Tedious & Simple Method In Determining Specific volume For Isentropic Nozzle Flow Mass Flux

Earlier post "API Std 520 Part 1 Dec 2008 is Released" highlighted one of the main  changes was to use of isentropic nozzle flow method and/or ideal gas specific heat ratio for vapor/gas relief flow calculation.

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Isentropic nozzle flow method is considering one dimensional homogeneous flow is limiting in Pressure Relief Valve (PRV) nozzle with isentropic (adiabatic and reversible) expansion across the PRV nozzle. Maximum mass flux across the PRV nozzle will be determined follow by mass flow passing the PRV. In determining the maximum mass flux, an integration of specific volume (v) time differential pressure (dP) is required. This integration involve substantial derivation of specific volume (v) which change with pressure (P). If the system can be modelled in HYSYS, you may consider the following tedious and simplified method in determining the specific volume (v) with varies pressure (P).

Tedious method

The detailed method involve the fluid expanded isentropically across multiple expander with fix differential pressure (dP). Entire model is simulated using HYSYS with Isentropic expansion using Expanders. Stream 1 is the feed to PRV nozzle. Stream 1 is expanded isentropically (polytropic efficiency =100%) to stream 2 with fix differential pressure. Stream 2 is further expanded isentropically to stream 3, Stream 4 is further expanded isentropically to stream 4,.............

Mass density is extracted from each stream in order to use for integration of specific volume (v) time differential pressure (dP). Following is the example of specific volume (Inverse of Mass density).

Simple Method

A simple method is proposed hereafter. It basically utilize the capability of Property Table.

Step 1 : Enter stream 1 and open the Property Table Utility in Attachment tab.

Step 2 :From the Connections tab, select Variable 1 as Pressure with Incremental pressure from Outlet (e.g. 1 barg) to Inlet pressure (e.g. 12 barg).

Step 3 :From the Connections tab, select Variable 2 as Entropy with State mode. Enter the Entropy of Stream 1 here.

Step 4 : In Dep. Prop. tab, Add Mass Density. Now the system is ready for calculation. Click the Calculate button.

Now Mass density change according to pressure (with isentropic expansion) is ready.

Above method can be easily adopted for subcooled flashing, two phase flashing flow across the PRV nozzle.

Do you have better idea ?

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