of copper, which is in the basis defined by the amount of energy needed
to mine and the price of energy, ultimately defines how much copper can be mined. Hence
Tilton and Lagos are followed in that respect.
Identified resources Undiscovered resources
Demonstrated i
faced Probability range
Measured | Indicated Hypothetical Speculative
Economic
Inferred
Marginally Reserve fieserve nates:
economic Base
Sub- Base
Economic
Other Resource base
occurrences
Figure 19: Relation between reserves and resources. Based on the McKelvey Box (McKelvey
1973)
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper 17
The structure of resources and reserves further largely follows the McKelvey classification
box (McKelvey 1973), which is visible in Figure 19, but some simplifications have been
made with regard to official classification rules like the JORC code (JORC 2004). First, this
model makes no difference between the reserve base and the reserves of copper. The differ-
ence between these two concepts is defined by the cut off ore grade, which is the lowest ore
grade that can be mined with the current copper price. This makes it possible to model the
system without an explicit cut of grade for copper ore. The second difference is the simplifi-
cation of the relation between resource base and resources, which is here strictly economical
and the relation between resources and reserve base, which happens here by semi-autonomous
findings (and classifications) of the independent exploration or junior companies. The per-
formance indicator year left of copper mining is therefore not calculated by using the reserves,
but the reserve base divided by the global mined copper production.
This model allows deep sea mining to develop, if the marginal costs of copper are
higher than the marginal costs deep sea copper. The performance indicator relative part of
deep sea mining is calculated by dividing the deep sea mining production by the sum of deep
sea mining production and the global mined copper production.
Figure 20: Copper stocks view in the top down model
The amount of copper mined or refined is dependent on the capacities from the mine, smelt-
ing and refinery capacity sub model and possibly by a forecast of the copper demand. The
global consumption of refined copper is mainly determined in the total demand for copper
from the copper demand sub model and the availability of copper, which is dependent on the
global inventories of refined copper.
The inflow in this last stock is formed by two flows, the primary copper or global pro-
duction of refined copper and the secondary copper or copper recovered from scrap. The rela-
tion between these two, more particular the relation between copper recovered from scrap and
the sum of the global production of copper and the copper recovered from scrap, form the
performance indicator Recycling Input Rate (RIR).
18 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
A.1.2 Mine, smelting and refinery capacity
The sub model Mine, smelting and refinery capacity is visible in Figure 21. This figure con-
tains the structures which determine growth and decline of the world copper mining capacity,
the smelting and refining capacity and the deep sea mining capacity.
For all three capacities a similar structure was used, which makes use of three possible
states for the capacity. This structure resembles the two state structure used by Pruyt (Pruyt
2010, 6), but differs in the way that here a bad economic situation will lead to first parking of
the mining capacity and then, after continued losses, decommissioning. A second difference is
the lack of a learning effect due to the cumulatively mined metal. The assumption here is that
in a mature market these effects are comparatively small in relation to the increasing costs due
to the declining ore grade. The growth of for example the mining capacity, from the state
Mining capacity in preparation to the World copper mining capacity, uses a delay structure
with uncertain order:
Growth mining capacity =
DELAY N ( Preparation of capacity increase , Average mine permit term ,
Initial mining capacity in preparation / Average mine permit term , Delay
order mining capacity )
This is a way of modelling the structural uncertainty in the distribution of permit terms. The
delay order (green background) can now be changed using the EMA method. The preparation
of capacity increase is relative to the already existing (used) and the mining capacity in
preparation. First a comparison is made however between the marginal costs of conventional
mining and deep sea mining. The cheapest method will receive most of the new capacity.
Figure 21: Mine, smelting and refinery capacity view in the top down model
No separate capacity for the recycling is modelled, since in the real world copper system the
recycling happens with smelter and refinery capacity, as is demonstrated by the data of the
ICSG (ICSG 2010, 2011). The smelting and refinery capacity is thus bigger than the world
copper mining capacity. In the copper stocks sub model, the forecast recycling input rate is
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper 19
used to divide the refinery capacity between the flows of primary (mined) and secondary (re-
cycled) copper.
A.1.3 Copper demand
In the copper demand sub model (Figure 22), the total demand for copper is modelled by in-
fluences caused by developments in the intrinsic global demand for copper, the total avail-
ability of copper and the relation between copper and aluminium price, which is assumed to
be representative for all copper substitutes.
Calculating the effects of these developments starts by comparing each element with
its relevant counterpart to calculate their relation. These are intrinsic demand (A) and avail-
ability (B) for the copper price, price of copper (A) with the price of aluminium (B) for the
substitution and finally the intrinsic demand with the demand (A) and substituted demand (B)
for the effect of the intrinsic demand. The formulas are of the form:
Relation =(A /B ) “Amplifier
Since the values for A and B are always positive, this relation will have a value between 0 and
infinity as well, while the relation is equal to 1 when A and B balance. It is uncertain however
how big the influence of the relation between A and B will be. Therefore, the relation can be
amplified with a value around 1 (for example, between 0.25 and 4). This amplifying factor is
an extra uncertainty in the relation.
When calculating the effect of this relation, it is assumed that a balanced relation
should have no effect. Further, the extreme values (i.e. 0 and infinity) should have the same
effect. The following equation simulates this effect (with thanks to Bonthuis 2011):
Effect = 1-2 “( 1- Relation )
The values for effect are between -1 for Relation = 0, 0 for Relation = 1 and 1 for Relation =
o. This effect can also be amplified similar to the relation amplification. It is assumed that
this effect can change the demand directly (short term) or by the accumulation of the effect of
a longer period of time (long term). The sum of the short and long term effects define the
maximum de- or increase in demand, since all three relations are comparable to next equation
for the loss in demand due to price elasticity:
Loss in demand due to price elasticity =
( Short term copper price elasticity * Amplified effect of relative price on
demand + Long term copper price elasticity * Average long term effect on
demand ) * Total demand for copper
The total demand is subsequently calculated by solving the integral equation with the input
regarding the intrinsic demand and the outputs regarding the price and the substitution.
The intrinsic demand is, as was already explained in section A.1, dependent on the av-
erage global GDP per capita and the copper use related to GDP. The GDP per capita is mod-
elled by a typical ESDMA structure for random economic growth, which is formed by six
super positioned sinuses, for which the amplitudes and periods are set in the python shell. For
the world population the four different scenarios of the United Nations were used (UNPD
2011). For the copper use related to GDP also four distinct lookup functions were used,
which roughly represent the ideas presented in (W outers and Bol 2009, 18).
N
0 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
Figure 22: Copper demand view in the top down model
Substitution of copper demand takes place when the real price of copper (Svedberg and
Tilton 2006), which is equal to the marginal costs of copper when intrinsic global demand for
copper and total availability of copper balance, is at such an amount that it is cheaper to use
the substitute than the original resource. This is modelled by using a substitution threshold
value, which models the fact that the weight of aluminium needed to replace copper is not
equal to the weight of copper originally needed. This relation is then amplified, to increase (or
decrease the effect) of the substitution relation.
Relation between copper and aluminium price =
( Real price of copper / ( Substitution threshold * Price of aluminium ) ) *
Substitution amplifying factor
The method of modelling different uses is by changing the threshold value (Gordon et al.
1987, 66, 67). This assumes a similar price development of the different substitutes.
The two-stock structure for substitution, which is based on the one-stock-structure of
E. Pruyt (2010, 5), allows the model to “store” the amount of demand which was substituted.
This information is used for generating the new demand, since it is assumed that the part of
demand substituted will again be substituted, ceteris paribus, in the new demand.
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper 21
A.1.4 Economics of copper
Finally, in the sub model economics of copper (Figure 23, the marginal costs of copper and
marginal costs deep sea copper are calculated and with these values and the potential profit
due to the real price of copper, the in- and decreases of the capacities described in section
A.1.2.
Both marginal costs are calculated by looking at the cumulative mined copper and an
ore grade which corresponds to that amount. For any particular ore grade a certain amount of
energy is needed, which, together with some other cost factors, determines the marginal costs.
The marginal costs are compared to the copper price by either a forecast value, calcu-
lated with the first and second order derivatives, or the present costs and price. In a similar
manner as used for the effects on the demand, the potential profit has both direct and long
term effects on the development of new capacities.
Figure 23: Economics of copper view in the top down model
A.2 Bottom up model
In the bottom up model, the intrinsic demand is calculated by looking at the (quasi) autono-
mous increase in demand for separate uses of copper (Figure 24). These different uses are
modelled (Angerer et al. 2010) as subscripts of relevant elements which are further similar to
the top down model. The substitution is also dependent on the substitution possibilities and
the price of substitutes.
22 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
Copper use in
cect infastructare
Copper use in cars Comper nae
| Le Copper we instetonay
.
6 wa eccomntors
mo +
i
+ A Copper sein
‘Copper supply 4) Copper price (4 wmN ee
SX 3 ——
- a=
dono dts
Substation
possi
Figure 24; Simple CLD of the bottom up copper model
A.2.1 Differences with the top down model
In the bottom up demand are due to the differences explained earlier in this section, some al-
ternative structures modelled for the six different uses of copper visible in Figure 24. For this
purpose, all variables related to the use of copper are subscripted, just as the total demand for
copper and the rates to and from this stock and the substitution threshold values. The different
uses thus have different points at which substitution starts. These differences are therefore
mainly found in the sub models copper stocks and copper demand. Further, an extra sub
model was added for modelling the autonomous increases for the different uses, the sub
model bottom up demand.
A.2.2. Bottom up demand
In this sub model (Figure 25) the different major uses of copper, categorised in the same way
as presented in (Angerer et al. 2010), are modelled. Two of these uses, the automotive sector
and infrastructure, are strongly linked to the development of a more sustainable way of using
energy. Some different authors have thus hypothesised possible scenarios for these applica-
tions scenarios, which form input for the bottom up model.
The “dominance” and “pluralism” scenarios of electric vehicles for the automotive in-
dustry, developed by the Fraunhofer ISI, have been used for the automotive sector (A ngerer et
al. 2010, 18, 19). These scenarios regard the relative part of new cars build which have (semi)
electric propulsion. These types are, besides the conventional automobiles, the Hybrid Elec-
tric Vehicle (HEV), the Plug-in Hybrid Electric Vehicle (PHEV), the Battery Electric Vehicle
(BEV) and the city BEV. These are relevant, since the amount of copper per vehicle depends
heavily on the grade in which the vehicle has electric propulsion. For the development of the
electricity infrastructure, which is related to the development of decentralised sustainable en-
ergy sources, another scenario is presented in an article of Kleijn & van der V oet (2010).
With these embedded scenarios the model gives the opportunity to research the feasi-
bility of these scenarios from a copper availability perspective. Another option is that substi-
tution of copper will limit the amount of copper needed to make this world view possible.
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper 23
Figure 25: Bottom up demand view in the bottom up model
A.3 Regional model
Finally, the regional model (Figure 26), which uses the top down approach for the intrinsic
demand, tries to shed more light on the geopolitical sides of the copper system. The regions
have a resource dependant and not necessarily topographical division. Region 1 has most
money (the developed world), region 2 has the largest population (the upcoming economies)
and region 3 has most resources (the rest). This difference is also reached by subscripting the
relevant variables, which in this case of course also contains the supply variables.
Regional wold
population
¢ Efiect of GDP on
seanams — S/O i L a eon mings comer dense
Regbial copper
* spy
\)
Regional physical copper + supply loop
production sistem
S
Figure 26: Simple CLD of the top down copper model. All variables with a light green back-
ground are regionalised
A.3.1 Differences with the top down model
The regional model makes use of three distinct regions: the developed world (Europe, N-
America, Oceania and Japan), the upcoming economies (Asia without the CIS and Asean-10)
and the (resource abundant) developing countries (Africa, S-America, and Asean-10). These
areas correspond with respectively the more developed countries, the Asian part of the less
developed countries and the rest of the world (UNPD 2011).
In this model, just like in the bottom up model, the relevant variables have been sub-
scripted. In this case, these are all physical copper flows (the orange variables in Figure 27),
the capacities in the mine, smelting and refinery capacity sub model, the (intrinsic) demand
variables (including the economic situation and the population scenarios) in the copper de-
24 Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
mand sub model and finally the marginal costs and everything related in the economics of
copper sub model. Another change is the presence of flow for import and export of different
copper fabricates. The values for these flows are calculated in the copper transport sub model
discussed in next section.
Deep sea mining is more difficult to regionalise, especially when deep sea mining
takes place in international waters. The assumption made in the regional model to solve this
issue is that a mining concession means that the copper mining is regionalised. Since the re-
serve hase is part of a mining concession, this is the moment to bring in the regional division.
The regional “preference” to develop deep sea mining, is linked to the regional GDP per cap-
ita, since this can be considered an indicator for development.
Figure 27: Copper stocks view in the regional model
A.3.2. Copper transport
Import and export of copper products is modelled in the copper transport sub model (Figure
28). This happens by calculating the regional surplus and deficit for raw copper, the regional
surplus and deficit for copper scrap and the regional surplus and deficit for refined copper.
Regional surpluses are exported to regions with deficits. Both the exports and imports are
allocated by looking at the regional GDP per capita, where export is allocated from regions
with a lower GDP per capita and import to regions with a higher GDP per capita.
Auping, Pruyt & Kwakkel, 2012, The uncertain future of copper
Figure 28: Copper transport view in the regional model
25
Supporting materials for: Analysing the
Uncertain Future of Copper with Three
Exploratory System Dynamics Models
If you would like to receive the copper models used in this study, please contact the author at
w.l.auping (at) tudelft (dot) nl, or WillemAuping (at) HCSS (dot) nl
Yours truly,
The authors.
