Global Sensitivity Analysis in Life-Cycle Assessment of Early-Stage Technology using Detailed Process Simulation: Application to Dialkylimidazolium Ionic Liquid Production

The ability to assess the environmental performance of early-stage technologies at production scale is critical for sustainable process development. This paper presents a systematic methodology for uncertainty quantification in life-cycle assessment (LCA) of such technologies using global sensitivity analysis (GSA) coupled with a detailed process simulator and LCA database. This methodology accounts for uncertainty in both the background and foreground life-cycle inventories, and is enabled by lumping multiple background flows, either downstream or upstream of the foreground processes, in order to reduce the number of factors in the sensitivity analysis. A case study comparing the life-cycle impacts of two dialkylimidazolium ionic liquids is conducted to illustrate the methodology. Failure to account for the foreground process uncertainty alongside the background uncertainty is shown to underestimate the predicted variance of the end-point environmental impacts by a factor of two. Variance-based GSA furthermore reveals that only few foreground and background uncertain parameters contribute significantly to the total variance in the end-point environmental impacts. As well as emphasizing the need to account for foreground uncertainties in LCA of early-stage technologies, these results illustrate how GSA can empower more reliable decision-making in LCA.


B. Property Estimation and Process Flowsheeting
This section reviews the properties used for the pseudo components in Aspen-HYSYS (version 9) for process simulation and how they are estimated.
• For estimating the enthalpies of formation, the molecular structure of the cation and anion are first drawn and optimized in the molecular modelling and graphics software ArgusLab. The structure is then processed in the open-source software MOPAC, a quantum chemistry tool for calculating the charge density profiles and enthalpies of formation.
• The heat of formation of ionic liquids is obtained from the Born-Haber cycle, as shown in Equation (S1) below. 2 The lattice energy ∆H L is calculated from Equation (S2). 5 R is the ideal gas constant. n m and n x are parameters that depend on the nature of the cation and anion, respectively: they are equal to 3 for monoatomic ions, 5 for linear polyatomic ions, and 6 for non-linear polyatomic ions. p and q are the oxidation states of the cation and anion, respectively. The potential energy U pot is calculated from Equation (S3), where ρ m and M m are is the density and the molecular weight of the ionic liquid, and γ and δ are coefficients that depend on the stoichiometry of the ionic liquid.       Figure S2: 1-Chlorobutane process flow diagram S8

C. Environmental Assessment Data and Methodology
This section gathers all data related to LCA including the proxy data, processes and flows used for the LCI phase in addition to the midpoint results from the characterization phase. 90% by mass of carbon in waste stream is assumed to be completely burned in waste treatment to produce CO 2 as per the following complete combustion equation: The chemical oxygen demand (COD) or total oxygen consumed is assumed to be equivalent to the amount of oxygen needed to react with the amount of carbon remaining in the waste stream after treatment which is assumed to be 10% of total carbon BOD For worst case scenario, the biological oxygen demand (BOD) which is the oxygen consumed due to biological aerobic digestion by organisms is assumed to be equivalent to the amount of COD

TOC
The total organic carbon (TOC) which is the total amount of carbon is assumed to be equivalent to 10% of the total carbon in the waste stream which is the amount of carbon remaining after treatment DOC For waste case scenario, dissolved organic carbon (DOC) is assumed to be equivalent to TOC        Table S17: Uncertain model parameters, uncertainty sources and ranges in flowsheet simulation of 1-chlorobutane production. Each uncertain parameter is assumed to follow a triangular distribution.

Source Parameter Range Units
Process

E. Uncertainty Quantification Methodology and Results
This section provides further details about the computational methodology used for uncertainty quantification and apportionment using the RS-HDMR method of GSA. It also presents a comparison with the parameter rankings obtained using one-at-a-time sensitivity analysis.
• The uncertainty propagation was coordinated in Matlab. An XML file was created from the database ecoinvent (version 3.5) and imported to Matlab. This file was processed in order to retrieve the background processes and their connectivity as well as the corresponding background uncertainties. All these background uncertainties together with the foreground process uncertainties (Tables 1, S15, S16 & S17) were jointly sampled using quasi-random Sobol sequences. 9 For each sample, the foreground inventory flows were first computed using Aspen-HYSYS (version 9, interfaced with Matlab). • The variance-based global sensitivity analysis (GSA) was conducted using SobolGSA (version 3.1.1) 6,7 under Matlab. A separate GSA was conducted for each end-point impact z, using the sampled environmental impacts EI z as output values and the corresponding foreground uncertainty ω and lumped background uncertainties BEI up p,z (ϕ) as input scenarios. In doing so, notice that any cross-correlations between the uncertain inputs are indeed captured-as opposed to treating ω and BEI up p,z (ϕ) as independent uncertainties. Denoting the uncertainties as u 1 , . . . , u d for simplicity, The ANOVAbased decomposition of EI z is given by: EI z,i,j (u i , u j ) + · · · + EI z,1,2,...,d (u 1 , u 2 , . . . , u d ) The zeroth-order term EI z,0 , first-order terms EI z,i and second-order terms EI z,i,j in this decomposition were computed using the RS-HDMR method through SobolGSA. This method exploits the fact that for many practical models only low-order interactions between inputs carry a significant impact on the output. 8 The first-and second-order terms are approximated using truncated series expansion: where the choice of the orthogonal polynomial basis φ k depends on the probability distributions of the inputs-see, e.g., Wang et al. 12 for the case of triangular distributions. The polynomial orders K, M and N are determined automatically by SobolGSA for maximal accuracy. Moreover, the coefficients α i k and β ij mn can be estimated via regression and directly feed into the following formulas to estimate the partial variances of the first-and second-order effects, respectively: In turn, the first-and second-order Sobol indices can be computed as: where the total variance Var[EI z ] can be estimated directly from the output samples. Lastly, the total-order Sobol index for a given input u i as: SO z,i,tot = SO z,i + SO z,i,1 + · · · + SO z,i,d (S10) In practice, SO z,i,tot quantifies how much of the variance in environmental impacts EI z may be attributed to the uncertainty in input u i , either separately or in association with other uncertain inputs. When the difference between the first-and total-order Sobol index is small, SO z,i,tot ≈ SO z,i , the effect of the input u i on the output variance is essentially separable from, and therefore additive to, the effect of the other inputs.
• By contrast to GSA, the one-at-a-time sensitivity analysis (OTSA) was performed by sampling each uncertain foreground parameter separately, while keeping the rest of the (foreground and background) parameters at their nominal values. Moreover, the resulting output variance for each input u i was normalized by the total variance Var[EI z ] from the joint uncertainty propagation (see above), so the resulting index could be directly compared with the total-order Sobol index for the same input.
Comparisons between the total-order Sobol indices and the OTSA indices for each foreground parameter and each end-point impact in the production of [BMIM] [BF 4 ] and [BMIM][PF 6 ] are presented in Tables S18 and S19, respectively. These reveal massive differences in relative sensitivity of the background parameters, confirming the need to account for interaction effects and for a global analysis in general.   Table S20: Total-order Sobol indices for each immediate lumped background parameter (rows) and each end-point impact (columns) in the production of NaBF 4 . The first-and total-order Sobol indices are identical since this subproblem is linear.
Parameter Human Health Ecosystem Quality Resources