I believe what Bobby is drawing attention to is that the basis of HOW the cooling is proposed to be done hasn't been explained. For example, I believe that what is being proposed is a cool-down, recirculation loop for circulating stored, cold LPG. A quantity of cold, liquid LPG is going to be circulated through the 14 km pipeline. What will happen to the vaporized portion that is generated due to the heat pickup hasn't been explained (and may not be important for now). Certainly, the speed of the cool down is controlled by the available re-condensing capacity of the evaporated LPG. You can't cool down faster than that.
However, if this is true, then this is a classical unsteady state heat transfer operation and very complex to model and calculate. A lot of simplifying assumptions have to be made and more information is required.
It certainly can't be as simple as depicted in the Excel workbook.
Please elaborate and explain all the details of what is being proposed.