If you provide some additional detail, it would help us to give you a helpful answer. There are too many variables otherwise.
For a fuel oil pumparound pump in a crude unit, I might recommend API plan 11, flush off of discharge. This assumes that the product is cool enough (vapor pressure margin) that additional cooling is not needed.
For a charge pump to a fuel oil desulfurizer, I might recommend API plan 32, clean outside flush. The flush would be the finished product (desulfurized fuel oil) from the other end of the unit. These units often have flush systems piped up to flush a number of pumps with this same clean product.
For a charge pump to a distillate hydrotreater, we might have product that is hot enough to require cooling and outside flush might be more expensive. So I might recommend an API plan 23, with circulation from the seal chamber through a cooler and back to the seal. An API plan 23, circulation from an intermediate stage through a cooler and back to the seal, might be considered, also.
For a hydraulic recovery turbine on the outlet of a distillate hydrotreater, I would recommend no flush, with cooling water on a jacket around the seal chamber. This is because this stream would be saturated with hydrogen. Any pressure drop across an orifice would result in gas flashing out of solution. So plan 11 or 21 would be a problem. Plan 23 could be considered with great care on how it is flooded and vented at start-up.
For a transfer pump of fuel oil product from a storage tank, I might recommend API plan 11 or 13 depending on the configuration of the pump.
The recommendation for seal flush plan depends as much on the service and pump configuration as on the product.
