How to Increase Mass Flow Across RO When Choked Flow Already Occured ?

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Restriction orifice (RO) is widely used to in Oil and Gas, Refinery and Petrochemical chemical plant. Simple search on internet lead you to plenty of articles related to functionality, calculation and specification of restriction orifice. "Restrcition Orifice Used in Many Applications in Different Manners" brought out a few applications of RO in the industries. Earlier post "A refresh to Process Engineer on few phenomenons in restriction orifice" has summarized a few concepts that a process engineer may needs to understand for restriction orifice :

• Restriction orifice is used to limit flow to required or expected flowrate with the available differential pressure across.
• Vena contracta (VC) present just short distance downstream of restriction orifice
• Maximum velocity and minimum pressure at vena contracta (VC)
• Choked flow occurred when velocity at vena contracta (VC) reach sonic velocity (Ma=1). The corresponding downstream pressure (P2) at choked condition called critical pressure (Pc).
• Increase in upstream pressure (P1) will increase mass flow passing the restriction orifice but velocity at VC still maintaining at Ma=1

A young engineer asked... If compressible fluid composition and upstream pressure are fixed and choked flow already occurred, should there be other way to increase the mass flow passing the RO ?

For compressible fluid, mass flow passing through an fixed bore size RO is a function of

1. composition ( k, MW, ...)
2. driving force (Differential pressure) across RO (P1-P2)
3. density (function of P1, MW, z, T1)
   

If composition and upstream pressure (P1) are fixed,

1. composition (and therefore k, MW...) remain unchanged
2. reducing P2 lead to higher P1-P2 which will result higher mass flow passing RO. Mass flow increase will continue until until P2 reach critical pressure of fluid (Pc). Sonic velocity (Mach no =1) occurred at vena contrata, some distance downstream of RO. When P2 lower than Pc, further reduction of P2 will not result any mass flow increase.
3. reduce upstream temperature (T1) will results higher density and higher mass flow passing RO.
   

Thus, one of the way to increase mass flow through RO when gas composition and upstream pressure are fixed and choked flow already occurred is dropping upstream temperature (T1).

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