  In this work, we have studied accretion of the dark energies onto
Morris-Thorne wormhole. For quintessence like dark energy, the mass of the
wormhole decreases and phantom like dark energy, the mass of wormhole
increases. We have assumed two types of dark energy like variable modified
Chaplygin gas (VMCG) and generalized cosmic Chaplygin gas (GCCG). We have found
the expression of wormhole mass in both cases. We have found the mass of the
wormhole at late universe and this is finite. For our choices the parameters
and the function $B(a)$, these models generate only quintessence dark energy
(not phantom) and so wormhole mass decreases during evolution of the universe.
Next we have assumed 5 kinds of parametrizations of well known dark energy
models. These models generate both quintessence and phantom scenarios. So if
these dark energies accrete onto the wormhole, then for quintessence stage,
wormhole mass decreases upto a certain value (finite value) and then again
increases to infinite value for phantom stage during whole evolution of the
universe. We also shown these results graphically.
