The protests, which started on Sunday, have not yet affected production but they will, said Mohammad Al-Hamlan, deputy president of the Kuwait National Petroleum Company workers union.
"God willing, tomorrow morning, 68 tank farm workers will join the strike," he told Reuters.
Thirty two workers at the refinery's utility unit walked out on Sunday to protest a company decision to cut the number of workers assigned to the refinery's utility unit.
The union official said the utility unit was "the heart" of the refinery because it provides it with utilities like electricity and water.
Hamlan said output had not yet been affected by the strike so far, but it will be when more workers join the protest.
KNPC officials could not be reached for comment.
OPEC member Kuwait has two other refineries. The combined capacity of the three facilities is 930,000 bpd.
