Homogeneous equilibrium model HEM

Homogeneous Equilibrium Model (HEM) assumes uniform mixing of the phases across the. pipe diameter, no phase slip (mechanical equilibrium), thermal equilibrium between, the..phases and complete vapour/ liquid, equilibrium. Homogenous in the context of the HEM refers to the flow in the vent line. 

DIERS[11 recommend the use of the HEM for relief sizing purposes, because  

The HEM method will tend, if anything, to underestimate the relief flow capacity and so to oversize relief systems. This is provided the upstream conditions have been correctly specified (see 9.3.3). Another possible exception to the HEM tending to underestimate flow is when there is a large upwards static head change (equivalent to greater than about 10% of the pressure in the reactor), in which case a slip flow model could be more conservative. 

Care should be taken when using the HEM to size downstream disposal equipment. It may result in the flow rate being underestimated and the disposal system being undersized. It may be better to use a slip flow model in such cases. An alternative approach would be the application of an appropriate safety factor to a flow rate calculated using the HEM (see 7.2 (b)). 

This matters most when designing a disposal system, when it is important that the back pressure exerted by flow through the disposal system does not reduce G. It may be prudent to ensure that the back pressure is at least less than 50% of the upstream reactor pressure to ensure that choking in the relief system is maintained. For safety valve systems, lower back pressures may be necessary, even for balanced valves, see 9.7.3.  

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For two-phase flow through pipes, an overall dimensionless dis-eharge eoeffieient, /, is applied. Equation 12-11 is referred to as the equilibrium rate model (ERM) for low-quality ehoked flow. Leung [28] indieated that Equation 12-11 be multiplied by a faetor of 0.9 to bring the value in line with the elassie homogeneous equilibrium model (HEM). Equation 12-11 then beeomes... 

Two-phase flow models allow the calculation of both the two-phase mass flow rate per unit area (G) and also the critical pressure for choking. DIERS recommend the homogeneous equilibrium model (HEM, see 9.4.1) for this calculation. 

A discussion of the different types of assumption that can be made in two-phase flow models is given in Chapter 9. DIERS[8] recommended the use of the homogeneous equilibrium model (HEM) for relief sizing, and so, preferably, a code which implements the HEM should be chosen. The model will need to incorporate sufficiently non-ideal modelling of physical properties and provision for multiple line diameters and potential choke points, as required by the application. 

If the puncture occurs on a pipe which is at least 0.5 m from a vessel, it is justifiable to use a homogeneous equilibrium model (HEM) for which an analytical solution is available. The discharge rate pre-... 

In homogeneous equilibrium model (HEM) the velocity, temperature, and pressure between the phases or components are assumed equal. The two phases exit at the saturation temperature for the prevailing pressure. The mixture is treated as a single fluid. This model is particularly useful for high pressure and high flow rate conditions. The HEM governing equations, such as mass, momentum, and energy, resemble those for a pseudo-fluid with mixture properties and an equation of state which links the phases... 

In the calculation meshes with the two-phase condition, the homogeneous equilibrium model (HEM) is applied to the mass, momentum, and energy conservation equations. The following heat transfer correlations are used by referring to RELAP4 [13]. 

Assumption (f) of isothermal flow means that the method is different to the homogeneous equilibrium model (which assumes adiabatic flow). The difference between the two assumptions is usually small. The isothermal flow assumption gives a slightly simpler method and yields a conservative low value of G for relief sizing purposes. The DIERS Project Manual1111 gives the alternative version of Tangren et al/s method, which assumes adiabatic flow and is therefore equivalent to the HEM. 

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