Consequential database | The use of system expansion as allocation principle

The consequential database is one of the major innovations in the ecoinvent v3 database. We offer an example based on one important feature in the consequential database: the use of system expansion as allocation principle. What happens if two almost equally large amounts are subtracted?

Suppose a production process consumes 1 MJ of energy, but it also delivers 0.99999 MJ as a co product. With system expansion the net result is that the process consumes only 0.00001 MJ, as the delivered energy is subtracted from the consumed energy. Now see what happens if the energy consumption increases 0.1%; this will mean the consumption changes to 1.0010 MJ. After subtraction the net consumption is now 0.00011 MJ, and this is a factor 11 higher: There is an amplification factor of 11000!. This effect causes the database to be sensitive for rounding errors and it causes a problem in Monte Carlo calculations, where small changes are introduced on purpose. The problem only occurs when two almost equal numbers are subtracted.

SimaPro has a number of build in checks to warn you for this effect, so when you use the consequential database you will see two types of warning messages:

1. During calculation of the unit processes SimaPro checks if indeed two almost equally large numbers are subtracted, as this may mean a not completely reliable result due to rounding errors. In practice this may not be a big problem as the differences between two almost equal figures is a small number, but in some cases also small numbers matter. Theis effect also may lead to small differences between the system processes produced by ecoinvent and SimaPro, but our analysis shows that only in a few cases an emission is up to 6% different.

2. During Monte Carlo the amplification effect will unfortunately cause two problems. Some calculation runs will cause extremely high or low variations. When SimaPro finds the result of a calculation run is 15 orders of magnitude out of range it will produce an error. In some cases SimaPro will also find that the network cannot be solved, as the Monte Carlo run produces an impossible situation, and SimaPro will also stop. Unfortunately this means that in practice Monte Carlo cannot be used in the consequential database.

These problems do not occur in the allocation default version of ecoinvent v3.

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Eric Mieras
'Positive impact makes you meaningful'