Chemical & Process Technology: Suspicious Discrepancy In Supercritical Fluid Relieving Calculation

Sunday, April 4, 2010

Suspicious Discrepancy In Supercritical Fluid Relieving Calculation

Pressurized liquid or vapor-liquid in equilibrium or vapor only system during normal operation, when it is expose to external fire attack, heat inputs into vessel (or system) may possibly increase internal pressure and temperature. For system with high design pressure (or Maximum allowable working pressure, MAWP), the pressure relief valve (PRV) protecting the vessel (or system) may have same set pressure as the design pressure (or MAWP). Subject to design code of the vessel, overpressure allowed by code is different from code to code. Typically for ASME unfired vessel section VIII, the maximum allowable overpressure is 10% of set pressure. This will results maximum allowable accumulation pressure (or relieving pressure) reach at 110% of set pressure.

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In some event, the relieving pressure is higher than the fluid critical pressure. For example, a CO2 injection compressor, the injection pressure at is 65 barg. The design pressure may be 72 barg and relieving pressure is approximately 79.2 barg, is higher than CO2 critical pressure of 72.9 barg. The PRV is relieving at supercritical condition.

Conventional method in determining PRV orifice size is presented in API RP-521. Part 1. It considered all “un-wetted” vessels are same regardless the fluid is supercritical, a vapor or a gas. Nevertheless, one shall take note that this method based on the physical properties of air and the perfect gas laws with no change in fluid temperature.

Supercritical fluid may not follow perfect gas law
Low compressibility of supercritical fluid (e.g. 0.5 to 0.7)
Change in fluid temperature during relieving

API method may be conservative, there are chattering and oversized PRV and discharge problem. A rigorous method has been discussed by R.C. DOANE in "Designing for pressure safety valves in supercritical service" published in Hydrocarbon Processing Jan 2010. This method assuming all thermodynamic paths are well defined by a Process Simulator. Thermodynamic path of fluid from operating condition to relieving and drop to back pressure to PRV may be defined by four typical steps.

Constant Specific Volume path (Initial to Relieving)
Constant Pressure path (Extended relieving)
Constant Entropy path (PRV relieving path)

For Step 1, earlier post "Constant Density To Obtain Relieving Condition" has discussed similar subject previously.

For the step 3, another definition of PRV relieving path can be Isentalpic from relieving to throat follow by isentropic from throat to PRV backpressure as discussed in "Discussion on ISENTROPIC and ISENTHALPIC process via Relief Valve".

In the "Designing for pressure safety valves in supercritical service" article, table 1 "Supercritical relief valve sizing example problem—normal butane" has tabulated step-by-step calculation. This table has incorporated equation 1 to equation 10 in this article. The calculation consist of segment 1-to-2, 2-to-3, 3-to-4 and 4-to-5. In recent work in establishing similar task carried out by this example, one suspicious discrepancy is identified. Details as follow.

From segment 1-to-2 to segment 4-to-5, volumetric flow is increased from 1304 ft3/hr to 1315 ft3/hr (segment 2-to-3) and decreased in subsequent segments to 1250 ft3/hr. The volumetric flow is in the range of 1250 to 1315 ft3/hr. HOWEVER, mass flow is increased almost double from 6,374 lb/hr to 13,405 lb/hr (segment 2-to-3) and decreased in similar range (11620 to 12,371 lb/hr). Why there is significant different in segment 1-to-2 compare to other segment ?

Detail checking found that Mass Flux (G in lb/ft2s) is calculated by dividing Orifice Velocity (v) by Specific Volume (V) at orifice condition for segment 1-to-2. On the other hand, Mass Flux (G in lb/ft2s) is calculated by dividing Orifice Velocity (V) by Specific Volume (V) at outlet condition for other segments. Different method in calculating Mass Flux has created the discrepancy.

Opinion

As the flow is choked (or highest velocity for subsonic) at the PRV nozzle, Mass Flux (G in lb/ft2s) should be calculated by dividing Orifice Velocity (v) by Specific Volume (V) at orifice condition.

Well... Above query will be raised and response will be posted once we have received it.