*4.2. The ISO 14041 Influence (1999–2003)*

In the third article of the second route, Azapagic and Clift used the boron product system to examine the different allocation methods recommended by ISO 14041, which was just released in 1998 [25,93]. ISO 14041:1998 introduced the same three levels of the hierarchy of the present ISO 14044:2006. However, the second level included the following clarification: "the resulting allocation will not necessarily be in proportion to any simple measurement such as mass or molar flows of coproducts". Azapagic and Clift argued that, following ISO 14041, allocation by physical (causal) relationships had to be the result of mathematical system modeling [70,93]. Nevertheless, the ISO 14041 allocation underlying physical relationships allowed also allocations based on the "cause of the limits" of the amount of product output. This aspect emerges from the annex of ISO 14041:1998, where mass or volume allocations are suggested as representing physical relationships for road transportation because the quantity of materials transported is limited by the maximum load that the vehicle can carry [25]. Although these two approaches may at first appear contradictory, they are in line with Azapagic and Clift's work, who also concluded that in some cases (which include the transportation example), allocating based on a physical quantity leads to the same results obtained by marginal allocation [70,93]. In these cases, it may be correct to allocate based on a physical parameter representing the physical causation involved, and therefore, not arbitrarily [70,93].

Azapagic and Clift (1999a) highlighted that system expansion (enlargement) is not always applicable. This approach is not possible when the goal of the study requires to determine the impacts of only one of the products [93]. The reason is that, by expanding the functional unit to include the co-functions, the results at the level of one single product would not be available. They also investigated allocation in heat and power cogeneration plants. Due to lack of data, they could not model the system to represent physical causalities and therefore applied the "avoided burdens approach" (in later research "substitution"). Azapagic and Clift argued that substitution is a conceptually equivalent alternative to system expansion, and is suitable when one co-product displaces its production elsewhere, such as for energy recovery from waste or cogeneration [93].

Actually, annex B of ISO 14041 quoted the same example of system-expansion/substitution applied to energy from waste incineration [25]. Nevertheless, annex B specified that the expansion of the boundaries like this requires 1) that the goal of the study is aimed at assessing a change, "i.e., a comparison between two alternative scenarios for the same product" and 2) that the modeled change which will actually occur because of the decision supported by the LCA can be predicted with a fair degree of certainty [25]. To apply this type of expansion, the LCA should aim, therefore, to answer the question of what would have been the long-term marginal effect if the service had not been performed [25]. Hence, substitution became a possible system expansion approach in what nowadays is understood as consequential thinking. This annex with allocation examples is no more included in the current ISO 14044:2006.

In the lowest level of the allocation hierarchy of ISO 14041 [25], economic allocation became an example, and no more the only acknowledged allocation method as it was reported in the previous draft version [92]. Hence, in some cases, allocation based on a physical parameter could be preferred to an economic allocation, and this might have given birth to the natural-science ALCA school. Moreover, ISO 14041:1998 specified that the environmental impact should be allocated only to the products causing the release of the emissions (causality principle). ISO 14041:1998 proposed the example of a multi-input incineration process releasing cadmium emissions which should be allocated only to the input wastes that contain cadmium.

The fourth article [70] referred once again to LP-based marginal allocation, stating that this modeling applies "when the functional outputs can be varied independently", i.e., in partial joint production or combined production (see Appendix A for more details about these definitions). A naphtha cracking was proposed as an example of a system where the outputs can be independently varied (within physical and thermodynamic limits) by changing the operating conditions [70]. When that is not the case (i.e., full joint production; with a fixed ratio of products), "allocation by physical causality cannot be implemented" [70]. Linked to this impossibility, they provided the often-cited example of the ratio of sodium hydroxide (NaOH) and chlorine (Cl2) produced by electrolyzing brine, which is fixed by stoichiometry. Other examples that they mentioned about this impossibility are rapeseed oil/residue (ratio fixed by the chemical structure of the plant) and beef/leather (fixed by the physical structure of the animal) [70]. In these cases, the authors stated that ISO recommended economic allocation because it reflects "the socio-economic demands which cause the multiple-function systems to exist" [70]. They concluded that "allocation on an arbitrary basis, such as mass or energy flow, must be avoided" and "where physical causality between functional units and environmental burdens exists, the allocation should always be based on these causal relationships" [70]. The authors based their methodological choices on the 1997 voting draft of ISO 14041.

The ISO 14041:1998 was complemented by ISO/TR 14049:2000 [23]. This technical report defined system expansion as the addition of functions but lost the concept of system expansion with substitution when the goal is to assess a change. This is still missing in the current ISO 14044:2006 and ISO/TR 14049:2012 [2,24].

This ISO/TR provided two examples related to the disposal phase of the life cycle. The first example showed how to expand boundaries to compare two processes with different outputs, A and B, using the same inputs. As illustrated in case d of Figure A1 in Appendix A, the system boundary for each process needs to be expanded with an alternative process for making the other product. Then the two systems under comparison produce the same functional unit A+B. Moreover, it specified that the added processes shall be those that "would actually be involved when switching between the two analyzed systems" [23]. In the second example, open-loop recycling is solved with a closed-loop procedure that includes the entire recycling processes into the same system boundaries (like case c of Figure A1 in Appendix A).

Concerning allocation by physical property (e.g., mass or viscosity), ISO/TR 14049:2000 [23] emphasized that this type of allocation should be preferred to economic allocation only when it reflects the way in which the inputs and outputs are changed by quantitative changes in the products, (as, for example, in the transportation example in ISO 14041:1998, quoted above). This had to be proven by varying the ratio of co-products [23].

In 2001, Ekvall and Finnveden published a critical review on allocation in ISO 14041:1998 [72]. Ekvall and Finnveden stated that system expansion (in the form of substitution) could be used in a broader range of LCA goals than the one for which it is recommended by the annex of ISO 14041. For example, it can be used to account for indirect effects [72], similar to how the substitution method is used today in CLCAs.

In the same review, Ekvall and Finnveden (2001) identified the marginal allocation of [70] as a method corresponding to the second level in the ISO hierarchy (the first connection between the two parallel routes in Figure 6). In particular, Ekvall and Finnveden [72] explained that there were two possible interpretations for ISO allocation based on physical–causal relationships. Under the first interpretation, the "environmental burdens allocated to a function should be the burdens avoided if that function is no more delivered while the other functions are unaffected" [72]. This type of allocation is applicable when the environmental burdens are linear with the quantity of each of the functions delivered and, therefore, it is possible to eliminate the functions independently [72]. The second interpretation is that "the environmental burdens allocated to each of the functions should be proportional to the partial derivatives at the point of operation" [72]. This is a generalized description of the LP modeling of Azapagic and Clift.

Concerning the third level of ISO hierarchy, they emphasize that a rigorous interpretation of the standard leads to an allocation based on other causal relationships, e.g., economic value, and not in non-causal relationships (e.g., allocation based on "arbitrary physical property of the products such as mass, volume or energy content") [72]. As aforementioned, this strict approach was also the only one foreseen in the first draft of ISO hierarchy [92] and favored by the ALCA socio-economic school. At this point, the main path stopped to be bilateral and started a period of interconnection that led to the development and definition of what today is categorized as "consequential thinking".

#### *4.3. Consequential LCA Influence (2004–2008)*

In 2004, the keyword *consequential LCA* appeared for the first time on the main path [94]. In the same article, Ekvall and Weidema delineated the consequential LCA as commonly defined today. They stated that CLCA avoids allocation by applying substitution-type system expansion, using marginal data [94].

Following the main path of research, we found several articles on CLCA case studies. In the first article, Thrane conducted a CLCA of fish products [95]. The second article authored by Schmidt and Weidema [96] is focused on how to identify the marginal vegetable oil to be substituted in a CLCA of agricultural systems providing food and oil. Thrane [95] pointed out that, generally, the ISO allocation hierarchy can also be considered valid for CLCA. In fact, when system expansion (either by enlargement or by substitution) or subdivision is not applicable, it is also necessary to allocate by physical or other relationships in CLCA [95]. Dalgaard et al. [97] then performed a CLCA of soybean meal and avoided allocation by applying the substitution of marginal vegetable oil [97]. The fifth article of this period, authored by Thomassen et al., compares attributional and consequential LCAs of milk production [98]. They showed that depending on the modeling approach (ALCA or CLCA), the results significantly vary for the same system because of the different ways of dealing with multifunctionality (allocation versus system expansion with substitution). In the middle of this period, ISO 14044:2006 was released.
