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Streamlined LCA under uncertainty integrating a network of the petrochemical industry and optimisation techniques: Ecoinvent vs mathematical modelling Raul Calvo-Serrano, and Gonzalo Guillen Gosalbez ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.8b01050 • Publication Date (Web): 13 Apr 2018 Downloaded from http://pubs.acs.org on April 14, 2018

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ACS Sustainable Chemistry & Engineering

Streamlined LCA under uncertainty integrating a network of the petrochemical industry and optimisation techniques: Ecoinvent vs mathematical modelling Raul Calvo-Serranoa‡ and Gonzalo Guillén-Gosálbeza‡* a.

Centre for Process Systems Engineering, Imperial College of Science, Technology and

Medicine, South Kensington Campus, Roderic Hill Building, London SW7 2BY, United Kingdom *e-mail: [email protected]

Abstract

Environmental databases have recently become an essential instrument in the sustainability evaluation of products. Unfortunately, these repositories still contain a limited number of chemicals. Furthermore, they are based on an attributional LCA approach that considers fixed mass flows reflecting static industrial settings that are in practice dynamic, which might lead to errors. Building on some recent developments, we explore here an alternative approach to quantify the life cycle assessment (LCA) impact of chemicals based on a network representation

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of the petrochemical industry coupled with linear programming, stochastic modelling and allocation methods. This approach was applied to a network comprising 178 processes and 144 products, generating for most of the chemicals results that are consistent with those available in Ecoinvent for widely used impact categories such as GWP or ReCiPe. The network model provides estimates of the life cycle impact embodied in chemicals under varying yields and demands, even for chemicals missing in standard repositories. Overall, we advocate for the use of network models of the petrochemical industry capable of carrying out consequential LCA under uncertainty as a complement to existing databases. This would allow to enlarge the capabilities of LCA repositories, thereby promoting the wider use of LCA in the chemical industry by improving the transparency and flexibility of the LCIA phase.

Keywords: Process Networks, Streamlined Life Cycle Assessment, Linear Programming, Uncertainty, Ecoinvent INTRODUCTION The chemical industry is currently committed to achieve cleaner and more sustainable standards, a trend that has led to a plethora of environmental evaluation methodologies. Among them, Life Cycle Assessment (LCA) has become the prevalent one, mainly due to its holistic view and versatility as applied to a wide range of processes1–18. LCA is based on a detailed analysis of all the mass and energy flows exchanged with the environment in all the stages in the life cycle of a product, from cradle (resources extraction) to grave (recycling or disposal). Unfortunately, this in-depth analysis requires large amounts of data from different echelons in the products’ life cycle, which hampers the LCA application when such information is hard to gather in practice.


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Different methodologies, referred to as streamlined LCA (SLCA) approaches19–27, have been proposed to simplify the data required by a standard LCA. Some of them are based on shortcut models28, while the most common approach is to use information retrieved from an LCA database as proxy of the “true” data needed in the calculations. LCA repositories have experienced a widespread growth in the recent past. They contain full LCA results for a wide variety of products (including several hundred chemicals), which can be used to streamline calculations and cover data gaps. Examples of such repositories include Ecoinvent3.329, GaBi30, GREET31, as well as other more specific databases like PSILCA32, ESU World Food33, SHDB34, ProBas35 or Ökobaudat36. Furthermore, recently developed open source databases such as Exobiase37, NEEDS38 or ELCD39 provide a general framework for practitioners to upload their own data following well-defined standards. Unfortunately, these open-access repositories still contain a limited number of chemicals and processes, as data collection is highly resource and time consuming. The information provided by these LCA data repositories comes from full LCA studies applied to real facilities that consider their geographical and temporal context. In practice, these LCA results replace the missing data in a given LCA study under the assumption that the process on which the databases is based and the one under study are very similar to each other. As an example, assume we operate a plant implementing the hydrodealkylation of toluene process (HDA) that produces benzene from hydrogen and toluene. To calculate the life cycle impact of benzene, we need the emissions and waste of the main process, but also those embodied in the raw materials (hydrogen and toluene) and utilities (steam, cooling water and electricity) consumed. While we tend to have information at hand of our main process, the same does seldom hold for the upstream and downstream ones. Hence, to carry out the LCA of benzene


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production, we shall retrieve from an LCA repository the life cycle inventory entries (LCI) for hydrogen, toluene, steam, water and electricity (assuming that our suppliers implement the same technologies considered in the database). Using proxy data sourced from databases in a standard LCA study shows two main limitations. First, repositories contain at present a few hundred organic chemicals only (400 in Ecoinvent 3.329), so it is very likely that the compound we need in our calculations will not be available therein. Attempts have been made to address this shortcoming by developing predictive models of impact tailored to chemicals. In a seminal work, Wernet et al.25,27 presented a method of this type to predict the LCA impact of organic chemicals from molecular descriptors. This approach was later refined by Calvo-Serrano et al.40, who developed a mixed-integer programming framework to estimate the life cycle impact of chemicals from molecular descriptors together with thermodynamic properties (such as formation enthalpy or evaporation point). These methods treat chemical processes as full black-box models without enforcing any type of first principle, like mass and energy conservation. Hence, while they can help fill in data gaps, they may lead to larger errors, particularly if the training set used in the regressions is not large enough or if it fails to capture the main features of the products whose impact one seeks to extrapolate. The second limitation is that databases are based on an attributional LCA that assumes fixed flows and specific processes that might well differ from the ones implemented by the suppliers in the product’s supply chain. Indeed, changes in technologies across a chemical’s life cycle can lead to significantly different results. This is illustrated here via several examples where raw materials’ and utilities’ sources are substituted for alternative sources (i.e. same streams, different supply chain), observing notorious changes in the overall process environmental


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performance (see Figure S1 in the Supporting Information), which support the need to consider this alternatives in a flexible framework when carrying out an LCA. To circumvent this limitation, LCA databases tend to rely on uncertainty modelling, mainly using the Pedigree matrix41–44. This is a well-established LCA methodology that model the LCI entries (i.e. feedstocks, emissions and wastes) via probability distributions whose standard deviation depends on the degree of similarity (in terms of geographical, technological and temporal context) with the “true” missing data and its quality. This approach might fail to model the dynamic behaviour and specific features of process technologies45,46, as it is based on qualitative items that might fail to cover the entire range of uncertainties encountered in the chemical industry. Here, we explore and extend the capabilities of an alternative method to estimate the LCA impact of chemicals that can overcome the aforementioned limitations. The approach studied here capitalises on a recent work by DeRosa and Allen (2017)47, where the authors used a network model of the petrochemical industry to carry out a consequential LCA. Based on this strategy, we combine here a customised network-based model of the petrochemical industry with mathematical programming, stochastic modelling and allocation methods to estimate the life cycle impact of chemicals. The advantage of this approach is threefold. First, it relies on a detailed description of the chemical industry, as opposed to the data-driven methods mentioned above based on extrapolating impacts of similar chemicals. Second, the method combines the strengths of attributional and consequential LCA, as it is flexible enough to reproduce variations in technologies and demand patterns. Third, uncertainties affecting the LCA calculations can be modelled explicitly depending on their nature (e.g. process yields, demand, etc.), as opposed to what is done in LCA repositories that rely on fixed mass flow rates and yields, constant demand


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patterns and uncertainties modelled on the basis of qualitative information (i.e. the Pedigree matrix). We note that the network approach is similar to the input-output (IO) method48 used to predict the life cycle impact of a product from a matrix of economic transactions taking place between economic sectors and the associated impact embodied in them. The difference, however, is that the network model has degrees of freedom that can be optimised considering different criteria and constraints, while the IO method is based on systems of linear equations with no degrees of freedom reflecting the current structure of the economy. To demonstrate the capabilities of this approach and as a first step towards a detailed model of the whole chemical industry covering a wider range of chemicals absent in LCA databases, we have herein assembled a network of petrochemical technologies encompassing 178 technologies (processes) and 144 chemicals using data sourced from the literature49. As later discussed in more detail, this network leads to good estimates (around 20% relative error when compared to Ecoinvent values) for several widely used LCA impact categories, which are accompanied by confidence intervals derived from the main uncertainties affecting the calculations. Hence, the main novelties of this work are: (i) the incorporation of uncertainties in the framework presented by DeRosa and Allen (2017)47; (ii) the detailed description of how to allocate impacts in network models using auxiliary pools; (iii) the development of a network model based on public data made available to readers; (iv) the comparison with data retrieved from Ecoinvent; and (v) a discussion on how technological choices in the petrochemical industry can affect greatly the LCIA results based on numerical examples; these results reinforce the need for a more flexible approach as the one presented herein.

PROBLEM STATEMENT


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The analysis carried out here seeks to determine the LCA impacts of chemicals produced by a network of processes. Hence, given a network of interconnected technologies (each defined by mass yields, utilities consumption rates and operational cost) and a set of available feedstocks (and associated cost and environmental data), the goal of the analysis is to estimate the life cycle impact (in a set of damage categories) of a set of products in the network. Our approach to accomplish this task is described in the ensuing sections. METHODS In essence, our approach is based on the one presented by DeRosa and Allen (2017)47 and relies on optimising a network of technologies so as to generate mass flows consistent with a given industrial scenario. These flows are used afterwards to allocate the total impact among the different chemicals. Compared to the original approach, we focus here on explaining in detail how to allocate impacts in the network using pools of chemicals and, more importantly, show how to incorporate uncertainties in the estimations. In developing our framework, we also use open data to make the network available to any reader. The methodology can be divided into four steps: (i) building a process network of the chemical industry; (ii) optimisation of the process network to generate mass flows consistent with a given demand pattern, costs and environmental data; (iii) allocation of the network impacts among its products considering the flows generated in step ii; and (iv) uncertainty assessment of the results generated in previous steps. These steps are described in detail in the ensuing sections.


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Figure 1. Schematic of the proposed methodology, divided into 4 steps: Process network characterisation, Mass flows calculation, Impact evaluation and allocation and Uncertainty analysis.


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3.1. Step 1: Building a process network of the chemical industry The first step of the methodology builds a network of the petrochemical industry. This network is later used to calculate mass flows consistent with current demand patterns and technical and legal regulations and on the basis of which the environmental burdens generated by the network will be allocated. Optimisation theory and software packages enable a deep analysis of complex chemical process networks via network models (sometimes referred to as superstructures)8,50–55. These superstructures allow identifying optimal economic and/or environmental production pathways in a wide variety of applications47,55–66. Network-based modelling is particularly suited for the chemical industry, as most chemicals produced by specific processes are feedstocks in others, which creates significant synergies and feedback loops that are hard to analyse via simple heuristics or rules of thumb. The accuracy of the network is given by the number of technologies included and the level of detail attained in their modelling. A detailed nonlinear modelling of the processes involved may lead to lower errors, yet it may result in very complex formulations that are hard to handle. Hence, in order to make the network tractable, chemical processes are here represented via black-box models defined by three parameters: (i) mass balance coefficients; (ii) utilities consumption rates; and (iii) cost parameters. In essence, we follow here the same approach as in DeRosa and Allen (2017)47. While there are databases of the petrochemical industry, most of them apply fees and have some restrictions concerning data disclosure. To avoid this, here we use free data taken from Rudd et al.(1981)49. This work compiled information on 178 petrochemical technologies, ranging from the production of base chemicals from oil derivatives (e.g. acetylene from naphtha


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pyrolysis), to their use in the synthesis of finer chemicals (e.g. acrylic acid from the oxidation of acetylene). These technologies involve 144 chemicals, including oil derivatives and primary feedstocks (such as naphtha and coal), as well as platform and commodity chemicals (like ethylene and phthalic anhydride). Later during the article we shall discuss how we deal with the uncertainty in this data set. Figure 1 provides an excerpt of the complete network along with some details on the mathematical modelling of its elements (mainly technologies, substance pools and mass streams). A complete representation of the petrochemical network (Fig. S2) and a full enumeration of the chemicals and processes covered (Tables S2.1, S2.2 and S3) can be found in the Supporting Information. The network contains two types of nodes: technologies () and chemicals (). Technology nodes are modelled as black boxes, each described by utilities consumption rates ( expressed in Fuel Oil Equivalent Tonnes (FOET)/ kg processed by ), maximum operational capacity ( expressed in kg processed by ) and mass yields ( expressed in kg of / kg processed by ). These mass yields refer to the total input-output flows of the main products involved in each process, and therefore account for reaction stoichiometry (conversion rates) and efficiencies in separations and in any other process that affects the amount of chemical produced as output. All these process parameters are complemented by the utilities’ cost ( expressed in $/FOET) and the environmental impacts embodied in them ( expressed in units of impact/FOET). For simplicity, all the utilities are expressed in FOET following the original work by Rudd et al. (1981)49. This simplification is further discussed later during the article. Substance nodes model inputs and outputs of chemicals. These can either be feedstock (, inputs not produced by any technology), final products (, outputs not


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consumed by any technology) or intermediates (consumed and produced by one or more technologies in the network). In the following sections we describe in detail the mathematical approach used to estimate the life cycle impact of the chemicals produced by the petrochemical network described above. 3.2. Step 2: Deriving a mathematical model based on the network The network built in step 1 is used to assess the LCA impacts of the chemicals involved. To this end, we first determine the mass flows exchanged between technologies by solving an optimisation model M1 that seeks to minimise the total variable cost () that satisfies a set of product demands ( ). This provides the optimal production pathways and mass flow rates considering a set of constraints (reflecting any technical, legal and/or demand related aspects of the problem). The mass flow rate of main produced chemical in each technology ( expressed in kg processed by ) is the main decision variable optimised by the model. Hence, a reference chemical is defined for each process, which enables the calculation of all the inputs and outputs of a technology by multiplying its reference flow with mass yield coefficients. The mathematical optimisation problem in model M1 is described below. Objective function Model M1 seeks to minimise the total variable cost (, in $). Note, however, that other objective function could be used instead if enough data would be available (e.g. maximising total profit). As expressed in eq 1, this includes the cost of all the feedstocks purchased (amount of species purchased, denoted by variable , expressed in kg of , multiplied with their purchasing cost, parameter , expressed in $/kg of ) plus the cost of the utilities consumed by each technology (amount of mass processed in technology , variable , multiplied with the utilities consumed in that technology, parameter , and times their cost, parameter ).


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= ∑ + ∑

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(1)

Typically, the variable cost of a chemical technology takes into account additional factors in addition to the utility and raw materials expenditures, such as annualised investment or labour costs. However, we assume here that investment costs have already been recovered and that other variable costs are low and can thus be neglected (compared to the raw materials and utilities cost). When required, additional cost terms could be easily implemented in the previous expression without increasing its mathematical complexity. Mass balances As seen in eq 1, the total cost incurred by the network is a function of the material flows, which must satisfy the mass balances. To model these mass balances, we define the sets () and (), where () comprises all the technologies that consume chemical , while () comprises all the technologies that produce chemical . Considering these sets, the mass balances are expressed in compact form as follows: + ∑∈

( )

= ∑∈!"( ) + , ∀

(2)

In eq 2, the mass flow of chemical purchased from external suppliers ( ) plus the amount produced (∑∈

( ) )

should equal the quantity consumed (∑∈!"( ) ) plus the amount

sold to customers ( , in kg of chemical ). Note that parameter is expressed taken the main chemical produced in the technology as reference. Regarding the purchases of chemicals, only feedstocks () are purchased from suppliers, while other chemicals (final products and intermediates) are produced by at least one of the technologies in the network. Thus, eq 3 prevents purchases of chemicals that are not feedstocks. = 0, ∀ ∉

(3)


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The amount of chemicals sold, denoted by , should be greater or equal than the respective demand, as shown in eq 4: ≥ , ∀

(4)

Additionally, the output of each technology ( ) is limited by a maximum capacity ( ), as shown in eq 5. ≤ , ∀

(5)

The resulting linear programming (LP) model M1 can be expressed in compact form as follows: Min s.t. eqs. (1) – (5) , , ≥ 0 Note that this model can accommodate different objective functions as well as additional constraints in order to reflect the specific details of an industrial setting. 3.3. Step 2: Impact allocation based on optimal material flows The solution obtained from M1 provides the mass flows exchanged between the processes embedded in the network. From these flows, it is possible to calculate the total impact generated and allocate it among the final products. Note that there are several impact allocation methods available4,67. Among them, here we use without loss of generality mass allocation (i.e. the impact of a technology is allocated among its output streams according to their mass flow rate). We define at this point two additional parameters to perform the allocation: the LCA impact *+

embodied in the purchased feedstocks ( , in impact units/kg of chemical ) and the impact generated in the production and use of the utilities consumed by the technologies ( , in impact units / FOET). Hence, we consider only two sources of impact that require the definition


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of the parameters described above. Other impact sources have been disregarded due to their minor effect (relative to the two terms above) and due also to the lack of sufficient information to characterise them. Note, however, that they could be easily incorporated in the modelling approach. To model the allocation step, we assume that all the chemicals of the same type show the same unitary impact (i.e. impact per unit of mass). Streams containing the same substance may have been allocated different impacts depending on the processes that produce them. To harmonise their impact, we consider a virtual mixer where all the input streams achieve the same equalised impact regardless of their origin. Therefore, two variables are defined to model the impact before (both in impact units/kg of and after entering the process technologies: !, and

chemical ). The former represents the LCA impact allocated to chemical after exiting the equalising pool and harmonising its impact value. On the other hand, represents the impact allocated to chemical at the exit of technology . Note that the first variable only depends on the chemical, as all the streams of the same type show the same unitary impact. In contrast, the unitary impact of the output species from a technology depends on both the chemical/substance and the technology. With these variables and parameters, we define impact balances for the technologies in the network. We follow here a similar notation as in model M1, where the connections between chemicals and technologies are mathematically modelled using the sets . () and . () (representing all chemicals consumed and produced by j, respectively). The impact balance can then be defined as shown in eq 6, which forces the total impact embodied in the input streams plus the impact embodied in the utilities consumed by a technology j to be equal to the total impact embodied in all chemicals exiting the same technology.


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∗ ∑ ∈!"0 () ∗ !, + = ∑ ∈

0 ()

∗ , ∀

(6)

In eq 6, ∗ is a parameter representing the optimal mass flow rates of technologies obtained from the solution of model M1. To ensure the mass allocation, we force the unitary impact of all chemicals exiting the process to be the same. This is accomplished via the following constraint: 1 .

= 1 , ∀, ∀, ∈ (), ≠ ′

(7)

Note that the chemicals exiting the technologies may show different impacts depending on the technology generating them. Hence, to harmonise impacts, we define an impact balance in virtual pools of chemicals. Thus, eq 8 forces that, for each chemical , the impact embodied in the purchased amount (if any), plus the impact embodied in the streams produced by the technologies and containing such chemical must equal the impact embodied in the harmonised chemical exiting the pool (and afterwards sent to the corresponding technologies consuming it), plus the impact embodied in the amount of product sold. *+

∗ + ∑∈

∗ ( )

!, ∗ = ∑∈!"( ) ∗ !, + , ∀ (8)

As in eq 6, the values of the mass flow rates (∗ , ∗ and ∗ ) are obtained from the solution of model M1. Hence, the allocated LCA impacts for intermediates and final products can be obtained by solving model M2 defined by Eqs.(6) to (8). For further explanation regarding the calculation and allocation of environmental impacts, see section S5 in the Supporting Information. 3.4. Step 4: Uncertainty modelling and analysis An uncertainty analysis is carried out next to identify and model uncertainties affecting the environmental impact values. The main uncertain parameters in M1 are the product demands ,


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utilities consumption rates , and technologies yields of the main chemicals produced 4. ( such that chemical is the main product of technology ). Other uncertain factors (such as technological choices in the network or additional market requirements) have not been considered but could be easily incorporated with the necessary data. Demand patterns change over time according to market trends, while utilities consumption and mass balance coefficients are related to energy and mass efficiency, which are in turn associated with the type of technologies included in the network. LCA databases assume nominal parameters and then apply the Pedigree matrix to provide confidence intervals for the LCI and LCIA results. In our case, sampling methods are employed to generate a set of plausible scenarios, each entailing specific parameters values. The solution of M1 and M2 for each such scenario (i.e. sample) provides a set of LCA impact values, from which an average impact and associated confidence interval (considering a given significance level) can be obtained (see Figure 1). Note that some uncertain parameters in M1 might be correlated (e.g., process yields and utilities consumption), yet we here assume that they follow independent distributions. In case correlations between parameters are known, we could always generate correlated scenarios from the correlation matrix. RESULTS AND DISCUSSION We illustrate the capabilities of our approach by assessing 15 chemicals produced by the network (the only ones among the 144 chemicals that are produced but not consumed by any other process, that is, that are “truly” final products rather than intermediates). We focus on six environmental impact categories: Cumulative Energy Demand (CED), Global Warming Potential (GWP), and ReCiPE (ReCiPE T) along with its three sub-categories: Ecosystem Quality (EQ), Human Health (HH) and Resources (Res). Furthermore, we also calculate the life cycle carbon


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dioxide emissions (CO2Em), which despite being an LCI entry rather than an impact is widely used in LCA studies. Following our approach, all the parameters values in M1 (i.e. technology utility consumption rates, , and main yields, ) are obtained from Rudd et al. (1981)49 for the 178 technologies in the network. The purchase cost of the 29 raw materials ( ), and the demand of the 15 final products ( ) are shown in Table 1 (sources for these parameter values can be found in Tables S5 and S6 in the Supporting Information). Table 1, Final product demands adapted to UK 2016.

Product

Demand (kTon)

Product

Demand (kTon)

Acetic Anhydride

20.92

N-butanol

34.56

Bisphenol-A

49.19

Phthalic Anhydride

46.49

Glycerine

23.86

Propylene Glycol

22.11

Maleic Anhydride

45.60

Styrene

355.00

MDI/PMPPI

55.90

Terephthalic Acid

475.66

Melamine

28.80

Toluene-Diisocyanate

21.55

Methyl Isobutyl Ketone

3.24

Vinyl Acetate

59.69

Methyl Methacrylate

34.59

With regards to the demand, we consider a hypothetical UK demand for these chemicals. These data are unavailable in public sources, yet we estimate the demand for year 2016 assuming the same per capita consumption as in other countries for which this information is at hand, and considering in turn a 5% annual increase to harmonise values whenever the raw data corresponds to other previous years.


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Regarding the capacity limitation parameters ( ), these have been set so that demand can be fully met. In practice, these capacities should be consistent with the real capacity of the petrochemical industry in a country, but unfortunately we do lack the corresponding data for the *+

UK. The impact embodied in the utilities ( ) and raw materials ( ) are retrieved from the Ecoinvent 3.3 database29 accessed via SimaPro8.168. Based on these data, model M1 contains 406 equations and 458 continuous variables. It was solved in 0.016 CPU seconds with the software GAMS 24.4 interfacing with the solver CPLEX 12.6 on an Intel Core i5-4570 3.20 GHz computer. The optimal mass flows (∗ , ∗ and ∗ ) are obtained from M1 assuming that all chemicals are produced simultaneously (M1 satisfies all product demands). These flows are then used to solve M2, obtaining the allocated impact for every final product in each scenario ( !, + , where 5 represents the corresponding scenario). Model M2 features 322 variables and the same number of independent linear equations and is solved also with the same versions of GAMS and CPLEX. Regarding the uncertainty calculation, each uncertain parameter ( , and 4. ) is assigned a specific probability distribution based on sensible choices. For chemicals that have no demand in the nominal case ( = 0), the demand is set to zero in all the scenarios. For the rest, they are assumed to follow a normal distribution (using as mean values those shown in Table1 and assuming a 30% standard deviation in all of them). The utility consumption parameters affect significantly the total impact of the network. For this reason, it is critical to properly characterise their values and the associated uncertainties. Consequently, two different approaches were considered. In the first one, we converted the values obtained from Rudd et al. (1981)49 into 2016 values by assuming a 60% increase in efficiency in that period, which is consistent with historical reports on the petrochemical


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industry69. The projected value for 2016 is then modelled with a uniform distribution with its limits lying ±25% of the reference value. This approach led to average errors in the range 2060% (more details in section S8 of the Supporting Information). In the second approach, we applied the Pedigree matrix to handle the uncertainty in the original utility values. Hence, the utilities consumption was modelled with a lognormal distribution. The arithmetic standard deviation of the lognormal was then obtained from the Pedigree matrix (with scores 1,3,5,3,1,3), while the expected value was the raw value from year 1975 (slightly earlier than the publication date). In both cases, the process main product yields follow uniform distributions, ranging from their original values to a 25% improvement value (i.e. between 1 and 1.25 times their values). This potential yield increase has been considered to reflect improvements in process efficiencies regarding the conversion of raw materials to the main product (i.e. conversion and selectivity improvements), taking into account that in the original data 127 of the 178 processes consumed more materials that they were producing. These process data updates contrast the approach followed by Ecoinvent, where entry values are not modified (even if severely outdated), while only modifying their uncertainties (i.e. modifying the Pedigree matrix scores). Uncertainties are quantified via 2,000 random scenarios generated via Monte Carlo sampling on the previously defined probability distributions. Models M1 and M2 are re-calculated for each such scenario using the same software and hardware specified before (in this case, taking approximately 32 CPU seconds to solve the 2,000 model instances). The obtained results are compared with those available in Ecoinvent 3.3 (accessed via SimaPro8.168). The comparison is carried out by generating 2,000 scenarios for the LCI and LCIA results provided by Ecoinvent (the same amount as in the M1 and M2 calculations). These scenarios are generated using the Pedigree matrix for all the impacts and products considered,


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assessing in each case the LCI uncertainties of each inventory entry via the default Pedigree parameters available in SimaPro (which were defined according to the quality of the data available). For each such scenario, we then compare the values provided by M2 and the ones from Ecoinvent in order to finally calculate a relative error between both. Figures 2 and 3 display the uncertainty analysis results. We show the average of the impact provided by M2 across all the scenarios and the 25th and 75th percentiles of its distribution. Furthermore, a second set of results is generated using a single production approach: solving M1 satisfying only the demand for one final product at a time while setting the rest to zero. These additional results shed light on the extent to which the results are affected by interactions between products in the network. In the same figure, we also represent the Eco-invent results. From Figure 2, the relative errors shown in Figure 3 are obtained, which are computed in every scenario considering the results of the model and the values generated by SimaPro.


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Figure 2. Calculated (green) and original (from Ecoinvent, red) values for all 7 impacts and the emission considered, with their associated uncertainties (average and 25th and 75th percentiles). The calculated results are divided in Simultaneous Production approach (circles) and Single Production approach (diamonds).


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Figure 3. Relative errors between calculated impact values (using simultaneous production (a) or single production (b) approaches) and the Ecoinvent values. The red lines represent the average error while the blue bars extend over the percentiles 25th and 75th. The average of all relative error distributions is displayed for every category. Chemicals marked with “*” are produced with a network technology that differs from the one in Ecoinvent. To assess the quality of the results, we can consider three different indicators: the average relative error (the lower the better), the size of the confidence interval of the relative error (the smaller the better, as otherwise the mismatch could be quite significant in some scenarios), and whether the confidence intervals of the two impact values overlap (if they do so, it would imply


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that the value generated by M2 would fall within the uncertainty range of the Eco-invent value, thereby reflecting a good estimation). Considering these criteria, a summary of the key results is provided in Table S7 in the Supporting Information. The previous figures show that the estimates generated with the network agree reasonably well with the Ecoinvent data, having in most cases average relative errors between 20 and 30%. Also note that our approach tends to underestimate the Ecoinvent values (this consistently happens in 11 out of 15 chemicals). Some chemicals show lower errors, like MDI/PMPPI, with the lowest expected errors in many categories, between 12 and 29%, while in others the errors are significantly higher (terephthalic acid, with expected errors between 24 and 92%). In terms of categories, we find the best approximations in the CED (close to 20% on average relative error in both production scenarios) and the worst in the GWP and ReCiPe HH (around 30% in both scenarios). Looking at the confidence intervals, we find that the size of the confidence interval tends to be proportional to the expected error, with low errors having small uncertainty ranges (see for example the results for the maleic anhydride). Concerning the overlap between the confidence intervals of the calculated results with those reported by Ecoinvent, we find 32 overlaps (product and category) out of a total of 105 possible overlaps. The product overlapping the most is acetic anhydride, while the category with more overlaps is CED. On the contrary, the product overlapping the least is phthalic anhydride and the worst category in terms of overlaps is ReCiPe HH. As already mentioned, discrepancies between both approaches can be due to several reasons. The first is the absence of a term in our model to account for the impact of transport and infrastructure. These terms are specific to each technology and are hard to assess without adding


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additional uncertainties in the model. In any case, transport and infrastructure tend to account for only a small fraction (10% or less) of the total impact (e.g. 2.6% and 1.7% GWP contribution for the production of melamine and 1-butanol).For more details, see section S10 in the Supporting Information. The second source of discrepancy is the process data retrieved from Rudd et al. (1981) and the methodology they follow to calculate the utility parameters, which is not fully described in their work. The third is related to the fact that the technologies included in the network model may differ from the ones considered in Ecoinvent, at least for some specific chemicals. As an example, in Figure 3 we highlight (with “*”) those products for which our superstructure considers a technology that differs from the one in Ecoinvent. As observed, the expected error is larger in these products, like it happens in terephthalic acid or, to a lesser extent, in methyl methacrylate. Note as well that discrepancies between original and predicted impact values also depend on the type of approach, individual or simultaneous, that we follow. In general, we observe that the single production results tend to lie above the ones generated by the simultaneous approach (in 65 out of 105 cases). This is because the solution of model M1 for the single production approach is able to identify synergies between the different production pathways, providing overall lower mass flows and, proportionally, lower total impact. In the propylene glycol results, for instance, the single production results are always higher than in the simultaneous production and in some categories they match quite well those produced by Ecoinvent. Note that not all the categories behave in the same manner when moving from the simultaneous to the individual approach. For example, the average error in CED and GWP is slightly reduced (from 24 and 34% to 20 and 30% average errors, respectively), while in other categories they slightly increase, as in ReCiPe T and ReCiPe Res (from 24 and 25% to 25 and 27% respectively).


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Overall, besides differences in data, both approaches (network model and Ecoinvent) are based on different flows and allocation methods. Hence, it is not surprising that there is a mismatch between them. This mismatch can be high in some chemicals (more than 50% for terphthalic acid or n-butanol), and even higher when we use estimates of energy consumption taken from historical data rather than the Pedigree matrix, the latter being the standard LCA approach to deal with uncertainties. Hence, the question is then which of the two approaches (i.e. network model vs LCA repositories) should be followed depending on the goal and scope of the LCA study.

CONCLUSIONS In this work we applied a method to calculate the life cycle impact of chemicals based on the use of a network of interconnected technologies modelled via mathematical programming tools. This approach allows filling data gaps in LCA repositories and has the potential to enhance their capabilities by allowing for a more detailed and flexible representation of the chemical industry based on first principles. This approach combines the merits of attributional and consequential LCA within a single framework that can be easily adapted to reproduce the characteristics of a specific industrial scenario. To demonstrate how this approach would work, we applied it to a petrochemical network containing 178 processes and 144 chemicals. In general terms, the results are in good agreement with the ones available in LCA databases, with the error of the estimate varying depending on the product and impact category. This mismatch is due to the adoption of different assumptions and simplifications as well as data sources, which can be easily modified in the network-based model to reproduce a specific industrial setting.


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Overall, this work advocates for the development of customised models of the chemical industry for producing more realistic estimates of the chemicals’ impacts. It also points towards the combination of attributional and consequential approaches in LCA repositories so as to enhance their capabilities. ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: 00.0000/acs.est.0000000 LCA repositories variability analysis, Petrochemical network, List of technologies, List of chemicals, Environmental impact calculation and allocation example, Feedstock prices sources, Final product demands sources, Updated utility consumption results, Results summary, transport and infrastructure impact contribution. (PDF) AUTHOR INFORMATION Corresponding Author *e-mail: [email protected] Author Contributions ‡These authors contributed equally. REFERENCES (1)

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Synopsys: Chemical production pathways are described with process networks, which are later used to characterise their environmental impacts and uncertainty.


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