1. 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

2. 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

3. Foundations of Engineering- EGN 4930

4. Model Observation Reality Theory Foundations of Engineering- EGN 4930

5. Theory The rate of volume change of fluid leaving tank is proportional to the volume of fluid in the tank Model Model Assumptions Observation

6. Foundations of Engineering- EGN 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

7. Exponential Models - necessary condition The rate of change of a quantity should be proportional to the current amount of that quantity. h(t) time Height h(t), ft h 0, ft Emptying a tank Foundations of Engineering- EGN 4930

8. Exponential Models - closer look Height, h(t) [ft] Initial height, h 0 [ft] Flow, q [ft 2 /min] Resistance, R [min/cm 2 ] Area, A ft 2 Foundations of Engineering- EGN 4930

9. 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 Engineering- EGN 4930

10. Exponential Models - Half-life approach t 1/2 h0h0 h 0 /2 h 0 /4 2t 1/2 Every half-life, t 1/2, the level of tank will be halved. time (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).

11. 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 Engineering- EGN 4930

12. Observations: Red data points show measurements of time and tank level. Blue line is model predictions. Foundations of Engineering- EGN 4930

13. timeh1, realityh2, Model (min.)(feet)(feet) 01010 58.127.57 106.435.73 154.944.34 203.653.29 252.552.49 301.651.88 350.951.43 400.431.08 Foundations of Engineering- EGN 4930 Measured Height versus Model Prediction Height Values If model, observation, theory puzzle is working well, right two columns should have same ( very close) numbers

14. 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 model b) different theory or c) check observations or d) do all three Theory Rate of fluid volume change leaving tank is proportional to fluid volume in the tank Observation Measure how long it takes to empty half of the tank Model Model Assumptions Exit resistance is constant pressure difference across the pipe is the head pressure at the bottom of tank

15. Foundations of Engineering- EGN 4930 Theory Rate of fluid flow out of the tank is related to the square of the liquid height But you can check it out if 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

16. Dr. Carlos Smith’s (USF Chem. Eng. Professor) book, “Principles and Practices of Automatic Process Control, Chapter 4 Foundations of Engineering- EGN 4930 Theory Rate 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 out if you want to.

17. Foundations of Engineering- EGN 4930 Theory Rate 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 of Automatic Process Control” Observation Measure how long it takes to empty half of the tank

18. 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

19. Drying fluid properties Viscosity of airg/cm-s Specific heat of air @const Pcal/g- o C Density of air g/cm 3 Molecular weight of airg/mole Critical temperature of air o K Critical density of airg/cm 3 Solvent properties Molecular weight g/mole Critical TemperatureºK Critical Densityg/cm 3 Thermal ConductivityW/cm- o C Particle Properties Particle Densityg/cm 3 Data needed to solve TK Solver Model (computer crunching) Foundations of Engineering- EGN 4930 Data in red you will find in library Data in blue you will find in web pages for this project

20. 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

21. InputOutput Accumulation Generation Input - Output + Generation = Accumulation Form of a general balance equation Foundations of Engineering- EGN 4930

22. 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

23. Department of Chemical Engineering at USF Phone numbers (813) 974-3997 (813) 974-3651 (fax) Chairperson L. H. Garcia-Rubiogarcia@eng.usf.edu Undergraduate Advisors C. Beaverbeaver@eng.usf.edu C. Busotbusot@eng.usf.edu C. Smithcsmith@eng.usf.edu W. E. Lee (Bio-Engineering)lee@eng.usf.edu Room number Kopp Engineering building ENG 346 Foundations of Engineering- EGN 4930

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