For selection of ESD valve actuator supply, what are factors that decide whether ESD valve shall be hydraulic or pneumatic?  What are advantages of Hydraulic valves?

Both fluids are utilized, and also with a third variant 'gas over oil' combined to give an assured oil pressure.

Different solutions are used, depending on a number of factors. One important factor is of course the cheapest commercial solution available ('common practice for size, process fluid (not actuator fluid), pressure class, valve type, size, speed of closure, and branch/application)

No firm rules can in my mind be set down, but you will find firm opinions if you start with an exact application and process type.

Some general tendencies (not firm rules) can be put down:

Smaller valves(Safety valves), air used elswhere -> air
Larger valves, hydraulic used elsewhere -> hydraulic
Faster movement -> air or fallweight closed hydraulic cylinders if larger valvetypes.
Slower or controlled movement -> trotteled air or better controlled (perhaps) hydraulic.
Valves on hydraulic operated machines -> hydraulic
Submerged -> hydraulic
Valves remote from electricity or sources for common air or oil hydraulics -> electric, battery backed, or handpumped hydraulics or battery backed electric. More seldom air.

ESDV service actuation is "where at all possible" pneumatic.
The main reasons are fast exhaust of air = fast stroke, exhaust into atmosphere eliminates a discharge line back into a reservuoir (and possible back pressure/choking of exhaust).
Where extreme torque/thrust values are expected from actuator generally Hydraulic type is used, but when this is not available HPG actuators are used (High Pressure Gas) with pre-charged "power packs" at 180 or 220 Barg, reduced to around 65 Barg supply to actuators.
If you give exact details of where these are to be used, I can give precise information on possible solutions.

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