Lab test to compare the reactivity of liquid 1-heptene and liquid heptane
According to this Wikipedia article:  


  "In electrophilic halogenation the addition of elemental bromine or
  chlorine to alkenes yields vicinal dibromo- and dichloroalkanes
  (1,2-dihalides or ethylene dihalides), respectively. The decoloration
  of a solution of bromine in water is an analytical test for the
  presence of alkenes."  


Alkanes tend to be much less reactive toward bromine, so yes, your bromine water test should allow you to distinguish between heptane and 1-heptene.