Question:   Can the following equations be used for sizing pressure relief valves if the vapor happens to be steam?

A = W/CK_dP_lK_b(the square root of TZ/M)  (this is Equation 2)

A = W/735F₂K_d(the square root of ZT/MP₁(P₁-P₂)  (this is Equation 5)

Reply:  For critical flow, Equation 2 could be used for steam, however, Equation 8 is preferred since it was empirically derived through testing and will provide slightly more conservative values than your equation.  Additionally, the equation for steam in the ASME Code is identical to Equation 8.  Currently, there is no sub-critical steam equation counterpart to Equation 5 since steam is typically discharged to the atmosphere and is at critical conditions.  However, there is no reason that Equation 5 cannot be used for sub-critical steam applications.  The task force is planning on adding a sub-critical equation to the next revision of RP 520 Part I.

Question:   Why is the temperature not a variable in the following formula?

A = W/51.5P_lK_dK_NK_SH   (this is equation 8)

Reply:  Temperature has in essence been taken out of the equation for saturated steam since the experimental testing utilized saturated steam.  The empirical conversion factor 51.5 is fairly close to being a constant for all temperatures of saturated steam.  Temperature does, however, come into effect in Equation 8 for superheated steam as represented by the superheat correction factor, K_SH.

Question:   What is the definition of "drainage" as contained in API RP 520?

Reply:  The definition for "drainage" as contained in API Standard 2000, Table 4, is:  "a slope of not less than 1 percent away from the tank shall be provided for at least 50 feet toward the impounding area."  Also, API Standard 2000 states the capacity of the sump would have to be not less than the capacity of the largest tank which can drain into it.  A small sump with a sump pump does not fit this definition since there is always the possibility that the sump pump will not start and run for the required period.

Question:   The gas expansion in a vessel exposed to fire equations which were in API 520 Edition 4 were removed in API 520 Edition 5.  Why?

Reply:  The gas expansion equation does appear in both the fourth and fifth editions of RP 520 Part I.  However, the appendices and equations were rearranged such that the gas expansion equation now appears in a different location.  The gas expansion equation appears in the fifth edition in Appendix D on page 53.  In the fourth edition, all of the sizing equations for pressure relief valves (including the gas expansion equation) appear in Appendix C.  Note that there is also a separate appendix for fire relief requirements.  For the fifth edition, the equations for valve sizing were moved into the text portion of the RP and the name of Part I was changed.  The equation for gas expansion in a vessel exposed to fire (equation C-6), however, was moved into the relief appendix, since this was felt to be the appropriate location for it.  The fire relief requirements are presented in Appendix D of the fifth edition.

Question:   I am not clear on the meaning of the specific gravity definitions found in API RP 520.  Several times throughout the document, G (specific gravity) is defined as the examples below illustrate:

From page 28:
G = specific gravity of gas referred to air = 1.00 for air at 14.7 pounds per square inch absolute and 60 degrees F

From page 37:
G = specific gravity of the liquid at the flowing temperature referred to water = 1.00 at 70 degrees F

My question is, are these specific gravities at the relieving conditions (as defined in paragraph 1.2.3.2.11) for the fluid passing through the relieving device, or at standard conditions for the fluid being relieved?

Reply:  Vapor Sizing Equations:  The specific gravity term, G, in equation (4) of section 4.3.2 and equation (7) of section 4.3.3 refers to the relieving fluid at standard conditions; or 14.7 psig and 60 degrees F.  Liquid Sizing Equations:  The specific gravity term, G,  in equation (9) of section 4.5 and equation (12) of section 4.6, however, refers to the relieving fluid at relieving conditions. 

Question:   As per clause 4.3, Sizing for Gas or Vapor Relief, equation number 4 gives A = V(TZG)^1/2/1.175C.Kd.Pi.Kb where "G" has been indicated as Specific Gravity of the gas referred to in air = 1.0 for air at 14.7 PsiA and 60⁰F.   But in Table 8, "Properties of Gases," specific gravities of gases are given based on steam specific gravity as 1.0 and air specific gravity is given as 0.875.   Please clarify how these values can be used against "G" in the above equation.

Reply:   The specific gravity, G, used in equation 4.3 should be based on the density of air at standard conditions.  In other words, the specific gravity of air at 14.7 psia and 60⁰F is equal to 1.0.   The specific gravity, G, is the ratio of densities:  G= Y_fx/Y_s where Y_fx is the density of the relieving fluid at atmospheric or standard conditions and Y_s is the density of a standard fluid (air for vapors and gases) at atmospheric or standard conditions.  Table 8, "Properties of Gases" in the Fifth Edition of API RP 520 Part I (July 1990), correctly gave specific gravities of various gases where air was used as the standard basis.  This table could be used properly with Equation 4.3 

4.3.3

Question:   Referring to API RP 520, for calculating the required effective discharge area of the valve "A," the code provides three formulas as per clauses 4.3.2.1 and 4.3.3.1.  Out of these formulas, 3 and 4 (or) 6 and 7, I find that the variables are all the same except "M" and "G."  If we consider that the value of "A" should be the same while using formula 3 (or) 4, which are the formulas mentioned for safety valve sizing for critical flow, then we can equate these two formulas.  By this, we will obtain the value of "G" as equal to 0.0346M.   Similarly, if we equate the formulas 6 and 7, we will get the same value for G, equal to 0.0346M.  But the values given in Table 8, "Properties of Various Gases" for "G" (specific gravity) and "M" (molecular weight) are not in this proportion.  This implies that the value of valve size would be different if we consider the formula containing"M" with that of the formula containing "G."  This appears to be very strange.  I therefore request you to kindly explain or provide clarification at the earliest.

Reply:  You are correct in your evaluation of the equations presented in paragraphs 4.3.2.1 and 4.3.3.1.   Setting equations (3) and (4) or (6) and (7) equal to each other results in G = 0.0346M or G  = M/29.  Note that this is equal to M/M_air.  In Table 8, "Properties of Gases," in the Sixth Edition of API RP 520 Part I (March 1993) unfortunately the specific gravities shown are in error.  This explains why you were unable to obtain the same results from equations (3) and (6) using the M term as you did with equation (4) and (7) using G.  Table 8 of the Fifth Edition of API RP 520 Part I (July 1996) correctly gave specific gravities of various gases where air was used as the standard basis.  You will find that the table correctly gives G and M in the proper proportions.  We do not recommend usage of the specific gravities shown in Table 8 of the Sixth Edition for the equations presented in Section 4.0 of RP 520.   Instead, use the values from Table 8 of the Fifth Edition.  We are aware of the errors in Table 8 and will be correcting them in the next edition of RP 520.

Question:   Referring to API RP 520 Part I, section 4.6, mention is made to a formula change.   Can you please advise me what date this change came into effect?

Reply:  The rules for capacity certification of liquid service valves first appeared in the ASME Code 1983 Edition, Summer 1984 Addenda.  The formula for sizing of liquid service pressure relief valves requiring liquid capacity certification (reference paragraph 4.5 of API RP 520, Part I, Sixth Edition) first appeared in API RP 520 Part I, Fifth Edition, July 1990.  The previous liquid sizing formula using 25% overpressure and a correction factor for applications at overpressures from 10% to 25% (reference paragraph 4.6 of API RP 520, Part I, Sixth Edition) has remained for reference.

Question:   I am evaluating several relief valves.  One of the cases being evaluated is for blocked-in exchangers in which thermal expansion can occur.  API 520, Appendix C, Page 47, defines a method for calculating liquid expansion rates for such cases.  My question regarding this method has to do with the "cubical expansion coefficient" used in the calculation.  Table C-1 lists typical values for some hydrocarbons and water at 60 degrees F.  Talking to PSV vendors and others about the cubical expansion factor and how to calculate it for temperatures other than 60 degrees F leaves confusion as to how this value should be calculated.  I was told by one person from a valve manufacturing company to take the value in Table C-1 and multiply it times the temperature.  That resulted in a calculated flow rate that is exorbitant.   The Fifth Edition of Perry's Chemical Engineering Handbook, Page 3-227, Equation 3-3, defines a method to calculate an average "cubical expansion coefficient" over a range.  Equation 3-4 on the same page provides another method for calculating this coefficient.  Both equations give similar results that appear to be reasonable.   Would you please address this?  Specifically, are the methods for calculating the "cubical expansion coefficient" defined in Perry's satisfactory for use in the API 520, Appendix C methodology?

Reply:  In response to your question, first, please be advised that you do not multiply the cubical expansion coefficient by temperature as someone has suggested to you.  Although the cubical expansion coefficient is not a direct multiple of temperature, it is a function of temperature.   The material in RP 520, Part I, Appendix C, Page 47, gives typical values of the cubical expansion coefficient at 60 degrees F.  The use of formulas in Perry's Chemical Engineering Handbook will provide cubical expansion coefficients of sufficient accuracy to calculate thermal expansion requirements at other temperatures.

Question:   In Appendix D, section D.5.1, formulae for heat absorption across the wetted surface of a vessel are described.  We believe there is a typing error in equation [3], Q = 21,000 FA^-0.18.  We believe a factor of 34,500 should be used instead of 21,000.  In Edition 5, July 1990, the formula is correct, Q = 34,500 FA^0.82.   Can you please confirm our statement?

Reply:  You are correct.   The equation for heat input to a vessel due to fire where adequate drainage and fire fighting do not exist is:  Q = 34,500 FA^0.82.  This material has been transferred to RP 521 and is shown correctly in both the Third Edition, November 1990 and the Fourth Edition, March 1997.

Question:   There are two formulae in Section D.5.1 to calculate the heat absorption across the wetted surface of a vessel.  One should be used "when there are prompt fire-fighting efforts and drainage of flammable materials away from the vessel."   The other formula should be used "where adequate drainage and fire-fighting equipment do not exist."  Could you please give us examples of these two conditions.  Would a well-maintained petrochemical plant process area built in the late 60s and with normal fire-water supply, monitors, and hydrants, be considered under the first category and by that using the equation with the lower factor?

Reply:  A typical process plant with sewers to collect flammable liquids, a fire water system, and some type of fire brigade would be an example of a facility with good drainage and prompt fire fighting.   A pressure storage vessel (e.g., an LPG sphere) in an unattended remote location would be an example where you might expect inadequate drainage and less-than-prompt fire fighting.  Based on the brief description of your facility, it would appear that you could use the heat input equation with the lower factor (21,000).  However, that judgement is yours to make.

Question:   The last paragraph of Appendix D, Section D.6.2 of API Standard 520 states, "Should a pressure relief device be located in the liquid zone of a vessel exposed to fire conditions, the pressure relief device must be able to pass a volume of liquid equivalent to the displacement caused by vapor generated by the fire."  I would ask for further clarification of the meaning of the part of the sentence in italics.   I have spoken to a manufacturer of safety relief valves and they are also unable to fully understand the text.

Reply:   This discussion is directed towards vessels which are liquid-full, the most common concern, although it would be possible to have a comparable situation without a liquid-full vessel.  Normally when designing a relief valve for fire conditions in a vessel, the most desirable location for the relief valve is in either the top head (vertical vessel) or on the overhead line from the vessel.  Should fire occur a small amount of liquid would be relieved which would create a vapor space in the vessel.   At this point, vapor would be generated due to the fire which would be relieved.   If the location of the relief valve is located somewhere else on the vessel such as on the vessel itself, but on the side of the vessel well below the liquid level or on the feed line if the feed is liquid, then to relieve the pressure created by the fire, the relieving fluid would have to be liquid.  This would be the case until enough liquid is relieved to uncover the relief valve.  At this point, vapor would be relieved.   Since in almost all cases, vapor will be generated as soon as enough space is available for vapor to form, to relieve the pressure on the vessel as stated in RP 520, "the pressure relief device must be able to pass a volume of liquid equivalent to the displacement caused by vapor generated by the fire."

Question:   I am using a commercial software product for analyzing our PSV's and this software is using the charts in API 520 - Part I, Appendix E to determine the C factor.  This has resulted in C factors much lower than typically observed when ideal gas behavior is assumed.  I tried to duplicate some of the isentropic coefficients given in Figure E-1 and could not do so.  My values for isentropic coefficients were calculated via the following equation:

Isentropic Exponent = ln P2/P1/(ln P2/P1 - ln T2/T1)

As a test, using the SRK equation of state, I used 3-methyl pentane as a typical paraffinic component, isentropically expanded it from its dewpoint at 200 psia to 30 psia which resulted in a flash temperature of 268 degrees F.  Inserting these values into the above equation gives a value for the coefficient of 1.05.  Used of Chart E-1 yields a coefficient of 0.76.  Could you please look into this issue for me?  If Chart E-1 is correct, I would appreciate a little documentation as to its source and an explanation as to why my approach is wrong.   This issue is VERY pronounced in some of my PSV calculations since I have several instances of 200 Mol Wt gases relieving at 200 psi.  Note that the use of the E-1 chart shows values for the coefficient down near 0.5 which subsequently yields a C factor of about 220.  This makes a BIG effect on valve sizing compared to typical C factors of about 315.  My simulations of even these heavy gases is indicating coefficients of no less than 0.9, so again, there must be a gross error somewhere.

Reply:  The following is our response to your inquiry related to Appendix E of API RP 520 Part I and the isentropic expansion coefficient "n" as used in the PRV sizing equations for non-ideal gas applications.  The approach that you used to determine the isentropic expansion coefficient is correct.  You used an equation of state and isentropically flashed the fluid to the downstream pressure.  (Use the critical back pressure for critical flow applications.)  Knowing temperatures at two pressures then allowed you to utilize the following equation to determine "n."

n = ln P2/P1/(ln P2/P1 - ln T2/T1)

We have reproduced your value of 1.05 for "n" for 3-Methyl Pentane at 200 psia using simulation software.  We have tried to reproduce the work that is currently presented in Appendix E related to the isentropic expansion coefficient and have also failed to obtain agreement with the curves provided.  We have subsequently removed the curves from the next revision of RP 520 Part I and are only providing guidance as to how the coefficient should be determined.   At this time, the task force cannot recommend use of the curves presented in Appendix E.

Question:   We find in another standard, the densities of air, ammonia, and sulfur dioxide at N.T.P. are 1.293 Kg/M³, 0.771 Kg/M³, and 2.921 Kg/M³, respectively.  On this basis, if the air specific gravity is 0.875, as given in Table , the specific gravities of ammonia and sulfur dioxide would be equal to 0.522 and 1.98, respectively.  But the specific gravities given in your table are different.  We require your clarification in this respect.

Reply:  In the Sixth Edition of API RP 520 Part I (March 1993), unfortunately, the specific gravities shown are in error.   It appears that the table attempted to use steam as the basis since it has a specific gravity of 1.0, however, it looks like most of the other specific gravities are incorrect when compared to steam.  We do not recommend usage of the specific gravities shown in Table 8 of the Sixth Edition for equation 4.3.  Instead, use the values given from Table 8 of the Fifth Edition or calculate the specific gravity as shown above using air at standard conditions as the basis.  We are aware of the errors in Table 8 and will be correcting them in the next edition of RP 520.