BLEVE: Theory and Importance in Oil Recovery

Transcription

1 The Open Thermodynams Journal, 2008, 2, BLEVE: Theory and Importane n Ol Reovery Open Aess Anthony A. Clfford* Department of Chemstry, Unversty of Leeds, Leeds LS2 9JT, UK Abstrat: BLEVEs as phenomena are defned as extremely volent explosons that may our when lquds and hghdensty fluds under pressure are subjet to a falure n the ontanng vessel. Some examples are gven and the theory of BLEVEs explaned. Ol reovery and arbon apture and storage have made BLEVE relevant today. INTRODUCTION BLEVEs are extremely volent explosons that our very nfrequently. They an our wth lquds and hgh-densty fluds under pressure when there s a falure n the ontanng vessel. The aronym stands for Bolng Lqud Expandng Vapour Exploson, whh s probably a msnomer n vew of the explanaton below. The explosons are orders of magntude more volent than most explosons. Strong steel ontaners are hghly dstorted, flattened, broken nto pees and fragments propelled hundreds of metres. Fre or other forms of heatng may be nvolved, but not neessarly. The premses n whh the tanks were loated are ompletely destroyed. The subjet has urrent relevane beause of the use of arbon doxde, whh s prone to BLEVE under ommonly used ondtons, beause of ts use n ol reovery and arbon apture and storage (CCS). Consequently, most of the examples of alulaton n ths paper are of arbon doxde and ts mxtures wth methane. The term BLEVE s most often used to desrbe explosons n propane tankers followng a fre. Partular examples may or may not be true BLEVEs [1]. Explosons nvolvng flammable substanes lke propane nvolve a freball, whereas those nvolvng nflammable substanes do not, although they an be just as dramat. The study of these explosons s dffult beause of the element of hane nvolved n the proess. Other examples nvolve arbon doxde and water. The most atastroph example for ths gas was the exploson of a tank of arbon doxde at a plant n Worms, Germany [2]. A tank of 30 tonne apaty was shattered nto a number of pees and only 20% of the tank was present n the orgnal premses after the exploson. Most of the tank was propelled 300 metres nto the Rhne. There were three fataltes and a further eght asualtes. Why do BLEVEs our? There does not yet appear to be unversal agreement on the answer to ths queston. However, a theory developed by Professor Red and olleagues at MIT [3] shows that a very dramat physal event must our under ertan thermodynam ondtons, and ths s *Address orrespondene to ths author at the Department of Chemstry, Unversty of Leeds, Leeds LS2 9JT, UK; Tel: ; Fax: ; E-mals: tony@rtalproesses.om, A.A.Clfford@hem.leeds.a.uk X/08 lkely to be the explanaton (or at least one of the explanatons) of BLEVEs. A bref explanaton of ths theory an be gven wth the ad of Fg. (1), whh s a dagram of the relatonshp between the pressure n a substane and the volume t oupes as a lqud, gas or flud at onstant temperature,.e. the p-v ross-seton of the phase dagram. These sotherms were frst observed for arbon doxde by Thomas Andrews, workng n the north of Ireland. Fg. (1). Varaton of pressure wth volume ouped at onstant temperature and equlbrum shown as sold lnes: the hgher at the rtal temperature and the lower at a temperature below rtal. The metastable stuaton s shown as the dashed lne BS and the spnodal urve as the dotted lne. The ontnuous thk blak lne ABCD shows the behavour of the substane at a onstant temperature and at thermodynam equlbrum. In the seton AB, the substane s a lqud and as the volume t oupes s expanded the pressure falls dramatally. Eventually the pressure falls to the vapour pressure of the lqud at the partular temperature at B. The lqud then starts to evaporate to beome a lqud-gas 2008 Bentham Open

2 90 The Open Thermodynams Journal, 2008, Volume 2 Anthony A. Clfford mxture, and the pressure stays onstant at the vapour pressure. Eventually t reahes C, where the lqud has been ompletely onverted to gas. The pressure then drops as t s expanded further. However, f the pressure falls suddenly, perhaps due to a falure n the ontaner, the substane an beome an unstable lqud along the dashed path BS. Along the path BS the substane s metastable and an at any tme bol to return to the equlbrum horzontal lne BC. Although suh an event an be very volent t s not thought to be a BLEVE and s desrbed as bumpng. Typally volent bolng wll our before the pont S s reahed and a BLEVE wll not our, unless further rupture happens. (In prate these events an often be omplex.) One way of makng t less probable that the spnodal urve wll be reahed s to arrange for the drop n pressure followng falure to be slower, whh an be done n some stuatons. If the fall n pressure s slower ths gves more tme for the system to move from the metastable urve BS on to the equlbrum urve BC. Ths an be aheved by, for example, by attahng a tube to the outlet of a burstng ds to slow the rate of ext of gas. However, n the unlkely event that the pont S s reahed a speal and atastroph stuaton arses. S s known as a spnodal pont and the slope of the lne at ths pont s zero (.e. = 0 ). The dotted lne onnets these ponts at dfferent temperatures and s known as the spnodal urve, whh ends at the rtal pont. The speal nature of stuatons represented by ponts along ths urve are that large densty flutuatons an our beause of the nsenstvty of pressure to volume ( = 0 ). Ths s beause random moleular moton auses moleules to move exessvely nto some regons and sparsely nto others. These denstes are normally smoothed out by pressure dfferenes between the hgh- and low-densty regons. However, beause = 0 there s no pressure fore to do ths. These densty flutuatons annot easly be observed for obvous pratal reasons exept near the rtal pont, where the phenomenon s known as rtal opalesene. One the spnodal urve s reahed separaton nto lqud and gas must our and rapdly. The densty varatons develop spontaneously nto lqud and gas regons. Ths ours homogeneously throughout the whole lqud. The rse n pressure on to the vapour pressure lne BC s not large but t happens at great speed, homogeneously and at the tme-sale of moleular moton. The shok to the ontanng vessel s huge and a dsastrous BLEVE happens. For a BLEVE to our, the substane has therefore to fnd tself on the spnodal urve. As pratal ondtons do not normally allow pressures below atmospher, the system must ht the spnodal urve between 1 bar or thereabouts and the rtal pont where the urve ends. When a atastroph falure ours there s not tme for heat to pass nto the system and so the path durng falure s adabat. We must then assume that a smooth pressure drop ours the rupture and therefore the pressure drop wll be reversble, and thus not only adabat but also sentrop. Thus for a BLEVE to our the entropy of the system before falure must be below the entropy at the rtal pont but above the entropy on the spnodal urve at 1 bar. It s therefore possble to alulate the range of temperatures and pressures where the gas or gas mxture would reah ths seton of the spnodal urve followng atastroph falure. Ths range s represented by an envelope n temperaturepressure spae onvenently drawn on a dagram where the absssa (x-axs) represents temperature. The rght-hand (hgher temperature) boundary of ths envelope represents temperature-pressure ondtons where the entropy equals the rtal entropy. To the rght of ths boundary the entropy wll be above the rtal entropy and therefore not subjet to BLEVE. The rtal pont wll le on ths boundary. The left-hand (lower temperature) boundary of ths envelope represents temperature-pressure ondtons where the entropy equals the entropy on the spnodal urve at 1 bar. To the left of ths boundary the entropy wll be below the spnodal entropy at 1 bar and therefore not subjet to BLEVE. If there are two phases already present, as n a arbon doxde gas ylnder or fre extngusher, BLEVE should not our as the sudden development of two phases annot happen. However, there s some evdene from propane experments that BLEVE an our n the bulk of the lqud even though there s a vapour phase above t. CALCULATION OF CONDITIONS FOR BLEVE The Stryjek and Vera modfaton of the Peng-Robnson equaton of state (PRSV) was used for all alulatons [4]. Ths gves the pressure, p, from the molar volume, V, temperature, T, gas onstant, R, and two parameters a and b. RT a p = (1) 2 2 V b V + 2bV b b = RT p (2) / a = a T ) (3) ( a ( T = p (4) 2 2 ) R T / 1/ 2 2 = [ 1+ (1 ( T / T ) (5) )] 2 = + 1 ( T / T ) 1/ )(0.7 ( T / )) (6) 0 1( T 0 = (7) The bas parameters used for the omponents were also taken from Stryjek and Vera [4] and are shown n Table 1. For the mxtures the a and b values are alulated for eah omponent from the equatons for a and b above They are then ombned to gve values for a and b for the mxture usng the followng ombnng rules, where x are the mole fratons of the omponents and k j the bnary nteraton parameter. 1 / 2 a = x x ( a a ) (1 k ) (8) j j j b = x b (9) The bnary nteraton parameter for methane and arbon doxde was taken to be 0.1. j

3 BLEVE: Theory and Importane n Ol Reovery The Open Thermodynams Journal, 2008, Volume 2 91 The entropy, S 0 (298.14), of the deal gas at K and 1 atmosphere ( bar) was taken to be zero. It was not neessary to take nto aount the entropy of mxng as the alulaton nvolved omparson of entropes at dfferent ondtons of the same mxture. To obtan absolute entropes the absolute entropy at K and 1 bar must be added to the results here. E.g. for arbon doxde J K -1 mol -1 must be added. The entropy was for temperature T. s then T C p equal to the quantty T dt, where C p s the heat apaty at onstant pressure. Ths was obtaned from the equaton C p / R = a 0 + a 1 T + a 2 T 2 + a 3 T 3 + a 4 T 4, usng publshed values [6] gven n Table 2 for the parameters a 0 a 4. The entropy was then orreted for pressure p (n bar), stll as an deal gas, by addng the quantty Rln p. It s then orreted for non-dealty subtratng the departure funton obtaned from the PRSV equaton of state, whh s gven below. Rln pv da /dt V + b(1 2) (1 b / V ) + ln (10) RT 8b V + b(1+ 2 After these terms are ombned, the entropy, S, ould be obtaned (relatve to the entropy of the deal mxture at K and 1 bar). For the mxtures, the rtal ponts were obtaned. Ths was done by alulatng p and for a range of values of V, makng sure fnally that ths range nluded V. The temperature was then adjusted to fnd the lowest value where was always negatve,.e. was just nsde the superrtal state. Ths value s shown n Table 3 as the rtal temperature, T. The rtal pont was then taken as the lowest value of (n theory zero) and V and p at ths pont were taken as V and p and shown n Table 3. Table 3 also ontans for ompleteness the rtal parameters of the pure gases. For the pure gases and mxtures, the entropy was then alulated at the rtal pont. These data are shown n Table 3. Table 1. Bas Parameters for the Components. T, p and V are the Crtal Temperature, Pressure and Molar Volume, Respetvely. s the Aentr Fator and 1 the Addtonal Stryjek and Vera Parameter [4] T (K) p (bar) V 10 5 (m 3 mol -1 ) 1 Methane * Propane * CO * * = 0 above 0.7T. Table 2. Parameters Used for Heat Capaty Calulatons [5] a 0 a 1 a 2 a 3 a 4 Methane E E E E-11 Propane E E E E-11 CO E E E E-11 Table 3. Thermodynam Values for the Crtal Pont and Spnodal Pont at 1 Bar CO 2 Propane Methane 75% CO 2 25% CH 4 50% CO 2 50% CH 4 Crtal pont p (bar) V 10 5 (m 3 mol -1 ) T (K) S (J K -1 mol -1 ) Spnodal pont at 1 bar p (bar) V 10 5 (m 3 mol -1 ) T (K) S (J K -1 mol -1 )

4 92 The Open Thermodynams Journal, 2008, Volume 2 Anthony A. Clfford Next, for all gases and mxtures, the pont on the spnodal urve at 1 bar was obtaned by agan alulatng p and for a range of values of V and adjustng the temperature to fnd a value of V where p was 1 bar and was lose to zero and hangng from negatve to postve (.e. p was gong through a mnmum, ndatng a spnodal pont). The values of p, V and T for these spnodal ponts are gven n Table 3. The entropes were then alulated and also shown n Table 3. The rght-hand boundary of the BLEVE envelopes was then alulated. Ths was done for a range of temperatures by adjustng V so that the entropy was equal to the rtal entropy, and then alulatng the pressure. The temperature range was hosen to obtan pressures between 400 bar and the bottom angle of the BLEVE envelope. Calulatons were arred out at 10 C ntervals. The left-hand boundary was then alulated smlarly, adjustng to the entropy at the spnodal pont at 1 bar. The results are shown n Table 4. DISCUSSION OF THE RESULTS Fg. (2) shows the alulated BLEVE envelope for arbon doxde as the thk blak lnes. It s ompared wth that alulated by Km and Red [3], whh has been sanned nto the fgure. The urves are smlar but do not exatly onde. Ths s beause Km and Red used a dfferent method for obtanng entropes. They used the entropy values of referene [6] (a numeral orrelaton of expermental values) and adjusted them to the ondtons requred usng departure funtons. An analytal equaton of state s used here, whh s less aurate but more unversally applable, espeally for mxtures. For arbon doxde the BLEVE envelope s n Table 4. Numeral Results for the BLEVE Envelope Pressure-Temperature Lmts for the Pure Gases and Mxtures. LH and RH are the Left-Hand and Rght Hand Boundares the Envelope, Respetvely. The RH Lmt s Calulated from the Entropy at the Crtal Pont and the LH Lmt s Calulated from the Entropy on the Spnodal Curve at 1 Bar Pressure (Bar) Temp. ( C) CO 2 Propane Methane 75% CO 2 25% CH 4 50% CO 2 50% CH 4 LH RH LH RH LH RH LH RH LH RH

5 BLEVE: Theory and Importane n Ol Reovery The Open Thermodynams Journal, 2008, Volume 2 93 the regon where ondtons are typally used n proesses. Sne the dsaster referred to earler, arbon doxde s always stored ooled at atmospher pressure or where two phases are present. However for arbon apture and storage proessng of arbon doxde under pressure wll be requred and t wll be prudent to avod the BLEVE envelope. Smallsale experments have been arred out to attempt to produe BLEVE n rumstanes when BLEVE ould our [3,7], but t ould not be made to happen. It was beleved that bolng ourred before the spnodal urve was reahed. Fg. (2). The BLEVE envelope for pure arbon doxde, shown as the sold blak lnes. The results of Km and Red [3] are shown for omparson. Fg. (3) ompares the BLEVE envelopes for methane, arbon doxde and propane. As the rtal pont s on the BLEVE envelope, the urves follow the rtal temperatures. Thus for propane hgher temperatures are reahed and that s beleved to be the reason that propane BLEVEs our n fres. For methane the BLEVE envelope s at lower temperatures, removed from normal ambent ondtons. However when natural gas s transported as a lqud, t s ooled and t s mportant to avod the BLEVE envelope. Fg. (4) shows the BLEVE envelopes for mxtures of arbon doxde and methane, whh le between those of the pure gases. Curves lke these must be onsdered when desgnng proesses for the reovery of natural gas usng arbon doxde. Also, as the BLEVE envelopes are predted to be wder for mxtures [8], the urves overlap. To summarse, we have a stuaton where very atastroph explosons oasonally our, whh are orders of magntude more volent than most explosons. At the same tme we have a theory based on physal prnples, whh predts that n some rumstanes a phenomenon may our to produe these huge explosons. However, what we don t have s an expermental study showng that the theory and the physal manfestatons are defntely related. Experments on arbon doxde dd not result n BLEVEs and the study for propane dd not seem to aord wth the theory. Nevertheless, t s very lkely that the Red theory does explan at least some BLEVEs, although other theores may be vald n some ases. Fg. (3). The BLEVE envelopes for methane, arbon doxde and propane. Fg. (4). The BLEVE envelopes for methane, arbon doxde and two mxtures.

6 94 The Open Thermodynams Journal, 2008, Volume 2 Anthony A. Clfford In onluson for ompanes operatng proesses nvolvng gases under pressure, BLEVE alulatons should be arred out and the BLEVE envelope avoded durng operatons. If ths s not done, the hanes of a BLEVE event are stll small but, f t does happen, the onsequenes would be atastroph. REFERENCES [1] 22/07/2008. [2] W. E. Clayton and M. L. Grffn, Catastroph falure of a lqud arbon doxde storage vessel, Proess Saf. Prog., vol. 13, pp , Otober [3] M. E. Km and R. C. Red, The rapd depressurzaton of hot, hgh pressure lquds or superrtal fluds, n Chemal Engneerng at Superrtal Flud Condtons, M. E. Paulats, Ed. Ann Arbor: Ann Arbor Sene, 1983, pp [4] R. Stryjek and J. H. Vera, PRSV an mproved Peng-Robnson equaton of state for pure ompounds and mxtures, Can. J. Chem. Eng., vol. 64, pp , Aprl [5] B. E. Polng, J. M. Prausntz, and J. P. O Connell, The Propertes of Gases and Lquds, 5 th ed, New York: MGraw-Hll, [6] S Angus, B. Armstrong and K. M. de Reuh, Internatonal Thermodynam Tables of the Flud State Vol. 3 Carbon Doxde. Oxford: Pergamon Press, [7] H. Z. L and M. Perrut, Flash dsharge of superrtal flud and hgh pressure gas through ppes: expermental results and modellng, Chem. Eng. Commun., vol. 117, pp , September [8] B. L. Beegle, M. Modell and R. C. Red, Thermodynam stablty rtera for pure substanes and mxtures, AIChE J., vol.20, pp , November Reeved: Marh 13, 2008 Revsed: August 3, 2008 Aepted: September 8, 2008 Anthony A. Clfford; Lensee Bentham Open. Ths s an open aess artle lensed under the terms of the Creatve Commons Attrbuton Non-Commeral Lense ( whh permts unrestrted, non-ommeral use, dstrbuton and reproduton n any medum, provded the work s properly ted.