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Modelling material cascades — frameworks for the environmental assessment of recycling systems
Resources, Conservation and Recycling 31 (2000) 83–104 www.elsevier.com/locate/resconrec
Modelling material cascades — frameworks for the environmental assessment of recycling systems Jake McLaren a, Stuart Parkinson b, Tim Jackson b,* a
Nokia Mobile Phones, Nokia House, Summit A6enue, Farnborough, Hampshire GU14 ONG, UK b Centre for En6ironmental Strategy, Uni6ersity of Surrey, Guildford, Surrey GU2 7XH, UK Received 9 May 2000; accepted 22 June 2000
Abstract The authors develop a methodological framework for the environmental assessment of materials recycling systems. Typically such systems exhibit both dynamic and non-linear behaviour. By contrast, many existing environmental assessment techniques (such as Life Cycle Assessment and Materials Flow Analysis) employ a static linear model of the underlying system. This paper first reviews some of the attempts to develop dynamic non-linear models for materials systems. It then discusses the structural peculiarities of recycling systems drawing attention in particular to the presence of dynamic features (such as time lags between production and disposal) and non-linearities (such as the dependency of scrap collection energies on the flow of material through the recycling loop). The principal analytic task of this paper is to construct an illustrative case study, in which different modelling techniques are used to assess the energy requirements of a hypothetical recycling system possessing both dynamic and non-linear features. The difference in system energy intensity derived using the different types of model are analysed. Finally, the paper discusses the policy implications of these results. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Recycling; Material cascades; Energy analysis; Dynamic non-linear modelling; Life cycle assessment; Material flow accounting
* Corresponding author. Tel.: +44-1483-259072; fax: +44-1483-259394. E-mail address: [email protected] (T. Jackson). 0921-3449/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 3 4 4 9 ( 0 0 ) 0 0 0 7 3 - 2
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1. Introduction This paper develops a methodological framework for environmental assessment of material ‘cascades’ — complex systems of material use in which materials and products are re-used or recycled a number of times before being discarded (Clift and Longley, 1995; Jackson, 1996). Existing environmental assessment tools such as Energy Analysis and Life Cycle Assessment (LCA) have sometimes been applied to simple recycling systems, but application to multiple loop recycling processes is in its very early stages. Moreover, LCA and the related methodology of Materials Flow Analysis (MFA) essentially rely on static linear models of the underlying system. In the real world, the underlying systems exhibit dynamic and non-linear characteristics. Dynamic effects arise as a result of time-lags within the system — such as those implied by changes in product or material lifetimes. Non-linear effects can arise in a number of different ways. Typically, in material systems of the kind discussed here, they arise because the environmental impacts of particular life cycle stages are not uniform with respect to material flow through the system. This paper first reviews some earlier attempts to model these kinds of systems. It then provides a formal discussion of the dynamic and non-linear elements of material cascades, and of the models suitable for modelling such systems. The core analytic task of this paper is to present an illustrative case study, in which different kinds of modelling techniques have been used to assess the energy requirements of a hypothetical recycling system. The results from this case study illustrate clearly that for systems which exhibit dynamic and non-linear behaviour, different modelling techniques may produce rather different conclusions about the energy requirements (and hence the environmental performance) of the system. The policy implications of this result are discussed.
2. An overview of modelling approaches The literature on environmental modelling of complex material systems is expanding rapidly. In this section a limited overview of the field is provided. Both LCA and MFA approaches may be applied to environmental analysis of material cascades. The purpose and decision focus of each approach is different, and the unit of assessment differs also. An LCA approach is used to determine the life cycle environmental impacts associated with a given service provided by a product system (ISO, 1997). A simple application of LCA to material recycling might be to compare the life cycle impacts associated with producing a material from virgin extraction and processing, or via reprocessing of post use material. LCA can also be used to compare a unit of service provided by multiple outputs from a complex material cascade. Linear LCA models may address future product and material systems in the long or very long run using comparative static models (Frischknecht, 1998). Generally such models employ a forecast trend in demand and vary factors of production,
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technologies and technical performance exogenously in order to assess the environmental impact of the systems over time. In the case of a very long run system model used for investment decisions Frischknecht argues that: ‘‘The system model should concentrate on the representation of the status in the future and not on the detailed, dynamic modelling of the transition period from now to the final social situation predicted for the planning horizon.’’ (op cit, p71). Linear static modelling may be appropriate if the problem being considered does not require interim trends in objective functions to be transparent; or if the decision being made does not require consideration of system functions which are non-linear, in particular with respect to material throughput. However, if significant non-linear system functions do exist, or if decision makers are interested in viewing the trends in objective functions over time, then comparative static linear LCA approaches may not be able to produce appropriate simulation of the system in question. MFA is used to analyse the flows and accumulations of materials and substances, both through the physical economy and into the environment. Use of three model types in MFA has been distinguished (Udo de Haes et al., 1998); book keeping, static modelling, and dynamic modelling. Book keeping describes a material flow model for a given year or time period, in which inputs cannot formally be computed from the outputs, and vice versa. A static model is a consistent framework that describes a formalised process, in which outputs can be computed from the inputs. Commonly MFA studies are static models, or comparative static linear models for a series of time periods. However, MFA can be used dynamically in order to account for time lags between processes, and the magnitude of stocks and flows for the time period under study (e.g. Moll, 1993). Material flow models may be hybrid approaches that integrate LCA or streamlined LCA studies within an MFA framework. Modelling complex material systems has also been carried out using linear programming (LP) techniques. In the case where relationships between activities in the material system in question and environmental burdens is linear, this approach may appropriate for several reasons (Azapagic 1996). Firstly, modelling the whole product system using linear programming allows for interactions between different parts of a multi-component system with multiple-outputs. Secondly, the LP is useful for solving the problem of allocation of environmental burdens which result from marginal changes in activities. Thirdly, adopting an LP approach allows for optimisation according to parameters or constraints. Several authors have adopted LP techniques to assess the environmental implications of different recycling rates in complex production and recycling systems. For example Hannon and Brodrick (1982) presented a detailed LP model of the US iron and steel sector which optimised the energy and labour efficiency of the sector. Leach et al. (1997) have developed an LP model of the life cycle impacts of paper use within London, while Weaver et al. (1995) have investigated the European pulp
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and paper sector at the European level using an LP model. Optimisation for static linear models is relatively straightforward using linear programming techniques. However, optimal control or dynamic optimization, which involves algorithms that predict time-dependent trajectories, is a more challenging problem (Diwekar and Small, 1998). A handful of researchers have worked on the application of dynamic, non-linear modelling to LCA and MFA studies. For example, Pistikopoulos et al. (1995) developed a methodology for the dynamic modelling and control of chemical process technology, while Huppes et al. (1997) have applied signal processing methods to the assessment of emission characteristics. Kandelaars and van den Berg (1997) have used control theory in environmental policy models of material/ product chains. Ruth and Harrington (1998) have carried out some dynamic modelling of material and energy flows in an MFA context, while Ruth (1995) has applied a dynamic, non-linear modelling framework to the environmental assessment of mining and extraction processes for metal resources. The particular problems proposed by modelling the non-linear and dynamic properties of cascade recycling systems have not been addressed in the literature in any depth, and are a recognised research need for the further development of both LCA and MFA methodologies (Wrisberg et al., 1997; Bringezu et al., 1998). The objective of this paper is to address this need. In particular a typology of modelling approaches to recycling systems is developed, and the application of these different approaches to a hypothetical case study is illustrated.
3. Characteristics of material cascades The kinds of systems with which this paper is concerned typically involve the extraction of primary resources for the manufacture of a high-quality material or product, the distribution of the product for consumption or use, the degradation of the product through use, collection at the end of its initial life, and then various cycles of re-use, reconditioning, or the recycling of its component materials before final disposal. Fig. 1 shows a simple example of such a system involving only one recycling loop. The flows Fi represent the quantity of material flowing through each of a set (D) of stages in the life cycle. For the purposes of the illustrative exercise in this paper, one is concerned with the total energy requirements E associated with the life cycle of the product. If the specific energy requirement is denoted by ei (i.e. the energy requirement per unit of mass flow) through each stage of the life cycle, then the total system energy requirement in any one time period can be expressed as: E = % ei Fi
(1)
iD
Typically, a model of the system will require the specification of a set of exogenous inputs Uk (such as UD, say, the demand for the product or URF the recycling fraction). Together with the flow variables, these parameters will define a
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set of constraints describing the physical basis of the model. So, for example, mass flow principles suggest (on the basis of Fig. 1) constraints such as the following: FR =URF ×UD
(2)
FV =FP −FX
(3)
FR =UD −FV −FI
(4)
Eq. (2) constrains the flow through the recycling loop according to the exogenously determined recycling fraction. Eq. (3) expresses the fact that the flow of products into the domestic stock in use during any time period is equal to the
Fig. 1. Schematic life cycle representation of a recycling system.
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quantity produced less the quantity of products exported. Eq. (4) constrains the contribution to demand from recycling in any time period according to the demand for products, the virgin production rate and the imported product flow. Expanding these constraints to cover all the material flow relations allows one to build up a complete mathematical model of the energy and material flows through the system. Clearly, the constraints themselves are determined crucially by specific assumptions about the kind of system represented, and those illustrated here are relatively simple. More complicated models might include a number of additional factors such as production stocks for both virgin and secondary production, home and prompt scrap recycling, the import or export of raw materials as well as products, and so on. For the purposes of this exercise, however, the flows represented in Fig. 1 provides an adequate illustration of the kinds of systems in which the authors are interested. Mathematical models of systems such as those illustrated in Fig. 1 can be classified according to their structure, which in turn varies according to the problem to which the model is applied. The most relevant classifications to this study are those discussed in Section 2, namely time dependency and linearity. Considering first time dependency, a model may be said to be either static or dynamic. A static model (also known as a stationary or steady state model) is capable of simulating a system at only one point in time, under the condition that the output(s) must be in steady state equilibrium with the input(s) (Huppes et al., 1997). A dynamic model, on the other hand, can display time-varying behaviour, which may or may not be in equilibrium. As with time dependency, considerations of linearity lead to models being classified into two groups: linear and non-linear. Young (1993) defines the following properties possessed by linear models: 1. Proportionality. A change in the input leads to a proportional change in the output; 2. Superposition. The total effect of several inputs applied simultaneously to a linear system produces the same result as if they were applied independently; 3. Stability. Linear models are inherently stable, and do not effect amplification of any inputs; 4. Conservativity. All external outputs at any point in time equal the inputs. Non-linear models are not so easy to specify, except in a negative sense, i.e. they do not have all four of these properties. Using these classifications, one can therefore define four model types: static linear, static non-linear, dynamic linear and dynamic non-linear. The decision about which type to use depends on the system to be modelled. In the following subsections each of these different types of model are discussed. It is worth pointing out here that one of the factors to be taken into account in deciding which type of model to employ is the degree of difficulty or simplicity with which a particular model type can be solved. Static linear models are generally easy to solve, whilst dynamic non-linear systems often require larger data sets and significant computing power. Hence, if a system can be simplified, it is often wise to do so. This point is returned to in Section 5 of the paper.
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3.1. Case 1: static linear The underlying model on which most current LCA and MFA studies are based is essentially static and linear: that is it simulates the system at only one point (or period) in time, under the condition that outputs are in steady-state equilibrium with inputs (Huppes et al., 1997; Clift et al., 1998). In mathematical terms, this implies (a) that a change in any of the inputs Uk leads to a proportional change in the output of the model, the total energy consumption, E; and (b) that this change will instantaneously result in a new equilibrium state of the system, i.e. the system is always in equilibrium. Formally, condition (a) is expressed as follows. (E =pk (Uk
(5)
where pk is a constant for all k. It can be shown formally that the condition (5) is equivalent to requiring that ei is constant for each i. In other words, the linear model is sufficient to model the system provided that the specific energy requirement can be expressed as a constant for each stage of the life cycle. It is relatively straightforward to extend a simple static linear analysis at a single point in time to systems with time-varying characteristics, provided that the outputs remain in equilibrium with the inputs. Modelling a material flow system with time-varying input parameters is sometimes called quasi-dynamic. Examples of characteristics in material cascade systems that can be treated this way include improvements in technology efficiency over time, or exogenous changes in the recycling rate.
3.2. Case 2: static non-linear Linear models possess the property that a change in the input leads to a proportional change in the output (Young, 1993). This assumption is inherent in many existing environmental management tools, including LCA, MFA and energy analysis (Boustead and Hancock, 1979), and is frequently justified by the assumption that only marginal changes are considered (Clift et al., 1998). In real-world systems, however this assumption is not always valid. In the case of a static non-linear model, the assumption of proportionality between changes in outputs and changes in inputs is removed. Hence, whilst total energy consumption E is still dependent on inputs Uk, the linearity conditions no longer hold true. Consequently, the specific energy ei of process i is not a constant and can vary with the material flows Fj through particular stages of the life cycle. ei ei (Fj :j Di, Di ¤D)
(6)
Of particular interest when modelling material cascades is the non-linear relationship between the specific energy of recycling (i.e. the energy required per unit of material recycled), and the quantity of material recycled. So for example, one might find that:
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Fig. 2. Specific energy of scrap collection as a function of the recycling fraction.
eR ei
FR UD
(7)
In other words, the specific energy through the recycling process is a function of the recycling fraction URF. Lox et al. (1994) and Karlsson (1998) suggest that this relationship is governed by a U-shaped curve (see Fig. 2). For low values of the recycling rate, the specific energy of recycling may be rather high, since the infrastructure costs are high per unit of energy flowing through the system. As the recycling rate rises, economies of scale reduce the energy cost of recycling a unit of material or product. At high recycling rates however, a reverse effect begins to come into play: the need to collect more dispersed material leads to an increase in the specific energy of recycling. Non-linear relationships may also exist between the specific energy of recycling and quantity of material recycled, due to the build up of impurities within a material cascade, or the degradation of materials due to multiple use and reprocessing.
3.3. Case 3: dynamic linear Many real-world systems exhibit time-varying behaviour, in which the outputs are not necessarily in equilibrium with the inputs. Such systems require representation with fully dynamic models, which are capable of simulating time lags within the system. In formal terms dynamic linear models are constrained by the requirements (a) that a change in any of the inputs, Uk, leads to a proportional change in the output, total energy consumption, E; and (b) that there will be a time lag before the system reaches a new equilibrium state. To satisfy the condition (a), the same requirements for linearity discussed in the static linear case are imposed, but in this case on E, Fi and Uk as functions E(t), Fi (t) and Uk (t) of time. To satisfy condition (b), one must overtly acknowledge the time lags in the system. Thus, for example:
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Fj (t) Fj (t, Fj (t´):t´ B t, j Di, Di ¤ D)
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(8)
In other words, Fi, the material flow through life cycle stage i, may now be a function of time, and indeed of various other material flows over time. The principal application of fully dynamic modelling to material cascades is in simulating the time lag between production and the end of service life for a product or material. So for example it would be reasonable to suppose that: FW(t) FW(t, UD(t − n))
(9)
In other words the flow into the waste management sector at time t is a function of the demand for products at time (t− n), where n is the lifetime the material or product in the economy. Several authors of MFA studies have used dynamic modelling approach to simulate the effect of product life span in determining the results from various environmental policy instruments (e.g. Kandelaars and van den Berg, 1997; Lohm et al., 1997). A fully dynamic model could be used to assess the environmental implications of, for example, changes in the service life of material products. In reality, such changes may be due to a variety of technological, economic, and cultural factors. Typically, however, they are likely to arise through increased obsolescence or improved durability of products (Stahel and Jackson, 1993). Dynamic models may also be applied in order to investigate a combination of policy issues in parallel. For example, some studies have constructed scenario approaches in which total system energy requirements are modelled for each of a number of hypothetical scenarios specified by time-varying technology change, recycling rates, product life span, demand patterns, production delays and stock characteristics (e.g. McLaren et al., 1998; Sundin et al., 1999; Michaelis and Jackson, 2000a,b).
3.4. Case 4: dynamic non-linear In extending this analysis to look at the dynamic non-linear case, one bears in mind the appropriate constraints from previous cases, i.e. that (a) a change in the inputs (Uk ) does not necessarily lead to a proportional change in the output; (b) that there will be a time lag before the system reaches a new equilibrium state. In this case, the flows Fi will once again be of the form given by Eq. (8). Furthermore, one might expect to see non-linear, time-dependent functions associated with the specific energy through life cycle stages. Thus: ei ei (t) ei (t, Fj :j Di, Di ¤ D)
(10)
For example, the specific energy associated with mining raw materials might be expressed by a function eM of a form given by:
t
eM eM % FM(t´) t´ = 0
(11)
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In other words, the specific energy associated with mining at time t is a function of the total material mined up to that time. A number of authors have commented on this complex relationship (Hall et al., 1992; Ruth, 1995; Cleveland and Ruth, 1996). Cleveland and Ruth (1996) point out that technological efficiency improvements may reduce the specific energy requirements over time; but a decline in the ore quality will offset and eventually overtake these improvements. Thus the specific energy of mining will generally be represented by an increasing function of the total material mined. It should be noted that the relationship governing the specific energy of mining is both non-linear and dynamic, since at any one time, the specific energy depends on the ore quality, and hence on the integral over time of the material mined in all previous periods.
4. An illustrative case study In this section the application of the four different modelling types defined in the previous section to an illustrative materials flow case study is demonstrated. Specifically the energy requirements associated with a hypothetical material recycling system over a notional time period 1995–2025 were investigated.
4.1. System description and assumptions For the purposes of this exercise the existence of a hypothetical material recycling system of the kind illustrated in Fig. 1 is supposed. For purposes of simplicity, however, consideration of imports and exports in the system are excluded (the shaded components in Fig. 1). Furthermore, one assumes here that scrap for recycling originates solely at the post-use stage and that there is only one recycling loop. More complex cascades might include multiple re-use, reconditioning and recycling loops (Stahel and Jackson, 1993). Formally, the material cascade is defined as a set of material flows F( j, t) for each stage j of the material or product cycle and for each time period t. The system boundary is defined as a set of processes required to deliver materials or products for consumption within a given geographical boundary. Data on the material flows and the specific energy requirements adopted in this illustrative study have been extrapolated from the general magnitudes and trends experienced in the UK steel cycle 1959–94 (Michaelis and Jackson, 2000a). However, these data have been used in purely illustrative fashion, and it would be inappropriate to draw conclusions about the iron and steel sector from this analysis and premature to use the results to make any specific policy recommendations. This example is merely intended to show the potential application of different modelling methodologies to a dynamic, non-linear system. In order to simulate the environmental impacts of the system, an objective function is first defined which is based on the total system energy requirements E(t) at any time period t. This total system energy is defined quite generally by analogy with Eq. (1) above as:
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E(t) = % e( j, t)F( j, t) j
where j ranges over the stages of the life cycle and e( j, t) e( j, t, F( j, t)) is the specific energy associated with the stage j during the time period t, assuming a material flow F( j, t) through that stage at that time. For the purposes of this study, an objective function related to the energy intensity of the material or product system is defined next. Eq. (12) defines the energy requirement o(t) per unit of material or product in the use stage in each year t. Thus: o(t) =
E(t) Q(t)
(12)
where Q(t) is the total quantity of material or product in use at time t. Such an objective function could be construed as providing an (inverse) indicator of the energy efficiency of the system as a function of time in the following sense: a low value o means that the system has a high resource or energy efficiency and, vice-versa, a high energy per unit of use means a less energy efficient system. It is worth noting that a third objective function might also have been defined by the integral over time of the system energy function. Such an objective function would be relevant, for example, for optimisation with respect to long-term energy consumption, and long-lived energy related pollutants. A similar approach has been recommended to assess long-term impacts of landfilling (Bates, 1998). This kind of optimisation is beyond the scope of this paper, although it would be a straightforward extension of the model described here. A number of basic assumptions have been made in constructing the model. In the first place it has been assumed that the demand for manufactured material remains constant at 15 Mt/year during the simulation period. This is roughly the mean consumption for UK steel over the past 30 years (Michaelis and Jackson, 2000a). It was assumed that the system is initially at steady-state equilibrium, i.e. all variables are constant. The analyses begin with the system in this state to make sure that any subsequent observed behaviour can be unambiguously associated with changes in the system inputs. The mean use time for products manufactured using the material is assumed to be 15 years. The amount of scrap available for recycling is defined by the recycling fraction, which is an input (exogenous) variable. At equilibrium, the value of this variable is set at 50%. All scrap available for recycling is assumed to be recycled because of the lower cost associated with reprocessing. Thus the shortfall between output from reprocessing and demand for material for manufacture is made up by virgin production. All virgin production is produced using a more energy intensive process, and reprocessed using a more efficient process. The magnitude of the specific energy requirements of the virgin and recycling processes are roughly equivalent to those associated with a system in which all virgin steel is manufactured using the basic oxygen furnace, and recycled material is processed in an electric-arc furnace (Michaelis and Jackson, 2000a).
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Further, it was assumed that all scrap for recycling originates solely at the post-use stage, and that scrap arising during virgin production or manufacture is assumed to be recycled within processes from which they originate. Finally it was assumed that the system is driven exogenously by constant year on year demand for new materials and thus it is to be expected that the magnitude of stock in use can vary. This assumption does not effect the analysis unduly, except in the case where use time (service life) varies. This is discussed further in Section 4.3.2. The case study model, and analysis described here has been constructed using the Stella modelling software package.1 This approach is in common with that adopted by Ruth (1995), Cleveland and Ruth (1996), Kandelaars and van den Berg (1997) and Ruth and Harrington (1998). Boelens and Olsthoorn (1998) suggest that opportunities may exist to develop dynamic MFA models by coupling FLUX software with Stella language, or alternatively in development of Petri Net or expert systems modelling approaches.
4.2. Analysis definition In this section, the construction of six distinct types of analysis to determine the energy intensity — defined in terms of o(t) — of the simple cascade system over the 30 year period is defined. These six analysis types are defined in Table 1. Table 1 Summary of scenario descriptions Model type used
Scenario description
Analysis 1
Static linear
Analysis 2
Static non-linear
Analysis 3
Dynamic linear
Analysis 4
Dynamic linear
Analysis 5
Dynamic non-linear
Energy intensity calculated for 1995 Specific energy of recycling is constant Energy intensity calculated for 1995 Specific energy of recycling varies non-linearly with recycling fraction (Fig. 2) Product use time 15 years Recycling fraction 50% Specific energy functions vary linearly over time (Fig. 3) As in Analysis 3 except that: – product use time decreases from 15 to 13 years (Fig. 4) As in Analysis 3 except that:
Analysis 6
Dynamic non-linear
– recycling fraction increases from 50 to 100% over time (Fig. 4); and – specific energy of collection varies non-linearly with recycling fraction (Fig. 2) As Analysis 3 except that – resource extraction is non-linear with respect to cumulative resource extraction (Fig. 5); and – virgin processing energy varies non-linearly over time (Fig. 6)
1
STELLA is a product of High Performance Systems Inc. B http://www.hps-inc.com/\
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Table 2 Specific energy values and sources (base year 1995) Process
Values
Reference
Extraction
1.2 GJ/t — constant over time (1.0 t steel needs: 1.63 t iron ore @ 0.59 GJ/t 0.43 t coal @ 0.50 GJ/t) 16 GJ/t
ETH (1997)
Virgin material production (Blast furnace-basic oxygen furnace) Reprocessing (Electric arc furnace) Manufacturing Collection for recycling
Transport to landfill
1% per year efficiency increase, reflective of efficiency gains in steel production processes in last 35 years 8.5 GJ/t 1% per year efficiency increase, reflective of efficiency gains in steel production processes in last 35 years 1 GJ/t — constant over time Constant over time Linear analyses-0.25 GJ/t Non-linear analyses-U shaped function: Min. = 0.25 GJ/t; Max. is 24× larger 0.05 GJ/t Waste transport: 14 t lorry, 2.35 MJ/t km. 200 landfill sites — 20 km mean distance
ETH (1997) Michaelis (1998) ETH (1997) Michaelis (1998) Michaelis (1998) Michaelis (1998)
Assumption
Estimate
Essentially, there are two static analyses. Both of these analyses calculate the energy intensity of the system at a single point in time, taken as the year 1995. In the static linear analysis (Analysis 1), the specific energy associated with scrap collection is constant with respect to the flow of material through the recycling loop. The static non-linear analysis (Analysis 2) models a possible non-linearity in the collection energy, as illustrated in Fig. 2. In addition to these two static analysis, there are four dynamic analyses, two of which are linear and two of which are non-linear. The two linear dynamic analyses adopt different assumptions about dynamic elements of the system such as the product use time. The two non-linear dynamic analyses adopt different assumptions about specific non-linearities in the system (see Table 1). Table 2 details the values of the specific energy functions for each of the life cycle stages in the year 1995 (at the start of the scenario period), and the assumptions made about changes in these parameters over time (for the dynamic analyses). Table 2 also provides sources for the literature references from which these assumptions were taken. Fig. 3 shows the assumptions made about the variation of specific energy functions with respect to time for the dynamic analyses. Fig. 4 illustrates the assumptions made about the product use time and the variation of the recycling fraction for Analyses 4 and 5, respectively. Fig. 5 shows the variation in the specific energy of mining assumed in Analysis 6, and Fig. 6 introduces the (time) non-linearity in processing energy assumed in Analysis 6.
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Fig. 3. Variation with time of specific energies for different life cycle stages.
Fig. 4. Variation of product use time (Analysis 4) and recycling rate (Analysis 5).
Fig. 5. Specific energy for mining as a function of cumulative resource extraction (Analysis 6).
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Fig. 6. Variation with time of specific energies for virgin processing (Analysis 6).
The main purpose of the exercise described in this section is to illustrate the application of the four model types to an investigation of the system effects of three exogenous variables: post-use recycling fraction, the product use time, and specific energy for resource extraction. Specifically, the aims are: to compare a static linear model (Analysis 1), where the specific energy of scrap collection is constant, against a static non-linear model (Analysis 2), where the specific energy of scrap collection is related to recycling fraction by a U-shaped function (Fig. 2); to compare a dynamic linear model in which the product use time is kept constant (Analysis 3) against a dynamic linear model in which the product use time is varied according to Fig. 4 (Analysis 4); to compare a dynamic linear model in which the recycling rate and the specific energy associated with scrap collection are constant (Analysis 3), against a dynamic non-linear model (Analysis 5) in which the specific energy of scrap collection varies both with time (Fig. 4) and with material flow through the recycling loop (Fig. 2); to compare a dynamic linear model in which the specific energy of extraction is constant and that of virgin production is decreasing linearly (Analysis 3) against a dynamic non-linear model (Analysis 6) in which (a) the specific energy of extraction is related to cumulative resource extraction (Fig. 5); and (b) the specific energy of virgin production varies non-linearly with time (Fig. 6).
4.3. Results In this subsection the results of the four comparisons specified above are presented.
4.3.1. Static linear 6ersus static non-linear results (Analyses 1 and 2) Both the static linear analyses assess the system at a single point in time, 1995. For Analysis 1, the values for the specific energy functions are as shown in Table
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2, and the specific energy associated with scrap collection is assumed to be a constant 0.25 GJ/t (as indicated by the dashed line in Fig. 2) for all values of the recycling fraction. Modelling the system using a series of static linear models (each with a different recycling fraction) allows one to determine how the energy per unit of use, o, varies with the recycling fraction. Fig. 7 reveals that (according to Analysis 1) the system becomes progressively more energy efficient as the recycling rate increases. This is exactly as one might expect, since the reprocessed material consistently requires a lower specific energy than virgin material. Analysis 2, however, provides a different picture of the relationship between o and the recycling fraction. In this case, the non-linear U-shaped function for scrap collection energy (shown by the solid line in Fig. 2) is introduced into the analysis. Fig. 7 illustrates that if the system is operating with a recycling rate between 40 and 60%, a linear approximation of the non-linear function is probably acceptable. However, it is clear that the two analyses differ for recycling rates which are either very low or very high. At low recycling rates, this difference is not substantial: although the collection energy is higher, the volume throughput in the recycling loop is rather low, so that the total system energy intensity is dominated by the virgin production route. However, at higher values of the recycling rate the increased energy of collection begins to affect the system efficiency. In fact, the system operates at its most efficient at around 80% recycling rate and then becomes less efficient again as the recycling fraction is increased. This is in contrast to the static linear analysis which implies that 100% recycling yields the minimum system energy intensity. The policy implications of this comparison should be clear: if policy instruments were set as a result of a static linear analysis then 100% recycling rate would be encouraged. In fact, however, if there were non-linearities in the system of the kind illustrated by Fig. 2, then this policy prescription would increase the energy
Fig. 7. The effect of non-linearities in scrap collection energy (static analysis).
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Fig. 8. The impact of changed product use times (dynamic analysis).
requirements over the case where the recycling rate was set lower. The findings of non-linear analysis indicate that a recycling rate of around 80% would bring about the lowest system energy burden.
4.3.2. Dynamic linear results (Analyses 3 and 4) Fig. 8 illustrates the comparison between Analyses 3 and 4. Both of these analyses model the system energy intensity o(t) assuming that the system is not in steady-state equilibrium, i.e. that it is dynamic. In particular, both Analyses assume time lags between the production of materials or products and their emergence from the use phase. Fig. 8 reveals that the energy intensity calculated under Analysis 3 shows a declining trend not dissimilar to the one illustrated in Fig. 7. However, it is important to note the trend in Fig. 8 is due here to improvements in the energy efficiency in virgin and scrap materials processing over time (Fig. 3), rather than to variations in the recycling fraction. Specifically, no flow non-linearities are involved in Fig. 8. Now that a fully dynamic modelling approach is adopted however, it is possible to investigate the effects of delays within the system. Analysis 3 assumes a constant service life of 15 years, i.e. it assumes that material remains delayed within the ‘stock in use’ for that period. In Analysis 4 the impact of a reduction in the product life from 15 to 13 years as shown in Fig. 4 is investigated. This might be equivalent to, for example, the service life of an average high quality washing machine being reduced as a result of increased product obsolescence (Euromonitor 1992). Before explaining the differences between the results of Analyses 3 and 4, as seen in Fig. 8, it is first necessary to understand the assumption that the recycling system is driven exogenously by a constant demand, and that the magnitude of stock in use can vary. This means that any variation in time delays (i.e. the use time) within the system will result in changes in this stock, not changes in the level of manufacture. This assumption has been made for ease of modelling.
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For about the first 15 years of the simulation the results of Analysis 4 are the same as 3. This is because the shorter lifetime products have not yet emerged from the use stock. However, once these products begin to be discarded, the efficiency of the system undergoes some dramatic changes. Firstly, Analysis 4 becomes briefly more efficient due to the temporary increase in availability of post-use scrap. However, this effect is short-lived as the reduced use time has the corresponding effect of reducing the quantity of material in the use stock (for a constant rate of manufacture), thus making the system less efficient. This trend continues until the system energy intensity settles into a path running parallel to that of Analysis 3, but at a lower level of efficiency (energy consumption per unit of use is around 20% higher in Analysis 4 than in Analysis 3 by the end of the simulation). This comparison illustrates that changes in the product use time can have a significant impact on the energy intensity of the system. It also demonstrates that transient states can be investigated using dynamic modelling: one advantage of this more complex approach.
4.3.3. Dynamic linear 6ersus dynamic non-linear results In this subsection, the dynamic linear results of Analysis 3 are compared against the two dynamic non-linear analyses (Analyses 5 and 6). Analysis 3 assumes a constant recycling rate of 50% and no variation of the specific energy of scrap collection. In Analysis 5 the impact of increasing the recycling rate from 50 to 100% over the first 15 years of the scenario period as shown in Fig. 4 is modelled. In addition, Analysis 5 differs from Analysis 3 in assuming that the specific energy of recycling follows the non-linear U-shaped function defined in Fig. 2. Fig. 9 compares the results of Analysis 3 against Analysis 5. It can been seen that both analyses begin with the same results at 50% recycling rate, but as the recycling rate increases Analysis 5 becomes more efficient because of the lower impacts associated with reprocessing. However, the system reaches a point at around 80%
Fig. 9. The effect of variation in recycling rate and scrap collection energy (dynamic analysis).
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Fig. 10. The effect of non-linearities in extraction and processing energies (dynamic analysis).
recycling in 2005 after which the increasing collection energy offsets savings due to reprocessing, thus decreasing overall system efficiency. By the time the recycling level in Analysis 5 reaches 100% (in about 2010), the system energy intensity is higher than under Analysis 3, even though the latter only assumes 50% recycling. This comparison exemplifies the importance of accounting for non-linear functions when they may significantly affect the system analysis. Finally, Analysis 6 attempts to model potential non-linearities in processing and extraction energies. Firstly, it assumes a long run increase in energy costs associated with material extraction according to the hyperbolic function shown in Fig. 5. In addition, this Analysis assumes that the effects of extracting progressively lower quality ore cause knock-on effects in processing, increasing the energy requirements during the processing phase as shown in Fig. 6. The effect of both these combined assumptions is illustrated in Fig. 10. Initially, the system energy intensity falls below that in Analysis 3 as a result of the reduced specific energy for resource extraction (Fig. 5). Later on however, the energy intensity rises above the linear case, as a result of increases in specific energy functions for both resource extraction and virgin processing.
5. Summary and conclusions The analysis presented in this paper has attempted to illustrate how dynamic, non-linear modelling can be used to model the complexities of material cascades — systems involving materials use, re-use and recycling loops. It has been argued that such methods may, in certain circumstances, provide a more accurate representation of the underlying system than traditional static, linear techniques such as those mainly adopted in current LCA or MFA studies. In particular, a hypothetical case study has been constructed, and it has shown that different modelling techniques provide rather different conclusions about the energy intensity of systems that exhibit such behavior.
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The policy implications of these results should be obvious: restricting analysis to conventional static linear modelling techniques may sometimes produce misleading analytic results, and stimulate inappropriate policies as a result. In those cases where significant non-linear or dynamic effects within the system are indicated by the available data, more sophisticated modelling using dynamic and non-linear techniques is required before it is possible to formulate appropriate policy, for example, about optimum recycling rates. In this paper, the system energy intensity has been used as an objective function. However, the implications of this work extend beyond energy analysis. The environmental impacts of energy consumption are well-documented (Jackson, 1992, 1997, e.g.). It would be straightforward to extend the work described here to an assessment of energy-related emissions such as carbon dioxide, sulphur dioxide, nitrogen oxides, particulate matter and so on. Extending the analysis to other kinds of pollutants is also relatively straightforward, although optimising with respect to more than one output requires definition of multiple environmental objective functions (Azapagic and Clift, 1995). It should be noted that the available data do not always support the use of the more sophisticated, and more complex, modelling techniques described in this paper. It is not axiomatic that a dynamic modelling approach should be adopted when modelling a dynamic system, since the question being asked may not require consideration of system dynamics. The same can be said with respect to modelling system non-linearities. Within certain boundaries, linear functions may offer a perfectly adequate of approximation of non-linear characteristics of the system. In some cases, therefore, static, linear modelling is sufficient to make informed policy decisions — at least over short time-periods in particular system configurations. In other cases however, dynamic, non-linear models will be necessary to capture the complexity of the underlying system. Finally, it should be noted that occasionally, even though significant dynamic or non-linear system characteristics exist, the data required to model these effects are unavailable or inadequate to the task. This situation means that realistic modelling of material cascades may well remain problematic and implies that policy-making in relation to re-use and recycling is inherently uncertain. Addressing the implications of this uncertainty is beyond the scope of this paper.
Acknowledgements The authors are grateful for financial support during the duration of this study from the UK Engineering and Physical Sciences Research Council (EPSRC), and the UK Royal Academy of Engineering. We are also grateful for critical inputs from participants at the SETAC-Europe Annual Meeting held in Bordeaux in April 1998 and the International Resource Accounting and Modelling Workshop held in Groningen in September 1998, at which earlier versions of this paper were presented.
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Modelling material cascades — frameworks for the environmental assessment of recycling systems Jake McLaren a, Stuart Parkinson b, Tim Jackson b,* a
Nokia Mobile Phones, Nokia House, Summit A6enue, Farnborough, Hampshire GU14 ONG, UK b Centre for En6ironmental Strategy, Uni6ersity of Surrey, Guildford, Surrey GU2 7XH, UK Received 9 May 2000; accepted 22 June 2000
Abstract The authors develop a methodological framework for the environmental assessment of materials recycling systems. Typically such systems exhibit both dynamic and non-linear behaviour. By contrast, many existing environmental assessment techniques (such as Life Cycle Assessment and Materials Flow Analysis) employ a static linear model of the underlying system. This paper first reviews some of the attempts to develop dynamic non-linear models for materials systems. It then discusses the structural peculiarities of recycling systems drawing attention in particular to the presence of dynamic features (such as time lags between production and disposal) and non-linearities (such as the dependency of scrap collection energies on the flow of material through the recycling loop). The principal analytic task of this paper is to construct an illustrative case study, in which different modelling techniques are used to assess the energy requirements of a hypothetical recycling system possessing both dynamic and non-linear features. The difference in system energy intensity derived using the different types of model are analysed. Finally, the paper discusses the policy implications of these results. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Recycling; Material cascades; Energy analysis; Dynamic non-linear modelling; Life cycle assessment; Material flow accounting
* Corresponding author. Tel.: +44-1483-259072; fax: +44-1483-259394. E-mail address: [email protected] (T. Jackson). 0921-3449/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 3 4 4 9 ( 0 0 ) 0 0 0 7 3 - 2
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1. Introduction This paper develops a methodological framework for environmental assessment of material ‘cascades’ — complex systems of material use in which materials and products are re-used or recycled a number of times before being discarded (Clift and Longley, 1995; Jackson, 1996). Existing environmental assessment tools such as Energy Analysis and Life Cycle Assessment (LCA) have sometimes been applied to simple recycling systems, but application to multiple loop recycling processes is in its very early stages. Moreover, LCA and the related methodology of Materials Flow Analysis (MFA) essentially rely on static linear models of the underlying system. In the real world, the underlying systems exhibit dynamic and non-linear characteristics. Dynamic effects arise as a result of time-lags within the system — such as those implied by changes in product or material lifetimes. Non-linear effects can arise in a number of different ways. Typically, in material systems of the kind discussed here, they arise because the environmental impacts of particular life cycle stages are not uniform with respect to material flow through the system. This paper first reviews some earlier attempts to model these kinds of systems. It then provides a formal discussion of the dynamic and non-linear elements of material cascades, and of the models suitable for modelling such systems. The core analytic task of this paper is to present an illustrative case study, in which different kinds of modelling techniques have been used to assess the energy requirements of a hypothetical recycling system. The results from this case study illustrate clearly that for systems which exhibit dynamic and non-linear behaviour, different modelling techniques may produce rather different conclusions about the energy requirements (and hence the environmental performance) of the system. The policy implications of this result are discussed.
2. An overview of modelling approaches The literature on environmental modelling of complex material systems is expanding rapidly. In this section a limited overview of the field is provided. Both LCA and MFA approaches may be applied to environmental analysis of material cascades. The purpose and decision focus of each approach is different, and the unit of assessment differs also. An LCA approach is used to determine the life cycle environmental impacts associated with a given service provided by a product system (ISO, 1997). A simple application of LCA to material recycling might be to compare the life cycle impacts associated with producing a material from virgin extraction and processing, or via reprocessing of post use material. LCA can also be used to compare a unit of service provided by multiple outputs from a complex material cascade. Linear LCA models may address future product and material systems in the long or very long run using comparative static models (Frischknecht, 1998). Generally such models employ a forecast trend in demand and vary factors of production,
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technologies and technical performance exogenously in order to assess the environmental impact of the systems over time. In the case of a very long run system model used for investment decisions Frischknecht argues that: ‘‘The system model should concentrate on the representation of the status in the future and not on the detailed, dynamic modelling of the transition period from now to the final social situation predicted for the planning horizon.’’ (op cit, p71). Linear static modelling may be appropriate if the problem being considered does not require interim trends in objective functions to be transparent; or if the decision being made does not require consideration of system functions which are non-linear, in particular with respect to material throughput. However, if significant non-linear system functions do exist, or if decision makers are interested in viewing the trends in objective functions over time, then comparative static linear LCA approaches may not be able to produce appropriate simulation of the system in question. MFA is used to analyse the flows and accumulations of materials and substances, both through the physical economy and into the environment. Use of three model types in MFA has been distinguished (Udo de Haes et al., 1998); book keeping, static modelling, and dynamic modelling. Book keeping describes a material flow model for a given year or time period, in which inputs cannot formally be computed from the outputs, and vice versa. A static model is a consistent framework that describes a formalised process, in which outputs can be computed from the inputs. Commonly MFA studies are static models, or comparative static linear models for a series of time periods. However, MFA can be used dynamically in order to account for time lags between processes, and the magnitude of stocks and flows for the time period under study (e.g. Moll, 1993). Material flow models may be hybrid approaches that integrate LCA or streamlined LCA studies within an MFA framework. Modelling complex material systems has also been carried out using linear programming (LP) techniques. In the case where relationships between activities in the material system in question and environmental burdens is linear, this approach may appropriate for several reasons (Azapagic 1996). Firstly, modelling the whole product system using linear programming allows for interactions between different parts of a multi-component system with multiple-outputs. Secondly, the LP is useful for solving the problem of allocation of environmental burdens which result from marginal changes in activities. Thirdly, adopting an LP approach allows for optimisation according to parameters or constraints. Several authors have adopted LP techniques to assess the environmental implications of different recycling rates in complex production and recycling systems. For example Hannon and Brodrick (1982) presented a detailed LP model of the US iron and steel sector which optimised the energy and labour efficiency of the sector. Leach et al. (1997) have developed an LP model of the life cycle impacts of paper use within London, while Weaver et al. (1995) have investigated the European pulp
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and paper sector at the European level using an LP model. Optimisation for static linear models is relatively straightforward using linear programming techniques. However, optimal control or dynamic optimization, which involves algorithms that predict time-dependent trajectories, is a more challenging problem (Diwekar and Small, 1998). A handful of researchers have worked on the application of dynamic, non-linear modelling to LCA and MFA studies. For example, Pistikopoulos et al. (1995) developed a methodology for the dynamic modelling and control of chemical process technology, while Huppes et al. (1997) have applied signal processing methods to the assessment of emission characteristics. Kandelaars and van den Berg (1997) have used control theory in environmental policy models of material/ product chains. Ruth and Harrington (1998) have carried out some dynamic modelling of material and energy flows in an MFA context, while Ruth (1995) has applied a dynamic, non-linear modelling framework to the environmental assessment of mining and extraction processes for metal resources. The particular problems proposed by modelling the non-linear and dynamic properties of cascade recycling systems have not been addressed in the literature in any depth, and are a recognised research need for the further development of both LCA and MFA methodologies (Wrisberg et al., 1997; Bringezu et al., 1998). The objective of this paper is to address this need. In particular a typology of modelling approaches to recycling systems is developed, and the application of these different approaches to a hypothetical case study is illustrated.
3. Characteristics of material cascades The kinds of systems with which this paper is concerned typically involve the extraction of primary resources for the manufacture of a high-quality material or product, the distribution of the product for consumption or use, the degradation of the product through use, collection at the end of its initial life, and then various cycles of re-use, reconditioning, or the recycling of its component materials before final disposal. Fig. 1 shows a simple example of such a system involving only one recycling loop. The flows Fi represent the quantity of material flowing through each of a set (D) of stages in the life cycle. For the purposes of the illustrative exercise in this paper, one is concerned with the total energy requirements E associated with the life cycle of the product. If the specific energy requirement is denoted by ei (i.e. the energy requirement per unit of mass flow) through each stage of the life cycle, then the total system energy requirement in any one time period can be expressed as: E = % ei Fi
(1)
iD
Typically, a model of the system will require the specification of a set of exogenous inputs Uk (such as UD, say, the demand for the product or URF the recycling fraction). Together with the flow variables, these parameters will define a
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set of constraints describing the physical basis of the model. So, for example, mass flow principles suggest (on the basis of Fig. 1) constraints such as the following: FR =URF ×UD
(2)
FV =FP −FX
(3)
FR =UD −FV −FI
(4)
Eq. (2) constrains the flow through the recycling loop according to the exogenously determined recycling fraction. Eq. (3) expresses the fact that the flow of products into the domestic stock in use during any time period is equal to the
Fig. 1. Schematic life cycle representation of a recycling system.
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quantity produced less the quantity of products exported. Eq. (4) constrains the contribution to demand from recycling in any time period according to the demand for products, the virgin production rate and the imported product flow. Expanding these constraints to cover all the material flow relations allows one to build up a complete mathematical model of the energy and material flows through the system. Clearly, the constraints themselves are determined crucially by specific assumptions about the kind of system represented, and those illustrated here are relatively simple. More complicated models might include a number of additional factors such as production stocks for both virgin and secondary production, home and prompt scrap recycling, the import or export of raw materials as well as products, and so on. For the purposes of this exercise, however, the flows represented in Fig. 1 provides an adequate illustration of the kinds of systems in which the authors are interested. Mathematical models of systems such as those illustrated in Fig. 1 can be classified according to their structure, which in turn varies according to the problem to which the model is applied. The most relevant classifications to this study are those discussed in Section 2, namely time dependency and linearity. Considering first time dependency, a model may be said to be either static or dynamic. A static model (also known as a stationary or steady state model) is capable of simulating a system at only one point in time, under the condition that the output(s) must be in steady state equilibrium with the input(s) (Huppes et al., 1997). A dynamic model, on the other hand, can display time-varying behaviour, which may or may not be in equilibrium. As with time dependency, considerations of linearity lead to models being classified into two groups: linear and non-linear. Young (1993) defines the following properties possessed by linear models: 1. Proportionality. A change in the input leads to a proportional change in the output; 2. Superposition. The total effect of several inputs applied simultaneously to a linear system produces the same result as if they were applied independently; 3. Stability. Linear models are inherently stable, and do not effect amplification of any inputs; 4. Conservativity. All external outputs at any point in time equal the inputs. Non-linear models are not so easy to specify, except in a negative sense, i.e. they do not have all four of these properties. Using these classifications, one can therefore define four model types: static linear, static non-linear, dynamic linear and dynamic non-linear. The decision about which type to use depends on the system to be modelled. In the following subsections each of these different types of model are discussed. It is worth pointing out here that one of the factors to be taken into account in deciding which type of model to employ is the degree of difficulty or simplicity with which a particular model type can be solved. Static linear models are generally easy to solve, whilst dynamic non-linear systems often require larger data sets and significant computing power. Hence, if a system can be simplified, it is often wise to do so. This point is returned to in Section 5 of the paper.
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3.1. Case 1: static linear The underlying model on which most current LCA and MFA studies are based is essentially static and linear: that is it simulates the system at only one point (or period) in time, under the condition that outputs are in steady-state equilibrium with inputs (Huppes et al., 1997; Clift et al., 1998). In mathematical terms, this implies (a) that a change in any of the inputs Uk leads to a proportional change in the output of the model, the total energy consumption, E; and (b) that this change will instantaneously result in a new equilibrium state of the system, i.e. the system is always in equilibrium. Formally, condition (a) is expressed as follows. (E =pk (Uk
(5)
where pk is a constant for all k. It can be shown formally that the condition (5) is equivalent to requiring that ei is constant for each i. In other words, the linear model is sufficient to model the system provided that the specific energy requirement can be expressed as a constant for each stage of the life cycle. It is relatively straightforward to extend a simple static linear analysis at a single point in time to systems with time-varying characteristics, provided that the outputs remain in equilibrium with the inputs. Modelling a material flow system with time-varying input parameters is sometimes called quasi-dynamic. Examples of characteristics in material cascade systems that can be treated this way include improvements in technology efficiency over time, or exogenous changes in the recycling rate.
3.2. Case 2: static non-linear Linear models possess the property that a change in the input leads to a proportional change in the output (Young, 1993). This assumption is inherent in many existing environmental management tools, including LCA, MFA and energy analysis (Boustead and Hancock, 1979), and is frequently justified by the assumption that only marginal changes are considered (Clift et al., 1998). In real-world systems, however this assumption is not always valid. In the case of a static non-linear model, the assumption of proportionality between changes in outputs and changes in inputs is removed. Hence, whilst total energy consumption E is still dependent on inputs Uk, the linearity conditions no longer hold true. Consequently, the specific energy ei of process i is not a constant and can vary with the material flows Fj through particular stages of the life cycle. ei ei (Fj :j Di, Di ¤D)
(6)
Of particular interest when modelling material cascades is the non-linear relationship between the specific energy of recycling (i.e. the energy required per unit of material recycled), and the quantity of material recycled. So for example, one might find that:
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Fig. 2. Specific energy of scrap collection as a function of the recycling fraction.
eR ei
FR UD
(7)
In other words, the specific energy through the recycling process is a function of the recycling fraction URF. Lox et al. (1994) and Karlsson (1998) suggest that this relationship is governed by a U-shaped curve (see Fig. 2). For low values of the recycling rate, the specific energy of recycling may be rather high, since the infrastructure costs are high per unit of energy flowing through the system. As the recycling rate rises, economies of scale reduce the energy cost of recycling a unit of material or product. At high recycling rates however, a reverse effect begins to come into play: the need to collect more dispersed material leads to an increase in the specific energy of recycling. Non-linear relationships may also exist between the specific energy of recycling and quantity of material recycled, due to the build up of impurities within a material cascade, or the degradation of materials due to multiple use and reprocessing.
3.3. Case 3: dynamic linear Many real-world systems exhibit time-varying behaviour, in which the outputs are not necessarily in equilibrium with the inputs. Such systems require representation with fully dynamic models, which are capable of simulating time lags within the system. In formal terms dynamic linear models are constrained by the requirements (a) that a change in any of the inputs, Uk, leads to a proportional change in the output, total energy consumption, E; and (b) that there will be a time lag before the system reaches a new equilibrium state. To satisfy the condition (a), the same requirements for linearity discussed in the static linear case are imposed, but in this case on E, Fi and Uk as functions E(t), Fi (t) and Uk (t) of time. To satisfy condition (b), one must overtly acknowledge the time lags in the system. Thus, for example:
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Fj (t) Fj (t, Fj (t´):t´ B t, j Di, Di ¤ D)
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(8)
In other words, Fi, the material flow through life cycle stage i, may now be a function of time, and indeed of various other material flows over time. The principal application of fully dynamic modelling to material cascades is in simulating the time lag between production and the end of service life for a product or material. So for example it would be reasonable to suppose that: FW(t) FW(t, UD(t − n))
(9)
In other words the flow into the waste management sector at time t is a function of the demand for products at time (t− n), where n is the lifetime the material or product in the economy. Several authors of MFA studies have used dynamic modelling approach to simulate the effect of product life span in determining the results from various environmental policy instruments (e.g. Kandelaars and van den Berg, 1997; Lohm et al., 1997). A fully dynamic model could be used to assess the environmental implications of, for example, changes in the service life of material products. In reality, such changes may be due to a variety of technological, economic, and cultural factors. Typically, however, they are likely to arise through increased obsolescence or improved durability of products (Stahel and Jackson, 1993). Dynamic models may also be applied in order to investigate a combination of policy issues in parallel. For example, some studies have constructed scenario approaches in which total system energy requirements are modelled for each of a number of hypothetical scenarios specified by time-varying technology change, recycling rates, product life span, demand patterns, production delays and stock characteristics (e.g. McLaren et al., 1998; Sundin et al., 1999; Michaelis and Jackson, 2000a,b).
3.4. Case 4: dynamic non-linear In extending this analysis to look at the dynamic non-linear case, one bears in mind the appropriate constraints from previous cases, i.e. that (a) a change in the inputs (Uk ) does not necessarily lead to a proportional change in the output; (b) that there will be a time lag before the system reaches a new equilibrium state. In this case, the flows Fi will once again be of the form given by Eq. (8). Furthermore, one might expect to see non-linear, time-dependent functions associated with the specific energy through life cycle stages. Thus: ei ei (t) ei (t, Fj :j Di, Di ¤ D)
(10)
For example, the specific energy associated with mining raw materials might be expressed by a function eM of a form given by:
t
eM eM % FM(t´) t´ = 0
(11)
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In other words, the specific energy associated with mining at time t is a function of the total material mined up to that time. A number of authors have commented on this complex relationship (Hall et al., 1992; Ruth, 1995; Cleveland and Ruth, 1996). Cleveland and Ruth (1996) point out that technological efficiency improvements may reduce the specific energy requirements over time; but a decline in the ore quality will offset and eventually overtake these improvements. Thus the specific energy of mining will generally be represented by an increasing function of the total material mined. It should be noted that the relationship governing the specific energy of mining is both non-linear and dynamic, since at any one time, the specific energy depends on the ore quality, and hence on the integral over time of the material mined in all previous periods.
4. An illustrative case study In this section the application of the four different modelling types defined in the previous section to an illustrative materials flow case study is demonstrated. Specifically the energy requirements associated with a hypothetical material recycling system over a notional time period 1995–2025 were investigated.
4.1. System description and assumptions For the purposes of this exercise the existence of a hypothetical material recycling system of the kind illustrated in Fig. 1 is supposed. For purposes of simplicity, however, consideration of imports and exports in the system are excluded (the shaded components in Fig. 1). Furthermore, one assumes here that scrap for recycling originates solely at the post-use stage and that there is only one recycling loop. More complex cascades might include multiple re-use, reconditioning and recycling loops (Stahel and Jackson, 1993). Formally, the material cascade is defined as a set of material flows F( j, t) for each stage j of the material or product cycle and for each time period t. The system boundary is defined as a set of processes required to deliver materials or products for consumption within a given geographical boundary. Data on the material flows and the specific energy requirements adopted in this illustrative study have been extrapolated from the general magnitudes and trends experienced in the UK steel cycle 1959–94 (Michaelis and Jackson, 2000a). However, these data have been used in purely illustrative fashion, and it would be inappropriate to draw conclusions about the iron and steel sector from this analysis and premature to use the results to make any specific policy recommendations. This example is merely intended to show the potential application of different modelling methodologies to a dynamic, non-linear system. In order to simulate the environmental impacts of the system, an objective function is first defined which is based on the total system energy requirements E(t) at any time period t. This total system energy is defined quite generally by analogy with Eq. (1) above as:
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E(t) = % e( j, t)F( j, t) j
where j ranges over the stages of the life cycle and e( j, t) e( j, t, F( j, t)) is the specific energy associated with the stage j during the time period t, assuming a material flow F( j, t) through that stage at that time. For the purposes of this study, an objective function related to the energy intensity of the material or product system is defined next. Eq. (12) defines the energy requirement o(t) per unit of material or product in the use stage in each year t. Thus: o(t) =
E(t) Q(t)
(12)
where Q(t) is the total quantity of material or product in use at time t. Such an objective function could be construed as providing an (inverse) indicator of the energy efficiency of the system as a function of time in the following sense: a low value o means that the system has a high resource or energy efficiency and, vice-versa, a high energy per unit of use means a less energy efficient system. It is worth noting that a third objective function might also have been defined by the integral over time of the system energy function. Such an objective function would be relevant, for example, for optimisation with respect to long-term energy consumption, and long-lived energy related pollutants. A similar approach has been recommended to assess long-term impacts of landfilling (Bates, 1998). This kind of optimisation is beyond the scope of this paper, although it would be a straightforward extension of the model described here. A number of basic assumptions have been made in constructing the model. In the first place it has been assumed that the demand for manufactured material remains constant at 15 Mt/year during the simulation period. This is roughly the mean consumption for UK steel over the past 30 years (Michaelis and Jackson, 2000a). It was assumed that the system is initially at steady-state equilibrium, i.e. all variables are constant. The analyses begin with the system in this state to make sure that any subsequent observed behaviour can be unambiguously associated with changes in the system inputs. The mean use time for products manufactured using the material is assumed to be 15 years. The amount of scrap available for recycling is defined by the recycling fraction, which is an input (exogenous) variable. At equilibrium, the value of this variable is set at 50%. All scrap available for recycling is assumed to be recycled because of the lower cost associated with reprocessing. Thus the shortfall between output from reprocessing and demand for material for manufacture is made up by virgin production. All virgin production is produced using a more energy intensive process, and reprocessed using a more efficient process. The magnitude of the specific energy requirements of the virgin and recycling processes are roughly equivalent to those associated with a system in which all virgin steel is manufactured using the basic oxygen furnace, and recycled material is processed in an electric-arc furnace (Michaelis and Jackson, 2000a).
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Further, it was assumed that all scrap for recycling originates solely at the post-use stage, and that scrap arising during virgin production or manufacture is assumed to be recycled within processes from which they originate. Finally it was assumed that the system is driven exogenously by constant year on year demand for new materials and thus it is to be expected that the magnitude of stock in use can vary. This assumption does not effect the analysis unduly, except in the case where use time (service life) varies. This is discussed further in Section 4.3.2. The case study model, and analysis described here has been constructed using the Stella modelling software package.1 This approach is in common with that adopted by Ruth (1995), Cleveland and Ruth (1996), Kandelaars and van den Berg (1997) and Ruth and Harrington (1998). Boelens and Olsthoorn (1998) suggest that opportunities may exist to develop dynamic MFA models by coupling FLUX software with Stella language, or alternatively in development of Petri Net or expert systems modelling approaches.
4.2. Analysis definition In this section, the construction of six distinct types of analysis to determine the energy intensity — defined in terms of o(t) — of the simple cascade system over the 30 year period is defined. These six analysis types are defined in Table 1. Table 1 Summary of scenario descriptions Model type used
Scenario description
Analysis 1
Static linear
Analysis 2
Static non-linear
Analysis 3
Dynamic linear
Analysis 4
Dynamic linear
Analysis 5
Dynamic non-linear
Energy intensity calculated for 1995 Specific energy of recycling is constant Energy intensity calculated for 1995 Specific energy of recycling varies non-linearly with recycling fraction (Fig. 2) Product use time 15 years Recycling fraction 50% Specific energy functions vary linearly over time (Fig. 3) As in Analysis 3 except that: – product use time decreases from 15 to 13 years (Fig. 4) As in Analysis 3 except that:
Analysis 6
Dynamic non-linear
– recycling fraction increases from 50 to 100% over time (Fig. 4); and – specific energy of collection varies non-linearly with recycling fraction (Fig. 2) As Analysis 3 except that – resource extraction is non-linear with respect to cumulative resource extraction (Fig. 5); and – virgin processing energy varies non-linearly over time (Fig. 6)
1
STELLA is a product of High Performance Systems Inc. B http://www.hps-inc.com/\
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Table 2 Specific energy values and sources (base year 1995) Process
Values
Reference
Extraction
1.2 GJ/t — constant over time (1.0 t steel needs: 1.63 t iron ore @ 0.59 GJ/t 0.43 t coal @ 0.50 GJ/t) 16 GJ/t
ETH (1997)
Virgin material production (Blast furnace-basic oxygen furnace) Reprocessing (Electric arc furnace) Manufacturing Collection for recycling
Transport to landfill
1% per year efficiency increase, reflective of efficiency gains in steel production processes in last 35 years 8.5 GJ/t 1% per year efficiency increase, reflective of efficiency gains in steel production processes in last 35 years 1 GJ/t — constant over time Constant over time Linear analyses-0.25 GJ/t Non-linear analyses-U shaped function: Min. = 0.25 GJ/t; Max. is 24× larger 0.05 GJ/t Waste transport: 14 t lorry, 2.35 MJ/t km. 200 landfill sites — 20 km mean distance
ETH (1997) Michaelis (1998) ETH (1997) Michaelis (1998) Michaelis (1998) Michaelis (1998)
Assumption
Estimate
Essentially, there are two static analyses. Both of these analyses calculate the energy intensity of the system at a single point in time, taken as the year 1995. In the static linear analysis (Analysis 1), the specific energy associated with scrap collection is constant with respect to the flow of material through the recycling loop. The static non-linear analysis (Analysis 2) models a possible non-linearity in the collection energy, as illustrated in Fig. 2. In addition to these two static analysis, there are four dynamic analyses, two of which are linear and two of which are non-linear. The two linear dynamic analyses adopt different assumptions about dynamic elements of the system such as the product use time. The two non-linear dynamic analyses adopt different assumptions about specific non-linearities in the system (see Table 1). Table 2 details the values of the specific energy functions for each of the life cycle stages in the year 1995 (at the start of the scenario period), and the assumptions made about changes in these parameters over time (for the dynamic analyses). Table 2 also provides sources for the literature references from which these assumptions were taken. Fig. 3 shows the assumptions made about the variation of specific energy functions with respect to time for the dynamic analyses. Fig. 4 illustrates the assumptions made about the product use time and the variation of the recycling fraction for Analyses 4 and 5, respectively. Fig. 5 shows the variation in the specific energy of mining assumed in Analysis 6, and Fig. 6 introduces the (time) non-linearity in processing energy assumed in Analysis 6.
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Fig. 3. Variation with time of specific energies for different life cycle stages.
Fig. 4. Variation of product use time (Analysis 4) and recycling rate (Analysis 5).
Fig. 5. Specific energy for mining as a function of cumulative resource extraction (Analysis 6).
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Fig. 6. Variation with time of specific energies for virgin processing (Analysis 6).
The main purpose of the exercise described in this section is to illustrate the application of the four model types to an investigation of the system effects of three exogenous variables: post-use recycling fraction, the product use time, and specific energy for resource extraction. Specifically, the aims are: to compare a static linear model (Analysis 1), where the specific energy of scrap collection is constant, against a static non-linear model (Analysis 2), where the specific energy of scrap collection is related to recycling fraction by a U-shaped function (Fig. 2); to compare a dynamic linear model in which the product use time is kept constant (Analysis 3) against a dynamic linear model in which the product use time is varied according to Fig. 4 (Analysis 4); to compare a dynamic linear model in which the recycling rate and the specific energy associated with scrap collection are constant (Analysis 3), against a dynamic non-linear model (Analysis 5) in which the specific energy of scrap collection varies both with time (Fig. 4) and with material flow through the recycling loop (Fig. 2); to compare a dynamic linear model in which the specific energy of extraction is constant and that of virgin production is decreasing linearly (Analysis 3) against a dynamic non-linear model (Analysis 6) in which (a) the specific energy of extraction is related to cumulative resource extraction (Fig. 5); and (b) the specific energy of virgin production varies non-linearly with time (Fig. 6).
4.3. Results In this subsection the results of the four comparisons specified above are presented.
4.3.1. Static linear 6ersus static non-linear results (Analyses 1 and 2) Both the static linear analyses assess the system at a single point in time, 1995. For Analysis 1, the values for the specific energy functions are as shown in Table
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2, and the specific energy associated with scrap collection is assumed to be a constant 0.25 GJ/t (as indicated by the dashed line in Fig. 2) for all values of the recycling fraction. Modelling the system using a series of static linear models (each with a different recycling fraction) allows one to determine how the energy per unit of use, o, varies with the recycling fraction. Fig. 7 reveals that (according to Analysis 1) the system becomes progressively more energy efficient as the recycling rate increases. This is exactly as one might expect, since the reprocessed material consistently requires a lower specific energy than virgin material. Analysis 2, however, provides a different picture of the relationship between o and the recycling fraction. In this case, the non-linear U-shaped function for scrap collection energy (shown by the solid line in Fig. 2) is introduced into the analysis. Fig. 7 illustrates that if the system is operating with a recycling rate between 40 and 60%, a linear approximation of the non-linear function is probably acceptable. However, it is clear that the two analyses differ for recycling rates which are either very low or very high. At low recycling rates, this difference is not substantial: although the collection energy is higher, the volume throughput in the recycling loop is rather low, so that the total system energy intensity is dominated by the virgin production route. However, at higher values of the recycling rate the increased energy of collection begins to affect the system efficiency. In fact, the system operates at its most efficient at around 80% recycling rate and then becomes less efficient again as the recycling fraction is increased. This is in contrast to the static linear analysis which implies that 100% recycling yields the minimum system energy intensity. The policy implications of this comparison should be clear: if policy instruments were set as a result of a static linear analysis then 100% recycling rate would be encouraged. In fact, however, if there were non-linearities in the system of the kind illustrated by Fig. 2, then this policy prescription would increase the energy
Fig. 7. The effect of non-linearities in scrap collection energy (static analysis).
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Fig. 8. The impact of changed product use times (dynamic analysis).
requirements over the case where the recycling rate was set lower. The findings of non-linear analysis indicate that a recycling rate of around 80% would bring about the lowest system energy burden.
4.3.2. Dynamic linear results (Analyses 3 and 4) Fig. 8 illustrates the comparison between Analyses 3 and 4. Both of these analyses model the system energy intensity o(t) assuming that the system is not in steady-state equilibrium, i.e. that it is dynamic. In particular, both Analyses assume time lags between the production of materials or products and their emergence from the use phase. Fig. 8 reveals that the energy intensity calculated under Analysis 3 shows a declining trend not dissimilar to the one illustrated in Fig. 7. However, it is important to note the trend in Fig. 8 is due here to improvements in the energy efficiency in virgin and scrap materials processing over time (Fig. 3), rather than to variations in the recycling fraction. Specifically, no flow non-linearities are involved in Fig. 8. Now that a fully dynamic modelling approach is adopted however, it is possible to investigate the effects of delays within the system. Analysis 3 assumes a constant service life of 15 years, i.e. it assumes that material remains delayed within the ‘stock in use’ for that period. In Analysis 4 the impact of a reduction in the product life from 15 to 13 years as shown in Fig. 4 is investigated. This might be equivalent to, for example, the service life of an average high quality washing machine being reduced as a result of increased product obsolescence (Euromonitor 1992). Before explaining the differences between the results of Analyses 3 and 4, as seen in Fig. 8, it is first necessary to understand the assumption that the recycling system is driven exogenously by a constant demand, and that the magnitude of stock in use can vary. This means that any variation in time delays (i.e. the use time) within the system will result in changes in this stock, not changes in the level of manufacture. This assumption has been made for ease of modelling.
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For about the first 15 years of the simulation the results of Analysis 4 are the same as 3. This is because the shorter lifetime products have not yet emerged from the use stock. However, once these products begin to be discarded, the efficiency of the system undergoes some dramatic changes. Firstly, Analysis 4 becomes briefly more efficient due to the temporary increase in availability of post-use scrap. However, this effect is short-lived as the reduced use time has the corresponding effect of reducing the quantity of material in the use stock (for a constant rate of manufacture), thus making the system less efficient. This trend continues until the system energy intensity settles into a path running parallel to that of Analysis 3, but at a lower level of efficiency (energy consumption per unit of use is around 20% higher in Analysis 4 than in Analysis 3 by the end of the simulation). This comparison illustrates that changes in the product use time can have a significant impact on the energy intensity of the system. It also demonstrates that transient states can be investigated using dynamic modelling: one advantage of this more complex approach.
4.3.3. Dynamic linear 6ersus dynamic non-linear results In this subsection, the dynamic linear results of Analysis 3 are compared against the two dynamic non-linear analyses (Analyses 5 and 6). Analysis 3 assumes a constant recycling rate of 50% and no variation of the specific energy of scrap collection. In Analysis 5 the impact of increasing the recycling rate from 50 to 100% over the first 15 years of the scenario period as shown in Fig. 4 is modelled. In addition, Analysis 5 differs from Analysis 3 in assuming that the specific energy of recycling follows the non-linear U-shaped function defined in Fig. 2. Fig. 9 compares the results of Analysis 3 against Analysis 5. It can been seen that both analyses begin with the same results at 50% recycling rate, but as the recycling rate increases Analysis 5 becomes more efficient because of the lower impacts associated with reprocessing. However, the system reaches a point at around 80%
Fig. 9. The effect of variation in recycling rate and scrap collection energy (dynamic analysis).
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Fig. 10. The effect of non-linearities in extraction and processing energies (dynamic analysis).
recycling in 2005 after which the increasing collection energy offsets savings due to reprocessing, thus decreasing overall system efficiency. By the time the recycling level in Analysis 5 reaches 100% (in about 2010), the system energy intensity is higher than under Analysis 3, even though the latter only assumes 50% recycling. This comparison exemplifies the importance of accounting for non-linear functions when they may significantly affect the system analysis. Finally, Analysis 6 attempts to model potential non-linearities in processing and extraction energies. Firstly, it assumes a long run increase in energy costs associated with material extraction according to the hyperbolic function shown in Fig. 5. In addition, this Analysis assumes that the effects of extracting progressively lower quality ore cause knock-on effects in processing, increasing the energy requirements during the processing phase as shown in Fig. 6. The effect of both these combined assumptions is illustrated in Fig. 10. Initially, the system energy intensity falls below that in Analysis 3 as a result of the reduced specific energy for resource extraction (Fig. 5). Later on however, the energy intensity rises above the linear case, as a result of increases in specific energy functions for both resource extraction and virgin processing.
5. Summary and conclusions The analysis presented in this paper has attempted to illustrate how dynamic, non-linear modelling can be used to model the complexities of material cascades — systems involving materials use, re-use and recycling loops. It has been argued that such methods may, in certain circumstances, provide a more accurate representation of the underlying system than traditional static, linear techniques such as those mainly adopted in current LCA or MFA studies. In particular, a hypothetical case study has been constructed, and it has shown that different modelling techniques provide rather different conclusions about the energy intensity of systems that exhibit such behavior.
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The policy implications of these results should be obvious: restricting analysis to conventional static linear modelling techniques may sometimes produce misleading analytic results, and stimulate inappropriate policies as a result. In those cases where significant non-linear or dynamic effects within the system are indicated by the available data, more sophisticated modelling using dynamic and non-linear techniques is required before it is possible to formulate appropriate policy, for example, about optimum recycling rates. In this paper, the system energy intensity has been used as an objective function. However, the implications of this work extend beyond energy analysis. The environmental impacts of energy consumption are well-documented (Jackson, 1992, 1997, e.g.). It would be straightforward to extend the work described here to an assessment of energy-related emissions such as carbon dioxide, sulphur dioxide, nitrogen oxides, particulate matter and so on. Extending the analysis to other kinds of pollutants is also relatively straightforward, although optimising with respect to more than one output requires definition of multiple environmental objective functions (Azapagic and Clift, 1995). It should be noted that the available data do not always support the use of the more sophisticated, and more complex, modelling techniques described in this paper. It is not axiomatic that a dynamic modelling approach should be adopted when modelling a dynamic system, since the question being asked may not require consideration of system dynamics. The same can be said with respect to modelling system non-linearities. Within certain boundaries, linear functions may offer a perfectly adequate of approximation of non-linear characteristics of the system. In some cases, therefore, static, linear modelling is sufficient to make informed policy decisions — at least over short time-periods in particular system configurations. In other cases however, dynamic, non-linear models will be necessary to capture the complexity of the underlying system. Finally, it should be noted that occasionally, even though significant dynamic or non-linear system characteristics exist, the data required to model these effects are unavailable or inadequate to the task. This situation means that realistic modelling of material cascades may well remain problematic and implies that policy-making in relation to re-use and recycling is inherently uncertain. Addressing the implications of this uncertainty is beyond the scope of this paper.
Acknowledgements The authors are grateful for financial support during the duration of this study from the UK Engineering and Physical Sciences Research Council (EPSRC), and the UK Royal Academy of Engineering. We are also grateful for critical inputs from participants at the SETAC-Europe Annual Meeting held in Bordeaux in April 1998 and the International Resource Accounting and Modelling Workshop held in Groningen in September 1998, at which earlier versions of this paper were presented.
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