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D r a f t

D r a f t. Life Cycle Assessment A product-oriented method for sustainability analysis UNEP LCA Training Kit Module h – The mathematics of LCI. D r a f t. Representation of processes Representation of goal definition Balancing Environmental interventions Overall LCI structure Advantages

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D r a f t

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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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