When to use double pipe heat exchanger and shell and tube heat exchanger?

It depends on the material you are handling . Normally double pipe is used for highly volatile materials  with corrosive properties while shell and tube is used for  materials  with less corrosive properties .

In shell and tube heat exchanger when velocity of liquid phase tends to zero you can solve this problem by replacing with double pipe heat exchanger.

According to my knowledge Double Pipe heat exchanger used for small heat transfer and Shell and tube is used when large heat transfer is required.