A potential problem in one of our quick close valves was brought to my attention.  

During normal operation, the actuator to the main valve is held closed by an 80 psi instrument air line.  Upon loss of air, the main valve is meant to close quickly by way of a quick exhaust valve (QEV).  

Please see the linked figures:  
1. http://files.engineering.com/getfile.aspx?folder=9e60e342-ac73-4193-9f2b-8ce2b4d3fb52&file=Normal_operation_of_valve.JPG
2.  http://files.engineering.com/getfile.aspx?folder=33eb8beb-73ab-4a07-b3ef-5c4ebf3db9c5&file=Loss_of_air_condition_for_valve.JPG  
3.  Further description of the QEV operation can be found here: http://files.engineering.com/getfile.aspx?folder=6e71a13a-3b50-4c0f-b8d2-4cc10ca738c5&file=QEV.JPG).    

The potential problem seems to arise on cycling the main valve. There appears to be no vent to atmosphere, thus when the main valve loses air supply, the QEV vents air back into the actuator, equalizing the pressure and increasing the closing speed of the main valve (spring return closes the main valve).  

When the main valve is opened again, that air remains in the line.  Thus when the actuator closes, it has to overcome a greater pressure in the line than it did initially.  For example, equalizing pressure occurs at 50 psi, then 50 psi must be overcome to close the actuator. On the next cycle, however, the air will still be in the exhaust line and the equalizing pressure when the air supply is removed will be higher, say 60 psi.  Thus as the valve is cycled, it appears that it will eventually reach a state where the air supply pressure will not overcome the pressure in the exhaust line of the actuator.  

If someone could explain how this closed loop system is supposed to work, I would appreciate it.  I am not very experienced in closed-loop valve systems so I may be missing som.

To me it seems that you have an on/off valve that has a spring to close pneumatic actuator.

In closed position the actuator has no air pressure. When you feed 80 psi instrument air to the quick exhaust valve, probably with a solenoid valve, it will direct the air flow to the actuator and the valve will open.
The air on the other side of the flapper is pushed out.

At this moment you have 80 psi on both sides of the quick exhaust membrane.

The moment you switch the solenoid valve the supply line will go to 0 psi and the quick exhaust will trip. All instrument air in the actuator is relieved at the quick exhaust valve. The springs will force the actuator to close completely. The back side of the flapper will suck in fresh air from the outside.

I do not see how you can vent air back into the actuator while closing the main valve.

And you may have a closed loop purge in the actuator air system.  This is very common offshore to avoid salt laden air from entering the actuator.  Often the exhaust includes a pilot valve with a check valve to the atmosphere.  The solenoid valve is not connected to the actuator, instead activates the pilot valve.  In one case the pilot valve applies instrument air to the actuator.  In the trip case the pilot valve blocks the air supply and bleeds the actuator.  The bleed port is also connected to the vent side of the pilot valve so that the instrument air bleed fills the cylinder instead of salt sea air.  Perhaps you can find a typical example at the engineering toolkit site or via a search.

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