1. 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

2. 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

3. Foundations of Engineering- EGN 4930

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

6. 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 Foundations of Engineering- EGN 4930

7. Exponential Models - necessary condition The rate of change of a quantity should be proportional to the current amount of that quantity. h(t) Emptying a tank h0 , ft Height h(t) , ft time Foundations of Engineering- EGN 4930

8. Exponential Models - closer look Initial height, h0 [ft] Height, h(t) [ft] Area, A ft2 Resistance, R [min/cm2] Flow, q [ft2/min] 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 Every half-life, t1/2, the level of tank will be halved. h0 h0/2 time h0/4 (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). t1/2 2t1/2 Foundations of Engineering- EGN 4930

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. Measured Height versus Model Prediction Height Values timeh1, realityh2, Model (min.) (feet) (feet) 01010 58.127.57 106.435.73 15 4.944.34 203.653.29 252.552.49 301.651.88 350.951.43 400.43 1.08 If model, observation, theory puzzle is working well, right two columns should have same ( very close) numbers Foundations of Engineering- EGN 4930

14. 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 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 Foundations of Engineering- EGN 4930

15. ObservationMeasure 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 Model Model for this new theory is for another day. But you can check it out if you want to. Foundations of Engineering- EGN 4930

16. ObservationMeasure 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 Model The model for this new theory is 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 Engineering- EGN 4930

17. ObservationMeasure 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 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” Foundations of Engineering- EGN 4930

18. Fluidized Bed Dryer Model Properties of solvent to be removed Properties of particles to be dried Properties of drying fluid Foundations of Engineering- EGN 4930

19. Data in red you will find in library Data in blue you will find in web pages for this project Data needed to solve TK Solver Model (computer crunching) Drying fluid properties Viscosity of air g/cm-s Specific heat of air @const P cal/g-oC Density of air g/cm3 Molecular weight of air g/mole Critical temperature of air oK Critical density of air g/cm3 Solvent properties Molecular weight g/mole Critical Temperature ºK Critical Density g/cm3 Thermal Conductivity W/cm-oC Particle Properties Particle Density g/cm3 Foundations of Engineering- EGN 4930

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

22. 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 Engineering- EGN 4930

23. Department of Chemical Engineering at USF Chairperson L. H. Garcia-Rubio garcia@eng.usf.edu Undergraduate Advisors C. Beaver beaver@eng.usf.edu C. Busot busot@eng.usf.edu C. Smith csmith@eng.usf.edu W. E. Lee (Bio-Engineering)lee@eng.usf.edu • Phone numbers • (813) 974-3997 • (813) 974-3651 (fax) Room number Kopp Engineering building ENG 346 Foundations of Engineering- EGN 4930

24. Thanksforyour time. We hope thepresentation put a bit of lighton the subject. Foundations of Engineering- EGN 4930