During the time that Egypt was a Roman province, it shipped large quantities of grain to Rome until 330 AD. The article Trade Routes and Commercial Products of Roman Pompeii says:
Egypt was supplying the city of Rome with almost a third of its annual grain needs by the mid first century A.D.
This required a large number of grain ships which, once they had unloaded the grain, presumably made their way back to Egypt. Researching what cargo they carried on the return journey has proven quite challenging. They carried wine and other items in amphorae, and then I came across this in Handbook to Life in Ancient Rome:
On their return journey, these boats often carried refuse (such as rubble from the fire of Rome in 64).
Aside from the economic desirability of not having ships return to Egypt with no cargo, why was Rome exporting its trash to Egypt? Presumably it had some economic value and was perhaps being recycled in some way, or was it simply being used as ballast (as suggested by pluckedkiwi's comment)?
A talk at a workshop, Repair, Recycling and Rubbish in the Roman Economy, given on 23.2.2018 in Berlin mentions "an emphasis on Egypt" but no paper seems to be available yet relating to this potentially useful source.