In a test for alkenes the bromine water is added and the colour does not change, is an alkene present?

An alkene is not present as the solution would turn colourless if an alkene was in the solution. This reaction is called an addition reaction and the reason bromine is decolourised is because a colourless dibromo compound is formed called dibromoethane.

The test for telling the difference between a saturated alkane and unsaturated alkene involves adding bromine water, which is brown in colour - the unsaturated alkene has a double bond and can react with the bromine, causing a colour change to colourless. As alkanes do not have a double bond, they are unable to react with the bromine and hence the brown colouration will persist. Therefore no colour change indicates the presence of a saturated alkane.