Prvs 4b. sizing - fluid characteristics at discharge conditions

1. PRV Sizing - Fluid
charact. at disch. condit.
Presented by
David Alexandre

2. Definitions
PRV Sizing – Fluid characteristics at discharge conditions

3. Definition
▪ Critical point
▪ a critical point, also known as a critical state, occurs under conditions (such as specific values of temperature, pressure or
composition) at which no phase boundaries exist. There are multiple types of critical points, including vapour–liquid critical
points and liquid–liquid critical points
▪ Supercritical fluid
▪ A supercritical fluid is any substance at a temperature and pressure above its critical point, where distinct liquid and gas
phases do not exist. For instance, steam above 220 barg is supercritical.
▪ Sub-cooled liquid
▪ fluid under mechanical and or thermodynamic conditions that force it to be a liquid. It is a liquid at a temperature lower than
the saturation temperature at a given pressure
▪ Highly sub-cooled liquid
▪ To reinforce that the liquid does not flash when decompressed (passing through the PRV).
▪ Saturated fluid
▪ Saturated liquid (water): A saturated liquid contains as much thermal energy as it can without boiling
▪ Saturated vapour (steam): a saturated vapour contains as little thermal energy as it can without condensing
▪ Sub-saturated fluid
▪ At any pressure, liquid below its saturation temperature is said to be in a sub saturated state.
▪ For instance: water, P=1 atm then T < 100°C or P= 10 atm then T< 180°C
▪ Non-condensable gas
▪ A non-condensable gas is a gas that is not easily condensed under normal process conditions. Common non-condensable
gases include air, oxygen, nitrogen, hydrogen, carbon dioxide, carbon monoxide and hydrogen sulfide.
PRV Sizing – Fluid charact. at discharge conditions

4. Definition
▪ Entropy
▪ Entropy is a measure of disorder or also a measure of progressing towards thermodynamic equilibrium.
▪ Expression is S = Q/T (Heat transfer Q at a certain temperature T)
▪ Isentropic process
▪ Said also Isoentropic (ISO means equal in Greek)
▪ The entropy of the system remains constant
▪ Isentropic nozzle flux
▪ General expression used for any homogeneous fluid provided the relationship of fluid density to pressure at constant
entropy is known
PRV Sizing – Fluid charact. at discharge conditions

5. Alternative sizing methods
PRV Sizing – Fluid characteristics at discharge conditions

6. Alternative sizing methods
▪ API STD 520 - Appendix B (2008)
▪ Review of flow equations used in sizing pressure relief devices.
▪ Provide theoretical foundation that are used in the development of the sizing equations provided in the main body of the
API STD 520 (usual sizing equations, for ideal gas specific heat (estimate for the isentropic expansion coefficient).
▪ Provide sizing techniques that could be used in situations where the assumptions made to develop the sizing equations
are not appropriate.
▪ Provide isentropic nozzle flux equations for homogeneous fluids.
▪ API STD 520 - Appendix C (2008)
▪ Sizing for two-phase liquid/vapour relief
▪ The isentropic nozzle flux equation is also used in the development of the two-phase flow sizing equations.
PRV Sizing – Fluid charact. at discharge conditions

7. Alternative sizing methods
▪ API STD 520 - Appendix B (2008)
▪ W = G.A.π[K]
Where
▪ G is the theoretical mass flux through the nozzle, Ib/s·tt2 (kg/s·m2);
▪ W is the mass flow through the PRV, Ib/s (kg/s);
▪ A is the effective discharge area of the PRY, tt2 (m2);
▪ π[K] is the product of all applicable correction factors (no units).
▪ G is an expression (formula) of
▪ v is the specific volume of the fluid, ft3/1b (m3/kg);
▪ p is the mass density of the fluid, Ib/ft3 (kg/m3);
▪ P is the stagnation pressure of the fluid, psia (Pa);
▪ l is the fluid condition at the inlet to the nozzle;
▪ j is the fluid condition at the throat of the nozzle where the cross-sectional area is minimized.
PRV Sizing – Fluid charact. at discharge conditions

8. 8
PRV Sizing – Fluid charact. at discharge conditions
Alternative sizing methods
▪ Appendix C – two-phase liquid / vapour relief scenarios for PRVs.
Scenario Example
Section of API STD 520
Appendix C
(2008)
Former
Appendix D
(2000)
Two phase system (liquid vapour mixtures,
including saturated liquid) enters PRV and
flashes. No non-condensable a gas present. Also
includes fluids both above and below the
thermodynamic critical point in condensing two-
phase flow.
Saturated liquid/vapour propane system enters
PRV and the liquid propane flashes.
C.2.1 or C.2.2 D.2.1
Two-phase system (highly sub-cooled liquid and
either non-condensable gas, condensable vapour
or both) enters PRV and does not flash.
Highly sub-cooled propane and
nitrogen enters PRV and propane does not
flash.
C.2.1 or C.2.2 D.2.1
Two-phase system (the vapour at the inlet
contains some non-condensable gas and the
liquid is either saturated or sub-cooled) enters
PRV and flashes. Non-condensable gas enters
PRV.
Saturated liquid/vapour propane system and
nitrogen enters PRV and the liquid propane
flashes.
C.2.1 or C.2.2 D.2.3
Sub-cooled liquid (including saturated liquid)
enters PRV and flashes. No condensable vapour
or non-condensable gas enters PRV.
Sub-cooled propane enters PRV and flashes. C.2.1 or C.2.3 D.2.2

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