Embed Size (px)
DESCRIPTION
k
Citation preview
GCPS 2013 __________________________________________________________________________
NFPA 68 –New Gas Venting Equations
Samuel A. Rodgers Honeywell
15801 Woods Edge Road, Colonial Heights, VA 23834 [email protected]
Robert Zalosh
Firexplo 20 Rockland St., Wellesley, MA 02481
Prepared for Presentation at American Institute of Chemical Engineers
2013 Spring Meeting 9th Global Congress on Process Safety
San Antonio, Texas April 28 – May 1, 2013
UNPUBLISHED
AIChE shall not be responsible for statements or opinions contained in papers or printed in its publications
GCPS 2013 __________________________________________________________________________
NFPA 68 – New Gas Venting Equations
Samuel A. Rodgers Honeywell
15801 Woods Edge Road, Colonial Heights, VA 23834 [email protected]
Robert Zalosh
Firexplo 20 Rockland St., Wellesley, MA 02481
Keywords: NFPA, gas, deflagration venting, vent area, burning velocity, KG, obstacles, flame enhancement
Abstract
The 2013 edition of NFPA 68 Standard on Explosion Protection by Deflagration Venting will replace vent area sizing equations containing the gas Deflagration Index, KG, for high-pressure applications with equations containing the laminar burning velocity, Su. Modified Swift-Epstein equations replace both gas venting equations in previous editions of NFPA 68. A scale-dependent flame enhancement factor, λ, has been included in both the low-strength and high-strength methods to account for turbulence and flame instabilities prevalent in many large enclosure deflagrations. The new vent sizing method predicts vent areas that are equal to or larger than the vent areas actually used in the overwhelming majority of tests in unobstructed large enclosures, and in many tests with large-scale obstacles simulating large process equipment. While further work needs to be done to address corrections for enclosures with congested piping arrays, the framework has been set to facilitate this activity going forward. This paper addresses the gas equations implemented in the 2013 edition, modifications to prior vent area corrections and examples of vent sizing.
1. Introduction The primary purpose of NFPA-68 Standard on Explosion Protection by Deflagration Venting [1] is to provide users with suitable vent design methods that can prevent structural failure of enclosures for design basis deflagration scenarios. The 2013 edition of NFPA 68 will have a new gas venting method that, for the first time, has equations and parameters that allow users to specify scenarios that go beyond the particular gas or vapor and the enclosure size, geometry, and pressure resistance. This paper has been written to describe how the new equations have been developed and how they provide a more consistent, as well as more flexible, method over the entire range of enclosure strengths and flammable gases and vapors.
GCPS 2013 __________________________________________________________________________
The equations in all editions of NFPA-68 represent the enclosure strength in terms of the design value of maximum reduced pressure, Pred, developed in the vented explosion. Since vented gas explosions can have widely varied and complex transient pressures, we start here with a discussion of how Pred is related to the transient pressures. 2. Transient and Peak Pressures in Vented Gas Deflagrations Vented gas deflagration pressure transients have different forms depending on the relative influence of the inherent flammable mixture burning velocity, the vent actuation pressure, turbulent combustion effects, flame instabilities and acoustic waves. Figure 1 is an example of a pressure transient reported by Cooper, et al., [2] in which most of these phenomena occur. There are four labeled pressure peaks associated with the following phenomena. P1 occurs when the vent is fully open. P2 occurs at the onset of burned gas venting (and associated increase in vent volume flow rate) and igniting unburned gas outside the vent. P3 occurs when the enclosure is filled with burned gas such that there is a sharp reduction in the generation rate of gaseous combustion products. P4, the highest peak pressure in this example, is associated with amplified acoustic oscillations due to a coupling of acoustic waves and residual combustion associated with cellular flames. These amplified pressure oscillations have too high a frequency for most structures to respond. However, low pass filtering of those oscillations to produce smooth pressure at a structural response time scale would probably result in a peak pressure between the P3 and P4 values shown in Figure 1. Many tabulations of measured peak pressures from vented gas deflagration tests do not describe the details of which measured or filtered peak pressure is being reported. Therefore, there is some inherent ambiguity associated with the reported peak pressures with regard to their direct applicability to the Pred values to be used for vent design.
Figure 1: Vented Deflagration Pressure versus Time (from Cooper, et al. 1986) When flame speeds are high there is yet another issue concerning reported Pred values. Whereas the pressure increase is spatially uniform in the enclosure when flame speeds are small in comparison to sound speed, pressure differences start to occur at high flame speeds. This is illustrated in Figure 2, which shows the pressure transients measured at six locations by
GCPS 2013 __________________________________________________________________________
Lowensmith, et al., [3] during a methane-hydrogen mixture deflagration in a 69 m3 enclosure with piping. The measured peak flame speed was 263 m/s, about 75% of the unburned gas-air mixture sound speed. The highest peak pressure in Figure 2 (about 1300 mbar-g) is almost twice as high as the lowest peak pressure measured in the enclosure. The highest peak pressure was measured in a corner of the enclosure where compression waves probably steepen and induce complex interactions with the wall structure.
Figure 1: Deflagration Pressures Measured at Six Locations in the Enclosure (Lowensmith, et
al. 2010) In view of the ambiguities and structural significance in the reported peak pressures, it is important for deflagration vent design methods to predict vent areas and Pred values that are comfortably larger than the actual reported measured values. The most appropriate vent area design method is not necessarily the one that produces best agreement with reported measured Pred values. It is more important to have a design method that can be used readily to determine appropriate required vent areas and vent deployment pressures in applications that go beyond the test conditions. In high flame speed applications where it may be important to determine pressure variations within the enclosure, it could be more appropriate to use Computational Fluid Dynamics methods to estimate local pressures, and to supplement vent designs based on a single Pred value. 3. NFPA-68 Gas Venting Equation History The history of NFPA-68 gas equations is presented to illustrate the various approaches that have been taken and how the prescribed pressures and vent areas compare to various test data. Until the 2013 edition, the NFPA approaches did not explicitly address the effect of internal obstacles on vent area. The constants were, however, chosen to conservatively protect industrial equipment and building enclosures based on available data at the time of a particular edition. 3.1 NFPA-68 1978 Edition
GCPS 2013 __________________________________________________________________________
One of the earliest approaches to design of deflagration vents was the vent ratio, that is, the ratio of vent area to enclosure volume. This desired ratio was established based on volumetric scaling of early small-scale test data [4], and was intended to be conservative. In 1978, NFPA-68 [5] presented a model to determine required vent area for gas and dust deflagrations based on the method of Runes [6] as in Equation 1. This model was intended for low-pressure applications, as in buildings. Relying on a limited dataset, the values of the constant, C, were established as in Table 1.
PLLCAv
21 ••= [Eq. 1]
where:
Av = necessary building vent area, ft2 or m2 C = constant, characteristic of the fuel gas, dependent upon the units (English or SI) used. L1 = smallest dimension of the rectangular building enclosure to be vented, ft or meters. L2 = second smallest dimension of the rectangular building enclosure to be vented, ft or meters. P = maximum internal building pressure which can be withstood by the weakest building member which is desired not to vent or break, lbf/in2, or kN/m2
Table 1. C-Factors for Runes Equation Combustible C-Factor (psi)1/2 C-Factor (kN/m2)1/2
Gases with Flame Speed like Propane 2.6 6.8
Ethylene 4 10.5
Hydrogen 6.4 17
Organic Dusts 2.6 6.8
Organic Mists 2.6 6.8
High Flame Speed Metal Dusts 4 10.5 The relevant C-Factors were separated into groups on the basis of laminar burning velocity, Su. For a baseline case enclosure with a footprint of 24 ft by 24 ft and a height of 12 ft, L1 is 12 ft and L2 is 24 ft. With an enclosure Pred of 0.10 bar-g = 1.45 psig and a gas like propane, the required vent area would be 622 ft2, corresponding to two entire walls and 15% of a third wall area. 3.2 NFPA-68 1988 Edition In 1988 NFPA-68 [7] adopted two new relations for deflagration venting of gases, one for low-strength enclosures with Pred less than 0.1 bar-g and one for high strength enclosures up to a Pred of 2 bar-g.. While the Runes equation used the minimum enclosure cross-sectional area, the 1988 equation used the ratio of vent area to enclosure surface area and is a simplification of the Swift-Epstein [8] low pressure derivation. Swift [9] derived C-factors for a number gases and
GCPS 2013 __________________________________________________________________________
dusts, assuming a burning velocity enhancement factor, λ, of 5 and a discharge coefficient of 0.7. The C-Factors in the 1988 edition of NFPA-68 were developed by the NFPA Explosion Protection Committee enveloping the test data that were available circa 1987. This resulted in the values shown in Table 2. Equation 2 and its C-factors were intended to conservatively envelope the typical situation of initially quiescent gas release in an enclosure with limited or no turbulence-inducing obstacles. Surface area of equipment and contained structures was specifically excluded. The 1988 equation was retained through the 2007 edition of NFPA-68.
( )21
red
sv
PACA •= [Eq. 2]
Where:
Av = vent area (ft2 or m2) C = venting equation gas/dust constant As = internal surface area of enclosure (ft2 or m2) Pred = maximum internal overpressure that can be withstood by the weakest structural element (psi or kPa)
Table 2. C-Factors for NFPA-68 1988 Combustible C-Factor (psi)1/2 C-Factor (kPa)1/2
Anhydrous Ammonia 0.05 0.13
Methane 0.14 0.37
Gases with Fundamental Burning Velocity less than 1.3 times
that of Propane 0.17 0.45
St-1 Dusts 0.10 0.26
St-2 Dusts 0.12 0.30
St-3 Dusts 0.20 0.51 For the baseline case of an enclosure with a footprint of 24 ft by 24 ft and a height of 12 ft, internal surface area is 2304 ft2. With an enclosure Pred of 0.10 bar-g = 1.45 psig, and a gas like propane, the required vent area would be 325 ft2, corresponding to one entire wall and 13% of another wall area. For high-strength (Pred > 0.10 bar-g) enclosures, Bartknecht [10] presented a set of nomographs based on mostly unpublished large-scale test data. The nomographs were also eventually reduced to equation form as in Equation 3 and included in NFPA 68-1988 for high strength enclosures. The coefficients for Equation 3 are shown in Table 3.
( ) ( ) ( )dredstat
bv PPcVaA ••••= exp [Eq. 3]
Where:
GCPS 2013 __________________________________________________________________________
Av = vent area, m2 V = enclosure volume, m3 Pred = maximum pressure developed during venting, bar-g Pstat = vent closure release pressure, bar-g
Table 3. Coefficients for Bartknecht Relation Combustible a b c d
Methane 0.105 0.770 1.230 -0.823
Propane 0.148 0.703 0.942 -0.671
Coke Gas 0.150 0.695 1.380 -0.707
Hydrogen 0.279 0.680 0.755 -0.393 For the baseline case of an enclosure with a footprint of 24 ft by 24 ft and a height of 12 ft, enclosure volume is 196 m3. The nomographs and equation for a Pstat of 0.05 bar-g and a Pred of 0.11 bar-g, produce a minimum required vent area of 28 m2 = 300 ft2. This required vent area is 92% of the vent area required by the low strength equation at a comparable Pred value and the two methods produce similar results at the demarcation. 3.3 NFPA-68 1998 Edition As a result of the widespread adoption of the Bartknecht nomographs in both Europe and North America, there was a need to have a high-strength enclosure design method that would be applicable to other gases beyond those listed in Table 3. The parameter used by Bartknecht and others to represent a flammable gas or vapor rate of burning and associated rate of enclosure pressure is the gas Deflagration Index, KG, with the following definition.
31
max
VdtdPKG •
= [Eq. 4]
Here (dP/dt)max is the maximum rate of pressure rise measured in a closed vessel deflagration with the worst-case (usually near-stoichiometric) concentration of the flammable gas or vapor. The measured (dP/dt)max is normalized to a vessel volume (V) of 1 m3. Although simple theoretical considerations, assuming gas burning velocities that are independent of scale, suggest that KG should be a constant for different size vessels, the closed vessel test data shows that KG does increase with increasing volume. This effect is discussed in Annex C of NFPA 68-2007 [11]. With the broad acceptance of KG, Bartknecht [12] published the following equation for gas venting based on KG. NFPA-68 [13] adopted Equation 5 directly for high-strength enclosures with Pred greater than 0.1 bar-g.
GCPS 2013 __________________________________________________________________________
( )[ ] ( ){ } 32572.0582.0
10 1.0175.00567.0log127.0 VPPPKA statredredGv •−+•−= −−[Eq. 5]
where:
Av = Vent area, m2 KG = Deflagration Index, <550 bar-m/sec Pstat = vent closure release pressure, <0.5 bar-g Pred = maximum pressure developed during venting, <2 bar-g V = enclosure volume, <1000 m3
In order to use Equation 5 for different gases, values of KG need to be “normalized” by the benchmark values of KG = 100 bar-m/s for propane and 55 bar-m/s for methane. For L/D <2, vent area is not adjusted. For L/D from 2 to 5, the vent area, Av, is increased by adding more vent area, ΔA, calculated from Equation 6, which was based on a review of limited Bartknecht data [12] for elongated enclosures.
750
22
−
=Δ DLKA
AGv
[Eq. 6]
For the baseline case of a propane-air deflagration in a 196 m3 enclosure with a Pred of 0.11 bar-g, Equation 5 requires a vent area of 24 m2 = 259 ft2, which is somewhat less than the value (28 m2) determined previously from the Bartknecht nomograph curve fit. The high strength equation vent area was approximately 80% of that using the low-strength equation. 3.4 NFPA-68 2007 Edition For the 2002 edition some changes were made to account for vent inertia, but the basic gas venting equations remained the same. In the 2007 edition of NFPA-68 [13], the committee developed a correlation for the low-strength Venting Parameter, C, as a function of Fundamental Burning Velocity, shown in Equation 7. This correlation increased the benchmark C-Factor for propane from 0.17 to approximately 0.2 psi 1/2. Methane also increased from 0.14 to approximately 0.16 psi 1/2. For C (psi 1/2):
( ) ( ) 0416.0101.6101.6 425 +•+•= −−uu SSC [Eq. 7]
When Equation 2 is used with the new C-Factor for propane and the baseline case at a Pred of 0.10 bar-g, the result is a required vent area of 380 ft2 = 35 m2, which is 46% higher than
GCPS 2013 __________________________________________________________________________
Equation 5 produces at a Pred of 0.11 bar-g. The change in C-Factor resulted in a larger and more significant discontinuity in NFPA 68 required vent areas near the demarcation between the low-strength and high-strength equations. 3.5 Issues with the NFPA-68 Equations One fundamental issue with the NFPA-68 2007 edition equations is the use of the laminar burning velocity, Su, in the low-strength enclosure equation, while the high-strength equation uses KG. The laminar burning velocity is the more fundamental parameter, and there are numerous reported measured values of Su for a wide variety of gases and gas mixtures. Table D.1 of NFPA 68-2007 [11] is one such tabulation. Therefore, it is desirable to replace Equation 5 with an equation using Su. It is also desirable for the high-strength and low-strength equations to produce the same or much closer vent areas than exists now at the demarcation value of Pred for the applicability of the two equations. This is particularly so due to a significant number of enclosures designed near the current demarcation value of 0.1 bar-g. Since the value of C in Equation 2 is a constant for a given value of Su, the Swift-Epstein low strength equation in NFPA 68-2007 uses only the enclosure surface area and a fuel factor to determine vent area to produce a given pressure, Pred. While attractive in its simplicity, it does not account for the well-known variation of turbulent burning velocities and flame instability manifestations with increasing enclosure scale. Therefore, the use of empirical C values based on a limited range of test volumes may cause calculated vent areas to be under-sized for large volume applications such as large buildings. Conversely, the enveloping of the data to select the C values is probably producing unnecessarily large vent areas for applications with volumes smaller than about 10 m3. This was the conclusion of Razus and Krause [14] when they compared the pressures calculated from the NFPA 68 equations with those of other vent area equations and to test data that mostly involved enclosure volumes in the range 0.6 m3 to 1 m3. Another major effect not accounted for in the 2007 and earlier editions of NFPA 68 is the influence of internal equipment and structures within the enclosure. The magnitude of the effect of these turbulence-inducing obstacles was investigated by Zalosh in a 2008 NFPA Fire Protection Research Foundation project [15]. Test data on this effect was compiled from eight test programs involving vented gas explosions in enclosures with volumes between 2.5 m3 and 2688 m3. This report provided graphs and correlations to show how the ratio of NFPA-68 calculated vent areas to actual vent area varies with the obstacle/enclosure surface area and volume ratios for both small and large obstacles. One of those graphs is shown here as Figure 3. All the vent area ratio data in Figure 3 are less than one when the surface area ratio, As_obstacle/As_enclosure is greater than 0.46. Some of the data in Figure 3 show vent area ratios less than one at As_obstacle/As_enclosure ratios as low as 0.21. Thus, a critical value for As_obstacle/As_enclosure , or Aobs/As, to indicate a need for greater vent area could be expressed as in Equation 8, where the precise value, in the range 0.21 to 0.46, depends on whether the obstacles are small or large compared to the characteristic dimension of the enclosure.
GCPS 2013 __________________________________________________________________________
46.021.0 <
<
crs
obs
AA
[Eq 8]
Figure 3. Plot of Calculated to Experimental Vent Area Ratio vs Obstacle/Enclosure Surface Area Ratio [15]
One other important drawback of the 2007 and previous NFPA 68 gas venting methods is the need to design vents for a scenario in which the flammable gas-air mixture is at near-stoichiometric proportions throughout almost the entire enclosure volume. This drawback is particularly problematic for large building applications in which there is only a limited amount of flammable gas or vapor. NFPA 68-2007 does have a partial volume provision in the dust explosion vent design methodology, but not for gas venting. 4. Development of the NFPA-68 2013 Gas Venting Equations 4.1 Development Approach The latest revision of NFPA-68 is the first step in moving away from the constant C-factor and KG parameters toward a consistent use of the laminar burning velocity, Su, and scale-dependent
GCPS 2013 __________________________________________________________________________
C values. The goal was to develop a single equation spanning the required strength or Pred range, as had been done earlier for dusts. A gas venting task group was charged with compiling test data, evaluating a number of candidate vent area equations, reviewing and incorporating the work of the Fire Protection Research Foundation, and making recommendations on a consistent approach for all Pred values. The NFPA gas venting task group worked on this charge over a period of two years on a volunteer basis. Various gas vent area equations were examined from the standpoint of 1) ease of use; 2) producing vent areas that were at least as large as the vent areas in most large enclosure experiments; and 3) having a fundamental foundation based on the laminar burning velocity and the key enclosure characteristics including volume scaling considerations that can potentially account for flame instabilities, flame stretch, and turbulence inducing flame accelerations. In terms of the key enclosure characteristics, it was considered preferable to use the enclosure internal surface area because that is the maximum flame surface area in the absence of flame wrinkling and stretching. Since it is also the enclosure parameter in the existing NFPA 68 low strength equations, it is already being used in many NFPA 68 applications. The goal of a single equation was not achieved because fundamentally based vent design equations need to account for the fundamentally different vent flow regimes associated with subsonic and sonic vent flows. The task group recommendation was to retain separate low and high strength relations, both based on the Swift-Epstein formulations described in references 8 and 16, respectively. A cross-over of Pred of 0.5 bar-g was determined based on a criterion that the two equations produce similar results for many applications in the Pred range of 0.2 bar-g to 0.5 bar-g. However the original constant turbulent flame enhancement factor, λ, in these references has been replaced with a volume scaling prescription based on the empirical equations reported by Rota, et al. [17] based on best fit comparisons to test data available circa 1990. In addition to the Rota turbulent adjustments, there are additional adjustments to include effects of internal obstacles as well as enclosure length to diameter ratio. While not discussed here, a Partial Volume adjustment has also been added, permitting reduced vent areas when the potential quantity of gas released is not sufficient to produce a stoichiometric mixture throughout the enclosure. 4.2 Swift-Epstein Equations Epstein, Swift and Fauske [16] derived deflagration vent area equations for sonic flow through the vent of a spherical vessel. Subsequently Swift and Epstein [8] developed a similar solution for sub-sonic incompressible flow. Equations 9 and 10 are the related NFPA-68 correlations for sub-sonic flow, applicable to low strength enclosures with Pred < 0.5 bar-g. The form of Equation 9 is identical to the prior NFPA-68 1988 solution with a different expression for C. The Committee modified the original expression for C in Equation 10, making some adjustments that are described in the Postscript section.
( )210
red
sv
P
ACA •= [Eq. 9]
GCPS 2013 __________________________________________________________________________
C is determined from Equation 10, including the burning velocity as the product of fundamental burning velocity and flame enhancement factor.
( ) 21
0
1
0
max 111
1
2+
−
++=
PP
PCG
SCb
du
uuγλρ
[Eq. 10]
Where:
Av0 = the minimum vent area calculated from Equation 6 (m2), As = the enclosure internal surface area (m2), Pred = the maximum pressure developed in a vented enclosure during a vented deflagration (bar-g), Pmax =the maximum pressure developed in a contained deflagration by ignition of the same gas-air mixture (bar-g), P0 = the enclosure pressure prior to ignition (bar-g), Su = fundamental burning velocity of gas-air mixture (m/sec), ρu = mass density of unburned gas-air mixture (kg/m3) = 1.2 for flammable gases with stoichiometric concentrations less than 5 volume percent, and an initial temperature of 20oC, Gu = unburned gas-air mixture sonic flow mass flux = 230.1 kg/m2-sec for air at an enclosure initial temperature of 20oC, λ = ratio of gas-air mixture burning velocity accounting for turbulence and flame instabilities in vented deflagration to the fundamental (laminar) burning velocity, γb = ratio of specific heats for burned gas-air mixture = 1.1 to 1.2 depending on the gas mixture Cd = vent flow discharge coefficient = 0.70 unless the vent occupies an entire wall of the enclosure, in which case a value of 0.80 can be used.
As with the 2007 low-strength solution, the vent release pressure, Pstat, is not explicitly included and continues to be arbitrarily set below Pred. When Pred ≤ 0.1 bar-g, Pstat must be less than or equal to (Pred - 0.024 bar). When Pred > 0.1 bar-g, Pstat must be less than 0.75 Pred. Equations 11 and 12 are the NFPA-68 correlations for sonic flow, applicable to high strength enclosures with Pred > 0.5 bar-g. Contrary to the low-strength correlation, the vent release pressure, Pstat, is explicitly included.
GCPS 2013 __________________________________________________________________________
du
uu
red
red
sv CGS
PP
PP
AAb
b
λρ
δγ
γ
−
++
++−
=1
max
1
max
0
1
1
1
11
[Eq. 11]
1)1()1(
1)1()1(
1
0
max
/1
0
−
++
−
++
=b
b
PP
PPstat
γ
γ
δ [Eq. 12]
Where:
Pstat = nominal vent deployment or burst pressure (bar-g) 4.3 Flame Stretch and Instabilities
NFPA 68-2013 evaluates λ in stages with a baseline value, λ0, then increased for the effect of turbulence-generating obstacles to become λ1, and finally increased for enclosure length to diameter ratio to become λ. 4.3.1 λ0 – Baseline Spherical, Unobstructed Rota, et al [17] developed a similar simplified model for spherical combustion, but continued to determine a value for λ without internal obstructions from the product of two effects, the flame growth inside the enclosure, shown here as ϕ1, and the flame flow through the vent, shown here as ϕ2. They evaluated three constants, θ, β1 and β2, to minimize the error between their simplified approach and a dataset of approximately 160 experiments. The NFPA 68 version simplifies the equations by setting a value of 4000 for the cellular flame Reynolds number originally part of ϕ1. Additionally, the original Rota equations use the ratio of flame volume to enclosure volume in the exponent of ϕ2 while the NFPA-68 version conservatively evaluates the flame growth effect at the point where the flame volume is equal to the vessel volume. Equations 13 through 18 are required to evaluate λ0.
210 ϕϕλ = [Eq. 13]
GCPS 2013 __________________________________________________________________________
<=
otherwise
if
f
fθϕ
4000
Re
4000Re,1
1 [Eq. 14]
u
heuu
f
DS
μ
ρ
=2
Re [Eq. 15]
=
uSv
2
612 10
Re,1max
β
βϕ [Eq. 16]
u
vvu
v
Du
μ
ρ
=2
Re [Eq. 17]
( )otherwiseabarPif
Pu ured
u
redv _,_9.0_
200000
<•
=ρ [Eq. 18]
where:
µu = the unburned gas-air mixture dynamic viscosity = 1.8x10-5 kg/m-sec for gas concentrations less than 5 vol% at ambient temperatures, Dhe = the enclosure hydraulic equivalent diameter as determined in Chapter 6 [of NPFA 68-2013] (m), Dv = the vent diameter as determined through iterative calculation (m), θ = 0.39, β1 = 1.23, β2 = 0.0487 m/sec.
Since the vent diameter in Equation 17 is a result of the analysis, the entire evaluation of required vent area becomes iterative. This means not only the basic equation but also corrections due to vent panel inertia and vent ducts are solved iteratively.
GCPS 2013 __________________________________________________________________________
Figures 4 and 5 show how the two components of λ0, ϕ1 and ϕ2, change with enclosure volume. For both figures, the high-strength Equation 11 was iterated to a small vent area that would produce a Pred of 95% of Pmax with Pstat at 90% of Pmax, essentially a closed volume deflagration. ϕ1 increases with volume at a rate proportional to Su while ϕ2 increases at a rate inversely proportional to Su. As a result of these two effects, λ0 increases with volume with the magnitude of the increase depending on the gas laminar burning velocity. Very large increases are produced for hydrogen due to flame instability induced increases in surface area, as represented by the ϕ1 variation shown in Figure 4. On the other hand, vent flow has more effect on flame enhancement for slower burning gases, as seen by variation in ϕ2 shown in Figure 5.
Figure 4: Variation of ϕ1 with Spherical Enclosure Volume
0
2
4
6
8
10
0.001 0.01 0.1 1 10 100 1000
ϕ1
Enclosure Volume, m3
Methane
Propane
Hydrogen
GCPS 2013 __________________________________________________________________________
Figure 5: Variation of ϕ2 with Spherical Enclosure Volume 4.3,2 λ1 – Surface Area of Obstructions In the interest of ease of use, the range of critical internal obstacle surface areas represented by Equation 8 was reduced to a single value, that is, when the surface area of the internal obstacles exceeds 40% of the enclosure surface area. NFPA-68 requires an estimation of the total external surface area, Aobs, of equipment and other objects within the enclosure such as:
• Piping – Piping, tubing and conduit with diameters greater than ½ inch.
• Building Supports – Internal structural columns, beams, and joists.
• Stairways – Stairways and railings.
• Smaller Equipment – Equipment with a characteristic dimension in the range 2 inches to 20 inches
As a practical matter, there is conflicting guidance in NFPA-68 concerning idealizing the enclosure surface area while at the same time considering the surface area of internal obstacles. At this time a degree of judgment is needed and the listed elements directly attached to or very near to the enclosure surface would not be “obstacles”. For instance, the wall and flat ceiling
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.001 0.01 0.1 1 10 100 1000
ϕ2
Enclosure Volume, m3
Methane
Propane
Hydrogen
GCPS 2013 __________________________________________________________________________
support beams might not be included while mezzanine steel supports and stairways would be included. A 1 inch thick by 11 inch deep fiberglass composite stair tread with 1-inch square open rectangular construction might be considered a 1 inch by 11 inch rectangle, ignoring all of the surface created by the 1-inch openings. After estimating the surface area of the obstructions, if this does not exceed 40% of the enclosure surface, no adjustment is made and λ1 = λ0. When Aobs is > 0.4As, λ is increased linearly as in Equation 19.
+•=
s
obs
AA
6.001 λλ for Aobs/As > 0.40 [Eq. 19]
4.3.3 λ – Length to Diameter Ratio of Enclosure The 2007 edition of NFPA-68 effectively limited the low-strength correlation to an L/D of 3 by prescribing the maximum length of a protected enclosure with a single end-mounted vent to be 3 times the hydraulic diameter of the enclosure. At the same time, the high-strength correlation applied a correction factor beginning at L/D = 2. The current formulation compromises and applies a similar correction factor beginning at L/D = 2.5. If the L/D does not exceed 2.5, no adjustment is made and λ = λ1. For L/D values from 2.5 to 5, and for Pred no higher than 2 bar-g, λ is increased as in Equation 20.
)15.2
1(
2
1
−+•= D
Lλλ [Eq. 20]
5. Comparison to Large-Scale Test Data The task group assembled a database of over 200 tests, mostly in unobstructed enclosures, with volumes of at least 1 m3. These are in addition to the database of over 150 tests previously compiled by Zalosh [15] for tests in large enclosures with obstructions. A subset of the unobstructed enclosure data pertaining to gas-filled compact enclosures (L/D ≤ 2.5) was selected for comparison with calculations using the λ-adjusted Swift-Epstein equations described above. The test program enclosures and gases selected for comparison calculations are listed in Table 4.
Table 4. Large-Scale Unobstructed Enclosure Test Programs Used for Vent Area Calculations Enclosure Geometry Enclosure
Volume (m3) Gases Tested Number of
Tests Reference
Cube, Cylinder 1 Methane 13 Bartknecht 1981 [10] Cylinder 1 Hydrogen, 29.6% 2 Pasman [18] Sphere 2 Methane 2 Bartknecht [10]
Cylinder 2.5 Propane 9 DeGood & Chatrathi [19 ]
GCPS 2013 __________________________________________________________________________
Enclosure Geometry Enclosure Volume (m3)
Gases Tested Number of Tests
Reference
Cube 5.2 Propane 1 Van Wingerden et al [20 ] Box/Room 11.2 Methane 1 Zalosh [21 ]
Cube 22 Methane 7 Thorne et al [22] Cube 22 Propane 5 Thorne et al [22] Cube 25 Hydrogen 12% 5 Cerchiara&Carcassi,[23]
Cylinder 29 Propane 24 Swift-Epstein [8] Box/Room 34 Methane 2 Zalosh [21 ]
Sphere 60 Propane 8 Bartknecht [10] Box/Room 64 H2 (18%), C3H8, CH4 10 Bauwens et al [24] Box/Room 69 Methane 2 Lowensmith et al [3]
After calculating the required vent area from the reported value of Pred in each test, the calculated vent area was divided by the actual vent area used in the test. The resulting vent area ratios, Av,calc/Av,exp , are shown plotted versus enclosure volume in Figure 6. The calculated vent areas are equal to or greater than the actual test vent areas for all enclosure volumes greater than 1 m3. The only tests in which calculated vent areas are smaller than actual vent areas are for the 1 m3 cube data reported by Bartknecht. Comparisons of this particular Bartknecht data with calculations using other vent sizing equations in Table 3 of Razus and Krause [14] indicate that this is one of the few data sets for which most of the vent sizing methods underestimate the reported Pred values or vent areas. Figure 7 is a plot of the ratio of the calculated to actual test vent area against the reported Pred values. The plot shows most of the ratios greater than 2 are for Pred values less than 0.5 bar-g. This indicates that the low-pressure Swift-Epstein equations (9 and 10) seem to produce larger than required vent areas more often than do the high-pressure versions of the equations (11 and 12). As in Figure 6, the only ratios less than 1 are for the Bartknecht 1 m3 methane data set.
GCPS 2013 __________________________________________________________________________
Figure 6: Ratio of Calculated to Actual Vent Area versus Enclosure Volume
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
1 10 100
Av, calc/Av, exp
Enclosure Volume, m3
Methane; 9.5-10%
Propane 4-5.5%
Hydrogen 12-18%
GCPS 2013 __________________________________________________________________________
Figure 7: Ratio of Calculated to Actual Vent Area versus Measured Pred The new NFPA 68-2013 Swift-Epstein equations have also been used to calculate vent areas for a subset of the obstructed enclosure data compiled in the Fire Protection Research Foundation report [15]. The five data sets used for the calculations and comparisons are listed in Table 5. Three of the test programs used simulated piping arrays as obstructions, and the other two programs used larger obstructions. Table 5. Obstructed Enclosure Test Data Used for Vent Area Calculations Test Program or
Organization Year Size of Test
Enclosure (m3) Type of Obstacles Number of
Tests Reference
Christian Michelson
Research Institute
1986 27 Pipe Arrays 12 GexCon Gas Explosion Handbook
Monsanto-Fenwal 1982 82.1 Baffle partitions 8 Howard and Karabinis [25]
Solvex Full-Scale 1993 550 Pipe Arrays 17 Bimson et al. [26]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.0 0.5 1.0 1.5 2.0
Av, calc/Av, exp
Pred (barg)
Methane; 9.5-10%
Propane 4-5.5%
Hydrogen 12-18%
GCPS 2013 __________________________________________________________________________
Test Program or Organization
Year Size of Test Enclosure (m3)
Type of Obstacles Number of Tests
Reference
BFETS 1998 1638, 2688
Low-Density and High-Density Offshore Platform
Modules1
27 Selby and Burgan [27]
Baker Risk 2006 98 Piping Array 4 reported
Thomas et al [28]
Figure 8 is a plot of Av,calc/Av,exp using the NFPA 68-2013 vent sizing equations versus Aobs/As, i.e. the analogous plot to Figure 3 for which the calculated vent areas were obtained using the NFPA 68-2007 vent area equations. Unlike Figure 3, most of the vent area ratios in Figure 8 are larger than one even for Aobs/As values greater than 0.50. The remaining under-sized vent areas in Figure 8 are for the GexCon 1986 and Baker Risk 2006 piping arrays, i.e. for small-scale repeated obstructions. These repeated piping array structures are similar to the simulated piping arrays that produce high flame speeds and pressures in large-scale vapor cloud explosion test programs. In other words, the flame acceleration mechanisms associated with heavily congested piping arrays are not sensitive to the level of confinement associated with varying vent areas. The Baker Risk 2006 tests were, in fact, conducted with all four enclosure walls being vented. The data shown in Figure 8 suggest that the new NFPA 68-2013 algorithm for including equipment obstructions in the deflagration vent area calculations is a step in the right direction, but does not accurately account for extreme flame accelerations associated with heavily congested piping. Additional work, accounting for the scale and repeated nature of the obstructions is needed.
1 Low-density BFETS module had compressor and control room mockups, while the high-density module had additional vessels, pipe racks and cable trays.
GCPS 2013 __________________________________________________________________________
Figure 8. Plot of Calculated to Experimental Vent Area Ratio vs Obstacle/Enclosure Surface Area Ratio – NFPA 68-2013 6. Conclusion NFPA-68 has developed a new method for required gas deflagration vent area sizing calculations. The 2013 equations are essentially a more transparent casting of the Swift-Epstein-Fauske derivations to provide a framework for including approaches to model flame accelerations and flame wrinkling/stretching in large enclosures with and without internal obstacles. These equations compare favorably with the reference data sets for unobstructed and minimally obstructed enclosures. For a typical medium volume (196 m3) unobstructed enclosure containing propane, designed for a Pred of approximately 0.1 bar-g = 1.45 psig, the new method produces vent area results comparable to prior NFPA vent sizing methods as seen in Table 6.
Table 6. Comparison of Historical Gas Vent Sizing Methods NFPA 68 Edition Method Basic Equation
Number Vent Area, ft2
1978 Runes 1 622 1988 Swift Simplified (low Pred) 2 325 1988 Bartknecht Nomograph (high Pred) 3 300 1998 Bartknecht Correlation (high Pred) 5 259
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Av, calc/Av, exp
Aobs/As
"BFETS Phase 2, 1998"Baker Risk, 2006Shell SOLVEX 1993GexCon 1986Monsanto-Fenwal 1982
GCPS 2013 __________________________________________________________________________
NFPA 68 Edition Method Basic Equation Number
Vent Area, ft2
2007 Swift Simplified, C=f(Su) 2 & 7 380 2012 S-E Modified (low Pred) 9 & 10 389
Calculated vent areas using the new method now also prevent under-sized vent areas for large enclosures with large equipment representative of many petrochemical process structures. However, the new methodology does not yet reproduce large-scale test data with repeated small obstacles simulating highly congested piping arrays and more work on this issue is necessary. 7. PostScript – Background of the NFPA-68 Formulation The NFPA-68 formulations appear different in two respects from the Swift-Epstein derivations. First, the pressure terms include a factor of 1 and second, the frictionless sonic mass flow, Gu, is shown in both. The first difference is the result of NFPA-68 traditionally using gauge pressures instead of absolute pressures and assuming atmospheric pressure to be 1 bar, as opposed to 1 atm. This is a minor difference for simplicity. More importantly, the original derivations both are based on a dimensionless group, B, relating the maximum burning rate to the maximum flow through the vent. B is defined slightly differently in each case, including a mass flux term, G’, and the vent discharge coefficient, Cd, in the low pressure solution while only including G explicitly in the high pressure solution as in Equations a and b, respectively. For low pressure (low-strength),
vd
suu
AGCASB
'
ρλ≡ [Eq. a]
For high pressure (high-strength),
v
suu
GAASB ρλ≡ [Eq. b]
G’ and G are different parameters. By recasting each in terms of sonic velocity, au, the NFPA-68 formulation can be explained. G’ is described initially as the incompressible mass rate of discharge and defined traditionally as in Equation c.
( )[ ] 21
12' PPPCG aud −= ρ [Eq. c]
Without changing the symbol, the maximum value of G’ is then taken as the frictionless mass flow when Pa/P <<1, resulting in Equation d. Cd is then shown explicitly in the dimensionless group B as in Equation a.
GCPS 2013 __________________________________________________________________________
( ) 21
2' uPG ρ= [Eq. d]
The factor CdG’/ρu, included in the low pressure group B, can be written in terms of sonic velocity, au, for an ideal gas as in Equation e.
uud
u
d aCGCγρ2' = [Eq. e]
The description of G in the high pressure derivation is the sonic mass flow per unit area, not the frictionless sonic mass flow, as indicated in the footnote to page 3 of their paper [15]. G/ρu can similarly be written in terms of sonic velocity as in Equation f.
( ) ( )11
1
2−+
+
=uu
uud
u
aCGγγ
γρ [Eq. f]
Combining Equations e and f, shows that the ratio of the two original mass flow parameters is a function of γu and, equal to approximately 2 when γu is 1.36.
( ) ( ) 209.2
1
2
2
'11
≈=
+
= −+ uu
u
ud
GGC
γγ
γ
γ [Eq. g]
Finally separating Cd from G clarifies the NFPA-68 formulations.
udd GCGGC 22' =≈ [Eq. h]
8. Acknowledgments The authors wish to acknowledge the significant assistance of Steve Stuart and Michael Davies as members of the Gas Venting Task Group compiling the test data, as well as Alfonso Ibarreta for investigating and recommending appropriate methods to calculate gas mixture burning velocities. 9. References [1] NFPA 68, Standard on Explosion Protection by Deflagration Venting, 2013 edition,
National Fire Protection Association, Quincy, MA.
GCPS 2013 __________________________________________________________________________
[2] M.G. Cooper, M. Fairweather, and J.P. Tite, "On the Mechanisms of Pressure
Generation in Vented Explosions," Combustion and Flame 65 (1986): 1-14.
[3] B. J. Lowesmith, C. Mumby, G. Hankinsom and J. S. Puttock- Vented Confined
Explosions Involving Methane/Hydrogen Mixtures- 3rd ICHS, September 16-18, 2009.
[4] E. Cousins and P. Cotton, “The Protection of Closed Vessels Against Internal Explosions,” ASME Paper No. 51-RPI-2, 1951.
[5] NFPA 68, Explosion Venting, 1978 edition, National Fire Protection Association, Quincy, MA.
[6] E. Runes, “Explosion Venting,” Loss Prevention – Volume 6, (1972): 68-73, AIChE, New York, NY.
[7] NFPA 68, Guide for Venting of Deflagrations, 1988 edition, National Fire Protection Association, Quincy, MA.
[8] I. Swift and M. Epstein, “Performance of Low Pressure Explosion Vents,” Plant/Operation Progress (Vol. 6, No. 2) 1987: 98-105.
[9] I. Swift, “Designing Explosion Vents Easily and Accurately,” Chemical Engineering April 11, (1988): 65-68.
[10] W. Bartknecht, Explosions Course, Prevention, Protection. Berlin: Springer-Verlag (1981)
[11] NFPA 68, Standard on Explosion Protection by Deflagration Venting, 2007 edition, National Fire Protection Association, Quincy, MA.
[12] W. Bartknecht, Explosions-Schutz: Grundlagen und Anwendung. Berlin: Springer-Verlag (1993)
[13] NFPA 68, Guide for Venting of Deflagrations, 1998 edition, National Fire Protection Association, Quincy, MA.
[14] D. Razus and U. Krause, “Comparison of empirical and semi-empirical calculation methods for venting of gas explosions,” Fire Safety Journal 36 (2001): 1-23.
[15] R. G. Zalosh, “Explosion Venting Data and Modeling Literature Review,” Fire Protection Research Foundation Report, 2008.
[16] M. Epstein, I. Swift and H.K. Fauske “Estimation of Peak Pressure for Sonic-Vented Hydrocarbon Explosions in Spherical Vessels,” Combustion and Flame 66 (1986): 1-8.
[17] R. Rota, P. Canu, S. Carra and M. Morbidelli, “Vented Gas Deflagration Modeling: A Simplified Approach,” Combustion and Flame 85 (1991): 319-330.
[18] Pasman H., Groothuisen Th. P., Goojier, P.- Design of pressure relief vents- Proceedings of First International Symposium on Loss Prevention, Delft- Amsterdam: Elsevier, 1974, pp 185-189
[19] R. DeGood, K. Chatrathi, “Comparative analysis of test work studying factors influencing pressures developed in vented deflagrations,” Journal of Loss Prevention 4 (5) (1991): 297-305.
GCPS 2013 __________________________________________________________________________
[20] van Wingerden C. J. M., Zeeuwen J. P.- Venting of Gas Explosions in Large Rooms- 4th International Symposium on Loss Prevention and Safety Promotion in the ProcessIndustries, EFCE Publication Series, No. 33, Vol. 3, F38-F47, 12-16 September (1983)
[21] R. G. Zalosh, “Gas Explosion Tests in Room-like Vented Enclosures” Loss Prevention, Vol 13, AIChE, 1979
[22] Thorne P. F., Rogowski Z. W., Field, P.- Performance of Low Inertia Explosion Reliefs Fitted to a 22 m3 Cubical Chamber- 4th International Symposium on Loss Prevention and Safety Promotion in the Process Industries, EFCE Publication Series, No. 33, Vol. 3, F1-F10, 12-16 September (1983)
[23] Cerchiara and Carcassi- “Quantification of the Uncertainty of the Peak Pressure Value in the Vented Deflagrations of Air-Hydrogen Mixtures,” 2nd ICHS 2007
[24] Bauwens, C. R., Chaffee, J and Dorofeev, S. B.- Vented Explosion Overpressures from Combustion of Hydrogen and Hydrocarbon Mixtures- 3rd ICHS, September 16-18, 2009
[25] Howard W. B., Karabinis A. H.- Tests of Explosion Venting of Buildings- Plant/Operations Progress, 1, 51-68 (1982)
[26] Bimson, B., Bull, D., Creswell, T., Marks, P., Masters, A., Prothero, A., Puttock, J., Rowson, J. and Samuels, B. (1993). “An Experimental Study of the Physics of Gaseous Deflagrations in a Very Large Vented Enclosure.” International Colloquium on the Dynamics of Explosions and Reactive Systems.
[27] Selby, C. and Burgan, B. (1996). “Blast & Fire Engineering for Topside Structures, Phase II, Final Summary Report, The Steel Construction Institute, SCI Publication 253.
[28] Thomas, J. K., Kolbe, M., Goodrich, M., and Salzano, E. (2006). Elevated Internal Pressures in Vented Deflagration Tests. AIChE 40th Annual Loss Prevention Symposium. Orlando, AIChE.
