Dear Farid,
All the above explanations have answered your question properly.
From my limited experience, the best way to calculate PSV backpressure would be to consider all piping up to the flare stack/tip. From my understanding, it seems that you are referring to an existing plant thus all the relevant Process and Piping documents should be available e.g. P&IDs, isometrics, safeguarding memorandum, PSV as-built datasheets etc.
Next, it is advisable to use commercially available flare hydraulics softwares e.g. Aspen Flare System Analyzer (Flarenet), Farris iPRSM etc. But I would recommend to proceed using Aspen Flarenet. You can refer to the following steps as reference, it may be may not be applicable to your case. Of course, the detail tutorials should come with the software.
(i) Build your model in Flarenet from the PSV, tailpipes, subheaders, main headers, flare KOD, and flare stack/tip. The pressure drop for your flare riser & tip can normally be found from Vendor datasheet. For piping, input all the straight lengths and fittings as per as-built isometrics.
(ii) For the PSV, input the relevant PSV and relief scenario data at the relieving conditions. For the fluid compositions, you can define the compositions in Flarenet as you normally did in VMGSim.
(iii) You can select the calculation method in Flarenet which suit your particular application the most. I would recommend using Peng Robinson VLE method and Lee Kesler for the enthalpy method. For pressure drop calculation, you can use Beggs & Brill.
(iv) Once all the inputs are correct, you can run the flarenet model and get your results for particular PSV backpressure, Mach no. etc.
From my limited 4 years experience, I have come across cases in which the original Process engineer does not calculate the correct backpressure for the PSV. A common mistake was to calculate the total backpressure only for the governing scenarios. Always remember, there might be different governing scenarios for the PSV orifice area, for the inlet line losses, and backpressures.
You can refer to API Std 520 & 521 for more details.
Hope this sharing can help you.
p/s: I seem to recognize your face but I cannot remember exactly.