How sonic log detect the primary porosity but not the secondary porosity? porosity is just porosity

The sonic tool measure the interval transit time, ∆t, or the time in microseconds for an acoustic wave to travel through one foot or meter of formation, along a path parallel to the borehole.The primary porosity can be find from the Wyllie equation as ( ∆t log- ∆t matrix/ ∆t Fluid- ∆t matrix). to know the matrix you have to know the lithology in order to choose the matrix, and ∆tlog can be know from the log curve of sonic tool.

Dear Mr. Khan, It seems to be that your question was 4 years ago. however, if you did not get the answer, I would say that sonic measure of intervals transit time and therefore, will take the fater pathway through porous (no vuggy or fractures will be calculated). that means if the sonic porosity is less than other logs porosity such as density and/or neutron, then the difference will be the secondary porosity which for instance could be caused by the diagenetic process such as dissolution. 

hope this answer helps you.

The sonic tool measure the interval transit time, ∆t, or the time in microseconds for an acoustic wave to travel through one foot or meter of formation, along a path parallel to the borehole.The primary porosity can be calculated from the Wyllie equation as ( ∆t log- ∆t matrix/ ∆t Fluid- ∆t matrix). 

It does not because the acoustic wave emitted from the sonic tool always chooses the fastest way to travel through the rock i.e rock matrix and not for example through fractures that will consist the secondary porosity