It's not that difficult.
Pans ops has the details and it's free to download.
SIDs are predicated on a 3.3% gradient. This is based on 2.5% OIS + .8% for error.
If during the survey an obstacle penetrates the 2.5% gradient the the gradient required to that obstacle is calculated and .8% is added. This gradient is then stated on the SID i.e. 7% required until 3000'. above that height then 3.3% is assumed.
SIDs are written for AEO and it's up to the operator to come up with a OEI procedure.
OEI gradients are published in the AFM. (Some also include AEO gradients)
If you don't have AEO look at the OEI gradient and if it's above the SID gradient or 3.3% if no gradient is stated then it's safe to fly the SID with or without an engine failure.
If it's less than the stated gradient and no company OEI SID is published or you don't have AEO gradient data call your chief pilot and ask him to provide the required data to safely operate.