We currently require vertical storage for all multi-stage compressor and turbine rotors. We also store multi-stage pump rotors vertically, when practical. The risks of horizontal storage have to do with run-out more than balance. A long thin rotor with multiple interference fit parts can bow in horizontal storage. This bow might straighten out when the machine runs. But, that is a high risk to take.
As much as orientation, storage in a controlled environment is very important. Our storage canisters are all set up for nitrogen purge to prevent corrosion.
I have granted exceptions related to vertical storage in a few cases. For barrel machines with full internal bundles, the weight of the diaphragms between stages may be a problem in a vertical orientation. For a few of these, I have approved horizontal storage. These internal bundles can still be stored vertically, but the canister may need to support the diaphragms separately so that this weight does not hang on the impellers. For a bare rotor, vertical is always better. The support should be at the top so that the rotor is hanging. If this is not practical, the rotor could be supported from the bottom, in compression rather than tension. This is not preferred, but is still better than horizontal storage.
Johnny Pellin