Transcript Department of Chemical Engineering Project Foundations of Engineering - EGN 4930

Foundations of Engineering - EGN 4930
Department of Chemical Engineering Project
An Introduction to Modeling
by
Richard Gilbert
Nihat Gürmen
10/19/98
University of South Florida, Tampa
Foundations of Engineering - EGN 4930
Objectives for Chemical Engineering Project
• Exponential Model
- understand how to explore a mathematical
model in engineering
• Fluidized Bed Model
- acquire library research skills
- get a feel of what chemical engineers do
Reality
Foundations of
EngineeringEGN 4930
Observation
Reality
Model
Theory
Foundations of
EngineeringEGN 4930
Theory
The rate of volume change
of fluid leaving tank is
proportional to the volume
of fluid in the tank
Observation
Model
Model Assumptions
Foundations of
EngineeringEGN 4930
Theory
The rate of volume change
of fluid leaving tank is
proportional to the volume
of fluid in the tank
Model
Model Assumptions
Pressure difference across
the pipe is the head pressure
at the bottom of the tank
Observation
Resistance
of exit
pipe is constant
Foundations of
EngineeringEGN 4930
Exponential Models - necessary condition
The rate of change of a quantity should be
proportional to the current amount of that quantity.
Emptying a tank
h(t)
h0 , ft
h(t )  h0e
a 
 t 
b 
Height
h(t) , ft
time
Foundations of
EngineeringEGN 4930
Exponential Models - closer look
Initial height, h0 [ft]
Height,
h(t) [ft]
Area, A ft2
Resistance, R [min/cm2]
Flow, q
h(t )  h0e
[ft2/min]
p h


R R
 1/ A  

t
 R 
Foundations of
EngineeringEGN 4930
Theory
The rate of volume change
of fluid leaving tank is
proportional to the volume
of fluid in the tank
Model
Model Assumptions
Pressure difference across
the pipe is the head pressure
at the bottom of the tank
Resistance
of exit
pipe is constant
Observation
Measure how
long it takes
to empty half
of the tank
Foundations of
EngineeringEGN 4930
Exponential Models - Half-life approach
h(t )  h0e
 1/ A  

t
 R 
Every half-life, t1/2,
1 A  0.693
R
t1/ 2
h(t )  h0 e
 0.693 

t
 t1 2 


h0
the level of tank
will be halved.
h0/2
h0/4
t1/2 2t1/2
(when the time after the tank starts to
drain = [0.693(R) / (1/A)] the model predicts
that the tank will be half full
( or half empty depending on your mood).
time
Foundations of
EngineeringEGN 4930
Theory
The rate of volume change
of fluid leaving tank is
proportional to the volume
of fluid in the tank
Model
Model Assumptions
Pressure difference across
the pipe is the head pressure
at the bottom of the tank
Resistance
of exit
pipe is constant
Observation
Measure how long
it takes to empty
half of the
tank
Compare this
time with model
predicted time
to empty half
of the tank
Foundations of
EngineeringEGN 4930
Observations:
Red data points show measurements
of time and tank level.
Blue line is model predictions.
Foundations of
EngineeringEGN 4930
Measured Height versus Model Prediction Height Values
time
(min.)
0
5
10
15
20
25
30
35
40
h1, reality
(feet)
10
8.12
6.43
4.94
3.65
2.55
1.65
0.95
0.43
h2, Model
(feet)
10
7.57
5.73
4.34
3.29
2.49
1.88
1.43
1.08
If model, observation, theory puzzle
is working well, right two columns
should have same ( very close) numbers
Foundations of
EngineeringEGN 4930
Theory
Observation
Measure how
long it takes to
empty half
of the tank
Rate of fluid
volume change
leaving tank is
proportional to fluid
volume in the tank
Model
Puzzle for fluid flow from the
bottom of a full tank does not fit
together. Try again with
a) new model
b) different theory
or
c) check observations
or
d) do all three
Model Assumptions
Exit resistance
is constant
pressure difference
across the pipe is
the head pressure
at the bottom of
tank
Foundations of
EngineeringEGN 4930
Observation
Measure how
long it takes to empty
half of
the tank
Theory
Rate of fluid
flow out of the
tank is related
to the square
of the liquid
height
Re ality
Model
Model for this
new theory
is for another
day.
But you can check it out
if you want to.
Foundations of
EngineeringEGN 4930
Observation
Measure how
long it takes to empty
half of
the tank
Theory
Rate of fluid
flow out of the
tank is related
to the square
Model
of the liquid
The model for this
height
new theory is
Reality
for another
day.
But you can check it out
if you want to.
Dr. Carlos Smith’s
(USF Chem. Eng. Professor) book,
“Principles and Practices of
Automatic Process Control, Chapter 4
Foundations of
EngineeringEGN 4930
Observation
Measure how
long it takes to empty
half of
the tank
Theory
Rate of fluid
flow out of the
tank is related
to the square
of the liquid
Model
height
The new theory
Reality
model is for
another day.
But you can
check it out if
you want to in Dr. Smith’s
controls book.
“Principles and Practices of
Automatic Process Control”
Foundations of
EngineeringEGN 4930
Fluidized Bed Dryer Model
Properties of solvent to be removed
Properties of particles to be dried
Properties of drying fluid
Foundations of
EngineeringEGN 4930
Data needed to solve TK Solver Model (computer crunching)
Drying fluid properties
Viscosity of air
Specific heat of air @const P
Density of air
g/cm3
Molecular weight of air
Critical temperature of air
Critical density of air
Particle Properties
Particle Density g/cm3
Data in red you will find
in library
Data in blue you will find
in web pages for this project
g/cm-s
cal/g-oC
g/mole
oK
g/cm3
Solvent properties
Molecular weight
Critical Temperature
Critical Density
Thermal Conductivity
g/mole
ºK
g/cm3
W/cm-oC
Foundations of
EngineeringEGN 4930
How does chemical engineering fit into the picture ?
Both models are solutions to the balance equations.
Balance equations - UUUhhh ?!?!?
• Accounting for engineering
• Gives a way of defining changes in a system
Foundations of
EngineeringEGN 4930
Form of a general balance equation
Accumulation
Generation
Input
Output
Input - Output + Generation = Accumulation
Foundations of
EngineeringEGN 4930
Chemical engineering
If you choose to be a chemical engineer you
will master the skills necessary to define a
system in terms of
• mass balance,
• energy balance, and
• momentum balance equations.
Foundations of
EngineeringEGN 4930
Department of Chemical Engineering at USF
Chairperson
L. H. Garcia-Rubio
[email protected]
Undergraduate Advisors
C. Beaver
[email protected]
C. Busot
[email protected]
C. Smith
[email protected]
W. E. Lee (Bio-Engineering)
[email protected]
Room number
Phone numbers
Kopp Engineering building
• (813) 974-3997
ENG 346
• (813) 974-3651 (fax)
Foundations of
EngineeringEGN 4930
Thanks for your time.
We hope the presentation
put a bit of light on the
subject.
Foundations of
EngineeringEGN 4930