# Pollution Modeling II

friends welcome to the seventh lecture on
the online course title hse management in offshore and petroleum engineering we are
talking about lectures in module one where we are focusing on environmental issues that
arise exclusively from oil and gas industries exploration and production and processing
in this lecture we just title as pollution modeling two will continue to discuss atmospheric
pollution in the last lecture we discussed about the
continues models which is a plume dispersion model
we have given you the equation to find the concentration of the plume dispersion which
is happening in the side in terms of x y z coordinates where h is also involved x is
an implicit function sigma x an implicit value in the function let us discuss some special
cases about this so let us try to recollect x is in the direction or is in the windward
direction y is in the cross wind direction and z is along the lets say vertical axis let us discuss some special cases
the general equation is what is given to you in the last lecture let us substitute back
some conditions in the general equation there are special conditions for specific cases
for plume dispersion models plume refers to continuous dispersion lets say case one the
ground level central line concentration you want to find so to determine the ground level
central line concentration the moment i say i am interested only in central line so i
then i should substitute y as zero because i am not looking at the cross wind direction
at all the moment i say ground level concentration i should also say z as zero then therefore
my concentration will be now given as zero zero zero q by two pi sigma z and sigma y
of u which is a wind velocity exponential of minus half h by sigma z square call equation
number one the next case case two where i want the concentration at the ground along
the center line and in this case we are interested at h is also equal to zero the release height
is practically at the ground level itself in that case c x zero zero for the plume dispersion
model will be simply given by q by two pi sigma z sigma y of u which i call as equation
number two in both these expressions you can notice that
x is implicitly present within the dispersion coefficients it is very important observation
made by brode in nineteen fifty nine what is their observation he says that the maximum
plume concentration always occurs at the release point probably this is one of the basis on
which these equations that derived interestingly for releases above the ground the maximum
concentration occurs along the center line of the down wind direction
so this implies a simple statement saying the plume concentration along the cross wind
will be always will be lesser than that along the x direction
where we all know that x direction is the down wind direction now the distance at which
the ground level concentration would occur is given by sigma z is h by root equation
number three and the maximum concentration is given by c max which is two q by e pi u
h square sigma z by sigma y and call this as equation number four this about the discussion what we had a special
cases for the plume dispersion model let us discuss puff dispersion model which in intermittent
release model the puff dispersion model describes instantaneous release of the material you can give a example of
this certain release of a chemical from a ruptured vessel can be a classical example what could be the
consequences of such kind of instantaneous releases which occur essentially because of
these kind of accidents because ruptured vessel is sort of an accident let us say the consequences
could be it will result in a large vapor cloud which is essentially formed nearer or i should
say from the rupture point which essentially originates from the ruptured point now i want
to estimate the average concentration of this kind of release average concentration of puff
release is given by c x y z where the terms x y z directions remains same as that of the
plume model which is given by q instantaneous two pi to the power three by two sigma x sigma
y sigma z multiplied by exponential of minus half of x minus ut by sigma x square multiplied
by exponential of minus half of y by sigma y square multiplied by exponential of minus
half z plus h by sigma z the whole square plus exponential of minus half of z plus h
by sigma z the whole square which i put a bracket here and a bracket here this becomes
an entire product with these two terms call equation number five where the terms have
the same meaning as we in explain in the plume model let us now consider some special cases of
puff model lets say case one we wanted to find out the total integrated dose
at the ground level which is given by dose so in this case you will easily see z will
be zero because i am locking at the ground level so dose x y zero we can say concentration
as well of the dose is given by q instantaneous by pi sigma y and sigma z of u exponential
minus half y by sigma y square minus of minus half h by sigma z square equation number six the next case could be concentration on the
ground bellow the puff center which can be given by i am also not looking
at the cross wind value which can be q instantaneous root two pi three by two
one by sigma x sigma y and sigma z oh this is sigma y square call equation number seven
the next case could be the puff center on the ground
the moment i say this i should say h is zero which can be given by is q instantaneous by
root two pi three by two sigma sigma z sigma x sigma y exponential minus half h by sigma
z eight the maximum puff concentration is a very important item which is to be also
computed the maximum puff center is located at the release height itself concentration
center will be located at the release height and the center of puff is located at x is
equal to u t u t where u is the wind velocity it can be easily understood that the maximum
concentration will always occur directly below the puff center the next interesting discussion on the atmospheric
pollution modeling and dispersion modeling is isopleths
what are isopleths isopleths actually are representative values which are used to measure
the cloud boundary at a fixed concentration isopleths are plots used to measure the cloud
boundary that is what is the extension of the cloud
at a fixed concentration so if you know the concentration one can always estimate what
did the spread of this particular dispersion so cloud boundary so basically the term iso
stands for a meaning that it represents lines of constant concentration
thats why the term iso has come there are different steps which are followed to find
out or to draw or to plot an isopleth graphically we will see the figure let us say step number one so i now looking
for steps to plot isopleth let say this is my windward direction so thats my wind direction
let say this is my release point once it is released and this is of course
a center line along the windward direction so center line means the cross wind dimensions
or relativity zero so let us mark certain points along the center line so the first step is draw the center line
along their wind direction locate the release point select or mark concentration points
along the center line which are called fixed points these points what has been selected
along a center line or fixed points where the concentration is known to me is known
rather i can compute that in step number two i want to find the off
center the distances to isopleths which are nothing but y y values at each point
along the center line so we know there are many points we have along the center line
may be x one x two x three x four and so on at each point where the concentration is known
to me i am interested to estimate the off center distance depending upon the concentration
along the windward direction at fixed chosen points along the center line so how do you
get that so y can be given by a simple equation here which depends on sigma y and square root
of twice of natural logarithm of c x zero zero at any time t divided by c x y zero at
any time t equation number seven so in this case where c x zero zero t is the downwind
ground center line concentration whereas c x y zero is the isopleth concentration
at point x comma y where x is chosen by u at fixed points along the center line step number three
plot y for both directions at each fixed points let us try to do it here so now we can call them as isopleth these
are nothing but isopleth offset which you computed from the
equation seven knowing the concentration c x zero zero t and c x y zero t from the equations
which you have desribed in the earlier slides now step number four
connect the points so let us connect them now this spot we call as isopleths so one
can easily draw the isopleths by using this four steps where an equation is involved one
can easily compute that now in this it is important that i have to
estimate the dispersion coefficients to really understand the release scenarios using plume
and puff models so plume is a continuous release where as puff is an instantaneous release
of a gas or a cloud vapor how they are getting dispersed in the atmosphere how they are modeled
to account for atmospheric pollution is what we are trying to capture so i would like to
now estimate the dispersion coefficients they are very important they are required
to model the release scenario both for plume and puff model is very well explained by wiltox
two thousand one wiltox said that the dispersion coefficients depend on the stability class
and the downwind distance these are the two factors on which the dispersion coefficients
will depend on stability class we already know it can be also derived from pascal stability
class which accounts for the humidity relative temperature rain fog etcetera everything and
of course the downwind distance is the point of interest along the x direction where the
wind velocity is considered to be in the prerogative direction let us now look at the steps to compute the
dispersion coefficients step number one as it depends on the stability class you have
got a first identify the pasquill stability class applicable to a specific location so
identify the pasquill stability class which essentially an alphabetic character named
as a b c d e or f this of course depends on an obtain from
materilergical data it also depends on wind speed it also depends on heat radiation it
also depends upon cloud cover which is also a path of relective humidity at a specific
site so identify the stability class once you identify
then classify the area the classifications could be is it rural or urban because a wind
velocity a wind speed is dependent on various parameters which we already discussed in the
previous lectures is it flat or hilly is it having any water body etcetera so classify
the area so then one can find the dispersion coefficients
by two ways one can find them graphically from the figures which i am going to show
you now or one can also calculate the dispersion coefficients from the empirical relationship
or equations which i will show you subsequently so step number three derive the dispersion
coefficients either from the figures which i am going to show you or using the equations
which i am going to give you remember they all depend on any respective downward distance
because as i just now showed you the dispersion coefficient depends on two parameters one
is the stability class which you are identified the second is the downward distance x along
the wind prerogative direction so for every distance of your choice you have to compute
the dispersion coefficient which is case specific site specific distance specific from the release
source i may request you to look at the screen now
the screen shows dispersion coefficients for the plume model for a rural release there
are two figures shown in the screen the left one is enabling you to complete sigma y values
the right one enables you to compute sigma z values which are required for estimating
the coefficients the horizontal axis indicates the downward distance along the windward direction
in kilo meters and different colors having given as a legend for different pasquills
stability class varying from a to f as you can see from the figure so for a specific
distance which you are identified for a specific pasquills stability class let us say in this
case a can always find possibly what is the sigma y value and correspondingly what is
the sigma z value for rural release for a plume model similarly look at the screen now you have
figure illustrating dispersion coefficients for the plume model for urban release so again
it shows pasquill stability class varying from a to f similarly a to f for sigma z value
and sigma y value as similar to that of the rural release which you saw in the previous
slide so one can easily for a known downward distance in kilo meter for a known pasquills
stability class given as a legend here one can easily find the sigma y value and sigma
z value which are required to compute the dispersion coefficients similarly the dispersion
coefficients for puff model is also given to you on the screen in the similar understanding
once the dispersion coefficients for either the plume model or the puff model are estimated
then one can easily find out the concentration at any fixed point along the downward distance
what is interesting for us one can also estimate the dispersion coefficients from the equations so estimating dispersion coefficients that
is sigma x sigma y and sigma z sigma y and sigma z which are used to find the concentration
let us now estimate them using equations earlier we discussed estimating them for the graphical
method so if you talk about plume model please understand x is the downward distance
downwind distance which you have to fix in meters measured from the release source once
you know this value which is the only variable even the graphical method also this is the
only variable of course the other variable was the pasquills stability class which you
are identifying i can also use dispersion coefficients from this equations please look
at the table now which is showing the dispersion coefficients or plume model for two different
conditions rural and urban which you classified for different stability class a to f and a
to f in both categories you get dispersion coefficients sigma y and sigma z which has
equations given where in this equation the only variable what you see here is the capital
x where capital x is the down wind direction or the distance which you have to substitute
in meters in this equation so for a plume model you can either find out the dispersion
coefficients from the graphical method or from the table or equations given to you in
the slide similarly if you look at the screen now you
will now find the dispersion coefficients equations for the puff model for the rural
conditions for different stability class varying from a to f as a pasquills stability class
and it can be either sigma y or sigma x because puff depends upon the concentration point
below the release point on the ground and of course sigma z the only variable in this
equations for every stability class for a rural condition is x where x is the downwind
distance substituted in meters we are in judgment in this lecture we are
able to explain you the dispersion coefficient and the concentration of the plume and puff
releases which are instantaneous and continuous models which uses different kind of plots
and equations to compute the concentration of the release material we have also discussed
the importance and explanation of isopleths how are they plotted and how are they useful
in estimating atmospheric pollution from any release source which happens as an output
source which comes out from a process industry in our whole discussion we are focusing the
process industry to be or considering the process industry to be a petroleum refinery
which actually works on crude oil to get a commercial outlet of the product from the
crude oil do you have any doubts please post them to
nptel website on a periodic discussion forum and let us have or share the information what
are we learned thank you very much