What is "In" and What is "Out" in Engineering Problem Solving
Mordechai ShachamChem. Eng. Dept., Ben-Gurion University, Beer-Sheva
84105,Israel
Michael B. CutlipChem. Eng.Dept.,University of Connecticut, Storrs,CT
06269,USA
Neima BraunerFaculty of Engineering, Tel-Aviv University, Tel-Aviv,
69978, Israel
A Typical Reaction Engineering ProblemHydrodealkylation of Mesitylene
*Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice-Hall
Mesitylene m-Xylene, desired
product
Toluene, undesired
product5.0
22
5.011
21
1
21
/
/
/
HXT
HMM
TMX
MM
TMH
CCkr
CCkr
rrddC
rddC
rrddC
Hydrodealkylation of Mesitylene (2) – Analytical 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.
Define new variables
Substituting the new variables to the ODE system and additional manipulation yields
)(
)(
212
11
2
1
AA
AM
A
A
XXk
Xk
dX
dX
This Equation can be brought into the form of the Bernoulli equation yielding the solution :
12
/1121
2 /1
)/1(/ 12
kk
XXkkX
kkMAMAM
A
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
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
Problem Solving with Mathematical Software Packages
MathematicalModel
Physical Properties
Solution Algorithm
Documentation
Mathematical Software Package
User Supplied
The USER supplies the mathematical model and the data The package provides the numerical solution and documantation.
Hydrodealkylation of Mesitylene – Numerical Solution
Clear, precise and detailed definition of the mathematical model
Solution is obtained by a single key press
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 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?
Is the Solution Technique as Important as the Analysis of the Results (Optimization vs. Reaction Engineering)?
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.
Conclusions
The Introduction of the Mathematical Software Packages has Added very Fast, Convenient and Accurate Tools to the Problem Solving Toolbox of the Engineer.
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.
The Decision whether to Keep Teaching the Traditional Techniques Represent a Major Challenge.