The couling equation is a DIERS methodology that allows the user to change the flow regime model from homogeneous to a less conservative model such as bubbly, churn-turbulent or any user define flow regime. These less conservative flow regime models predict a two-phase flow based on the assumption of vapor-liquid disengagement between the vessel and the relief nozzle. The selection of an appropriate model application to a given stem requires judgment augmented by empirical data.
While much progress was made in providing effective models for complex multiphase behavior in process vessels, practical utilization has been limited. Identification of complex chemically reacting systems as churn-turbulent or viscous-bubbly or any other flow model is not possible on the basis of readily available physical property data. For this reason a large segment of the users of the DIERS methodologies make the "conservative", default assumption of homogeneous (no vapor-liquid disengagement) vessel behavior.
For many reacting systems, this assumption is not overly conservation because of the limited disengagement actually observed. For other systems, particular gas generating decomposition reactions with limited volatility, the results of this assumption can lead to a large impractical vent size. In other specialized instances, the assumption of homogeneous behavior is not conservation. Hence, their remains an incentive to utilize explicit vapor-disengagement, however limited, is present in all venting processes. (Harold Fisher Vapor-Liquid Onset/Disengagement Modeling for Emergency Relief Discharge Evaluation).
Also reference the DIERS Project Manual download coupling equation section
Coupling Equation Bubbly Flow Regime (Input Data)
From the Mach II Basic Data Tab, select "Main", from bottom left corner to enter data for the coupling equation. First select "Rating Mode", for flow regime select "bubbly", the value of epsilon will pre-load based on the flow regime selected, enter the standard orifice size of 6.38 in2 ,that was calculated based on homogeneous design. The API should already be selected. For this case we will perform the typical "equilibrium", and no slip model For calculation type, choose "Fire", and enter the relieving pressure, heat of vaporization, and two-phase relieving rate from fire.
Vessel Data Tab
From the "Main" data tab, select "Vessel", from the bottom left of screen, now enter the vessel data. If you choose to transfer from "two-phase" and "vessel calculator" you will need to rerun the two-phase making sure you transfer data from single-phase to insure you still have the correct data.