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Understanding Life Cycle Assessment: Advanced Mathematical Concepts and Environmental Interventions

This module from the UNEP LCA Training Kit offers a comprehensive guide to the mathematical foundations of Life Cycle Inventory (LCI). It covers the representation of processes such as electricity and fuel production, goal definitions, and balancing supply and demand through mathematical equations. Key topics include environmental interventions and their associated scaling factors, culminating in an overall structure for LCI. Attendees will gain insights into advanced theoretical concepts, such as perturbation theory and stochastic theory, providing transparency and guidance for software implementation in sustainability analyses.

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Understanding Life Cycle Assessment: Advanced Mathematical Concepts and Environmental Interventions

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  1. D r a f t Life Cycle AssessmentA product-oriented methodfor sustainability analysisUNEP LCA Training KitModule h – The mathematics of LCI

  2. D r a f t • Representation of processes • Representation of goal definition • Balancing • Environmental interventions • Overall LCI structure • Advantages • New concepts Contents

  3. Representation of processes (1) D r a f t • Production of electricity: • in flow diagram terms: • in mathematical terms: 2 liter of fuel 10 kWh of electricity 1 kg of CO2 0.1 kg of SO2

  4. Representation of processes (2) D r a f t • Production of fuel: • in flow diagram terms: • in mathematical terms: 100 liter of fuel 10 kg of CO2 50 liter of crude oil 2 kg of SO2

  5. Representation of goal definition D r a f t • Functional unit/reference flow: • in flow diagram terms: • in mathematical terms: 1000 kWh of electricity ? kg of CO2 ? liter of crude oil ? kg of SO2 (? liter of fuel)

  6. Balancing (1) • Need to match supply and demand: 200 liter 1000 kWh 100 liter 200 liter 2 liter 1000 kWh 10 kWh  2  100 10 kg CO2 20 kg CO2 100 kg CO2 1 kg CO2 ? kg CO2 120 kg CO2 100 kg CO2

  7. Balancing (1) • Need to scale processes: • production of electricity by a factor of 100 • production of fuel by a factor of 2 • More formally: balance equations: • Or in matrix terms:

  8. Balancing (2) • From concrete equations with matrix coefficients • … to abstract equations with symbols • … that can be solved by standard techniques • … and becoming concrete again

  9. Environmental interventions (1) • Apply same scaling factors to environmental flows: • In matrix terms

  10. Environmental interventions (2) • From concrete equations with matrix coefficients • … to abstract equations with symbols • … in which we can insert the previous result • … and becoming concrete again

  11. Overall LCI structure • Combining balancing and interventions: • with the intensity matrix

  12. Advantages of mathematical treatment • Explicit treatment, transparent • Guidance for software implementation • New insight in LCA • e.g., allocation • Advanced theoretical concepts: • perturbation theory • covariance structure • stochastic theory

  13. New concepts • Terms: • technology matrix, scaling vector, intervention matrix, final demand vector, intensity matrix, … • Techniques: • matrix conditioning, principal components analysis, …

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