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
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 Engineering- EGN 4930
Model
Observation
Reality
Theory
Foundations of Engineering- EGN 4930
Foundations of Engineering- EGN 4930
TheoryThe rate of volume change of fluid leaving tank is proportional to the volume of fluid in the tank
ModelModel Assumptions
Observation
Foundations of Engineering- EGN 4930
TheoryThe rate of volume change of fluid leaving tank is proportional to the volume of fluid in the tank
ModelModel Assumptions Pressure difference across the pipe is the head pressure at the bottom of the tank
Resistance of exit pipe is constant
Observation
Exponential Models - necessary condition
The rate of change of a quantity should be proportional to the current amount of that quantity.
h(t)
time
t
b
a
ehth 0)(Height
h(t) , ft
h0 , ft
Emptying a tank
Foundations of Engineering- EGN 4930
Exponential Models - closer look
t
R
A
ehth/1
0)(
R
h
R
p
Height,
h(t) [ft]
Initial height, h0 [ft]
Flow, q [ft2/min]
Resistance, R [min/cm2]Area, A ft2
Foundations of Engineering- EGN 4930
TheoryThe rate of volume change of fluid leaving tank is proportional to the volume of fluid in the tank
ModelModel 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 Engineering- EGN 4930
Foundations of Engineering- EGN 4930
Exponential Models - Half-life approach
t
R
A
ehth/1
0)(
2/1
693.01
tR
A
t
tehth 21
693.0
0)(t1/2
h0
h0/2
h0/4
2t1/2
Every half-life, t1/2,
the level of tank
will be halved.
time(when the time after the tank starts todrain = [0.693(R) / (1/A)] the model predictsthat the tank will be half full ( or half empty depending on your mood).
TheoryThe rate of volume change of fluid leaving tank is proportional to the volume of fluid in the tank
ModelModel 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
tankCompare this time with model predicted time to empty half of the tank
Foundations of Engineering- EGN 4930
Observations: Red data points show measurements of time and tank level. Blue line is model predictions.
Foundations of Engineering- EGN 4930
time h1, reality h2, Model(min.) (feet) (feet) 0 10 10 5 8.12 7.5710 6.43 5.7315 4.94 4.3420 3.65 3.2925 2.55 2.4930 1.65 1.8835 0.95 1.4340 0.43 1.08
Foundations of Engineering- EGN 4930
Measured Height versus Model Prediction Height Values
If model, observation, theory puzzleis working well, right two columnsshould have same ( very close) numbers
Foundations of Engineering- EGN 4930
Puzzle for fluid flow from the bottom of a full tank does not fit together. Try again with
a) new modelb) different theory
or c) check observations
or d) do all three
TheoryRate of fluid volume change leaving tank is proportional to fluid volume in the tankObservation
Measure how long it takes to empty half of the tank Model
Model AssumptionsExit resistance
is constant pressure difference across the pipe is the head pressure at the bottom of tank
Foundations of Engineering- EGN 4930
Reality
TheoryRate of fluid flow out of the tank is related to the square of the liquid height
But you can check it outif you want to.
Model Model for this new theory is for another day.
Observation Measure how long it takes to empty half of the tank
Dr. Carlos Smith’s (USF Chem. Eng. Professor) book, “Principles and Practices of Automatic Process Control, Chapter 4
Foundations of Engineering- EGN 4930
RealityTheoryRate of fluid flow out of the tank is related to the square of the liquid height
Observation Measure how long it takes to empty half of the tank
Model The model for this new theory is for another day.
But you can check it outif you want to.
Foundations of Engineering- EGN 4930
RealityTheoryRate of fluid flow out of the tank is related to the square of the liquid height
Model The new theory model is for another day.
But you can check it out if you want to in Dr. Smith’s controls book.
“Principles and Practices ofAutomatic Process Control”
Observation Measure how long it takes to empty half of the tank
Fluidized Bed Dryer Model
Properties of solvent to be removed
Properties of drying fluid
Properties of particles to be dried
Foundations of Engineering- EGN 4930
Drying fluid propertiesViscosity of air g/cm-sSpecific heat of air @const P cal/g-oCDensity of air g/cm3
Molecular weight of air g/moleCritical temperature of air oKCritical density of air g/cm3
Solvent propertiesMolecular weight g/moleCritical Temperature ºKCritical Density g/cm3
Thermal Conductivity W/cm-oC
Particle PropertiesParticle Density g/cm3
Data needed to solve TK Solver Model (computer crunching)
Foundations of Engineering- EGN 4930
Data in red you will find in libraryData in blue you will findin web pages for this project
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 Engineering- EGN 4930
Input Output
Accumulation
Generation
Input - Output + Generation = Accumulation
Form of a general balance equation
Foundations of Engineering- EGN 4930
Chemical engineering
• mass balance,
• energy balance, and
• momentum balance equations.
If you choose to be a chemical engineer you will master the skills necessary to define a system in terms of
Foundations of Engineering- EGN 4930
Department of Chemical Engineering at USF
Phone numbers
• (813) 974-3997
• (813) 974-3651 (fax)
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
Kopp Engineering building
ENG 346
Foundations of Engineering- EGN 4930
Foundations of Engineering- EGN 4930
Thanks for your time.We hope the presentation put a bit of light on the subject.
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