The need of PWHT or not is ruled by the Code under which the vessel was designed. Was it ASME VIII Section 1 or 2? Was it AD Merkblatter?Was it any other else? If the applicable code demands to HT the vessel, then it must be heat treated. 316 L is a low carbon stainless steel (C = 0,04 percent) which will undergo heat treatment without developing sensitization nor intergranular corrosion.
A vessel like that must have been calculated by a competent engineer or engineering company. It is his (or their) duty to give you a satisfactory advice on the matter.
Giovanni S. Crisi
Sao Paulo - Brazil