Build Up Back Pressure

I have to size a PSV for wellhead flow line. The set pressure is 1100 psig. PSV is to vent into atmospher. If PSV outlet flange is 6" and it discharges into a 10" vent line. Pressure required d/s PSV to have flow through vent line is 135 psig. If i reduce pressure there wont be flow due to pressure drop in the vent line. But at this pressure total pressure drop through 6*10 reducer and 250 ft vent line is 80 psi. What should i call build up back pressure for psv, 135 psig or 80 psig?

I'm a little confused by your discussion what is happening. I don't understand the difference between the two cases to identify why in the first you need 135 psig and in the second, you need only 80 psig.

Built-up backpressure is the additional outlet pressure created on the PSV outlet when it is flowing. If your PSV goes to atmosphere then the pressure on the outlet of the PSV is zero. You then do your discharge line calculations with the PSV flowing at its full capacity (not the required capacity from your process calculations but the actual capacity of the PSV which will be greater) and determine the pressure at the outlet of the PSV to flow the PSV's capacity to atmosphere. If that number is 135 psig, then 135 psig is your built-up back pressure. This is also greater than 10% of your set pressure so a conventional PSV is not acceptable, you would need a balanced bellows PSV, a pilot operated PSV or a larger outlet line.

Back pressure on the PSV can also be a combination of imposed backpressure plus built-up backpressure. Let's say the PSV is discharging into a system that is maintained at 50 psig. When the PSV is flowing, you calculate you need (using the previous numbers) 135 psig at the PSV outlet to flow into the system. In this case, the superimposed backpressure is 50 psig and the built-up back pressure is 85 psig.

If you haven't already, I would recommend looking at API 520 and API 521.