Synonyms for Seep:

n.

leak (noun)
trickle, flow gently, flow.
seep (noun)
ooze.

v.

leak (verb)
drain, percolate, exude, flow, bleed, trickle, ooze, weep.
reject (verb)
cut, exclude, check, excrete, blacklist, curtail, belch, excise, chop, drain, spew, reject, discard, lop, evacuate, eject, exude, deep-six, scrap, eliminate, jettison, trash, disclaim, oppugn, blackball, shed, jilt, exhaust, deny, clip, abandon, disgorge, snip, secrete, junk, vent, cull, discharge, shear, crop, bar, disallow, disapprove, vomit, erupt, emit.

Other synonyms:

weep. transpire. run out
trickle.