Environ. Sci. Technol. 2009, 43, 8251–8256
The Path Exchange Method for Hybrid LCA M A N F R E D L E N Z E N * ,† A N D ROBERT CRAWFORD‡ ISA, School of Physics, A28, The University of Sydney NSW 2006, Australia, and Future Generation Fellow, Faculty of Architecture, Building and Planning, The University of Melbourne, Parkville, Victoria 3010, Australia
Received July 13, 2009. Revised manuscript received September 6, 2009. Accepted September 10, 2009.
Hybrid techniques for Life-Cycle Assessment (LCA) provide a way of combining the accuracy of process analysis and the completeness of input-output analysis. A number of methods have been suggested to implement a hybrid LCA in practice, with the main challenge being the integration of specific process data with an overarching input-output system. In this work we present a new hybrid LCA method which works at the finest input-output level of detail: structural paths. This new Path Exchange method avoids double-counting and system disturbance just as previous hybrid LCA methods, but instead of a large LCA database it requires only a minimum of external information on those structural paths that are to be represented by process data.
1. Introduction Hybrid techniques for Life-Cycle Assessment (LCA) provide awayofcombiningtheadvantagesofprocessandinput-output analysis, which are accuracy and completeness (1-3). A number of methods have been suggested to implement a hybrid LCA in practice, however most of them have in common that on-site and lower-order indirect effects are covered by process analysis using application-specific data while higher-order indirect effects are covered by inputoutput analysis using economy-wide average-sector data. One hybrid LCA method is the matrix-based Integrated Hybrid LCA by Suh and Heijungs (4, 5), where the conventional monetary input-output table is extended by embedding in it a process database in physical units. Strømman and co-workers (6) recently presented a Tiered Hybrid LCA method, and discuss the problem of double-counting and overlap when substituting input-output-based information with process information. Treloar (7) was first to apply Structural Path Analysis (SPA) to LCA (for further applications of SPA see 8-13). Treloar observed that changing the transaction coefficient for a particular element, or node, in an input-output matrix used for LCA would affect all supply chain paths that contain that node, even if the changed coefficients applied only to a particular path. Treloar correctly recognized that SPA provides a means to avoid such undesired “global” effects. In this paper we present a formal and general exposition of the Path Exchange method for hybrid LCA. The basic idea of this method is Graham Treloar’s. While he applied it a few times, mostly to embodied energy and water in the con* Corresponding author e-mail:
[email protected]. † The University of Sydney. ‡ The University of Melbourne. 10.1021/es902090z CCC: $40.75
Published on Web 09/24/2009
2009 American Chemical Society
struction sector (14, 15), he unfortunately did not have the opportunity to develop a general methodology, to solve a number of problems and undertake further research as discussed in his last published document (14), to contrast and integrate his method with other hybrid LCA methods, notably with the work by Strømman and co-workers (6), and thus to make his method accessible to the wider field of LCA. These tasks are the subject of this paper. Due to restrictions in journal space, and because of the novelty of the approach, this paper deals largely with methodological issues, albeit supported by practical examples. A real-world application of this method is being published in parallel (16). The article unfolds as follows: we will first briefly review the basic input-output and SPA theory, as well as hybrid LCA techniques, in the following Section. In Section 3 we will then develop a general methodology of the Path Exchange method, presenting novel features such as cross-influence issues between changed paths, and path splitting. A practical example will illustrate the relationship between the Path Exchange method and other methods. Section 5 concludes.
2. Input-Output, SPA, and Hybrid LCA Theory The result of generalized input-output analyses are 1 × N vector of multipliers, that is embodiments of factors (such as energy, resources, and pollutants) per monetary unit of final consumption of commodities produced by N industry sectors. A multiplier vector m can be calculated from a 1 × N intensity vector q (or a row-wise bundled M × N intensity matrix q) containing sectoral factor inputs per unit of gross output, and from an N × N direct requirements matrix A according to m ) q(I - A)-1
(1)
where I is the N × N unity matrix. The factor inventory Q for a given economic activity represented by a N × 1 commodity inputs vector y is then simply Q ) my
(2)
Intensity vectors and direct requirements matrices can be derived from input-output transaction matrices and inputoutput physical satellite accounts published regularly by statistical agencies around the world. The basic equations are given here only for supporting the following exposition. For further details the reader is referred to previous articles in this journal (2, 17, 18), as well as introductory articles elsewhere (19-23). Structural Path Analysis (SPA) was introduced into economics and regional science in 1984 (24, 25). To systematically determine environmentally important supply chains, the total factor multipliers as in eq 1 can be decomposed into contributions from all supply chains, by “unravelling” the Leontief inverse using its series expansion (see 11, 26, 27) q(I - A)-1 ) q + qA + qA2 + qA3 + ...
(3)
Equation 3 is also referred to as a Production Layer Decomposition, because the power terms correspond to subsequent production rounds. Combining eqs 1 and 3, a multiplier for industry i can be written as VOL. 43, NO. 21, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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N
mi )
∑
(
˜ B′) Q ) (B
qj(δji + Aji + (A2)ji + (A3)ji + ...)
j)1
N
)
∑ j)1
N
qj δji + Aji +
∑
N
AjkAki +
k)1
N
∑ ∑A A
jl lkAki
l)1 k)1
+ ...
)
(4)
where i, j, k, and l denote industries, and δij ) 1 if i ) j and δij ) 0 otherwise. A first-order structural path from industry j into industry i of first order is represented by a product qjAji, while a second-order structural path from industry k via industry j into industry i is represented by a product qkAkjAji, and so on. There are N structural paths of first order, N2 paths of second order, and, in general, Nn paths of nth order. An index pair (ij) shall be referred to as a node. mi is thus a sum over a direct factor input qi ) Σj ) 1 N qjδji, occurring in industry i itself, and higher-order structural paths. The succession of indices (jl lk ki in eq 4) can loop over identical sectors, in which case SPA unfolds loop flows into linear paths. Equation 4 can be evaluated by sequential backward scanning of the production chain tree from final demand to the various locations of factor usage (13). The result of one execution of an SPA algorithm for a particular production factor is a list of the top structural paths, ranked in terms of their contribution to the total factor multiplier. Let y* ) {y*1,y*2,y*3,y*4,...} ) {y*}l
(6)
be N* × 1 detailed components of final demand. These components could be for example detailed company data. In general, N* > N, because applications data y* is usually more specific than their aggregation y used in the inputoutput calculus. Assuming activities y* can be allocated to input-output categories through a concordance matrix H, the total factor requirement Q can then be decomposed into sectoral contributions according to N
Q ) my )
N*
∑ ∑m H k
kly* l
(7)
k)1 l)1
2.1. Hybrid LCA. An example for a first-order structural path is qcoalAcoal-electricityyelectricity, representing for example the emissions of methane (q) from coal mines supplying power plants (A) which in turn support the activity y. The coefficients q and A are economy-wide averages derived from published national accounts. Assume now that the activity y sources electricity not from an average power plant, but from a plant that is fitted with advanced firing technology and as such uses less coal to produce a unit of output, i.e., the coal input coefficient A′ for that plant is lower than the economy-wide average A. Changing Acoal-electricity to Acoal-electricity′ in the direct requirements matrix A in eq 1 would mean assuming that all power plants in the nation were of the advanced type. This is an example for the undesired effect thatsin principlesall hybrid LCA techniques are designed to avoid. To support the methodological exposition of the Path Exchange method, we review two hybrid LCA methods that both make extensive use of input-output analysis: integrated and tiered hybrid LCA. 2.1.1. Integrated Hybrid LCA. Integrated hybrid LCA is a matrix-based hybrid LCA method, where the conventional monetary input-output table is extended by embedding in it a process database in physical units. Written in terms of direct requirements coefficients, the extended input-output model reads (28, 29) 8252
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[
-Cd
˜ A u
-C I - A
corr
]() -1
˜f f
(8)
where Q is once again the total factor inventory (or the amount of environmental intervention as called by Suh ˜ is the 28, 29), the B matrices are the factor intensities, A process technology coefficient matrix expressed in physical units, Acorr is the input-output technology coefficients matrix expressed in monetary units, Cu and Cd are the so-called upstream and downstream cutoff matrices expressed in mixed units, and the f matrices hold final demand from both process and input-output systems in physical and monetary units, respectively. The hybridization of the conventional input-output method by Integrated Hybrid LCA lies in the addition of the process technology database, which adds potentially hundreds of detailed processes that differ from the national average production recipe inherent in A. A user then has the choice of representing their activities as detailed processes ˜f instead of as aggregated input-output sectors f. The upstream cutoff matrix holds those inputs into the processes that are not covered by the process database, expressed in monetary units per physical unit. The downstream cutoff matrix holds the deliveries of process outputs to input-output sectors, expressed in physical units per monetary unit. The inputs added in the upstream cutoff matrix are missing from the process database, and are added to complete the input bill. The downstream cut-offs are in principle contained in the original input-output matrix A, therefore those inputs by processes have to be subtracted from the monetary inputs of the input-output sectors. In other words, to avoid double counting, the corrected Acorr is constructed from the original input-output system A by taking out whatever is covered by the process system. Peters and Hertwich (30) examine Suh’s work (29), especially with respect to the downstream cutoff matrix Cd. These authors conclude that, unless LCA process sectors form a significant part of the economy, the contribution of Cd to the inputs contained in the input-output table will be negligible. Given this, they ask whether the compilation of sales of processes to the economy, followed by their subtraction from the monetary input-output data, is worth the effort. In his reply, Suh (31) argues that the fact that the downstream cutoff contribution is generally small is no reason to automatically set this term to zero. Further, he makes the point that Cd is constructed by the LCA practitioner by consecutively adding upstream and downstream process components to the process tree, and that Cd does not require an LCA of all economic sectors. In his Appendix A, Suh (29) presents a detailed method for correcting the monetary supply and use matrices for process flows double-counted by Cu and Cd. This correction involves concordances between the process and the input-output system, as well as price vectors for process inputs and outputs. The actual subtraction from the input-output system is done by (a) transforming the initial functional flow records matrix into supply use form, (b) reclassifying into input-output classification with concordance matrices, (c) multipliying the reclassified process use and supply matrices with price vectors, and (d) subtracting the resulting matrices from the supply and use input-output tables. 2.1.2. Double-Counting Issues: The Tiered Hybrid Adjustment Method. Strømman and co-workers (6), SPH in the following) use a tiered hybrid model to illustrate doublecounting issues. In the following we will examine this system because the double-counting issues are relevant for the integrated hybrid method as well as the Path Exchange method. SPH propose an algorithm to combine partially overlapping physical and monetary data in a tiered hybrid system.
In essence, their algorithms deal with correcting doublecounting incidents that occur when (a) a part of demand from the foreground system is decoupled from the inputoutput background system and coupled to the process background system, and (b) the sectors under demand in the process and input-output system have intersecting coverages. In designing their method, SPH examine differences in the definition and coverage of process and input-output sectors, and then use SPA and price data to remove potential overlap by subtracting doubled-counted contributions from the input-output system. SPH assume that the definition of input-output sectors at least covers that of the process sectors, but that process data are preferred. Unlike Suh (29), SPH do not correct the input-output matrix by subtracting the coverage of processes, but instead allow their process and input-output matrices to contain intersecting data. Their main focus is then to remove double-counting from the input-output system during the performance of the LCA, using SPA and adjustment techniques. SPH provide the example of producing a pressurized vessel, where the steel making up the vessel is described using the process system, and the assembly of the vessel is described using the input-output system. The demand for the vessel is split into a fraction for an “LCA steel process” demanded from the process system, and a fraction for a “mechanical engineering service” demanded from the input-output system. SPH then take out the double-counted steel that is already contained in the supply chains of the input-output sector “mechanical engineering”. The doublecounted set of input-output paths that is to be replaced by process data is identified by SPH as the set of top-ranking paths resulting from an SPA of “mechanical engineering” that just covers the monetary value of the quantity of steel described in the process data. In other words, SPH’s method can be explained as “identify top-ranking input-output paths that start with steel and end in mechanical engineering, and take as many as them as you need to cover the value of the steel modelled using the process system, and take these paths out of the input-output system, tier by tier”. Lenzen (32) comments that the input-output paths identified for deletion by SPH’s SPA may not be paths that correspond to the process data that replaces them. Instead, Lenzen (32) argues that only those input-output paths should be deleted that correspond in their definition to the preferred process data, and that this should be irrespective of whether those input-output paths match the monetary value of the process data items or not (see a response by Strømman (33)). This “exchange by definition” is the essence of the Path Exchange method described in the following Section.
3. The Path Exchange Method The basic idea of the Path Exchange method is to carry out a hybridization of the life-cycle inventory only at the highest level of detailsstructural paths. It has as a starting point the results of an SPA carried out on the conventional monetary input-output matrices, and then allows correcting the total factor inventory by exchanging subpath-level average input-output information for corresponding specific process information. As such, the Path Exchange method • does not operate at all at the matrix level, but at the structural path level only, and hence avoids system disturbance; • does not need an embedding of a LCA process database as in the integrated hybrid method and the tiered hybrid method; • allows adjusting only parts of structural paths, and such avoids the need to ensure perfect matching (value or
coverage) between process and input-output data as in the tiered hybrid adjustment method. Regarding the first point: Treloar (7) had already demonstrated that exchanging a coefficient in an input-output matrix would lead to an undesired global change in a lifecycle inventory, and therefore had suggested appraising the more detailed SPA as a means to streamline the data collection for the process part of a hybrid LCA. However, Treloar did not deal with the question of whether process data had the same coverage as the input-output paths it replaced. While this issue is also at the heart of the work of Strømman and co-workers (6), p 250), their solution is different from the Path Exchange method. 3.1. Basic Methodology. The following introduction is cast in general terms as well as a hypothetical application, so that the reader can understand the relevance of the method to real-world tasks. Assume that a detailed activity vector y* (for example the steel vessel) has been aggregated into input-output format y (for example the “mechanical engineering” sector), and an input-output analysis been performed on y, including an SPA. The Path Exchange method proceeds as follows. (1) Examine input-output structural paths, with preference for important paths, and establish whether corresponding process data can be found for any of them. Example: A user works with a path exchange software, and examines the paths “CO2 emissions from fuel combustion > Steel (S) > Engineering (E) > User”, and “CO2 emissions from fuel combustion > Metal ore mining (M) > Steel (S) > Engineering (E) > User”. The user has located process data items relating to these paths. (2) Establish the nature (q or A) of the process data item P in terms of eq 4. P can be an intensity q, or a node coefficient A, to replace corresponding input-output information in a path S ) qi Aij Ajk ... Alm ym. Example: The user understands the breakdown of the paths as S ) qSCO2 AS, E yE and S ) qMCO2 AM, S AS,E yE. The user has ascertained through the engineering firm F they have contracted that the steel used for the vessel is made via a special (“LCA”) route that only emits X tonnes of CO2 per tonne of steel. Information on the price of that steel exists as πs. Then, the CO2 emissions intensity of the LCA steel is P(1) ) X/πs, and this information corresponds to qSCO2. F has also installed advanced (“LCA”) machining technology and only uses Y tonnes of steel to produce a vessel. Given the price πv of a vessel, the LCA steel-to-vessel input coefficient is P(2) ) Yπs/ πv, and this information corresponds to AS,E. Finally, the user finds out from the literature that LCA-steel makers have to use unconventional (“LCA”) metal ores that cause aboveaverage specific CO2 emissions of P(3) ) Z kg/$ when mined and this information corresponds to qMCO2. (3) Establish the coverage of these process data points. Since process sectors are usually more detailed than input-output sectors, it is likely that the coverage of the process data item is smaller than the coverage of the corresponding structural path component (compare (6), Sec. 2.3). In this case, estimate the proportion σ of q or A to which P applies. Here, the detailed breakdown of y into y* may prove helpful. Example: Assume a user has recorded two account items y1* “$75,000 - vessel from engineering firm F ”, and y2* “$25,000 - pipes from engineering firm G ”, which both become aggregated in one input-output sector in y. The user’s account y* reveals that their contract with firm F represents only 75% of their purchases from mechanical engineering firms, and that 12% of purchases from F are on items other than the vessel. Firm F ’s in-house data shows further that they use conventional steel for the vessel’s sensor flanges (2% of vessel mass), and inlets and outlets (5% of mass). Therefore, σ(2) ) 75% (1 - 12%) (1-2%-5%) ) 61.4%. Furthermore, the user finds out that only 95% of CO2 VOL. 43, NO. 21, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Upstream influence of transaction coefficient changes, illustrated in a tree diagram. emissions reported for the LCA steel route are from fuel combustion. Therefore, σ(1) ) 75% (1 - 12%) (1 -2% - 5%) 95% ) 58.3%. (4) For process data items representing indicator intensities, change qi(1) into P(1), then from the entire life-cycle inventory Q, and from the appropriate tier of the Production Layer (1) (1) ym , Decomposition, subtract σ(1) S(1) ) σ(1) qi(1) Aij(1) Ajk(1) ... Alm (1) (1) ym . Log the adjustment and add σ(1) S′(1) ) σ(1) P(1) Aij(1) Ajk(1) ... Alm ∆(1) ) σ(1) (S′(1) - S(1)) in a change register. Example: The user (1) 2 and σ(1), and logs the change. selects qCO S , enters P (5) For process data items representing transaction coefficients, change Ajk(2) into P(2), then from the entire life-cycle inventory Q, and from the appropriate tier of the Production (2) (2) ym , Layer Decomposition, subtract σ(2) S(2) ) σ(2) mj(2) Ajk(2) ... Alm (2) (2) (2) (2) (2) (2) (2) and add σ S′ ) σ mj P ... Alm ym . Log the adjustment ∆(2) ) σ(2) (S′(2) - S(2)) in the change register. Note that here, the full multiplier m is used instead of q, and also that this multiplier is applied to node j, and not i, so that the coefficient change will affect all paths upstream from the changed node, but only those. Example: The user selects AS,E, enters P(2) and σ(2), and logs the change. The user brings up the path “Metal ore mining > Steel > Engineering > User”, and notices that in this path the S-E node coefficient does not have the average value AS,E, but the value P(2) applied to a percentage σ(2) of the path. Even though the coefficient change from AS,E to P(2) was undertaken while examining the shorter path “Steel > Engineering > User”, the software has recognized the upstream influence of the coefficient change (see Section 3.2). (6) In terms of eq 2, the adjusted factor inventory Q′ is equal to the initial input-output-based factor inventory Q, plus all (positive and negative) adjustments. (7) A change of any part of y represents a change in the monetary activity vector, and must be treated as a change in the specification of the functional unit. This happens outside the Path Exchange method. 3.2. Upstream Influence of Transaction Coefficient Changes. When a transaction coefficient in a particular path is changed, this has consequences for all longer paths that contain the subpath from the consumer node (y) up to the two nodes between which the transaction coefficient change has occurred. Take for example the supply chain system in Figure 1a. Assume that the user wants to change the coefficient for the transaction “Steel > Engineering”, as explained in Section 3.1 (Figure 1b). Anything that the steel maker uses to operate, and in turn to supply the engineering firm that supplies the user, must go through the already changed downstream path: “ > Steel > Engineering > User”. In other words, if the engineering firm that the user has contracted uses less steel per vessel, then it also uses indirectly less metal ore per unit of steel per vessel, less mining machinery per vessel, less explosives per vessel, and so on. 8254
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The coefficient change at Steel > Engineering must therefore affect the path “Metal ore > Steel > Engineering”, and in fact must affect all longer paths that contain the nodes of the changed subpath “Steel > Engineering > User” (Figure 1b). These paths form an entire subtree (dashed lines in Figure 1b) branching off at the supplying node of the changed transaction. A subsequent second coefficient change in the path “Metal ore > Steel > Engineering > User”, carried out at the node “Metal ore > Steel”, in turn affects a subtree (dotted lines in Figure 1c) of the previous subtree (dashed). These upstream influences of transaction coefficient changes exist irrespective of the factor q that determines the unit of the path. This is because, if the engineering firm that the user has contracted uses less steel per vessel, and indirectly uses less metal ore, mining machinery, etc. per vessel, then it will also cause less greenhouse gas emissions, water consumption, etc. along these paths. This means that transaction coefficient changes are always made independent of a particular factor. 3.3. Changing Multipliers. Section 3.1 above dealt with changes of the q or A components of structural paths. However, in principle, it is possible to come across external data for the multiplier m of a particular process, for example an estimate of embodied energy, emissions, or water. This situation would suggest changing m at various tiers. Since my ) qy + mAy ) qy + qAy + mA2y, and so on, one possibility would be to change the entire canopy mi that sits upstream of the trunk Aij Ajk ... Alm ym of the tree T ) mi Aij Ajk ... Alm ym. However such a capability is not implemented in a straightforward way, because of the following. First, if prior to, or after changing the multiplier mi in the tree T, the intensity of any path S with at least the nodes Aij Ajk ... Alm ym has been, or is to be changed, then either changing from T ) mi Aij Ajk ... Alm ym to T′ ) m′i Aij Ajk ... Alm ym may need to override the path change from S ) qn ... Aij Ajk... Alm ym to S′ ) q′n ... Aij Ajk... Alm ym, or vice versa. This is the case for process data that do not provide any information on the multipliers’ tier or path composition. In these cases, there would be no basis for netting the subtree change T to T′ with regard to the path change S to S′, contained within T and T′. Second, the information collected from a (nonintegrated) process database on total embodiments may be subject to an unknown truncation error (see for example 34, 35). In this case, changing a multiplier would introduce a truncation error into the hybrid LCA. Third, a tier-wise correction cannot be made to the Production Layer Decomposition (eq 3) if it is not known how the process data on multipliers are distributed across input-output tiers.
Nothwithstanding, but subject to the above restrictions, a multiplier-exchange capability can be implemented in a software tool. 3.4. Example. This section will illustrate the different ways in which the three methods described in Sections 2.1 and 3 deal with circumstances that are posed in the example of producing a pressurized vessel, using LCA steel, machining, and metal ore. All three methods have in common that process data are preferred for the description of the unconventional (“LCA”) items, while the remainder is to be modeled using input-output sectors. 3.4.1. Integrated Hybrid Method. To represent the particular process features of the example in Section 3.1, an integrated hybrid database would have to distinguish in its ˜ the LCA vessel machining process, the LCA LCA database A steel, as well as the LCA metal ores mining. The vessel machining process would represent the steel types used for the vessel and flanges, the amount of steel needed and so on, and this process would link mostly to the LCA steel, and less to the input-output steel sector. Similarly, the LCA steel process would link to the LCA metal ore and the inputoutput metal ore sectors. With all three LCA processes in the LCA database, the integrated hybrid method would yield the same results as the Path Exchange method. If for example the vessel machining were not part of the LCA database, and the assembly cost were allocated to the input-output sector “mechanical engineering” linked to the input-output steel sector, a double-counting incident a` la Strømman (6) would occur. The difference between the integrated hybrid and the Path Exchange method lies in the degree of flexibility. In the former ˜ of the integrated hybrid method, the process coefficients A matrix are generally fixed, for example by the LCA database provider. This means that if a particular process were not contained in the LCA database, the LCA practitioner would need to augment and rebalance the matrix themselves. This would entail the adding of an entire column and row containing all inputs and outputs of each process, even if only one characteristic were different from the economywide average sector. A second difference exists with respect to the balancing. If in the Path Exchange method a transaction coefficient is changed, the remaining coefficients can be, but are not automatically adjusted. This means that the inputs and outputs of the two nodes connected by the changed transactions may be out of balance. Such imbalances are generally of minor importance, because the changed paths often represent only a small fraction of the total factor inventory. In contrast, the LCA processes in the integrated hybrid matrix represent economy-wide totals, and the corresponding input-output sectors must be netted in order to avoid distortions. 3.4.2. Tiered Hybrid Method. In the system used by SPH, there exists overlap between the “mechanical engineering” input-output sector and the “steel” process sector, since “mechanical engineering” already includes upstream steel inputs. The difference between SPH’s tiered approach and the Path Exchange method is that SPH take out as many high-ranking input-output structural paths starting with steel and ending in mechanical engineering, as needed for matching the value of the LCA steel, but irrespective of the identity of the structural paths, and the Path Exchange method takes out the input-output structural path “steel > mechanical engineering” irrespective of its value or rank. Further, the “LCA steel” is made from “LCA ore”, which is also represented in the process system. However, the LCA ore is not purchased directly for the activity examined, but only demanded via the process sector “LCA steel”, and as a second-order effect it would thus escape SPH’s
double-counting identification algorithm, which would only look at correcting for double-counting of the process path “steel > engineering”, and not for double-counting of the process path “metal ore > steel > engineering”. This is because ore (priced πore) for steel for the vessel is a pf ˘ vessel, second-order path of the shape πore App ore, steel Asteel, vessel x but SPH only deal with double-counted foreground pf x˘lt. Hence these methods would demand x˘ of the shape Akl yield different results. 3.4.3. Path Exchange Method. The Path Exchange method would call up for example the input-output path “metal ore CO2 AM,S AS,E yE), and f steel f mechanical engineering: (S ) qM replace this path (and only this) with “LCA ore f LCA steel f LCA machining” (S′ ) P(3) AM,S P(2) yE), as explained in Section 3.1. This exchange is done irrespective of any potential differences in the monetary value between S and S′. That is, the path AM,S AS,E yE may have a different value than AM,S P(2) yE. The main issue is that the new emissions intensity P(3) matches the monetary valuation of AM,S P(2) yE. There is no double counting, because there is no other LCA metal ore left to supply the steel and engineering sector along this particular path. Also, there is no global disturbance since the change was made at the path level and not at the matrix level.
4. Discussion Hybrid techniques for Life-Cycle Assessment (LCA) provide a way of combining the accuracy of process analysis and the completeness of input-output analysis. A number of methods have been suggested to implement a hybrid LCA in practice, with the main challenge being the integration of specific process data and an overarching input-output system. In this work we present a new hybrid LCA method which works at the finest input-output level of detail: structural paths. This new Path Exchange method avoids double-counting and system disturbance just as previous hybrid LCA methods, but instead of a large LCA database it requires only a minimum of external information on those structural paths that are to be represented by process data. In particular: (a) The Path Exchange method captures feedback loops between the process and the input-output system, by exchanging higher-order transaction coefficients, and thus allows for example the adequate modeling of scrap recycling and reuse. (b) The detail provided by the Path Exchange method comes at a lower labor and data cost compared to other methods (see Table 1 in (28)). It is straightforward to couple a path exchange module directly to corporate financial accounting systems. (c) In the Path Exchange method, the user’s choice is not limited to process data offered by LCA database providers; the path exchange user is in principle able to replace economy-wide average, input-output structural path components with any information whatsoever. (d) The Path Exchange method solves problems associated with ambiguous overlap between process and input-output databases. This is achieved by (1) managing overlap at the path level, rather than at the sector-level at the process-input-output frontier, and (2) allowing the user to replace only a fraction of a path that relates to a particular purchase. A first real-world application of the Path Exchange method to a hybrid LCA of an organization is being published in parallel (16). Provided this new approach is met positively, the ensuing challenge would be in adopting existing process databases to communicate with Path Exchange software, and in particular to enable the use of matrix data on whole process systems. VOL. 43, NO. 21, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Acknowledgments This article is dedicated to Graham Treloar, who intuitively developed the basic idea of the Path Exchange method elaborated in this paper, but who sadly died in 2008. Olivier Baboulet provided critical comments on an earlier draft of this paper.
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