Second-Order Analytical Uncertainty Analysis in Life Cycle Assessment

Life cycle assessment (LCA) results are inevitably subject to uncertainties. Since the complete elimination of uncertainties is impossible, LCA results should be complemented by an uncertainty analysis. However, the approaches currently used for uncertainty analysis have some shortcomings: statistical uncertainty analysis via Monte Carlo simulations are inherently uncertain due to their statistical nature and can become computationally inefficient for large systems; analytical approaches use a linear approximation to the uncertainty by a first-order Taylor series expansion and thus, they are only precise for small input uncertainties. In this article, we refine the analytical uncertainty analysis by a more precise, second-order Taylor series expansion. The presented approach considers uncertainties from process data, allocation, and characterization factors. We illustrate the refined approach for hydrogen production from methane-cracking. The production system contains a recycling loop leading to nonlinearities. By varying the strength of the loop, we analyze the precision of the first- and second-order analytical uncertainty approaches by comparing analytical variances to variances from statistical Monte Carlo simulations. For the case without loops, the second-order approach is practically exact. In all cases, the second-order Taylor series approach is more precise than the first-order approach, in particular for large uncertainties and for production systems with nonlinearities, for example, from loops. For analytical uncertainty analysis, we recommend using the second-order approach since it is more precise and still computationally cheap.