Vertical submersible pump (semi-submersible) is also called submersible slurry pump, it is used to pump slurry( which content large solids) and waste water. In drilling rig mud system, it is used as 2 functions: 
1 As feeding pump of shale shaker, to pump the slurry from mud pit to shale shaker inlet pipe, usually it is HDD mud system, water well drilling mud system. In oil drilling mud system, they do not need a shale shaker feed pump.
2 As feeding pump of decanter centrifuge.
In some liquid mud plant, they may use the vertical submersible pump as transfer pump.