Department of Chemical Engineering Project An Introduction to Modeling by Richard Gilbert Nihat Gürmen 10/19/98 University of South Florida, Tampa Foundations

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



TheoryThe rate of volume change of fluid leaving tank is proportional to the volume of fluid in the tank

ModelModel Assumptions

Observation



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


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





Observation

Measure how long it takes to empty half of the tank



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).




Observation Measure how long it takes to empty half of the

tankCompare this time with model predicted time to empty half of the tank


Observations: Red data points show measurements of time and tank level. Blue line is model predictions.


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


Measured Height versus Model Prediction Height Values

If model, observation, theory puzzleis working well, right two columnsshould have same ( very close) numbers


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


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


RealityTheoryRate of fluid flow out of the tank is related to the square of the liquid height


Model The model for this new theory is for another day.

But you can check it outif you want to.


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”


Fluidized Bed Dryer Model

Properties of solvent to be removed

Properties of drying fluid

Properties of particles to be dried


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)


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


Input Output

Accumulation

Generation

Input - Output + Generation = Accumulation

Form of a general balance equation


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


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



Thanks for your time.We hope the presentation put a bit of light on the subject.

Documents

Department of Chemical Engineering Project An Introduction to Modeling by Richard Gilbert Nihat Gürmen 10/19/98 University of South Florida, Tampa Foundations