I don't understand the control function. You say one valve is monitoring and the other is throttling.
Monitoring what? Upstream Pressure, Downstream Pressure, Differential Pressure, or Flow? Is it throttling to maintain a constant flow, or constant upstream pressure, or constant downstream pressure?
If the control function is put on standby, opening the other set of valves could have one of several effects.
You can't look at a system as some independently functioning valves without knowing how extra flow will affect the upstream or downstream piping. You need to know how the upstream system capacity relates to the downstream system capacity with any given change in flow.
If there is excess capacity downstream to carry away the extra flow, change may be small. But...
If the Downstream System Packs
If the extra flow packs up the downstream system, pressure throughout the system will tend to increase.
1.) If the valves are set to control downstream pressure, they will begin to close and reduce flow to keep the downstream pressures from building, which will tend to raise upstream pressure.
2.) If the valves are set to control upstream pressure, they will begin to open so as to keep the tendency of the system pressure to increase from increasing that upstream pressure.
3.) If they are set to hold constant flow, they will begin to open more. They would have to now that the downstream pressure is going higher. That would pack the downstream piping even more and possibly eventually reaching the capacity of the downstream system, at which point the downstream and upstream pressure will begin to increase. Eventually the valve would open all the way and system pressure would begin increasing everywhere.
Upstream System Evacuates
If the upstream system can supply the extra flow without reducing pressure, change may be small. If the increasing flow tends to evacuate the upstream piping and reduce pressure upstream of the valves, the upstream pressure, and the pressue in the whold system will tend to fall.
1.) If the valves are set to hold downstream pressure, they will begin opening to try to hold downstream pressure. If they can't when full open, the upstream pressure will fall as well.
2.) If the valves are set to hold upstream pressure, they will begin closing to try to hold upstream pressure. If they can't, then they will continue closing until they are fully closed and pressure is held.
3.) If the valves are set to hold flow, they will try to open, either reaching downstream system capacity and holding upstream pressure, or continuing to open and reducing upstream pressure in the process. Possibly, as they continue to open, reducing upstream pressure to the point where that matches downstream pressure.
Valves are part of the piping system. You can't tell what the valves will do, unless you know how the upstream capacity relates to the downstream capacity. It's like trying to figure out where your pump will operate by ignoring the system curve and only looking at the pump curve. That only works on the test bench.
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