where an integration over all the entering parcels and the injection time has been performed. The domain \(\partial\Omega^+\) represents the boundaries location were the parcels entered the volume. \(S\left(t,\vec{x}\right)\) is the volume (mass, moles number) of water around \(\vec{x}\). These parcels have entered \(\Omega\) at different times (i.e. were injected in the control volume at different times) and therefore, have different ages. The probability of each age can be given by: