The Development of a Generalised Jet Mixing Model for the Derivation of Exclusion Zones in Hazardous Area Classification

Transcription

1 The Developent of a Generalised Jet Mixing Model for the Derivation of Exclusion Zones in Hazardous Area Classification Katherine McCobe, Peter Tait, Jason Whitley LogiCas Ltd. 33 Boundary Street, Spring Hill Brisbane, Queensland ABSTRACT Available resources for deterining the extent of zoning surrounding the release of flaable/cobustible gases fro systes not covered in AS/NZS are currently liited to various international standards (i.e. API, IGE/SR/). These standards are quite restrictive in the gases that they can odel and the percentage of LEL to which the distances apply. In order to avoid advanced coputational fluid dynaics, which is an expensive and tie consuing exercise, a jet ixing odel has been developed to predict the concentration and velocity gradients downstrea of jets of cobustible gases. The dynaics within the jet have been odelled using a cobination of equations for under-expanded jets and subsonic isotheral jets in conjunction with oentu balances and derived entrainent functions to siulate the effects of cross wind on the displaceent and dilution of the plue. The results of the odel have been copared with a nuber of different standards and appear to line up reasonably well with inherent safety factors. However, unlike the standards, this jet ixing odel is capable of odelling a flaable gas of any coposition, to any desired percentage of the lower explosive liit and under a range of cross-wind velocities. As such the generalised odel allows for a uch wider variety of applications in hazardous area classification. The paper discusses the developent of this odel and coparisons with key established standards. INTRODUCTION It is necessary to quantify the extent of a zone surrounding potential sources of flaable gas release in which the gas still poses an explosive risk with any ignition sources in the area. AS/NZS defines the concentration boundary of a zone for a continuous and priary or secondary release by applying a safety factor to the lower explosive liit (LEL) of. or. respectively. The standards available for deterining these distances are liited to specific gas copositions, environental conditions and the percentage of LEL to which they apply. This paper outlines the developent of a generalised finite eleent jet ixing odel capable of siulating the concentration boundary of a jet of gas issuing into a crosswind. The priary input variables include gas coposition, wind velocity and percent of LEL defining the zone boundary.

2 A nuber of siplifying assuptions were ade in the developent of this odel; i. The gas behaves as an ideal gas. ii. The axiu conservative hazardous zone is calculated corresponding to a iniu abient air density (% relative huidity and axiu abient air teperature). iii. Buoyancy effects are negligible. iv. The projected area of the jet perpendicular to the wind is taken to be the area of the vertical plane fro the centreline out to the concentration boundary (no curvature is taken into account). v. Isentropic expansion to the discharge. vi. No building or ground effects. In the case of a sonically choked jet the odel was developed to siulate the two ain regions of the jet: the sonic shock barrel and the following subsonic region. The shock barrel odel was developed on the founding equations of Che-haing (969). The subsonic region of the jet was odelled using concentration and velocity decay equations for round isotheral jets developed by Field et.al (967). SONICALLY CHOKED JET: DYNAMICS OF THE SHOCK BARREL The odel developed for sonically choked conditions utilised equations for underexpanded jets developed by Che-haing (969) presented in Turbulent Jets of Air, Plasa and Real Gas. These equations are used to siulate the behaviour of the jet in the area between the discharge and the Mach disc (known as the shock barrel) where the gas is supersonic (refer figure ). Fig. : Shock barrel (Ewan and Moodie, 986) Expansion waves fored at the edge of the discharge result in an increase in jet velocity above Mach. Supersonic flow terinates at the Mach disc where the gas falls to abient pressure.

3 Previous studies conducted by Che-haing (969) deterined the following relationship for the length of the shock barrel (3.M (3.M [( nm [( nm ) ) ( M ( M ) ) ] + ( M ] + ( M ) ) d ) t n ) d For For n < n > Where n is the pressure ratio, d is the diaeter of the discharge, M is the Mach nuber and t is a diensionless function of the Mach nuber. The excess pressure fro the discharge to the Mach disc goes towards increasing the oentu of the jet. With a jet velocity of ach at the shock plane this iplies an increase in the ass of the jet as a result of the entrainent of air. The increased voluetric flow rate of the jet is used to calculate an equivalent diaeter of the Mach disc. A revised concentration of the gas is also deterined at this point fro the ass of entrained air. Fro the shock disc the jet is travelling at subsonic velocities and can therefore be described with classical subsonic jet ixing equations. The concentration and equivalent diaeter calculated above are used as inputs for this siulation. SUB-SONIC JET IN CROSS FLOW The subsonic flow odel was developed based on equations for round isotheral jets discharging into a quiescent environent as reported in Cobustion and Incineration Processes: Applications in Environental Engineering by Niessen (99). These equations have their foundation in the work of Field et.al (967) and provide the basis for odelling the dynaics of the jet under stagnant wind conditions. The concentration and velocity at any radial and axial distance fro the discharge can be expressed as ρ j C = C ρa d (.8d Exp( 7. ) + y x y ) V ρ j = 6.3V ρa d (.6d Exp( 96 + y) x y ) Where x and y are the radial and axial distances fro the centreline of the discharge respectively, d is the pseudo diaeter of the Mach disc and the subscripts, j and a represent initial, jet and abient properties respectively. A concentration atrix of the jet is developed and the noinated LEL boundary identified. With the contour of the jet in a stagnant environent a oentu balance is 3

4 then incorporated into the odel to siulate the effects of cross wind on the displaceent of the jet. Centreline Displaceent At a noinated wind speed a certain ass of air will contact the projected area of the jet providing oentu in the horizontal direction. The projected area of the jet is taken as the vertical plane through the centreline out to the calculated radial boundary in each axial eleent of the jet. This area is used to calculate the ass of wind ipacting the jet and hence the oentu transferred to the horizontal coponent of the jet. The following oentu balance has been developed & ( i)( v v, ( i)) + & ( i) v, ( i) = & w w j h j j h j ( i + ) v j, h( i + ) Where w and v w are the ass flow and velocity of the wind ipacting the jet respectively, j and v j,h are the ass flow and horizontal velocity coponent of the jet respectively and i represents the jet eleent nuber (refer figure ). Fig. : A) Displaced jet in cross flow, B) Projected area of the jet available for ipacting wind As the horizontal velocity of the jet approaches the wind velocity it can be seen that the cross flow oentu contribution ter reduces to zero and no further oentu is iparted to the jet (as you would expect).

5 The resultant vector of the horizontal velocity coponent of the jet with the decaying centreline velocity plots the displaced trajectory. The centreline velocity (C c) is defined by Field et.al (967) C c = C ρ j ρ a d (.8d + y) This equation represents the decay of the centreline velocity as the ass of the jet increases with entrainent of abient fluid. This however is under stagnant wind conditions and it is expected that additional air entrainent will occur with increasing cross wind velocity. Conserving the oentu of the jet, the centreline velocity is revised to incorporate the additional entrainent with cross wind. This will effectively increase the decay of the centreline velocity with axial distance fro the discharge resulting in a ore pronounced bend in the jet trajectory. The displaced horizontal centreline distance is added to the previously calculated radial distance to the noinated percent of LEL in order to define the new displaced jet boundary in cross wind. Jet Dilution Although the jet dynaics equations presented by Niessen (99) include air entrainent, this is under stagnant wind conditions. With a steady cross flow of wind contacting the jet, it is assued a fraction of this ipacting wind will becoe entrained in the flow. The additional air entrainent will further dilute the jet and reduce the axiu radial distance to the LEL. Studies perfored by Lee and Chu (3) on the additional entrainent of air in a jet in cross flow have developed the following equation Q = π B[ α ( V, V cosφ) + βv sinφ S S j h w w ] Where Q is the additional voluetric entrainent rate, B is the characteristic radius of the jet, S is the axial distance fro the discharge, φ is the angle of the jet centreline to the horizontal, α s is a shear entrainent coefficient and β is a cross flow entrainent coefficient. The cosine ter in the equation takes into account the vertical oentu of the jet: although the horizontal velocity of the jet will increase with respect to the differential velocity with crosswind the vertical oentu of the jet is also a factor in the calculation of the centreline displaceent and hence the shear entrainent. The jet will continue to entrain abient fluid due to shear forces until the horizontal velocity of the jet equals the crosswind velocity and the jet is bent over 9degrees: these two conditions do not necessarily occur at the sae point in the jet. The crosswind entrainent ter provides an additional dilution as the wind ipacts the jet perpendicular to the flow and falls to zero as the centreline bends towards the horizontal.

6 An additional factor is added to the above entrainent equation to adjust the ass of entrained fluid by the relative cross wind velocity to jet centreline velocity Vw Q = π B[ α + S ( V j, h Vw cosφ) βvw sinφ] S Vc Considering two identical jets issuing into a high and low velocity crosswind, this ter siply states that the jet in the high velocity crosswind will entrain ore fluid in proportion to the decaying centreline velocity. MODEL RESULTS: COMPARISON WITH THE STANDARDS API : Pressure Relieving and Depressuring Systes In coparing the results of the odel with the standard API it was found that the odel was producing the correct trends. The radial distance to % of the LEL was found to increase with lower wind velocities as oentu effects doinated in displacing the plue before reaching a critical wind velocity, beyond which point dilution becae the controlling process (refer figure 3). Radial Distance () Maxiu Radial Distance Vs. Wind Velocity. Vent API Radial Distance () Maxiu Radial Distance Vs. Wind Velocity.8 Vent API Radial Distance () Maxiu Radial Distance Vs. Wind Velocity. Vent API Radial Distance () Maxiu Radial Distance Vs. Wind Velocity. Vent 6 API Fig. 3: Radial Distance vs. Wind Velocity calculated in the odel as copared with API for vent diaeters ranging fro to (with calculated safety factors incorporated in the odel). The odel was copared against API with ethane at 3 C, 3kPaa as the basis. 6

7 The axial distance calculated by the odel was found to continually decrease with increasing wind velocity (refer figure ). Axial Distance () 3... Maxiu Axial Distance Vs. Wind Velocity. Vent 3 API Axial Distance () Maxiu Axial Distance Vs. Wind Velocity.8 Vent 3 API Axial Distance () 3 Maxiu Axial Distance Vs. Wind Velocity. Vent 3 API Axial Distance () Maxiu Axial Distance Vs. Wind Velocity. Vent API Fig. : Axial Distance vs. Wind Velocity calculated in the odel as copared with API for vent diaeters ranging fro to (with calculated safety factors incorporated in the odel). However the absolute values of the radial and axial distances at varying wind velocities were found to significantly underestiate those called for by API. This was suggested to be the result of an inherent conservatis in the standard. The fundaental jet ixing equations developed by Field et.al (967) for a jet issuing into a quiescent environent that for the basis of this odel are well established and experientally verified. The fact that the results of the siulation under zero wind conditions require these ultiplicative factors to bring the results up to that of API (zero wind) indicates that the standard does eploy soe safety factors for the purposes of zoning hazardous areas (refer table ). Given the constantly changing environental conditions on a site and their effect on the turbulent dynaics of a jet, it is unsurprising that API eploys safety factors for deterining the extent of a hazardous area, particularly the radial distance. For a vertical release scenario it is the radial distance that is the iportant value for deterining the extent of the zone, hence the radial safety factor is significantly larger than the axial value. These factors would also account for the stochastic behaviour of the jet and the foration of tie varying eddies that would serve to increase the radial extent of the zone beyond that calculated by the concentration equations of Field et.al (967). 7

8 IGE/SR/: Hazardous Area Classification of Natural Gas Installations The British Standard IGE/SR/ provides tables for the horizontal and vertical dispersion of vertical natural gas jets under ideal venting conditions. The calculations are based on a iniu wind speed of./s and apply to liquid-free natural gas with a cobined gas coposition of ethane and inerts of greater than 89% by volue in the teperature range of - C to 3 C. Our odel was tested at various vent diaeters and ass flows to copare to IGE/SR/. The axial distances calculated were found to underestiate the standard at./s cross wind. However the axiu calculated axial distance (under no wind conditions) lined up well with the distances required by IGE/SR/ (refer figure ). Siilar to API this was considered to be an inherent conservatis in the standard. It should also be noted that the axial and radial distances presented in the IGE/SR/ tables show a stepwise oveent: ultiple consecutive ass flows have the sae zone distance (a conservative approach by IGE/SR/). Axial Distance () ' Maxiu Axial Distance Vs. Mass Flow. Vent IGE/SR/ Axial Distance () ' Maxiu Axial Distance Vs. Mass Flow.8 Vent IGE/SR/ Axial Distance () ' Maxiu Axial Distance Vs. Mass Flow. Vent IGE/SR/ Axial Distance () ' Maxiu Axial Distance Vs. Mass Flow. Vent IGE/SR/ Fig. : Axial Distance vs. Mass Flow calculated in the odel as copared with IGE/SR/ for vent diaeters ranging fro to (with calculated safety factors incorporated in the odel). Siilar to the odel coparison with API the radial distance calculated was consistently saller than the horizontal dispersion distances presented in IGE/SR/. A safety factor of 3.7 was incorporated into the odel for a vent size in order to atch the values in the standard. This factor was found to be consistent over vent The odel coparison with IGE/SR/ is based on ethane at 3 C. 8

9 diaeters ranging fro (the sallest diaeter in the standard) to. Above the odel results start to deviate fro the standard (refer figure 6). Radial Distance () ' Maxiu Radial Distance Vs. Mass Flow. Vent IGE/SR/ Radial Distance () ' Maxiu Radial Distance Vs. Mass Flow.8 Vent 8 6 IGE/SR/ Radial Distance () ' Maxiu Radial Distance Vs. Mass Flow. Vent IGE/SR/ Radial Distance () ' Maxiu Radial Distance Vs. Mass Flow. Vent IGE/SR/ Fig. 6: Radial Distance vs. Mass Flow calculated in the odel as copared with IGE/SR/ for vent diaeters ranging fro to (with calculated safety factors incorporated in the odel). The following table outlines the calculated safety factors that have been incorporated in the odel to eet the required radial and axial distances presented in the two standards. Table : Calculated safety factors applied to the odel to atch the established standards. Radial Safety Factor Axial Safety Factor API 6..7 IGE/SR/ 3.7. Based on the required safety factors it is clear that API is ore conservative in defining hazardous areas than IGE/SR/. 9

10 DISCUSSION The odel incorporating the previously defined safety factors appears to atch the distances required for these two ain established standards used in defining hazardous areas for both subsonic and choked flow up to a vent diaeter of. As such, it provides a rapid tool for assessing required zones for releases with the ability to switch between the requireents of API and IGE/SR/. As the odel is not liited to the use of high concentration hydrocarbon ixtures (C- C as per API ) nor restricted to specific concentrations (% LEL as per API or % LEL as per IGE/SR/) and can odel for any cross wind velocity, it has proven to be a useful tool in assessing the required zoning for a wide variety of eissions. It has proven particularly useful in calculating zones for eissions containing species other than C-C and for ixtures containing significant quantities of inert coponents.

11 REFERENCES Che-haing, C., (969). Axially Syetric Supersonic Turbulent Jets Discharged fro a Nozzle with Underexpansion IN: Abraovich, G.N., ed. Turbulent Jets of Air, Plasa and Real Gas. New York, USA: Consultants Bureau. p. Ewan, B.B., Moodie, K., (986). Structure and Velocity Measureents in Underexpanded Jets. Cobustion Science and Technology, (-6), p7-88. Field, M.A., Gill, D.W., Morgan, B.B., Hawksley, P.E.W., (967). Cobustion of Pulverised Coal, Surrey, England: British Coal Utilization Research Association. Lee, J.H.W., Chu, V.H., (3). Turbulent Jets and Plues: a Lagrangian approach. Massachusetts, USA: Kluwer Acadeic Publishers. Niessen, W.R., (99). Cobustion and Incineration Processes. nd ed. New York, USA: Marcel Dekker Inc. BIOGRAPHY The authors work for LogiCas - an Australian ulti-disciplinary engineering copany that perfors nuerous hazardous area classification assignents. The paper will be presented by Kate McCobe. Kate McCobe graduated in Cheical Engineering 9 fro the University of Queensland and works as a process engineer with LogiCas. Assignents have included the definition of hazardous areas for gaseous ixtures that are not strictly covered by the established standards such as heat treatent gas atospheres, gas ixtures containing hydrogen fro reduction furnaces and hydrogenation activities and exhaust gases fro cobustion processes operating under reducing conditions.