Estimating Flame Speeds for Use with the BST Blast Curves. Timothy A. Melton and Jeffrey D. Marx

Transcription

1 Estimating Flame Speeds or Use with the BST Blast Curves Timothy A. elton and Jerey D. arx Presented At American Institute o Chemical Engineers 008 Spring National eeting New Orleans, Louisiana April 6-10, 008 Quest Consultants Inc th Avenue N.W. Norman, Oklahoma Telephone: Fax: ino@questconsult.com URL: QUEST

2 Estimating Flame Speeds or Use with the BST Blast Curves Timothy A. elton and Jerey D. arx Quest Consultants Inc., 908 6th Avenue NW, Norman, OK USA ABSTRACT The Baker-Strehlow-Tang (BST) vapor cloud explosion model is one o the most common methods used to estimate overpressures or the purpose o locating buildings in relation to process units. This model suers rom a problem common to all simpliied explosion models: the user is required to pick the strength o the explosion using one or more simple parameters. In the BST model, the uel reactivity, lame expansion, and obstacle density parameters are used to select a lame speed rom a limited matrix o possible values. This paper presents the Quest odel or Estimation o Flame Speeds (QEFS), a systematic approach to estimating lame speed that does not rely on the BST categories. It provides or a continuous range o lame speeds that can then be used with the existing BST blast curves to calculate the characteristics o the vapor cloud explosion. The QEFS approach provides the user with a method or describing a VCE that is more detailed than the BST model, and establishes a more reined system or predicting the consequences o vapor cloud explosions. 1. INTRODUCTION Any release o a lammable luid in a petrochemical acility has the potential to generate a lammable vapor cloud that, i ignited, could produce a vapor cloud explosion (VCE). I the VCE generates damaging levels o overpressure, the possibility o human injury/death, asset damage, or event escalation becomes a concern. The concern or human injury or death is most oten addressed in the orm o a building siting study. Because people are somewhat less likely to be injured or killed when outside, as compared to when inside a building, the siting study ocuses on the potential impacts to buildings within and around petrochemical acilities. It then becomes the task o process saety proessionals to estimate the potential or VCE events, and their resulting overpressure impacts on buildings. Prediction o the overpressures resulting rom a VCE is typically done using one o two categories o models: computational luid dynamics (CFD) models and simpliied models. CFD models calculate the overpressure ield by solving the Navier-Stokes equations numerically and incorporating dierent sub-models to account or turbulence and combustion reactions. Results are oten strongly dependent on the location and strength o the ignition point, the location and composition o the lammable cloud throughout its volume, and the location and coniguration o any obstacles or obstructions within the cloud. The time required to calculate the overpressures resulting rom a single ignition point/cloud geometry/location geometry can be signiicant. Given the number o combinations o ignition points and Copyright 008, Quest Consultants Inc., 908 6th Avenue N.W., Norman, Oklahoma 73069, USA. All rights reserved. Copyright is owned by Quest Consultants Inc. Any person is hereby authorized to view, copy, print, and distribute documents subject to the ollowing conditions. 1. Document may be used or inormational purposes only.. Document may only be used or non-commercial purposes. 3. Any document copy or portion thereo must include this copyright notice. -1- QUEST

3 cloud geometries (e.g., changes in wind direction or wind speed) that can inluence a given lammable release; it is generally prohibitive to use CFD or risk assessment or building siting purposes. Simpliied models such as the Baker-Strehlow-Tang (BST) model or the TNO ulti-energy model use inormation taken rom CFD studies to generate curves deining the relationship between explosion overpressure and distance rom the explosion center. These curves can then be used in a more general manner to estimate the overpressure impacts generated by an exploding vapor cloud. However, both approaches, require the user to estimate the strength o the explosion as a unction o the reactivity o the lammable material and the degree o coninement or congestion present in the cloud. This inormation is then used to determine which strength curve (in the case o the TNO model) or lame speed (in the case o the BST model) is used to calculate the overpressure o the explosion as a unction o distance rom the center o the explosion. The TNO ulti-energy model provides little guidance or selecting the explosion strength curve. Curves or strengths in the range o 1 to 10 are provided, and it is let to the user to determine how the reactivity o the lammable gas and the degree o coninement or congestion relate to one o these curves. The BST model is based on a simple set o guidelines that result in a selection o a lame speed, which corresponds to an overpressure vs. distance curve. Three parameters are used to determine the lame speed to be used: reactivity o the lammable gas, the degree o coninement o the lammable cloud, and the degree o obstruction due to obstacles within the lammable cloud. Reactivity is divided into three categories: low, medium, and high. According to the current BST model, materials having a laminar lame speed greater than 0.75 m/s are considered high reactivity [] while those having a laminar lame speed below 0.4 m/s are considered low reactivity[] (the threshold or high reactivity was originally set at 0.8 m/s [1]). All other materials are considered to be medium reactivity. The eect o the coninement o the lammable cloud is taken into account by determining the number o dimensions in which the burning gas may expand. 3-D expansion allows the burning cloud to expand reely in all directions and results in the slowest lame acceleration and lowest overpressures. -D expansion, such as a lame between two lat plates, generates higher overpressures because the combustion gases have ewer directions in which to expand resulting is a higher lame acceleration. Finally, 1-D expansion is used or planar lames propagating in pipes. The eect o obstacles in the lammable cloud is characterized by the obstacle density, classiied as low, medium, or high. In the original Baker-Strehlow model, low obstacle density was deined as having an area blockage ratio (ABR) o less than 10%, while high obstacle density was deined as an ABR o 40% or greater, and everything in between is considered medium [1]. One problem with the BST scheme is that there are oten large jumps in lame speed between categories o coninement, reactivity, or obstruction. This problem was irst addressed by Baker in a 1998 paper [] where a new coninement category, ½-D, was added or those situations that were more conined than the 3-D case, but less so than the -D case. The lame speeds used or the ½-D coninement were simply the arithmetic average o the lame speeds or the -D and 3-D cases or a given reactivity and congestion class. Even with this extension, large discontinuities remained among the categories or lame speed according to the prescribed methodology. These discontinuities drive the need or a new method to determine lame speed based upon quantiiable properties o the lammable gas and its surroundings that varies smoothly across the range o conditions that are ound in actual process plants. The model presented in this paper provides a method or estimating the maximum lame speed that may be expected ollowing ignition o a lammable cloud. That lame speed may then be used with the BST blast curves to estimate the overpressure impacts in the area surrounding a vapor cloud explosion. -1- QUEST

4 . PARAETERS AFFECTING FLAE SPEED.1 Reactivity Fuel reactivity is a measure o the propensity o the lame ront in a given lammable mixture to accelerate and create overpressures or potentially undergo a delagration-to-detonation transition (DDT). In the BST model, reactivity is classiied as high, medium, or low based on the laminar lame speed o the uel-air mixture. These categories have been given boundaries, eectively placing certain materials in each category. For example, the laminar lame speed o ethylene, depending on the cited reerence, ranges between 0.64 and 0.83 m/s. In the original Baker-Strehlow model, the division between medium and high reactivity categories was 0.8 m/s [1]. In 1998, this division was re-deined as 0.75 m/s. This clearly makes ethylene a borderline uel one that may either be deined as medium or high reactivity. In the latest published BST model [9], ethylene is explicitly categorized as a high reactivity material, as their experimental work deined ethylene as the high reactivity material. This then begs the question: what about ethylene oxide (laminar lame speed 1.0 m/s) or acetylene (laminar lame speed 1.6 m/s)? These two materials are clearly more reactive than ethylene, but are still categorized as high reactivity. The BST model eectively says that an ethylene explosion will be as severe as an ethylene oxide explosion, when all other parameters are held constant.. Congestion Congestion in the original Baker-Strehlow VCE [1] model was classiied as high, medium, or low based on the area blockage ratio (ABR) o obstructions in the path o the expanding lame ront. Later guidelines produced or the BST model in light o more recent data seem to suggest that the volume blockage ratio (VBR) is a better parameter or classiying an obstructed area [9]. In practice, both blockage ratios will eect how ast a lame accelerates, but, or a uniorm obstacle ield, the two are related simply by the pitch-todiameter ratio o the obstacles. I the obstacles included in the ABR are not repeated quasi-uniormly throughout the obstacle ield but are only present in distinct planes, their eect would be more accurately portrayed by something similar to a coninement parameter..3 Coninement The eect o coninement is included in the BST model by identiying the number o dimensions that are available to the products o combustion or expansion. Expansion into ree space is considered 3-D expansion, expansion between two parallel planes is considered -D expansion, and expansion in a pipe is considered 1-D expansion. The 1-D case was removed in the more recent publications discussing the BST model [9]. To handle the case o a rangible or partially-conining plane, such as a very closely spaced pipe rack, the BST model added a.5-d classiication which simply averaged the -D and 3-D lame speed results..4 Other Factors Several researchers [3,6,9] have acknowledged that the overall dimensions o the lammable vapor cloud beore ignition directly aect the inal lame speed and consequent overpressures o the vapor cloud explosion. Since a lame will accelerate until it undergoes DDT or reaches a maximum sustainable value, the maximum dimension o a lammable cloud is expected to be an important variable in the creation o overpressure. In addition, research [3,4,5,6] suggests that the scale o obstacles within the congested area also aects the maximum lame speed that may be achieved. Both o these actors should be included in any correlation or the prediction o lame speeds in vapor clouds. -- QUEST

5 3. NEW ODEL FOR ESTIATING FLAE SPEED Portions o existing modeling methodologies and experimental data sets have been used in order to create a new model that provides the capability or more detailed descriptions o explosion scenarios. This new model bases the prediction o overpressure on the ollowing parameters: Laminar lame speed is used as the characteristic property or uel reactivity. Volume blockage ratio and average obstacle diameter deine the level o congestion. Coninement is characterized as the number o conining planes, or walls, that are available to conine the expanding gases. Length, width, and height o the explosion source region are used to deine the volume o gas and the maximum lame acceleration path, or run-up distance. The new method or deining release-speciic lame speed combines inormation rom the European ERGE and EERGE tests [11] and the BST model [10] with the new values or lame speed given or use in the BST model by Pierorazio, et al. [9]. 3.1 Fundamental Correlations The original Baker-Strehlow curves were presented in terms o w, the velocity o heat addition in the numerical calculations relative to a Lagrangian (moving) coordinate system. However, the actual lame speed measured in experiments,, is based on an Eulerian (ixed) coordinate system. When presenting the new BST curves, Tang and Baker [10] presented the curves in terms o, the measured lame velocity. To convert rom w to velocities, they determined the overpressure or a range o values o w and then converted them to using the ollowing equation derived rom acoustic theory: p max p 0 p 0 = ( 1 ) where: p max p 0 = the maximum overpressure attained, bara = the ambient pressure, bara = the lame speed relative to a ixed observer, expressed as a ach number Based on extensive experimental research programs perormed during the ERGE and EERGE projects [3,4,5,6], TNO, in the GAES project, developed the ollowing correlation or explosion overpressure in 3-D lame expansion conditions [7]: where: VBR L P0 = 084. D 75. Sl D P 0 = the overpressure (equivalent to p max p0 in equation 7, above), bar VBR = the volume blockage ratio L = the maximum distance a lame may propagate in the obstructed region (i.e., the run-up distance), m D = the average obstacle diameter, m ( ) -3- QUEST

6 S l = the laminar lame speed o the lammable gas, m/s Combining equation 1 with equation, yields:.75 VBR L.4 p0 = 0.84 S D 1+ D l ( 3 ) which gives a the ollowing quadratic equation in :.4 po RHS3D RHS3D 0 = ( 4 ) where RHS 3D is the right hand side o equation 3:.75 VBR L RHS3D= 0.84 S D D l ( 5 ) To simpliy, p 0 was set equal to 1 bar, giving the solutions to this equation as: RHS3D ± RHS3D RHS3D = ( 6 ) 4.8 Since all terms in RHS 3D are positive, and must be positive, the only physically meaningul solution remaining is: RHS3D + RHS3D RHS3D = ( 7 ) 4.8 The GAES project also produced a correlation or overpressure achieved by -D lame expansion [7], which takes the same orm as equation. A solution or lame speed can be derived in the same manner as presented or the 3-D correlation using.5 VBR L RHSD= 3.38 S D D l ( 8 ) in place o RHS 3D in equations 4, 6, and 7. A inal correction is applied to the calculated lame speed or the number o planes that conine the expanding products o combustion. Assuming the entire mixture is burned, there is a relationship between the initial and inal dimensions o the unburned gases and products o combustion and the available directions in which the cloud may expand. Deining α as the ratio o the volume o the products o combustion divided by the initial lammable gas volume (i.e. the expansion ratio), or a spherical cloud (3-D expansion): Vb α = = V u π rb π r u ( 9 ) -4- QUEST

7 where: V u = volume o unburned gas V b = volume o combustion products r u = radius, unburned gas r b = radius, combustion products which leads to: 3 rb = α ru ( 10 ) Similarly, or -D expansion: α π rb h = π ru h ( 11 ) where: h = the height o the cylinder or: r = α r ( 1 ) b And inally, or 1-D expansion: u where: or: π R rb α = π R ru R r u r b r b = the radius o the pipe = length, unburned gas in the pipe = length, combustion products in the pipe ( 13 ) = α r ( 14 ) u To correct the lame speed to account or coninement, a curve it o the ratio o burned cloud to unburned cloud radii versus the number o conining planes was made. The values resulting rom Equations 10, 1, and 14 were used to generate the curve it with α = 7, a typical expansion ratio or common hydrocarbon uels in air. This is also the value assumed in the derivation o Equation 1, as presented in Tang and Baker [10]. The equation resulting rom this curve it is: 1 NPF = nplanes ( 15) where: NPF = lame speed correction actor nplanes = number o conining planes For true 3-D spherical expansion, nplanes = 0. For a typical explosion at grade level, nplanes = 1. For -D expansion, such as a lame propagating between a loor and a ceiling, nplanes =. For 1-D expansion, such as a lame ront moving in one direction in a pipe, nplanes = 5. Planes that are not completely solid or rigid may be accounted or using a raction o a plane. The lame speed correction actor, NPF, does not ully account or increases in lame speed as the number o conining planes increases. This is seen directly when comparing the lame speed predicted by the -D GAES correlation (applying equation 8 to equation 7) to the lame speed predicted by the 3-D GAES -5- QUEST

8 correlation (applying equation 5 to equation 7) and adjusting by NPF when nplanes is equal to. In order to supplement NPF, lame speeds are also corrected so that they match the -D GAES correlation. This is accomplished by applying the ollowing actor to the lame speed when nplanes is equal to : β =, D,3 D NPF ( nplanes = ) (16) This can be implemented in a general orm, such that it can be applied to all calculations o lame speed, using the ollowing relationship: [ β ] =,3D NPF 1 + ( 1)( nplanes 1) (17) 3. Flame Speed Limits One problem with equation 7 is that it does not limit the predicted lame speed or large values o L or S l, allowing it to increase nearly as ast as the cube o their values. This is a direct result o the correlation itting the data within the scope o the ERGE and EERGE tests. In reality, or a given obstacle coniguration, geometry, and lammable gas mixture, there is a limit to the lame speed that can be achieved. This lame speed may be either subsonic or the cloud may undergo a delagration-to-detonation transition (DDT) in which the lame ront becomes a detonation propagating at roughly the Chapman-Jouguet (C-J) detonation velocity or the lammable mixture. For most common lammable hydrocarbons in air, this speed is roughly 1800 m/s or = 5.. The lame speeds suggested by the latest BST model [9] are applied as the upper limit lame speeds to be used in this model, as they have been scaled up to account or industrial scale lammable clouds [9] and account or DDTs. For purposes o this model, any lame that accelerates to a calculated velocity greater than = 3.0 is considered to have undergone DDT [8,1] and the lame speed is set to the C-J velocity, = 5.. The parameters in the new model described in this paper corresponding to the existing BST conditions are listed in Table 1. Table 1 BST Flame Speed Parameters BST Parameter Reactivity Obstacle Density Expansion Category New odel Parameter Corresponding Parameter Value Low (e.g., ethane) 0.37 m/s edium (e.g., Propane) S l 0.43 m/s High (e.g., Ethylene) 0.76 m/s Low edium VBR High D 1 -D nplanes 1-D 5-6- QUEST

9 The characteristic obstacle diameter or the BST tests was inches ( meters) and the length available or lame acceleration was 15 meters [9]. To determine the maximum allowable lame speed or any given combination o VBR, S l, D, L and nplanes, the given values are linearly interpolated rom the values presented in Pierorazio, et al. [9]. This approach is consistent with the approach used in Baker, et al. [] to determine lame speed or expansion geometries between 3-D and -D, i.e. ½-D expansion. The result o these correlations is a model that estimates the lame speed based on VBR, D, S l, L and the number o conining planes. The resulting lame speed is compared to the published BST model, which provides a matrix o lame speeds as a unction o reactivity, obstacle density, and lame expansion. The BST matrix values are used as maximum lame speed values or the set o parameters given in Table 1. Values between or outside the BST matrix elements are calculated by linear interpolation (as was done or Baker s ½-D lame expansion category). This methodology provides an extended, systematic approach or estimating lame speeds resulting rom the combustion o a lammable cloud in an obstructed and/or conined region. Predicted lame speeds are used with the existing BST blast curves to produce estimates o overpressure at a distance rom the explosion source. 4. RESULTS As discussed in the paper outlining the most recent version o the BST model [9], the distance that is available or the lame to accelerate, i.e. the run-up distance, can have a signiicant eect on the lame speed attained in a lammable gas cloud. The lame speeds presented in the original Baker-Strehlow (BS) model [1] were generated in a test rig whose largest dimension was less than 6 eet (1.8 meters) [9]. The lame speeds used in the newest BST model are based on tests where the largest dimension was 48 eet (14.6 meters) with the published lame speed results scaled up to account or the maximum size o a typical industrial plant. One test o the QEFS model is to determine the lame speed versus run-up distance or the test conigurations used in the newest BST model when speciic parameters are varied. Figure 1 shows the results or the 3-D, medium reactivity case. The curves plotted in Figure 1 show our VBR values the medium value o 4.3% used in the latest BST experiments, the low congestion value o 1.5% used in the latest BST experiments, and two intermediate values to show how the model behaves as the VBR is adjusted. Figure shows the new lame speed model or the 3-D, high congestion case. In the new BST model [9], the cloud undergoes a DDT i the uel reactivity is high. The older BS model [] ailed to predict this behavior. Four curves or varying reactivity (laminar lame speed) are shown. The lowest laminar lame speed, 0.43 m/s or propane, corresponds to the medium reactivity category in the newest BST experiments. The highest laminar lame speed, 1.0 m/s or ethylene oxide, corresponds to the high reactivity category in the newest BST experiments. Curves or ethylene (S l = 0.75 m/s, high reactivity in BST) and cyclopropane (S l = 0.5 m/s, medium reactivity in BST) are also shown illustrate how the new model or lame speeds allows or a continuous spectrum o predicted values between the extremes o the BST categories. -7- QUEST

10 0.5 edium Congestion 0.4 VBR 4.3% Flame Speed, VBR 3.5% VBR.5% 0.1 VBR 1.5% Low Congestion Run-Up Distance, m Figure 1 Flame Speed vs. Run-Up Distance 3-D, Propane, D = " Ethylene Oxide Ethylene DDT High Reactivity Flame Speed, Propane Cyclopropane edium Reactivity Run-Up Distance, m Figure Flame Speed vs. Run-Up Distance 3-D, VBR=4.3%, D = -8- QUEST

11 5. CONCLUSIONS The model described in this paper provides a method to better describe the characteristics o a vapor cloud explosion over a wide range o conditions. It combines elements o the work conducted by Baker and the European ERGE/EERGE projects, thus incorporating data rom the two largest, modern vapor cloud explosion test projects. With the ability to model the reactivity o a lammable gas cloud based on laminar lame speed instead o a low, medium, or high classiication, the model is able to more accurately describe a wide range o lammable gases and mixtures. Also, due to the ability to describe the obstacle congestion with a volume blockage ratio parameter and an average obstacle diameter, the analyst can provide a better description o the region that a lammable cloud occupies. Using the predicted lame speed and the curves or overpressure and impulse presented in the BST model, process saety experts may calculate the impacts the explosion o a lammable cloud will have on buildings in proximity to petrochemical acilities. -9- QUEST

12 6. REFERENCES 1. Baker, Q.A.,.J. Tang, E. Scheier, and G.J. Silva, Vapor Cloud Explosion Analysis, 8 th Loss Prevention Symposium, AIChE, April, (1994).. Baker, Q.A., C.. Doolittle, G.A., Fitzgerald, and.j.tang, Recent Developments in the Baker- Strehlow VCE Analysis ethodology, Process Saety Progress, v.17, No.4 (1998). 3. ercx, W.P.., editor, odelling and Experimental Research into Gas Explosions, Overall inal report o the project ERGE, CEC contract STEP-CT-0111(SSA), European Commission, Directorate General XII, Brussels, Belgium (1994a). 4. ercx, W.P.., A.C. Van den Berg, and Y. ouilleau, odelling and experimental research into gas explosions, Contribution o TNO-PL to the ERGE project, TNO report, PL 1993-C137, Rijswijk, The Netherlands (1994b). 5. ercx, W.P.., A.C. Van den Berg, and Ph. Van Dongen, Extended odelling and experimental research into gas explosions, Contribution o TNO-PL to the ERGE project, TNO report, PL C16, Rijswijk, The Netherlands (1996). 6. ercx, W.P.., editor, Extended odelling and Experimental Research into Gas Explosions, Final summary report o the project EERGE, CEC contract EV5VCT93074, European Commission, Directorate General XII, Brussels, Belgium (1997). 7. ercx, W.P.., A.C. van den Berg, and D. van Leeuwen, Application o correlations to quantiy the source strength o vapour cloud explosions in realistic situations. Final report or the project: GAES, TNO report PL 1998-C53, Rijswijk, The Netherlands (1998) 8. Oran, E.S. and V.. Gamezo, Origins o the delagration-to-detonation transition in gas-phase combustion, Combustion and Flame, 148 (007). 9. Pierorazio, A.J., J.K.Thomas, Q.A.Baker, and D.E.Ketchum, An Update to the Baker-Strehlow-Tang Vapor Cloud Explosion Prediction ethodology Flame Speed Table, Process Saety Progress, v.4, no.1 (005). 10. Tang,.J. and Q.A.Baker, A New Seto Blast Curves rom Vapor Cloud Explosion, Process Saety Progress, v.18, no.4 (1999). 11. Van den Berg, A.C. and A.L. os, Research to improve guidance on separation distance or the multienergy method (RIGOS), HSE Research Report 369, (005). 1. Vasil ev, A.A., Estimation o Critical Conditions or the Detonation-to-Delagration Transition, Combustion, Explosion, and Shock Waves, v.4, no. (006) QUEST