What is "In" and What is "Out" in Engineering Problem Solving Mordechai Shacham

1. What is "In" and What is "Out" in Engineering Problem Solving Mordechai Shacham Chem. Eng. Dept., Ben-Gurion University, Beer-Sheva 84105,Israel Michael B. Cutlip Chem. Eng.Dept.,University of Connecticut, Storrs,CT 06269,USA Neima Brauner Faculty of Engineering, Tel-Aviv University, Tel-Aviv, 69978, Israel

2. A Typical Reaction Engineering Problem Hydrodealkylation of Mesitylene m-Xylene, desired Mesitylene product Toluene, undesired product *Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice-Hall

3. Hydrodealkylation of Mesitylene (2) – Analytical Solution* Define new variables Substituting the new variables to the ODE system and additional manipulation yields This Equation can be brought into the form of the Bernoulli equation yielding the solution : *Fogler, H. S., Elements of Chemical Reaction Engineering, 2nd Ed., 1986. Analytical solution is replaced by numerical solution in the 3rd Ed., in 1999.

4. Chemical Engineer’s Problem Solution Techniques - 1980 Analytical solutions, including Model simplification by neglecting less important terms Model manipulation to bring it into a solvable form Short-cut solution techniques Replacing the problem with a simpler one that can be solved Graphical solutions Trial and error solution techniques Numerical solution, including Computer language programming and debugging

5. Shortcomings of the Traditional Solution Techniques Manual and Graphical Solution Techniques Tedious, time consuming error prone process Oversimplification may lead to wrong results Precision mabe limited to a few decimal digits Time constraints prevent screening of a large number of alternatives to find an optimal solution Computer Language Programming Requires skills in programming, numerical and optimization methods Tedious, time consuming error prone process

6. Problem Solving with Mathematical Software Packages Mathematical Physical Properties Model User Supplied Solution Algorithm Mathematical Software Package Documentation The USER supplies the mathematical model and the data The package provides the numerical solution and documantation.

7. Hydrodealkylation of Mesitylene – Numerical Solution Clear, precise and detailed definition of the mathematical model Solution is obtained by a single key press

8. Considerations in Determining whether Teaching with the Traditional Methods is Justified What is the Subject Matter of the Course (Analytical Solution Techniques vs. Reaction Engineering)? Is the Solution Technique as Important as the Analysis of the Results (Optimization vs. Reaction Engineering)? Is the Range of the Solution Limited or Extrapolation to Infinity is Required? Can an Analytical Solution be Generalized to a Wide Range of Similar Problems? Can the Extra Effort Required to Obtain a Graphical Solution be Justified by the Better Understanding Gained from Visualization of the Solution?

9. McCabe-Thiele versus Ponchon-Savarit Methods Rigorous distillation column models are very complex a simplified model such as McCabe-Thiele is needed for visualization of the important aspects. The additional benefits of the more complex Ponchon-Savarit is marginal.

10. Conclusions The Introduction of the Mathematical Software Packages has Added very Fast, Convenient and Accurate Tools to the Problem Solving Toolbox of the Engineer. The Decision whether to Keep Teaching the Traditional Techniques Represent a Major Challenge. This Decision Must be Based on a Cost/Benefit Analysis whether the Pedagogical Benefits of the Traditional Method can Justify the Time Invested. Proper Use of Numerical Methods for Problem Solving Requires Familiarity with some Important Terms Associated with such Solutions (such as Singular Matrices, Stiff Equations etc.). This Requires adding a Numerical Methods Course to the Curriculum.