Working of Burner Management System of Fired Heater

Purpose of PCV: This valve also called as Minimum Fire Pressure Regulator, this PCV is essential when the fuel gas control valve (PCV or FV) lacks sufficient turn down to light the first burner (API-556).
During startup, this valve aids in more controlled igniting conditions by adding time to allow proper gas to air mixture for smoother combustion. The absence of this valve could result in a sudden fluctuation of fuel gas to the main burner, extinguishing the pilot burner or causing backfire.
According to the EMERSON Process Management, as shown in the diagram below, the purpose of the bypass pressure regulator valve, is to regulate pressure while minimum firing.
This regulator not only helps minimize the complexity of the burner management system, but also reduces operator interaction during start-up. Simply set the regulator to the required set point during commissioning and it can remain untouched through multiple start-ups.
Purpose of Bypass Globe Valve: This valve is used to hand over the main fuel gas control valve for maintenance while the unit is running normal. Control valve is taken out of service gradually opening the bypass valve.
Controlling Temperature of Heater outlet: In this case heater outlet temperature controller, works as master controller and it generates the output as per temperature difference requirement. This demand signal is sent to fuel gas controller (Pressure or Flow) which then directs the final control element (Control Valve) to take action as per temperature requirement.

As per P&ID provided by you, the tag of the valve is PCV0125. Normally the set pressure of such a valve is ~more than 0.5 Kg/cm2. Please check the specification sheet of this valve and find its set pressure.
0.1 Kg/cm2 be the set point of ESD/heater shut down at low pressure.
There are many options to perform the leak test of the circuit;

1. The leak test can be performed by opening the bypass globe valve or main valve QV-0101 and isolating the valves of the PCV. Because you are exposing equal pressure upstream and downstream of the PCV.

2. Another option of performing the leak test is to attach a Nitrogen hose at 3/4″ RFG-V06699.

Hope you get the answer.