+1 vote

When there a co-products in a process and “none” is chosen for allocation, the process is double counted in the Tec-matrix (all flows exempt the product and coproduct of the process are double counted). Is this by purpose? Wouldn’t it be more coherent to automatically allocate 0 impact to the co-product?

+1 vote

Best answer

When we say no allocation in openLCA, it means "pull in the processes into the technology matrix A and intervention matrix B according their product demand without applying any allocation factors".

Here is a small example: suppose we have a process `p1` that has an output of 0.5 units of product `p11`, 1.5 units of product `p12`, and 2.0 units of emission `e1`. Then there are two processes `p2` and `p3` that consume one unit of `p11` and `p12` respectively. Finally, there is a process `p4` that consumes one unit of `p2` and `p3`. Here is the product system graph of that example:

and the model in a tiny syntax (`->` means output, `<-` means input):

p1 -> 0.5 p11

p1 -> 1.5 p12

p1 -> 2.0 e1

p2 <- 1.0 p11

p3 <- 1.0 p12

p4 <- 1.0 p2

p4 <- 1.0 p3

For the example the technology matrix then looks like this:

A = [ 0.5 0.0 -1.0 0.0 0.0 ; *# p11*

0.0 1.5 0.0 -1.0 0.0 ; *# p12*

0.0 0.0 1.0 0.0 -1.0 ; *# p2*

0.0 0.0 0.0 1.0 -1.0 ; *# p3*

0.0 0.0 0.0 0.0 1.0 ] *# p4*

The intervention matrix B then looks like this when allocation is set to `none` (no allocation factor is applied for `p11` and `p12`):

B = [ 2.0 2.0 0.0 0.0 0.0]

Now, when we want to calculate the system for one unit of `p4`, so we have a demand vector:

d = [ 0.0 ; *# p11*

0.0 ; *# p12*

0.0 ; *# p2*

0.0 ; *# p3*

1.0 ] *# p4*

we get the result `g = B * (A \ d)` of `5.333` units of `e1` (note that openLCA also reports the unlinked product amounts in this case).

When we apply allocation factors in process `p1` based on the product amounts we get a factor of `0.25` for `pp1` and 0.75 for product pp2. In the example above, only the intervention matrix changes:

B = [ 0.5 1.5 0.0 0.0 0.0]

... and we get the result of 2.0 units of `e1`.

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