On most conventional valves where superimposed back pressure exists, the back pressure is compensated for during production testing. In most cases the compensation is on a straight differential basis. As such, a valve that has a set pressure requirement of 100 psig but will be installed in a system where there is 10 psig constant superimposed back pressure will be net set on the test stand at 90 psig (relative to you, it opens at 100 psig, relative to the spring, it opens at 90 psig. The pressure in the vessel will be 100 psig on a pressure instrument). This is sometimes called the differential test pressure. A further variation of this is the cold differential test pressure (CDTP) which also takes the effects of temperature into account.
So, differential test (or set) pressure should only address the constant portion of the superimposed back pressure (There is sometimes a “variable superimposed” portion. This type of back pressure varies or changes over a range from a minimum to a maximum, or vice versa. The actual back pressure at any specific time depends on conditions in the piping system to which the outlet of the valve is connected).
P.S: Could you please give us the references of the 2 articles you have mentionned?
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