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.