3.1.3. Using Substitution as the Allocation Method

Another point of debate is the use of substitution for allocation (and not as a system expansion method). This type of allocation has been mentioned in the literature with different names, such as substitution-based allocation [9] and "proxy-based disaggregation" by substitution [35] and various versions of this method have been proposed (e.g., see Hermansson et al. who applied two different versions of this method to assess Kraft lignin [64]). By many practitioners, this option is perceived as the attributional way of using substitution. PEFCR guidance and PEF guide [28,29] propose that, when a by-product of a multifunctional system directly substitutes another product, such substitution might be considered as an allocation reflecting physical relationships. When this is the case, such substitution has to be based on a direct and empirically demonstrable relationship [28,65]. Pelletier et al. [65] stated that this is different from substitution based on marginal market models applied in consequential LCAs [65]. An example of such a substitution is when "manure nitrogen is applied to agricultural land, directly substituting an equivalent amount of the specific fertilizer nitrogen that the farmer would otherwise

have applied" [28,65]. Hence, it is assumed that the impact caused in the system by the production of the substituted by-product corresponds to the impact of the production of the replaced product (as shown in [66]). With substitution, the impact of a by-product should equal that of the product it substitutes, and so is independent on the actual process that produces it. Moreover, the application of this substitution-based allocation can lead to a negative impact that in ALCA would mean that the model has been built inconsistently [35]. As an example, this happens when the wrong product is chosen as the main product of the multifunctional system [66] or the substituted product is not a minor product, even if representing less than 50% of market value [67]. Even if the substituted co-products are chosen carefully (i.e., they represent small percentages in physical and economical terms), this method sometimes fails in ALCAs assessing multiple impact categories, resulting in negative impacts for some of them [13,67]. Moreover, PEFCR guidance and PEF guide [28,29] also allow the possibility of using indirect substitution as a form of allocation based on "other relationship". "Indirect substitution may be modeled as a form of allocation based on some other relationship when a co-product is assumed to displace a marginal or average market-equivalent product via market-mediated processes" [28].

#### *3.2. Selection of the ISO Allocation Criterion*

The main discussion on the allocation criterion concerns the nature of the so-called ISO "physical relationships" and "other relationships" [7,42].

The authors in line with the socio-economic school argue that allocation can be based on physical relationships only when the ratio of the output products can be varied since this allows the establishment of physical causality between functional units by mathematical modeling [68–73]. For example, Bernier et al. [74] assessed the impact of Kraft lignin and applied the physical causality principle to allocate the impact between pulp and lignin "by varying the quantity of lignin precipitated and then observing direct variations in the environmental loads". They also specified that this type of allocation was selected based on ISO standards, which recommends this type of allocation over allocation based on mass, energy or economic values. This school, therefore, interprets "physical relationships" as "physical causality relationships" and interpret "other relationships (e.g., economic value)" as "other causal relationships". Accordingly, they consider the allocation by other relationships as the only possible approach when it is not possible to change the ratio of production of the functional outputs of the system [69,72]. The practitioners following the view of this school often argue that, at this level, economic allocation is the recommended option, and only when it is not possible to use economic allocation, the allocation can be based on a physical parameter that should be selected based on the best proxy for economic revenues (e.g., see [7]). For example, this happens when there is a lack of market prices for one specific product [75]. However, the approximations of these causal relationships have always been a debated scientific issue [76]. For example, these relationships can be based on the common function of all co-products (as done by [77]).

The text-mining process revealed that only 28% of the LCA case studies selected an allocation method based on ISO relationships interpreted as "causal relationships". The percentage of studies following this interpretation varied significantly depending on the sectors considered (see Figure 5). In particular, it was very low in the studies focusing on anaerobic digestion, bioenergy and bio-based materials (5%–16%). On the other hand, this interpretation is largely present in the fossil fuels sector, where the allocation of emissions to single products is often based on linear programming models calculating marginal emissions by varying the amount of functional units [78,79]. Another example where this interpretation is largely present is in the dairy sector. The main reason is that many practitioners assessing dairy products often selected their allocation choice based on the recommendations of the International Dairy Federation [80], which adopts this interpretation.

**Figure 5.** The percentage of studies in each research area that used causality as the principle for the allocation choices per (sub-)cluster and overall. The number of studies per sector: anaerobic digestion (21), bioenergy (185), fossil counterparts (34), agriculture (63), aquaculture (14), dairy and meat (79), waste management (50), bio-based materials (52).

Conversely, the practitioners belonging to the natural-science school often refer to an allocation by physical parameter as ISO-second level allocation by interpreting "physical relationships" as allocation based on a physical parameter, e.g., mass or energy value [8,16,81–83]. On this basis, they prefer allocation based on a physical parameter (e.g., mass) over economic allocation because "ISO 14044 standard mentions economic allocation when no other possibility is available" [84]. The economic allocation may be selected by the practitioners following this view if allocation based on physical parameter "result in the attribution of a large proportion of burdens to low-value co-products" [9]. The same school often argued that an allocation based on a physical parameter is preferred over economic allocation since it is not affected by price fluctuations [82,85]. As a response, authors in line with the socio-economic school argue that the price fluctuation is not the important parameter for the allocation method, but the ratio of prices among all products, which is much less variable because it mainly depends on the fluctuating price of the common inputs to the process [86].

The preference expressed by the natural-science school is adopted by PEFCR guidance and PEF guide, which prefer allocation based on physical keys (e.g., mass or energy) to economic ones [28,29]. In the PEF guide, ISO "physical relationships" might have been interpreted as allocation based on physical parameters (this emerges from our understanding of annex X of PEF guide), leading to the preference for physical allocation keys. On the contrary, the ILCD handbook adopts the interpretation of "ISO physical relationships" from the socio-economic school and states that only when it is not possible to find clear physical *causal* relationships between the co-functions, allocation based on economic relationships can be used [27]. However, differently from what is usually preferred by the socio-economic school, the ILCD handbook does not give preference to economic allocation over non-causal physical properties such as energy content [27]. The ILCD handbook also adds a footnote to remark that energy allocation is not an allocation based on ISO causal physical relationship but a simplified allocation based on a physical property that is not causal [27].

To make an example of the implication of adopting one interpretation or the other, we can consider a biorefinery example that produces fuels (e.g., ethanol) and chemicals for materials (e.g., lactic acid) [87]. The natural-science school would prefer energy or mass allocation (considered by them as ISO second level) over economic allocation (considered ISO third level). Conversely, the socio-economic school would prefer economic allocation, arguing that mass and energy allocations (all considered ISO third level) are meaningless for such a biorefinery because of not representing any causality mechanism. They would also argue that it is not appropriate to use energy allocation when not all the co-products

are used for their energy content or to use mass allocation when there are energy products among the co-products.
