hi there,
could someone advice me When should I specify a pilot operated relief valve?

Thanks

Pilot operated safety valves tend to cost more than conventional safety valves, and so should be specified only when they serve an important service. One of the advantages of pilot operated valves is that they are relatively unaffected by backpressure. Thus when the total backpressure may build to an appreciable fraction of the set point, pilot operated valves would be favored.

hi how can we design the pressure relief valve?

The PRV is sized in the exact same manner as any relief device. You go through all the credible relieving scenarios and calculate the relieving flow for each. You then choose the controlling relieving condition. Give this to a selected manufacturer who will then advise on the proper pilot operated PRV to use.

Now to get picky in terminology. Process Engineers DO NOT design relief devices. We only size them by providing the controlling flow and associated relieving conditions and fluid properties and pass this information to the manufacturer.