Air  Pollution  :  L  5

01/11/2017

Some  Useful  Concepts:

• Maximum  mixing  height/  depth  ?  

• Ventilation  coefficient  ?

• Wind-­‐rose  diagram  ?

Atmospheric Stability and Mixing Depth

• The amount of air available to dilute pollutants is related to the wind speed and to the extent to which emissions can rise into the atmosphere.

• An estimate of this (dilution process) can be obtained by determining “maximum mixing depth”

Estimation of Maximum mixing depth and ventilation coefficient

• Following the logic presented earlier, the maximum mixing depth can be estimated by plotting maximum surface temperature and drawing a line parallel to the dry adiabatic lapse rate from the point of maximum surface temperature to the point at which the line intersects the ambient or natural temperature profile (usually of early morning or night)

Ventilation Coefficient (m2/s) = MMD (m) * Avg wind speed within mixing depth (m/s) This parameter is used as an indicator of the atmosphere’s dispersive capability If ventilation coefficient< 6000 m2/s, air pollution potential is considered to be high.

MMD

Ambient temp. profile

Tmax Æ T Æ

Z

Wind-­rose  diagram  

Maximum  Ground  Level  ConcentrationUnder  moderately  stable  to  near  neutral  conditions,

zy k σσ 1=

The  ground   level  concentration  at  the  center  line  is

( ) ⎥⎦

⎤⎢⎣

⎡−= 2

2

21 2

exp0,0,zz

Huk

QxCσσπ

The  maximum  occurs  at

2 0/ HddC zz =σ⇒=σ

Once  σz is  determined,  x  can  be  known  and  subsequently  C.

( ) [ ]u

Qu

QxCzyzy σσ

=−σπσ

= 1171.01exp0,0,

Discussion….

• 1.  In  the  Holland's  formula  for  finding  the  plume  rise,  there  is  a  direct  proportionality  of  Plume  rise  with  the  stack  diameter.  But  this  is  against  the  intuitive  reasoning  that  we  gave  in  class.  If  the  stack  diameter  decreases,  the  exit  velocity  of  the  gases  increase  and  hence  the  Plume  rise  must  increase.  

• Why  the  formula  suggest  the  opposite  thing?

• 2.  In  the  case  of  perfect  absorption,  which  formula  should  be  used.  Is  it  the  one  where  only  the  (z-­‐H)^2  term  appears  in  the  exponent.  

• Also,  should  we  always  consider  perfect  reflection  in  case  there  is  nothing  specified  about  the  type  surface?

Wark & Warner, “Air Pollution: Its Origin & Control”

( ) ( ) ( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡

σ

+−+⎥

⎦

⎤⎢⎣

⎡

σ

−−

⎥⎥⎦

⎤

⎢⎢⎣

⎡

σ−

σπσ= 2

2

2

2

2

2

2exp

2exp

2exp

2,,

zzyzy

HzHzyu

QzyxC

Point Source at Elevation H

• Assumes no interference or limitation to dispersion in any directiondispersion in any direction

d l i f li f lx0 and z0 are location of centerline of plumey0 taken as base of the stackz0 is HQ = emission strength of source (mass/time) – g/su = average wind speed thru the plume – m/sC = concentration – g/m3 (Notice this is not ppm)

19

Vy and Vz are horizontal and vertical standard deviations in meters

Point Source at Elevation H with Reflection

Notice this is also equation 4-8 in text, it is the second equation 4-8 on theit is the second equation 4 8 on the bottom of page 149

40

Point Source at Elevation H without Reflection

• 3 terms– gives concentration on the centerline of the plume– gives concentration as you move in the sideways direction (r y

2direction), direction doesn’t matter because (r y)2 gives a positive value

– gives concentration as you move in the vertical direction (r z direction) direction doesn’t matter because (r (z H))2 gives adirection), direction doesn t matter because (r (z – H))2 gives a positive value

• Concentrations are symmetric about y-axis and z-axis• Same concentration at (z-H) = 10 m as (z-H) =10 m

21

• Same concentration at (z-H) 10 m as (z-H) 10 m• Close to ground symmetry is disturbed

Effect  of  Inversion

18

Virtual Source Also Used to Model ReflectionOff of the Top of the Mixed Layer

(added to direct plume concentration)

Eventually well-mixed

Plume Reflection off of the top of the mixed layer

wind

zii

18

Virtual Source Also Used to Model ReflectionOff of the Top of the Mixed Layer

(added to direct plume concentration)

Eventually well-mixed

Plume Reflection off of the top of the mixed layer

wind

zii

• 3.  Why  Gaussian  dispersion  model  is  only  limited  to  finding  concentration  of  pollutants  beyond  X  =  50  m?  

• 4.  In  the  example  that  we  did  in  class  for  the  Briggs  method,  the  final  condition  that  whether  x  >  xf is  not  included.  The  desired  location(x)  for  concentration  measurement  is  not  specified.  

• Is  the  information  insufficient  in  the  question?

• 5.  Logical  explanation  of  why  the  stability  decreased  with  the  wind  in  the  table  that  we  had  in  the  slides??

Line Sources

• Imagine that a line source, such as a highway, consists of an infinite number of g y,point sources

• The roadway can be broken into finiteThe roadway can be broken into finite elements, each representing a point source, and contributions from each element areand contributions from each element are summed to predict net concentration

61

Line SourcesLine Sources• When wind direction is normal to line of emission

G d l l i d i d• Ground level concentration downwind

C( 0) 2 ( 0 5H2)C(x,0) = ___ 2q ___ exp(-0.5H2)(2Π)0.5 Vz u Vz

2

q = source strength per unit distance (g/s * m)

Concentration should be uniform in the y-direction at a given x

62

g

Line SourcesLine Sources• For ground level (H = 0), could also use breathing

heightheight

C(x 0) = 2q exp( 0 5H2)

1

C(x,0) = ___ 2q ___ exp(-0.5H )(2Π)0.5 Vz u Vz

2

63

Instantaneous Release of a Puff• Pollutant released quickly

E l i• Explosion• Accidental spill• Release time << transport time• Also based on Gaussian distributionAlso based on Gaussian distribution

function

65

Instantaneous  Release  of  a  PuffInstantaneous Release of a Puff

• Equation 4-41 to predict maximum ground level q p gconcentration

Cmax = _____2Qp____(2Π)3/2 Vx Vy Vz

Receptor downwind would see a gradual increase in t ti til t f ff d d thconcentration until center of puff passed and then

concentration would decreaseAssume V = V

66

Assume Vx Vy

Maximum  Ground  Level  Concentration

Puff ExampleA tanker spill on the freeway releases 400 000 grams of chlorineA tanker spill on the freeway releases 400,000 grams of chlorine. What exposure will vehicles directly behind the tanker (downwind) receive if x =100 m? Assume very stable conditions.

From Table 4-7,

69

Figure 4-9 and Table 4-7

68

Puff ExampleA tanker spill on the freeway releases 400 000 grams of chlorineA tanker spill on the freeway releases 400,000 grams of chlorine. What exposure will vehicles directly behind the tanker (downwind) receive if x =100 m? Assume very stable conditions.

From Table 4-7, Vy = 0.02(100m)0.89 = 1.21

F T bl 4 7 0 05(100 )0 61 0 83From Table 4-7, Vz = 0.05(100m)0.61 = 0.83

Cmax = _____2Qp____ = ____2(400000 g)_____ = 42,181 g/m3

(2Π)3/2 Vx Vy Vz (2Π)3/2(1.21)(1.21)(0.83)

72