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T

his article presents the funda-mental concepts of the dischargecoefficient, KD, of a relief valve

or a safety relief valve, and flowresistance factor, KR, of a rupturedisk, and their proper use in sizingan emergency relief system. Whenthese devices are used to protect apressure vessel, they must be certi-fied according to ASME code in theU.S. Both the discharge coefficientand the flow resistance factor are di-mensionless numbers determined bymeasurement and theoretical compu-tation. These factors are prescribedin Performance Test Code (PTC) 25 of

ASME VIII, Division 1.

Discharge coefficientThe discharge coefficient of a relief

valve or safety relief valve is the ratioof the measured relieving capacity ofthe valve to its theoretical relievingcapacity computed by a prescriptivetheoretical equation matching thetest fluid, test pressure, temperatureand flow area of the valve. In thedetermination of the discharge coef-ficient, there is a choice of the test

fluid among steam, air, gas or water.The deviation of the discharge coef-ficient from the value of unity comesfrom the deficiency of either the flowmodel (mass flux through the valveas a function of density and pressure)or the fluid model (density as a func-tion of pressure), or both. Although the

value of the discharge coefficient isnormally less than 1, a value greaterthan 1 indicates either a poor choice ofmodels or erroneous data. Such valuesof discharge coefficients greater thanone should be discarded unless a de-liberate use results in a safer designof the intended equipment.

Flow resistance factor

The flow resistance factor of a disk,KR, is not a ratio of flow or a ratioof resistance, but rather, it is a di-mensionless term that expresses thenumber of velocity heads lost due tothe flow through the rupture disk. Itis the calculated flow resistance fac-tor of the piping system, including thedisk between two pressure taps in thePTC 25 rig using air or gas as the testfluid, minus the calculated flow resis-tance factor of the same piping sys-tem between the same pressure taps

with identical mass flowrate of air, butwithout the disk. The current calcula-tion method of the test code strictlyapplies to those disks whose area isthe same as that of the pipe, but yieldsacceptable flow predictions if the arearatio (minimum net flow area of diskdivided by flow area of pipe) is at least0.8. In the determination of theKR forliquid, the disk is broken with water,followed by testing with air.

The current method of reportingthe flow resistance coefficient in PTC

25, however, ignores the effect of thereduced flow area of some rupture-disk devices. It reports an apparentflow resistance factor that yieldsflow predictions, which differ fromthe true flow resistance factor pre-dictions of the disk, even when ex-pressed in terms of the same velocity.The calculated flow based on the flowresistance factor, as reported cur-rently through PTC 25, is apt to belower than the actual value in caseswith an area ratio lower than 0.8.This makes the best estimate flowfor effluent handling less conserva-tive, an issue that is under consider-

ation of the experts associated with

development of PTC 25.

Combination capacity factorThe combination capacity factor, CCF,applies when the combination of arupture disk and relief valve is used.CCF is the ratio of the measured re-lieving capacity of the combination tothe measured relieving capacity of thepressure relief valve alone.

The combination system of a rup-ture disk and a relief valve is testedin the rig in a closed-coupled position.

Therefore, if the disk of a combinationsystem is separated by a pipe, fittingsor fragments trap, the CCF (even thelower default value of 0.9) becomes in-

valid, and the flow estimation for sta-bility analysis or effluent handling willlikely be under-predicted, even after re-moving the CCF. This is especially truewhen the area ratio is less than 0.8.

The resistance of all the componentsof the line containing the disk shouldbe accounted for in determining thecapacity and stability of a combination

system. In addition, the possibility ofchoking at the disk should be checked.In extreme cases using a fragmentstrap, expert guidance should be soughtif forbidden components, such as whena fragmenting disk is used in a combi-nation system, cannot be avoided.

Table 1 outlines the basis of calcu-lating the flow capacity, pressure loss,and stability analysis of a device sys-tem. Where ASME area and ASMEKDare mentioned as a pair of data set inTable 1, the corresponding API areaand APIKD pair data set for the valvemay be used. Components of this dataset pair must not be mixed up. The

Feature Report

52 ChemiCal engineering www.Che.Com oCtober 2008

Engineering Practice

Dilip DasBayer CropScience

Discharge Coefficients and

Flow Resistance FactorsAn in depth understanding of the ASME code that

describes these terms enables engineers to properly

design pressure relief systems

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use of vessel pressure as the choiceof stagnation pressure is generallyacceptable, whether the device is apressure relief valve, rupture disk or acombination of the two. This is true aslong as the 3% rule for the inlet pres-sure loss is maintained for the relief

valve and combination, and the area

of the rupture disk in a combinationis at least equal to that of the nominalpipe size.

ASME VIII, Division 1Citations from ASME Code VIII, Div. 1are shown in the box on p. 54. Here, wewill explain and expand upon specificsegments of this code.Adjusting KD by the 0.9 factor. Re-moving the 0.9 factor (that is, to divide

ASMEKD by 0.9) as shown in Table 1for pressure loss or stability analysisis a judgment call, practiced by someexperts and widely used in industry,especially for pressure loss analysis.

However, this is neither mandated byASME Section VIII, as seen in Note1, nor by the Guidelines book. ASMESection VIII and the Guidelines book[1c,d] allow pressure loss and stabilityanalysis to be based on the nameplatecapacity (see the definition on p. 55)of the valve, which is in effect the flow

at 10% overpressure times 0.9. Thedanger of removing the 0.9 factor onpressure and stability analysis is thatit may lead to the selection of larger

valves with a much higher instanta-neous capacity. This will raise the po-tential for cycling problems and insta-bility of the valve, which the designeris trying to avoid in the first place. Itis also not economically justifiable toremove the 0.9 factor when the de-signer is trying to meet the 3% rulein an existing installation. When dy-namic simulation is used with ASME

KD and ASME flow area, the inlet lineloss for a system using a pressure re-

lief valve should be read against the10% overpressure (that is, 10% aboveset pressure, not 10% above maximumallowable working pressure), and notagainst any higher pressure at whichthe inlet pressure loss may exceed 3%of the differential set pressure of thepressure relief valve. The term over-

pressure refers to the set pressure ofthe pressure relief valve, whereas theterm accumulation has the referenceof maximum allowable working pres-sure of the equipment. Accumulationand overpressure become identicalwhen the pressure relief valve is setat maximum allowable working pres-sure. Therefore, percent overpressurehas no connection with maximum al-lowable working pressure.Combination systems. It is impliedthat when a rupture disk is used in acombination system as a fitting withappropriate, known flow-resistancefactor, KRGL, the minimum net flow

ChemiCal engineering www.Che.Com oCtober 2008 53

Table 1. Basis of calculation of the capacity, pressure loss and staBility analysis

dv c v gp, p0

rvg

p -b

c g

Pressure relief valve alonewith 3% limit on inlet loss

Vesselpressure [1e]

Use ASME area andASME KD

Use relieving capac-ity based on ASMEarea, but ASMEKD/0.9 See Note 1& Adjusting KDbythe 0.9 Factor

Not required for reliev-ing capacity study,but required for pres-sure loss and stabilityanalysis (Note 1)

Pressure relief valve alonewith higher than 3% limit oninlet loss as in someapplication with pilot oper-ated valve, or best esti-mate case

Vessel pressureminusinlet line loss [1e]

Same as above Same as above Required for relievingcapacity study, pres-sure loss, and stabilityanalysis.Involves trial-and-errorfor P0

Rupture disk alone Vessel pressure Use disk as a fittingwith KRGLof disk along

with piping compo-nents. Multiply thecalculated capacitywith 0.9 to specify therelieving capacity ofthe disk (Note 1)

Stability analysis isnot performed but

maintenance ofcode limited pres-sure of protectedequipment is re-quired

Required in relievingcapacity

Pressure relief valve andrupturedisk combinationwith 3% limit on inlet loss

Vessel pressure Use ASME area andASME KDx CCF (Note 3)

Use relieving capac-ity based on ASMEarea and ASME KD/(0.9 x CCF) . SeeNote 1, Adjusting KDby the 0.9 Factor,and Note 3

Not required for reliev-ing capacity study,but required for pres-sure loss and stabilityanalysis (Note 1)

Pressure relief valve andrupture disk combinationwith higher than 3% limiton inlet loss, or best esti-mate case

Vessel pressureminusinlet line loss

Same as above Same as above Required for relievingcapacity study, pres-sure loss, and stabilityanalysis.Involves trial-and-errorfor P0

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area of the disk does not have to matchthe flow area of the device inlet undercertain circumstances. Its nominalsize must be at least the same as thenominal size of the device inlet, its in-clusion in the inlet line must meet the3% rule, and its capacity in combina-tion with a relief valve must be estab-

lished by test. The reader is warnedthat the CCF becomes invalid if thedisk and the relief valve are installedapart with piping in between. Whenthe combination capacity factor be-comes inapplicable due to lack of closecoupling in the layout or lack of CCFtest data, but with an appropriate non-fragmenting disk, the default value of0.9 for CCF applies. Note that the 3%rule applies to compressible flow, al-though its adherence in liquid serviceis considered a good engineering prac-tice for valves with liquid trim.Understanding ASME terms. Thestatic pressure referred to in the dis-

charge line should not erroneously beunderstood as irreversible pressureloss. Set pressure is actually the setpressure of a balanced valve and pilot

valve, but the differential set pressureof a conventional valve. Other valvetypes refers to balanced valve andpilot valves. By referring to no chance

of interference, the code cautionsagainst the use of fragmenting metaldisk and graphite disk in a combina-tion system. Use of such disks invali-dates the application of CCF, and ad-

vice from an expert should be soughtunder this circumstance [3a].

When using a disk, which is individ-ually certified, but not in combinationwith a valve, the default CCF valueof 0.9 may be used, provided the arearatio is not less than one. When thearea ratio is less than one, the capac-ity of the combination system shouldbe checked after a consideration ofinlet line loss.

Using a rupture disk alone. InNote 2, notice the and conjunctionin (a); all conditions (1), (2), and (3)must apply in order to use the 0.62discharge coefficient. For example, ifthe disk is installed at the end of tenpipe diameters from the vessel nozzle,this method of using the discharge co-

efficient equal to 0.62 does not apply.When this method applies, the mini-mum net flow area of the disk applies.In this method, the piping system istreated as a nozzle. This rule may becalled the 8-5-0.62-MNFA Rule.

DefinitionsIn the following paragraphs, defini-tions of some terms are given in theorder that various flows are computed.Differential pressure. This expres-sion is defined by Equation (1) in thebox on p. 55.Accumulation. This is the pressureabove the maximum allowable work-

Citation from aSmE Viii, DiViSion 1

Note 1The nominal pipe size of all piping, valves and fittings, and vesselcomponents between a pressure vessel and its safety, safety relief,

or pilot operated pressure relief valves shall be at least as large asthe nominal size of the device inlet, and the flow characteristics ofthe upstream system shall be such that the cumulative total of allnon-recoverable inlet losses shall not exceed 3% of the valve setpressure. The inlet pressure losses will be based on valve name-plate capacity corrected for the characteristics of the flowing fluid[2a] (compressible fluid). The flow characteristics of the dischargesystem of high lift, top guided, safety, safety relief, or pilot oper-ated pressure relief valves in compressible fluid service shall besuch that the static pressure developed at the discharge flange ofa conventional direct spring loaded valve will not exceed 10% ofthe set pressure of when flowing at a stamp capacity. Other valvetypes exhibit various tolerance of back pressure and the manufac-turers recommendation should be followed [2b].

The opening provided through the rupture disk, after burst, [mustbe] sufficient to permit a flow equal to the capacity of the valve [ina combination system], and there is no chance of interference withthe proper functioning of the valve; but in no case shall this areabe less than the area of the inlet of the valve unless the capac-ity and the functioning of the specific combination of rupture diskdevice and pressure relief valve have been established by test inaccordance with UG-132 [2c].[Authors comment: This implies full-area disks unless disk flow

diameter is larger than the nominal pipe size of the valve.]

Note 2The rated flow capacity of a pressure relief system which uses arupture disk device as the sole relief device shall be determined by

a value calculated under the requirements of (a) using a coefficientof discharge or (b) using the flow resistance [as shown] below.(a) When the rupture disk device discharges to atmosphere and

(1) is installed within eight pipe diameters from the vessel nozzle

entry; and (2) with a length of discharge pipe not greater thanfive diameters from the rupture disk device; and (3) the nominaldiameters of the inlet and discharge piping are equal to or greater

than the stamped NPS [nominal pipe size] designator of the de-vice, the calculated relieving capacity of a pressure relief systemshall not exceed a value based on the applicable theoretical flowequation[see UG-131(e)(2)and Appendix 11] for the variousmedia multiplied by a coefficient of discharge K equal to 0.62.The area in the theoretical equation shall be the minimum net flowarea [mnfa] as specified by the rupture disk manufacturer. Theminimum net flow area for sizing purpose shall not exceed thenominal pipe size area of the rupture disk device.

(b) The calculated capacity of any pressure relief system maybe determined by analyzing the total system resistance to flow.This analysis shall take into consideration the flow resistanceof the rupture disk device [KR], piping and piping componentsincluding the exit nozzle of the vessel, elbows, tees, reducers,

and valves. The calculation shall be made using accepted engi-neering practices for determining fluid flow [relieving capacity]through piping systems. This calculated relieving capacity shallbe multiplied by a factor of 0.9 or less to allow for uncertaintiesinherent in this method [2d].

Note 3For closed coupled installation of a rupture disk and pressure relief

valve, use the default value of CCF (combination capacity factor)as 0.9 if the Red Book value (certified value) of the selected com-bination pair of rupture disk and pressure relief valve is not avail-able. As an alternative to removing the 0.9 factor, the name plateflow capacity for the valve alone using ASME area and ASMEKDat 10% overpressure can be calculated, and then multiply by

CCF to get the flow for pressure loss analysis for the same concernexpressed in (a) in authors comments under Note 1. The flow re-sistance factor, KR, and other resistances in inlet piping must beconsidered to compute the inlet pressure loss.

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ing pressure (or design pressure whencalculations are not made to establishthe maximum allowable working pres-sure). Accumulation is expressed as apercentage of the maximum allowableworking pressure.

Minimum required relief capacity.Symbolized by Wmin, this is the massflowrate required to limit the pressurerise to the pressure at maximum al-lowed accumulation, which is 10% fornon-fire contingency and 21% for firecontingency. For a fire contingencywith thermally stable single-compo-nent liquid, with maximum pressurebelow 90% of the critical pressure,without specific volume correction,this is obtained by dividing the fireheat load with the latent heat of va-

porization at the maximum pressure,if two-phase flow is ruled out.Ideal nozzle flow area of a reliefvalve. This value is symbolized as Aid-

eal. Using Wmin, the ideal nozzle flowarea is calculated with KD = 1, nozzlelength = 0, all fitting resistances = 0 andthe properties of the relieving fluid.The minimum real nozzle flowarea.Areal, min is described by the fol-lowing equation:Areal, min =Aideal/KDCode mass velocity. The code mass

velocity, Gcode, is obtained by dividingthe minimum required relief capacitywith real nozzle flow area, as shownby Equation (2).

(2)

Code relief capacity. To determineWcode, select the ASME area,AASME,of the relief valve, whose certified

KD was used to calculate real nozzleflow area, so that the selected areamatches or is the next higher in valuecompared with calculated real nozzleflow area. Then calculate Wcode usingthe following equation.

(3)

Nameplate capacity. The name-plate capacity corrected for the prop-erties of the fluid, W10%, is expressedby Equation (4) in the box above.

The nameplate capacity is used tostamp the valve at the manufactur-ers shop. Please note that the name-plate capacity is in effect the flow at10% overpressure times 0.9, sincethe code KD has a multiplier of 0.9.This flow as such is acceptable forpressure-loss computation by ASME.Removing the 0.9 factor for pressureloss analysis is a judgment call thatis not exercised by some experts. Infact, this removal of 0.9 factor is alsonot recommended by the Guidelinesbook [1c]. At least one expert [3d]does not recommend removing the0.9 factor if this results in a larger

valve size; the danger of selecting alarger valve is that this may drasti-cally increase the instantaneous flowand raise the potential of cycling

problems and instability.Best estimate flowrate at 10%overpressure. The best estimateflowrate at 10% overpressure is de-fined by Equation (5) in the box. Inthe Guidelines book [1b], the bestestimate flowrate, also uses: inletstagnation pressure = vessel pressure inlet loss. If the rigorous accountingof inlet loss is not included, the bestestimate flowrate computed as shownabove can be up to 3% higher than a

value obtained by rigorous account-

ing of the inlet loss.The best estimate flowrate at 10%

overpressure, Equation (5), is option-ally used for calculating the inlet andoutlet line pressure losses even thoughthe nameplate capacity flowrate, isalso acceptable by ASME [2a] for pres-sure loss calculation.

According to Reference [1c], theinlet line loss is computed based onthe relieving capacity for a pressurerelief valve or a combination systemwith a disk with full area ratio to ex-

amine if the 3% rule is obeyed. Therelieving capacity needed for thiscomputation is the ASME nameplaterated capacity at 10% overpressurecorrected for the properties of thefluid. This capacity may be deter-mined without a consideration of thepiping resistances.

However, the disk and the pressurerelief valve must be close-coupled inthe actual installation, because CCFapplies only to close-coupled systems.When the combination system is not

close-coupled (if there is pipe betweenthe disk and the pressure relief valve,for example), flow capacity and inletloss computation for a combinationsystem should consider the inlet linepressure loss. This, in turn, shouldconsider the inclusion of the flow re-sistance factor of the disk.Best estimate flow for effluent han-dling. This estimate can be calculatedwith the following equation.

(6)

The Guidelines book [1b], as wellas the CCflow program, use calculated

Equations (1), (4) and (5)

(1)

(4)

(5)

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inlet stagnation pressure in best es-timate flow calculation, if significantinlet loss exists.

TheKRGL of rupture diskThe certified flow resistance factor,

KRGL, of a rupture disk is the dimen-sionless flow resistance factor mea-sured by the manufacturers of thedisk according to the PerformanceTest Code (ASME PTC 25-2001) [4].This factor, when multiplied by corre-sponding velocity head, gives the cor-responding irreversible loss throughthe device in terms of fluid head. Themeasurement of the flow resistancefactor is based on the same principle

that is applied to pipe fittings. For con-stant-density (incompressible) fluids,the following equation is used.

(7)

The factor in the denominator,u2/2gc, is called the velocity head.When multiplied with the certifiedflow resistance factor, it gives thepressure loss across the device in head

of fluid. The pressure loss is measuredagainst a metered flow (and hence u)across the device, so the value ofKRGLcan be determined from the knowndensity of the test fluid. This equationis not, however, used in the measure-ment ofKRGL. The compressible flowequations of Levenspiel [12] and Lap-pel [13] are used instead, because airor gas is used for measurement.

The total flow resistance factor of apiping system,N, also known as fric-tional length parameter or overall loss

coefficient, is conventionally expressedas follows.

(8)

In the PTC 25 setup, there is apressure tap designated as tap Bupstream of the disk, and a pressuretap designated as tap C downstreamof disk. Thus, the setup consists of anupstream piping section, the mid-sec-tion holding the device, and a down-stream piping section. The total flowresistance factor, including the device,

is calculated based on metered flowand pressure difference between taps.Then, the flow resistance factor of thepipe sections alone, without the de-

vice, is calculated. From the differenceof these two resistance factors,KR, de-

vice is determined as follows.

(9)

The flow resistance factor N be-tween pressure tap B and pressure tapC, including the disk, is determined bythe compressible flow equation of Lev-enspiel and Lapple. The Fanning fric-tion factor,f, is calculated from known

pressure loss, flowrate and physicalproperties of air across a section ofpipe of known length before pressuretap B. This friction factor is then usedto calculate the flow resistance factorof the pipe portion only between pres-sure tap B and pressure tap C.

It is important to note that, in thecurrent test code, the velocity throughthe device is based on the full insideflow area of the pipe, and not on theminimum net flow area of the disk.

The total irreversible loss in piping

containing a disk that is connected toa vessel and relieving to atmospheremay be summarized as follows:

Total irreversible loss =entrance loss + inlet piping loss

+ device loss + pressure recovery lossin expansion from device to pipe

+ loss in tail pipe.

The irreversible pressure loss dueto a rupture disk with an area ratioless than unity consists of two parts:the irreversible loss due to disk, which

can be computed using the True-KRand ideal-nozzle inlet contraction, andthe pressure recovery loss if the flow isnot choked, which has to be calculatedusing a separate method. The pressurerecovery loss does not apply to full-bore disks. The concern arises fromthe fact that the measured loss acrossthe device in the certification rig is thesum of the loss in the device plus theloss in any expansion from the deviceto the pipe flow area, with no consid-eration of the possibility of choking inthe device. Thus, for reduced area de-

vices, the observed or apparentKRGL,based on inside full flow area, in-

creases asymptotically with test pres-sure (higher flowrate), even thoughthe trueKRGL, based on minimum netflow area of device, is constant. Also,

the choking effect is not accounted for(calculation based on pipe area cannotchoke, but the actual flow can be lim-ited by choking in the design case, soflow is over-estimated by the presentmethod of calculating, using apparent

KRGL). The choked flow in a reducedarea device can be reached at seem-ingly high ratios of recovered down-stream pressure to device inlet stag-nation pressure. This translates to 0.6or higher, as opposed to the theoretical

value of 0.53 for free discharge of air

from an ideal nozzle [8a].Also, the certifiedKRGL is close to

the observed maximum value at thehigher flowrates, and it is certainly

very conservative at lower designflows. All this adds up to a underesti-mate of flowrate for the effluent han-dling system. For the estimation ofbest estimate flow for stability analy-sis or effluent handling, the flow esti-mate is conservative, as a low estimateleads to a bigger disk for area ratio of0.8 or higher. However, it can differ by

10% or more from the calculated flowbased on actual area of the disk foran area ratio on the order of 0.5, evenafter the mandated code factor of 0.9is removed [3c].

Such low area ratio occurs whensome rupture disks with vacuum sup-ports are selected. Such disks with lowarea ratio should be avoided in combi-nation with a relief valve, and in un-avoidable circumstances expert adviceshould be sought.

Understanding parametersThe symbolKwith subscripts such as

D orR, and the parametersN, CD , andCVare used in literature to symbolizedifferent concepts. It is easy to slipinto a misunderstanding, particularlywhen the thought process of authorsfails to be translated appropriately. Ingeneral,KD and CD are used to denotethe discharge coefficient of the flow ca-pacity of a pressure relief device, pres-sure relief valve or disk, whileKR de-notes the flow resistance factor of thedisk only. The parameter N denotesthe flow resistance factor of a pipingsystem of which the device is just a fit-

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ting, like an elbow. All the parametersKD,KR, CD, andNare dimensionless.The flow coefficient parameter CV,used in control engineering for control

valves, is a dimensional parameter.For liquid service, for example, CVof acontrol valve denotes the flow of waterat 60F in gallons per minute for apressure loss of 1 psi across the valve.

A relationship between the flow coef-ficient parameter, CV and flow resis-tance factor,KR of a control valve forincompressible flow may be given bythe following equation.

(11)

A relationship betweenKR,KD, andCD for incompressible flow, such as aliquid, is as follows [14a].

(12)

(13)

An approximate relationship be-tween KR, KD, and CD for compress-ible flow is described by Equation (14)in the box above [14c].

KR in Equation (14) should be usedwith velocity based on the full-boreinlet diameter of the device for thecomputation of pressure loss. If basedon the velocity through the orifice(device nozzle) for the computationof pressure loss, then the term in thedenominator is excluded.

The predictedKR from the above com-pressible flow equation is higher thantrueKR. This means that Equation (14)overestimates the parameters.

KD for gas or liquid flowThe values of discharge coefficientsfor gases are very different fromthose of liquids, because gas coef-ficients are measured under chokedflow for which the nozzle is the flow-controlling element in the valve, andis well represented by the isentropicnozzle flow model. Liquid coefficientsare determined under un-choked con-ditions reflecting the influence of theentire valve (nozzle and the body) onthe flow, which is not accounted bythe isentropic nozzle model.

One expert advises to use gas dis-charge coefficient for choked flow, and

liquid discharge coefficient for un-choked flow [14b] for gas, vapor, liquidor two-phase flow. The determinationof choking at the device requires thethermodynamic conditions at the de-

vice. Therefore, one can appreciatewhy one expert suggests the computa-tion of inlet line pressure loss for the

determination of the relieving capac-ity of a pressure relief valve [9].

Alternatively, the discharge co-efficient for two-phase flow can beevaluated from certified dischargecoefficients as a smooth function ofomega parameter and backpressure[15]. According to this expert, thedischarge coefficient for non-flash-ing two-phase flow (such as air andwater) lies between the liquid dis-charge coefficient and gas dischargecoefficient. The discharge coefficient

for flashing two-phase flow (such assteam and water) is higher than thegas discharge coefficient, but lessthan 1. The procedure of determin-ing the two-phase flow coefficientusing this experts latest method isan iterative process involving the de-termination of choked condition.

Account for piping system in CDAn approximate relationship betweenthe flow resistance factor of a pipingsystem and CD of the same piping sys-tem may be adapted from an equationgiven by Fauske [11a], as is given byEquation (15) in the box.

Note that if the discharge pipe ventsto atmosphere or any unconfinedspace,KR, exit = 0 because the kineticenergy change is zero [14d]. Dr. Fauskehas presented equations for mass fluxusing the CD and the physical proper-ties at stagnation conditions, and hascompared the predicated mass flux

against the experimental data, whichprovides a good agreement.

KD of a safety relief valveThe relieving capacity of a safety re-lief valve is determined by the ASMEby two methods.The slope method. This method isbased on the principle that flow islinearly proportional to absolute pres-sure. In this method the slope deter-mined by the ratio (measured capacity absolute flow pressure) is for a set

of three valves for each combination ofsize, design, and pressure setting. Thetest values are averaged, and all thetest values are verified to ensure thatthey lie within 5% of the average

value. The relieving capacity stampedon the valve shall not exceed 90% ofthe average slope, multiplied by theabsolute accumulation pressure.The coefficient of dischargemethod. For each design, at leastthree valves for each of three differ-ent sizes (total of nine valves) aretested for the coefficient of discharge.The average of the coefficients of thenine tests shall be multiplied by 0.9

Equations 14, 15, 16

(14)

(15)

(16)

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and this product shall be taken asthe discharge coefficient for design,and be reported in the Red Book.This value shall not be greater than0.878 (that is, 0.9 x 0.975). This isthe value, called the Red Book KDor Code KD, which is used for cal-culating the relieving capacity of asafety relief valve. The same Code

KD is used to calculate the name-

plate capacity at 10% overpressureand study pressure loss.

KD of a relief valveThe coefficient of discharge is definedby Equation (16) in the box on p. 57.

Thus, the coefficient of discharge ofa relief valve is a dimensionless, em-pirical flow, capacity correction factor,which is usually less than unity. It

represents the limitation of the theo-retical computational model as usedin the code, and deviation of the valvenozzle from an ideal nozzle.

In Equation (16), the actual flow ismeasured by a flowmeter using theslope method. The theoretical flow isdetermined by equations that are pro-

vided in the code for valves certifiedfor Sections I, III, IV, and VIII (Divs.

nomEnClaturE

A Flow area, in.2 Aideal Ideal nozzle flow area, in.2

Arealmin Minimum real nozzle flow area, in.2 AASME Flow area of pressure relief valve, in.2Areal ratiominimum net flow area of a rupture disk divided by

the full bore area, dimensionless. C Constant for gas or vapor based on the ratio of spe-

cific heats (cp/cv) D Pipe inside diameter, ft d Pipe inside diameter, in. f Fanning friction factor, dimensionless Gcode Mass velocity required for the pressure relief valve as

a minimum by ASME code, lb/hin.2 gc Dimensional constant, 32.174 lbft/(s2.lbf) KD Coefficient of discharge KRGL Flow resistance factor of a rupture disk for gas or liq-

uid service, dimensionless KRG Flow resistance factor of a rupture disk for gas ser-vice, dimensionless

KRL Flow resistance factor of a rupture disk for liquid ser-vice, dimensionless*

L Length of pipe, ft Lbc Length of pipe between tap B and tap C in PTC test

rig, ft M Molecular weight, lb/lbmol N Flow resistance factor of a piping system, dimension-

less P (Set pressure, psig x 1.1+ atmospheric pressure, psia)

or (Set pressure, psia + 3) whichever is greater fortheoretical flow equation, psia

Pd Pressure at discharge of valve, psia

P Pressure differential, lbf/ft2 T Temperature in R

u Fluid velocity, ft/s w Water density, lb/ft3 Wcode Relief capacity required by ASME code based on the

certified flow area of selected relief valve, lb/h Wmin Minimum required relief capacity to limit the pressure

loss to the code-allowed limit, lb/h WT Theoretically computed relieving capacity of a pres-

sure relief valve, lb/h W10% Nameplate capacity of a pressure relief valve at 10%

overpressure, lb/h. This flow is acceptable for pres-sure loss computation.

W10%,Best estimate Best estimate flowrate at 10% overpressure,generally used for line pressure loss calculation. Thisflow is higher than W10% because of division by 0.9

and 0.9(CCF), lb/h WBest estimate, effluent handlingBest estimate flow rate for effluenthandling, lb/h

Z Compressibility factor, dimensionless Fluid density, lb/ft3

Acronyms:API American Petroleum Institute

ASME American Society of Mechanical EngineersCCF Combination Capacity Factor: A relief flow capacity

correction factor determined by PTC 25 apparatus

*At the time of publication, the KR value is determined using air or gas. This

value is used with the velocity head in the applicable fluid phase (vapor, liquid,or two-phase) to compute pressure loss

References1. Guidelines for Pressure Relief and Effluent

Handling Systems, CCPS, AIChE, New York,NY [1a: p. 185; 1b: p. 189; 1c: p. 187; 1d: p.184; 1e: p. 255, p. 256, p. 182]

2. 2004 ASME Boiler & Pressure Vessel Code,Division 1, ASME, New York, N.Y. [2a: Ap-pendix M-6(a), p. 584; 2b: Appendix M-7(c),p. 584; 2c: UG-127, (a)(3)(b)(5), p. 89; 2d:UG-127, (a)(2)(b), p. 89; 2e:UG-131(e)(2)(e),p. 94; 2f: UG-132 (b)(c)(d), p . 96]

3. Huff, J.E, Huff Consulting Services, Stock-ton, CA, Personal communication [Dr. Huffis the authors initiating preceptor in theDIERS technology].[3a: May 2007; 3b, 3c, 3d:June 2007]

4. Huff, J.E, Flow Characteristics of RuptureDisc Devices: Models for Certification andDesign, Huff Consulting Services, DIERSUsers Group Meeting, Las Vegas, 05/02/06.

5. Performance Test Code 25-2001, publishedFebruary 2002 ASME, New York, N.Y.

6. Pressure Relief Certification, NB-18 [RedBook], The National Board of Boiler andPressure Vessel Inspectors [614-888-8320]

7. Huff, J.E. and K. R. Shaw, Measurement ofFlow Resistance of Rupture Disk Devices,Plant/Operations Progress, 11, No. 3, pages187-200 (July 1992). [Basis of ASME PTC 25:Current certification method].

8. Huff, J.E., Restrictive Rupture Disc Devices:A Calculation Method for Certification andDesign, Topical Conference Proceedings ofthe 2001 Process Plant Safety Symposium,

AIChE Spring National Meeting, pp. 578-584

(April 2001)9. Fisher, H, Fisher Inc., Personal Communica-tion June,2007

10. Das, D. K. and R.K. Prabhudesai, ChemicalEngineering, PE License Review, Kaplan AEC

education, Chicago, IL.(2007) [10a: p. 157]

11. Fauske, H. K., Similarity Between Two-phase Flashing and Compressible Gas PipeFlows, Process Safety, Fauske & Associates,Inc., Burr Ridge, IL, Fall 2001 [11a: p. 6]

12. Levenspiel, O., The Discharge of Gases froma Reservoir through a Pipe,AIChE Journal,pp. 402-403 (May 1977)

13. Lapple, C.E., Isothermal and Adiabatic Flowof Compressible Fluid, Trnas. AIChE, 39, pp.385-432 (1943).

14. Darby, Ron, Chemical Engineering Fluid Me-chanics, Second edition, Marcel Dekker, Inc.,NY(2001)[14a,14b: personal communication,September 2007], [14c:p. 310; 14d: p. 213]

15. Leung, J. C., A theory on the discharge co-efficient for the safety relief valve, Journalof Loss Prevention in the process industries,Elsevier Ltd., 17 (2004) pp. 301-313

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1 & 2). For Section VIII, the theoreti-cal flow is determined by selecting theappropriate expression from Equation

(17) in the box above.

Determination of the CCFThe combination capacity factor (CCF)is determined in applications wherea rupture disk is used upstream of apressure relief valve in a closed cou-pled position [2f].

The capacity of the pressure reliefvalve as an individual valve is deter-mined according to the code procedureat a pressure 10% or 3 psi, whicheveris greater, above the valve set pressure

(Wcode,valve).The rupture disk device shall then

be installed at the inlet of the pres-sure relief valve and the disk burst tooperate the valve. The capacity testshall be performed on the combinationat 10% or 3 psi, whichever is greater,above the valve set pressure, dupli-cating the individual pressure relief

valve capacity test (Wcode, valve+disk).From the results of these tests, whichmust fall within a range of 10% of theaverage capacity, the CCF is math-

ematically computed as follows.

(18)

Thus, if the combination of rupturedisk, irrespective of its area ratio, andpressure relief valve is used as a close-coupled system in the actual instal-lation, and the 3% rule is followed,the inclusion of theKRGL value of thedisk in the inlet line is not requiredin the determination of the capacity.This method, although not theoreti-cally correct, is acceptable within thetolerance of errors inherent in the

analysis, and relieves the designerfrom avoidable strenuous exercises.One expert recommends a conserva-

tive practice: whenever a combina-tion system is used, the inlet line loss,which includes the inlet line with allfittings as well as the rupture diskshould be considered both during theinlet stagnation pressure determina-tion and the pressure loss analysis [9].This approach, although theoreticallyrigorous, requires trial-and-error, andis computationally intensive for multi-component systems with reaction evenwith the help of a computer. This maynot be necessary under circumstances

explained above. However, if the diskis separated from the relief valve inthe actual installation or the 3% ruleis violated, the CCF value does notapply, and theKRGL value of the diskmust be considered in the inlet line,both for capacity determination andstability analysis.

Edited by Kate Torzewski

(17)

AuthorDilip K. Das is a principal

engineer in Bayer Crop-Sciences Kansas City engi-neering department (8400Hawthorn Rd., Kansas City,MO 64120; Tel:816-242-2879;Fax: 816-242-2693; E-mail:[email protected].) where he is currentlyin charge of emergency reliefsystem design, and previ-ously held process engineer-

ing positions at Ciba-Geigy, Rhone-Poulenc,Stauffer Chemicals, and C. F. Braun. He holdsa B.S. (honors) in chemistry from Rajshahi Uni-

versity in Pakistan, and a B.S.Ch.E. (Honors)from Jadavpur University in India. He earnedan M.S.Ch.E from University of Washington(Seattle), and was trained at MIT in expert sys-tem in process engineering. Das is a registeredengineer in the states of N.Y., N.J., La., and Mo.

He is a past chair and director of AIChEs Kan-sas City chapter, and is currently the chairmanof SuperChems Technical Steering Committeeunder the Design Institute of Emergency ReliefSystem (DIERS).

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