Sherif:
After spending more than 50 years practicing process and project engineering as well as managing engineering projects, I can strongly state:
You should take the need of pressure relief valve on the discharge of a positive displacement pump AS MANDATORY. Common sense should tell you that unless you do that, you are running the risk of either burning up the pump's driver, or causing a pipe, pump, or other mechanical rupture.
You should always send the discharge of a pressure relief valve to a safe environment. This can be the original source or supply suction tank - but always with consideration for any potential over pressure or mechanical failure in the same.
NEVER, NEVER send the discharge of a pressure relief valve to the suction of the pump. I consider this a potentially dangerous and very stupid thing to even think about. Whoever dreamed of this "option" doesn't have any experience, knowledge, or process design capability. Serious and major chemical process companies never allow this to be done.
Who is the "genius" that is suggesting that a positive displacement pump doesn't need a discharge pressure relief valve? He/she have probably never attended or participated in a Hazop and should be banned from one for lacking any common sense with respect to safety and potential hazards.
I have always tried to design my centrifugal pumps so that their maximum attainable discharge pressure never reaches the MAWP of any piping or vessels it is connected to on the discharge side. This obviously allows me to eliminate the need for any pressure relief device on the discharge of the centrifugal pump. Depending on the dead head pressure this may or may not be applicable.
There are no references required to prove what I have stated. Common sense and experience among any capable process design engineer deems it so. The countless Hazops I have attended and led clearly demonstrate these facts. Our forums on this website have expounded these basic and well-known principles for many years. All you have to do is read through them and learn these basic process truths from other engineers.
I am very concerned that no one on this thread has yet to mention that ALL centrifugal pumps exhibit what is called a maximum dead head pressure. Knowing this - and the experienced knowledge that if your down-stream piping and equipment have a MAWP above that dead head pressure you logically cannot justify the need for a pressure relief valve. This leads me to believe that today's engineers know little if anything about pumps - especially centrifugal pumps. Shame.