Rankin Chemical Technologies, Inc.
engineering · consulting · process design

Two-Phase Relief Dynamic Analysis Example

Time-dependent analysis of a two-phase flow relief event is needed to properly estimate required relief flow area, because the amount of vapor that is vented at the onset of two-phase flow is likely to be quite small relative to the total mass vent rate.  Because of this phenomenon, the pressure may rise above the allowable limits set forth by the ASME Code, even though the mass being vented is quite large.

To properly assess the pressure response over time, a mass and energy balance is created around the vessel and evaluated at sufficiently small time intervals.  As material (vapor and liquid) is removed through the PRD vent, the total volume lost must be replaced by vapor in order for the pressure to remain constant.  If an excess of vapor is generated during this time interval, the pressure will rise.  Some of the heat exchanged during the overpressure scenario is absorbed by the liquid as sensible heat, while the remainder is used to generate vapor.

In the process heating failure example cited here, dynamic analysis of the indicated two-phase relief event was performed.  It was assumed that throughout the event non-condensable gases were not generated as a result of chemical reaction.

Dynamic Analysis Response Graphs

Looking at the above graph, maximum pressure is reached at approximately 530 seconds after the initiation of relief, and complete disengagement to all-vapor flow occurs after 570 seconds.  Accumulated pressure inside the vessel reaches a maximum of 172 psig, or almost 15% above MAWP.  As this scenario per ASME Code has a maximum allowable accumulation of 10%, the PRD is undersized for two-phase flow.

Due to the foamy nature of the liquid mixture, vapor quality (mass fraction of vapor in the two-phase stream) is low during the onset of relief, even at the PRD nozzle inlet.  As venting continues and the liquid level drops, the quality gradually rises until complete disengagement occurs, at which point the flow becomes all vapor.

The Omega Parameter, widely used in the application of the DIERS Homogeneous Equilibrium Model (HEM), is shown to decrease to near unity at disengagement.


The existing 3-L-4 relief valve in this example is adequately sized for all-vapor flows, but does not provide sufficient protection during a two-phase flow event.  In fact, pressure accumulates to 15% above the vessel MAWP.  Evaluating the system with different relief valve sizes showed that a 4x6 valve with an "N" orifice was required to limit the accumulated pressure to below 10% per the ASME Code.

A new pressure response of the recommended 4-N-6 valve is shown below:

Vessel Pressure Response - Improved

As seen in the revised response graph above, pressure in the vessel accumulates to just 8.7% above MAWP, which is below the limit of 10% set forth by the ASME Code.  With this larger valve installed, the modeling indicates that if the process upset is allowed to continue unmitigated, almost 1,500 lbs of liquid would be expelled at the tailpipe discharge until disengagement to all-vapor flow.  Therefore, containment of the hot liquid (e.g. with a knockout pot/separator) becomes a potential safety consideration.


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