Chemical & Process Technology: A refresh to Process Engineer on few phenomenons in restriction orifice

Friday, December 21, 2007

A refresh to Process Engineer on few phenomenons in restriction orifice

Restriction orifice is widely used to in Oil and Gas, Refinery and Petrochemical chemical plant. Make a simple search on internet, you may find plenty of articles related to functionality, calculation and specification of restriction orifice. The intention in this post is not to repeat what others has discussed in details but as a refresher to those who already knew about it and inform those who still unclear or misunderstood about restriction orifice.

What is restriction orifice ?
I have asked above question to young engineer with 2-3 years experience. The answer given by some of them were ”To reduce pressure drop like control valve but with fixed opening”. It sounded correct. Fluid passing restriction orifice with fixed opening and involve pressure drop across it. In my opinion, this is a misconception on functionality. Restriction orifice is used to limit flow to required or expected flowrate with the available differential pressure across.

How restriction orifice works ?
A fluid passing a fixed opening in restriction orifice, the fluid streamline will converge and squeeze through the opening. As it pass the opening, the momentum will keep it continue converge for short distance and diverge as the momentum is lost. The smallest cross sectional area between convergence and divergence is the well known vena contracta (VC). The velocity at VC is at maximum due to minimum cross sectional area for flow. Base on Bernoulli theorem, the pressure at VC is lowest.

As fluid passing the restriction orifice, converging towards vena contracta and diverge once it pass VC results two observations. Velocity is increased till maximum at VC and decreased after it passed VC. On the other hand, pressure is decreased till minimum at VC and increased to downstream pressure (backpressure). The increased pressure from VC is called pressure recovery.

NON-Choked flow vs Choked Flow
When the differential pressure (dP) between restriction orifice upstream and downstream is low, the driving force to put fluid passing the restriction flow is low. The velocity at VC is rather low and far below sonic velocity. This flowing condition is normally known as Non-Choke Flow. As downstream pressure (Pd) is decreased, this increased the differential pressure (dP). Higher driving force will push more fluid passing the opening and velocity at VC is increase as well. The downstream pressure will decrease until a pressure where velocity at VC is at Sonic velocity (Mach no=1), the downstream pressure is called Critical pressure (Pc) and the flowing condition is called Choked flow. Further decrease in downstream pressure will NOT affect the flow rate passing the restriction orifice as the velocity at VC already at it maximum (Ma=1).

Critical pressure
Critical pressure can be estimated based on absolute upstream pressure

where k is the specific heat ratio

Should flowrate increase if upstream pressure is increased at choked flow ?
As upstream pressure is increased, the fluid density will increase accordingly. It will reduce velocity at VC and more mass is allowed to pass through the restriction orifice. Thus, increase in upstream pressure will increase mass flow passing the restriction orifice but velocity at VC still maintaining at Ma=1.

Example
A pipe with a hole is a typical example of choked flow condition. The pipe internal pressure (Pu) is releasing gas to atmosphere. As the atmospheric pressure is lower than the critical pressure, it is a choked flow condition.

Now connect a small pipe to pipe at hole. There is frictional head loss on the small pipe, thus the pressure at the outlet of hole (or backpressure to hole) is total of frictional pressure lose plus atmospheric pressure. Nevertheless, the back pressure to hole is still below critical pressure, those there is no impact to flowrate.

If the pipe length of small pipe is increased, back pressure to hole will increase as well. It will increase upto the critical pressure of the fluid. Now, it is at the limit of choked flow. Further increased in back pressure will put the system in non-choked flow condition and flowrate will start to drop.

Above typically answer why choked flow is always occurred and flow rate is maintained constant although flare backpressure fluctuate (with condition below critical pressure).

Summary
There are some 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 at choked condition called critical pressure.
Increase in upstream pressure will increase mass flow passing the restriction orifice but velocity at VC still maintaining at Ma=1

4 Comments:

Anonymous said...: There is an error in the equation to calculate the Critical Flow Pressure. The correct equation is as given in API 520:

Pc = Pu [2/(k+1)] raised to power (k/k-1); January 2, 2008 at 7:45 AM
Webworm said...: Hi,
Thanks. Checked and updated.; January 2, 2008 at 7:50 AM
Anonymous said...: When the fluid is steam and the RO is a sharp edge orifice, there is not critical pressure.; November 17, 2008 at 10:04 AM
Webworm said...: "When the fluid is steam and the RO is a sharp edge orifice, there is not critical pressure."

Thanks for input.

If you can elaborate more or cites the references, that will be great !; November 17, 2008 at 1:22 PM