rupture disk equations

EQUATIONS IN ANY CONSISTENT UNITS

Mass Flow rate, any consistent units:

Volumetric Flow rate, any consistent units:

For liquids that are more viscous than water, a correction factorcan be applied that is found as follows. First calculate theuncorrected area. Then, using the area of the next largerstandard disk size, calculate the Reynolds number:

Find the correction factor from Figure A. Then divide theoriginal uncor-rected area by this factor. If the liquid is soviscous that the Reynolds number is not on the graph, you mayconsult OSECO for evaluation. Please also note the limits onReynolds Number shown in Figure A. A curve fitted equation forthis correction is also presented in Figure A.

REACTION FORCE

Reaction force for mass flow rate, any consistent units:

If the flow rate is given in volumetric rather than mass units,the equa-tions above can be used by substituting (D x Q) for W.For the equations above, the following legend applies:

A - disk areaF - reaction forcegc - the gravitational constantK - discharge coefficient (ASME permits 0.62): - dynamic or absolute viscosityP - pressure drop across the diskD - fluid densityQ - volumetric flow rate W - mass flow rate

EQUATIONS IN CONVENTIONAL U.S. UNITS

Mass flow rate, conventional U.S. units:

Volumetric flow rate, conventional U.S. units:

For liquids that are more viscous than water (viscosity greaterthan 1 cp), a correction factor can be found using the proceduredetailed under "EQUA-TIONS IN ANY CONSISTENT SET OF UNITS" above. The Reynolds number can be calculated from:

Reaction force for mass flow rate, conventional U.S. units:

For conventional U.S. units in the above equations, the followingapplies: A - square inches F - pounds K - 0.62 per the ASME Code (included in equation constant) W - pounds per hour Q - gallons per minute D - pounds per cubic foot : - centipoise P - pounds per square inch

For discharge coefficients K other than 0.62, multiply A ascalculated above by 0.62/K. To use specific gravity of theliquid rather than density, sub-stitute 62.37 x specific gravityfor density D in either of the above equations.

EQUATIONS IN METRIC UNITS

Mass flow rate, metric units:

Volumetric flow rate, metric units:

For liquids that are more viscous than water (viscosity greaterthan 1x10-3 Pa-sec), a correction factor can be found using theprocedure detailed under "EQUATIONS IN ANY CONSISTENT SET OFUNITS" above. The Reynolds number can be calculated from:

Reaction force for mass flow rate, metric units:

For metric units in the equations above, the following applies: A - square millimeters F - Newtons K - 0.62 per the ASME Code (included in equation constant) W - kilograms per hour Q - cubic meters per second D - kilograms per cubic meter : - Pa-sec (kg/m-sec) P - bars

For discharge coefficients K other than 0.62, multiply A ascalculated above by 0.62/K.

GASES AND VAPORS

Flow of a gas or vapor through a ruptured disk will be at sonicvelocity if the ratio of outlet to inlet pressure is sufficientlylow. As a rule of thumb, this will occur if the inlet pressureexceeds 15 psig and the relief device vents to atmosphere.

From an analytical standpoint, sonic flow will occur when theratio of out-let to inlet absolute pressures P2/P1 is less thanor equal to the critical pressure ratio rc, defined by:

For this equation: k - ratio of specific heat at constant pressure to specificheat at constant volume (Cp/Cv)

Subsonic flow will occur when P2/P1 is greater than rc.

The equations for gas or vapor flow shown below are the same foreither so-nic or subsonic flow except for the evaluation of thegas flow constant C included in the equations. Definition ofthis constant is shown below.

EQUATIONS IN ANY CONSISTENT SET OF UNITS

Mass flow rate, any consistent units:

Volumetric flow rate, actual conditions, any consistentunits:Volumetric flow rate, standard conditions, any consistentunits:

For sonic flow (P2/P1 < rc), the gas flow constant C is given by

For subsonic flow (P2/P1 > rc),Reaction force for sonic flow, anyconsistent units:

If flow is subsonic, the reaction force will be less than thevalue given by this equation.

For the equations shown above, the following legend applies:

A - disk area F - reaction force gc - gravitational constant

K - 0.62 per ASME Codek - ratio of specific heats

M - molecular weightP - inlet pressure, gauge valueP1 - inlet pressure, absolute valueP2 - outlet pressure, absolute valueR* - Universal Gas Constant,T - temperature, absolute value VA - volumetric flow rate, actual conditionsVS - volumetric flow rate, standard conditionsW - mass flow rateZ - compressibility factor

EQUATIONS IN CONVENTIONAL U.S. UNITS

Mass flow rate, conventional U.S. units:

Volumetric flow rate, actual conditions, conventional U.S. units:

Volumetric flow rate, standard conditions, conventional U.S.units:

For the above equations, the following applies: A - square inches W - pounds per hour VA - actual cubic feet per minute VS - standard cubic feet per minute (14.7 psia at 60

oF) K - 0.62 per the ASME Code (included in equation constant) P1 - pounds per square inch absolute T - oR (degrees Rankine)

If the compressibility factor Z is not known, Figure B can beutilized to determine this factor. Using Z = 1.0 is frequentlydone when there is insufficient data to determine the value of Z. If the specific gravity of the gas (relative to air at standardconditions) is known but the molecular weight is not known,substitute 28.964 x specific gravity for M in the equation forstandard conditions.

For sonic flow (P2/P1 < rc), the gas flow constant C changes tothe equation below :

For subsonic flow, (P2/P1 > rc), changes to the equation below:

Reaction force for sonic flow, conventional U.S. units:

In the equation immediately above: F - poundf

If flow is subsonic, the value given by this equation will be anupper limit of the reaction force.

EQUATIONS IN METRIC UNITS

Mass flow rate, metric units:

Volumetric flow rate, actual conditions, metric units:

Volumetric flow rate, standard conditions, metric units:

For the above equations, the following legend applies:

A - square millimeters W - kilograms per hour VA - actual cubic meters per second VS - standard cubic meters per second (1 bar absolute at15oC) K - 0.62 per the ASME Code (included in equation constant) P1 - bars absolute T - oK (degrees Kelvin)

For sonic flow (P2/P1 < rc), the gas flow constant C is given by:

For subsonic flow (P2/P1 > rc), C changes to the equation below:

Reaction force for sonic flow, metric units:

In the equation immediately above: F - Newtons

If flow is subsonic, the value given by this equation will be anupper limit to the reaction force.

STEAM

EQUATIONS IN CONVENTIONAL U.S. UNITS (Sonic flow, P2/P1 less than 0.55.)

Superheated steam (Napier's empirical equation):

Dry saturated steam, pressures up to 1500 psig:

Dry saturated steam, pressures between 1500 and 3200 psig:

Wet steam:

For the above equations, the following applies: A - square inches W - pounds per hour )T - degrees of superheat - oF (degrees Fahrenheit) K - 0.62 per the ASME Code P1 - inlet pressure - psia )X - (100 - % steam quality)

The reaction force for steam discharge can be found by using theequation for gases and vapors with k = 1.33 .

EQUATIONS IN METRIC UNITS (Sonic flow, P2/P1 less than 0.55.)

Superheated steam (Napier's empirical equation):

Dry saturated steam, pressures up to 102 bar:

Dry saturated steam, pressures between 102 and 220 bar:

Wet steam:

For the above equations, the following applies:

A - square millimeters W - kilograms per hour )T - degrees of superheat in oC (degrees Celsius orCentigrade) K - 0.62 per ASME Code P1 - inlet pressure - bar absolute )X - (100 - % steam quality)

EXAMPLE 1, LIQUIDS

Determine the rupture disk size required for relieving thefollowing conditions:

Vessel MAWP 45 psigFlow Requirement 1500 gallons per minuteBack Pressure 5 psigSpecific Gravity 0.85Application Primary Relief

Use 10% over-pressure as permitted by ASME code. Volumetric flowrate, conventional U.S. units:

Using discharge areas in Table B, the required nominal disk sizeis 4 inch for a STD or CO type rupture disk and a 3 inch FAS orPCR type rupture disk.

EXAMPLE 2, GASES

Determine the rupture disk size required for relieving thefollowing conditions:

Vessel MAWP 150 psigFlow Requirement 5000 actual cubic feet per minuteBack Pressure 20 psigFlow Temperature 250oF (degrees Fahrenheit)Flow Media Air (M = 29, k = 1.4, use Z = 1)Application Primary Relief

Use 10% over-pressure as permitted by ASME code. Flow pressureratio:

Critical pressure ratio:

P2/P1 is less than rc, therefore the flow will be sonic. Forconventional U.S. units:

Given the required flow in actual cubic feet per minute:


EXAMPLE 3, GASESDetermine the rupture disk size required for relieving thefollowing conditions:

Vessel MAWP 15 psigFlow Requirement 2000 standard CFMBack Pressure 5 psigFlow Temperature -40oF (degrees Fahrenheit)Media Specific Gravity 0.72

Specific Heat Ratio 1.26 Compressibility Factor 0.95

Application Primary Relief

In this case 10% of gauge pressure is less than 3 psi, therefore3 psi over-pressure is permitted by ASME code. Flow pressureratio:

Critical pressure ratio:

P2/P1 is greater than rc, therefore the flow will be subsonic. For conventional U.S. units:

Given the required flow in standard cubic feet per minute:


rupture disk equations

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