Dispersion Model 2. Dr. AA Department of Chemical Engineering University Teknology Malaysia

Transcription

1 Dispersion Model Dr. AA Departent of heical Engineering Universit Teknolog Malasia

2 Pasquill-Gifford Model

3 Pasquill-Gifford Model ases through 0 described previousl depend on the specification of a value for the edd diffusivit, K j. In general, K j changes with position, tie, wind velocit, and prevailing weather conditions and it is difficult to deterine. Sutton solved this difficult b proposing the following definition for a dispersion coefficient ut n with siilar relations given for and. The dispersion coefficients,,, and represent the standard deviations of the concentration in the downwind, crosswind and vertical (,,) directions, respectivel. Values for the dispersion coefficients are uch easier to obtain eperientall than edd diffusivities 3

4 Table Atospheric Stabilit lasses for Use with the Pasquill-Gifford Dispersion Model Da radiation intensit Night cloud cover Wind speed (/s) al & Strong Mediu Slight loud clear < A A B B 3 A B B E E 3 5 B B D E 5 6 D D D D > 6 D D D Stabilit class for puff odel : A,B : unstable,d : neutral E,F : stable 4

5 Figure 0 Horiontal dispersion coefficient for Pasquill-Gifford plue odel. The dispersion coefficient is a function of distance downwind and the atospheric stabilit class. 5

6 Figure Vertical dispersion coefficient for Pasquill-Gifford plue odel. The dispersion coefficient is a function of distance downwind and the atospheric stabilit class. 6

7 Figure Horiontal dispersion coefficient for puff odel. This data is based onl on the data points shown and should not be considered reliable at other distances. 7

8 Figure 3 Vertical dispersion coefficient for puff odel. This data is based onl on the data points shown and should not be considered reliable at other distances. 8

9 Table 3 Equations and data for Pasquill- Gifford Dispersion oefficients Equations for continuous plues Stabilit class () A = B = = D = E = F =

10 Stabilit class A B () () Z = log 0 = log (log 0 )² Z = log 0 = log (log 0 )² Z = D E F Z = log 0 = log (log 0 )² Z = log 0 = log (log 0 )² Z = log 0 = log 0-0.9(log 0 )² 0

11 Data for puff releases Stabilit condition = 00 = 4000 () () () () Unstable Neutral Ver stable

12 This case is identical to ase 7. The solution has a for siilar to Equation 33. (38) The ground level concentration is given at = 0. (39) 3 * ep,,, ut Q t 3 * ep,0,, ut Q t ase Puff. Instantaneous point sorce at ground level. oordinates fied at release point. onatant wind in direction onl with constant velocit u

13 The ground level concentration along the -ais is given at = = 0.,0,0, t 3 Q * ep ut (40) The centre of the cloud is found at coordinates (ut,0,0). The concentration at the centre of this oving cloud is given b ut, 0,0, t * Q 3 (4) The total integrated dose, D tid received b an individual standing at fied coordinates (,,) is the tie integral of the concentration.,,,, tdt 0 D, tid (4) 3

14 The total integrated dose at ground level is found b integrating Equation 39 according to Equation 4. The result is - D tid,,0 Q ep * u (43) The total integrated dose along the -ais on the ground is Dtid, 0, 0 Q * u (44) Frequentl the cloud boundar defined b a fied concentration is required. The line connecting points of equal concentration around the cloud boundar is called an isopleth. 4

15 For a specified concentration, <> *, the isopleths at ground level are deterined b dividing the equation for the centreline concentration, Equation 40, b the equation for the general ground level concentration, Equation 39. This equation is solved directl for. ln,0,0, t,,0, t (45) The procedure is. Specif <> *, u, and t.. Deterine the concentrations, <> (,0,0,t), along the -ais using Equation40. Define the boundar of the cloud along the -ais. 3. Set <> (,,0,t) = <> * in Equation 45 and deterine the values of at each centreline point deterined in step. The procedure is repeated for each value of t required. 5

16 6 This case is identical to ase 9. The solution has a for siilar to Equation 35. (46) The ground level concentration is given at = 0. (47) ep,, u Q ep,0, u Q ase - Plue. ontinuous, stead state, source at ground level, wind oving in direction at constant velocit u

17 The concentration along the centreline of the plue directl downwind is given at = = 0.,0,0 Q u (48) The isopleths are found using a procedure identical to the isopleth procedure used for ase. For continuous ground level releases the aiu concentration occurs at the release point. 7

18 8 This case is identical to ase 0. The solution has a for siilar to Equation 36. (49) ep ep ep,, r r H H u Q ase 3 Plue. ontinuous, Stead State Source at Heignt H, above ground level, wind oving in direction at constant velocit u

19 9 The ground level concentration is found b setting = 0. (50) The ground centreline concentrations are found b setting = = 0. (5) ep,, r H u Q ep,0,0 r H u Q

20 The aiu ground level concentration along the -ais, <> a, is found using. a Q r euh (5) The distance downwind at which the aiu ground level concentration occurs is found fro H r (53) The procedure for finding the aiu concentration and the downwind distance is to use Equation 53 to deterine the distance followed b Equation 5 to deterine the aiu concentration. 0

21 For this case the centre of the puff is found at = ut. The average concentration is given b (54) 3 ep ep ep,,, r r H H Q t ase 4 Puff. Instantaneous point source at height H, above ground level. oordinate sste on ground oves with puff

22 The tie dependence is achieved through the dispersion coefficients, since their values change as the puff oves downwind fro the release point. If wind is absent (u = 0), Equation 54 will not predict the correct result. At ground level, = 0, and the concentration is coputed using (55) 3 * ep,0,, r H Q t

23 3 The concentration along the ground at the centreline is given at an = = 0, (56) The total integrated dose at ground level is found b application of Equation 4 to Equation 55. The result is (57) 3 * ep,0,0, r Q H t * tid ep,0, r H u Q D

24 ase 5 Puff. Instantaneous point source at height H, above ground level. oordinate sste fied on ground at release point For this case, the result is obtained using a transforation of coordinates siilar to the transforation used for ase 7. The result is,,, t (P uff ep equations sste, Equations with oving 54 through 56 H r coordinate ) (58) where t is the tie since the release of the puff. 4

25 oparison of Plue and Puff Model Plue is based on stead state, Puff is based on transient state The puff odel can also be used for continuous releases b representing the release as a succession of puffs. For leaks fro pipes and vessels, if t p is the tie to for one puff, then the nuber of puffs fored, n, is given b n t t p (59) 5

26 where t is the duration of the spill. The tie to for one puff, t p, is deterined b defining an effective leak height, H eff. Then, t p H u eff (60) where u is the wind speed. Epirical results show that the best H eff to use is H eff For a continuous leak, height of leak. 5 (6) Q Q * t p (6) 6

27 and for instantaneous release divided into a nuber of saller puffs, Q * Q * total n (63) where (Q * ) total is the release aount. This approach works for liquid spills, but not for vapor releases. For vapor releases a single puff is suggested. The puff odel is also used to represent changes in wind speed and direction. 7

28 On an overcast da, a stack with an effective height of 60 eters is releasing sulphur dioide at the rate of 80 gras per second. The wind speed is 6 eters per second. Deterine a. The ean concentration of SO on the ground 500 eters downwind. b. The ean concentration on the ground 500 eters downwind and 50 eters crosswind. c. The location and value of the aiu ean concentration on ground level directl downwind. 8

29 a. This is a continuous release. The ground concentration directl downwind is given b Equation 5.,0,0 Q ep u H r (5) Fro Table, the stabilit class is D. the dispersion coefficients are obtained fro Figures 0 and. The resulting values are = 36 eters and = 8.5 eters. Substituting into Equation 5 500,0, s g g s 3 ep

30 b. The ean concentration 50 eters crosswind is found using Equation 50 and setting = 50. The results fro part a are applied directl, 500,50,0 500,0, g g ep 3 3 ep

31 c. The location of the aiu concentration is found fro Equation 53, H r Fro Figure, the dispersion coefficient has this value at = 500. At = 500, fro Figure 0, = 00. The aiu concentration is deterined using Equation 5, a Q r euh 80 g s s g 3 3

32 hlorine is used in a particular cheical process. A source odel stud indicates that for a particular accident scenario.0 kg of chlorine will be released instantaneousl. The release will occur at ground level. A residential area is 500 awa fro the chlorine source. Deterine a. The tie required for the centre of the cloud to reach the residential area. Assue a wind speed of /s. b. The aiu concentration of chlorine in the residential area. opare this with a TLV for chlorine of 0.5 pp. What stabilit conditions and wind speed procedures the aiu concentration? c. Deterine the distance the cloud ust travel to disperse the cloud to a aiu concentration below the TLV. Use the conditions of Part b. d. Deterine the sie of the cloud, based on the TLV, at a point 5 k directl downwind on the ground. Assue the conditions of Part b. 3

33 a. For a distance of 500 and a wind speed of /s, the tie required for the centre of the cloud to reach the residential area is t u 500 s 50 s 4. in This leaves ver little tie for eergenc warning. 33

34 b. The aiu concentration will occur at the centre of the cloud directl downwind fro the release. The concentration is given b Equation 4. ut, 0,0, t * Q 3 (4) The stabilit conditions are selected to aiie <> in Equation 4. This requires dispersion coefficients of iniu value. Fro Figures and 3, this occurs under stable condition. Fro Table, this will occur at night with a - 3 /s wind. 34

35 Assue a slow oving cloud of /s. fro Figures and 3, at 500, = 5. and =.. also assue =. Fro equation 4,.0 3 kg kg 3 40 g 3 Assuing a pressure of at and a teperature of 98 K, the concentration in pp is 737 pp. This is uch higher than the TLV of 0.5 pp. An individuals within the iediate residential area, and an personnel within the plant will be ecessivel eposed if the are outside and downwind fro the source. 35

36 c. Fro Table - 8, the TLV of 0.5 pp is.45 g/³ or kg/³. The concentration at the centre of the cloud is given b Equation 4. Substituting the known values, kg σ σ 3 This equation is satisfied at the correct distance fro the release point. A trial and error procedure is required. The procedure is. Select a distance,.. Deterine,, and using Figures and heck if dispersion coefficients satisf above equation. 0. kg σ 3 σ 36

37 The procedure is continued until the equation is satisfied. This produces the following results, Guessed distance (k) ² ² The distance is interpolated to about 0.3 k. This is quite a substantial distance considering that onl.0 kg of chlorine is released. 37

38 d. The downwind centreline concentration is given b Equation 40.,0,0, t 3 Q * ep ut (40) The tie required for the centre of the plue to arrive is 5000 t 500 s u s At a downwind distance of 5 k, fro Figures and 3, 44 and 8 Substituting the nubers provided, kg kg ep

39 where has units of eters. Rearranging and cobining leads to a quadratic equation, The cloud is 64 eters wide at this point, based on the TLV concentration. At /s, it will take approiatel, 64 8 s s to pass. An appropriate eergenc procedure would be to alert residents to sta indoors with the windows closed and ventilation off until the cloud passes. An effort b the plant to reduce the quantit of chlorine released is also indicated. 39

40 Figure 6 indicates that the release characteristics of a puff or plue are dependent on the initial release oentu and buoanc. The initial oentu and buoanc will change the effective height of release. A release that occurs at ground level but in an upward spouting jet of vaporiing liquid will have a greater effective height than a release without a jet. Siilarl, a release of vapor at a teperature higher than the abient air teperature will rise due to buoanc effects, increasing the effective height of the release. Both of these effects are deonstrated b the traditional sokestack release shown in Figure 4. The aterial released fro the sokestack contains oentu, based on its upward velocit within the stack pipe, and it is also buoant, since its teperature is higher than the abient teperature. 40

41 Figure 4 gases. Sokestack plue deonstrating initial buoant rise of hot 4

42 Thus, the aterial continues to rise after its release fro the stack. The upward rise is slowed and eventuall stopped as the released aterial cools and the oentu is dissipated. For sokestack releases, Turner suggests using the epirical Holland forula to copute the additional height due to the buoanc and oentu of the release, r.5 u sd 3 u.680 T Pd s T T s a (64) 4

43 where ΔH r is the correlation to the release height, H r ū s is the stack gas eit velocit, in /s d is the inside diaeter, in ū is the wind speed, in /s P is the atospheric pressure, in b T s is the stack gas teperature, in K T a is the air teperature, in K For heavier than air vapors, if the aterial is released above ground level, the aterial will initiall fall towards the ground until it disperses enough to reduce the cloud densit. 43

44 Building and structures provide barriers to vapor clouds and ground releases. The behaviour of vapor clouds oving around buildings and structures is not well understood. 44