M E 433
Professor John M. Cimbala
Lecture 19
Today, we will:
•
Discuss the Gaussian puff diffusion model (sudden burst of air pollution from a point)
•
If time, begin to discuss particle vs. steam plumes and how to distinguish them
From equation sheet:
σ=
axb , σ zi = cx d , but x in units of m, not km, and
Gaussian puff diffusion model: σ=
xi
yi
σyi and σzi in units of m. Use these empirical values for the instantaneous diffusion
coefficients, depending on atmospheric stability conditions:
Stability
a
b
c
Unstable
Neutral
Very stable
0.14
0.06
0.02
0.92
0.92
0.89
0.53
0.15
0.05
d
0.73
0.70
0.61
Adapted from Slade (1968), as found in Heinsohn and Kabel (1999).
Absorbing ground:
2
2
2
 


mj

 z − H   
−
1
x
Ut
y
 
=
c j ( x, y , z , t )
exp − 
 + 
 + 
 
σ
σ
σ
2

p 2pσ xiσ yiσ zi
  xi   yi   zi   
(1)
Example: Gaussian puff diffusion
Given: A ground-level tank containing 10 kg of hydrogen cyanide (HCN) ruptures at a
chemical plant early in the morning. The atmosphere is very stable, and a gentle breeze is
blowing at U = 1.5 m/s. The ground absorbs the HCN on contact. Workers downwind of the
explosion are exposed to the HCN.
To do:
(a) Estimate the dose of HCN that would constitute hazardous conditions for the workers.
(b) Predict the dose directly downwind at x = 1.5 km.
(c) Plot dose vs. x. How far downstream is this hazardous to people on the ground?
Solution:
(a)
(b)
Equation for ground level dose, absorbing ground:
2
2 
 
mj
 1  y   H  
=
+
D j ( x, y,0
exp − 
)
 σ   σ   
p U σ yiσ zi
2

  yi   zi   
(c) I used Excel – will show in class.
Email I received from a former student in 2015 (to motivate you):
Hi Professor Cimbala,
My name is ____ and I was in your ME 433 class last Spring. I recently began working for
____ Corporation. ... On one of my first days on the job my boss mentioned to the group
how ____ needed to obtain the radius of exposure (ROE) of H2S from our wells in the event
of a blow-out. H2S, as I am sure you know, is a deadly chemical that is present in the
majority of oil and gas wells. Recalling all the work we did with plume models in class, I
quickly told my boss that I would be able to handle the project.
Attached you will find the finished project. I recently showed my boss and coworkers and
they were blown away by all of the calculations and user friendly design of the workbook.
All that is required of ____ is to have an estimate of the ROE of each producing well,
however, my knowledge of plotting plumes enabled me to take it to the next level and
create an interactive workbook. The workbook enables anyone to input the H2S content
and flow rate of the well in order to determine the ROE and general shape of the plume in
the event of a blow-out. The information I make available to the user helps first responders
determine who might be in harm’s way if a blow-out were to occur.
I am sending this email to you for two reasons. The first is to express my satisfaction with
your course and your teaching methods. By the end of the semester I believe I had learned
more than I had in any other class at Penn State. The second is that I hope you might share
this with your current class as a testament of how applicable the course is in the real world,
especially in the oil and gas industry. Hopefully by seeing this they will realize how
important it is to take your class, and even more generally, school, seriously.