I will also add that chatter is more likely where the fluid is of non compressible nature, ie., liquid. Also, chatter is caused by various other factors or a combination of them. Besides an oversized PRV, chatter can be caused by long inlet piping causing inlet pressure drops, inlet piping that has flow diameter smaller than the PRV inlet size, high back pressure, varying flow rates, incorrect installation, etc., etc,. Also the design of PRV used affects performance. a modulating pilot operated pressure relief valve can be a solution. but not always. Most common PRV chatter is caused by oversized PRV selections and inlet pressure drops.
PS: I future, Please post PRV related questions in the specifica Safety/Relief Valve Forum. Thanks.
Per ISO-4126, only the term Safety Valve is used regardless of application or design.