In the following, the principles of the dynamic LCI model are briefly recalled. Then, the development of the new database for the temporal parameters of the ecoinvent processes is presented, followed by the method of integration of the LCI model, database, and LCIA dynamic models into the global framework. Besides the case study, a more simplified and didactic example to understand the framework behind the tool can be found in the work of Tiruta-Barna et al. (2016).
Principles of the dynamic LCI model
The dynamic LCI model was initially developed by Tiruta-Barna et al. (2016). The reader is invited to refer to this and to the SI1 for a detailed presentation. Here, we recall the main features of the model that are important to understand the following steps. The model relies on the classical LCI structure (technology A and environmental intervention B matrices). It introduced a fundamental novelty with the adoption of a process/supply chain modeling perspective instead of an accounting point of view. The unit processes composing the life cycle inventory (foreground and background) are considered as operations having a proper functioning over time. The reference unit and the material/energy interventions of each have a distinct temporal profile. Furthermore, the intermediary exchanges among unit processes are positioned over a timeline depending on specific supply models, e.g., continuous, intermittent, and single punctual supply. As a result, mass and energy quantities listed in the dataset of a specific activity are no longer considered average quantities for a reference flow in a representative time period. Instead, the model allows the following to be calculated, the quantity requested by an activity, when and for how long it will be supplied to that activity, when and for how long it is stored before or after delivery, and when and for how long it was produced by the supplier.
Production and supply are described by temporal parameters and functions (also shown in Table S1 and Fig. S1 in SI1—Electronic Supplementary Material). All processes are characterized by (i) a production function α(t) for the reference flow and an emission profile β(t), which can be discrete values or functions of time; (ii) parameters r, the duration of an activity between the raw material input and the product output, T, the lifetime of the infrastructure supporting an activity, and t0, the starting time of an activity. The supply is defined through parameters: δ, a no-activity period, and τ, the frequency of a product supply. These temporal parameters can be manually defined for the foreground processes, but a database must be developed for background processes, and this is presented in the following section. The model was implemented in DyPLCA, a web-based tool, which was then used in the works of Shimako et al. (2016, 2017, 2018). This tool is a very first version, modified and adapted in the present work for integrating the ecoinvent database with a temporal database of all processes, and coupling it with LCIA dynamic models.
Temporal database development
The temporal database was developed in an ecospold format for the Default, Consequential and Recyc system models of ecoinvent 3.2 from SimaPro. A representative sample of the database is provided in SI2. The rules and simplifications below apply.
Rules for the choice of the time parameters
(i) Functions α(t) (for production flows) and β(t) (for environmental interventions) are defined for the period r. Period T is a multiple of r. Functions can be constant or variable over time; they are replicated identically for all periods r covering the T lifetime. In the current version of the database, for the sake of simplification, α and β are defined once for each activity, i.e., they apply to all inputs and outputs of that activity, although the framework supports a specific definition for each individual flow.
(ii) Production functions that are calendar-dependent are defined over 1 year, starting in January, regardless of whether the activity starts at another moment. For example, if a product whose production takes a year (r = 1 year) is requested in October, the production process starts in October of the previous year. In this case, the specific activity intensity at that moment in time is considered. A potential issue is that a process often involves a series of consecutive steps. For example, in agricultural processes, sowing occurs before maintaining, which precedes harvesting. Applying the calendar dependence, sowing would start after harvesting, which does not make sense. This issue does not apply, however, as long as α is the same for all material and energy inputs/outputs of a process, which is the case in the current version of the database.
(iii) Supply scheduling and frequency is defined by δ (delay period) and τ (interval between supplies). These parameters shall be defined per material/energy flow, per product type, and combination of processes (supply and demand), as presented in Tiruta-Barna et al. (2016). These relationships are complex as they depend on supply and demand in the real market. For the sake of simplification, in the temporal database, those parameters were attributed to each supplier (or producer) process. Three types of supply profiles were defined: (1) Continuous, the product is supplied without interruption; for example, this is the case with an electricity supply. Here, τ is set equal to r meaning that the interval between production batches is the same as the production time. (2) Intermittent, when products are supplied in series of equal intermittent batches. τ specifies the duration of these time intervals. In general, τ is set equal to T of the consumer process if it is supplied once per lifetime (e.g., an infrastructure). It is set equal to δ for consumables that are frequently supplied but can be stored. It can also be set equal to either r of the producing process if production, and thus supply, are seasonal; or r of the consuming process, for example, in the case of frequently supplied consumables that are directly consumed at each production cycle of the consumer process. (3) Services, whenever the activity starts at the same time or later than the activity of the consumer process (t0). This is the case of services occurring during the consumer process, e.g., “Fertilising, by broadcaster {RoW}| processing | Alloc Def, “U” for agriculture.” Services occurring at different moments (but with equal periods) are also considered, for example, mowing may occur at different moments during agricultural processes. In general, two types of processes are considered as services: (a) waste treatment processes (assuming that waste is generated and treated while the process is running) and (b) the majority of the processes that end with “processing” in their names. Services processes hold an ID (“S”) in the database.
Exceptions to the general rule are:
Processes used by other processes, e.g., “Beverage carton converting {GLO}| processing,” “Wood preservation service, logs, pressure vessel, preservative not included {RER}| processing,” and “rock crushing.”
Services not occurring simultaneously with other processes; namely all the vehicle and machinery maintenance processes, e.g., “Maintenance, barge {RER}| processing.”
Services encompassing the complete production period, e.g., “Polystyrene foam slab for perimeter insulation {CH}| processing,” “Router, internet {CH}| processing” and “Wire drawing, copper {RER}| processing.”
Transport processes, e.g., “Transport, freight train {AT}| processing.”
Services that are performed afterwards, e.g., “Venting of argon, crude, liquid {GLO}| processing.”
Waste treatment (including out of order equipment, machinery), e.g., “Used lorry, 16 metric ton {CH}| treatment of”
“Sowing {CA-QC}| sowing,” which is considered as a service (for plant cultivation) even though “processing” is not mentioned in its title.
Further specific rules adopted for some of the ecoinvent processes are given in SI1, Section 2.5.
Processes without temporal profile
In ecoinvent 3.2, several processes do not reflect actual physical activities. For example, “market” processes gather several products without any physical transformation, i.e., there are no emissions, waste generation, and consumed resources or products. These processes are considered to occur instantaneously and hold an ID in the database (“M”); no temporal characteristics are needed for these.
Market processes (and exceptions)
These include market mixes and/or transport. For example, a process where different alternative production processes are given as inputs with their relative share as quantity. Sometimes, “market for” is not specified in the process name; for example, “Cement, unspecified {CH}| production.” Exceptions to the rule are (i) electricity markets including the activity of electricity transmission, for which temporal characterization is required. This means that this transportation activity is not covered by another process. The specific case of processes transforming high voltage to medium voltage is an exception of the exception. Temporal characterization is not needed; the material for the activity is already included in the medium voltage market processes containing the activity of transmission. (ii) a few fossil fuel markets, such as natural gas markets or imports; these include natural gas transportation, which must be characterized. Diesel markets (e.g., “Diesel {RoW}| market for” and “Diesel {CH}| market for”) also include the transportation of the diesel.
Processes only linking with other processes/markets
Two families of processes are considered (i) obsolete processes, without any function and link to other processes. The description often contains the following statement: “This process is no longer part of the ecoinvent 3 database and will not be updated. Please, choose another process.” An example is “Hard coal ash (waste treatment) {RoW}| cement production, pozzolana and fly ash 11–35%, non-US.” Waste treatment processes are also concerned. (ii) Non-obsolete processes, linking other processes together without any activity involved (1) processes substituting another process in the consequential version, e.g., “Sodium hydroxide, without water, in 50% solution state {GLO}| sodium hydroxide to generic market for neutralising agent.” The latter translates an extra demand of sodium hydroxide in an extra demand of neutralizing agent (e.g., sodium carbonate); consequently, it makes a link with its production dataset, which requires characterization. (2) Import processes, e.g., “Aluminium, primary, ingot {IAI Area, EU27 & EFTA}| aluminium, ingot, primary, import from Africa.” (3) Processes linking with one or several processes under one name, e.g., “Heat and power co-generation unit, 50 kW electrical, common components for heat+electricity {RER}| construction.” Another example is “Heat pump, 30 kW {RER}| production.”
Empty processes
This is the case, for example, for waste treatment products in the Recyc version of the database, to which cut-off is applied. Examples are “Digester sludge {GLO}| digester sludge, Recycled Content cut-off” or “Inert waste {CH}| clinker production | Alloc Def, U.”
Development of the integrated framework
Principles of computation of temporally differentiated LCI results
The objective is to obtain the life cycle environmental interventions (β functions) scaled to the functional unit (FU) and distributed over time. Further integration of the functions over time shall yield the static LCI results. This is achieved by combining (i) the conventional LCI inventory datasets from ecoinvent, (ii) the temporal parameters and functions associated with these datasets, and (iii) implementing an efficient graph search algorithm.
The combination was achieved practically in the web-based tool named DyPLCA, as a new, extended version of the initial tool cited by Tiruta-Barna et al. (2016) and Shimako et al. (2016, 2017, 2018). The algorithm works on a network of processes created based on the topology of matrix A, starting from the FU. A backward timeline is first defined, starting with the delivery of the FU. Then, the graph search implementation of the dynamic LCI model provides the amount of reference units for each process as well as its position along the timeline. Practically, a case study is first modeled in LCA software (SimaPro or OpenLCA) in a static manner. Then, matrices A and B are exported and further imported into DyPLCA in order to retrieve the values of intermediary and elementary flows. The temporal database is used to associate the temporal parameters to all the background processes used. In the foreground, the links between activities and the temporal parameters associated are directly added by the practitioner through the DyPLCA web interface (more details are given in SI1 – Electronic Supplementary Material).
The algorithm is computationally intensive; therefore, calculation time is critical. Memory usage during the computation and the size of the datasets has to be carefully addressed to avoid disruptive latencies. To this end, the search algorithm uses thresholds and stop conditions. Discretization steps are considered in order to accommodate the continuous dynamic LCI model to discrete time-series.
In the following, the functioning of the algorithm is detailed.
Implementation of the graph search algorithm
Once a project is properly configured (as described in SI1 - Electronic Supplementary Material), it can be computed. First, the “search” step resolves the start date and material quantity for each activity in the project. Then, the “distribution” step computes the distribution over time for the interventions for each activity. The distribution step is computed right after each activity gets resolved during the search step.
Search step
Life cycle processes are linked together by a producer/supplier-consumer/user relationship, based on matrix A. This is formally the adjacency matrix to a network where processes are nodes and producer-consumer relations are links. Although possibly large (15000 processes for ecoinvent 3.2), this material network remains a compact graph. Each link represents all the possible activities between a producer and a consumer. In order to obtain the complete list of activities concerned by one specific case study, one needs to obtain the complete activity network. This is an extended graph including, for each activity, its start date and material quantity over the timeline. In order to produce the activity network, a search is performed in the material network. The links indicate the flow of material or service between a producer and a consumer. This search starts from the final consumer (the FU), follows incoming links backwards to the producer, and finally, computes the start time and material quantities. The main issue to address here is that the network of processes involves loops that require a no-end graph and search algorithm. Indeed, the algorithm goes from one process to another in the loops without end, as the quantities exchanged by the processes (over time) are smaller and smaller but not null. This effect is not seen when the time dimension is ignored, as the quantities are calculated by matrix inversion to obtain the solution directly. A similarity can be drawn with the resolution of an integral by power series expansion. The solution can only be approximated as the expansion goes to infinity without reaching it.
In order to resolve this issue, the search algorithm uses boundary parameters. Once reached, these stop the search. The time limit parameter defines the maximum number of years the search algorithm can go back. This corresponds to an end time date of the timeline that was set in the past. Activities starting earlier than this date are excluded from the search. The threshold parameter defines a cut-off ratio on the quantities of the reference unit requested for each activity. Whenever the requested quantity is below the cut-off, that part of the network is discarded from the search (Table S2 in SI1 - Electronic Supplementary Material).
Distribution step
As long as the search algorithm proceeds, environmental interventions associated with each activity are computed. They are further associated to a given moment in the timeline with a specific discrete resolution. This generates large data tables containing the time series of the different environmental intervention types over the timeline. This step is controlled by two parameters. The step size parameter (Table S2 in SI1 - Electronic Supplementary Material) defines the interval of time between each data point of the time series. The smaller the step size, the bigger the size of the resulting time series. There is virtually no limit to how small the step size can be. However, the tool sets a threshold on the step size based on the available memory during the calculation. The numerical precision parameter (Table S2 in SI1 - Electronic Supplementary Material) is used during the computation of mathematical integrals for the α functions. This precision defines the step used for the numerical integrations. Integrals are computed over an interval equal to r (Table S3 in SI1 - Electronic Supplementary Material). Therefore, the precision should be orders of magnitude lower than r in order to render realistic values.
Linking temporally differentiated LCI results to dynamic LCIA models
Temporally differentiated LCI results are obtained as:
- βk, i, j functions per substance k and intermediary flow (i,j) between processes i and j;
- γk functions, representing the emission profile of a substance k over the life cycle.
Results are obtained in the form of discrete values over time and can be used with dynamic LCIA models. Final outputs are impact indicators calculated at each time step along the timeline, which results from the combination of the dynamic LCI and LCIA models. These results can be obtained individually per process and substance, per substance on the life cycle, aggregated per impact category, etc.
Climate change, human toxicity, and ecotoxicity models have been implemented, based on Shimako et al. (2016, 2017, and 2018). As these methods were presented in the cited articles, they are not described extensively here.
Climate change impact is assessed by two indicators (based on IPCC models, 2007, 2013): (1) radiative forcing, which is instantaneous and cumulated in time—it replaces the conventional global warming potential GWP; (2) global mean temperature change as a function of time—it replaces the global temperature potential GTP.
Toxicity and ecotoxicity models are based on USEtox (Rosenbaum et al. 2008; Mackay 2002). Human toxicity (cancer and non-cancer) and ecotoxicity indicators are calculated as instantaneous and cumulated indicators, both as a function of time.
The main differences with respect to temporal climate change and toxicity from literature (Levasseur et al. 2010; Lebailly et al. 2014) are (1) the impact models are implemented in their initial dynamic form in order to directly obtain indicators in function of time and in order to avoid the use of characterization factors (otherwise a huge number of CF values would have to be calculated). The models were resolved in full dynamic conditions with the emission function βk, i, j and γk as input data. (2) The approach is flexible, allowing the use of different time steps and adaptation to the granulometry of LCI.
The use of dynamic LCIA models allows us to exploit the full potential of the full temporally differentiated LCI results. The resolution of LCI results can be as high as permitted by the calculation time or can be chosen in accordance with the impact category (e.g., higher resolution for toxicity, lesser for climate change, Shimako et al. 2018).
Moreover, conventional LCIA indicators and dynamic CF can also be used over limited time intervals.
At this stage, the outcomes only present curves of impacts over time. Being able to provide single values would characterize the overall impact over time and allow for comparison and possibly decision support. To this end, the integration of these results over a given time period should be undertaken, as it has been done for the GWP100 over 100 years. As already mentioned in the introduction, additionally, a discounting of impact over time can be considered, implying the lesser valuing of impacts later over time. This is commonly done using a constant annual periodic factor of x%, in which the impact diminishes over time with a factor 1/(1+year)x. Such an approach was applied by Levasseur et al. (2010) and will be exemplified with the case study.