# Allocation in multifunctional processes

+1 vote
104 views
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?
in openLCA

+1 vote
by (7.1k points)
selected

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:

# p11  p12   p2    p3    p4
= [ 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`):

# p11  p12  p2   p3   p4
= [ 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:

= [ 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:

# p11  p12  p2   p3   p4
= [ 0.5  1.5  0.0  0.0  0.0]

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

by (7.1k points)
I agree. Maybe this could be explained in more detail in the user guide.